Finite Group Databasebeta

← C7×#24470 #13201686

Subgroups — C7×#24470 #13201686

Order 1792.

1360 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3489C211yesmaximal, characteristic
2C7×#3056C211yesmaximal, characteristic, complemented
3C2×C7×#456C211yesmaximal, characteristic, complemented
4C7×#3007C211yesmaximal, characteristic, complemented
5C2×C7×#421C211yesmaximal, characteristic, complemented
6C7×#2621C211yesmaximal, characteristic, complemented
7C7×#2040C211yesmaximal, characteristic, complemented
8C7×#2038C211yesmaximal, characteristic, complemented
9C7×#2007C211yesmaximal, characteristic, complemented
10C7×#2005C211yesmaximal, characteristic, complemented
11C7×#1901C211yesmaximal, characteristic, complemented
12C7×#1897C211yesmaximal, characteristic, complemented
13C7×#1882C211yesmaximal, characteristic, complemented
14C7×#1860C211yesmaximal, characteristic, complemented
15C7×#1793C211yesmaximal, characteristic, complemented
16C2×C7×2−1+4C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C2×C7×#137C2211yescharacteristic
19C2×C7×#137C2211yescharacteristic
20C2×C7×#137C2211yescharacteristic, complemented
21C22×C7×M16C2211yescharacteristic
22C7×D4×Q8—21no—
23C7×#548—21no—
24C7×#547—21no—
25C7×#547—22no—
26C7×#546—21no—
27C7×#546—22no—
28C7×#537—21no—
29C7×#537C2211yescharacteristic
30C7×#536—21no—
31C7×#536C2211yescharacteristic
32C2×C7×C4⋊Q8C2211yescharacteristic, complemented
33C7×#525—21no—
34C7×#525C2211yescharacteristic
35C2×C7×C22⋊Q8—21no—
36C2×C7×C22⋊Q8C2211yescharacteristic
37C2×C7×C22⋊Q8C2211yescharacteristic
38C7×#520C2211yescharacteristic
39C2×C7×#117C2211yescharacteristic
40C7×#470—21no—
41C7×#468—21no—
42C7×#467—21no—
43C7×#465—21no—
44C7×#456—24no—
45C7×#452—21no—
46C7×#452—21no—
47C7×#451—21no—
48C7×#450—21no—
49C7×#428C2211yescharacteristic, complemented
50C7×#421—24no—
51C2×C7×#104C2211yescharacteristic
52C2×C7×#104C2211yescharacteristic
53C2×C7×#104C2211yescharacteristic
54C2×C7×#104C2211yescharacteristic
55C2×C7×#104C2211yescharacteristic, complemented
56C2×C7×#104C2211yescharacteristic, complemented
57C7×#419C2211yescharacteristic, complemented
58C7×#417C2211yescharacteristic
59C7×#417C2211yescharacteristic
60C7×#417C2211yescharacteristic, complemented
61C2×C7×#101C2211yescharacteristic, complemented
62C2×C7×#101C2211yescharacteristic, complemented
63C7×#407C2211yescharacteristic
64C7×#398—22no—
65C7×#397—22no—
66C7×#391C2211yescharacteristic, complemented
67C7×#391C2211yescharacteristic, complemented
68C7×#382C2211yescharacteristic, complemented
69C7×#343C2211yescharacteristic, complemented
70C7×#343C2211yescharacteristic, complemented
71C7×#339C2211yescharacteristic, complemented
72C7×#339C2211yescharacteristic, complemented
73#24470C711yesmaximal, characteristic, direct product factor, Sylow
