Finite Group Databasebeta

← C7×#24464 #13201680

Subgroups — C7×#24464 #13201680

Order 1792.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3488C211yesmaximal, characteristic, complemented
2C7×#3055C211yesmaximal, characteristic, complemented
3C2×C7×#453C211yesmaximal, characteristic, complemented
4C7×#3006C211yesmaximal, characteristic, complemented
5C22×C7×#104C211yesmaximal, characteristic, complemented
6C7×#2856C211yesmaximal, characteristic, complemented
7C7×#2039C211yesmaximal, characteristic, complemented
8C7×#2037C211yesmaximal, characteristic, complemented
9C7×#2006C211yesmaximal, characteristic, complemented
10C7×#2002C211yesmaximal, characteristic, complemented
11C7×#1900C211yesmaximal, characteristic, complemented
12C7×#1896C211yesmaximal, characteristic, complemented
13C7×#1883C211yesmaximal, characteristic, complemented
14C7×#1859C211yesmaximal, characteristic, complemented
15C7×#1792C211yesmaximal, characteristic, complemented
16C2×C7×H(5,𝔽2)C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C7×AGL(1,ℤ/8)C2211yescharacteristic, complemented
20C2×C7×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×C7×M16C2211yescharacteristic, complemented
22C7×#550—21no—
23C7×#548—21no—
24C7×#546—21no—
25C7×#546—22no—
26C7×D42—22no—
27C7×D42—21no—
28C7×#537—21no—
29C7×#537C2211yescharacteristic
30C7×#535—21no—
31C7×#535C2211yescharacteristic
32C2×C7×#127C2211yescharacteristic, complemented
33C7×#525—21no—
34C7×#525C2211yescharacteristic
35C2×C7×#121—21no—
36C2×C7×#121—22no—
37C2×C7×#121C2211yescharacteristic
38C2×C7×#121C2211yescharacteristic, complemented
39C7×#520C2211yescharacteristic
40C22×C42×C7C2211yescharacteristic, complemented
41C7×#469—21no—
42C7×#468—21no—
43C7×#466—21no—
44C7×#465—21no—
45C7×#453—24no—
46C7×#449—21no—
47C7×#449—21no—
48C7×#448—21no—
49C7×#447—21no—
50C7×#428C2211yescharacteristic, complemented
51C2×C7×#104—24no—
52C2×C7×#104C2211yescharacteristic
53C2×C7×#104C2211yescharacteristic
54C2×C7×#104C2211yescharacteristic, complemented
55C2×C7×#104C2211yescharacteristic, complemented
56C2×C7×#104C2211yescharacteristic, complemented
57C2×C7×#104C2211yescharacteristic, complemented
58C7×#418C2211yescharacteristic, complemented
59C7×#417C2211yescharacteristic
60C7×#417C2211yescharacteristic, complemented
61C7×#417C2211yescharacteristic, complemented
62C2×C7×#100C2211yescharacteristic, complemented
63C2×C7×#100C2211yescharacteristic, complemented
64C7×#407C2211yescharacteristic, complemented
65C7×#390—22no—
66C7×#390C2211yescharacteristic, complemented
67C7×#390C2211yescharacteristic, complemented
68C7×#384C2211yescharacteristic, complemented
69C7×#343C2211yescharacteristic, complemented
70C7×#343C2211yescharacteristic, complemented
71C7×#339C2211yescharacteristic, complemented
72C7×#339C2211yescharacteristic, complemented
73#24464C711yesmaximal, characteristic, direct product factor, Sylow
74C7×H(5,𝔽2)—22no—
75C7×H(5,𝔽2)—22no—
76C7×H(5,𝔽2)—41no—
77C7×H(5,𝔽2)—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—41no—
85C2×C7×#41—41no—
