Finite Group Databasebeta

← C2×C7×#3507 #13239993

Subgroups — C2×C7×#3507 #13239993

Order 1792.

7130 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3507C2132yesmaximal, direct product factor
2C2×C7×#559C212yesmaximal, complemented
3C2×C7×#557C212yesmaximal, complemented
4C2×C7×#556C212yesmaximal, complemented
5C2×C7×#556C214yesmaximal, complemented
6C2×C7×#554C212yesmaximal, complemented
7C2×C7×#552C214yesmaximal, complemented
8C2×C7×#539C214yesmaximal, complemented
9C2×C7×#536C212yesmaximal, complemented
10C2×C7×#533C211yesmaximal, characteristic, complemented
11C2×C7×#532C211yesmaximal, characteristic
12C2×C7×#529C214yesmaximal, complemented
13C2×C7×#520C212yesmaximal, complemented
14C22×C4×C7×Q8C211yesmaximal, characteristic, complemented
15C22×C7×#41C2212yes—
16C23×C7×Q8C2211yescharacteristic
17C7×#559C22132yescomplemented
18C7×#557C22132yescomplemented
19C7×#556C22132yescomplemented
20C7×#556C22164yescomplemented
21C7×#554C22132yescomplemented
22C7×#552C22164yescomplemented
23C7×#539C22164yescomplemented
24C7×#536C22132yescomplemented
25C7×#533C22116yescomplemented
26C7×#532C22116yes—
27C2×C7×C4⋊Q8C2211yescharacteristic
28C2×C7×C4⋊Q8C2211yescharacteristic
29C2×C7×C4⋊Q8C2211yescharacteristic
30C2×C7×C4⋊Q8C2214yes—
31C2×C7×#127C2211yescharacteristic
32C7×#529C22164yescomplemented
33C2×C7×#126C2218yes—
34C2×C7×#126C2218yes—
35C2×C7×#125C2214yes—
36C2×C7×#125C2212yes—
37C2×C7×#125C2218yes—
38C2×C7×#124C2214yes—
39C2×C7×#124C2212yes—
40C2×C7×#124C2214yes—
41C2×C7×#123C2218yes—
42C2×C7×#123C2218yes—
43C2×C7×C22⋊Q8C2212yes—
44C2×C7×C22⋊Q8C2212yes—
45C2×C7×C22⋊Q8C2214yes—
46C2×C7×C22⋊Q8C2214yes—
47C2×C7×C22⋊Q8C2218yes—
48C2×C7×#121C2212yes—
49C2×C7×#121C2212yes—
50C7×#520C22132yescomplemented
51C2×C4×C7×Q8C2212yes—
52C2×C4×C7×Q8C2212yes—
53C2×C4×C7×Q8C2212yes—
54C2×C4×C7×Q8C2212yes—
55C2×C4×C7×Q8C2214yes—
56C2×C4×C7×Q8C2214yes—
57C2×C4×C7×Q8C2212yes—
58C2×C4×C7×Q8C2212yes—
59C2×C4×C7×Q8C22116yescomplemented
60C2×C4×C7×D4C2218yes—
61C2×C4×C7×D4C2214yes—
62C2×C4×C7×D4C2214yes—
63C2×C4×C7×D4C2212yes—
64C2×C4×C7×D4C2212yes—
65C2×C7×#117C2212yes—
66C2×C7×#117C2214yes—
67C2×C7×#117C2218yes—
68C22×C7×C4⋊C4C2211yescharacteristic
69C22×C7×C4⋊C4C2212yes—
70C22×C7×C4⋊C4C2214yes—
71C22×C42×C7C2212yes—
72C22×C42×C7C2211yescharacteristic
73C2×#3507C711yesmaximal, characteristic, direct product factor, Sylow
74C2×C7×#41—216no—
75C2×C7×#41C23116yes—