74C7×2−1+4—22no—
75C7×2−1+4—22no—
76C7×2−1+4—41no—
77C7×2−1+4—41no—
78C2×C7×#41—21no—
79C2×C7×#41—21no—
80C2×C7×#41—21no—
81C2×C7×#41—21no—
82C2×C7×#41—22no—
83C2×C7×#41—22no—
84C2×C7×#41—22no—
85C2×C7×#41—41no—
86C2×C7×#41—41no—
87C2×C7×#41D411yescharacteristic
88C2×C7×#41D411yescharacteristic
89C2×C7×#41C2311yescharacteristic
90C2×C7×#41C2311yescharacteristic
91C2×C7×#41C2311yescharacteristic
92C22×C7×Q8—21no—
93C22×C7×Q8—21no—
94C22×C7×Q8D411yescharacteristic
95C22×C7×Q8C2311yescharacteristic
96C22×C7×Q8C2311yescharacteristic
97C22×C7×D4—21no—
98C22×C7×D4D411yescharacteristic
99C23×C4×C7—21no—
100C23×C4×C7C2311yescharacteristic
101C7×#137—22no—
102C7×#137—22no—
103C7×#137—22no—
104C7×#137—41no—
105C7×#137—41no—
106C7×#137—41no—
107C2×C7×Q16—21no—
108C2×C7×Q16—21no—
109C2×C7×Q16—21no—
110C2×C7×SD16—21no—
111C2×C7×SD16—21no—
112C2×C7×SD16—21no—
113C2×C7×M16—21no—
114C2×C7×M16—22no—
115C2×C7×M16—41no—
116C2×C7×M16C2311yescharacteristic
117C2×C7×M16C2311yescharacteristic
118C2×C7×M16C2311yescharacteristic
119C2×C7×M16C2311yescharacteristic
120C22×C7×C8—21no—
121C7×C4⋊Q8—22no—
122C7×C4⋊Q8—21no—
123C7×C4⋊Q8—22no—
124C7×C4⋊Q8—41no—
125C7×#124—22no—
126C7×#124—21no—
127C7×#123—22no—
128C7×#123—22no—
129C7×#123—22no—
130C7×#123—21no—
131C7×#123—22no—
132C7×C22⋊Q8—22no—
133C7×C22⋊Q8—22no—
134C7×C22⋊Q8—22no—
135C7×C22⋊Q8—21no—
136C7×C22⋊Q8—21no—
137C7×C22⋊Q8—21no—
138C7×C22⋊Q8—21no—
139C7×C22⋊Q8—21no—
140C7×C22⋊Q8—21no—
141C7×C22⋊Q8—21no—
142C7×C22⋊Q8—21no—
143C7×C22⋊Q8—21no—
144C7×C22⋊Q8—21no—
145C7×C22⋊Q8—21no—
146C7×C22⋊Q8—21no—
147C7×C22⋊Q8D411yescharacteristic
148C7×C22⋊Q8D411yescharacteristic
149C7×#121—22no—
150C7×#121—22no—
151C7×#121—22no—
152C7×#121—21no—
153C7×#121—21no—
154C7×#121—22no—
155C7×#121D411yescharacteristic
156C7×#121D411yescharacteristic
157C7×#120—22no—
158C7×#120—21no—
159C4×C7×Q8—21no—
160C4×C7×D4—22no—
161C4×C7×D4—22no—
162C4×C7×D4—21no—
163C4×C7×D4—22no—
164C4×C7×D4—21no—
165C4×C7×D4—21no—
166C7×#117—21no—
167C7×#117—22no—
168C7×#117—41no—
169C7×#117C2311yescharacteristic
170C2×C7×C4⋊C4—22no—
171C2×C7×C4⋊C4—21no—
172C2×C7×C4⋊C4—21no—
173C2×C7×C4⋊C4—21no—
174C2×C7×C4⋊C4—22no—
175C2×C7×C4⋊C4D412yes—
176C2×C7×C4⋊C4C2311yescharacteristic
177C2×C7×C4⋊C4C2311yescharacteristic
178C2×C7×C22⋊C4—22no—
179C2×C7×C22⋊C4—21no—
180C2×C7×C22⋊C4—21no—
181C2×C7×C22⋊C4D412yes—
182C2×C42×C7C2311yescharacteristic
183C2×C42×C7C2311yescharacteristic
184C7×#107—21no—
185C7×#106—21no—
186C7×#104—22no—
187C7×#104—22no—
188C7×#104—22no—
189C7×#104—22no—
190C7×#104—41no—
191C7×#104D414yescomplemented
192C7×#103—21no—
193C7×#103—21no—
194C7×#103—21no—
195C7×#103—21no—
196C7×#103—21no—
197C7×#102—21no—
198C7×#102—21no—
199C7×#102—21no—
200C7×#101—22no—
201C7×#101—41no—
202C7×C22⋊C8—21no—
203C7×C22⋊C8—21no—