86C2×C7×#41D411yescharacteristic, complemented
87C2×C7×#41D411yescharacteristic, complemented
88C2×C7×#41C2311yescharacteristic
89C2×C7×#41C2311yescharacteristic
90C2×C7×#41C2311yescharacteristic
91C22×C7×Q8D411yescharacteristic, complemented
92C22×C7×D4—21no—
93C22×C7×D4—22no—
94C22×C7×D4—22no—
95C22×C7×D4—21no—
96C22×C7×D4—21no—
97C22×C7×D4—21no—
98C22×C7×D4—22no—
99C22×C7×D4D412yes—
100C22×C7×D4D411yescharacteristic, complemented
101C22×C7×D4C2311yescharacteristic
102C22×C7×D4C2311yescharacteristic
103C23×C4×C7—21no—
104C23×C4×C7—21no—
105C23×C4×C7C2311yescharacteristic
106C7×AGL(1,ℤ/8)—22no—
107C7×AGL(1,ℤ/8)—22no—
108C7×AGL(1,ℤ/8)—22no—
109C7×AGL(1,ℤ/8)—41no—
110C7×AGL(1,ℤ/8)—41no—
111C7×AGL(1,ℤ/8)—41no—
112C2×C7×SD16—21no—
113C2×C7×SD16—21no—
114C2×C7×SD16—21no—
115C2×C7×D8—21no—
116C2×C7×D8—21no—
117C2×C7×D8—21no—
118C2×C7×M16—21no—
119C2×C7×M16—22no—
120C2×C7×M16—41no—
121C2×C7×M16C2311yescharacteristic
122C2×C7×M16C2311yescharacteristic
123C2×C7×M16C2311yescharacteristic
124C2×C7×M16C2311yescharacteristic
125C22×C7×C8—21no—
126C7×#127—22no—
127C7×#127—21no—
128C7×#127—22no—
129C7×#127—41no—
130C7×#124—22no—
131C7×#124—21no—
132C7×#123—22no—
133C7×#123—21no—
134C7×C22⋊Q8—22no—
135C7×C22⋊Q8—21no—
136C7×C22⋊Q8—21no—
137C7×C22⋊Q8D411yescharacteristic, complemented
138C7×C22⋊Q8D411yescharacteristic, complemented
139C7×#121—22no—
140C7×#121—22no—
141C7×#121—22no—
142C7×#121—22no—
143C7×#121—22no—
144C7×#121—21no—
145C7×#121—21no—
146C7×#121—21no—
147C7×#121—21no—
148C7×#121—21no—
149C7×#121—21no—
150C7×#121—22no—
151C7×#121—21no—
152C7×#121—21no—
153C7×#121—21no—
154C7×#121—21no—
155C7×#121—21no—
156C7×#121—21no—
157C7×#121—48no—
158C7×#121D411yescharacteristic, complemented
159C7×#121D411yescharacteristic, complemented
160C7×#120—22no—
161C7×#120—22no—
162C7×#120—22no—
163C7×#120—21no—
164C7×#120—22no—
165C4×C7×Q8—21no—
166C4×C7×D4—22no—
167C4×C7×D4—22no—
168C4×C7×D4—21no—
169C4×C7×D4—22no—
170C4×C7×D4—21no—
171C4×C7×D4—21no—
172C7×#117—21no—
173C7×#117C2311yescharacteristic
174C2×C7×C4⋊C4—21no—
175C2×C7×C4⋊C4—22no—
176C2×C7×C4⋊C4C2311yescharacteristic
177C2×C7×C4⋊C4C2311yescharacteristic
178C2×C7×C22⋊C4—22no—
179C2×C7×C22⋊C4—22no—
180C2×C7×C22⋊C4—22no—
181C2×C7×C22⋊C4—21no—
182C2×C7×C22⋊C4D412yes—
183C2×C42×C7—22no—
184C2×C42×C7—21no—
185C2×C42×C7—41no—
186C2×C42×C7C2311yescharacteristic
187C2×C42×C7C2311yescharacteristic
188C7×#107—21no—
189C7×#106—21no—
190C7×#104—22no—
191C7×#104—22no—
192C7×#104—22no—
193C7×#104—22no—
194C7×#104—41no—
195C7×#104D414yescomplemented
196C7×#103—21no—
197C7×#103—21no—
198C7×#103—21no—
199C7×#102—21no—
200C7×#102—21no—
201C7×#102—21no—
202C7×#102—21no—
203C7×#102—21no—
204C7×#100—22no—
205C7×#100—41no—
206C7×C22⋊C8—21no—
207C7×C22⋊C8—21no—
208#3488C2×C711yescharacteristic, complemented
209#3055C2×C711yescharacteristic, complemented
210C2×#453C2×C711yescharacteristic, complemented
211#3006C2×C711yescharacteristic, complemented
212C22×#104C2×C711yescharacteristic, complemented
213#2856C2×C711yescharacteristic, complemented
214#2039C2×C711yescharacteristic, complemented
