Finite Group Databasebeta

← C7×#15179 #13192395

Subgroups — C7×#15179 #13192395

Order 1792.

1946 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic
2C2×C7×#391C211yesmaximal, characteristic, complemented
3C2×C7×#391C211yesmaximal, characteristic, complemented
4C2×C7×#389C211yesmaximal, characteristic, complemented
5C2×C7×#380C211yesmaximal, characteristic
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
7C7×#1442C212yesmaximal, complemented
8C7×#1441C212yesmaximal, complemented
9C7×#1440C212yesmaximal
10C7×#1439C212yesmaximal
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C2×C7×C22⋊Q8—24no—
15C2×C7×C22⋊Q8—24no—
16C2×C7×C22⋊Q8—24no—
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C42×C7C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C7×#391—24no—
29C7×#391—24no—
30C7×#389—24no—
31C7×#380—24no—
32C4×C7×C22⋊C4—24no—
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42C2×C7×#95C2212yes—
43#15179C711yesmaximal, characteristic, direct product factor, Sylow
44C25×C7C2311yescharacteristic
45C22×C7×Q8—22no—
46C22×C7×Q8—22no—
47C22×C7×Q8—22no—
48C22×C7×Q8—22no—
49C22×C7×Q8—22no—
50C22×C7×Q8—22no—
51C22×C7×Q8D414yes—
52C23×C4×C7—22no—
53C23×C4×C7—22no—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7D414yes—
59C23×C4×C7C2312yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2312yes—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2312yes—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C7×C22⋊Q8—232no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—24no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—24no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—42no—
83C2×C7×C4⋊C4D414yes—
84C2×C7×C4⋊C4D414yes—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4Q814yescomplemented
97C2×C42×C7—22no—
98C2×C42×C7—22no—
99C2×C42×C7—22no—
100C2×C42×C7—22no—
101C2×C42×C7—22no—
102C2×C42×C7—22no—
103C7×#95—22no—
104C7×#95—22no—
105C7×#95—24no—
106C7×#95—24no—
107C7×#95—24no—
108C7×#95—24no—
109C7×#95—24no—
110C7×#95—24no—
111C7×#95—24no—
112C7×#95—42no—
113C22×C22⋊Q8C2×C711yescharacteristic
114C2×#391C2×C711yescharacteristic, complemented
115C2×#391C2×C711yescharacteristic, complemented
116C2×#389C2×C711yescharacteristic, complemented
117C2×#380C2×C711yescharacteristic
118C2×C4×C22⋊C4C2×C711yescharacteristic
119#1442C2×C712yescomplemented
120#1441C2×C712yescomplemented
121#1440C2×C712yes—
122#1439C2×C712yes—
123C4⋊#95C2×C711yescharacteristic, complemented
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—21no—
131C24×C7—21no—
132C24×C7—21no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7C2×D412yes—
137C24×C7C2×Q812yes—
138C24×C7#4112yes—
139C24×C7C2411yescharacteristic
140C2×C7×Q8—28no—
141C2×C7×Q8—28no—
142C2×C7×Q8—28no—
143C2×C7×Q8—44no—
144C2×C7×Q8—44no—
145C2×C7×Q8—44no—
146C2×C7×Q8—44no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—22no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—21no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—21no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—28no—
196C22×C4×C7—28no—
197C22×C4×C7—28no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—44no—
206C22×C4×C7—44no—
207C22×C4×C7—44no—
208C22×C4×C7—44no—
209C22×C4×C7C2×D414yes—
210C22×C4×C7C2×D414yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2×D414yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×Q812yes—
218C22×C4×C7C2×Q812yes—
219C22×C4×C7#4112yes—
