Finite Group Databasebeta

← C7×#24466 #13201682

Subgroups — C7×#24466 #13201682

Order 1792.

1418 conjugacy classes of subgroups.

The subgroup lattice has 1036 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
5C22×C7×#104C211yesmaximal, characteristic, complemented
6C7×#2857C211yesmaximal, characteristic, complemented
7C7×#2039C211yesmaximal, characteristic, complemented
8C7×#2038C211yesmaximal, characteristic, complemented
9C7×#2007C211yesmaximal, characteristic, complemented
10C7×#2005C211yesmaximal, characteristic, complemented
11C7×#1901C211yesmaximal, characteristic, complemented
12C7×#1896C211yesmaximal, characteristic, complemented
13C7×#1882C211yesmaximal, characteristic, complemented
14C7×#1859C211yesmaximal, 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
39C22×C42×C7C2211yescharacteristic
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
50C2×C7×#104—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×#391C2211yescharacteristic, complemented
65C7×#391C2211yescharacteristic, complemented
66C7×#389—22no—
67C7×#384C2211yescharacteristic, complemented
68C7×#380—22no—
69C7×#343C2211yescharacteristic, complemented
70C7×#343C2211yescharacteristic, complemented
71C7×#339C2211yescharacteristic, complemented
72C7×#339C2211yescharacteristic, complemented
73#24466C711yesmaximal, 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×C7—21no—
101C23×C4×C7C2311yescharacteristic
102C7×#137—22no—
103C7×#137—22no—
104C7×#137—22no—
105C7×#137—41no—
106C7×#137—41no—
107C7×#137—41no—
108C2×C7×Q16—21no—
109C2×C7×Q16—21no—
110C2×C7×Q16—21no—
111C2×C7×SD16—21no—
112C2×C7×SD16—21no—
113C2×C7×SD16—21no—
114C2×C7×M16—21no—
115C2×C7×M16—22no—
116C2×C7×M16—41no—
117C2×C7×M16C2311yescharacteristic
118C2×C7×M16C2311yescharacteristic
119C2×C7×M16C2311yescharacteristic
120C2×C7×M16C2311yescharacteristic
121C22×C7×C8—21no—
122C7×C4⋊Q8—22no—
123C7×C4⋊Q8—21no—
124C7×C4⋊Q8—22no—
125C7×C4⋊Q8—41no—
126C7×#124—22no—
127C7×#124—21no—
128C7×#123—22no—
129C7×#123—22no—
130C7×#123—22no—
131C7×#123—21no—
132C7×#123—22no—
133C7×C22⋊Q8—22no—
134C7×C22⋊Q8—22no—
135C7×C22⋊Q8—22no—
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⋊Q8—21no—
148C7×C22⋊Q8D411yescharacteristic
149C7×C22⋊Q8D411yescharacteristic
150C7×#121—22no—
151C7×#121—22no—
152C7×#121—22no—
153C7×#121—21no—
154C7×#121—21no—
155C7×#121—22no—
156C7×#121D411yescharacteristic
157C7×#121D411yescharacteristic
158C7×#120—22no—
159C7×#120—21no—
160C4×C7×Q8—21no—
161C4×C7×D4—22no—
162C4×C7×D4—22no—
163C4×C7×D4—21no—
164C4×C7×D4—22no—
165C4×C7×D4—21no—
166C4×C7×D4—21no—
167C7×#117—21no—
168C7×#117C2311yescharacteristic
169C2×C7×C4⋊C4—22no—
170C2×C7×C4⋊C4—21no—
171C2×C7×C4⋊C4—22no—
172C2×C7×C4⋊C4—22no—
173C2×C7×C4⋊C4—21no—
174C2×C7×C4⋊C4D412yes—
175C2×C7×C4⋊C4C2311yescharacteristic
176C2×C7×C4⋊C4C2311yescharacteristic
177C2×C7×C22⋊C4—22no—
178C2×C7×C22⋊C4—21no—
179C2×C7×C22⋊C4D412yes—
180C2×C42×C7—22no—
181C2×C42×C7—21no—
182C2×C42×C7—41no—
183C2×C42×C7C2311yescharacteristic
184C2×C42×C7C2311yescharacteristic
185C7×#107—21no—
186C7×#106—21no—
187C7×#104—22no—
188C7×#104—22no—