215#2037C2×C711yescharacteristic, complemented
216#2006C2×C711yescharacteristic, complemented
217#2002C2×C711yescharacteristic, complemented
218#1900C2×C711yescharacteristic, complemented
219#1896C2×C711yescharacteristic, complemented
220#1883C2×C711yescharacteristic, complemented
221#1859C2×C711yescharacteristic, complemented
222#1792C2×C711yescharacteristic, complemented
223C24×C7—22no—
224C24×C7—21no—
225C24×C7—21no—
226C24×C7C2×D411yescharacteristic
227C24×C7C2×D412yes—
228C7×#41—21no—
229C7×#41—21no—
230C7×#41—22no—
231C7×#41—22no—
232C7×#41—21no—
233C7×#41—21no—
234C7×#41—21no—
235C7×#41—21no—
236C7×#41—21no—
237C7×#41—21no—
238C7×#41—21no—
239C7×#41—21no—
240C7×#41—42no—
241C7×#41—42no—
242C7×#41—41no—
243C7×#41—41no—
244C7×#41—42no—
245C7×#41—42no—
246C7×#41—42no—
247C7×#41—42no—
248C7×#41—42no—
249C7×#41—42no—
250C7×#41C2×D412yes—
251C7×#41#4112yes—
252C2×C7×Q8—21no—
253C2×C7×Q8—22no—
254C2×C7×Q8—41no—
255C2×C7×Q8C2×D411yescharacteristic
256C2×C7×Q8C2×D411yescharacteristic
257C2×C7×Q8C2×D411yescharacteristic
258C2×C7×D4—21no—
259C2×C7×D4—22no—
260C2×C7×D4—22no—
261C2×C7×D4—22no—
262C2×C7×D4—22no—
263C2×C7×D4—21no—
264C2×C7×D4—21no—
265C2×C7×D4—21no—
266C2×C7×D4—21no—
267C2×C7×D4—21no—
268C2×C7×D4—22no—
269C2×C7×D4—22no—
270C2×C7×D4—22no—
271C2×C7×D4—21no—
272C2×C7×D4—22no—
273C2×C7×D4—21no—
274C2×C7×D4—21no—
275C2×C7×D4—21no—
276C2×C7×D4—21no—
277C2×C7×D4—21no—
278C2×C7×D4—21no—
279C2×C7×D4—21no—
280C2×C7×D4—21no—
281C2×C7×D4—21no—
282C2×C7×D4—21no—
283C2×C7×D4—21no—
284C2×C7×D4—21no—
285C2×C7×D4—21no—
286C2×C7×D4—41no—
287C2×C7×D4—42no—
288C2×C7×D4—42no—
289C2×C7×D4—44no—
290C2×C7×D4—44no—
291C2×C7×D4—44no—
292C2×C7×D4—42no—
293C2×C7×D4—42no—
294C2×C7×D4—44no—
295C2×C7×D4—44no—
296C2×C7×D4—42no—
297C2×C7×D4—42no—
298C2×C7×D4—44no—
299C2×C7×D4—44no—
300C2×C7×D4—41no—
301C2×C7×D4—41no—
302C2×C7×D4—84no—
303C2×C7×D4C2×D411yescharacteristic
304C2×C7×D4C2×D411yescharacteristic
305C2×C7×D4C2×D411yescharacteristic
306C22×C4×C7—21no—
307C22×C4×C7—21no—
308C22×C4×C7—21no—
309C22×C4×C7—21no—
310C22×C4×C7—21no—
311C22×C4×C7—21no—
312C22×C4×C7—22no—
313C22×C4×C7—24no—
314C22×C4×C7—21no—
315C22×C4×C7—21no—
316C22×C4×C7—22no—
317C22×C4×C7—21no—
318C22×C4×C7—21no—
319C22×C4×C7—21no—
320C22×C4×C7—21no—
321C22×C4×C7—21no—
322C22×C4×C7—42no—
323C22×C4×C7—42no—
324C22×C4×C7—42no—
325C22×C4×C7—42no—
326C22×C4×C7C2×D411yescharacteristic
327C22×C4×C7C2×D411yescharacteristic
328C22×C4×C7C2×D411yescharacteristic
329C22×C4×C7C2×D411yescharacteristic
330C22×C4×C7C2×D411yescharacteristic
331C22×C4×C7C2×D412yes—
332C22×C4×C7C2411yescharacteristic
333C7×SD16—42no—
334C7×SD16—42no—
335C7×SD16—42no—
336C7×D8—42no—
337C7×D8—42no—
338C7×D8—42no—
339C7×M16—21no—
340C7×M16—21no—
341C7×M16—21no—
342C7×M16—21no—
343C7×M16—21no—
344C7×M16—21no—
345C7×M16—21no—
346C7×M16—42no—
347C7×M16C2×D412yescomplemented
348C2×C7×C8—21no—
349C2×C7×C8—21no—
350C2×C7×C8—21no—
351C2×C7×C8—21no—
352C2×C7×C8—42no—
353C7×C4⋊C4—22no—
354C7×C4⋊C4—22no—
355C7×C4⋊C4—21no—
356C7×C4⋊C4—21no—
357C7×C4⋊C4—21no—
358C7×C4⋊C4—21no—
359C7×C4⋊C4—21no—
