Finite Group Databasebeta

← C7×#25970 #13203186

Subgroups — C7×#25970 #13203186

Order 1792.

1032 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#474C211yesmaximal, characteristic, complemented
2C2×C7×#417C211yesmaximal, characteristic
3C7×#2440C211yesmaximal, characteristic, complemented
4C7×#2339C211yesmaximal, characteristic
5C7×#2095C211yesmaximal, characteristic, complemented
6C7×#2068C211yesmaximal, characteristic, complemented
7C7×#2066C211yesmaximal, characteristic, complemented
8C7×#2024C211yesmaximal, characteristic, complemented
9C7×#1864C211yesmaximal, characteristic, complemented
10C7×#1862C211yesmaximal, characteristic, complemented
11C7×#1852C211yesmaximal, characteristic, complemented
12C7×#1851C211yesmaximal, characteristic, complemented
13C7×#1809C211yesmaximal, characteristic, complemented
14C7×#1802C211yesmaximal, characteristic, complemented
15C7×#1788C211yesmaximal, characteristic
16C22×C7×#41C2211yescharacteristic
17C22×C7×M16C2211yescharacteristic
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C7×C22⋊Q8—21no—
20C2×C4×C7×D4C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C7×#474—24no—
24C2×C7×#107C2211yescharacteristic
25C2×C7×#107C2211yescharacteristic
26C2×C7×#107C2211yescharacteristic
27C2×C7×#106C2211yescharacteristic
28C2×C7×C4⋊C8C2211yescharacteristic
29C2×C7×C4⋊C8C2211yescharacteristic
30C7×#417—24no—
31C2×C7×#103C2211yescharacteristic
32C2×C7×#103C2211yescharacteristic
33C2×C7×#103C2211yescharacteristic
34C2×C7×#103C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C2×C7×#102C2211yescharacteristic
37C2×C7×#102C2211yescharacteristic
38C2×C7×#102C2211yescharacteristic
39C2×C7×C22⋊C8C2211yescharacteristic
40C7×#398—21no—
41C7×#395—21no—
42C7×#391C2211yescharacteristic
43C7×#391C2211yescharacteristic
44C7×#389C2211yescharacteristic
45C7×#389C2211yescharacteristic
46C7×#386—21no—
47C7×#386—21no—
48C7×#385—21no—
49C7×#384C2211yescharacteristic
50C7×#381—21no—
51C7×#380C2211yescharacteristic
52C7×#380C2211yescharacteristic
53C4×C7×C22⋊C4C2211yescharacteristic
54C2×C7×#95—21no—
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#336C2211yescharacteristic
60C7×#336C2211yescharacteristic
61#25970C711yesmaximal, characteristic, direct product factor, Sylow
62C2×C7×#41—22no—
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—41no—
66C2×C7×#41—41no—
67C2×C7×#41Q814yescomplemented
68C22×C7×Q8—21no—
69C22×C7×Q8C2311yescharacteristic
70C22×C7×D4—21no—
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7—21no—
74C23×C4×C7—21no—
75C23×C4×C7—21no—
76C23×C4×C7C2311yescharacteristic
77C2×C7×M16—22no—
78C2×C7×M16—22no—
79C2×C7×M16—41no—
80C22×C7×C8C2311yescharacteristic
81C22×C7×C8C2311yescharacteristic
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C7×C4⋊Q8—22no—
85C7×C4⋊Q8—41no—
86C7×C22⋊Q8—44no—
87C4×C7×D4—22no—
88C4×C7×D4—22no—
89C4×C7×D4—41no—
90C4×C7×D4—41no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—41no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4—21no—
107C2×C7×C22⋊C4—21no—
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4D411yescharacteristic
110C2×C7×C22⋊C4D411yescharacteristic
111C2×C42×C7C2311yescharacteristic
112C2×C42×C7C2311yescharacteristic
113C7×#107—22no—
114C7×#107—22no—
115C7×#107—41no—
116C7×#106—41no—
117C7×C4⋊C8—22no—
118C7×C4⋊C8—41no—
119C7×#103—22no—
120C7×#103—22no—
121C7×#103—41no—
122C7×#103—41no—
123C7×#102—22no—
124C7×#102—22no—
125C7×#102—22no—
126C7×#102D414yes—
127C7×C22⋊C8—22no—
128C7×#95—21no—
129C7×#95—21no—
130C7×#95—21no—
