Finite Group Databasebeta

← C7×#24468 #13201684

Subgroups — C7×#24468 #13201684

Order 1792.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 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
5C2×C7×#421C211yesmaximal, characteristic, complemented
6C7×#2619C211yesmaximal, characteristic, complemented
7C7×#2040C211yesmaximal, characteristic, complemented
8C7×#2037C211yesmaximal, characteristic, complemented
9C7×#2006C211yesmaximal, characteristic, complemented
10C7×#2002C211yesmaximal, characteristic, complemented
11C7×#1900C211yesmaximal, characteristic, complemented
12C7×#1897C211yesmaximal, characteristic, complemented
13C7×#1883C211yesmaximal, characteristic, complemented
14C7×#1860C211yesmaximal, 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×#121C2211yescharacteristic
37C2×C7×#121C2211yescharacteristic, complemented
38C7×#520C2211yescharacteristic
39C2×C7×#117C2211yescharacteristic, complemented
40C7×#469—21no—
41C7×#468—21no—
42C7×#466—21no—
43C7×#465—21no—
44C7×#453—24no—
45C7×#449—21no—
46C7×#449—21no—
47C7×#448—21no—
48C7×#447—21no—
49C7×#428C2211yescharacteristic, complemented
50C7×#421—24no—
51C2×C7×#104C2211yescharacteristic
52C2×C7×#104C2211yescharacteristic
53C2×C7×#104C2211yescharacteristic, complemented
54C2×C7×#104C2211yescharacteristic, complemented
55C2×C7×#104C2211yescharacteristic, complemented
56C2×C7×#104C2211yescharacteristic, complemented
57C7×#418C2211yescharacteristic, complemented
58C7×#417C2211yescharacteristic
59C7×#417C2211yescharacteristic, complemented
60C7×#417C2211yescharacteristic, complemented
61C2×C7×#100C2211yescharacteristic, complemented
62C2×C7×#100C2211yescharacteristic, complemented
63C7×#407C2211yescharacteristic, complemented
64C7×#394—22no—
65C7×#392—22no—
66C7×#390C2211yescharacteristic, complemented
67C7×#390C2211yescharacteristic, complemented
68C7×#382C2211yescharacteristic, complemented
69C7×#343C2211yescharacteristic, complemented
70C7×#343C2211yescharacteristic, complemented
71C7×#339C2211yescharacteristic, complemented
72C7×#339C2211yescharacteristic, complemented
73#24468C711yesmaximal, 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×C7C2311yescharacteristic
105C7×AGL(1,ℤ/8)—22no—
106C7×AGL(1,ℤ/8)—22no—
107C7×AGL(1,ℤ/8)—22no—
108C7×AGL(1,ℤ/8)—41no—
109C7×AGL(1,ℤ/8)—41no—
110C7×AGL(1,ℤ/8)—41no—
111C2×C7×SD16—21no—
112C2×C7×SD16—21no—
113C2×C7×SD16—21no—
114C2×C7×D8—21no—
115C2×C7×D8—21no—
116C2×C7×D8—21no—
117C2×C7×M16—21no—
118C2×C7×M16—22no—
119C2×C7×M16—41no—
120C2×C7×M16C2311yescharacteristic
121C2×C7×M16C2311yescharacteristic
122C2×C7×M16C2311yescharacteristic
123C2×C7×M16C2311yescharacteristic
124C22×C7×C8—21no—
125C7×#127—22no—
126C7×#127—21no—
127C7×#127—22no—
128C7×#127—41no—
129C7×#124—22no—
130C7×#124—21no—
131C7×#123—22no—
132C7×#123—21no—
133C7×C22⋊Q8—22no—
134C7×C22⋊Q8—21no—
135C7×C22⋊Q8—21no—
136C7×C22⋊Q8D411yescharacteristic, complemented
137C7×C22⋊Q8D411yescharacteristic, complemented
138C7×#121—22no—
139C7×#121—22no—
140C7×#121—22no—
141C7×#121—22no—
142C7×#121—22no—
143C7×#121—21no—
144C7×#121—21no—
145C7×#121—21no—
146C7×#121—21no—
147C7×#121—21no—