360C7×C4⋊C4—21no—
361C7×C4⋊C4—44no—
362C7×C4⋊C4C2×D411yescharacteristic
363C7×C4⋊C4C2×D411yescharacteristic
364C7×C22⋊C4—22no—
365C7×C22⋊C4—22no—
366C7×C22⋊C4—22no—
367C7×C22⋊C4—22no—
368C7×C22⋊C4—22no—
369C7×C22⋊C4—21no—
370C7×C22⋊C4—21no—
371C7×C22⋊C4—21no—
372C7×C22⋊C4—21no—
373C7×C22⋊C4—22no—
374C7×C22⋊C4—22no—
375C7×C22⋊C4—21no—
376C7×C22⋊C4—44no—
377C7×C22⋊C4—44no—
378C7×C22⋊C4—41no—
379C7×C22⋊C4—41no—
380C42×C7—22no—
381C42×C7—21no—
382C42×C7—21no—
383C42×C7—21no—
384C42×C7—21no—
385C42×C7—42no—
386C42×C7C2×D412yescomplemented
387C2×H(5,𝔽2)C22×C711yescharacteristic
388C22×#41C22×C711yescharacteristic
389C2×AGL(1,ℤ/8)C22×C711yescharacteristic
390C2×AGL(1,ℤ/8)C22×C711yescharacteristic, complemented
391C2×AGL(1,ℤ/8)C22×C711yescharacteristic, complemented
392C22×M16C22×C711yescharacteristic, complemented
393#550—21no—
394#548—21no—
395#546—21no—
396#546—22no—
397D42—22no—
398D42—21no—
399#537—21no—
400#537C22×C711yescharacteristic
401#535—21no—
402#535C22×C711yescharacteristic
403C2×#127C22×C711yescharacteristic, complemented
404#525—21no—
405#525C22×C711yescharacteristic
406C2×#121—21no—
407C2×#121—22no—
408C2×#121C22×C711yescharacteristic
409C2×#121C22×C711yescharacteristic, complemented
410#520C22×C711yescharacteristic
411C22×C42C22×C711yescharacteristic, complemented
412#469—21no—
413#468—21no—
414#466—21no—
415#465—21no—
416#453—24no—
417#449—21no—
418#449—21no—
419#448—21no—
420#447—21no—
421#428C22×C711yescharacteristic, complemented
422C2×#104—24no—
423C2×#104C22×C711yescharacteristic
424C2×#104C22×C711yescharacteristic
425C2×#104C22×C711yescharacteristic, complemented
426C2×#104C22×C711yescharacteristic, complemented
427C2×#104C22×C711yescharacteristic, complemented
428C2×#104C22×C711yescharacteristic, complemented
429#418C22×C711yescharacteristic, complemented
430#417C22×C711yescharacteristic
431#417C22×C711yescharacteristic, complemented
432#417C22×C711yescharacteristic, complemented
433C2×#100C22×C711yescharacteristic, complemented
434C2×#100C22×C711yescharacteristic, complemented
435#407C22×C711yescharacteristic, complemented
436#390—22no—
437#390C22×C711yescharacteristic, complemented
438#390C22×C711yescharacteristic, complemented
439#384C22×C711yescharacteristic, complemented
440#343C22×C711yescharacteristic, complemented
441#343C22×C711yescharacteristic, complemented
442#339C22×C711yescharacteristic, complemented
443#339C22×C711yescharacteristic, complemented
444C23×C7—21no—
445C23×C7—21no—
446C23×C7—21no—
447C23×C7—22no—
448C23×C7—22no—
449C23×C7—21no—
450C23×C7—21no—
451C23×C7—22no—
452C23×C7—22no—
453C23×C7—41no—
454C23×C7—42no—
455C23×C7—44no—
456C23×C7—42no—
457C23×C7—42no—
458C23×C7—42no—
459C23×C7—42no—
460C23×C7—42no—
461C23×C7—41no—
462C23×C7—41no—
463C23×C7—41no—
464C23×C7—81no—
465C23×C7—82no—
466C23×C7—82no—
467C23×C7#12011yescharacteristic
468C23×C7#12011yescharacteristic
469C23×C7C22×D411yescharacteristic
470C7×Q8—21no—
471C7×Q8—21no—
472C7×Q8—21no—
473C7×Q8—21no—
474C7×Q8—21no—
475C7×Q8—42no—
476C7×Q8#12112yescomplemented
477C7×D4—22no—
478C7×D4—22no—
