Finite Group Databasebeta

← C2×#11743827 #14261960

Subgroups — C2×#11743827 #14261960

Order 1792.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6551C211yesmaximal, characteristic, complemented
2C23×Q8×D7C211yesmaximal, characteristic, complemented
3C2×C7×D4×Q8C211yesmaximal, characteristic, complemented
4C2×#90508C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D7C211yesmaximal, characteristic, complemented
6#11743827C2132yesmaximal, direct product factor
7C2×#90418C213yesmaximal, complemented
8C2×#90415C213yesmaximal, complemented
9C2×#90324C213yesmaximal, complemented
10C2×#90319C213yesmaximal, complemented
11C2×#90323C213yesmaximal, complemented
12C2×#90318C213yesmaximal, complemented
13C2×#90267C211yesmaximal, characteristic, complemented
14C2×#90263C211yesmaximal, characteristic, complemented
15C2×#90238C213yesmaximal, complemented
16C2×#90243C213yesmaximal, complemented
17C23×C7×Q8C2211yescharacteristic
18C23×C7×Q8C2211yescharacteristic, complemented
19C2×#6551—216no—
20C2×#6551C22116yescomplemented
21C22×#1161C2213yes—
22C22×#1161C2211yescharacteristic, complemented
23C22×Q8×D7—216no—
24C22×Q8×D7C2213yes—
25C22×Q8×D7C2213yes—
26C22×Q8×D7C2211yescharacteristic
27C22×Q8×D7C2211yescharacteristic
28C22×Q8×D7C22116yescomplemented
29C22×Q8×D7C2213yescomplemented
30C22×#1157C2213yes—
31C22×#1157C2213yescomplemented
32C23×C4×D7C2213yes—
33C23×Dic14C2213yes—
34C7×D4×Q8C22116yescomplemented
35C2×C7×C4⋊Q8C2213yescomplemented
36C2×C7×C22⋊Q8C2213yes—
37C2×C7×C22⋊Q8C2213yescomplemented
38C2×C4×C7×Q8C2211yescharacteristic, complemented
39C2×C4×C7×D4C2213yes—
40#90508C22116yescomplemented
41Q8×C22⋊D7C22116yescomplemented
42C2×#6510C2213yescomplemented
43C2×#6509C2213yes—
44C2×#6509C2213yescomplemented
45C2×Q8×Dic7C2211yescharacteristic, complemented
46C2×#6507C2213yescomplemented
47C2×#6502C2213yes—
48C2×#6500C2211yescharacteristic
49C2×#6493C2213yes—
50C2×C4×C22⋊D7C2213yes—
51C2×C4×C22⋊D7C2213yes—
52C2×#6487C2213yescomplemented
53#90418C22148yescomplemented
54#90415C22148yescomplemented
55#90324C22148yescomplemented
56#90323C22148yescomplemented
57#90319C22148yescomplemented
58#90318C22148yescomplemented
59#90267C22116yescomplemented
60#90263C22116yescomplemented
61#90243C22148yescomplemented
62#90238C22148yescomplemented
63C2×#6460C2213yescomplemented
64C2×#6459C2213yes—
65C2×#6459C2216yescomplemented
66C2×#6459C2216yescomplemented
67C2×#6458C2213yes—
68C2×#6457C2213yes—
69C2×#6457C2216yes—
70C2×#6456C2216yes—
71C2×#6455C2213yes—
72C2×#6451C2216yescomplemented