131C7×#95—21no—
132C7×#95—21no—
133C7×#95—21no—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95D411yescharacteristic
137C7×#95D411yescharacteristic
138C2×#474C2×C711yescharacteristic, complemented
139C2×#417C2×C711yescharacteristic
140#2440C2×C711yescharacteristic, complemented
141#2339C2×C711yescharacteristic
142#2095C2×C711yescharacteristic, complemented
143#2068C2×C711yescharacteristic, complemented
144#2066C2×C711yescharacteristic, complemented
145#2024C2×C711yescharacteristic, complemented
146#1864C2×C711yescharacteristic, complemented
147#1862C2×C711yescharacteristic, complemented
148#1852C2×C711yescharacteristic, complemented
149#1851C2×C711yescharacteristic, complemented
150#1809C2×C711yescharacteristic, complemented
151#1802C2×C711yescharacteristic, complemented
152#1788C2×C711yescharacteristic
153C24×C7—21no—
154C24×C7C2×D411yescharacteristic
155C7×#41—28no—
156C7×#41—44no—
157C7×#41—44no—
158C7×#41—44no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—42no—
165C2×C7×Q8—42no—
166C2×C7×Q8—81no—
167C2×C7×Q8C2×Q812yes—
168C2×C7×D4—24no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—42no—
173C2×C7×D4—42no—
174C2×C7×D4C2×D412yes—
175C2×C7×D4C2×Q812yes—
176C2×C7×D4#4112yes—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—24no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—42no—
190C22×C4×C7—42no—
191C22×C4×C7—42no—
192C22×C4×C7—42no—
193C22×C4×C7—42no—
194C22×C4×C7—42no—
195C22×C4×C7—42no—
196C22×C4×C7—42no—
197C22×C4×C7—81no—
198C22×C4×C7—81no—
199C22×C4×C7—81no—
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×Q812yes—
206C22×C4×C7#4112yes—
207C22×C4×C7C2411yescharacteristic
208C7×M16—44no—
209C2×C7×C8—21no—
210C2×C7×C8—21no—
211C2×C7×C8—21no—
212C2×C7×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8C2×D412yes—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—42no—
233C7×C4⋊C4—42no—
234C7×C4⋊C4—42no—
235C7×C4⋊C4—42no—
236C7×C4⋊C4—42no—
237C7×C4⋊C4—81no—
238C7×C4⋊C4C2×D412yes—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—22no—
241C7×C22⋊C4—42no—
242C7×C22⋊C4—42no—
243C7×C22⋊C4—42no—
244C7×C22⋊C4—81no—
245C42×C7—21no—
246C42×C7—21no—
247C42×C7—21no—
248C42×C7—21no—
249C22×#41C22×C711yescharacteristic
250C22×M16C22×C711yescharacteristic
251C2×C4⋊Q8C22×C711yescharacteristic
252C2×C22⋊Q8—21no—
253C2×C4×D4C22×C711yescharacteristic
254C2×C4×D4C22×C711yescharacteristic
255C22×C4⋊C4C22×C711yescharacteristic
256#474—24no—
257C2×#107C22×C711yescharacteristic
258C2×#107C22×C711yescharacteristic
259C2×#107C22×C711yescharacteristic
260C2×#106C22×C711yescharacteristic
261C2×C4⋊C8C22×C711yescharacteristic
262C2×C4⋊C8C22×C711yescharacteristic
263#417—24no—
264C2×#103C22×C711yescharacteristic
265C2×#103C22×C711yescharacteristic
266C2×#103C22×C711yescharacteristic
267C2×#103C22×C711yescharacteristic
268C2×#102C22×C711yescharacteristic
269C2×#102C22×C711yescharacteristic
270C2×#102C22×C711yescharacteristic
271C2×#102C22×C711yescharacteristic
272C2×C22⋊C8C22×C711yescharacteristic
273#398—21no—
274#395—21no—
275#391C22×C711yescharacteristic
276#391C22×C711yescharacteristic
277#389C22×C711yescharacteristic
278#389C22×C711yescharacteristic
279#386—21no—
280#386—21no—
281#385—21no—
282#384C22×C711yescharacteristic
283#381—21no—
284#380C22×C711yescharacteristic
285#380C22×C711yescharacteristic
286C4×C22⋊C4C22×C711yescharacteristic
287C2×#95—21no—
288#340C22×C711yescharacteristic
289#340C22×C711yescharacteristic
290#340C22×C711yescharacteristic
291#340C22×C711yescharacteristic
292#336C22×C711yescharacteristic