479C7×D4—21no—
480C7×D4—21no—
481C7×D4—21no—
482C7×D4—21no—
483C7×D4—21no—
484C7×D4—42no—
485C7×D4—42no—
486C7×D4—44no—
487C7×D4—42no—
488C7×D4—44no—
489C7×D4—41no—
490C7×D4—41no—
491C7×D4—41no—
492C7×D4—41no—
493C7×D4—44no—
494C7×D4—42no—
495C7×D4—41no—
496C7×D4—41no—
497C7×D4—41no—
498C7×D4—41no—
499C7×D4—41no—
500C7×D4—41no—
501C7×D4—41no—
502C7×D4—41no—
503C7×D4—88no—
504C7×D4—81no—
505C7×D4—82no—
506C7×D4—82no—
507C7×D4—82no—
508C7×D4—82no—
509C7×D4—82no—
510C7×D4—82no—
511C7×D4#12112yescomplemented
512C2×C4×C7—22no—
513C2×C4×C7—22no—
514C2×C4×C7—21no—
515C2×C4×C7—22no—
516C2×C4×C7—21no—
517C2×C4×C7—21no—
518C2×C4×C7—21no—
519C2×C4×C7—21no—
520C2×C4×C7—21no—
521C2×C4×C7—21no—
522C2×C4×C7—21no—
523C2×C4×C7—21no—
524C2×C4×C7—22no—
525C2×C4×C7—21no—
526C2×C4×C7—21no—
527C2×C4×C7—22no—
528C2×C4×C7—22no—
529C2×C4×C7—21no—
530C2×C4×C7—22no—
531C2×C4×C7—21no—
532C2×C4×C7—21no—
533C2×C4×C7—21no—
534C2×C4×C7—42no—
535C2×C4×C7—42no—
536C2×C4×C7—42no—
537C2×C4×C7—48no—
538C2×C4×C7—44no—
539C2×C4×C7—41no—
540C2×C4×C7—41no—
541C2×C4×C7—41no—
542C2×C4×C7—41no—
543C2×C4×C7—41no—
544C2×C4×C7—41no—
545C2×C4×C7—42no—
546C2×C4×C7—42no—
547C2×C4×C7—41no—
548C2×C4×C7—82no—
549C2×C4×C7#12011yescharacteristic
550C2×C4×C7#12011yescharacteristic
551C2×C4×C7C22×D411yescharacteristic
552C2×C4×C7C22×D411yescharacteristic
553C2×C4×C7C22×D411yescharacteristic
554C2×C4×C7C2×#4111yescharacteristic
555C2×C4×C7H(5,𝔽2)11yescharacteristic
556C2×C4×C7H(5,𝔽2)11yescharacteristic
557C7×C8—22no—
558C7×C8—41no—
559C7×C8—41no—
560C7×C8—41no—
561H(5,𝔽2)—22no—
562H(5,𝔽2)—22no—
563H(5,𝔽2)—41no—
564H(5,𝔽2)—41no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—41no—
572C2×#41—41no—
573C2×#41C7×D411yescharacteristic, complemented
574C2×#41C7×D411yescharacteristic, complemented
575C2×#41C23×C711yescharacteristic
576C2×#41C23×C711yescharacteristic
577C2×#41C23×C711yescharacteristic
578C22×Q8C7×D411yescharacteristic, complemented
579C22×D4—21no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4C7×D412yes—
587C22×D4C7×D411yescharacteristic, complemented
588C22×D4C23×C711yescharacteristic
589C22×D4C23×C711yescharacteristic
590C23×C4—21no—
591C23×C4—21no—
592C23×C4C23×C711yescharacteristic
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—22no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)—41no—
598AGL(1,ℤ/8)—41no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×SD16—21no—
602C2×D8—21no—
603C2×D8—21no—
604C2×D8—21no—
605C2×M16—21no—
606C2×M16—22no—
607C2×M16—41no—
608C2×M16C23×C711yescharacteristic
609C2×M16C23×C711yescharacteristic
610C2×M16C23×C711yescharacteristic
611C2×M16C23×C711yescharacteristic
612C22×C8—21no—
613#127—22no—
614#127—21no—
615#127—22no—
616#127—41no—
617#124—22no—
618#124—21no—
619#123—22no—
620#123—21no—
621C22⋊Q8—22no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8C7×D411yescharacteristic, complemented
625C22⋊Q8C7×D411yescharacteristic, complemented
626#121—22no—
627#121—22no—
628#121—22no—
629#121—22no—
630#121—22no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—22no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—48no—
