Finite Group Databasebeta

← C7×#62877 #13240093

Subgroups — C7×#62877 #13240093

Order 1792.

6394 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3565C214yesmaximal, complemented
2C7×#3565C214yesmaximal, complemented
3C7×#3563C214yesmaximal, complemented
4C7×#3559C214yesmaximal, complemented
5C7×#3555C214yesmaximal, complemented
6C7×#3553C214yesmaximal, complemented
7C7×#3552C214yesmaximal, complemented
8C7×#3552C214yesmaximal, complemented
9C7×#3547C214yesmaximal, complemented
10C7×#3544C214yesmaximal, complemented
11C7×#3541C218yesmaximal, complemented
12C7×#3512C212yesmaximal, complemented
13C7×#3511C212yesmaximal, complemented
14C7×#3504C212yesmaximal, complemented
15C7×#3503C212yesmaximal, complemented
16C7×#3493C211yesmaximal, characteristic, complemented
17C7×#3493C211yesmaximal, characteristic, complemented
18C7×#3492C212yesmaximal, complemented
19C2×C7×#544C211yesmaximal, characteristic, complemented
20C7×#3455C212yesmaximal, complemented
21C7×#564C2214yescomplemented
22C7×#563C2218yes—
23C7×#563C2218yes—
24C7×#563C2214yescomplemented
25C7×#563C2218yescomplemented
26C7×#563C2214yescomplemented
27C7×#563C2218yescomplemented
28C7×#562C2218yes—
29C7×#562C2218yes—
30C7×#562C2214yescomplemented
31C7×Q82C2214yescomplemented
32C7×#557C2214yescomplemented
33C7×#557C2214yescomplemented
34C7×#557C2214yescomplemented
35C7×#557C2214yescomplemented
36C7×#556C2214yes—
37C7×#556C2218yes—
38C7×#556C2214yes—
39C7×#556C2214yescomplemented
40C7×#556C2214yescomplemented
41C7×#555C2214yes—
42C7×#555C2214yes—
43C7×#555C2214yescomplemented
44C7×#554C2214yes—
45C7×#554C2214yes—
46C7×#554C2218yes—
47C7×#554C2218yes—
48C7×#554C2218yes—
49C7×#554C2214yescomplemented
50C7×#554C2214yescomplemented
51C7×#554C2214yescomplemented
52C7×#554C2214yescomplemented
53C7×#553C2214yes—
54C7×#553C2214yes—
55C7×#553C2214yes—
56C7×#553C2214yes—
57C7×#553C2218yes—
58C7×#553C2218yes—
59C7×#553C2218yes—
60C7×#553C2214yescomplemented
61C7×#553C2214yescomplemented
62C7×#552C2214yes—
63C7×#552C2214yes—
64C7×#552C2218yes—
65C7×#552C2214yes—
66C7×#552C2214yes—
67C7×#552C2214yescomplemented
68C7×#552C2218yescomplemented
69C7×#552C2218yescomplemented
70C7×#552C2214yescomplemented
71C7×D4×Q8C2218yes—
72C7×D4×Q8C2214yescomplemented
73C7×D4×Q8C2214yescomplemented
74C7×#548C2218yes—
75C7×#548C2218yes—
76C7×#547C2214yes—
77C7×#547C2214yes—
78C7×#547C2218yes—
79C7×#547C2214yescomplemented
80C7×#547C2214yescomplemented
81C7×#544C2214yes—
82C7×#544C2214yes—
83C7×#544C2214yes—
84C7×#544C2214yes—
85C7×#544C2212yes—
86C7×#544C2211yescharacteristic
87C7×#544C2211yescharacteristic
88C7×#544C2214yescomplemented
89C7×#544C2218yescomplemented
90C7×#544C2214yescomplemented
91C7×#544C2214yescomplemented
92C7×#544C2214yescomplemented
93C7×#542C2212yes—
94C7×#542C2212yes—
95C7×#542C2218yes—
96C7×#542C2218yes—
97C7×#542C2212yes—
98C7×#542C2212yes—
99C7×#542C2218yes—
100C7×#542C2214yescomplemented
101C7×#542C2214yescomplemented
102C7×#542C2218yescomplemented
103C7×#541C2212yes—
104C7×#541C2218yes—
105C7×#541C2212yes—
106C7×#541C2218yescomplemented
107C7×#541C2214yescomplemented
108C7×#541C2218yescomplemented
109C7×#541C2218yescomplemented
110C7×#540C2212yes—
111C7×#540C2212yes—
112C7×#540C2214yescomplemented
113C7×#539C2218yes—
114C7×#539C2218yes—
115C7×#539C2214yes—
116C7×#539C2214yes—
117C7×#539C2218yes—
118C7×#539C2218yescomplemented
119C7×#539C2218yescomplemented
120C7×#538C2214yes—
121C7×#538C2214yes—
122C7×#538C2214yes—
123C7×#538C2214yes—
124C7×#537C2212yes—
125C7×#537C2211yescharacteristic
126C7×#537C2211yescharacteristic
127C7×#537C2218yes—
128C7×#536C2218yes—
129C7×#536C2218yescomplemented
130C7×#533C2212yes—
131C7×#533C2214yescomplemented
132C7×#533C2214yescomplemented
133C7×#533C2214yescomplemented
134C7×#532C2212yes—
135C7×#532C2214yescomplemented
136C2×C7×C4⋊Q8C2212yes—
137C2×C7×C4⋊Q8C2212yes—
138C2×C7×C4⋊Q8C2214yescomplemented
139C7×#529C2214yes—
140C7×#529C2214yes—
141C7×#529C2214yes—
142C7×#529C2214yes—
143C7×#529C2214yes—
144C7×#529C2214yes—
145C7×#529C2214yescomplemented
146C7×#529C2214yescomplemented
147C2×C7×#125C2212yes—
148C2×C7×#125C2212yes—
149C2×C7×#125C2214yescomplemented
150C7×#525C2212yes—
151C7×#525C2212yes—
152C7×#525C2218yes—
153C2×C7×C22⋊Q8C2214yes—
154C7×#520C2212yes—
155C7×#520C2212yes—
156C7×#520C2212yes—
157C7×#520C2212yes—
158C4×C7×#41C2212yes—
