Finite Group Databasebeta

← C7×#24794 #13202010

Subgroups — C7×#24794 #13202010

Order 1792.

1026 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#468C211yesmaximal, characteristic, complemented
2C2×C7×#468C211yesmaximal, characteristic, complemented
3C2×C7×#436C211yesmaximal, characteristic, complemented
4C2×C7×#428C211yesmaximal, characteristic, complemented
5C7×#2416C211yesmaximal, characteristic
6C7×#2415C211yesmaximal, characteristic, complemented
7C7×#2067C211yesmaximal, characteristic, complemented
8C7×#2066C211yesmaximal, characteristic, complemented
9C7×#2036C211yesmaximal, characteristic, complemented
10C7×#2034C211yesmaximal, characteristic, complemented
11C7×#1968C211yesmaximal, characteristic, complemented
12C7×#1942C211yesmaximal, characteristic, complemented
13C7×#1875C211yesmaximal, characteristic, complemented
14C7×#1872C211yesmaximal, characteristic, complemented
15C7×#1809C211yesmaximal, characteristic, complemented
16C22×C7×SD16C2211yescharacteristic
17C22×C7×M16C2211yescharacteristic
18C22×C7×M16C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121—21no—
22C2×C7×#121C2211yescharacteristic
23C2×C7×#121C2211yescharacteristic
24C2×C4×C7×D4C2211yescharacteristic
25C2×C7×#117C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C7×#468—24no—
28C7×#468—24no—
29C7×#436—24no—
30C7×#428—24no—
31C2×C7×#107C2211yescharacteristic
32C2×C7×#107C2211yescharacteristic
33C2×C7×#107C2211yescharacteristic
34C2×C7×#106C2211yescharacteristic
35C2×C7×#106C2211yescharacteristic
36C2×C7×C4⋊C8C2211yescharacteristic
37C2×C7×#103C2211yescharacteristic
38C2×C7×#103C2211yescharacteristic
39C2×C7×#103C2211yescharacteristic
40C2×C7×#102C2211yescharacteristic
41C2×C7×#102C2211yescharacteristic
42C2×C7×#102C2211yescharacteristic
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×C22⋊C8C2211yescharacteristic
45C2×C4×C7×C8C2211yescharacteristic
46C7×#397—21no—
47C7×#396—21no—
48C7×#394—21no—
49C7×#394—21no—
50C7×#391C2211yescharacteristic
51C7×#390C2211yescharacteristic
52C7×#389—21no—
53C7×#389C2211yescharacteristic
54C7×#389C2211yescharacteristic
55C7×#388—21no—
56C7×#386—21no—
57C7×#380C2211yescharacteristic
58C7×#380C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#340C2211yescharacteristic
62C7×#340C2211yescharacteristic
63#24794C711yesmaximal, characteristic, direct product factor, Sylow
64C22×C7×Q8C2311yescharacteristic
65C22×C7×D4—21no—
66C22×C7×D4—21no—
67C22×C7×D4D411yescharacteristic
68C22×C7×D4C2311yescharacteristic
69C23×C4×C7—21no—
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C2×C7×SD16—22no—
73C2×C7×SD16—22no—
74C2×C7×SD16—22no—
75C2×C7×M16—22no—
76C2×C7×M16—22no—
77C2×C7×M16—22no—
78C2×C7×M16—22no—
79C2×C7×M16—22no—
80C2×C7×M16D414yescomplemented
81C22×C7×C8C2311yescharacteristic
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C7×C22⋊Q8—22no—
86C7×C22⋊Q8—22no—
87C7×C22⋊Q8—22no—
88C7×C22⋊Q8—41no—
89C7×#121—22no—
90C7×#121—22no—
91C7×#121—22no—
92C7×#121—41no—
93C7×#121—44no—
94C4×C7×D4—22no—
95C4×C7×D4—22no—
96C7×#117—22no—
97C7×#117—41no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—41no—
105C2×C7×C4⋊C4D411yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4D411yescharacteristic
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C42×C7—21no—
124C2×C42×C7C2311yescharacteristic
125C7×#107—22no—
126C7×#107—22no—
127C7×#107D414yescomplemented
128C7×#106—22no—
129C7×#106—22no—
130C7×C4⋊C8—22no—
131C7×#103—22no—
132C7×#103—22no—
133C7×#103—41no—
134C7×#102—22no—
