Finite Group Databasebeta

← C2×#11743813 #14262196

Subgroups — C2×#11743813 #14262196

Order 1792.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6551C211yesmaximal, characteristic, complemented
2C23×#1161C211yesmaximal, characteristic, complemented
3C2×C7×D4×Q8C211yesmaximal, characteristic, complemented
4C2×#90508C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D7C211yesmaximal, characteristic, complemented
6#11743813C2132yesmaximal, direct product factor
7C2×#90417C213yesmaximal, complemented
8C2×#90415C213yesmaximal, complemented
9C2×#90322C213yesmaximal, complemented
10C2×#90321C213yesmaximal, complemented
11C2×#90320C213yesmaximal, complemented
12C2×D7×C22⋊Q8C213yesmaximal, complemented
13C2×#90267C211yesmaximal, characteristic, complemented
14C2×#90265C211yesmaximal, characteristic, complemented
15C2×#90241C213yesmaximal, complemented
16C2×#90238C213yesmaximal, complemented
17C23×C7×Q8C2211yescharacteristic
18C23×C7×Q8C2211yescharacteristic, complemented
19C2×#6551—216no—
20C2×#6551C22116yescomplemented
21C22×#1161—216no—
22C22×#1161C2213yes—
23C22×#1161C2213yes—
24C22×#1161C2211yescharacteristic
25C22×#1161C2211yescharacteristic
26C22×#1161C22116yescomplemented
27C22×#1161C2213yescomplemented
28C22×Q8×D7C2213yescomplemented
29C22×Q8×D7C2211yescharacteristic, complemented
30C22×#1157C2213yescomplemented
31C22×#1157C2213yescomplemented
32C23×D28C2213yes—
33C23×C4×D7C2213yes—
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×#6509C2213yescomplemented
44C2×#6509C2213yescomplemented
45C2×Q8×Dic7C2211yescharacteristic, complemented
46C2×#6507C2213yescomplemented
47C2×#6502C2211yescharacteristic
48C2×#6500C2213yes—
49C2×#6493C2213yescomplemented
50C2×C4×C22⋊D7C2213yes—
51C2×C4×C22⋊D7C2213yescomplemented
52C2×#6487C2213yes—
53#90417C22148yescomplemented
54#90415C22148yescomplemented
55#90322C22148yescomplemented
56#90321C22148yescomplemented
57#90320C22148yescomplemented
58D7×C22⋊Q8C22148yescomplemented
59#90267C22116yescomplemented
60#90265C22116yescomplemented
61#90241C22148yescomplemented
62#90238C22148yescomplemented
63C2×#6460C2213yescomplemented
64C2×#6459C2213yescomplemented
65C2×#6459C2216yescomplemented
66C2×#6458C2216yescomplemented
67C2×#6458C2213yescomplemented
68C2×#6457C2216yescomplemented
69C2×#6457C2216yescomplemented
70C2×#6457C2213yescomplemented
71C2×#6456C2213yescomplemented
72C2×D7×C4⋊C4C2216yescomplemented
73C2×D7×C4⋊C4C2213yescomplemented
74C2×#6447C2213yescomplemented