645#121C7×D411yescharacteristic, complemented
646#121C7×D411yescharacteristic, complemented
647#120—22no—
648#120—22no—
649#120—22no—
650#120—21no—
651#120—22no—
652C4×Q8—21no—
653C4×D4—22no—
654C4×D4—22no—
655C4×D4—21no—
656C4×D4—22no—
657C4×D4—21no—
658C4×D4—21no—
659#117—21no—
660#117C23×C711yescharacteristic
661C2×C4⋊C4—21no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4C23×C711yescharacteristic
664C2×C4⋊C4C23×C711yescharacteristic
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4C7×D412yes—
670C2×C42—22no—
671C2×C42—21no—
672C2×C42—41no—
673C2×C42C23×C711yescharacteristic
674C2×C42C23×C711yescharacteristic
675#107—21no—
676#106—21no—
677#104—22no—
678#104—22no—
679#104—22no—
680#104—22no—
681#104—41no—
682#104C7×D414yescomplemented
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#100—22no—
692#100—41no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22×C7—21no—
696C22×C7—21no—
697C22×C7—21no—
698C22×C7—21no—
699C22×C7—21no—
700C22×C7—22no—
701C22×C7—21no—
702C22×C7—21no—
703C22×C7—42no—
704C22×C7—42no—
705C22×C7—41no—
706C22×C7—41no—
707C22×C7—41no—
708C22×C7—41no—
709C22×C7—42no—
710C22×C7—42no—
711C22×C7—41no—
712C22×C7—41no—
713C22×C7—41no—
714C22×C7—42no—
715C22×C7—41no—
716C22×C7—84no—
717C22×C7—82no—
718C22×C7—82no—
719C22×C7—82no—
720C22×C7—82no—
721C22×C7—81no—
722C22×C7—81no—
723C22×C7—81no—
724C22×C7—164no—
725C22×C7#45312yescomplemented
726C22×C7C2×#12011yescharacteristic
727C22×C7D4211yescharacteristic
728C22×C7#54611yescharacteristic
729C4×C7—24no—
730C4×C7—21no—
731C4×C7—21no—
732C4×C7—22no—
733C4×C7—42no—
734C4×C7—41no—
735C4×C7—41no—
736C4×C7—42no—
737C4×C7—41no—
738C4×C7—41no—
739C4×C7—81no—
740C4×C7C2×#12111yescharacteristic
741C4×C7#53411yescharacteristic
742C4×C7D4211yescharacteristic
743C4×C7#54611yescharacteristic
744C24—22no—
745C24—21no—
746C24—21no—
747C24C2×C7×D411yescharacteristic
748C24C2×C7×D412yes—
749#41—21no—
750#41—21no—
751#41—22no—
752#41—22no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—21no—
757#41—21no—
758#41—21no—
759#41—21no—
760#41—21no—
761#41—42no—
762#41—42no—
763#41—41no—
764#41—41no—
765#41—42no—
766#41—42no—
767#41—42no—
768#41—42no—
769#41—42no—
770#41—42no—
771#41C2×C7×D412yes—
772#41C7×#4112yes—
773C2×Q8—21no—
774C2×Q8—22no—
775C2×Q8—41no—
776C2×Q8C2×C7×D411yescharacteristic
777C2×Q8C2×C7×D411yescharacteristic
778C2×Q8C2×C7×D411yescharacteristic
779C2×D4—21no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—41no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—84no—
824C2×D4C2×C7×D411yescharacteristic
825C2×D4C2×C7×D411yescharacteristic
826C2×D4C2×C7×D411yescharacteristic
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—24no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4C2×C7×D411yescharacteristic
848C22×C4C2×C7×D411yescharacteristic
849C22×C4C2×C7×D411yescharacteristic
850C22×C4C2×C7×D411yescharacteristic
851C22×C4C2×C7×D411yescharacteristic
852C22×C4C2×C7×D412yes—
853C22×C4C24×C711yescharacteristic
854SD16—42no—
855SD16—42no—
856SD16—42no—