220C22×C4×C7#4112yes—
221C22×C4×C7#4112yes—
222C22×C4×C7#4112yes—
223C22×C4×C7#4112yes—
224C7×C4⋊C4—216no—
225C7×C4⋊C4—28no—
226C7×C4⋊C4—28no—
227C7×C4⋊C4—48no—
228C7×C4⋊C4—44no—
229C7×C22⋊C4—28no—
230C7×C22⋊C4—216no—
231C7×C22⋊C4—28no—
232C7×C22⋊C4—48no—
233C42×C7—44no—
234C42×C7—44no—
235C23×Q8C22×C711yescharacteristic
236C24×C4C22×C711yescharacteristic
237C2×C22⋊Q8—24no—
238C2×C22⋊Q8—24no—
239C2×C22⋊Q8—24no—
240C22×C4⋊C4C22×C712yes—
241C22×C4⋊C4C22×C711yescharacteristic
242C22×C4⋊C4C22×C712yes—
243C22×C4⋊C4C22×C711yescharacteristic
244C22×C4⋊C4C22×C711yescharacteristic
245C22×C22⋊C4C22×C712yes—
246C22×C22⋊C4C22×C711yescharacteristic
247C22×C22⋊C4C22×C712yes—
248C22×C22⋊C4C22×C711yescharacteristic
249C22×C42C22×C711yescharacteristic
250C22×C42C22×C711yescharacteristic
251#391—24no—
252#391—24no—
253#389—24no—
254#380—24no—
255C4×C22⋊C4—24no—
256C2×#95C22×C712yes—
257C2×#95C22×C712yes—
258C2×#95C22×C712yes—
259C2×#95C22×C712yes—
260C2×#95C22×C712yes—
261C2×#95C22×C712yes—
262C2×#95C22×C711yescharacteristic
263C2×#95C22×C712yes—
264C2×#95C22×C711yescharacteristic
265C2×#95C22×C712yes—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—22no—
270C23×C7—22no—
271C23×C7—22no—
272C23×C7—22no—
273C23×C7—22no—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—22no—
278C23×C7—22no—
279C23×C7—22no—
280C23×C7—22no—
281C23×C7—22no—
282C23×C7—22no—
283C23×C7—22no—
284C23×C7—41no—
285C23×C7—41no—
286C23×C7—41no—
287C23×C7—41no—
288C23×C7—41no—
289C23×C7—41no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7C22⋊Q814yes—
301C23×C7C22×D411yescharacteristic
302C23×C7C22×D411yescharacteristic
303C23×C7C22×D411yescharacteristic
304C23×C7C22×D411yescharacteristic
305C23×C7C22×Q811yescharacteristic
306C23×C7C2×#4111yescharacteristic
307C23×C7C2×#4111yescharacteristic
308C23×C7C2×#4111yescharacteristic
309C23×C7C2×#4111yescharacteristic
310C23×C7C2×#4111yescharacteristic
311C23×C7C2×#4111yescharacteristic
312C23×C7H(5,𝔽2)11yescharacteristic
313C23×C72−1+411yescharacteristic
314C23×C72−1+411yescharacteristic
315C23×C72−1+411yescharacteristic
316C7×Q8—416no—
317C2×C4×C7—24no—
318C2×C4×C7—24no—
319C2×C4×C7—22no—
320C2×C4×C7—24no—
321C2×C4×C7—22no—
322C2×C4×C7—24no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—24no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—24no—
330C2×C4×C7—22no—
331C2×C4×C7—24no—
332C2×C4×C7—24no—
333C2×C4×C7—24no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—41no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7—41no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—42no—
359C2×C4×C7—41no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—42no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—42no—
369C2×C4×C7—41no—
370C2×C4×C7—42no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—416no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7#12014yes—
382C2×C4×C7#12114yes—
383C2×C4×C7#12114yes—
384C2×C4×C7#12114yes—
385C2×C4×C7#12314yes—
386C2×C4×C7#12314yes—
387C2×C4×C7#12414yes—
388C25C23×C711yescharacteristic
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—22no—
393C22×Q8—22no—
394C22×Q8—22no—
395C22×Q8C7×D414yes—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4C7×D414yes—
403C23×C4C23×C712yes—
404C23×C4C23×C712yes—
405C23×C4C23×C712yes—
406C23×C4C23×C712yes—
407C23×C4C23×C711yescharacteristic
408C23×C4C23×C711yescharacteristic
409C23×C4C23×C711yescharacteristic