159C4×C7×#41C2212yes—
160C2×C7×#117C2211yescharacteristic
161C2×C7×#117C2211yescharacteristic
162C22×C7×C4⋊C4C2211yescharacteristic
163#62877C711yesmaximal, characteristic, direct product factor, Sylow
164C2×C7×#41C2312yes—
165C2×C7×#41C2312yes—
166C2×C7×#41C2318yes—
167C2×C7×#41C2318yes—
168C22×C7×Q8C2314yes—
169C22×C7×Q8C2318yes—
170C23×C4×C7C2311yescharacteristic
171C23×C4×C7C2312yes—
172C7×C4⋊Q8C2314yes—
173C7×C4⋊Q8C2314yes—
174C7×C4⋊Q8C2318yes—
175C7×C4⋊Q8C2314yes—
176C7×C4⋊Q8C2314yes—
177C7×C4⋊Q8C2314yes—
178C7×C4⋊Q8C2314yes—
179C7×C4⋊Q8C2312yes—
180C7×C4⋊Q8C2318yes—
181C7×C4⋊Q8C2318yes—
182C7×C4⋊Q8C2314yes—
183C7×C4⋊Q8C2314yes—
184C7×C4⋊Q8C2312yes—
185C7×C4⋊Q8C2312yes—
186C7×C4⋊Q8C2314yes—
187C7×C4⋊Q8C2314yes—
188C7×C4⋊Q8C2318yes—
189C7×C4⋊Q8C2318yes—
190C7×C4⋊Q8C2318yes—
191C7×C4⋊Q8C2318yes—
192C7×#127C2312yes—
193C7×#126C2314yes—
194C7×#126C2314yes—
195C7×#126C2314yes—
196C7×#126C2314yes—
197C7×#126C2314yes—
198C7×#126C2314yes—
199C7×#126C2314yes—
200C7×#126C2314yes—
201C7×#126C2318yes—
202C7×#126C2318yes—
203C7×#126C2318yes—
204C7×#126C2318yes—
205C7×#126C2318yes—
206C7×#126C2318yes—
207C7×#126C2318yes—
208C7×#126C2318yes—
209C7×#126C2318yes—
210C7×#126C2318yes—
211C7×#126C2318yes—
212C7×#126C2318yes—
213C7×#125C2314yes—
214C7×#125C2314yes—
215C7×#125C2318yes—
216C7×#125C2314yes—
217C7×#125C2314yes—
218C7×#125C2314yes—
219C7×#125C2314yes—
220C7×#125C2312yes—
221C7×#125C2318yes—
222C7×#125C2318yes—
223C7×#125C2314yes—
224C7×#125C2314yes—
225C7×#125C2314yes—
226C7×#125C2314yes—
227C7×#125C2314yes—
228C7×#125C2314yes—
229C7×#125C2314yes—
230C7×#125C2314yes—
231C7×#125C2312yes—
232C7×#125C2318yes—
233C7×#125C2314yes—
234C7×#125C2314yes—
235C7×#125C2318yes—
236C7×#125C2318yes—
237C7×#125C2318yes—
238C7×#125C2318yes—
239C7×#125C2318yes—
240C7×#125C2318yes—
241C7×#125C2318yes—
242C7×#125C2318yes—
243C7×#124C2314yes—
244C7×#124C2314yes—
245C7×#124C2314yes—
246C7×#124C2314yes—
247C7×#124C2314yes—
248C7×#124C2314yes—
249C7×#124C2312yes—
250C7×#124C2312yes—
251C7×#124C2318yes—
252C7×#124C2318yes—
253C7×#124C2318yes—
254C7×#124C2318yes—
255C7×#124C2318yes—
256C7×#123C2314yes—
257C7×#123C2314yes—
258C7×#123C2318yes—
259C7×#123C2318yes—
260C7×#123C2314yes—
261C7×#123C2314yes—
262C7×#123C2314yes—
263C7×#123C2314yes—
264C7×#123C2314yes—
265C7×#123C2314yes—
266C7×#123C2314yes—
267C7×#123C2314yes—
268C7×#123C2318yes—
269C7×#123C2318yes—
270C7×#123C2318yes—
271C7×#123C2318yes—
272C7×#123C2318yes—
273C7×#123C2318yes—
274C7×#123C2318yes—
275C7×#123C2318yes—
276C7×#123C2318yes—
277C7×#123C2318yes—
278C7×C22⋊Q8C2318yes—
279C7×C22⋊Q8C2318yes—
280C7×C22⋊Q8C2318yes—
281C7×C22⋊Q8C2318yes—
282C7×C22⋊Q8C2318yes—
283C7×C22⋊Q8C2318yes—
284C7×C22⋊Q8C2312yes—
285C7×C22⋊Q8C2312yes—
286C7×C22⋊Q8C2312yes—
287C7×C22⋊Q8C2312yes—
288C7×C22⋊Q8C2314yes—
289C7×C22⋊Q8C2314yes—
290C7×C22⋊Q8C2314yes—
291C7×C22⋊Q8C2314yes—
292C7×C22⋊Q8C2314yes—
293C7×C22⋊Q8C2314yes—
294C7×C22⋊Q8C2314yes—
295C7×C22⋊Q8C2314yes—
296C7×C22⋊Q8C2314yes—
297C7×C22⋊Q8C2314yes—
298C7×C22⋊Q8C2318yes—
299C7×C22⋊Q8C2314yes—
300C7×C22⋊Q8C2314yes—
301C7×C22⋊Q8C2318yes—
302C7×C22⋊Q8C2318yes—
303C7×C22⋊Q8C2318yes—
304C7×C22⋊Q8C2318yes—
305C7×C22⋊Q8C2318yes—
306C7×C22⋊Q8C2318yes—
307C7×C22⋊Q8C2318yes—
308C7×C22⋊Q8C2318yes—
309C7×C22⋊Q8C2318yes—
310C7×C22⋊Q8C2318yes—
311C7×C22⋊Q8C2318yes—
312C7×C22⋊Q8C2318yes—
313C7×C22⋊Q8C2318yes—
314C7×C22⋊Q8C2318yes—
315C7×C22⋊Q8C2318yes—
316C7×C22⋊Q8C2318yes—
317C7×#121C2318yes—
318C7×#121C2318yes—
319C7×#121C2312yes—
320C7×#121C2312yes—
321C7×#121C2312yes—
322C7×#121C2312yes—
323C7×#121C2314yes—
324C7×#121C2314yes—
325C7×#121C2314yes—
326C7×#121C2314yes—
327C7×#121C2314yes—
328C7×#121C2314yes—
329C7×#121C2314yes—
330C7×#121C2314yes—
331C7×#121C2314yes—
332C7×#121C2314yes—
333C7×#121C2318yes—
334C7×#121C2314yes—
335C7×#121C2314yes—
336C7×#121C2318yes—
337C7×#121C2318yes—
338C7×#121C2318yes—
339C7×#121C2318yes—
340C7×#120C2314yes—
341C7×#120C2314yes—
342C4×C7×Q8C2312yes—
343C4×C7×Q8C2312yes—
344C4×C7×Q8C2312yes—
345C4×C7×Q8C2312yes—
346C4×C7×Q8C2314yes—
347C4×C7×Q8C2314yes—
348C4×C7×Q8C2314yes—
349C4×C7×Q8C2314yes—
350C4×C7×Q8C2314yes—
351C4×C7×Q8C2314yes—
352C4×C7×Q8C2314yes—
353C4×C7×Q8C2314yes—
354C4×C7×Q8C2318yes—
355C4×C7×Q8C2318yes—
356C4×C7×Q8C2318yes—
357C4×C7×Q8C2318yes—
358C4×C7×Q8C2318yes—
359C4×C7×D4C2314yes—
360C4×C7×D4C2314yes—
361C4×C7×D4C2314yes—
362C4×C7×D4C2314yes—