857D8—42no—
858D8—42no—
859D8—42no—
860M16—21no—
861M16—21no—
862M16—21no—
863M16—21no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—42no—
868M16C2×C7×D412yescomplemented
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—42no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—44no—
883C4⋊C4C2×C7×D411yescharacteristic
884C4⋊C4C2×C7×D411yescharacteristic
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—21no—
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—21no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—21no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—41no—
900C22⋊C4—41no—
901C42—22no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—42no—
907C42C2×C7×D412yescomplemented
908C2×C7—21no—
909C2×C7—21no—
910C2×C7—22no—
911C2×C7—41no—
912C2×C7—42no—
913C2×C7—81no—
914C2×C7—82no—
915C2×C7—81no—
916C2×C7—161no—
917C2×C7#241011yescharacteristic
918C2×C7C2×#45311yescharacteristic
919C2×C7#301811yescharacteristic
920C23—21no—
921C23—21no—
922C23—21no—
923C23—22no—
924C23—22no—
925C23—21no—
926C23—21no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—42no—
931C23—44no—
932C23—42no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—81no—
941C23—82no—
942C23—82no—
943C23C7×#12011yescharacteristic
944C23C7×#12011yescharacteristic
945C23C22×C7×D411yescharacteristic
946Q8—21no—
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—42no—
952Q8C7×#12112yescomplemented
953D4—22no—
954D4—22no—
955D4—21no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—42no—
961D4—42no—
962D4—44no—
963D4—42no—
964D4—44no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—44no—
970D4—42no—
971D4—41no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—88no—
980D4—81no—
981D4—82no—
982D4—82no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4C7×#12112yescomplemented
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—48no—
1014C2×C4—44no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—41no—
1024C2×C4—82no—
1025C2×C4C7×#12011yescharacteristic
1026C2×C4C7×#12011yescharacteristic
1027C2×C4C22×C7×D411yescharacteristic
1028C2×C4C22×C7×D411yescharacteristic
1029C2×C4C22×C7×D411yescharacteristic
1030C2×C4C2×C7×#4111yescharacteristic
1031C2×C4C7×H(5,𝔽2)11yescharacteristic
1032C2×C4C7×H(5,𝔽2)11yescharacteristic
1033C8—22no—
1034C8—41no—
1035C8—41no—
1036C8—41no—
1037C7#2446411yescharacteristic, direct product factor, Sylow
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22C7×#45312yescomplemented
1069C22C2×C7×#12011yescharacteristic
1070C22C7×D4211yescharacteristic
1071C22C7×#54611yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×C7×#12111yescharacteristic
1084C4C7×#53411yescharacteristic
1085C4C7×D4211yescharacteristic
1086C4C7×#54611yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C7×#241011yescharacteristic
1097C2C2×C7×#45311yescharacteristic
1098C2C7×#301811yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
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
1. C7×#3488C2semidirect
2. C7×#3055C2semidirect
3. C2×C7×#453C2semidirect