293#336C22×C711yescharacteristic
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—21no—
297C23×C7—22no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7C22⋊Q812yes—
308C23×C7C22×D411yescharacteristic
309C7×Q8—22no—
310C7×Q8—22no—
311C7×Q8—41no—
312C7×Q8—41no—
313C7×Q8—84no—
314C7×D4—22no—
315C7×D4—22no—
316C7×D4—22no—
317C7×D4—48no—
318C7×D4C22⋊Q814yescomplemented
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—21no—
324C2×C4×C7—21no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—21no—
331C2×C4×C7—22no—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—48no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—84no—
358C2×C4×C7—84no—
359C2×C4×C7—84no—
360C2×C4×C7C22⋊Q812yes—
361C2×C4×C7AGL(1,ℤ/8)12yes—
362C2×C4×C7#13712yes—
363C2×C4×C7C22×D411yescharacteristic
364C2×C4×C7C22×Q811yescharacteristic
365C2×C4×C7C2×#4111yescharacteristic
366C2×C4×C7C2×#4111yescharacteristic
367C2×C4×C7H(5,𝔽2)11yescharacteristic
368C2×C4×C7H(5,𝔽2)11yescharacteristic
369C7×C8—22no—
370C7×C8—41no—
371C7×C8—41no—
372C7×C8—41no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—41no—
377C2×#41—41no—
378C2×#41C7×Q814yescomplemented
379C22×Q8—21no—
380C22×Q8C23×C711yescharacteristic
381C22×D4—21no—
382C22×D4C23×C711yescharacteristic
383C23×C4—21no—
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—21no—
387C23×C4C23×C711yescharacteristic
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—41no—
391C22×C8C23×C711yescharacteristic
392C22×C8C23×C711yescharacteristic
393C22×C8C23×C711yescharacteristic
394C22×C8C23×C711yescharacteristic
395C4⋊Q8—22no—
396C4⋊Q8—41no—
397C22⋊Q8—44no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—41no—
401C4×D4—41no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4C23×C711yescharacteristic
411C2×C4⋊C4C23×C711yescharacteristic
412C2×C4⋊C4C23×C711yescharacteristic
413C2×C4⋊C4C23×C711yescharacteristic
414C2×C4⋊C4C23×C711yescharacteristic
415C2×C4⋊C4C23×C711yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4C7×D411yescharacteristic
421C2×C22⋊C4C7×D411yescharacteristic
422C2×C42C23×C711yescharacteristic
423C2×C42C23×C711yescharacteristic
424#107—22no—
425#107—22no—
426#107—41no—
427#106—41no—
428C4⋊C8—22no—
429C4⋊C8—41no—
430#103—22no—
431#103—22no—
432#103—41no—
433#103—41no—
434#102—22no—
435#102—22no—
436#102—22no—
437#102C7×D414yes—
438C22⋊C8—22no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95C7×D411yescharacteristic
448#95C7×D411yescharacteristic
449C22×C7—22no—
450C22×C7—22no—
451C22×C7—22no—
452C22×C7—24no—
453C22×C7—41no—
454C22×C7—42no—
455C22×C7—42no—
456C22×C7—42no—
457C22×C7—41no—
458C22×C7—42no—
459C22×C7—41no—
460C22×C7—42no—
461C22×C7—42no—
462C22×C7—41no—
463C22×C7C2×C22⋊Q811yescharacteristic
464C22×C7D4211yescharacteristic
465C22×C7#54611yescharacteristic
466C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C7C2×#13711yescharacteristic
468C22×C7#57611yescharacteristic
469C22×C7#57811yescharacteristic
470C4×C7—22no—
471C4×C7—22no—
472C4×C7—22no—
473C4×C7—41no—
474C4×C7—42no—
475C4×C7—42no—
476C4×C7—41no—
477C4×C7—81no—
478C4×C7—81no—
479C4×C7—81no—
480C4×C7—81no—
481C4×C7—81no—
482C4×C7C2×C22⋊Q811yescharacteristic
483C4×C7#54311yescharacteristic
484C4×C7#54611yescharacteristic
485C4×C7#55111yescharacteristic
486C24—21no—
487C24C2×C7×D411yescharacteristic
488#41—28no—
489#41—44no—
490#41—44no—
491#41—44no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—81no—
500C2×Q8C2×C7×Q812yes—
501C2×D4—24no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C2×C7×D412yes—
508C2×D4C2×C7×Q812yes—