363C4×C7×D4C2312yes—
364C4×C7×D4C2312yes—
365C4×C7×D4C2312yes—
366C4×C7×D4C2312yes—
367C4×C7×D4C2318yes—
368C4×C7×D4C2318yes—
369C4×C7×D4C2318yes—
370C4×C7×D4C2318yes—
371C4×C7×D4C2314yes—
372C4×C7×D4C2314yes—
373C4×C7×D4C2314yes—
374C4×C7×D4C2314yes—
375C4×C7×D4C2314yes—
376C4×C7×D4C2314yes—
377C4×C7×D4C2314yes—
378C4×C7×D4C2314yes—
379C4×C7×D4C2318yes—
380C4×C7×D4C2318yes—
381C4×C7×D4C2314yes—
382C4×C7×D4C2314yes—
383C4×C7×D4C2314yes—
384C4×C7×D4C2314yes—
385C4×C7×D4C2318yes—
386C4×C7×D4C2318yes—
387C4×C7×D4C2318yes—
388C7×#117C2312yes—
389C7×#117C2312yes—
390C7×#117C2312yes—
391C7×#117C2312yes—
392C7×#117C2314yes—
393C7×#117C2314yes—
394C7×#117C2312yes—
395C7×#117C2312yes—
396C7×#117C2314yes—
397C7×#117C2314yes—
398C7×#117C2314yes—
399C7×#117C2314yes—
400C7×#117C2314yes—
401C7×#117C2314yes—
402C7×#117C2318yes—
403C7×#117C2318yes—
404C7×#117C2318yes—
405C7×#117C2318yes—
406C7×#117C2318yes—
407C7×#117C2318yes—
408C2×C7×C4⋊C4C2312yes—
409C2×C7×C4⋊C4C2312yes—
410C2×C7×C4⋊C4C2314yes—
411C2×C7×C4⋊C4C2314yes—
412C2×C7×C4⋊C4C2311yescharacteristic
413C2×C7×C4⋊C4C2311yescharacteristic
414C2×C7×C4⋊C4C2311yescharacteristic
415C2×C7×C4⋊C4C2311yescharacteristic
416C2×C7×C4⋊C4C2314yes—
417C2×C7×C4⋊C4C2314yes—
418C2×C7×C4⋊C4C2314yes—
419C2×C7×C4⋊C4C2314yes—
420C2×C7×C4⋊C4C2314yes—
421C2×C7×C4⋊C4C2314yes—
422C2×C7×C4⋊C4C2314yes—
423C2×C7×C4⋊C4C2318yes—
424C2×C7×C4⋊C4C2318yes—
425C2×C7×C4⋊C4C2318yes—
426C2×C7×C22⋊C4C2312yes—
427C2×C7×C22⋊C4C2312yes—
428C2×C42×C7C2312yes—
429C2×C42×C7C2312yes—
430C2×C42×C7C2314yes—
431C2×C42×C7C2314yes—
432#3565C2×C714yescomplemented
433#3565C2×C714yescomplemented
434#3563C2×C714yescomplemented
435#3559C2×C714yescomplemented
436#3555C2×C714yescomplemented
437#3553C2×C714yescomplemented
438#3552C2×C714yescomplemented
439#3552C2×C714yescomplemented
440#3547C2×C714yescomplemented
441#3544C2×C714yescomplemented
442#3541C2×C718yescomplemented
443#3512C2×C712yescomplemented
444#3511C2×C712yescomplemented
445#3504C2×C712yescomplemented
446#3503C2×C712yescomplemented
447#3493C2×C711yescharacteristic, complemented
448#3493C2×C711yescharacteristic, complemented
449#3492C2×C712yescomplemented
450C2×#544C2×C711yescharacteristic, complemented
451#3455C2×C712yescomplemented
452C24×C7C2411yescharacteristic
453C7×#41—28no—
454C7×#41—28no—
455C7×#41—88no—
456C7×#41—88no—
457C2×C7×Q8—84no—
458C2×C7×Q8—88no—
459C2×C7×Q8C2412yes—
460C2×C7×Q8C2412yes—
461C2×C7×Q8C2414yes—
462C2×C7×Q8C2414yes—
463C2×C7×Q8C2418yes—
464C2×C7×Q8C2414yes—
465C2×C7×Q8C2418yes—
466C2×C7×Q8C2418yes—
467C2×C7×Q8C2414yes—
468C2×C7×D4C2414yes—
469C2×C7×D4C2414yes—
470C2×C7×D4C2412yes—
471C2×C7×D4C2412yes—
472C2×C7×D4C2414yes—
473C2×C7×D4C2414yes—
474C2×C7×D4C2414yes—
475C2×C7×D4C2414yes—
476C2×C7×D4C2414yes—
477C2×C7×D4C2414yes—
478C2×C7×D4C2418yes—
479C2×C7×D4C2414yes—
480C2×C7×D4C2414yes—
481C22×C4×C7—24no—
482C22×C4×C7—82no—
483C22×C4×C7C2411yescharacteristic
484C22×C4×C7C2414yes—
485C22×C4×C7C2414yes—
486C22×C4×C7C2412yes—
487C22×C4×C7C2412yes—
488C22×C4×C7C2412yes—
489C22×C4×C7C2412yes—
490C22×C4×C7C2412yes—
491C22×C4×C7C2412yes—
492C22×C4×C7C2414yes—
493C22×C4×C7C2414yes—
494C22×C4×C7C2414yes—
495C22×C4×C7C2414yes—
496C22×C4×C7C2414yes—
497C22×C4×C7C2418yes—
498C22×C4×C7C2418yes—
499C22×C4×C7C2418yes—
500C22×C4×C7C2418yes—
501C22×C4×C7C2418yes—
502C22×C4×C7C2411yescharacteristic
503C7×C4⋊C4C2414yes—
504C7×C4⋊C4C2414yes—
505C7×C4⋊C4C2412yes—
506C7×C4⋊C4C2414yes—
507C7×C4⋊C4C2414yes—
508C7×C4⋊C4C2414yes—
509C7×C4⋊C4C2412yes—
510C7×C4⋊C4C2414yes—
511C7×C4⋊C4C2412yes—
512C7×C4⋊C4C2414yes—
513C7×C4⋊C4C2418yes—
514C7×C4⋊C4C2418yes—
515C7×C4⋊C4C2414yes—
516C7×C4⋊C4C2418yes—
517C7×C4⋊C4C2414yes—
518C7×C4⋊C4C2418yes—
519C7×C4⋊C4C2414yes—
520C7×C4⋊C4C2411yescharacteristic
521C7×C4⋊C4C2411yescharacteristic
522C7×C4⋊C4C2412yes—
523C7×C4⋊C4C2412yes—
524C7×C4⋊C4C2411yescharacteristic
525C7×C4⋊C4C2411yescharacteristic
526C7×C4⋊C4C2418yes—
527C7×C4⋊C4C2418yes—
528C7×C4⋊C4C2418yes—
529C7×C4⋊C4C2418yes—
530C7×C4⋊C4C2418yes—
531C7×C4⋊C4C2418yes—
532C7×C4⋊C4C2418yes—
533C7×C4⋊C4C2418yes—
534C7×C4⋊C4C2418yes—
535C7×C4⋊C4C2418yes—
536C7×C4⋊C4C2412yes—
537C7×C4⋊C4C2414yes—
538C7×C4⋊C4C2414yes—
539C7×C4⋊C4C2414yes—
540C7×C4⋊C4C2418yes—
541C7×C4⋊C4C2414yes—
542C7×C4⋊C4C2414yes—
543C7×C4⋊C4C2414yes—
544C7×C4⋊C4C2414yes—
545C7×C4⋊C4C2414yes—
546C7×C4⋊C4C2414yes—
547C7×C4⋊C4C2414yes—