410C23×C4C23×C711yescharacteristic
411C23×C4C23×C711yescharacteristic
412C23×C4C23×C711yescharacteristic
413C22⋊Q8—232no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4C7×D414yes—
428C2×C4⋊C4C7×D414yes—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4C7×Q814yescomplemented
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447#95—22no—
448#95—22no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—42no—
457C22×C7—24no—
458C22×C7—24no—
459C22×C7—24no—
460C22×C7—42no—
461C22×C7—42no—
462C22×C7—42no—
463C22×C7—42no—
464C22×C7—42no—
465C22×C7—42no—
466C22×C7—42no—
467C22×C7—42no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7C2×#12011yescharacteristic
473C22×C7C2×#12111yescharacteristic
474C22×C7C2×#12111yescharacteristic
475C22×C7C2×#12111yescharacteristic
476C22×C7C2×C22⋊Q811yescharacteristic
477C22×C7C2×#12311yescharacteristic
478C22×C7C2×#12311yescharacteristic
479C22×C7#52511yescharacteristic
480C22×C7C2×#12411yescharacteristic
481C22×C7#52911yescharacteristic
482C22×C7#52911yescharacteristic
483C22×C7#53311yescharacteristic
484C22×C7#53311yescharacteristic
485C22×C7#53611yescharacteristic
486C22×C7#53711yescharacteristic
487C22×C7#54111yescharacteristic
488C22×C7#54111yescharacteristic
489C22×C7#54211yescharacteristic
490C22×C7#54211yescharacteristic
491C22×C7#54611yescharacteristic
492C22×C7#54611yescharacteristic
493C22×C7#54711yescharacteristic
494C22×C7#54711yescharacteristic
495C22×C7#54811yescharacteristic
496C22×C7#54811yescharacteristic
497C22×C7#54811yescharacteristic
498C22×C7#54811yescharacteristic
499C22×C7D4×Q811yescharacteristic
500C22×C7D4×Q811yescharacteristic
501C22×C7D4×Q811yescharacteristic
502C22×C7#55011yescharacteristic
503C22×C7#55211yescharacteristic
504C22×C7#55211yescharacteristic
505C22×C7#55411yescharacteristic
506C22×C7#55611yescharacteristic
507C4×C7—42no—
508C4×C7—44no—
509C4×C7—44no—
510C4×C7—42no—
511C4×C7—42no—
512C4×C7—42no—
513C4×C7—42no—
514C4×C7—44no—
515C4×C7—82no—
516C4×C7#39418yes—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24C2×C7×D412yes—
530C24C2×C7×Q812yes—
531C24C7×#4112yes—
532C24C24×C711yescharacteristic
533C2×Q8—28no—
534C2×Q8—28no—
535C2×Q8—28no—
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8—44no—
539C2×Q8—44no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4C2×C7×D414yes—
603C22×C4C2×C7×D414yes—
604C22×C4C2×C7×D412yes—
605C22×C4C2×C7×D414yes—
606C22×C4C2×C7×D412yes—
607C22×C4C2×C7×D412yes—
608C22×C4C2×C7×D412yes—
609C22×C4C2×C7×D412yes—
610C22×C4C2×C7×Q812yes—
611C22×C4C2×C7×Q812yes—
612C22×C4C7×#4112yes—
613C22×C4C7×#4112yes—
614C22×C4C7×#4112yes—
615C22×C4C7×#4112yes—
616C22×C4C7×#4112yes—
617C4⋊C4—216no—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C22⋊C4—216no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—48no—
626C42—44no—
627C42—44no—
628C2×C7—44no—
629C2×C7C2×#39411yescharacteristic
630C2×C7#240711yescharacteristic
631C2×C7#240911yescharacteristic
632C2×C7#241511yescharacteristic
633C2×C7#241711yescharacteristic
634C2×C7#242111yescharacteristic
635C2×C7#242311yescharacteristic
636C2×C7#242611yescharacteristic
637C2×C7#242711yescharacteristic
638C2×C7#242911yescharacteristic
639C2×C7#242911yescharacteristic
640C2×C7#248911yescharacteristic
641C2×C7#249211yescharacteristic
642C2×C7#262511yescharacteristic
643C2×C7#285511yescharacteristic
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23C7×C22⋊Q814yes—