509C2×D4C7×#4112yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4C2×C7×D411yescharacteristic
534C22×C4C2×C7×D411yescharacteristic
535C22×C4C2×C7×D411yescharacteristic
536C22×C4C2×C7×D411yescharacteristic
537C22×C4C2×C7×D411yescharacteristic
538C22×C4C2×C7×Q812yes—
539C22×C4C7×#4112yes—
540C22×C4C24×C711yescharacteristic
541M16—44no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8C2×C7×D412yes—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—81no—
571C4⋊C4C2×C7×D412yes—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C2×C7—42no—
583C2×C7—44no—
584C2×C7#243711yescharacteristic
585C2×C7#307911yescharacteristic
586C2×C7#308311yescharacteristic
587C2×C7#326411yescharacteristic
588C2×C7#327611yescharacteristic
589C2×C7#331411yescharacteristic
590C2×C7#333011yescharacteristic
591C23—22no—
592C23—22no—
593C23—21no—
594C23—22no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C7×C22⋊Q812yes—
605C23C22×C7×D411yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—41no—
609Q8—41no—
610Q8—84no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—48no—
615D4C7×C22⋊Q814yescomplemented
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4C7×C22⋊Q812yes—
658C2×C4C7×AGL(1,ℤ/8)12yes—
659C2×C4C7×#13712yes—
660C2×C4C22×C7×D411yescharacteristic
661C2×C4C22×C7×Q811yescharacteristic
662C2×C4C2×C7×#4111yescharacteristic
663C2×C4C2×C7×#4111yescharacteristic
664C2×C4C7×H(5,𝔽2)11yescharacteristic
665C2×C4C7×H(5,𝔽2)11yescharacteristic
666C8—22no—
667C8—41no—
668C8—41no—
669C8—41no—
670C7#2597011yescharacteristic, direct product factor, Sylow
671C22—22no—
672C22—24no—
673C22—22no—
674C22—22no—
675C22—41no—
676C22—42no—
677C22—41no—
678C22—42no—
679C22—42no—
680C22—41no—
681C22—41no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22C2×C7×C22⋊Q811yescharacteristic
686C22C7×D4211yescharacteristic
687C22C7×#54611yescharacteristic
688C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
689C22C2×C7×#13711yescharacteristic
690C22C7×#57611yescharacteristic
691C22C7×#57811yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C2×C7×C22⋊Q811yescharacteristic
705C4C7×#54311yescharacteristic
706C4C7×#54611yescharacteristic
707C4C7×#55111yescharacteristic
708C2—42no—
709C2—44no—
710C2C7×#243711yescharacteristic
711C2C7×#307911yescharacteristic
712C2C7×#308311yescharacteristic
713C2C7×#326411yescharacteristic
714C2C7×#327611yescharacteristic
715C2C7×#331411yescharacteristic
716C2C7×#333011yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C4×C7×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#474C2semidirect
3. C7×#2440C2semidirect
5. C7×#2095C2semidirect
6. C7×#2068C2semidirect
7. C7×#2066C2semidirect
8. C7×#2024C2semidirect
9. C7×#1864C2semidirect
10. C7×#1862C2semidirect
11. C7×#1852C2semidirect
12. C7×#1851C2semidirect
13. C7×#1809C2semidirect
14. C7×#1802C2semidirect
61. #25970C7direct (N × H)
67. C2×C7×#41Q8semidirect
138. C2×#474C2×C7semidirect
140. #2440C2×C7semidirect
142. #2095C2×C7semidirect
143. #2068C2×C7semidirect
144. #2066C2×C7semidirect
145. #2024C2×C7semidirect
146. #1864C2×C7semidirect
147. #1862C2×C7semidirect
148. #1852C2×C7semidirect
149. #1851C2×C7semidirect
150. #1809C2×C7semidirect
151. #1802C2×C7semidirect
318. C7×D4C22⋊Q8semidirect
378. C2×#41C7×Q8semidirect
615. D4C7×C22⋊Q8semidirect
670. C7#25970direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4742
C2×C7×#4172
C7×#24402
C7×#23392
C7×#20952
C7×#20682
C7×#20662
C7×#20242
C7×#18642
C7×#18622
C7×#18522
C7×#18512
C7×#18092
C7×#18022
C7×#17882
#259707