548C7×C4⋊C4C2418yes—
549C7×C4⋊C4C2414yes—
550C7×C4⋊C4C2414yes—
551C7×C4⋊C4C2414yes—
552C7×C4⋊C4C2414yes—
553C7×C4⋊C4C2414yes—
554C7×C4⋊C4C2414yes—
555C7×C22⋊C4C2412yes—
556C7×C22⋊C4C2412yes—
557C7×C22⋊C4C2412yes—
558C7×C22⋊C4C2418yes—
559C7×C22⋊C4C2412yes—
560C7×C22⋊C4C2414yes—
561C7×C22⋊C4C2414yes—
562C7×C22⋊C4C2418yes—
563C7×C22⋊C4C2418yes—
564C7×C22⋊C4C2418yes—
565C7×C22⋊C4C2414yes—
566C7×C22⋊C4C2414yes—
567C7×C22⋊C4C2414yes—
568C7×C22⋊C4C2414yes—
569C7×C22⋊C4C2414yes—
570C7×C22⋊C4C2414yes—
571C7×C22⋊C4C2414yes—
572C7×C22⋊C4C2414yes—
573C7×C22⋊C4C2418yes—
574C7×C22⋊C4C2418yes—
575C7×C22⋊C4C2418yes—
576C7×C22⋊C4C2418yes—
577C7×C22⋊C4C2414yes—
578C7×C22⋊C4C2414yes—
579C7×C22⋊C4C2414yes—
580C7×C22⋊C4C2414yes—
581C7×C22⋊C4C2418yes—
582C7×C22⋊C4C2414yes—
583C7×C22⋊C4C2414yes—
584C7×C22⋊C4C2414yes—
585C7×C22⋊C4C2414yes—
586C42×C7C2412yes—
587C42×C7C2412yes—
588C42×C7C2414yes—
589C42×C7C2414yes—
590C42×C7C2412yes—
591C42×C7C2412yes—
592C42×C7C2414yes—
593C42×C7C2414yes—
594C42×C7C2414yes—
595C42×C7C2414yes—
596C42×C7C2414yes—
597C42×C7C2414yes—
598C42×C7C2418yes—
599C42×C7C2418yes—
600C42×C7C2418yes—
601C42×C7C2418yes—
602#564C22×C714yescomplemented
603#563C22×C718yes—
604#563C22×C718yes—
605#563C22×C714yescomplemented
606#563C22×C718yescomplemented
607#563C22×C718yescomplemented
608#563C22×C714yescomplemented
609#562C22×C718yes—
610#562C22×C718yes—
611#562C22×C714yescomplemented
612Q82C22×C714yescomplemented
613#557C22×C714yescomplemented
614#557C22×C714yescomplemented
615#557C22×C714yescomplemented
616#557C22×C714yescomplemented
617#556C22×C714yes—
618#556C22×C714yes—
619#556C22×C718yes—
620#556C22×C714yescomplemented
621#556C22×C714yescomplemented
622#555C22×C714yes—
623#555C22×C714yes—
624#555C22×C714yescomplemented
625#554C22×C714yes—
626#554C22×C714yes—
627#554C22×C718yes—
628#554C22×C718yes—
629#554C22×C718yes—
630#554C22×C714yescomplemented
631#554C22×C714yescomplemented
632#554C22×C714yescomplemented
633#554C22×C714yescomplemented
634#553C22×C714yes—
635#553C22×C714yes—
636#553C22×C714yes—
637#553C22×C714yes—
638#553C22×C718yes—
639#553C22×C718yes—
640#553C22×C718yes—
641#553C22×C714yescomplemented
642#553C22×C714yescomplemented
643#552C22×C714yes—
644#552C22×C714yes—
645#552C22×C714yes—
646#552C22×C714yes—
647#552C22×C718yes—
648#552C22×C714yescomplemented
649#552C22×C714yescomplemented
650#552C22×C718yescomplemented
651#552C22×C718yescomplemented
652D4×Q8C22×C718yes—
653D4×Q8C22×C714yescomplemented
654D4×Q8C22×C714yescomplemented
655#548C22×C718yes—
656#548C22×C718yes—
657#547C22×C714yes—
658#547C22×C714yes—
659#547C22×C718yes—
660#547C22×C714yescomplemented
661#547C22×C714yescomplemented
662#544C22×C714yes—
663#544C22×C714yes—
664#544C22×C714yes—
665#544C22×C714yes—
666#544C22×C712yes—
667#544C22×C711yescharacteristic
668#544C22×C711yescharacteristic
669#544C22×C714yescomplemented
670#544C22×C714yescomplemented
671#544C22×C714yescomplemented
672#544C22×C714yescomplemented
673#544C22×C718yescomplemented
674#542C22×C712yes—
675#542C22×C712yes—
676#542C22×C712yes—
677#542C22×C712yes—
678#542C22×C718yes—
679#542C22×C718yes—
680#542C22×C718yes—
681#542C22×C714yescomplemented
682#542C22×C714yescomplemented
683#542C22×C718yescomplemented
684#541C22×C712yes—
685#541C22×C712yes—
686#541C22×C718yes—
687#541C22×C714yescomplemented
688#541C22×C718yescomplemented
689#541C22×C718yescomplemented
690#541C22×C718yescomplemented
691#540C22×C712yes—
692#540C22×C712yes—
693#540C22×C714yescomplemented
694#539C22×C714yes—
695#539C22×C714yes—
696#539C22×C718yes—
697#539C22×C718yes—
698#539C22×C718yes—
699#539C22×C718yescomplemented
700#539C22×C718yescomplemented
701#538C22×C714yes—
702#538C22×C714yes—
703#538C22×C714yes—
704#538C22×C714yes—
705#537C22×C712yes—
706#537C22×C711yescharacteristic
707#537C22×C711yescharacteristic
708#537C22×C718yes—
709#536C22×C718yes—
710#536C22×C718yescomplemented
711#533C22×C712yes—
712#533C22×C714yescomplemented
713#533C22×C714yescomplemented
714#533C22×C714yescomplemented
715#532C22×C712yes—
716#532C22×C714yescomplemented
717C2×C4⋊Q8C22×C712yes—
718C2×C4⋊Q8C22×C712yes—
719C2×C4⋊Q8C22×C714yescomplemented
720#529C22×C714yes—
721#529C22×C714yes—
722#529C22×C714yes—
723#529C22×C714yes—
724#529C22×C714yes—
725#529C22×C714yes—
726#529C22×C714yescomplemented
727#529C22×C714yescomplemented
728C2×#125C22×C712yes—