204C7×#95—22no—
205C7×#95—22no—
206C7×#95—22no—
207#3489C2×C711yescharacteristic
208#3056C2×C711yescharacteristic, complemented
209C2×#456C2×C711yescharacteristic, complemented
210#3007C2×C711yescharacteristic, complemented
211C2×#421C2×C711yescharacteristic, complemented
212#2621C2×C711yescharacteristic, complemented
213#2040C2×C711yescharacteristic, complemented
214#2038C2×C711yescharacteristic, complemented
215#2007C2×C711yescharacteristic, complemented
216#2005C2×C711yescharacteristic, complemented
217#1901C2×C711yescharacteristic, complemented
218#1897C2×C711yescharacteristic, complemented
219#1882C2×C711yescharacteristic, complemented
220#1860C2×C711yescharacteristic, complemented
221#1793C2×C711yescharacteristic, complemented
222C24×C7—21no—
223C24×C7C2×D411yescharacteristic
224C7×#41—21no—
225C7×#41—21no—
226C7×#41—22no—
227C7×#41—22no—
228C7×#41—21no—
229C7×#41—21no—
230C7×#41—21no—
231C7×#41—21no—
232C7×#41—21no—
233C7×#41—21no—
234C7×#41—21no—
235C7×#41—21no—
236C7×#41—42no—
237C7×#41—42no—
238C7×#41—41no—
239C7×#41—41no—
240C7×#41—42no—
241C7×#41—42no—
242C7×#41—42no—
243C7×#41—42no—
244C7×#41—44no—
245C7×#41—44no—
246C7×#41—42no—
247C7×#41—42no—
248C7×#41C2×D412yes—
249C7×#41#4112yes—
250C2×C7×Q8—22no—
251C2×C7×Q8—21no—
252C2×C7×Q8—21no—
253C2×C7×Q8—21no—
254C2×C7×Q8—21no—
255C2×C7×Q8—21no—
256C2×C7×Q8—21no—
257C2×C7×Q8—21no—
258C2×C7×Q8—22no—
259C2×C7×Q8—21no—
260C2×C7×Q8—21no—
261C2×C7×Q8—21no—
262C2×C7×Q8—21no—
263C2×C7×Q8—21no—
264C2×C7×Q8—21no—
265C2×C7×Q8—41no—
266C2×C7×Q8—42no—
267C2×C7×Q8—42no—
268C2×C7×Q8—42no—
269C2×C7×Q8—42no—
270C2×C7×Q8C2×D411yescharacteristic
271C2×C7×Q8C2×D411yescharacteristic
272C2×C7×Q8C2×D411yescharacteristic
273C2×C7×D4—21no—
274C2×C7×D4—22no—
275C2×C7×D4—22no—
276C2×C7×D4—21no—
277C2×C7×D4—21no—
278C2×C7×D4—21no—
279C2×C7×D4—21no—
280C2×C7×D4—21no—
281C2×C7×D4—22no—
282C2×C7×D4—21no—
283C2×C7×D4—21no—
284C2×C7×D4—41no—
285C2×C7×D4—42no—
286C2×C7×D4—42no—
287C2×C7×D4C2×D411yescharacteristic
288C2×C7×D4C2×D411yescharacteristic
289C2×C7×D4C2×D411yescharacteristic
290C22×C4×C7—21no—
291C22×C4×C7—21no—
292C22×C4×C7—21no—
293C22×C4×C7—21no—
294C22×C4×C7—21no—
295C22×C4×C7—22no—
296C22×C4×C7—22no—
297C22×C4×C7—21no—
298C22×C4×C7—21no—
299C22×C4×C7—22no—
300C22×C4×C7—21no—
301C22×C4×C7—21no—
302C22×C4×C7—21no—
303C22×C4×C7—21no—
304C22×C4×C7—21no—
305C22×C4×C7—21no—
306C22×C4×C7—21no—
307C22×C4×C7—42no—
308C22×C4×C7—42no—
309C22×C4×C7C2×D412yes—
310C22×C4×C7C2×D411yescharacteristic
311C22×C4×C7C2×D411yescharacteristic
312C22×C4×C7C2×D411yescharacteristic
313C22×C4×C7C2×D411yescharacteristic
314C22×C4×C7C2×D411yescharacteristic
315C22×C4×C7C2×D412yes—
316C22×C4×C7C2411yescharacteristic
317C7×Q16—42no—
318C7×Q16—42no—
319C7×Q16—42no—
320C7×SD16—42no—
321C7×SD16—42no—
322C7×SD16—42no—