75C2×#6447C2216yescomplemented
76C2×#6446C2213yescomplemented
77C2×#6445C2213yes—
78C2×D7×C22⋊C4C2216yes—
79C2×#6441C2213yes—
80C2×#6438C2213yescomplemented
81C2×C4×D28C2213yescomplemented
82C2×C4×D28C2213yescomplemented
83C2×#6435C2213yescomplemented
84C2×#3489—71nomaximal, Sylow
85C24×D7C2313yes—
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⋊D7C2311yescharacteristic
97C22×C22⋊D7C2313yes—
98C22×C22⋊D7C2311yescharacteristic
99C22×C22⋊D7C2313yes—
100C23×Dic7C2311yescharacteristic
101#6551—2128no—
102C2×#1161—28no—
103C2×#1161—2128no—
104C2×#1161—224no—
105C2×#1161—224no—
106C2×#1161—224no—
107C2×#1161D4116yescomplemented
108C2×#1161C23124yes—
109C2×#1161C23124yes—
110C2×#1161C2318yes—
111C2×#1161C2318yes—
112C2×#1161C23124yescomplemented
113C2×Q8×D7—28no—
114C2×Q8×D7—224no—
115C2×Q8×D7C23124yescomplemented
116C2×Q8×D7C2318yescomplemented
117C2×#1157—224no—
118C2×#1157—224no—
119C2×#1157C23124yescomplemented
120C2×#1157C23124yescomplemented
121C22×D28—224no—
122C22×D28C2313yes—
123C22×D28C2313yes—
124C22×D28C2316yes—
125C22×D28C23124yes—
126C22×D28C2313yes—
127C22×D28C2313yes—
128C22×C4×D7—224no—
129C22×C4×D7C2313yes—
130C22×C4×D7C2313yes—
131C22×C4×D7C2316yes—
132C22×C4×D7C2313yes—
133C22×C4×D7C2313yes—
134C22×C4×D7C23124yes—
135C22×C4×D7C2316yes—
136C22×C4×D7C2313yes—
137C22×Dic14C2313yes—
138C22×Dic14C2313yes—
139C7×C4⋊Q8C23124yescomplemented
140C7×C22⋊Q8C23124yes—
141C7×C22⋊Q8C23124yescomplemented
142C4×C7×Q8C2318yescomplemented
143C4×C7×D4C23124yes—
144C2×C7×C4⋊C4C2313yes—
145C2×C7×C4⋊C4C2316yes—
146C2×C7×C4⋊C4C2313yes—
147C2×C7×C22⋊C4C2313yes—
148C2×C7×C22⋊C4C2313yes—
149C2×C42×C7C2313yes—
150C2×C22⋊Dic7C2313yes—
151C2×C22⋊Dic7C2311yescharacteristic
152#6510C23124yescomplemented
153#6509C23124yescomplemented
154#6509C23124yescomplemented
155Q8×Dic7C2318yescomplemented
156#6507C23124yescomplemented
157#6502C2318yes—
158#6500C23124yes—
159#6493C23124yescomplemented
160C4×C22⋊D7C23124yes—
161C4×C22⋊D7C23124yescomplemented
162C2×(C2×D7)⋊C4C2313yes—
163C2×(C2×D7)⋊C4C2313yes—
164C2×(C2×D7)⋊C4C2311yescharacteristic
165C2×(C2×D7)⋊C4C2313yes—
166C2×(C2×D7)⋊C4C2316yes—
167C2×(C2×D7)⋊C4C2316yes—
168C2×(C2×D7)⋊C4C2313yes—
169C2×(C2×D7)⋊C4C2313yes—
170C2×C4⋊Dic7C2313yes—
171C2×C4⋊Dic7C2313yes—
172#6487C23124yes—
173C2×Dic7⋊C4C2311yescharacteristic
174C2×Dic7⋊C4C2313yes—
175C2×Dic7⋊C4C2313yes—
176C2×Dic7⋊C4C2313yes—
177C2×Dic7⋊C4C2316yes—
178C2×C4×Dic7C2313yes—
179#6460C23124yescomplemented
180#6459C23124yescomplemented