4. C7×#3006C2semidirect
5. C22×C7×#104C2semidirect
6. C7×#2856C2semidirect
7. C7×#2039C2semidirect
8. C7×#2037C2semidirect
9. C7×#2006C2semidirect
10. C7×#2002C2semidirect
11. C7×#1900C2semidirect
12. C7×#1896C2semidirect
13. C7×#1883C2semidirect
14. C7×#1859C2semidirect
15. C7×#1792C2semidirect
19. C2×C7×AGL(1,ℤ/8)C22semidirect
20. C2×C7×AGL(1,ℤ/8)C22semidirect
21. C22×C7×M16C22semidirect
32. C2×C7×#127C22semidirect
38. C2×C7×#121C22semidirect
40. C22×C42×C7C22semidirect
50. C7×#428C22semidirect
54. C2×C7×#104C22semidirect
55. C2×C7×#104C22semidirect
56. C2×C7×#104C22semidirect
57. C2×C7×#104C22semidirect
58. C7×#418C22semidirect
60. C7×#417C22semidirect
61. C7×#417C22semidirect
62. C2×C7×#100C22semidirect
63. C2×C7×#100C22semidirect
64. C7×#407C22semidirect
66. C7×#390C22semidirect
67. C7×#390C22semidirect
68. C7×#384C22semidirect
69. C7×#343C22semidirect
70. C7×#343C22semidirect
71. C7×#339C22semidirect
72. C7×#339C22semidirect
73. #24464C7direct (N × H)
86. C2×C7×#41D4semidirect
87. C2×C7×#41D4semidirect
91. C22×C7×Q8D4semidirect
100. C22×C7×D4D4semidirect
137. C7×C22⋊Q8D4semidirect
138. C7×C22⋊Q8D4semidirect
158. C7×#121D4semidirect
159. C7×#121D4semidirect
195. C7×#104D4semidirect
208. #3488C2×C7semidirect
209. #3055C2×C7semidirect
210. C2×#453C2×C7semidirect
211. #3006C2×C7semidirect
212. C22×#104C2×C7semidirect
213. #2856C2×C7semidirect
214. #2039C2×C7semidirect
215. #2037C2×C7semidirect
216. #2006C2×C7semidirect
217. #2002C2×C7semidirect
218. #1900C2×C7semidirect
219. #1896C2×C7semidirect
220. #1883C2×C7semidirect
221. #1859C2×C7semidirect
222. #1792C2×C7semidirect
347. C7×M16C2×D4semidirect
386. C42×C7C2×D4semidirect
390. C2×AGL(1,ℤ/8)C22×C7semidirect
391. C2×AGL(1,ℤ/8)C22×C7semidirect
392. C22×M16C22×C7semidirect
403. C2×#127C22×C7semidirect
409. C2×#121C22×C7semidirect
411. C22×C42C22×C7semidirect
421. #428C22×C7semidirect
425. C2×#104C22×C7semidirect
426. C2×#104C22×C7semidirect
427. C2×#104C22×C7semidirect
428. C2×#104C22×C7semidirect
429. #418C22×C7semidirect
431. #417C22×C7semidirect
432. #417C22×C7semidirect
433. C2×#100C22×C7semidirect
434. C2×#100C22×C7semidirect
435. #407C22×C7semidirect
437. #390C22×C7semidirect
438. #390C22×C7semidirect
439. #384C22×C7semidirect
440. #343C22×C7semidirect
441. #343C22×C7semidirect
442. #339C22×C7semidirect
443. #339C22×C7semidirect
476. C7×Q8#121semidirect
511. C7×D4#121semidirect
573. C2×#41C7×D4semidirect
574. C2×#41C7×D4semidirect
578. C22×Q8C7×D4semidirect
587. C22×D4C7×D4semidirect
624. C22⋊Q8C7×D4semidirect
625. C22⋊Q8C7×D4semidirect
645. #121C7×D4semidirect
646. #121C7×D4semidirect
682. #104C7×D4semidirect
725. C22×C7#453semidirect
868. M16C2×C7×D4semidirect
907. C42C2×C7×D4semidirect
952. Q8C7×#121semidirect
987. D4C7×#121semidirect
1037. C7#24464direct (N × H)
1068. C22C7×#453semidirect

Maximal subgroups

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

subgroupindex
C7×#34882
C7×#30552
C2×C7×#4532
C7×#30062
C22×C7×#1042
C7×#28562
C7×#20392
C7×#20372
C7×#20062
C7×#20022
C7×#19002
C7×#18962
C7×#18832
C7×#18592
C7×#17922
#244647