189C7×#104—22no—
190C7×#104—22no—
191C7×#104—41no—
192C7×#104D414yescomplemented
193C7×#103—21no—
194C7×#103—21no—
195C7×#103—21no—
196C7×#103—21no—
197C7×#103—21no—
198C7×#102—21no—
199C7×#102—21no—
200C7×#102—21no—
201C7×#101—22no—
202C7×#101—41no—
203C7×C22⋊C8—21no—
204C7×C22⋊C8—21no—
205C7×#95—22no—
206C7×#95—22no—
207#3489C2×C711yescharacteristic
208#3056C2×C711yescharacteristic, complemented
209C2×#456C2×C711yescharacteristic, complemented
210#3007C2×C711yescharacteristic, complemented
211C22×#104C2×C711yescharacteristic, complemented
212#2857C2×C711yescharacteristic, complemented
213#2039C2×C711yescharacteristic, complemented
214#2038C2×C711yescharacteristic, complemented
215#2007C2×C711yescharacteristic, complemented
216#2005C2×C711yescharacteristic, complemented
217#1901C2×C711yescharacteristic, complemented
218#1896C2×C711yescharacteristic, complemented
219#1882C2×C711yescharacteristic, complemented
220#1859C2×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—21no—
296C22×C4×C7—22no—
297C22×C4×C7—22no—
298C22×C4×C7—24no—
299C22×C4×C7—21no—
300C22×C4×C7—21no—
301C22×C4×C7—22no—
302C22×C4×C7—21no—
303C22×C4×C7—21no—
304C22×C4×C7—21no—
305C22×C4×C7—21no—
306C22×C4×C7—21no—
307C22×C4×C7—21no—
308C22×C4×C7—42no—
309C22×C4×C7—42no—
310C22×C4×C7—42no—
311C22×C4×C7—42no—
312C22×C4×C7C2×D412yes—
313C22×C4×C7C2×D411yescharacteristic
314C22×C4×C7C2×D411yescharacteristic
315C22×C4×C7C2×D411yescharacteristic
316C22×C4×C7C2×D411yescharacteristic
317C22×C4×C7C2×D411yescharacteristic
318C22×C4×C7C2×D412yes—
319C22×C4×C7C2411yescharacteristic
320C7×Q16—42no—
321C7×Q16—42no—
322C7×Q16—42no—
323C7×SD16—42no—
324C7×SD16—42no—
325C7×SD16—42no—
326C7×M16—21no—
327C7×M16—21no—
328C7×M16—21no—
329C7×M16—21no—
330C7×M16—21no—
331C7×M16—21no—
332C7×M16—21no—
333C7×M16—42no—
334C7×M16C2×D412yes—
335C2×C7×C8—21no—
336C2×C7×C8—21no—
337C2×C7×C8—21no—
338C2×C7×C8—21no—
339C2×C7×C8—42no—
340C7×C4⋊C4—22no—
341C7×C4⋊C4—22no—
342C7×C4⋊C4—22no—
343C7×C4⋊C4—22no—
344C7×C4⋊C4—21no—
345C7×C4⋊C4—22no—
346C7×C4⋊C4—22no—
347C7×C4⋊C4—21no—
348C7×C4⋊C4—21no—
349C7×C4⋊C4—21no—
350C7×C4⋊C4—21no—
351C7×C4⋊C4—21no—
352C7×C4⋊C4—44no—
353C7×C4⋊C4—44no—
354C7×C4⋊C4—41no—
355C7×C4⋊C4—41no—
356C7×C4⋊C4C2×D411yescharacteristic
357C7×C4⋊C4C2×D411yescharacteristic
358C7×C22⋊C4—22no—
359C7×C22⋊C4—22no—
360C7×C22⋊C4—22no—
361C7×C22⋊C4—22no—
362C7×C22⋊C4—22no—
363C7×C22⋊C4—21no—
364C7×C22⋊C4—22no—
365C7×C22⋊C4—22no—
366C7×C22⋊C4—21no—
367C7×C22⋊C4—21no—
368C7×C22⋊C4—21no—
369C7×C22⋊C4—21no—
370C7×C22⋊C4—41no—
371C7×C22⋊C4—41no—
372C42×C7—22no—
373C42×C7—21no—
374C42×C7—21no—
375C42×C7—21no—
376C42×C7—21no—
377C42×C7—42no—
378C42×C7C2×D412yes—
379C2×2−1+4C22×C711yescharacteristic
380C22×#41C22×C711yescharacteristic
381C2×#137C22×C711yescharacteristic
382C2×#137C22×C711yescharacteristic
383C2×#137C22×C711yescharacteristic, complemented
384C22×M16C22×C711yescharacteristic
385D4×Q8—21no—
386#548—21no—
387#547—21no—
388#547—22no—
389#546—21no—
390#546—22no—
391#537—21no—
392#537C22×C711yescharacteristic
393#536—21no—
394#536C22×C711yescharacteristic