181#6459C23148yescomplemented
182#6458C23148yescomplemented
183#6458C23124yescomplemented
184#6457C23148yescomplemented
185#6457C23148yescomplemented
186#6457C23124yescomplemented
187#6456C23124yescomplemented
188D7×C4⋊C4C23148yescomplemented
189D7×C4⋊C4C23124yescomplemented
190#6447C23124yescomplemented
191#6447C23148yescomplemented
192#6446C23124yescomplemented
193#6445C23124yes—
194D7×C22⋊C4C23148yes—
195#6441C23124yes—
196#6438C23124yescomplemented
197C4×D28C23124yescomplemented
198C4×D28C23124yescomplemented
199#6435C23124yescomplemented
200C22×2−1+4—71no—
201C23×#41—71no—
202#3489—732no—
203C2×D4×Q8—71no—
204C2×D4×Q8D711yescharacteristic, complemented
205C2×#548—71no—
206C2×#548—71no—
207C2×#547—73no—
208C2×#547—73no—
209C2×#546—73no—
210C2×#546—73no—
211C2×#537—73no—
212C2×#536—73no—
213C2×#525—73no—
214C22×C22⋊Q8—73no—
215C2×#520—71no—
216C24×C7C2411yescharacteristic
217C24×C7C2411yescharacteristic
218C23×D7—212no—
219C23×D7—212no—
220C23×D7—46no—
221C23×D7C2413yes—
222C23×D7C2411yescharacteristic
223C23×D7C24112yes—
224C23×D7C2413yes—
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×C7C2413yes—
239C22×C4×C7C2411yescharacteristic
240C22×C4×C7C2413yes—
241C22×C4×C7C24112yes—
242C22×C4×C7C24112yes—
243C22×C4×C7C2413yes—
244C2×C22⋊D7—24no—
245C2×C22⋊D7—212no—
246C2×C22⋊D7—24no—
247C2×C22⋊D7—46no—
248C2×C22⋊D7C2414yes—
249C2×C22⋊D7C24112yes—
250C2×C22⋊D7C2414yes—
251C2×C22⋊D7C24112yes—
252C22×Dic7—24no—
253C22×Dic7C2414yes—
254C22×Dic7C2411yescharacteristic
255C22×Dic7C2413yes—
256C22×Dic7C2411yescharacteristic
257C22×Dic7C2413yes—
258C22×Dic7C2411yescharacteristic
259#1161—232no—
260#1161—296no—
261#1161—296no—
262#1161—296no—
263#1161C2×D4164yescomplemented
264Q8×D7—232no—
265Q8×D7—296no—
266#1157—296no—
267#1157—296no—
268C2×D28—224no—
269C2×D28—212no—
270C2×D28—212no—
271C2×D28—296no—
272C2×D28—46no—
273C2×D28C2×D4124yes—
274C2×D28C24112yes—
275C2×D28C24112yes—
276C2×D28C24124yes—
277C2×D28C24112yes—
278C2×D28C24112yes—
279C2×C4×D7—212no—
280C2×C4×D7—224no—
281C2×C4×D7—212no—
282C2×C4×D7—212no—
283C2×C4×D7—212no—
284C2×C4×D7—296no—
285C2×C4×D7—412no—
286C2×C4×D7C2×D4124yes—
287C2×C4×D7C24112yes—
288C2×C4×D7C24112yes—
289C2×C4×D7C24124yes—
290C2×C4×D7C24112yes—
291C2×C4×D7C24112yes—
292C2×C4×D7C24124yes—
293C2×C4×D7C24112yes—
294C2×Dic14—212no—
295C2×Dic14—212no—
296C2×Dic14C24112yes—
297C2×Dic14C24112yes—
298C7×C4⋊C4C24112yes—
299C7×C4⋊C4C24124yes—
300C7×C4⋊C4C24112yes—
301C7×C22⋊C4C24112yes—