73C2×#6450C2213yescomplemented
74C2×#6448C2216yescomplemented
75C2×#6447C2213yes—
76C2×#6446C2213yes—
77C2×#6445C2213yes—
78C2×(C22⋊D7)⋊C4C2216yes—
79C2×#6441C2213yes—
80C2×#6438C2213yescomplemented
81C2×C4×D28C2213yes—
82C2×#6435C2213yes—
83C2×C4×Dic14C2213yescomplemented
84C2×#3486—71nomaximal, Sylow
85C24×D7C2311yescharacteristic
86C22×C7×Q8—28no—
87C22×C7×Q8—28no—
88C22×C7×Q8C2313yes—
89C22×C7×Q8C2318yes—
90C22×C7×Q8C2313yes—
91C22×C7×Q8C2311yescharacteristic
92C22×C7×Q8C2318yescomplemented
93C22×C7×D4C2311yescharacteristic
94C23×C4×C7C2313yes—
95C23×C4×C7C2313yes—
96C22×C22⋊D7C2313yes—
97C22×C22⋊D7C2311yescharacteristic
98C22×C22⋊D7C2311yescharacteristic
99C22×C22⋊D7C2313yes—
100C23×Dic7C2313yes—
101#6551—2128no—
102C2×#1161—28no—
103C2×#1161—224no—
104C2×#1161C23124yes—
105C2×#1161C2318yescomplemented
106C2×Q8×D7—28no—
107C2×Q8×D7—2128no—
108C2×Q8×D7—224no—
109C2×Q8×D7—224no—
110C2×Q8×D7—224no—
111C2×Q8×D7D4116yescomplemented
112C2×Q8×D7C23124yes—
113C2×Q8×D7C23124yes—
114C2×Q8×D7C2318yes—
115C2×Q8×D7C2318yes—
116C2×Q8×D7C23124yescomplemented
117C2×#1157—224no—
118C2×#1157—224no—
119C2×#1157C23124yes—
120C2×#1157C23124yescomplemented
121C22×D28C2313yes—
122C22×D28C2313yes—
123C22×D28C2313yes—
124C22×C4×D7—224no—
125C22×C4×D7C2313yes—
126C22×C4×D7C2313yes—
127C22×C4×D7C2316yes—
128C22×C4×D7C2313yes—
129C22×C4×D7C2313yes—
130C22×C4×D7C23124yes—
131C22×C4×D7C2313yes—
132C22×Dic14—224no—
133C22×Dic14C2313yes—
134C22×Dic14C2313yes—
135C22×Dic14C2316yes—
136C22×Dic14C23124yes—
137C22×Dic14C2313yes—
138C7×C4⋊Q8C23124yescomplemented
139C7×C22⋊Q8C23124yes—
140C7×C22⋊Q8C23124yescomplemented
141C4×C7×Q8C2318yescomplemented
142C4×C7×D4C23124yes—
143C2×C7×C4⋊C4C2313yes—
144C2×C7×C4⋊C4C2316yes—
145C2×C7×C4⋊C4C2313yes—
146C2×C7×C22⋊C4C2313yes—
147C2×C7×C22⋊C4C2313yes—
148C2×C42×C7C2313yes—
149C2×C22⋊Dic7C2311yescharacteristic
150C2×C22⋊Dic7C2313yes—
151#6510C23124yescomplemented
152#6509C23124yes—
153#6509C23124yescomplemented
154Q8×Dic7C2318yescomplemented
155#6507C23124yescomplemented
156#6502C23124yes—
157#6500C2318yes—
158#6493C23124yes—
159C4×C22⋊D7C23124yes—
160C4×C22⋊D7C23124yes—
161C2×(C2×D7)⋊C4C2311yescharacteristic
162C2×(C2×D7)⋊C4C2313yes—
163C2×(C2×D7)⋊C4C2311yescharacteristic
164C2×(C2×D7)⋊C4C2313yes—
165C2×(C2×D7)⋊C4C2316yes—
166C2×(C2×D7)⋊C4C2313yes—
167C2×(C2×D7)⋊C4C2313yes—
168C2×(C2×D7)⋊C4C2316yes—
169C2×C4⋊Dic7C2313yes—
170C2×C4⋊Dic7C2313yes—
171#6487C23124yescomplemented
172C2×Dic7⋊C4C2313yes—
173C2×Dic7⋊C4C2313yes—
174C2×Dic7⋊C4C2313yes—
175C2×Dic7⋊C4C2316yes—