323C7×M16—21no—
324C7×M16—21no—
325C7×M16—21no—
326C7×M16—21no—
327C7×M16—21no—
328C7×M16—21no—
329C7×M16—21no—
330C7×M16—42no—
331C7×M16C2×D412yes—
332C2×C7×C8—21no—
333C2×C7×C8—21no—
334C2×C7×C8—21no—
335C2×C7×C8—21no—
336C2×C7×C8—42no—
337C7×C4⋊C4—22no—
338C7×C4⋊C4—22no—
339C7×C4⋊C4—22no—
340C7×C4⋊C4—22no—
341C7×C4⋊C4—21no—
342C7×C4⋊C4—22no—
343C7×C4⋊C4—22no—
344C7×C4⋊C4—21no—
345C7×C4⋊C4—21no—
346C7×C4⋊C4—21no—
347C7×C4⋊C4—21no—
348C7×C4⋊C4—21no—
349C7×C4⋊C4—42no—
350C7×C4⋊C4—44no—
351C7×C4⋊C4—41no—
352C7×C4⋊C4—41no—
353C7×C4⋊C4C2×D411yescharacteristic
354C7×C4⋊C4C2×D411yescharacteristic
355C7×C22⋊C4—22no—
356C7×C22⋊C4—22no—
357C7×C22⋊C4—22no—
358C7×C22⋊C4—22no—
359C7×C22⋊C4—22no—
360C7×C22⋊C4—21no—
361C7×C22⋊C4—22no—
362C7×C22⋊C4—22no—
363C7×C22⋊C4—21no—
364C7×C22⋊C4—21no—
365C7×C22⋊C4—21no—
366C7×C22⋊C4—21no—
367C7×C22⋊C4—42no—
368C7×C22⋊C4—41no—
369C7×C22⋊C4—41no—
370C42×C7—22no—
371C42×C7—21no—
372C42×C7—21no—
373C42×C7—21no—
374C42×C7—21no—
375C42×C7C2×D412yes—
376C2×2−1+4C22×C711yescharacteristic
377C22×#41C22×C711yescharacteristic
378C2×#137C22×C711yescharacteristic
379C2×#137C22×C711yescharacteristic
380C2×#137C22×C711yescharacteristic, complemented
381C22×M16C22×C711yescharacteristic
382D4×Q8—21no—
383#548—21no—
384#547—21no—
385#547—22no—
386#546—21no—
387#546—22no—
388#537—21no—
389#537C22×C711yescharacteristic
390#536—21no—
391#536C22×C711yescharacteristic
392C2×C4⋊Q8C22×C711yescharacteristic, complemented
393#525—21no—
394#525C22×C711yescharacteristic
395C2×C22⋊Q8—21no—
396C2×C22⋊Q8C22×C711yescharacteristic
397C2×C22⋊Q8C22×C711yescharacteristic
398#520C22×C711yescharacteristic
399C2×#117C22×C711yescharacteristic
400#470—21no—
401#468—21no—
402#467—21no—
403#465—21no—
404#456—24no—
405#452—21no—
406#452—21no—
407#451—21no—
408#450—21no—
409#428C22×C711yescharacteristic, complemented
410#421—24no—
411C2×#104C22×C711yescharacteristic
412C2×#104C22×C711yescharacteristic
413C2×#104C22×C711yescharacteristic
414C2×#104C22×C711yescharacteristic
415C2×#104C22×C711yescharacteristic, complemented
416C2×#104C22×C711yescharacteristic, complemented
417#419C22×C711yescharacteristic, complemented
418#417C22×C711yescharacteristic
419#417C22×C711yescharacteristic
420#417C22×C711yescharacteristic, complemented
421C2×#101C22×C711yescharacteristic, complemented
422C2×#101C22×C711yescharacteristic, complemented
423#407C22×C711yescharacteristic
424#398—22no—
425#397—22no—
426#391C22×C711yescharacteristic, complemented
427#391C22×C711yescharacteristic, complemented
428#382C22×C711yescharacteristic, complemented
429#343C22×C711yescharacteristic, complemented
430#343C22×C711yescharacteristic, complemented
431#339C22×C711yescharacteristic, complemented
432#339C22×C711yescharacteristic, complemented
433C23×C7—21no—
434C23×C7—21no—