76C22×C7×Q8—28no—
77C22×C7×Q8C2312yes—
78C22×C7×Q8C2312yes—
79C22×C7×Q8C2318yes—
80C22×C7×Q8C2312yes—
81C22×C7×Q8C2312yes—
82C22×C7×Q8C2312yes—
83C22×C7×D4C2314yes—
84C22×C7×D4C2312yes—
85C22×C7×D4C2312yes—
86C22×C7×D4C2312yes—
87C23×C4×C7C2312yes—
88C23×C4×C7C2314yes—
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2312yes—
91C23×C4×C7C2311yescharacteristic
92C23×C4×C7C2318yes—
93C23×C4×C7C2311yescharacteristic
94C7×C4⋊Q8C2318yes—
95C7×C4⋊Q8C2318yes—
96C7×C4⋊Q8C2318yes—
97C7×C4⋊Q8C23132yes—
98C7×#127C2318yes—
99C7×#126C23164yes—
100C7×#126C23164yes—
101C7×#125C23132yes—
102C7×#125C23116yes—
103C7×#125C23164yes—
104C7×#124C23132yes—
105C7×#124C23116yes—
106C7×#124C23132yes—
107C7×#123C23164yes—
108C7×#123C23164yes—
109C7×C22⋊Q8C23116yes—
110C7×C22⋊Q8C23116yes—
111C7×C22⋊Q8C23132yes—
112C7×C22⋊Q8C23132yes—
113C7×C22⋊Q8C23164yes—
114C7×#121C23116yes—
115C7×#121C23116yes—
116C4×C7×Q8C23116yes—
117C4×C7×Q8C23116yes—
118C4×C7×Q8C23116yes—
119C4×C7×Q8C23116yes—
120C4×C7×Q8C23132yes—
121C4×C7×Q8C23132yes—
122C4×C7×Q8C23116yes—
123C4×C7×Q8C23116yes—
124C4×C7×D4C23164yes—
125C4×C7×D4C23132yes—
126C4×C7×D4C23132yes—
127C4×C7×D4C23116yes—
128C4×C7×D4C23116yes—
129C7×#117C23116yes—
130C7×#117C23132yes—
131C7×#117C23164yes—
132C2×C7×C4⋊C4C2312yes—
133C2×C7×C4⋊C4C2312yes—
134C2×C7×C4⋊C4C2312yes—
135C2×C7×C4⋊C4C2318yes—
136C2×C7×C4⋊C4C2314yes—
137C2×C7×C4⋊C4C2314yes—
138C2×C7×C4⋊C4C2318yes—
139C2×C7×C4⋊C4C23116yes—
140C2×C7×C4⋊C4C23132yes—
141C2×C7×C4⋊C4C2312yes—
142C2×C7×C4⋊C4C2314yes—
143C2×C7×C4⋊C4C2318yes—
144C2×C7×C4⋊C4C2312yes—
145C2×C7×C4⋊C4C2312yes—
146C2×C7×C4⋊C4C2312yes—
147C2×C7×C4⋊C4C2314yes—
148C2×C7×C4⋊C4C2318yes—
149C2×C7×C4⋊C4C2312yes—
150C2×C7×C22⋊C4C2314yes—
151C2×C7×C22⋊C4C2314yes—
152C2×C7×C22⋊C4C2318yes—
153C2×C7×C22⋊C4C2318yes—
154C2×C7×C22⋊C4C2314yes—
155C2×C7×C22⋊C4C2318yes—
156C2×C42×C7C2314yes—
157C2×C42×C7C2311yescharacteristic
158C2×C42×C7C2311yescharacteristic
159C2×C42×C7C2314yes—
160C2×C42×C7C2311yescharacteristic
161C2×C42×C7C2311yescharacteristic
162C2×C42×C7C23116yes—
163C2×C42×C7C2318yes—
164C2×C42×C7C2318yes—
165C2×C42×C7C2314yes—
166#3507C2×C7132yesdirect product factor
167C2×#559C2×C712yescomplemented
168C2×#557C2×C712yescomplemented
169C2×#556C2×C712yescomplemented
170C2×#556C2×C714yescomplemented
171C2×#554C2×C712yescomplemented
172C2×#552C2×C714yescomplemented
173C2×#539C2×C714yescomplemented
174C2×#536C2×C712yescomplemented