176C2×Dic7⋊C4C2313yes—
177C2×C4×Dic7C2316yes—
178C2×C4×Dic7C2313yes—
179#6460C23124yescomplemented
180#6459C23124yes—
181#6459C23148yescomplemented
182#6459C23148yescomplemented
183#6458C23124yes—
184#6457C23124yes—
185#6457C23148yes—
186#6456C23148yes—
187#6455C23124yes—
188#6451C23148yescomplemented
189#6450C23124yescomplemented
190#6448C23148yescomplemented
191#6447C23124yes—
192#6446C23124yes—
193#6445C23124yes—
194(C22⋊D7)⋊C4C23148yes—
195#6441C23124yes—
196#6438C23124yescomplemented
197C4×D28C23124yes—
198#6435C23124yes—
199C4×Dic14C23124yescomplemented
200C22×2−1+4—71no—
201C24×Q8—71no—
202#3486—732no—
203C2×D4×Q8—71no—
204C2×D4×Q8—73no—
205C2×D4×Q8—73no—
206C2×D4×Q8D711yescharacteristic, complemented
207C2×#548—71no—
208C2×#548—73no—
209C2×#548—71no—
210C2×#548—73no—
211C2×#536—73no—
212C2×#536—73no—
213C2×#525—73no—
214C2×#525—73no—
215C2×#519—71no—
216C24×C7C2411yescharacteristic
217C24×C7C2411yescharacteristic
218C23×D7—24no—
219C23×D7—24no—
220C23×D7—24no—
221C23×D7C2414yes—
222C23×D7C2413yes—
223C23×D7C2411yescharacteristic
224C23×D7C2411yescharacteristic
225C2×C7×Q8—232no—
226C2×C7×Q8—232no—
227C2×C7×Q8—212no—
228C2×C7×Q8—212no—
229C2×C7×Q8C2×D418yes—
230C2×C7×Q8C24112yes—
231C2×C7×Q8C24112yes—
232C2×C7×Q8C2414yes—
233C2×C7×D4—24no—
234C2×C7×D4C2414yes—
235C22×C4×C7—212no—
236C22×C4×C7—212no—
237C22×C4×C7C2413yes—
238C22×C4×C7C2411yescharacteristic
239C22×C4×C7C2413yes—
240C22×C4×C7C2413yes—
241C22×C4×C7C24112yes—
242C22×C4×C7C24112yes—
243C22×C4×C7C2413yes—
244C2×C22⋊D7—212no—
245C2×C22⋊D7—24no—
246C2×C22⋊D7—24no—
247C2×C22⋊D7—212no—
248C2×C22⋊D7C24112yes—
249C2×C22⋊D7C2414yes—
250C2×C22⋊D7C2414yes—
251C2×C22⋊D7C24112yes—
252C22×Dic7—212no—
253C22×Dic7C24112yes—
254C22×Dic7C2411yescharacteristic
255C22×Dic7C2413yes—
256C22×Dic7C2411yescharacteristic
257C22×Dic7C2413yes—
258C22×Dic7C2413yes—
259#1161—232no—
260#1161—296no—
261Q8×D7—232no—
262Q8×D7—296no—
263Q8×D7—296no—
264Q8×D7—296no—
265Q8×D7C2×D4164yescomplemented
266#1157—296no—
267#1157—296no—
268C2×D28—212no—
269C2×D28—212no—
270C2×D28—212no—
271C2×D28C24112yes—
272C2×D28C24112yes—
273C2×D28C24112yes—
274C2×C4×D7—212no—
275C2×C4×D7—212no—
276C2×C4×D7—212no—
277C2×C4×D7—212no—
278C2×C4×D7—224no—
279C2×C4×D7—296no—
280C2×C4×D7C2×D4124yes—
281C2×C4×D7C24112yes—
282C2×C4×D7C24112yes—
283C2×C4×D7C24124yes—
284C2×C4×D7C24112yes—
285C2×C4×D7C24112yes—
286C2×C4×D7C24112yes—
287C2×Dic14—212no—
288C2×Dic14—224no—
289C2×Dic14—212no—
290C2×Dic14—296no—
291C2×Dic14C2×D4124yes—
292C2×Dic14C24112yes—
293C2×Dic14C24112yes—