302C7×C22⋊C4C24112yes—
303C42×C7C24112yes—
304C22⋊Dic7C24112yes—
305C22⋊Dic7C2414yes—
306(C2×D7)⋊C4C24112yes—
307(C2×D7)⋊C4C24112yes—
308(C2×D7)⋊C4C2414yes—
309(C2×D7)⋊C4C24112yes—
310(C2×D7)⋊C4C24124yes—
311(C2×D7)⋊C4C24124yes—
312(C2×D7)⋊C4C24112yes—
313(C2×D7)⋊C4C24112yes—
314C4⋊Dic7C24112yes—
315C4⋊Dic7C24112yes—
316Dic7⋊C4C2414yes—
317Dic7⋊C4C24112yes—
318Dic7⋊C4C24112yes—
319Dic7⋊C4C24112yes—
320Dic7⋊C4C24124yes—
321C4×Dic7C24112yes—
322C2×2−1+4—716no—
323C2×2−1+4—1416no—
324C22×#41—71no—
325C22×#41—73no—
326C22×#41—73no—
327C22×#41—71no—
328C22×#41—716no—
329C22×#41—73no—
330C22×#41—73no—
331C22×#41—73no—
332C22×#41—1416no—
333C23×Q8—73no—
334C23×Q8—71no—
335C23×Q8C2×D711yescharacteristic
336C23×Q8C2×D711yescharacteristic, complemented
337C23×D4—73no—
338C24×C4—73no—
339D4×Q8—716no—
340D4×Q8C2×D7116yescomplemented
341#548—716no—
342#548—716no—
343#547—748no—
344#547—748no—
345#546—748no—
346#546—748no—
347#537—748no—
348#536—748no—
349C2×C4⋊Q8—73no—
350C2×C4⋊Q8C2×D713yescomplemented
351C2×#124—73no—
352C2×#124—73no—
353#525—748no—
354C2×#123—73no—
355C2×#123—76no—
356C2×#123—76no—
357C2×#123—73no—
358C2×C22⋊Q8—73no—
359C2×C22⋊Q8—73no—
360C2×C22⋊Q8—73no—
361C2×C22⋊Q8—748no—
362C2×C22⋊Q8—76no—
363C2×C22⋊Q8—73no—
364C2×C22⋊Q8—73no—
365C2×C22⋊Q8—73no—
366C2×C22⋊Q8C2×D713yes—
367C2×C22⋊Q8C2×D713yescomplemented
368C2×#121—71no—
369C2×#121—73no—
370C2×#121—76no—
371C2×#121—73no—
372C2×#121—73no—
373C2×#121—76no—
374C2×#120—73no—
375C2×#120—73no—
376#520—716no—
377C2×C4×Q8—71no—
378C2×C4×Q8C2×D711yescharacteristic, complemented
379C2×C4×D4—73no—
380C2×C4×D4—73no—
381C2×C4×D4—73no—
382C2×C4×D4—73no—
383C2×C4×D4—73no—
384C2×C4×D4C2×D713yes—
385C2×#117—73no—
386C22×C4⋊C4—73no—
387C22×C4⋊C4—76no—
388C22×C22⋊C4—76no—
389C23×C7—22no—
390C23×C7—22no—
391C23×C7—22no—
392C23×C7—22no—
393C23×C7—22no—
394C23×C72−1+414yescomplemented
395C23×C7C2512yes—
396C23×C7C2512yes—
397C23×C7C2511yescharacteristic
398C22×D7—26no—
399C22×D7—26no—
400C22×D7—22no—
401C22×D7—26no—
402C22×D7—22no—
403C22×D7—26no—
404C22×D7—224no—
405C22×D7—22no—
406C22×D7—26no—
407C22×D7—224no—
408C22×D7—412no—
409C22×D7—448no—
410C22×D7C22×D4112yes—
411C22×D7C2516yes—
412C22×D7C2512yes—
413C22×D7C2516yes—
414C7×Q8—224no—
415C7×Q8—224no—
416C7×Q8C22×D4116yes—
417C7×D4—28no—
418C2×C4×C7—26no—
419C2×C4×C7—26no—
420C2×C4×C7—22no—
421C2×C4×C7—26no—
422C2×C4×C7—224no—
423C2×C4×C7—224no—
424C2×C4×C7C22×D4112yes—
425C2×C4×C7C2516yes—
426C2×C4×C7C2516yes—