148C7×#121—21no—
149C7×#121—22no—
150C7×#121—21no—
151C7×#121—21no—
152C7×#121—21no—
153C7×#121—21no—
154C7×#121—21no—
155C7×#121—21no—
156C7×#121D411yescharacteristic, complemented
157C7×#121D411yescharacteristic, complemented
158C7×#120—22no—
159C7×#120—22no—
160C7×#120—22no—
161C7×#120—21no—
162C7×#120—22no—
163C4×C7×Q8—21no—
164C4×C7×D4—22no—
165C4×C7×D4—22no—
166C4×C7×D4—21no—
167C4×C7×D4—22no—
168C4×C7×D4—21no—
169C4×C7×D4—21no—
170C7×#117—21no—
171C7×#117—22no—
172C7×#117—41no—
173C7×#117C2311yescharacteristic
174C2×C7×C4⋊C4—21no—
175C2×C7×C4⋊C4—21no—
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⋊C4—22no—
182C2×C7×C22⋊C4—22no—
183C2×C7×C22⋊C4D412yes—
184C2×C42×C7C2311yescharacteristic
185C2×C42×C7C2311yescharacteristic
186C7×#107—21no—
187C7×#106—21no—
188C7×#104—22no—
189C7×#104—22no—
190C7×#104—22no—
191C7×#104—22no—
192C7×#104—41no—
193C7×#104D414yescomplemented
194C7×#103—21no—
195C7×#103—21no—
196C7×#103—21no—
197C7×#102—21no—
198C7×#102—21no—
199C7×#102—21no—
200C7×#102—21no—
201C7×#102—21no—
202C7×#100—22no—
203C7×#100—41no—
204C7×C22⋊C8—21no—
205C7×C22⋊C8—21no—
206C7×#95—22no—
207#3488C2×C711yescharacteristic, complemented
208#3055C2×C711yescharacteristic, complemented
209C2×#453C2×C711yescharacteristic, complemented
210#3006C2×C711yescharacteristic, complemented
211C2×#421C2×C711yescharacteristic, complemented
212#2619C2×C711yescharacteristic, complemented
213#2040C2×C711yescharacteristic, complemented
214#2037C2×C711yescharacteristic, complemented
215#2006C2×C711yescharacteristic, complemented
216#2002C2×C711yescharacteristic, complemented
217#1900C2×C711yescharacteristic, complemented
218#1897C2×C711yescharacteristic, complemented
219#1883C2×C711yescharacteristic, complemented
220#1860C2×C711yescharacteristic, complemented
221#1792C2×C711yescharacteristic, complemented
222C24×C7—22no—
223C24×C7—21no—
224C24×C7—21no—
225C24×C7C2×D412yes—
226C24×C7C2×D411yescharacteristic
227C7×#41—21no—
228C7×#41—21no—
229C7×#41—22no—
230C7×#41—22no—
231C7×#41—21no—
232C7×#41—21no—
233C7×#41—21no—
234C7×#41—21no—
235C7×#41—21no—
236C7×#41—21no—
237C7×#41—21no—
238C7×#41—21no—
239C7×#41—42no—
240C7×#41—42no—
241C7×#41—41no—
242C7×#41—41no—
243C7×#41—42no—
244C7×#41—42no—
245C7×#41—42no—
246C7×#41—42no—
247C7×#41—42no—
248C7×#41—42no—
249C7×#41C2×D412yes—
250C7×#41#4112yes—
251C2×C7×Q8—21no—
252C2×C7×Q8—22no—
253C2×C7×Q8—41no—
254C2×C7×Q8C2×D411yescharacteristic
255C2×C7×Q8C2×D411yescharacteristic
256C2×C7×Q8C2×D411yescharacteristic
257C2×C7×D4—21no—
258C2×C7×D4—22no—
259C2×C7×D4—22no—
260C2×C7×D4—22no—
261C2×C7×D4—22no—
262C2×C7×D4—21no—
263C2×C7×D4—21no—
264C2×C7×D4—21no—
265C2×C7×D4—21no—
266C2×C7×D4—21no—
267C2×C7×D4—22no—
268C2×C7×D4—22no—
269C2×C7×D4—22no—
270C2×C7×D4—21no—
271C2×C7×D4—22no—
272C2×C7×D4—21no—
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—41no—
286C2×C7×D4—42no—
287C2×C7×D4—42no—
288C2×C7×D4—44no—
289C2×C7×D4—42no—
290C2×C7×D4—42no—
291C2×C7×D4—44no—
292C2×C7×D4—44no—
293C2×C7×D4—42no—
294C2×C7×D4—42no—
295C2×C7×D4—41no—
296C2×C7×D4—41no—
297C2×C7×D4—82no—
298C2×C7×D4—82no—
299C2×C7×D4—82no—
300C2×C7×D4—82no—
301C2×C7×D4—84no—