729C2×#125C22×C712yes—
730C2×#125C22×C714yescomplemented
731#525C22×C712yes—
732#525C22×C712yes—
733#525C22×C718yes—
734C2×C22⋊Q8C22×C714yes—
735#520C22×C712yes—
736#520C22×C712yes—
737#520C22×C712yes—
738#520C22×C712yes—
739C4×#41C22×C712yes—
740C4×#41C22×C712yes—
741C2×#117C22×C711yescharacteristic
742C2×#117C22×C711yescharacteristic
743C22×C4⋊C4C22×C711yescharacteristic
744C23×C7—22no—
745C23×C7—41no—
746C23×C7—41no—
747C23×C7C2512yes—
748C23×C7C2514yes—
749C23×C7C2514yes—
750C23×C7C2511yescharacteristic
751C7×Q8—24no—
752C7×Q8—24no—
753C7×Q8—48no—
754C7×Q8—44no—
755C7×Q8—44no—
756C7×Q8—48no—
757C7×Q8—48no—
758C7×Q8—44no—
759C7×Q8—44no—
760C7×D4—28no—
761C7×D4—28no—
762C7×D4—24no—
763C7×D4—24no—
764C7×D4—44no—
765C7×D4—44no—
766C7×D4—44no—
767C7×D4—44no—
768C7×D4—44no—
769C7×D4—48no—
770C7×D4—44no—
771C7×D4—44no—
772C7×D4—44no—
773C2×C4×C7—22no—
774C2×C4×C7—24no—
775C2×C4×C7—24no—
776C2×C4×C7—28no—
777C2×C4×C7—28no—
778C2×C4×C7—44no—
779C2×C4×C7—48no—
780C2×C4×C7—42no—
781C2×C4×C7—44no—
782C2×C4×C7—42no—
783C2×C4×C7—48no—
784C2×C4×C7—44no—
785C2×C4×C7—42no—
786C2×C4×C7—42no—
787C2×C4×C7—44no—
788C2×C4×C7—48no—
789C2×C4×C7—48no—
790C2×C4×C7—48no—
791C2×C4×C7—44no—
792C2×C4×C72−1+414yes—
793C2×C4×C7C2514yes—
794C2×C4×C7C2514yes—
795C2×C4×C7C2514yes—
796C2×C4×C7C2511yescharacteristic
797C2×C4×C7C2511yescharacteristic
798C2×C4×C7C2512yes—
799C2×C4×C7C2512yes—
800C2×C4×C7C2514yes—
801C2×C4×C7C2514yes—
802C2×C4×C7C2514yes—
803C2×C4×C7C2514yes—
804C2×C4×C7C2512yes—
805C2×C4×C7C2512yes—
806C2×C4×C7C2514yes—
807C2×C4×C7C2518yes—
808C2×C4×C7C2512yes—
809C2×#41C23×C712yes—
810C2×#41C23×C712yes—
811C2×#41C23×C718yes—
812C2×#41C23×C718yes—
813C22×Q8C23×C714yes—
814C22×Q8C23×C718yes—
815C23×C4C23×C711yescharacteristic
816C23×C4C23×C712yes—
817C4⋊Q8C23×C714yes—
818C4⋊Q8C23×C714yes—
819C4⋊Q8C23×C718yes—
820C4⋊Q8C23×C714yes—
821C4⋊Q8C23×C714yes—
822C4⋊Q8C23×C714yes—
823C4⋊Q8C23×C714yes—
824C4⋊Q8C23×C712yes—
825C4⋊Q8C23×C718yes—
826C4⋊Q8C23×C718yes—
827C4⋊Q8C23×C714yes—
828C4⋊Q8C23×C714yes—
829C4⋊Q8C23×C712yes—
830C4⋊Q8C23×C712yes—
831C4⋊Q8C23×C714yes—
832C4⋊Q8C23×C714yes—
833C4⋊Q8C23×C718yes—
834C4⋊Q8C23×C718yes—
835C4⋊Q8C23×C718yes—
836C4⋊Q8C23×C718yes—
837#127C23×C712yes—
838#126C23×C714yes—
839#126C23×C714yes—
840#126C23×C714yes—
841#126C23×C714yes—
842#126C23×C714yes—
843#126C23×C714yes—
844#126C23×C714yes—
845#126C23×C714yes—
846#126C23×C718yes—
847#126C23×C718yes—
848#126C23×C718yes—
849#126C23×C718yes—
850#126C23×C718yes—
851#126C23×C718yes—
852#126C23×C718yes—
853#126C23×C718yes—
854#126C23×C718yes—
855#126C23×C718yes—
856#126C23×C718yes—
857#126C23×C718yes—
858#125C23×C714yes—
859#125C23×C714yes—
860#125C23×C718yes—
861#125C23×C714yes—
862#125C23×C714yes—
863#125C23×C714yes—
864#125C23×C714yes—
865#125C23×C712yes—
866#125C23×C718yes—
867#125C23×C718yes—
868#125C23×C714yes—
869#125C23×C714yes—
870#125C23×C714yes—
871#125C23×C714yes—
872#125C23×C714yes—
873#125C23×C714yes—
874#125C23×C714yes—
875#125C23×C714yes—
876#125C23×C712yes—
877#125C23×C718yes—
878#125C23×C714yes—
879#125C23×C714yes—
880#125C23×C718yes—
881#125C23×C718yes—
882#125C23×C718yes—
883#125C23×C718yes—
884#125C23×C718yes—
885#125C23×C718yes—
886#125C23×C718yes—
887#125C23×C718yes—
888#124C23×C714yes—
889#124C23×C714yes—
890#124C23×C714yes—
891#124C23×C714yes—
892#124C23×C714yes—
893#124C23×C714yes—
894#124C23×C712yes—
895#124C23×C712yes—
896#124C23×C718yes—
897#124C23×C718yes—
898#124C23×C718yes—
899#124C23×C718yes—
900#124C23×C718yes—
901#123C23×C714yes—
902#123C23×C714yes—
903#123C23×C718yes—
904#123C23×C718yes—
905#123C23×C714yes—
906#123C23×C714yes—
907#123C23×C714yes—
908#123C23×C714yes—
909#123C23×C714yes—
910#123C23×C714yes—
911#123C23×C714yes—
912#123C23×C714yes—
913#123C23×C718yes—
914#123C23×C718yes—
915#123C23×C718yes—
916#123C23×C718yes—
917#123C23×C718yes—
918#123C23×C718yes—
919#123C23×C718yes—
920#123C23×C718yes—
921#123C23×C718yes—
922#123C23×C718yes—
923C22⋊Q8C23×C718yes—
924C22⋊Q8C23×C718yes—
925C22⋊Q8C23×C718yes—
926C22⋊Q8C23×C718yes—
927C22⋊Q8C23×C718yes—
928C22⋊Q8C23×C718yes—
929C22⋊Q8C23×C712yes—
930C22⋊Q8C23×C712yes—
931C22⋊Q8C23×C712yes—
932C22⋊Q8C23×C712yes—
933C22⋊Q8C23×C714yes—
934C22⋊Q8C23×C714yes—
935C22⋊Q8C23×C714yes—
936C22⋊Q8C23×C714yes—
937C22⋊Q8C23×C714yes—
938C22⋊Q8C23×C714yes—
939C22⋊Q8C23×C714yes—
940C22⋊Q8C23×C714yes—
941C22⋊Q8C23×C714yes—