175C2×#533C2×C711yescharacteristic, complemented
176C2×#532C2×C711yescharacteristic
177C2×#529C2×C714yescomplemented
178C2×#520C2×C712yescomplemented
179C22×C4×Q8C2×C711yescharacteristic, complemented
180C24×C7C2414yes—
181C24×C7C2411yescharacteristic
182C7×#41—264no—
183C2×C7×Q8—28no—
184C2×C7×Q8—28no—
185C2×C7×Q8—232no—
186C2×C7×Q8—28no—
187C2×C7×Q8—28no—
188C2×C7×Q8—44no—
189C2×C7×Q8C2418yes—
190C2×C7×Q8C2418yes—
191C2×C7×Q8C2418yes—
192C2×C7×Q8C2418yes—
193C2×C7×Q8C2418yes—
194C2×C7×D4—216no—
195C2×C7×D4—28no—
196C2×C7×D4—28no—
197C2×C7×D4—44no—
198C2×C7×D4C2418yes—
199C2×C7×D4C24116yes—
200C2×C7×D4C2418yes—
201C2×C7×D4C2418yes—
202C22×C4×C7—28no—
203C22×C4×C7—216no—
204C22×C4×C7—24no—
205C22×C4×C7—44no—
206C22×C4×C7—416no—
207C22×C4×C7—42no—
208C22×C4×C7#4118yes—
209C22×C4×C7C2414yes—
210C22×C4×C7C2418yes—
211C22×C4×C7C24116yes—
212C22×C4×C7C2411yescharacteristic
213C22×C4×C7C2414yes—
214C22×C4×C7C2414yes—
215C22×C4×C7C2414yes—
216C22×C4×C7C2411yescharacteristic
217C22×C4×C7C2414yes—
218C22×C4×C7C2411yescharacteristic
219C22×C4×C7C2414yes—
220C22×C4×C7C2418yes—
221C22×C4×C7C2414yes—
222C22×C4×C7C24132yes—
223C22×C4×C7C2414yes—
224C22×C4×C7C2411yescharacteristic
225C22×C4×C7C2411yescharacteristic
226C22×C4×C7C2411yescharacteristic
227C7×C4⋊C4C2418yes—
228C7×C4⋊C4C2418yes—
229C7×C4⋊C4C2418yes—
230C7×C4⋊C4C24132yes—
231C7×C4⋊C4C24116yes—
232C7×C4⋊C4C24116yes—
233C7×C4⋊C4C2418yes—
234C7×C4⋊C4C24116yes—
235C7×C4⋊C4C24132yes—
236C7×C4⋊C4C2418yes—
237C7×C4⋊C4C2418yes—
238C7×C4⋊C4C2418yes—
239C7×C4⋊C4C24116yes—
240C7×C4⋊C4C24132yes—
241C7×C4⋊C4C2418yes—
242C7×C22⋊C4C24116yes—
243C7×C22⋊C4C24116yes—
244C7×C22⋊C4C24132yes—
245C7×C22⋊C4C24132yes—
246C7×C22⋊C4C24116yes—
247C7×C22⋊C4C24132yes—
248C42×C7C24116yes—
249C42×C7C2414yes—
250C42×C7C2414yes—
251C42×C7C24116yes—
252C42×C7C2414yes—
253C42×C7C2414yes—
254C42×C7C24132yes—
255C42×C7C24116yes—
256C22×#41C22×C712yes—
257C23×Q8C22×C711yescharacteristic
258#559C22×C7132yescomplemented
259#557C22×C7132yescomplemented
260#556C22×C7132yescomplemented
261#556C22×C7164yescomplemented
262#554C22×C7132yescomplemented
263#552C22×C7164yescomplemented
264#539C22×C7164yescomplemented
265#536C22×C7132yescomplemented
266#533C22×C7116yescomplemented
267#532C22×C7116yes—
268C2×C4⋊Q8C22×C711yescharacteristic
269C2×C4⋊Q8C22×C711yescharacteristic
270C2×C4⋊Q8C22×C711yescharacteristic
271C2×C4⋊Q8C22×C714yes—
272C2×#127C22×C711yescharacteristic