302C2×C7×D4C2×D411yescharacteristic
303C2×C7×D4C2×D411yescharacteristic
304C2×C7×D4C2×D411yescharacteristic
305C22×C4×C7—21no—
306C22×C4×C7—21no—
307C22×C4×C7—21no—
308C22×C4×C7—21no—
309C22×C4×C7—21no—
310C22×C4×C7—22no—
311C22×C4×C7—21no—
312C22×C4×C7—21no—
313C22×C4×C7—22no—
314C22×C4×C7—21no—
315C22×C4×C7—21no—
316C22×C4×C7—21no—
317C22×C4×C7—21no—
318C22×C4×C7—21no—
319C22×C4×C7—21no—
320C22×C4×C7—42no—
321C22×C4×C7—42no—
322C22×C4×C7C2×D411yescharacteristic
323C22×C4×C7C2×D411yescharacteristic
324C22×C4×C7C2×D411yescharacteristic
325C22×C4×C7C2×D411yescharacteristic
326C22×C4×C7C2×D411yescharacteristic
327C22×C4×C7C2×D412yes—
328C22×C4×C7C2411yescharacteristic
329C7×SD16—42no—
330C7×SD16—42no—
331C7×SD16—42no—
332C7×D8—42no—
333C7×D8—42no—
334C7×D8—42no—
335C7×M16—21no—
336C7×M16—21no—
337C7×M16—21no—
338C7×M16—21no—
339C7×M16—21no—
340C7×M16—21no—
341C7×M16—21no—
342C7×M16—42no—
343C7×M16C2×D412yescomplemented
344C2×C7×C8—21no—
345C2×C7×C8—21no—
346C2×C7×C8—21no—
347C2×C7×C8—21no—
348C2×C7×C8—42no—
349C7×C4⋊C4—22no—
350C7×C4⋊C4—22no—
351C7×C4⋊C4—21no—
352C7×C4⋊C4—21no—
353C7×C4⋊C4—21no—
354C7×C4⋊C4—21no—
355C7×C4⋊C4—21no—
356C7×C4⋊C4—21no—
357C7×C4⋊C4—42no—
358C7×C4⋊C4C2×D411yescharacteristic
359C7×C4⋊C4C2×D411yescharacteristic
360C7×C22⋊C4—22no—
361C7×C22⋊C4—22no—
362C7×C22⋊C4—22no—
363C7×C22⋊C4—22no—
364C7×C22⋊C4—22no—
365C7×C22⋊C4—21no—
366C7×C22⋊C4—21no—
367C7×C22⋊C4—21no—
368C7×C22⋊C4—21no—
369C7×C22⋊C4—22no—
370C7×C22⋊C4—22no—
371C7×C22⋊C4—21no—
372C7×C22⋊C4—42no—
373C7×C22⋊C4—41no—
374C7×C22⋊C4—41no—
375C7×C22⋊C4—82no—
376C7×C22⋊C4—82no—
377C42×C7—22no—
378C42×C7—21no—
379C42×C7—21no—
380C42×C7—21no—
381C42×C7—21no—
382C42×C7C2×D412yescomplemented
383C2×H(5,𝔽2)C22×C711yescharacteristic
384C22×#41C22×C711yescharacteristic
385C2×AGL(1,ℤ/8)C22×C711yescharacteristic
386C2×AGL(1,ℤ/8)C22×C711yescharacteristic, complemented
387C2×AGL(1,ℤ/8)C22×C711yescharacteristic, complemented
388C22×M16C22×C711yescharacteristic, complemented
389#550—21no—
390#548—21no—
391#546—21no—
392#546—22no—
393D42—22no—
394D42—21no—
395#537—21no—
396#537C22×C711yescharacteristic
397#535—21no—
398#535C22×C711yescharacteristic
399C2×#127C22×C711yescharacteristic, complemented
400#525—21no—
401#525C22×C711yescharacteristic
402C2×#121—21no—
403C2×#121C22×C711yescharacteristic
404C2×#121C22×C711yescharacteristic, complemented
405#520C22×C711yescharacteristic
406C2×#117C22×C711yescharacteristic, complemented
407#469—21no—
408#468—21no—
409#466—21no—
410#465—21no—
411#453—24no—
412#449—21no—
413#449—21no—
414#448—21no—
415#447—21no—
416#428C22×C711yescharacteristic, complemented
417#421—24no—
418C2×#104C22×C711yescharacteristic
419C2×#104C22×C711yescharacteristic
420C2×#104C22×C711yescharacteristic, complemented
421C2×#104C22×C711yescharacteristic, complemented
422C2×#104C22×C711yescharacteristic, complemented
423C2×#104C22×C711yescharacteristic, complemented
424#418C22×C711yescharacteristic, complemented
425#417C22×C711yescharacteristic
426#417C22×C711yescharacteristic, complemented
427#417C22×C711yescharacteristic, complemented
428C2×#100C22×C711yescharacteristic, complemented