942C22⋊Q8C23×C714yes—
943C22⋊Q8C23×C718yes—
944C22⋊Q8C23×C714yes—
945C22⋊Q8C23×C714yes—
946C22⋊Q8C23×C718yes—
947C22⋊Q8C23×C718yes—
948C22⋊Q8C23×C718yes—
949C22⋊Q8C23×C718yes—
950C22⋊Q8C23×C718yes—
951C22⋊Q8C23×C718yes—
952C22⋊Q8C23×C718yes—
953C22⋊Q8C23×C718yes—
954C22⋊Q8C23×C718yes—
955C22⋊Q8C23×C718yes—
956C22⋊Q8C23×C718yes—
957C22⋊Q8C23×C718yes—
958C22⋊Q8C23×C718yes—
959C22⋊Q8C23×C718yes—
960C22⋊Q8C23×C718yes—
961C22⋊Q8C23×C718yes—
962#121C23×C718yes—
963#121C23×C718yes—
964#121C23×C712yes—
965#121C23×C712yes—
966#121C23×C712yes—
967#121C23×C712yes—
968#121C23×C714yes—
969#121C23×C714yes—
970#121C23×C714yes—
971#121C23×C714yes—
972#121C23×C714yes—
973#121C23×C714yes—
974#121C23×C714yes—
975#121C23×C714yes—
976#121C23×C714yes—
977#121C23×C714yes—
978#121C23×C718yes—
979#121C23×C714yes—
980#121C23×C714yes—
981#121C23×C718yes—
982#121C23×C718yes—
983#121C23×C718yes—
984#121C23×C718yes—
985#120C23×C714yes—
986#120C23×C714yes—
987C4×Q8C23×C712yes—
988C4×Q8C23×C712yes—
989C4×Q8C23×C712yes—
990C4×Q8C23×C712yes—
991C4×Q8C23×C714yes—
992C4×Q8C23×C714yes—
993C4×Q8C23×C714yes—
994C4×Q8C23×C714yes—
995C4×Q8C23×C714yes—
996C4×Q8C23×C714yes—
997C4×Q8C23×C714yes—
998C4×Q8C23×C714yes—
999C4×Q8C23×C718yes—
1000C4×Q8C23×C718yes—
1001C4×Q8C23×C718yes—
1002C4×Q8C23×C718yes—
1003C4×Q8C23×C718yes—
1004C4×D4C23×C714yes—
1005C4×D4C23×C714yes—
1006C4×D4C23×C714yes—
1007C4×D4C23×C714yes—
1008C4×D4C23×C712yes—
1009C4×D4C23×C712yes—
1010C4×D4C23×C712yes—
1011C4×D4C23×C712yes—
1012C4×D4C23×C718yes—
1013C4×D4C23×C718yes—
1014C4×D4C23×C718yes—
1015C4×D4C23×C718yes—
1016C4×D4C23×C714yes—
1017C4×D4C23×C714yes—
1018C4×D4C23×C714yes—
1019C4×D4C23×C714yes—
1020C4×D4C23×C714yes—
1021C4×D4C23×C714yes—
1022C4×D4C23×C714yes—
1023C4×D4C23×C714yes—
1024C4×D4C23×C718yes—
1025C4×D4C23×C718yes—
1026C4×D4C23×C714yes—
1027C4×D4C23×C714yes—
1028C4×D4C23×C714yes—
1029C4×D4C23×C714yes—
1030C4×D4C23×C718yes—
1031C4×D4C23×C718yes—
1032C4×D4C23×C718yes—
1033#117C23×C712yes—
1034#117C23×C712yes—
1035#117C23×C712yes—
1036#117C23×C712yes—
1037#117C23×C714yes—
1038#117C23×C714yes—
1039#117C23×C712yes—
1040#117C23×C712yes—
1041#117C23×C714yes—
1042#117C23×C714yes—
1043#117C23×C714yes—
1044#117C23×C714yes—
1045#117C23×C714yes—
1046#117C23×C714yes—
1047#117C23×C718yes—
1048#117C23×C718yes—
1049#117C23×C718yes—
1050#117C23×C718yes—
1051#117C23×C718yes—
1052#117C23×C718yes—
1053C2×C4⋊C4C23×C712yes—
1054C2×C4⋊C4C23×C712yes—
1055C2×C4⋊C4C23×C714yes—
1056C2×C4⋊C4C23×C714yes—
1057C2×C4⋊C4C23×C711yescharacteristic
1058C2×C4⋊C4C23×C711yescharacteristic
1059C2×C4⋊C4C23×C711yescharacteristic
1060C2×C4⋊C4C23×C711yescharacteristic
1061C2×C4⋊C4C23×C714yes—
1062C2×C4⋊C4C23×C714yes—
1063C2×C4⋊C4C23×C714yes—
1064C2×C4⋊C4C23×C714yes—
1065C2×C4⋊C4C23×C714yes—
1066C2×C4⋊C4C23×C714yes—
1067C2×C4⋊C4C23×C714yes—
1068C2×C4⋊C4C23×C718yes—
1069C2×C4⋊C4C23×C718yes—
1070C2×C4⋊C4C23×C718yes—
1071C2×C22⋊C4C23×C712yes—
1072C2×C22⋊C4C23×C712yes—
1073C2×C42C23×C712yes—
1074C2×C42C23×C712yes—
1075C2×C42C23×C714yes—
1076C2×C42C23×C714yes—
1077C22×C7—21no—
1078C22×C7—21no—
1079C22×C7—22no—
1080C22×C7—24no—
1081C22×C7—24no—
1082C22×C7—24no—
1083C22×C7—22no—
1084C22×C7—24no—
1085C22×C7—24no—
1086C22×C7—24no—
1087C22×C7—22no—
1088C22×C7—44no—
1089C22×C7C2×2−1+412yes—
1090C22×C7C2611yescharacteristic
1091C4×C7—21no—
1092C4×C7—21no—
1093C4×C7—24no—
1094C4×C7—24no—
1095C4×C7—28no—
1096C4×C7—24no—
1097C4×C7—22no—
1098C4×C7—24no—
1099C4×C7—24no—
1100C4×C7—22no—
1101C4×C7—22no—
1102C4×C7—24no—
1103C4×C7—24no—
1104C4×C7—22no—
1105C4×C7—24no—
1106C4×C7C2×2−1+414yes—
1107C24C24×C711yescharacteristic
1108#41—28no—
1109#41—28no—
1110#41—88no—
1111#41—88no—
1112C2×Q8—84no—
1113C2×Q8—88no—
1114C2×Q8C24×C712yes—
1115C2×Q8C24×C712yes—
1116C2×Q8C24×C714yes—
1117C2×Q8C24×C714yes—
1118C2×Q8C24×C718yes—
1119C2×Q8C24×C714yes—
1120C2×Q8C24×C718yes—
1121C2×Q8C24×C718yes—
1122C2×Q8C24×C714yes—
1123C2×D4C24×C714yes—
1124C2×D4C24×C714yes—
1125C2×D4C24×C712yes—
1126C2×D4C24×C712yes—
1127C2×D4C24×C714yes—
1128C2×D4C24×C714yes—
1129C2×D4C24×C714yes—
1130C2×D4C24×C714yes—
1131C2×D4C24×C714yes—
1132C2×D4C24×C714yes—
1133C2×D4C24×C718yes—
1134C2×D4C24×C714yes—
1135C2×D4C24×C714yes—
1136C22×C4—24no—
1137C22×C4—82no—
1138C22×C4C24×C711yescharacteristic
1139C22×C4C24×C714yes—
1140C22×C4C24×C714yes—
1141C22×C4C24×C712yes—
1142C22×C4C24×C712yes—
1143C22×C4C24×C712yes—