273#529C22×C7164yescomplemented
274C2×#126C22×C718yes—
275C2×#126C22×C718yes—
276C2×#125C22×C714yes—
277C2×#125C22×C712yes—
278C2×#125C22×C718yes—
279C2×#124C22×C714yes—
280C2×#124C22×C712yes—
281C2×#124C22×C714yes—
282C2×#123C22×C718yes—
283C2×#123C22×C718yes—
284C2×C22⋊Q8C22×C712yes—
285C2×C22⋊Q8C22×C712yes—
286C2×C22⋊Q8C22×C714yes—
287C2×C22⋊Q8C22×C714yes—
288C2×C22⋊Q8C22×C718yes—
289C2×#121C22×C712yes—
290C2×#121C22×C712yes—
291#520C22×C7132yescomplemented
292C2×C4×Q8C22×C712yes—
293C2×C4×Q8C22×C712yes—
294C2×C4×Q8C22×C712yes—
295C2×C4×Q8C22×C712yes—
296C2×C4×Q8C22×C714yes—
297C2×C4×Q8C22×C714yes—
298C2×C4×Q8C22×C712yes—
299C2×C4×Q8C22×C712yes—
300C2×C4×Q8C22×C7116yescomplemented
301C2×C4×D4C22×C718yes—
302C2×C4×D4C22×C714yes—
303C2×C4×D4C22×C714yes—
304C2×C4×D4C22×C712yes—
305C2×C4×D4C22×C712yes—
306C2×#117C22×C712yes—
307C2×#117C22×C714yes—
308C2×#117C22×C718yes—
309C22×C4⋊C4C22×C711yescharacteristic
310C22×C4⋊C4C22×C712yes—
311C22×C4⋊C4C22×C714yes—
312C22×C42C22×C712yes—
313C22×C42C22×C711yescharacteristic
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—28no—
317C23×C7—28no—
318C23×C7—28no—
319C23×C7C2×#4114yes—
320C23×C7C2518yes—
321C23×C7C2512yes—
322C23×C7C2511yescharacteristic
323C7×Q8—216no—
324C7×Q8—216no—
325C7×Q8—216no—
326C7×Q8—216no—
327C7×Q8—48no—
328C7×D4—232no—
329C7×D4—216no—
330C7×D4—216no—
331C7×D4—48no—
332C2×C4×C7—28no—
333C2×C4×C7—216no—
334C2×C4×C7—28no—
335C2×C4×C7—22no—
336C2×C4×C7—28no—
337C2×C4×C7—28no—
338C2×C4×C7—28no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—232no—
342C2×C4×C7—28no—
343C2×C4×C7—48no—
344C2×C4×C7—432no—
345C2×C4×C7—44no—
346C2×C4×C7C2×#4114yes—
347C2×C4×C7C2×#4114yes—
348C2×C4×C7C2×#41116yes—
349C2×C4×C72−1+414yes—
350C2×C4×C7C2512yes—
351C2×C4×C7C2518yes—
352C2×C4×C7C2518yes—
353C2×C4×C7C2518yes—
354C2×C4×C7C2512yes—
355C2×C4×C7C2518yes—
356C2×C4×C7C2512yes—
357C2×C4×C7C2518yes—
358C2×C4×C7C2512yes—
359C2×C4×C7C2512yes—
360C2×C4×C7C2512yes—
361C2×#41—216no—
362C2×#41C23×C7116yes—
363C22×Q8—28no—
364C22×Q8C23×C712yes—
365C22×Q8C23×C712yes—
366C22×Q8C23×C712yes—
367C22×Q8C23×C712yes—
368C22×Q8C23×C718yes—
369C22×Q8C23×C712yes—
370C22×D4C23×C712yes—
371C22×D4C23×C714yes—
372C22×D4C23×C712yes—
373C22×D4C23×C712yes—
374C23×C4C23×C714yes—
375C23×C4C23×C712yes—
376C23×C4C23×C711yescharacteristic
377C23×C4C23×C712yes—
378C23×C4C23×C711yescharacteristic
379C23×C4C23×C718yes—