429C2×#100C22×C711yescharacteristic, complemented
430#407C22×C711yescharacteristic, complemented
431#394—22no—
432#392—22no—
433#390C22×C711yescharacteristic, complemented
434#390C22×C711yescharacteristic, complemented
435#382C22×C711yescharacteristic, complemented
436#343C22×C711yescharacteristic, complemented
437#343C22×C711yescharacteristic, complemented
438#339C22×C711yescharacteristic, complemented
439#339C22×C711yescharacteristic, complemented
440C23×C7—21no—
441C23×C7—21no—
442C23×C7—21no—
443C23×C7—22no—
444C23×C7—21no—
445C23×C7—21no—
446C23×C7—22no—
447C23×C7—22no—
448C23×C7—41no—
449C23×C7—41no—
450C23×C7—42no—
451C23×C7—42no—
452C23×C7—44no—
453C23×C7—42no—
454C23×C7—42no—
455C23×C7—42no—
456C23×C7—42no—
457C23×C7—41no—
458C23×C7—41no—
459C23×C7—41no—
460C23×C7—81no—
461C23×C7—82no—
462C23×C7—82no—
463C23×C7#12011yescharacteristic
464C23×C7#12011yescharacteristic
465C23×C7C22×D411yescharacteristic
466C7×Q8—21no—
467C7×Q8—21no—
468C7×Q8—21no—
469C7×Q8—21no—
470C7×Q8—21no—
471C7×Q8—42no—
472C7×Q8#12112yes—
473C7×D4—22no—
474C7×D4—22no—
475C7×D4—21no—
476C7×D4—21no—
477C7×D4—21no—
478C7×D4—21no—
479C7×D4—21no—
480C7×D4—42no—
481C7×D4—42no—
482C7×D4—44no—
483C7×D4—42no—
484C7×D4—44no—
485C7×D4—44no—
486C7×D4—42no—
487C7×D4—41no—
488C7×D4—41no—
489C7×D4—41no—
490C7×D4—41no—
491C7×D4—41no—
492C7×D4—41no—
493C7×D4—41no—
494C7×D4—41no—
495C7×D4—41no—
496C7×D4—41no—
497C7×D4—41no—
498C7×D4—41no—
499C7×D4—81no—
500C7×D4—82no—
501C7×D4—82no—
502C7×D4—82no—
503C7×D4—82no—
504C7×D4—88no—
505C7×D4—82no—
506C7×D4—82no—
507C7×D4#12112yes—
508C2×C4×C7—21no—
509C2×C4×C7—21no—
510C2×C4×C7—21no—
511C2×C4×C7—21no—
512C2×C4×C7—21no—
513C2×C4×C7—21no—
514C2×C4×C7—21no—
515C2×C4×C7—21no—
516C2×C4×C7—21no—
517C2×C4×C7—22no—
518C2×C4×C7—21no—
519C2×C4×C7—21no—
520C2×C4×C7—22no—
521C2×C4×C7—21no—
522C2×C4×C7—22no—
523C2×C4×C7—21no—
524C2×C4×C7—21no—
525C2×C4×C7—21no—
526C2×C4×C7—22no—
527C2×C4×C7—42no—
528C2×C4×C7—42no—
529C2×C4×C7—42no—
530C2×C4×C7—44no—
531C2×C4×C7—41no—
532C2×C4×C7—41no—
533C2×C4×C7—41no—
534C2×C4×C7—41no—
535C2×C4×C7—41no—
536C2×C4×C7—41no—
537C2×C4×C7—42no—
538C2×C4×C7—41no—
539C2×C4×C7—41no—
540C2×C4×C7—42no—
541C2×C4×C7—41no—
542C2×C4×C7—41no—
543C2×C4×C7—82no—
544C2×C4×C7#12011yescharacteristic
545C2×C4×C7#12011yescharacteristic
546C2×C4×C7C22×D411yescharacteristic
547C2×C4×C7C22×D411yescharacteristic
548C2×C4×C7C22×D411yescharacteristic
549C2×C4×C7C2×#4111yescharacteristic
550C2×C4×C7H(5,𝔽2)11yescharacteristic
551C2×C4×C7H(5,𝔽2)11yescharacteristic
552C7×C8—22no—
553C7×C8—41no—
554C7×C8—41no—
555C7×C8—41no—
556H(5,𝔽2)—22no—
557H(5,𝔽2)—22no—
558H(5,𝔽2)—41no—
559H(5,𝔽2)—41no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—22no—
565C2×#41—22no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41C7×D411yescharacteristic, complemented
569C2×#41C7×D411yescharacteristic, complemented
570C2×#41C23×C711yescharacteristic
571C2×#41C23×C711yescharacteristic
572C2×#41C23×C711yescharacteristic
573C22×Q8C7×D411yescharacteristic, complemented
574C22×D4—21no—
575C22×D4—22no—
576C22×D4—22no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—22no—