294C2×Dic14C24124yes—
295C2×Dic14C24112yes—
296C7×C4⋊C4C24112yes—
297C7×C4⋊C4C24124yes—
298C7×C4⋊C4C24112yes—
299C7×C22⋊C4C24112yes—
300C7×C22⋊C4C24112yes—
301C42×C7C24112yes—
302C22⋊Dic7C2414yes—
303C22⋊Dic7C24112yes—
304(C2×D7)⋊C4C2414yes—
305(C2×D7)⋊C4C24112yes—
306(C2×D7)⋊C4C2414yes—
307(C2×D7)⋊C4C24112yes—
308(C2×D7)⋊C4C24124yes—
309(C2×D7)⋊C4C24112yes—
310(C2×D7)⋊C4C24112yes—
311(C2×D7)⋊C4C24124yes—
312C4⋊Dic7C24112yes—
313C4⋊Dic7C24112yes—
314Dic7⋊C4C24112yes—
315Dic7⋊C4C24112yes—
316Dic7⋊C4C24112yes—
317Dic7⋊C4C24124yes—
318Dic7⋊C4C24112yes—
319C4×Dic7C24124yes—
320C4×Dic7C24112yes—
321C2×2−1+4—716no—
322C2×2−1+4—1416no—
323C22×#41—73no—
324C22×#41—71no—
325C22×#41—73no—
326C22×#41—73no—
327C23×Q8—71no—
328C23×Q8—73no—
329C23×Q8—73no—
330C23×Q8—71no—
331C23×Q8—716no—
332C23×Q8—73no—
333C23×Q8—73no—
334C23×Q8—1416no—
335C23×Q8C2×D711yescharacteristic
336C23×Q8C2×D711yescharacteristic, complemented
337C24×C4—73no—
338D4×Q8—716no—
339D4×Q8—748no—
340D4×Q8—748no—
341D4×Q8C2×D7116yescomplemented
342#548—716no—
343#548—748no—
344#548—716no—
345#548—748no—
346#536—748no—
347#536—748no—
348C2×C4⋊Q8—73no—
349C2×C4⋊Q8—76no—
350C2×C4⋊Q8C2×D713yescomplemented
351C2×#124—73no—
352C2×#124—76no—
353C2×#124—73no—
354#525—748no—
355#525—748no—
356C2×#123—76no—
357C2×#123—73no—
358C2×#123—73no—
359C2×C22⋊Q8—73no—
360C2×C22⋊Q8—73no—
361C2×C22⋊Q8—73no—
362C2×C22⋊Q8—73no—
363C2×C22⋊Q8—76no—
364C2×C22⋊Q8—76no—
365C2×C22⋊Q8—73no—
366C2×C22⋊Q8—73no—
367C2×C22⋊Q8C2×D713yes—
368C2×C22⋊Q8C2×D713yescomplemented
369C2×#121—73no—
370C2×#121—73no—
371C2×#121—73no—
372C2×#121—73no—
373C2×#120—71no—
374C2×#120—73no—
375#519—716no—
376C2×C4×Q8—71no—
377C2×C4×Q8—73no—
378C2×C4×Q8—73no—
379C2×C4×Q8C2×D711yescharacteristic, complemented
380C2×C4×D4—73no—
381C2×C4×D4—73no—
382C2×C4×D4—76no—
383C2×C4×D4—76no—
384C2×C4×D4—73no—
385C2×C4×D4C2×D713yes—
386C2×#117—73no—
387C2×#117—73no—
388C23×C7—22no—
389C23×C7—22no—
390C23×C7—22no—
391C23×C7—22no—
392C23×C7—22no—
393C23×C72−1+414yescomplemented
394C23×C7C2512yes—
395C23×C7C2512yes—
396C23×C7C2511yescharacteristic
397C22×D7—232no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—28no—
403C22×D7—28no—
404C22×D7—28no—
405C22×D7—26no—
406C22×D7—26no—
407C22×D7—26no—
408C22×D7C22×D414yes—
409C22×D72−1+414yescomplemented
410C22×D7C2516yes—
411C22×D7C2512yes—
412C22×D7C2512yes—
413C7×Q8—224no—
414C7×Q8—224no—
415C7×Q8C22×D4116yes—
416C7×D4—28no—
417C2×C4×C7—26no—
418C2×C4×C7—26no—
419C2×C4×C7—26no—
420C2×C4×C7—22no—
421C2×C4×C7—224no—
422C2×C4×C7—224no—