395C2×C4⋊Q8C22×C711yescharacteristic, complemented
396#525—21no—
397#525C22×C711yescharacteristic
398C2×C22⋊Q8—21no—
399C2×C22⋊Q8C22×C711yescharacteristic
400C2×C22⋊Q8C22×C711yescharacteristic
401#520C22×C711yescharacteristic
402C22×C42C22×C711yescharacteristic
403#470—21no—
404#468—21no—
405#467—21no—
406#465—21no—
407#456—24no—
408#452—21no—
409#452—21no—
410#451—21no—
411#450—21no—
412#428C22×C711yescharacteristic, complemented
413C2×#104—24no—
414C2×#104C22×C711yescharacteristic
415C2×#104C22×C711yescharacteristic
416C2×#104C22×C711yescharacteristic
417C2×#104C22×C711yescharacteristic
418C2×#104C22×C711yescharacteristic, complemented
419C2×#104C22×C711yescharacteristic, complemented
420#419C22×C711yescharacteristic, complemented
421#417C22×C711yescharacteristic
422#417C22×C711yescharacteristic
423#417C22×C711yescharacteristic, complemented
424C2×#101C22×C711yescharacteristic, complemented
425C2×#101C22×C711yescharacteristic, complemented
426#407C22×C711yescharacteristic
427#391C22×C711yescharacteristic, complemented
428#391C22×C711yescharacteristic, complemented
429#389—22no—
430#384C22×C711yescharacteristic, complemented
431#380—22no—
432#343C22×C711yescharacteristic, complemented
433#343C22×C711yescharacteristic, complemented
434#339C22×C711yescharacteristic, complemented
435#339C22×C711yescharacteristic, complemented
436C23×C7—21no—
437C23×C7—21no—
438C23×C7—21no—
439C23×C7—22no—
440C23×C7—21no—
441C23×C7—21no—
442C23×C7—41no—
443C23×C7—42no—
444C23×C7—42no—
445C23×C7—81no—
446C23×C7#12011yescharacteristic
447C23×C7#12011yescharacteristic
448C23×C7C22×D411yescharacteristic
449C7×Q8—21no—
450C7×Q8—21no—
451C7×Q8—21no—
452C7×Q8—21no—
453C7×Q8—21no—
454C7×Q8—42no—
455C7×Q8—44no—
456C7×Q8—41no—
457C7×Q8—41no—
458C7×Q8—41no—
459C7×Q8—41no—
460C7×Q8—41no—
461C7×Q8—41no—
462C7×Q8—41no—
463C7×Q8—41no—
464C7×Q8#12112yes—
465C7×D4—22no—
466C7×D4—22no—
467C7×D4—21no—
468C7×D4—21no—
469C7×D4—21no—
470C7×D4—21no—
471C7×D4—21no—
472C7×D4—42no—
473C7×D4—42no—
474C7×D4—42no—
475C7×D4—44no—
476C7×D4—41no—
477C7×D4—41no—
478C7×D4—41no—
479C7×D4—41no—
480C7×D4—42no—
481C7×D4—81no—
482C7×D4—82no—
483C7×D4#12112yes—
484C2×C4×C7—22no—
485C2×C4×C7—22no—
486C2×C4×C7—21no—
487C2×C4×C7—22no—
488C2×C4×C7—21no—
489C2×C4×C7—21no—
490C2×C4×C7—21no—
491C2×C4×C7—21no—
492C2×C4×C7—21no—
493C2×C4×C7—21no—
494C2×C4×C7—21no—
495C2×C4×C7—21no—
496C2×C4×C7—22no—
497C2×C4×C7—21no—
498C2×C4×C7—21no—
499C2×C4×C7—22no—
500C2×C4×C7—22no—
501C2×C4×C7—21no—
502C2×C4×C7—22no—
503C2×C4×C7—21no—
504C2×C4×C7—21no—
505C2×C4×C7—22no—
506C2×C4×C7—21no—
507C2×C4×C7—22no—
508C2×C4×C7—22no—
509C2×C4×C7—42no—
510C2×C4×C7—42no—
511C2×C4×C7—42no—
512C2×C4×C7—48no—
513C2×C4×C7—44no—
514C2×C4×C7—41no—
515C2×C4×C7—44no—
516C2×C4×C7—41no—
517C2×C4×C7—41no—
518C2×C4×C7—41no—
519C2×C4×C7—41no—
520C2×C4×C7—41no—
521C2×C4×C7—42no—
522C2×C4×C7—42no—
523C2×C4×C7—41no—
524C2×C4×C7—41no—
525C2×C4×C7—41no—
526C2×C4×C7—41no—
527C2×C4×C7—82no—
528C2×C4×C7#12011yescharacteristic
529C2×C4×C7#12011yescharacteristic
530C2×C4×C7C22×D411yescharacteristic
531C2×C4×C7C22×D411yescharacteristic