435C23×C7—21no—
436C23×C7—21no—
437C23×C7—21no—
438C23×C7—41no—
439C23×C7—41no—
440C23×C7—42no—
441C23×C7—42no—
442C23×C7—81no—
443C23×C7#12011yescharacteristic
444C23×C7#12011yescharacteristic
445C23×C7C22×D411yescharacteristic
446C7×Q8—21no—
447C7×Q8—21no—
448C7×Q8—21no—
449C7×Q8—21no—
450C7×Q8—21no—
451C7×Q8—42no—
452C7×Q8—44no—
453C7×Q8—41no—
454C7×Q8—41no—
455C7×Q8—41no—
456C7×Q8—41no—
457C7×Q8—41no—
458C7×Q8—41no—
459C7×Q8—41no—
460C7×Q8—41no—
461C7×Q8#12112yes—
462C7×D4—22no—
463C7×D4—22no—
464C7×D4—21no—
465C7×D4—21no—
466C7×D4—21no—
467C7×D4—21no—
468C7×D4—21no—
469C7×D4—42no—
470C7×D4—42no—
471C7×D4—42no—
472C7×D4—42no—
473C7×D4—44no—
474C7×D4—41no—
475C7×D4—41no—
476C7×D4—41no—
477C7×D4—41no—
478C7×D4—81no—
479C7×D4—82no—
480C7×D4#12112yes—
481C2×C4×C7—21no—
482C2×C4×C7—21no—
483C2×C4×C7—21no—
484C2×C4×C7—21no—
485C2×C4×C7—21no—
486C2×C4×C7—21no—
487C2×C4×C7—21no—
488C2×C4×C7—21no—
489C2×C4×C7—21no—
490C2×C4×C7—22no—
491C2×C4×C7—21no—
492C2×C4×C7—21no—
493C2×C4×C7—22no—
494C2×C4×C7—21no—
495C2×C4×C7—22no—
496C2×C4×C7—21no—
497C2×C4×C7—21no—
498C2×C4×C7—22no—
499C2×C4×C7—21no—
500C2×C4×C7—22no—
501C2×C4×C7—22no—
502C2×C4×C7—22no—
503C2×C4×C7—42no—
504C2×C4×C7—42no—
505C2×C4×C7—42no—
506C2×C4×C7—44no—
507C2×C4×C7—41no—
508C2×C4×C7—41no—
509C2×C4×C7—44no—
510C2×C4×C7—41no—
511C2×C4×C7—41no—
512C2×C4×C7—41no—
513C2×C4×C7—41no—
514C2×C4×C7—42no—
515C2×C4×C7—41no—
516C2×C4×C7—41no—
517C2×C4×C7—42no—
518C2×C4×C7—41no—
519C2×C4×C7—41no—
520C2×C4×C7—41no—
521C2×C4×C7—41no—
522C2×C4×C7—41no—
523C2×C4×C7—82no—
524C2×C4×C7#12011yescharacteristic
525C2×C4×C7#12011yescharacteristic
526C2×C4×C7C22×D411yescharacteristic
527C2×C4×C7C22×D411yescharacteristic
528C2×C4×C7C22×D411yescharacteristic
529C2×C4×C7C2×#4111yescharacteristic
530C2×C4×C7H(5,𝔽2)11yescharacteristic
531C2×C4×C7H(5,𝔽2)11yescharacteristic
532C7×C8—22no—
533C7×C8—41no—
534C7×C8—41no—
535C7×C8—41no—
5362−1+4—22no—
5372−1+4—22no—
5382−1+4—41no—
5392−1+4—41no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—22no—
544C2×#41—21no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—41no—
548C2×#41—41no—
549C2×#41C7×D411yescharacteristic
550C2×#41C7×D411yescharacteristic
551C2×#41C23×C711yescharacteristic
552C2×#41C23×C711yescharacteristic
553C2×#41C23×C711yescharacteristic
554C22×Q8—21no—
555C22×Q8—21no—
556C22×Q8C7×D411yescharacteristic
557C22×Q8C23×C711yescharacteristic
558C22×Q8C23×C711yescharacteristic
559C22×D4—21no—
560C22×D4C7×D411yescharacteristic
561C23×C4—21no—
562C23×C4C23×C711yescharacteristic
563#137—22no—
564#137—22no—
565#137—22no—
566#137—41no—
567#137—41no—
568#137—41no—
569C2×Q16—21no—
570C2×Q16—21no—
571C2×Q16—21no—
572C2×SD16—21no—
573C2×SD16—21no—
574C2×SD16—21no—
575C2×M16—21no—
576C2×M16—22no—
577C2×M16—41no—
578C2×M16C23×C711yescharacteristic