427C2×C4×C7C2512yes—
428C2×C4×C7C2516yes—
429C2×C4×C7C2516yes—
430C22⋊D7—28no—
431C22⋊D7—224no—
432C22⋊D7—28no—
433C22⋊D7—412no—
434C2×Dic7—26no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—26no—
438C2×Dic7—28no—
439C2×Dic7C22×D414yes—
440C2×Dic7C2512yes—
441C2×Dic7C2516yes—
442C2×Dic7C2512yes—
443C2×Dic7C2516yes—
444C2×Dic7C2512yes—
445D28—248no—
446D28—224no—
447D28—224no—
448D28—412no—
449D28C22×D4148yes—
450C4×D7—224no—
451C4×D7—248no—
452C4×D7—224no—
453C4×D7—224no—
454C4×D7—224no—
455C4×D7—424no—
456C4×D7C22×D4148yes—
457Dic14—224no—
458Dic14—224no—
459C25—73no—
4602−1+4—14128no—
461C2×#41—716no—
462C2×#41—78no—
463C2×#41—724no—
464C2×#41—724no—
465C2×#41—724no—
466C2×#41—78no—
467C2×#41—724no—
468C2×#41—724no—
469C2×#41—1424no—
470C2×#41—1424no—
471C2×#41—1424no—
472C2×#41—1424no—
473C2×#41—1424no—
474C2×#41—14128no—
475C2×#41—148no—
476C22×Q8—28no—
477C22×Q8—28no—
478C22×Q8—724no—
479C22×Q8—78no—
480C22×Q8—73no—
481C22×Q8—73no—
482C22×Q8—1424no—
483C22×Q8—148no—
484C22×Q8C22×D713yes—
485C22×Q8C22×D713yes—
486C22×Q8C22×D718yes—
487C22×Q8C22×D711yescharacteristic
488C22×Q8C22×D718yescomplemented
489C22×D4—71no—
490C22×D4—73no—
491C22×D4—71no—
492C22×D4—73no—
493C22×D4—73no—
494C22×D4—73no—
495C22×D4—76no—
496C22×D4—73no—
497C22×D4—724no—
498C22×D4—73no—
499C22×D4—1424no—
500C22×D4C22×D711yescharacteristic
501C23×C4—73no—
502C23×C4—71no—
503C23×C4—76no—
504C23×C4—73no—
505C23×C4—73no—
506C23×C4—73no—
507C23×C4—73no—
508C23×C4—724no—
509C23×C4—76no—
510C23×C4—1424no—
511C23×C4C22×D713yes—
512C23×C4C22×D713yes—
513C4⋊Q8—724no—
514C4⋊Q8C22×D7124yescomplemented
515#124—724no—
516#124—724no—
517#123—724no—
518#123—748no—
519#123—748no—
520#123—724no—
521C22⋊Q8—724no—
522C22⋊Q8—724no—
523C22⋊Q8—724no—
524C22⋊Q8—748no—
525C22⋊Q8—724no—
526C22⋊Q8—724no—
527C22⋊Q8—724no—
528C22⋊Q8C22×D7124yes—
529C22⋊Q8C22×D7124yescomplemented
530#121—78no—
531#121—724no—
532#121—748no—
533#121—724no—
534#121—724no—
535#121—748no—
536#120—724no—
537#120—724no—
538C4×Q8—78no—
539C4×Q8C22×D718yescomplemented
540C4×D4—724no—
541C4×D4—724no—
542C4×D4—724no—
543C4×D4—724no—
544C4×D4—724no—
545C4×D4C22×D7124yes—
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—71no—
553C2×C4⋊C4—73no—
554C2×C4⋊C4—724no—
555C2×C4⋊C4—748no—
556C2×C4⋊C4C22×D713yes—
557C2×C4⋊C4C22×D716yes—
558C2×C4⋊C4C22×D713yes—
559C2×C22⋊C4—73no—
560C2×C22⋊C4—71no—
561C2×C22⋊C4—76no—
562C2×C22⋊C4—76no—
563C2×C22⋊C4—73no—
564C2×C22⋊C4—73no—
565C2×C22⋊C4—71no—