380C23×C4C23×C711yescharacteristic
381C4⋊Q8C23×C718yes—
382C4⋊Q8C23×C718yes—
383C4⋊Q8C23×C718yes—
384C4⋊Q8C23×C7132yes—
385#127C23×C718yes—
386#126C23×C7164yes—
387#126C23×C7164yes—
388#125C23×C7132yes—
389#125C23×C7116yes—
390#125C23×C7164yes—
391#124C23×C7132yes—
392#124C23×C7116yes—
393#124C23×C7132yes—
394#123C23×C7164yes—
395#123C23×C7164yes—
396C22⋊Q8C23×C7116yes—
397C22⋊Q8C23×C7116yes—
398C22⋊Q8C23×C7132yes—
399C22⋊Q8C23×C7132yes—
400C22⋊Q8C23×C7164yes—
401#121C23×C7116yes—
402#121C23×C7116yes—
403C4×Q8C23×C7116yes—
404C4×Q8C23×C7116yes—
405C4×Q8C23×C7116yes—
406C4×Q8C23×C7116yes—
407C4×Q8C23×C7132yes—
408C4×Q8C23×C7132yes—
409C4×Q8C23×C7116yes—
410C4×Q8C23×C7116yes—
411C4×D4C23×C7164yes—
412C4×D4C23×C7132yes—
413C4×D4C23×C7132yes—
414C4×D4C23×C7116yes—
415C4×D4C23×C7116yes—
416#117C23×C7116yes—
417#117C23×C7132yes—
418#117C23×C7164yes—
419C2×C4⋊C4C23×C712yes—
420C2×C4⋊C4C23×C712yes—
421C2×C4⋊C4C23×C712yes—
422C2×C4⋊C4C23×C718yes—
423C2×C4⋊C4C23×C714yes—
424C2×C4⋊C4C23×C714yes—
425C2×C4⋊C4C23×C718yes—
426C2×C4⋊C4C23×C7116yes—
427C2×C4⋊C4C23×C7132yes—
428C2×C4⋊C4C23×C712yes—
429C2×C4⋊C4C23×C714yes—
430C2×C4⋊C4C23×C718yes—
431C2×C4⋊C4C23×C712yes—
432C2×C4⋊C4C23×C712yes—
433C2×C4⋊C4C23×C712yes—
434C2×C4⋊C4C23×C714yes—
435C2×C4⋊C4C23×C718yes—
436C2×C4⋊C4C23×C712yes—
437C2×C22⋊C4C23×C714yes—
438C2×C22⋊C4C23×C714yes—
439C2×C22⋊C4C23×C718yes—
440C2×C22⋊C4C23×C718yes—
441C2×C22⋊C4C23×C714yes—
442C2×C22⋊C4C23×C718yes—
443C2×C42C23×C718yes—
444C2×C42C23×C714yes—
445C2×C42C23×C714yes—
446C2×C42C23×C711yescharacteristic
447C2×C42C23×C711yescharacteristic
448C2×C42C23×C714yes—
449C2×C42C23×C711yescharacteristic
450C2×C42C23×C711yescharacteristic
451C2×C42C23×C7116yes—
452C2×C42C23×C718yes—
453C22×C7—22no—
454C22×C7—22no—
455C22×C7—28no—
456C22×C7—28no—
457C22×C7—28no—
458C22×C7—28no—
459C22×C7—416no—
460C22×C7C22×#4114yes—
461C22×C7C22×#4112yes—
462C22×C7C2×2−1+412yes—
463C22×C7#58512yes—
464C22×C7C2611yescharacteristic
465C4×C7—28no—
466C4×C7—28no—
467C4×C7—22no—
468C4×C7—28no—
469C4×C7—28no—
470C4×C7—28no—
471C4×C7—22no—
472C4×C7—22no—
473C4×C7C22×#4114yes—
474C4×C7C22×#4114yes—
475C4×C7C2×2−1+414yes—
476C24C24×C714yes—
477C24C24×C711yescharacteristic
478#41—264no—
479C2×Q8—28no—
480C2×Q8—28no—
481C2×Q8—232no—
482C2×Q8—28no—
483C2×Q8—28no—
484C2×Q8—44no—
485C2×Q8C24×C718yes—
486C2×Q8C24×C718yes—
487C2×Q8C24×C718yes—
488C2×Q8C24×C718yes—
489C2×Q8C24×C718yes—