532C2×C4×C7C22×D411yescharacteristic
533C2×C4×C7C2×#4111yescharacteristic
534C2×C4×C7H(5,𝔽2)11yescharacteristic
535C2×C4×C7H(5,𝔽2)11yescharacteristic
536C7×C8—22no—
537C7×C8—41no—
538C7×C8—41no—
539C7×C8—41no—
5402−1+4—22no—
5412−1+4—22no—
5422−1+4—41no—
5432−1+4—41no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—22no—
548C2×#41—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41C7×D411yescharacteristic
554C2×#41C7×D411yescharacteristic
555C2×#41C23×C711yescharacteristic
556C2×#41C23×C711yescharacteristic
557C2×#41C23×C711yescharacteristic
558C22×Q8—21no—
559C22×Q8—21no—
560C22×Q8C7×D411yescharacteristic
561C22×Q8C23×C711yescharacteristic
562C22×Q8C23×C711yescharacteristic
563C22×D4—21no—
564C22×D4C7×D411yescharacteristic
565C23×C4—21no—
566C23×C4—21no—
567C23×C4C23×C711yescharacteristic
568#137—22no—
569#137—22no—
570#137—22no—
571#137—41no—
572#137—41no—
573#137—41no—
574C2×Q16—21no—
575C2×Q16—21no—
576C2×Q16—21no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×M16—21no—
581C2×M16—22no—
582C2×M16—41no—
583C2×M16C23×C711yescharacteristic
584C2×M16C23×C711yescharacteristic
585C2×M16C23×C711yescharacteristic
586C2×M16C23×C711yescharacteristic
587C22×C8—21no—
588C4⋊Q8—22no—
589C4⋊Q8—21no—
590C4⋊Q8—22no—
591C4⋊Q8—41no—
592#124—22no—
593#124—21no—
594#123—22no—
595#123—22no—
596#123—22no—
597#123—21no—
598#123—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C7×D411yescharacteristic
615C22⋊Q8C7×D411yescharacteristic
616#121—22no—
617#121—22no—
618#121—22no—
619#121—21no—
620#121—21no—
621#121—22no—
622#121C7×D411yescharacteristic
623#121C7×D411yescharacteristic
624#120—22no—
625#120—21no—
626C4×Q8—21no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—21no—
630C4×D4—22no—
631C4×D4—21no—
632C4×D4—21no—
633#117—21no—
634#117C23×C711yescharacteristic
635C2×C4⋊C4—22no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4C7×D412yes—
641C2×C4⋊C4C23×C711yescharacteristic
642C2×C4⋊C4C23×C711yescharacteristic
643C2×C22⋊C4—22no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4C7×D412yes—
646C2×C42—22no—
647C2×C42—21no—
648C2×C42—41no—
649C2×C42C23×C711yescharacteristic
650C2×C42C23×C711yescharacteristic
651#107—21no—
652#106—21no—
653#104—22no—
654#104—22no—
655#104—22no—
656#104—22no—
657#104—41no—
658#104C7×D414yescomplemented
659#103—21no—
660#103—21no—
661#103—21no—
662#103—21no—
663#103—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667#101—22no—
668#101—41no—
669C22⋊C8—21no—
670C22⋊C8—21no—
671#95—22no—
672#95—22no—
673C22×C7—21no—
674C22×C7—21no—
675C22×C7—21no—
676C22×C7—21no—
677C22×C7—21no—
678C22×C7—22no—
679C22×C7—21no—
680C22×C7—21no—
681C22×C7—42no—
682C22×C7—42no—
683C22×C7—41no—
684C22×C7—41no—
685C22×C7—41no—
686C22×C7—41no—
687C22×C7—41no—
688C22×C7—41no—
689C22×C7—41no—
690C22×C7—41no—
691C22×C7—84no—
692C22×C7#45612yescomplemented
693C22×C7C2×#12011yescharacteristic
694C22×C7D4211yescharacteristic
695C22×C7#54611yescharacteristic
696C4×C7—24no—
697C4×C7—21no—
698C4×C7—21no—
699C4×C7—22no—
700C4×C7—42no—
701C4×C7—42no—
702C4×C7—41no—
703C4×C7—41no—
704C4×C7—41no—
705C4×C7—42no—
706C4×C7—41no—