581C22×D4C7×D412yes—
582C22×D4C7×D411yescharacteristic, complemented
583C22×D4C23×C711yescharacteristic
584C22×D4C23×C711yescharacteristic
585C23×C4—21no—
586C23×C4C23×C711yescharacteristic
587AGL(1,ℤ/8)—22no—
588AGL(1,ℤ/8)—22no—
589AGL(1,ℤ/8)—22no—
590AGL(1,ℤ/8)—41no—
591AGL(1,ℤ/8)—41no—
592AGL(1,ℤ/8)—41no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×D8—21no—
597C2×D8—21no—
598C2×D8—21no—
599C2×M16—21no—
600C2×M16—22no—
601C2×M16—41no—
602C2×M16C23×C711yescharacteristic
603C2×M16C23×C711yescharacteristic
604C2×M16C23×C711yescharacteristic
605C2×M16C23×C711yescharacteristic
606C22×C8—21no—
607#127—22no—
608#127—21no—
609#127—22no—
610#127—41no—
611#124—22no—
612#124—21no—
613#123—22no—
614#123—21no—
615C22⋊Q8—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8C7×D411yescharacteristic, complemented
619C22⋊Q8C7×D411yescharacteristic, complemented
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—22no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121C7×D411yescharacteristic, complemented
639#121C7×D411yescharacteristic, complemented
640#120—22no—
641#120—22no—
642#120—22no—
643#120—21no—
644#120—22no—
645C4×Q8—21no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—22no—
650C4×D4—21no—
651C4×D4—21no—
652#117—21no—
653#117—22no—
654#117—41no—
655#117C23×C711yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4C23×C711yescharacteristic
659C2×C4⋊C4C23×C711yescharacteristic
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4C7×D412yes—
666C2×C42C23×C711yescharacteristic
667C2×C42C23×C711yescharacteristic
668#107—21no—
669#106—21no—
670#104—22no—
671#104—22no—
672#104—22no—
673#104—22no—
674#104—41no—
675#104C7×D414yescomplemented
676#103—21no—
677#103—21no—
678#103—21no—
679#102—21no—
680#102—21no—
681#102—21no—
682#102—21no—
683#102—21no—
684#100—22no—
685#100—41no—
686C22⋊C8—21no—
687C22⋊C8—21no—
688#95—22no—
689C22×C7—21no—
690C22×C7—21no—
691C22×C7—21no—
692C22×C7—21no—
693C22×C7—22no—
694C22×C7—21no—
695C22×C7—21no—
696C22×C7—21no—
697C22×C7—21no—
698C22×C7—41no—
699C22×C7—41no—
700C22×C7—41no—
701C22×C7—41no—
702C22×C7—42no—
703C22×C7—42no—
704C22×C7—41no—
705C22×C7—41no—
706C22×C7—41no—
707C22×C7—42no—
708C22×C7—41no—
709C22×C7—81no—
710C22×C7—81no—
711C22×C7—82no—
712C22×C7—82no—
713C22×C7—82no—
714C22×C7—82no—
715C22×C7—84no—
716C22×C7—81no—
717C22×C7—81no—
718C22×C7—81no—
719C22×C7—164no—
720C22×C7C2×#12011yescharacteristic
721C22×C7D4211yescharacteristic
722C22×C7#54611yescharacteristic
723C4×C7—21no—
724C4×C7—21no—
725C4×C7—22no—
726C4×C7—42no—
727C4×C7—41no—
728C4×C7—41no—
729C4×C7—42no—
730C4×C7—41no—
731C4×C7—41no—
732C4×C7—81no—
733C4×C7—81no—
734C4×C7C2×#12111yescharacteristic
735C4×C7#53411yescharacteristic
736C4×C7D4211yescharacteristic
737C4×C7#54611yescharacteristic
738C24—22no—
739C24—21no—
740C24—21no—
741C24C2×C7×D412yes—
742C24C2×C7×D411yescharacteristic
743#41—21no—
744#41—21no—
745#41—22no—
746#41—22no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—42no—
756#41—42no—
757#41—41no—
758#41—41no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41C2×C7×D412yes—
766#41C7×#4112yes—
767C2×Q8—21no—