679C23C22×C7×D411yescharacteristic
680C23C22×C7×D411yescharacteristic
681C23C22×C7×D411yescharacteristic
682C23C22×C7×D411yescharacteristic
683C23C22×C7×Q811yescharacteristic
684C23C2×C7×#4111yescharacteristic
685C23C2×C7×#4111yescharacteristic
686C23C2×C7×#4111yescharacteristic
687C23C2×C7×#4111yescharacteristic
688C23C2×C7×#4111yescharacteristic
689C23C2×C7×#4111yescharacteristic
690C23C7×H(5,𝔽2)11yescharacteristic
691C23C7×2−1+411yescharacteristic
692C23C7×2−1+411yescharacteristic
693C23C7×2−1+411yescharacteristic
694Q8—416no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—416no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4C7×#12014yes—
760C2×C4C7×#12114yes—
761C2×C4C7×#12114yes—
762C2×C4C7×#12114yes—
763C2×C4C7×#12314yes—
764C2×C4C7×#12314yes—
765C2×C4C7×#12414yes—
766C7#1517911yescharacteristic, direct product factor, Sylow
767C22—24no—
768C22—24no—
769C22—24no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22C2×C7×#12011yescharacteristic
783C22C2×C7×#12111yescharacteristic
784C22C2×C7×#12111yescharacteristic
785C22C2×C7×#12111yescharacteristic
786C22C2×C7×C22⋊Q811yescharacteristic
787C22C2×C7×#12311yescharacteristic
788C22C2×C7×#12311yescharacteristic
789C22C7×#52511yescharacteristic
790C22C2×C7×#12411yescharacteristic
791C22C7×#52911yescharacteristic
792C22C7×#52911yescharacteristic
793C22C7×#53311yescharacteristic
794C22C7×#53311yescharacteristic
795C22C7×#53611yescharacteristic
796C22C7×#53711yescharacteristic
797C22C7×#54111yescharacteristic
798C22C7×#54111yescharacteristic
799C22C7×#54211yescharacteristic
800C22C7×#54211yescharacteristic
801C22C7×#54611yescharacteristic
802C22C7×#54611yescharacteristic
803C22C7×#54711yescharacteristic
804C22C7×#54711yescharacteristic
805C22C7×#54811yescharacteristic
806C22C7×#54811yescharacteristic
807C22C7×#54811yescharacteristic
808C22C7×#54811yescharacteristic
809C22C7×D4×Q811yescharacteristic
810C22C7×D4×Q811yescharacteristic
811C22C7×D4×Q811yescharacteristic
812C22C7×#55011yescharacteristic
813C22C7×#55211yescharacteristic
814C22C7×#55211yescharacteristic
815C22C7×#55411yescharacteristic
816C22C7×#55611yescharacteristic
817C4—44no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—44no—
823C4—42no—
824C4—44no—
825C4—82no—
826C4C7×#39418yes—
827C2—44no—
828C2C2×C7×#39411yescharacteristic
829C2C7×#240711yescharacteristic
830C2C7×#240911yescharacteristic
831C2C7×#241511yescharacteristic
832C2C7×#241711yescharacteristic
833C2C7×#242111yescharacteristic
834C2C7×#242311yescharacteristic
835C2C7×#242611yescharacteristic
836C2C7×#242711yescharacteristic
837C2C7×#242911yescharacteristic
838C2C7×#242911yescharacteristic
839C2C7×#248911yescharacteristic
840C2C7×#249211yescharacteristic
841C2C7×#262511yescharacteristic
842C2C7×#285511yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#391C2semidirect
3. C2×C7×#391C2semidirect
4. C2×C7×#389C2semidirect
7. C7×#1442C2semidirect
8. C7×#1441C2semidirect
11. C7×C4⋊#95C2semidirect
43. #15179C7direct (N × H)
96. C2×C7×C22⋊C4Q8semidirect
114. C2×#391C2×C7semidirect
115. C2×#391C2×C7semidirect
116. C2×#389C2×C7semidirect
119. #1442C2×C7semidirect
120. #1441C2×C7semidirect
123. C4⋊#95C2×C7semidirect
440. C2×C22⋊C4C7×Q8semidirect
766. C7#15179direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C2×C7×#3912
C2×C7×#3892
C2×C7×#3802
C2×C4×C7×C22⋊C42
C7×#14422
C7×#14412
C7×#14402
C7×#14392
C7×C4⋊#952
#151797