579C2×M16C23×C711yescharacteristic
580C2×M16C23×C711yescharacteristic
581C2×M16C23×C711yescharacteristic
582C22×C8—21no—
583C4⋊Q8—22no—
584C4⋊Q8—21no—
585C4⋊Q8—22no—
586C4⋊Q8—41no—
587#124—22no—
588#124—21no—
589#123—22no—
590#123—22no—
591#123—22no—
592#123—21no—
593#123—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8C7×D411yescharacteristic
610C22⋊Q8C7×D411yescharacteristic
611#121—22no—
612#121—22no—
613#121—22no—
614#121—21no—
615#121—21no—
616#121—22no—
617#121C7×D411yescharacteristic
618#121C7×D411yescharacteristic
619#120—22no—
620#120—21no—
621C4×Q8—21no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—21no—
625C4×D4—22no—
626C4×D4—21no—
627C4×D4—21no—
628#117—21no—
629#117—22no—
630#117—41no—
631#117C23×C711yescharacteristic
632C2×C4⋊C4—22no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4C7×D412yes—
638C2×C4⋊C4C23×C711yescharacteristic
639C2×C4⋊C4C23×C711yescharacteristic
640C2×C22⋊C4—22no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4C7×D412yes—
644C2×C42C23×C711yescharacteristic
645C2×C42C23×C711yescharacteristic
646#107—21no—
647#106—21no—
648#104—22no—
649#104—22no—
650#104—22no—
651#104—22no—
652#104—41no—
653#104C7×D414yescomplemented
654#103—21no—
655#103—21no—
656#103—21no—
657#103—21no—
658#103—21no—
659#102—21no—
660#102—21no—
661#102—21no—
662#101—22no—
663#101—41no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666#95—22no—
667#95—22no—
668#95—22no—
669C22×C7—21no—
670C22×C7—21no—
671C22×C7—21no—
672C22×C7—21no—
673C22×C7—22no—
674C22×C7—21no—
675C22×C7—21no—
676C22×C7—21no—
677C22×C7—21no—
678C22×C7—41no—
679C22×C7—41no—
680C22×C7—41no—
681C22×C7—41no—
682C22×C7—41no—
683C22×C7—41no—
684C22×C7—41no—
685C22×C7—41no—
686C22×C7—81no—
687C22×C7—81no—
688C22×C7—84no—
689C22×C7C2×#12011yescharacteristic
690C22×C7D4211yescharacteristic
691C22×C7#54611yescharacteristic
692C4×C7—21no—
693C4×C7—21no—
694C4×C7—22no—
695C4×C7—42no—
696C4×C7—42no—
697C4×C7—41no—
698C4×C7—41no—
699C4×C7—41no—
700C4×C7—42no—
701C4×C7—41no—
702C4×C7—81no—
703C4×C7—81no—
704C4×C7—81no—
705C4×C7C2×#12111yescharacteristic
706C4×C7#53411yescharacteristic
707C4×C7D4211yescharacteristic
708C4×C7#54611yescharacteristic
709C24—21no—
710C24C2×C7×D411yescharacteristic
711#41—21no—
712#41—21no—
713#41—22no—
714#41—22no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—42no—
724#41—42no—
725#41—41no—
726#41—41no—
727#41—42no—
728#41—42no—
729#41—42no—
730#41—42no—
731#41—44no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×C7×D412yes—
736#41C7×#4112yes—
737C2×Q8—22no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—22no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—42no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8C2×C7×D411yescharacteristic
758C2×Q8C2×C7×D411yescharacteristic