423C2×C4×C7C22×D4112yes—
424C2×C4×C7C2516yes—
425C2×C4×C7C2512yes—
426C2×C4×C7C2516yes—
427C2×C4×C7C2516yes—
428C2×C4×C7C2516yes—
429C22⋊D7—224no—
430C22⋊D7—28no—
431C22⋊D7—28no—
432C22⋊D7—224no—
433C2×Dic7—26no—
434C2×Dic7—22no—
435C2×Dic7—26no—
436C2×Dic7—22no—
437C2×Dic7—224no—
438C2×Dic7C22×D4112yes—
439C2×Dic7C2512yes—
440C2×Dic7C2516yes—
441C2×Dic7C2512yes—
442C2×Dic7C2516yes—
443C2×Dic7C2516yes—
444D28—224no—
445D28—224no—
446D28—224no—
447C4×D7—224no—
448C4×D7—224no—
449C4×D7—224no—
450C4×D7—224no—
451C4×D7—248no—
452C4×D7C22×D4148yes—
453Dic14—224no—
454Dic14—248no—
455Dic14—224no—
456Dic14C22×D4148yes—
457C25—71no—
4582−1+4—14128no—
459C2×#41—724no—
460C2×#41—78no—
461C2×#41—724no—
462C2×#41—724no—
463C2×#41—1424no—
464C2×#41—1424no—
465C2×#41—1424no—
466C2×#41—148no—
467C22×Q8—28no—
468C22×Q8—28no—
469C22×Q8—716no—
470C22×Q8—78no—
471C22×Q8—724no—
472C22×Q8—724no—
473C22×Q8—78no—
474C22×Q8—724no—
475C22×Q8—73no—
476C22×Q8—76no—
477C22×Q8—73no—
478C22×Q8—73no—
479C22×Q8—724no—
480C22×Q8—1424no—
481C22×Q8—1424no—
482C22×Q8—14128no—
483C22×Q8—1424no—
484C22×Q8—1424no—
485C22×Q8—148no—
486C22×Q8C22×D713yes—
487C22×Q8C22×D713yes—
488C22×Q8C22×D718yes—
489C22×Q8C22×D711yescharacteristic
490C22×Q8C22×D718yescomplemented
491C22×D4—71no—
492C22×D4—73no—
493C22×D4—71no—
494C22×D4—73no—
495C22×D4—73no—
496C22×D4—73no—
497C22×D4—73no—
498C22×D4C22×D711yescharacteristic
499C23×C4—73no—
500C23×C4—73no—
501C23×C4—73no—
502C23×C4—73no—
503C23×C4—76no—
504C23×C4—73no—
505C23×C4—73no—
506C23×C4—724no—
507C23×C4—1424no—
508C23×C4C22×D713yes—
509C23×C4C22×D713yes—
510C4⋊Q8—724no—
511C4⋊Q8—748no—
512C4⋊Q8C22×D7124yescomplemented
513#124—724no—
514#124—748no—
515#124—724no—
516#123—748no—
517#123—724no—
518#123—724no—
519C22⋊Q8—724no—
520C22⋊Q8—724no—
521C22⋊Q8—724no—
522C22⋊Q8—724no—
523C22⋊Q8—748no—
524C22⋊Q8—748no—
525C22⋊Q8—724no—
526C22⋊Q8—724no—
527C22⋊Q8C22×D7124yes—
528C22⋊Q8C22×D7124yescomplemented
529#121—724no—
530#121—724no—
531#121—724no—
532#121—724no—
533#120—78no—
534#120—724no—
535C4×Q8—78no—
536C4×Q8—724no—
537C4×Q8—724no—
538C4×Q8C22×D718yescomplemented
539C4×D4—724no—
540C4×D4—724no—
541C4×D4—748no—
542C4×D4—748no—
543C4×D4—724no—
544C4×D4C22×D7124yes—
545#117—724no—
546#117—724no—
547C2×C4⋊C4—73no—
548C2×C4⋊C4—73no—
549C2×C4⋊C4—73no—
550C2×C4⋊C4—73no—
551C2×C4⋊C4—76no—
552C2×C4⋊C4—73no—
553C2×C4⋊C4—73no—
554C2×C4⋊C4C22×D713yes—
555C2×C4⋊C4C22×D716yes—
556C2×C4⋊C4C22×D713yes—
557C2×C22⋊C4—71no—
558C2×C22⋊C4—73no—
559C2×C22⋊C4—73no—
560C2×C22⋊C4—71no—