707C4×C7—81no—
708C4×C7—81no—
709C4×C7C2×#12111yescharacteristic
710C4×C7#53411yescharacteristic
711C4×C7D4211yescharacteristic
712C4×C7#54611yescharacteristic
713C24—21no—
714C24C2×C7×D411yescharacteristic
715#41—21no—
716#41—21no—
717#41—22no—
718#41—22no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—21no—
724#41—21no—
725#41—21no—
726#41—21no—
727#41—42no—
728#41—42no—
729#41—41no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—42no—
734#41—42no—
735#41—44no—
736#41—44no—
737#41—42no—
738#41—42no—
739#41C2×C7×D412yes—
740#41C7×#4112yes—
741C2×Q8—22no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—22no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—41no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8C2×C7×D411yescharacteristic
762C2×Q8C2×C7×D411yescharacteristic
763C2×Q8C2×C7×D411yescharacteristic
764C2×D4—21no—
765C2×D4—22no—
766C2×D4—22no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—41no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4C2×C7×D411yescharacteristic
779C2×D4C2×C7×D411yescharacteristic
780C2×D4C2×C7×D411yescharacteristic
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—24no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4C2×C7×D412yes—
804C22×C4C2×C7×D411yescharacteristic
805C22×C4C2×C7×D411yescharacteristic
806C22×C4C2×C7×D411yescharacteristic
807C22×C4C2×C7×D411yescharacteristic
808C22×C4C2×C7×D411yescharacteristic
809C22×C4C2×C7×D412yes—
810C22×C4C24×C711yescharacteristic
811Q16—42no—
812Q16—42no—
813Q16—42no—
814SD16—42no—
815SD16—42no—
816SD16—42no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16—21no—
821M16—21no—
822M16—21no—
823M16—21no—
824M16—42no—
825M16C2×C7×D412yes—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—42no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—21no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—41no—
846C4⋊C4—41no—
847C4⋊C4C2×C7×D411yescharacteristic
848C4⋊C4C2×C7×D411yescharacteristic
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—22no—
852C22⋊C4—22no—
853C22⋊C4—22no—
854C22⋊C4—21no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—21no—
858C22⋊C4—21no—
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—41no—
862C22⋊C4—41no—
863C42—22no—
864C42—21no—
865C42—21no—
866C42—21no—
867C42—21no—
868C42—42no—
869C42C2×C7×D412yes—
870C2×C7—21no—
871C2×C7—22no—
872C2×C7—21no—
873C2×C7—41no—
874C2×C7—42no—
875C2×C7—81no—
876C2×C7—81no—
877C2×C7#241011yescharacteristic
878C2×C7C2×#45611yescharacteristic
879C2×C7#301811yescharacteristic
880C23—21no—
881C23—21no—
882C23—21no—
883C23—22no—
884C23—21no—
885C23—21no—
886C23—41no—
887C23—42no—
888C23—42no—
889C23—81no—
890C23C7×#12011yescharacteristic
891C23C7×#12011yescharacteristic
892C23C22×C7×D411yescharacteristic
893Q8—21no—
894Q8—21no—
895Q8—21no—
896Q8—21no—
897Q8—21no—
898Q8—42no—
899Q8—44no—
900Q8—41no—
901Q8—41no—
902Q8—41no—
903Q8—41no—
904Q8—41no—
905Q8—41no—
906Q8—41no—
907Q8—41no—
908Q8C7×#12112yes—
909D4—22no—
910D4—22no—
911D4—21no—
912D4—21no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—44no—
920D4—41no—
921D4—41no—
922D4—41no—