759C2×Q8C2×C7×D411yescharacteristic
760C2×D4—21no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—22no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—41no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4C2×C7×D411yescharacteristic
775C2×D4C2×C7×D411yescharacteristic
776C2×D4C2×C7×D411yescharacteristic
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4C2×C7×D412yes—
797C22×C4C2×C7×D411yescharacteristic
798C22×C4C2×C7×D411yescharacteristic
799C22×C4C2×C7×D411yescharacteristic
800C22×C4C2×C7×D411yescharacteristic
801C22×C4C2×C7×D411yescharacteristic
802C22×C4C2×C7×D412yes—
803C22×C4C24×C711yescharacteristic
804Q16—42no—
805Q16—42no—
806Q16—42no—
807SD16—42no—
808SD16—42no—
809SD16—42no—
810M16—21no—
811M16—21no—
812M16—21no—
813M16—21no—
814M16—21no—
815M16—21no—
816M16—21no—
817M16—42no—
818M16C2×C7×D412yes—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—42no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—21no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—42no—
837C4⋊C4—44no—
838C4⋊C4—41no—
839C4⋊C4—41no—
840C4⋊C4C2×C7×D411yescharacteristic
841C4⋊C4C2×C7×D411yescharacteristic
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—22no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—21no—
848C22⋊C4—22no—
849C22⋊C4—22no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—42no—
855C22⋊C4—41no—
856C22⋊C4—41no—
857C42—22no—
858C42—21no—
859C42—21no—
860C42—21no—
861C42—21no—
862C42C2×C7×D412yes—
863C2×C7—21no—
864C2×C7—21no—
865C2×C7—41no—
866C2×C7—41no—
867C2×C7—42no—
868C2×C7—81no—
869C2×C7—81no—
870C2×C7#241011yescharacteristic
871C2×C7#302011yescharacteristic
872C2×C7#302211yescharacteristic
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—41no—
879C23—41no—
880C23—42no—
881C23—42no—
882C23—81no—
883C23C7×#12011yescharacteristic
884C23C7×#12011yescharacteristic
885C23C22×C7×D411yescharacteristic
886Q8—21no—
887Q8—21no—
888Q8—21no—
889Q8—21no—
890Q8—21no—
891Q8—42no—
892Q8—44no—
893Q8—41no—
894Q8—41no—
895Q8—41no—
896Q8—41no—
897Q8—41no—
898Q8—41no—
899Q8—41no—
900Q8—41no—
901Q8C7×#12112yes—
902D4—22no—
903D4—22no—
904D4—21no—
905D4—21no—
906D4—21no—
907D4—21no—
908D4—21no—
909D4—42no—
910D4—42no—
911D4—42no—
912D4—42no—
913D4—44no—
914D4—41no—
915D4—41no—
916D4—41no—
917D4—41no—
918D4—81no—
919D4—82no—
920D4C7×#12112yes—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—44no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—44no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—82no—
964C2×C4C7×#12011yescharacteristic
965C2×C4C7×#12011yescharacteristic
966C2×C4C22×C7×D411yescharacteristic
967C2×C4C22×C7×D411yescharacteristic
968C2×C4C22×C7×D411yescharacteristic
969C2×C4C2×C7×#4111yescharacteristic
970C2×C4C7×H(5,𝔽2)11yescharacteristic
971C2×C4C7×H(5,𝔽2)11yescharacteristic