561C2×C22⋊C4—73no—
562C2×C22⋊C4—71no—
563C2×C22⋊C4—73no—
564C2×C22⋊C4—76no—
565C2×C22⋊C4—76no—
566C2×C22⋊C4—73no—
567C2×C22⋊C4C22×D713yes—
568C2×C22⋊C4C22×D713yes—
569C2×C42—76no—
570C2×C42—73no—
571C2×C42C22×D713yes—
572C22×C7—22no—
573C22×C7—22no—
574C22×C7—28no—
575C22×C7—22no—
576C22×C7—22no—
577C22×C7—22no—
578C22×C7—44no—
579C22×C7C23×D412yes—
580C22×C7C2×2−1+412yes—
581C22×C7C2×2−1+412yes—
582C22×C7C2×2−1+414yescomplemented
583C22×C7C2611yescharacteristic
584C2×D7—232no—
585C2×D7—22no—
586C2×D7—22no—
587C2×D7—22no—
588C2×D7—22no—
589C2×D7—28no—
590C2×D7—28no—
591C2×D7—26no—
592C2×D7—26no—
593C2×D7—26no—
594C2×D7—412no—
595C2×D7C23×D414yes—
596C2×D7C2×2−1+414yescomplemented
597C4×C7—26no—
598C4×C7—26no—
599C4×C7—26no—
600C4×C7—22no—
601C4×C7C23×D4112yes—
602Dic7—26no—
603Dic7—22no—
604Dic7—26no—
605Dic7—22no—
606Dic7C23×D4112yes—
607C24—71no—
608C24—71no—
609C24—74no—
610C24—73no—
611C24—144no—
612C24—144no—
613C24—144no—
614C24C23×D711yescharacteristic
615C24C23×D711yescharacteristic
616#41—1496no—
617#41—1496no—
618#41—1496no—
619#41—1432no—
620C2×Q8—232no—
621C2×Q8—232no—
622C2×Q8—212no—
623C2×Q8—212no—
624C2×Q8—764no—
625C2×Q8—724no—
626C2×Q8—712no—
627C2×Q8—724no—
628C2×Q8—712no—
629C2×Q8—712no—
630C2×Q8—1424no—
631C2×Q8—1412no—
632C2×Q8—1496no—
633C2×Q8—1496no—
634C2×Q8—1496no—
635C2×Q8—1496no—
636C2×Q8—1432no—
637C2×Q8—1412no—
638C2×Q8D4×D718yes—
639C2×Q8C23×D7112yes—
640C2×Q8C23×D7112yes—
641C2×Q8C23×D714yes—
642C2×D4—24no—
643C2×D4—74no—
644C2×D4—712no—
645C2×D4—74no—
646C2×D4—712no—
647C2×D4—712no—
648C2×D4—712no—
649C2×D4—712no—
650C2×D4—1412no—
651C2×D4—1412no—
652C2×D4—1412no—
653C2×D4—144no—
654C2×D4—144no—
655C2×D4—1412no—
656C2×D4—1412no—
657C2×D4C23×D714yes—
658C22×C4—212no—
659C22×C4—212no—
660C22×C4—73no—
661C22×C4—724no—
662C22×C4—712no—
663C22×C4—712no—
664C22×C4—73no—
665C22×C4—71no—
666C22×C4—73no—
667C22×C4—71no—
668C22×C4—712no—
669C22×C4—712no—
670C22×C4—724no—
671C22×C4—712no—
672C22×C4—712no—
673C22×C4—1412no—
674C22×C4—1496no—
675C22×C4—1424no—
676C22×C4—1412no—
677C22×C4—1412no—
678C22×C4—1412no—
679C22×C4—1412no—
680C22×C4C23×D7112yes—
681C22×C4C23×D7112yes—
682C22×C4C23×D713yes—
683C22×C4C23×D711yescharacteristic
684C22×C4C23×D713yes—
685C22×C4C23×D713yes—
686C22×C4C23×D713yes—
687C4⋊C4—712no—
688C4⋊C4—712no—
689C4⋊C4—712no—
690C4⋊C4—724no—
691C4⋊C4—712no—
692C4⋊C4—712no—
693C4⋊C4—712no—
694C4⋊C4C23×D7112yes—
695C4⋊C4C23×D7124yes—
696C4⋊C4C23×D7112yes—
697C22⋊C4—74no—
698C22⋊C4—712no—
699C22⋊C4—712no—
700C22⋊C4—74no—
701C22⋊C4—712no—
702C22⋊C4—74no—