923D4—41no—
924D4—42no—
925D4—81no—
926D4—82no—
927D4C7×#12112yes—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—48no—
957C2×C4—44no—
958C2×C4—41no—
959C2×C4—44no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—82no—
972C2×C4C7×#12011yescharacteristic
973C2×C4C7×#12011yescharacteristic
974C2×C4C22×C7×D411yescharacteristic
975C2×C4C22×C7×D411yescharacteristic
976C2×C4C22×C7×D411yescharacteristic
977C2×C4C2×C7×#4111yescharacteristic
978C2×C4C7×H(5,𝔽2)11yescharacteristic
979C2×C4C7×H(5,𝔽2)11yescharacteristic
980C8—22no—
981C8—41no—
982C8—41no—
983C8—41no—
984C7#2446611yescharacteristic, direct product factor, Sylow
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—22no—
991C22—21no—
992C22—21no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—84no—
1004C22C7×#45612yescomplemented
1005C22C2×C7×#12011yescharacteristic
1006C22C7×D4211yescharacteristic
1007C22C7×#54611yescharacteristic
1008C4—24no—
1009C4—21no—
1010C4—21no—
1011C4—22no—
1012C4—42no—
1013C4—42no—
1014C4—41no—
1015C4—41no—
1016C4—41no—
1017C4—42no—
1018C4—41no—
1019C4—81no—
1020C4—81no—
1021C4C2×C7×#12111yescharacteristic
1022C4C7×#53411yescharacteristic
1023C4C7×D4211yescharacteristic
1024C4C7×#54611yescharacteristic
1025C2—21no—
1026C2—22no—
1027C2—21no—
1028C2—41no—
1029C2—42no—
1030C2—81no—
1031C2—81no—
1032C2C7×#241011yescharacteristic
1033C2C2×C7×#45611yescharacteristic
1034C2C7×#301811yescharacteristic
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. C22×C7×#104C2semidirect
6. C7×#2857C2semidirect
7. C7×#2039C2semidirect
8. C7×#2038C2semidirect
9. C7×#2007C2semidirect
10. C7×#2005C2semidirect
11. C7×#1901C2semidirect
12. C7×#1896C2semidirect
13. C7×#1882C2semidirect
14. C7×#1859C2semidirect
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
64. C7×#391C22semidirect
65. C7×#391C22semidirect
67. C7×#384C22semidirect
69. C7×#343C22semidirect
70. C7×#343C22semidirect
71. C7×#339C22semidirect
72. C7×#339C22semidirect
73. #24466C7direct (N × H)
192. C7×#104D4semidirect
208. #3056C2×C7semidirect
209. C2×#456C2×C7semidirect
210. #3007C2×C7semidirect
211. C22×#104C2×C7semidirect
212. #2857C2×C7semidirect
213. #2039C2×C7semidirect
214. #2038C2×C7semidirect
215. #2007C2×C7semidirect
216. #2005C2×C7semidirect
217. #1901C2×C7semidirect
218. #1896C2×C7semidirect
219. #1882C2×C7semidirect
220. #1859C2×C7semidirect
221. #1793C2×C7semidirect
383. C2×#137C22×C7semidirect
395. C2×C4⋊Q8C22×C7semidirect
412. #428C22×C7semidirect
418. C2×#104C22×C7semidirect
419. C2×#104C22×C7semidirect
420. #419C22×C7semidirect
423. #417C22×C7semidirect
424. C2×#101C22×C7semidirect
425. C2×#101C22×C7semidirect
427. #391C22×C7semidirect
428. #391C22×C7semidirect
430. #384C22×C7semidirect
432. #343C22×C7semidirect
433. #343C22×C7semidirect
434. #339C22×C7semidirect
435. #339C22×C7semidirect
658. #104C7×D4semidirect
692. C22×C7#456semidirect
984. C7#24466direct (N × H)
1004. C22C7×#456semidirect

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
C22×C7×#1042
C7×#28572
C7×#20392
C7×#20382
C7×#20072
C7×#20052
C7×#19012
C7×#18962
C7×#18822
C7×#18592
C7×#17932
#244667