135C7×#102—22no—
136C7×#102—41no—
137C7×C22⋊C8—22no—
138C7×C22⋊C8—22no—
139C4×C7×C8—22no—
140C7×#95—21no—
141C7×#95—21no—
142C7×#95—21no—
143C7×#95—21no—
144C7×#95—21no—
145C7×#95—21no—
146C2×#468C2×C711yescharacteristic, complemented
147C2×#468C2×C711yescharacteristic, complemented
148C2×#436C2×C711yescharacteristic, complemented
149C2×#428C2×C711yescharacteristic, complemented
150#2416C2×C711yescharacteristic
151#2415C2×C711yescharacteristic, complemented
152#2067C2×C711yescharacteristic, complemented
153#2066C2×C711yescharacteristic, complemented
154#2036C2×C711yescharacteristic, complemented
155#2034C2×C711yescharacteristic, complemented
156#1968C2×C711yescharacteristic, complemented
157#1942C2×C711yescharacteristic, complemented
158#1875C2×C711yescharacteristic, complemented
159#1872C2×C711yescharacteristic, complemented
160#1809C2×C711yescharacteristic, complemented
161C24×C7—21no—
162C24×C7C2×D411yescharacteristic
163C24×C7C2×D411yescharacteristic
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×D4—22no—
171C2×C7×D4—22no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—21no—
178C2×C7×D4—41no—
179C2×C7×D4—42no—
180C2×C7×D4—42no—
181C2×C7×D4—42no—
182C2×C7×D4—42no—
183C2×C7×D4—42no—
184C2×C7×D4—81no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—42no—
203C22×C4×C7—42no—
204C22×C4×C7—81no—
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7#4112yes—
211C22×C4×C7C2411yescharacteristic
212C7×SD16—44no—
213C7×M16—28no—
214C7×M16—44no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8C2×D412yes—
224C2×C7×C8C2×D412yes—
225C2×C7×C8C2×D412yes—
226C2×C7×C8#4112yes—
227C7×C4⋊C4—22no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—21no—
238C7×C4⋊C4—42no—
239C7×C4⋊C4—42no—
240C7×C4⋊C4—42no—
241C7×C4⋊C4—42no—
242C7×C4⋊C4—42no—
243C7×C4⋊C4C2×D412yes—
244C7×C4⋊C4C2×D412yes—
245C7×C22⋊C4—22no—
246C7×C22⋊C4—22no—
247C7×C22⋊C4—42no—
248C7×C22⋊C4—42no—
249C7×C22⋊C4—42no—
250C7×C22⋊C4—42no—
251C7×C22⋊C4—42no—
252C7×C22⋊C4—42no—
253C7×C22⋊C4—42no—
254C7×C22⋊C4—42no—
255C7×C22⋊C4—81no—
256C42×C7—21no—
257C42×C7—21no—
258C42×C7—42no—
259C22×SD16C22×C711yescharacteristic
260C22×M16C22×C711yescharacteristic
261C22×M16C22×C711yescharacteristic
262C2×C22⋊Q8C22×C711yescharacteristic
263C2×C22⋊Q8C22×C711yescharacteristic
264C2×#121—21no—
265C2×#121C22×C711yescharacteristic
266C2×#121C22×C711yescharacteristic
267C2×C4×D4C22×C711yescharacteristic
268C2×#117C22×C711yescharacteristic
269C22×C4⋊C4C22×C711yescharacteristic
270#468—24no—
271#468—24no—
272#436—24no—
273#428—24no—
274C2×#107C22×C711yescharacteristic
275C2×#107C22×C711yescharacteristic
276C2×#107C22×C711yescharacteristic
277C2×#106C22×C711yescharacteristic
278C2×#106C22×C711yescharacteristic
279C2×C4⋊C8C22×C711yescharacteristic
280C2×#103C22×C711yescharacteristic
281C2×#103C22×C711yescharacteristic
282C2×#103C22×C711yescharacteristic
283C2×#102C22×C711yescharacteristic
284C2×#102C22×C711yescharacteristic
285C2×#102C22×C711yescharacteristic
286C2×C22⋊C8C22×C711yescharacteristic
287C2×C22⋊C8C22×C711yescharacteristic
288C2×C4×C8C22×C711yescharacteristic
289#397—21no—
290#396—21no—
291#394—21no—
292#394—21no—
293#391C22×C711yescharacteristic
294#390C22×C711yescharacteristic
295#389—21no—
296#389C22×C711yescharacteristic
297#389C22×C711yescharacteristic
298#388—21no—
299#386—21no—
300#380C22×C711yescharacteristic
301#380C22×C711yescharacteristic
302#340C22×C711yescharacteristic
303#340C22×C711yescharacteristic
304#340C22×C711yescharacteristic