768C2×Q8—22no—
769C2×Q8—41no—
770C2×Q8C2×C7×D411yescharacteristic
771C2×Q8C2×C7×D411yescharacteristic
772C2×Q8C2×C7×D411yescharacteristic
773C2×D4—21no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—41no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—44no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—41no—
812C2×D4—41no—
813C2×D4—82no—
814C2×D4—82no—
815C2×D4—82no—
816C2×D4—82no—
817C2×D4—84no—
818C2×D4C2×C7×D411yescharacteristic
819C2×D4C2×C7×D411yescharacteristic
820C2×D4C2×C7×D411yescharacteristic
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4C2×C7×D411yescharacteristic
839C22×C4C2×C7×D411yescharacteristic
840C22×C4C2×C7×D411yescharacteristic
841C22×C4C2×C7×D411yescharacteristic
842C22×C4C2×C7×D411yescharacteristic
843C22×C4C2×C7×D412yes—
844C22×C4C24×C711yescharacteristic
845SD16—42no—
846SD16—42no—
847SD16—42no—
848D8—42no—
849D8—42no—
850D8—42no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—21no—
858M16—42no—
859M16C2×C7×D412yescomplemented
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—42no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—42no—
874C4⋊C4C2×C7×D411yescharacteristic
875C4⋊C4C2×C7×D411yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—42no—
889C22⋊C4—41no—
890C22⋊C4—41no—
891C22⋊C4—82no—
892C22⋊C4—82no—
893C42—22no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42C2×C7×D412yescomplemented
899C2×C7—21no—
900C2×C7—21no—
901C2×C7—41no—
902C2×C7—41no—
903C2×C7—42no—
904C2×C7—81no—
905C2×C7—82no—
906C2×C7—81no—
907C2×C7—161no—
908C2×C7#241011yescharacteristic
909C2×C7#301911yescharacteristic
910C2×C7#302111yescharacteristic
911C23—21no—
912C23—21no—
913C23—21no—
914C23—22no—
915C23—21no—
916C23—21no—
917C23—22no—
918C23—22no—
919C23—41no—
920C23—41no—
921C23—42no—
922C23—42no—
923C23—44no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—81no—
932C23—82no—
933C23—82no—
934C23C7×#12011yescharacteristic
935C23C7×#12011yescharacteristic
936C23C22×C7×D411yescharacteristic
937Q8—21no—
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—42no—
943Q8C7×#12112yes—
944D4—22no—
945D4—22no—
946D4—21no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—42no—
952D4—42no—
953D4—44no—
954D4—42no—
955D4—44no—
956D4—44no—
957D4—42no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—81no—
971D4—82no—
972D4—82no—
973D4—82no—
974D4—82no—
975D4—88no—
976D4—82no—
977D4—82no—
978D4C7×#12112yes—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—44no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—42no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—42no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—82no—
1015C2×C4C7×#12011yescharacteristic
1016C2×C4C7×#12011yescharacteristic
1017C2×C4C22×C7×D411yescharacteristic
1018C2×C4C22×C7×D411yescharacteristic
1019C2×C4C22×C7×D411yescharacteristic
1020C2×C4C2×C7×#4111yescharacteristic
1021C2×C4C7×H(5,𝔽2)11yescharacteristic
1022C2×C4C7×H(5,𝔽2)11yescharacteristic
1023C8—22no—
1024C8—41no—
1025C8—41no—
1026C8—41no—
1027C7#2446811yescharacteristic, direct product factor, Sylow
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×C7×#12011yescharacteristic