490C2×D4—216no—
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—44no—
494C2×D4C24×C718yes—
495C2×D4C24×C7116yes—
496C2×D4C24×C718yes—
497C2×D4C24×C718yes—
498C22×C4—28no—
499C22×C4—216no—
500C22×C4—24no—
501C22×C4—44no—
502C22×C4—416no—
503C22×C4—42no—
504C22×C4C7×#4118yes—
505C22×C4C24×C711yescharacteristic
506C22×C4C24×C714yes—
507C22×C4C24×C714yes—
508C22×C4C24×C714yes—
509C22×C4C24×C714yes—
510C22×C4C24×C711yescharacteristic
511C22×C4C24×C714yes—
512C22×C4C24×C711yescharacteristic
513C22×C4C24×C718yes—
514C22×C4C24×C714yes—
515C22×C4C24×C7116yes—
516C22×C4C24×C718yes—
517C22×C4C24×C714yes—
518C22×C4C24×C7132yes—
519C22×C4C24×C711yescharacteristic
520C22×C4C24×C711yescharacteristic
521C22×C4C24×C714yes—
522C22×C4C24×C711yescharacteristic
523C4⋊C4C24×C718yes—
524C4⋊C4C24×C718yes—
525C4⋊C4C24×C718yes—
526C4⋊C4C24×C7132yes—
527C4⋊C4C24×C7116yes—
528C4⋊C4C24×C7116yes—
529C4⋊C4C24×C718yes—
530C4⋊C4C24×C7116yes—
531C4⋊C4C24×C7132yes—
532C4⋊C4C24×C718yes—
533C4⋊C4C24×C718yes—
534C4⋊C4C24×C718yes—
535C4⋊C4C24×C7116yes—
536C4⋊C4C24×C7132yes—
537C4⋊C4C24×C718yes—
538C22⋊C4C24×C7116yes—
539C22⋊C4C24×C7116yes—
540C22⋊C4C24×C7132yes—
541C22⋊C4C24×C7132yes—
542C22⋊C4C24×C7116yes—
543C22⋊C4C24×C7132yes—
544C42C24×C7116yes—
545C42C24×C714yes—
546C42C24×C714yes—
547C42C24×C7116yes—
548C42C24×C714yes—
549C42C24×C714yes—
550C42C24×C7132yes—
551C42C24×C7116yes—
552C2×C7—24no—
553C2×C7—48no—
554C2×C7#350714yesdirect product factor
555C2×C7C23×#4111yescharacteristic
556C2×C7C22×2−1+411yescharacteristic
557C2×C7C2×#58511yescharacteristic
558C23—22no—
559C23—22no—
560C23—28no—
561C23—28no—
562C23—28no—
563C23C2×C7×#4114yes—
564C23C25×C718yes—
565C23C25×C712yes—
566C23C25×C711yescharacteristic
567Q8—216no—
568Q8—216no—
569Q8—216no—
570Q8—216no—
571Q8—48no—
572D4—232no—
573D4—216no—
574D4—216no—
575D4—48no—
576C2×C4—28no—
577C2×C4—216no—
578C2×C4—28no—
579C2×C4—22no—
580C2×C4—28no—
581C2×C4—28no—
582C2×C4—28no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—232no—
586C2×C4—28no—
587C2×C4—48no—
588C2×C4—432no—
589C2×C4—44no—
590C2×C4C2×C7×#4114yes—
591C2×C4C2×C7×#4114yes—
592C2×C4C2×C7×#41116yes—
593C2×C4C7×2−1+414yes—
594C2×C4C25×C712yes—
595C2×C4C25×C718yes—
596C2×C4C25×C718yes—
597C2×C4C25×C718yes—
598C2×C4C25×C712yes—
599C2×C4C25×C718yes—
600C2×C4C25×C712yes—
601C2×C4C25×C718yes—
602C2×C4C25×C712yes—
603C2×C4C25×C712yes—
604C2×C4C25×C712yes—