1144C22×C4C24×C712yes—
1145C22×C4C24×C712yes—
1146C22×C4C24×C712yes—
1147C22×C4C24×C714yes—
1148C22×C4C24×C714yes—
1149C22×C4C24×C714yes—
1150C22×C4C24×C714yes—
1151C22×C4C24×C714yes—
1152C22×C4C24×C718yes—
1153C22×C4C24×C718yes—
1154C22×C4C24×C718yes—
1155C22×C4C24×C718yes—
1156C22×C4C24×C718yes—
1157C22×C4C24×C711yescharacteristic
1158C4⋊C4C24×C714yes—
1159C4⋊C4C24×C714yes—
1160C4⋊C4C24×C712yes—
1161C4⋊C4C24×C714yes—
1162C4⋊C4C24×C714yes—
1163C4⋊C4C24×C714yes—
1164C4⋊C4C24×C712yes—
1165C4⋊C4C24×C714yes—
1166C4⋊C4C24×C712yes—
1167C4⋊C4C24×C714yes—
1168C4⋊C4C24×C718yes—
1169C4⋊C4C24×C718yes—
1170C4⋊C4C24×C714yes—
1171C4⋊C4C24×C718yes—
1172C4⋊C4C24×C714yes—
1173C4⋊C4C24×C718yes—
1174C4⋊C4C24×C714yes—
1175C4⋊C4C24×C711yescharacteristic
1176C4⋊C4C24×C711yescharacteristic
1177C4⋊C4C24×C712yes—
1178C4⋊C4C24×C712yes—
1179C4⋊C4C24×C711yescharacteristic
1180C4⋊C4C24×C711yescharacteristic
1181C4⋊C4C24×C718yes—
1182C4⋊C4C24×C718yes—
1183C4⋊C4C24×C718yes—
1184C4⋊C4C24×C718yes—
1185C4⋊C4C24×C718yes—
1186C4⋊C4C24×C718yes—
1187C4⋊C4C24×C718yes—
1188C4⋊C4C24×C718yes—
1189C4⋊C4C24×C718yes—
1190C4⋊C4C24×C718yes—
1191C4⋊C4C24×C712yes—
1192C4⋊C4C24×C714yes—
1193C4⋊C4C24×C714yes—
1194C4⋊C4C24×C714yes—
1195C4⋊C4C24×C718yes—
1196C4⋊C4C24×C714yes—
1197C4⋊C4C24×C714yes—
1198C4⋊C4C24×C714yes—
1199C4⋊C4C24×C714yes—
1200C4⋊C4C24×C714yes—
1201C4⋊C4C24×C714yes—
1202C4⋊C4C24×C714yes—
1203C4⋊C4C24×C718yes—
1204C4⋊C4C24×C714yes—
1205C4⋊C4C24×C714yes—
1206C4⋊C4C24×C714yes—
1207C4⋊C4C24×C714yes—
1208C4⋊C4C24×C714yes—
1209C4⋊C4C24×C714yes—
1210C22⋊C4C24×C712yes—
1211C22⋊C4C24×C712yes—
1212C22⋊C4C24×C712yes—
1213C22⋊C4C24×C718yes—
1214C22⋊C4C24×C712yes—
1215C22⋊C4C24×C714yes—
1216C22⋊C4C24×C714yes—
1217C22⋊C4C24×C718yes—
1218C22⋊C4C24×C718yes—
1219C22⋊C4C24×C718yes—
1220C22⋊C4C24×C714yes—
1221C22⋊C4C24×C714yes—
1222C22⋊C4C24×C714yes—
1223C22⋊C4C24×C714yes—
1224C22⋊C4C24×C714yes—
1225C22⋊C4C24×C714yes—
1226C22⋊C4C24×C714yes—
1227C22⋊C4C24×C714yes—
1228C22⋊C4C24×C718yes—
1229C22⋊C4C24×C718yes—
1230C22⋊C4C24×C718yes—
1231C22⋊C4C24×C718yes—
1232C22⋊C4C24×C714yes—
1233C22⋊C4C24×C714yes—
1234C22⋊C4C24×C714yes—
1235C22⋊C4C24×C714yes—
1236C22⋊C4C24×C718yes—
1237C22⋊C4C24×C714yes—
1238C22⋊C4C24×C714yes—
1239C22⋊C4C24×C714yes—
1240C22⋊C4C24×C714yes—
1241C42C24×C712yes—
1242C42C24×C712yes—
1243C42C24×C714yes—
1244C42C24×C714yes—
1245C42C24×C712yes—
1246C42C24×C712yes—
1247C42C24×C714yes—
1248C42C24×C714yes—
1249C42C24×C714yes—
1250C42C24×C714yes—
1251C42C24×C714yes—
1252C42C24×C714yes—
1253C42C24×C718yes—
1254C42C24×C718yes—
1255C42C24×C718yes—
1256C42C24×C718yes—
1257C2×C7—22no—
1258C2×C7—44no—
1259C2×C7—44no—
1260C2×C7—42no—
1261C2×C7C22×2−1+411yescharacteristic
1262C2×C7H(7,𝔽2)11yescharacteristic
1263C2×C72−1+611yescharacteristic
1264C23—22no—
1265C23—41no—
1266C23—41no—
1267C23C25×C712yes—
1268C23C25×C714yes—
1269C23C25×C714yes—
1270C23C25×C711yescharacteristic
1271Q8—24no—
1272Q8—24no—
1273Q8—48no—
1274Q8—44no—
1275Q8—44no—
1276Q8—48no—
1277Q8—48no—
1278Q8—44no—
1279Q8—44no—
1280D4—28no—
1281D4—28no—
1282D4—24no—
1283D4—24no—
1284D4—44no—
1285D4—44no—
1286D4—44no—
1287D4—44no—
1288D4—44no—
1289D4—48no—
1290D4—44no—
1291D4—44no—
1292D4—44no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—28no—
1297C2×C4—28no—
1298C2×C4—44no—
1299C2×C4—48no—
1300C2×C4—42no—
1301C2×C4—44no—
1302C2×C4—42no—
1303C2×C4—48no—
1304C2×C4—44no—
1305C2×C4—42no—
1306C2×C4—42no—
1307C2×C4—44no—
1308C2×C4—48no—
1309C2×C4—48no—
1310C2×C4—48no—
1311C2×C4—44no—
1312C2×C4C7×2−1+414yes—
1313C2×C4C25×C714yes—
1314C2×C4C25×C714yes—
1315C2×C4C25×C714yes—
1316C2×C4C25×C711yescharacteristic
1317C2×C4C25×C711yescharacteristic
1318C2×C4C25×C712yes—
1319C2×C4C25×C712yes—
1320C2×C4C25×C714yes—
1321C2×C4C25×C714yes—
1322C2×C4C25×C714yes—
1323C2×C4C25×C714yes—
1324C2×C4C25×C712yes—
1325C2×C4C25×C712yes—
1326C2×C4C25×C714yes—
1327C2×C4C25×C718yes—
1328C2×C4C25×C712yes—
1329C7#6287711yescharacteristic, direct product factor, Sylow
1330C22—21no—
1331C22—21no—
1332C22—22no—
1333C22—24no—
1334C22—24no—
1335C22—24no—
1336C22—22no—
1337C22—24no—
1338C22—24no—
1339C22—24no—
1340C22—22no—
1341C22—44no—
1342C22C2×C7×2−1+412yes—
1343C22C26×C711yescharacteristic
1344C4—21no—
1345C4—21no—
1346C4—24no—
1347C4—24no—
1348C4—28no—
1349C4—24no—
1350C4—22no—
1351C4—24no—
1352C4—24no—
1353C4—22no—
1354C4—22no—
1355C4—24no—
1356C4—24no—