305#340C22×C711yescharacteristic
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—21no—
316C23×C7—21no—
317C23×C7—21no—
318C23×C7—21no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7#12112yes—
327C23×C7C22×D411yescharacteristic
328C7×Q8—41no—
329C7×Q8—41no—
330C7×Q8—41no—
331C7×Q8—41no—
332C7×D4—44no—
333C7×D4—41no—
334C7×D4—41no—
335C7×D4—41no—
336C7×D4—41no—
337C7×D4—84no—
338C7×D4—84no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—22no—
350C2×C4×C7—21no—
351C2×C4×C7—22no—
352C2×C4×C7—21no—
353C2×C4×C7—21no—
354C2×C4×C7—21no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—84no—
379C2×C4×C7#12112yes—
380C2×C4×C7AGL(1,ℤ/8)12yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C2×#4111yescharacteristic
384C2×C4×C7C2×#4111yescharacteristic
385C2×C4×C7H(5,𝔽2)11yescharacteristic
386C2×C4×C72−1+411yescharacteristic
387C7×C8—22no—
388C7×C8—41no—
389C7×C8—41no—
390C7×C8#12114yescomplemented
391C22×Q8C23×C711yescharacteristic
392C22×D4—21no—
393C22×D4—21no—
394C22×D4C7×D411yescharacteristic
395C22×D4C23×C711yescharacteristic
396C23×C4—21no—
397C23×C4C23×C711yescharacteristic
398C23×C4C23×C711yescharacteristic
399C2×SD16—22no—
400C2×SD16—22no—
401C2×SD16—22no—
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—22no—
407C2×M16C7×D414yescomplemented
408C22×C8C23×C711yescharacteristic
409C22×C8C23×C711yescharacteristic
410C22×C8C23×C711yescharacteristic
411C22×C8C23×C711yescharacteristic
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—41no—
416#121—22no—
417#121—22no—
418#121—22no—
419#121—41no—
420#121—44no—
421C4×D4—22no—
422C4×D4—22no—
423#117—22no—
424#117—41no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4C7×D411yescharacteristic
433C2×C4⋊C4C23×C711yescharacteristic
434C2×C4⋊C4C23×C711yescharacteristic
435C2×C4⋊C4C23×C711yescharacteristic
436C2×C4⋊C4C23×C711yescharacteristic
437C2×C4⋊C4C23×C711yescharacteristic
438C2×C4⋊C4C23×C711yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4C7×D411yescharacteristic
449C2×C22⋊C4C7×D411yescharacteristic
450C2×C42—21no—
451C2×C42C23×C711yescharacteristic
452#107—22no—
453#107—22no—
454#107C7×D414yescomplemented
455#106—22no—
456#106—22no—
457C4⋊C8—22no—
458#103—22no—
459#103—22no—
460#103—41no—
461#102—22no—
462#102—22no—
463#102—41no—
464C22⋊C8—22no—
465C22⋊C8—22no—
466C4×C8—22no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—22no—
476C22×C7—41no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—41no—
481C22×C7—41no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—41no—
487C22×C7—81no—
488C22×C7—81no—
489C22×C7—81no—
490C22×C7—81no—
491C22×C7—81no—
492C22×C7—81no—
493C22×C7—81no—
494C22×C7C2×#12111yescharacteristic
495C22×C7D4211yescharacteristic
496C22×C7#54711yescharacteristic
497C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
498C22×C7#57511yescharacteristic
499C22×C7#57711yescharacteristic
500C22×C7#57811yescharacteristic
501C4×C7—22no—
502C4×C7—22no—
503C4×C7—41no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7—41no—
507C4×C7—81no—
508C4×C7—81no—
509C4×C7—81no—
510C4×C7—81no—
511C4×C7—81no—
512C4×C7C2×#12111yescharacteristic
513C4×C7#53711yescharacteristic
514C4×C7#54811yescharacteristic
515C4×C7#55311yescharacteristic
516C24—21no—
517C24C2×C7×D411yescharacteristic
518C24C2×C7×D411yescharacteristic
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—41no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—81no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—81no—
560C22×C4C2×C7×D411yescharacteristic