703C22⋊C4—712no—
704C22⋊C4—724no—
705C22⋊C4—724no—
706C22⋊C4—712no—
707C22⋊C4C23×D7112yes—
708C22⋊C4C23×D7112yes—
709C42—724no—
710C42—712no—
711C42C23×D7112yes—
712C2×C7—24no—
713C2×C7—42no—
714C2×C7#348614yescomplemented
715C2×C7C24×D411yescharacteristic
716C2×C7C22×2−1+411yescharacteristic
717C2×C7C22×2−1+411yescharacteristic
718D7—24no—
719D7—24no—
720D7—46no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—72no—
727C23—72no—
728C23—74no—
729C23—74no—
730C23—76no—
731C23—148no—
732C23—148no—
733C23—1432no—
734C23—142no—
735C23—142no—
736C23—142no—
737C23—148no—
738C23—142no—
739C23—146no—
740C23—146no—
741C23—146no—
742C23#655114yescomplemented
743C23C24×D712yes—
744C23C24×D712yes—
745C23C24×D711yescharacteristic
746Q8—224no—
747Q8—224no—
748Q8—748no—
749Q8—1448no—
750Q8—1424no—
751Q8—1424no—
752Q8C2×D4×D7116yes—
753D4—28no—
754D4—1424no—
755D4—1424no—
756D4—1424no—
757D4—148no—
758D4—148no—
759D4—1424no—
760D4—1424no—
761C2×C4—26no—
762C2×C4—26no—
763C2×C4—22no—
764C2×C4—26no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—76no—
768C2×C4—712no—
769C2×C4—748no—
770C2×C4—76no—
771C2×C4—72no—
772C2×C4—76no—
773C2×C4—72no—
774C2×C4—1424no—
775C2×C4—1448no—
776C2×C4—1424no—
777C2×C4—1424no—
778C2×C4—142no—
779C2×C4—146no—
780C2×C4—146no—
781C2×C4—142no—
782C2×C4—1424no—
783C2×C4—1424no—
784C2×C4C2×D4×D7112yes—
785C2×C4C24×D716yes—
786C2×C4C24×D712yes—
787C2×C4C24×D716yes—
788C2×C4C24×D716yes—
789C2×C4C24×D716yes—
790C7C2×#348611yescharacteristic, complemented, Sylow
791C22—22no—
792C22—22no—
793C22—28no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—74no—
799C22—74no—
800C22—1432no—
801C22—142no—
802C22—142no—
803C22—142no—
804C22—142no—
805C22—148no—
806C22—148no—
807C22—146no—
808C22—146no—
809C22—146no—
810C22—2812no—
811C22C22×D4×D712yes—
812C22C2×#655112yes—
813C22C2×#655114yescomplemented
814C22D7×2−1+412yes—
815C22C25×D711yescharacteristic
816C4—26no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—712no—
821C4—142no—
822C4—146no—
823C4—146no—
824C4—142no—
825C4C22×D4×D7112yes—
826C2—24no—
827C2—42no—
828C2—144no—
829C2—144no—
830C2—286no—
831C2#1174382714yesdirect product factor
832C2C23×D4×D711yescharacteristic
833C2C22×#655111yescharacteristic
834C2C2×D7×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×D4×Q8C2
socleC23×C7C25
hypercenterC2×D4×Q8D7
hypocenterC7C2×#3486
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#6551C2semidirect
2. C23×Q8×D7C2semidirect
3. C2×C7×D4×Q8C2semidirect
4. C2×#90508C2semidirect
5. C2×Q8×C22⋊D7C2semidirect