1357C4—22no—
1358C4—24no—
1359C4C2×C7×2−1+414yes—
1360C2—22no—
1361C2—42no—
1362C2—44no—
1363C2—44no—
1364C2C22×C7×2−1+411yescharacteristic
1365C2C7×H(7,𝔽2)11yescharacteristic
1366C2C7×2−1+611yescharacteristic
subgroupG/H
center, socleC22×C7C26
commutator, Frattini, cosocleC22C26×C7
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C7×#3565C2semidirect
2. C7×#3565C2semidirect
3. C7×#3563C2semidirect
4. C7×#3559C2semidirect
5. C7×#3555C2semidirect
6. C7×#3553C2semidirect
7. C7×#3552C2semidirect
8. C7×#3552C2semidirect
9. C7×#3547C2semidirect
10. C7×#3544C2semidirect
11. C7×#3541C2semidirect
12. C7×#3512C2semidirect
13. C7×#3511C2semidirect
14. C7×#3504C2semidirect
15. C7×#3503C2semidirect
16. C7×#3493C2semidirect
17. C7×#3493C2semidirect
18. C7×#3492C2semidirect
19. C2×C7×#544C2semidirect
20. C7×#3455C2semidirect
21. C7×#564C22semidirect
24. C7×#563C22semidirect
25. C7×#563C22semidirect
26. C7×#563C22semidirect
27. C7×#563C22semidirect
30. C7×#562C22semidirect
31. C7×Q82C22semidirect
32. C7×#557C22semidirect
33. C7×#557C22semidirect
34. C7×#557C22semidirect
35. C7×#557C22semidirect
39. C7×#556C22semidirect
40. C7×#556C22semidirect
43. C7×#555C22semidirect
49. C7×#554C22semidirect
50. C7×#554C22semidirect
51. C7×#554C22semidirect
52. C7×#554C22semidirect
60. C7×#553C22semidirect
61. C7×#553C22semidirect
67. C7×#552C22semidirect
68. C7×#552C22semidirect
69. C7×#552C22semidirect
70. C7×#552C22semidirect
72. C7×D4×Q8C22semidirect
73. C7×D4×Q8C22semidirect
79. C7×#547C22semidirect
80. C7×#547C22semidirect
88. C7×#544C22semidirect
89. C7×#544C22semidirect
90. C7×#544C22semidirect
91. C7×#544C22semidirect
92. C7×#544C22semidirect
100. C7×#542C22semidirect
101. C7×#542C22semidirect
102. C7×#542C22semidirect
106. C7×#541C22semidirect
107. C7×#541C22semidirect
108. C7×#541C22semidirect
109. C7×#541C22semidirect
112. C7×#540C22semidirect
118. C7×#539C22semidirect
119. C7×#539C22semidirect
129. C7×#536C22semidirect
131. C7×#533C22semidirect
132. C7×#533C22semidirect
133. C7×#533C22semidirect
135. C7×#532C22semidirect
138. C2×C7×C4⋊Q8C22semidirect
145. C7×#529C22semidirect
146. C7×#529C22semidirect
149. C2×C7×#125C22semidirect
163. #62877C7direct (N × H)
432. #3565C2×C7semidirect
433. #3565C2×C7semidirect
434. #3563C2×C7semidirect
435. #3559C2×C7semidirect
436. #3555C2×C7semidirect
437. #3553C2×C7semidirect
438. #3552C2×C7semidirect
439. #3552C2×C7semidirect
440. #3547C2×C7semidirect
441. #3544C2×C7semidirect
442. #3541C2×C7semidirect
443. #3512C2×C7semidirect
444. #3511C2×C7semidirect
445. #3504C2×C7semidirect
446. #3503C2×C7semidirect
447. #3493C2×C7semidirect
448. #3493C2×C7semidirect
449. #3492C2×C7semidirect
450. C2×#544C2×C7semidirect
451. #3455C2×C7semidirect
602. #564C22×C7semidirect
605. #563C22×C7semidirect
606. #563C22×C7semidirect
607. #563C22×C7semidirect
608. #563C22×C7semidirect
611. #562C22×C7semidirect
612. Q82C22×C7semidirect
613. #557C22×C7semidirect
614. #557C22×C7semidirect
615. #557C22×C7semidirect
616. #557C22×C7semidirect
620. #556C22×C7semidirect
621. #556C22×C7semidirect
624. #555C22×C7semidirect
630. #554C22×C7semidirect
631. #554C22×C7semidirect
632. #554C22×C7semidirect
633. #554C22×C7semidirect
641. #553C22×C7semidirect
642. #553C22×C7semidirect
648. #552C22×C7semidirect
649. #552C22×C7semidirect
650. #552C22×C7semidirect
651. #552C22×C7semidirect
653. D4×Q8C22×C7semidirect
654. D4×Q8C22×C7semidirect
660. #547C22×C7semidirect
661. #547C22×C7semidirect
669. #544C22×C7semidirect
670. #544C22×C7semidirect
671. #544C22×C7semidirect
672. #544C22×C7semidirect
673. #544C22×C7semidirect
681. #542C22×C7semidirect
682. #542C22×C7semidirect
683. #542C22×C7semidirect
687. #541C22×C7semidirect
688. #541C22×C7semidirect
689. #541C22×C7semidirect
690. #541C22×C7semidirect
693. #540C22×C7semidirect
699. #539C22×C7semidirect
700. #539C22×C7semidirect
710. #536C22×C7semidirect
712. #533C22×C7semidirect
713. #533C22×C7semidirect
714. #533C22×C7semidirect
716. #532C22×C7semidirect
719. C2×C4⋊Q8C22×C7semidirect
726. #529C22×C7semidirect
727. #529C22×C7semidirect
730. C2×#125C22×C7semidirect
1329. C7#62877direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C7×#35652
C7×#35632
C7×#35592
C7×#35552
C7×#35532
C7×#35522
C7×#35472
C7×#35442
C7×#35412
C7×#35122
C7×#35112
C7×#35042
C7×#35032
C7×#34932
C7×#34922
C2×C7×#5442
C7×#34552
#628777