972C8—22no—
973C8—41no—
974C8—41no—
975C8—41no—
976C7#2447011yescharacteristic, direct product factor, Sylow
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—22no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—81no—
995C22—81no—
996C22—84no—
997C22C2×C7×#12011yescharacteristic
998C22C7×D4211yescharacteristic
999C22C7×#54611yescharacteristic
1000C4—21no—
1001C4—21no—
1002C4—22no—
1003C4—42no—
1004C4—42no—
1005C4—41no—
1006C4—41no—
1007C4—41no—
1008C4—42no—
1009C4—41no—
1010C4—81no—
1011C4—81no—
1012C4—81no—
1013C4C2×C7×#12111yescharacteristic
1014C4C7×#53411yescharacteristic
1015C4C7×D4211yescharacteristic
1016C4C7×#54611yescharacteristic
1017C2—21no—
1018C2—21no—
1019C2—41no—
1020C2—41no—
1021C2—42no—
1022C2—81no—
1023C2—81no—
1024C2C7×#241011yescharacteristic
1025C2C7×#302011yescharacteristic
1026C2C7×#302211yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#3056C2semidirect
3. C2×C7×#456C2semidirect
4. C7×#3007C2semidirect
5. C2×C7×#421C2semidirect
6. C7×#2621C2semidirect
7. C7×#2040C2semidirect
8. C7×#2038C2semidirect
9. C7×#2007C2semidirect
10. C7×#2005C2semidirect
11. C7×#1901C2semidirect
12. C7×#1897C2semidirect
13. C7×#1882C2semidirect
14. C7×#1860C2semidirect
15. C7×#1793C2semidirect
20. C2×C7×#137C22semidirect
32. C2×C7×C4⋊Q8C22semidirect
49. C7×#428C22semidirect
55. C2×C7×#104C22semidirect
56. C2×C7×#104C22semidirect
57. C7×#419C22semidirect
60. C7×#417C22semidirect
61. C2×C7×#101C22semidirect
62. C2×C7×#101C22semidirect
66. C7×#391C22semidirect
67. C7×#391C22semidirect
68. C7×#382C22semidirect
69. C7×#343C22semidirect
70. C7×#343C22semidirect
71. C7×#339C22semidirect
72. C7×#339C22semidirect
73. #24470C7direct (N × H)
191. C7×#104D4semidirect
208. #3056C2×C7semidirect
209. C2×#456C2×C7semidirect
210. #3007C2×C7semidirect
211. C2×#421C2×C7semidirect
212. #2621C2×C7semidirect
213. #2040C2×C7semidirect
214. #2038C2×C7semidirect
215. #2007C2×C7semidirect
216. #2005C2×C7semidirect
217. #1901C2×C7semidirect
218. #1897C2×C7semidirect
219. #1882C2×C7semidirect
220. #1860C2×C7semidirect
221. #1793C2×C7semidirect
380. C2×#137C22×C7semidirect
392. C2×C4⋊Q8C22×C7semidirect
409. #428C22×C7semidirect
415. C2×#104C22×C7semidirect
416. C2×#104C22×C7semidirect
417. #419C22×C7semidirect
420. #417C22×C7semidirect
421. C2×#101C22×C7semidirect
422. C2×#101C22×C7semidirect
426. #391C22×C7semidirect
427. #391C22×C7semidirect
428. #382C22×C7semidirect
429. #343C22×C7semidirect
430. #343C22×C7semidirect
431. #339C22×C7semidirect
432. #339C22×C7semidirect
653. #104C7×D4semidirect
976. C7#24470direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34892
C7×#30562
C2×C7×#4562
C7×#30072
C2×C7×#4212
C7×#26212
C7×#20402
C7×#20382
C7×#20072
C7×#20052
C7×#19012
C7×#18972
C7×#18822
C7×#18602
C7×#17932
#244707