1060C22C7×D4211yescharacteristic
1061C22C7×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×C7×#12111yescharacteristic
1074C4C7×#53411yescharacteristic
1075C4C7×D4211yescharacteristic
1076C4C7×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C7×#241011yescharacteristic
1087C2C7×#301911yescharacteristic
1088C2C7×#302111yescharacteristic
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. C2×C7×#421C2semidirect
6. C7×#2619C2semidirect
7. C7×#2040C2semidirect
8. C7×#2037C2semidirect
9. C7×#2006C2semidirect
10. C7×#2002C2semidirect
11. C7×#1900C2semidirect
12. C7×#1897C2semidirect
13. C7×#1883C2semidirect
14. C7×#1860C2semidirect
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
37. C2×C7×#121C22semidirect
39. C2×C7×#117C22semidirect
49. C7×#428C22semidirect
53. C2×C7×#104C22semidirect
54. C2×C7×#104C22semidirect
55. C2×C7×#104C22semidirect
56. C2×C7×#104C22semidirect
57. C7×#418C22semidirect
59. C7×#417C22semidirect
60. C7×#417C22semidirect
61. C2×C7×#100C22semidirect
62. C2×C7×#100C22semidirect
63. C7×#407C22semidirect
66. C7×#390C22semidirect
67. C7×#390C22semidirect
68. C7×#382C22semidirect
69. C7×#343C22semidirect
70. C7×#343C22semidirect
71. C7×#339C22semidirect
72. C7×#339C22semidirect
73. #24468C7direct (N × H)
86. C2×C7×#41D4semidirect
87. C2×C7×#41D4semidirect
91. C22×C7×Q8D4semidirect
100. C22×C7×D4D4semidirect
136. C7×C22⋊Q8D4semidirect
137. C7×C22⋊Q8D4semidirect
156. C7×#121D4semidirect
157. C7×#121D4semidirect
193. C7×#104D4semidirect
207. #3488C2×C7semidirect
208. #3055C2×C7semidirect
209. C2×#453C2×C7semidirect
210. #3006C2×C7semidirect
211. C2×#421C2×C7semidirect
212. #2619C2×C7semidirect
213. #2040C2×C7semidirect
214. #2037C2×C7semidirect
215. #2006C2×C7semidirect
216. #2002C2×C7semidirect
217. #1900C2×C7semidirect
218. #1897C2×C7semidirect
219. #1883C2×C7semidirect
220. #1860C2×C7semidirect
221. #1792C2×C7semidirect
343. C7×M16C2×D4semidirect
382. C42×C7C2×D4semidirect
386. C2×AGL(1,ℤ/8)C22×C7semidirect
387. C2×AGL(1,ℤ/8)C22×C7semidirect
388. C22×M16C22×C7semidirect
399. C2×#127C22×C7semidirect
404. C2×#121C22×C7semidirect
406. C2×#117C22×C7semidirect
416. #428C22×C7semidirect
420. C2×#104C22×C7semidirect
421. C2×#104C22×C7semidirect
422. C2×#104C22×C7semidirect
423. C2×#104C22×C7semidirect
424. #418C22×C7semidirect
426. #417C22×C7semidirect
427. #417C22×C7semidirect
428. C2×#100C22×C7semidirect
429. C2×#100C22×C7semidirect
430. #407C22×C7semidirect
433. #390C22×C7semidirect
434. #390C22×C7semidirect
435. #382C22×C7semidirect
436. #343C22×C7semidirect
437. #343C22×C7semidirect
438. #339C22×C7semidirect
439. #339C22×C7semidirect
568. C2×#41C7×D4semidirect
569. C2×#41C7×D4semidirect
573. C22×Q8C7×D4semidirect
582. C22×D4C7×D4semidirect
618. C22⋊Q8C7×D4semidirect
619. C22⋊Q8C7×D4semidirect
638. #121C7×D4semidirect
639. #121C7×D4semidirect
675. #104C7×D4semidirect
859. M16C2×C7×D4semidirect
898. C42C2×C7×D4semidirect
1027. C7#24468direct (N × H)

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
C2×C7×#4212
C7×#26192
C7×#20402
C7×#20372
C7×#20062
C7×#20022
C7×#19002
C7×#18972
C7×#18832
C7×#18602
C7×#17922
#244687