561C22×C4C2×C7×D411yescharacteristic
562C22×C4C2×C7×D411yescharacteristic
563C22×C4C2×C7×D412yes—
564C22×C4C2×C7×D411yescharacteristic
565C22×C4C7×#4112yes—
566C22×C4C24×C711yescharacteristic
567SD16—44no—
568M16—28no—
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8C2×C7×D412yes—
579C2×C8C2×C7×D412yes—
580C2×C8C2×C7×D412yes—
581C2×C8C7×#4112yes—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4C2×C7×D412yes—
599C4⋊C4C2×C7×D412yes—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C42—21no—
612C42—21no—
613C42—42no—
614C2×C7—42no—
615C2×C7—81no—
616C2×C7—161no—
617C2×C7#241611yescharacteristic
618C2×C7#305511yescharacteristic
619C2×C7#306311yescharacteristic
620C2×C7#327211yescharacteristic
621C2×C7#327711yescharacteristic
622C2×C7#335111yescharacteristic
623C2×C7#335311yescharacteristic
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23C7×#12112yes—
645C23C22×C7×D411yescharacteristic
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650D4—44no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—84no—
656D4—84no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—84no—
697C2×C4C7×#12112yes—
698C2×C4C7×AGL(1,ℤ/8)12yes—
699C2×C4C22×C7×D411yescharacteristic
700C2×C4C22×C7×D411yescharacteristic
701C2×C4C2×C7×#4111yescharacteristic
702C2×C4C2×C7×#4111yescharacteristic
703C2×C4C7×H(5,𝔽2)11yescharacteristic
704C2×C4C7×2−1+411yescharacteristic
705C8—22no—
706C8—41no—
707C8—41no—
708C8C7×#12114yescomplemented
709C7#2479411yescharacteristic, direct product factor, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×C7×#12111yescharacteristic
732C22C7×D4211yescharacteristic
733C22C7×#54711yescharacteristic
734C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
735C22C7×#57511yescharacteristic
736C22C7×#57711yescharacteristic
737C22C7×#57811yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—42no—
742C4—42no—
743C4—41no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C2×C7×#12111yescharacteristic
750C4C7×#53711yescharacteristic
751C4C7×#54811yescharacteristic
752C4C7×#55311yescharacteristic
753C2—42no—
754C2—81no—
755C2—161no—
756C2C7×#241611yescharacteristic
757C2C7×#305511yescharacteristic
758C2C7×#306311yescharacteristic
759C2C7×#327211yescharacteristic
760C2C7×#327711yescharacteristic
761C2C7×#335111yescharacteristic
762C2C7×#335311yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#468C2semidirect
2. C2×C7×#468C2semidirect
3. C2×C7×#436C2semidirect
4. C2×C7×#428C2semidirect
6. C7×#2415C2semidirect
7. C7×#2067C2semidirect
8. C7×#2066C2semidirect
9. C7×#2036C2semidirect
10. C7×#2034C2semidirect
11. C7×#1968C2semidirect
12. C7×#1942C2semidirect
13. C7×#1875C2semidirect
14. C7×#1872C2semidirect
15. C7×#1809C2semidirect
63. #24794C7direct (N × H)
80. C2×C7×M16D4semidirect
127. C7×#107D4semidirect
146. C2×#468C2×C7semidirect
147. C2×#468C2×C7semidirect
148. C2×#436C2×C7semidirect
149. C2×#428C2×C7semidirect
151. #2415C2×C7semidirect
152. #2067C2×C7semidirect
153. #2066C2×C7semidirect
154. #2036C2×C7semidirect
155. #2034C2×C7semidirect
156. #1968C2×C7semidirect
157. #1942C2×C7semidirect
158. #1875C2×C7semidirect
159. #1872C2×C7semidirect
160. #1809C2×C7semidirect
390. C7×C8#121semidirect
407. C2×M16C7×D4semidirect
454. #107C7×D4semidirect
708. C8C7×#121semidirect
709. C7#24794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4682
C2×C7×#4362
C2×C7×#4282
C7×#24162
C7×#24152
C7×#20672
C7×#20662
C7×#20362
C7×#20342
C7×#19682
C7×#19422
C7×#18752
C7×#18722
C7×#18092
#247947