605C7C2×#350711yescharacteristic, direct product factor, Sylow
606C22—22no—
607C22—22no—
608C22—28no—
609C22—28no—
610C22—28no—
611C22—28no—
612C22—416no—
613C22C22×C7×#4114yes—
614C22C22×C7×#4112yes—
615C22C2×C7×2−1+412yes—
616C22C7×#58512yes—
617C22C26×C711yescharacteristic
618C4—28no—
619C4—28no—
620C4—22no—
621C4—28no—
622C4—28no—
623C4—28no—
624C4—22no—
625C4—22no—
626C4C22×C7×#4114yes—
627C4C22×C7×#4114yes—
628C4C2×C7×2−1+414yes—
629C2—24no—
630C2—48no—
631C2C7×#350714yesdirect product factor
632C2C23×C7×#4111yescharacteristic
633C2C22×C7×2−1+411yescharacteristic
634C2C2×C7×#58511yescharacteristic
subgroupG/H
center, socleC23×C7C25
commutator, Frattini, cosocleC22C26×C7
prime radicalC2×C7×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3507C2direct (N × H)
2. C2×C7×#559C2semidirect
3. C2×C7×#557C2semidirect
4. C2×C7×#556C2semidirect
5. C2×C7×#556C2semidirect
6. C2×C7×#554C2semidirect
7. C2×C7×#552C2semidirect
8. C2×C7×#539C2semidirect
9. C2×C7×#536C2semidirect
10. C2×C7×#533C2semidirect
12. C2×C7×#529C2semidirect
13. C2×C7×#520C2semidirect
14. C22×C4×C7×Q8C2semidirect
17. C7×#559C22semidirect
18. C7×#557C22semidirect
19. C7×#556C22semidirect
20. C7×#556C22semidirect
21. C7×#554C22semidirect
22. C7×#552C22semidirect
23. C7×#539C22semidirect
24. C7×#536C22semidirect
25. C7×#533C22semidirect
32. C7×#529C22semidirect
50. C7×#520C22semidirect
59. C2×C4×C7×Q8C22semidirect
73. C2×#3507C7direct (N × H)
166. #3507C2×C7direct (N × H)
167. C2×#559C2×C7semidirect
168. C2×#557C2×C7semidirect
169. C2×#556C2×C7semidirect
170. C2×#556C2×C7semidirect
171. C2×#554C2×C7semidirect
172. C2×#552C2×C7semidirect
173. C2×#539C2×C7semidirect
174. C2×#536C2×C7semidirect
175. C2×#533C2×C7semidirect
177. C2×#529C2×C7semidirect
178. C2×#520C2×C7semidirect
179. C22×C4×Q8C2×C7semidirect
258. #559C22×C7semidirect
259. #557C22×C7semidirect
260. #556C22×C7semidirect
261. #556C22×C7semidirect
262. #554C22×C7semidirect
263. #552C22×C7semidirect
264. #539C22×C7semidirect
265. #536C22×C7semidirect
266. #533C22×C7semidirect
273. #529C22×C7semidirect
291. #520C22×C7semidirect
300. C2×C4×Q8C22×C7semidirect
554. C2×C7#3507direct (N × H)
605. C7C2×#3507direct (N × H)
631. C2C7×#3507direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35072
C2×C7×#5592
C2×C7×#5572
C2×C7×#5562
C2×C7×#5542
C2×C7×#5522
C2×C7×#5392
C2×C7×#5362
C2×C7×#5332
C2×C7×#5322
C2×C7×#5292
C2×C7×#5202
C22×C4×C7×Q82
C2×#35077