6. #11743827C2direct (N × H)
7. C2×#90418C2semidirect
8. C2×#90415C2semidirect
9. C2×#90324C2semidirect
10. C2×#90319C2semidirect
11. C2×#90323C2semidirect
12. C2×#90318C2semidirect
13. C2×#90267C2semidirect
14. C2×#90263C2semidirect
15. C2×#90238C2semidirect
16. C2×#90243C2semidirect
18. C23×C7×Q8C22semidirect
20. C2×#6551C22semidirect
22. C22×#1161C22semidirect
28. C22×Q8×D7C22semidirect
29. C22×Q8×D7C22semidirect
31. C22×#1157C22semidirect
34. C7×D4×Q8C22semidirect
35. C2×C7×C4⋊Q8C22semidirect
37. C2×C7×C22⋊Q8C22semidirect
38. C2×C4×C7×Q8C22semidirect
40. #90508C22semidirect
41. Q8×C22⋊D7C22semidirect
42. C2×#6510C22semidirect
44. C2×#6509C22semidirect
45. C2×Q8×Dic7C22semidirect
46. C2×#6507C22semidirect
52. C2×#6487C22semidirect
53. #90418C22semidirect
54. #90415C22semidirect
55. #90324C22semidirect
56. #90323C22semidirect
57. #90319C22semidirect
58. #90318C22semidirect
59. #90267C22semidirect
60. #90263C22semidirect
61. #90243C22semidirect
62. #90238C22semidirect
63. C2×#6460C22semidirect
65. C2×#6459C22semidirect
66. C2×#6459C22semidirect
72. C2×#6451C22semidirect
73. C2×#6450C22semidirect
74. C2×#6448C22semidirect
80. C2×#6438C22semidirect
83. C2×C4×Dic14C22semidirect
92. C22×C7×Q8C23semidirect
105. C2×#1161C23semidirect
111. C2×Q8×D7D4semidirect
116. C2×Q8×D7C23semidirect
120. C2×#1157C23semidirect
138. C7×C4⋊Q8C23semidirect
140. C7×C22⋊Q8C23semidirect
141. C4×C7×Q8C23semidirect
151. #6510C23semidirect
153. #6509C23semidirect
154. Q8×Dic7C23semidirect
155. #6507C23semidirect
171. #6487C23semidirect
179. #6460C23semidirect
181. #6459C23semidirect
182. #6459C23semidirect
188. #6451C23semidirect
189. #6450C23semidirect
190. #6448C23semidirect
196. #6438C23semidirect
199. C4×Dic14C23semidirect
206. C2×D4×Q8D7semidirect
265. Q8×D7C2×D4semidirect
336. C23×Q8C2×D7semidirect
341. D4×Q8C2×D7semidirect
350. C2×C4⋊Q8C2×D7semidirect
368. C2×C22⋊Q8C2×D7semidirect
379. C2×C4×Q8C2×D7semidirect
393. C23×C72−1+4semidirect
409. C22×D72−1+4semidirect
490. C22×Q8C22×D7semidirect
512. C4⋊Q8C22×D7semidirect
528. C22⋊Q8C22×D7semidirect
538. C4×Q8C22×D7semidirect
582. C22×C7C2×2−1+4semidirect
596. C2×D7C2×2−1+4semidirect
714. C2×C7#3486semidirect
742. C23#6551semidirect
790. C7C2×#3486semidirect
813. C22C2×#6551semidirect
831. C2#11743827direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65512
C23×Q8×D72
C2×C7×D4×Q82
C2×#905082
C2×Q8×C22⋊D72
#117438272
C2×#904182
C2×#904152
C2×#903242
C2×#903192
C2×#903232
C2×#903182
C2×#902672
C2×#902632
C2×#902382
C2×#902432
C2×#34867