566C2×C22⋊C4—73no—
567C2×C22⋊C4—73no—
568C2×C22⋊C4—73no—
569C2×C22⋊C4—748no—
570C2×C22⋊C4C22×D713yes—
571C2×C22⋊C4C22×D713yes—
572C2×C42—73no—
573C2×C42C22×D713yes—
574C22×C7—22no—
575C22×C7—22no—
576C22×C7—28no—
577C22×C7—22no—
578C22×C7—22no—
579C22×C7—22no—
580C22×C7—44no—
581C22×C7C23×D412yes—
582C22×C7C2×2−1+412yes—
583C22×C7C2×2−1+414yescomplemented
584C22×C7#58512yes—
585C22×C7C2611yescharacteristic
586C2×D7—26no—
587C2×D7—26no—
588C2×D7—224no—
589C2×D7—22no—
590C2×D7—26no—
591C2×D7—22no—
592C2×D7—26no—
593C2×D7—22no—
594C2×D7—26no—
595C2×D7—448no—
596C2×D7—44no—
597C2×D7—412no—
598C2×D7C23×D4112yes—
599C4×C7—26no—
600C4×C7—26no—
601C4×C7—22no—
602C4×C7—26no—
603C4×C7C23×D4112yes—
604Dic7—26no—
605Dic7—22no—
606Dic7—22no—
607Dic7—26no—
608Dic7C23×D414yes—
609C24—73no—
610C24—73no—
611C24—71no—
612C24—712no—
613C24—1412no—
614C24—1412no—
615C24—286no—
616C24C23×D711yescharacteristic
617C24C23×D711yescharacteristic
618#41—764no—
619#41—1496no—
620#41—1496no—
621#41—1496no—
622#41—1496no—
623#41—1496no—
624#41—1432no—
625C2×Q8—232no—
626C2×Q8—232no—
627C2×Q8—212no—
628C2×Q8—212no—
629C2×Q8—712no—
630C2×Q8—712no—
631C2×Q8—1412no—
632C2×Q8—1496no—
633C2×Q8—1432no—
634C2×Q8—1412no—
635C2×Q8D4×D718yes—
636C2×Q8C23×D7112yes—
637C2×Q8C23×D7112yes—
638C2×Q8C23×D714yes—
639C2×D4—24no—
640C2×D4—74no—
641C2×D4—712no—
642C2×D4—74no—
643C2×D4—712no—
644C2×D4—724no—
645C2×D4—712no—
646C2×D4—712no—
647C2×D4—724no—
648C2×D4—712no—
649C2×D4—712no—
650C2×D4—1496no—
651C2×D4—1424no—
652C2×D4—1412no—
653C2×D4—144no—
654C2×D4—1412no—
655C2×D4—144no—
656C2×D4—1412no—
657C2×D4—286no—
658C2×D4—286no—
659C2×D4C23×D714yes—
660C22×C4—212no—
661C22×C4—212no—
662C22×C4—71no—
663C22×C4—724no—
664C22×C4—712no—
665C22×C4—74no—
666C22×C4—71no—
667C22×C4—73no—
668C22×C4—73no—
669C22×C4—71no—
670C22×C4—724no—
671C22×C4—712no—
672C22×C4—712no—
673C22×C4—712no—
674C22×C4—712no—
675C22×C4—724no—
676C22×C4—1412no—
677C22×C4—1496no—
678C22×C4—1412no—
679C22×C4—1424no—
680C22×C4—144no—
681C22×C4—1412no—
682C22×C4—1412no—
683C22×C4—2812no—
684C22×C4C23×D7112yes—
685C22×C4C23×D7112yes—
686C22×C4C23×D711yescharacteristic
687C22×C4C23×D713yes—
688C22×C4C23×D713yes—
689C22×C4C23×D713yes—
690C22×C4C23×D713yes—
691C4⋊C4—712no—
692C4⋊C4—712no—
693C4⋊C4—724no—
694C4⋊C4—74no—
695C4⋊C4—712no—
696C4⋊C4—712no—
697C4⋊C4—712no—
698C4⋊C4C23×D7112yes—
699C4⋊C4C23×D7124yes—
700C4⋊C4C23×D7112yes—
701C22⋊C4—712no—
702C22⋊C4—74no—
703C22⋊C4—724no—
704C22⋊C4—724no—
705C22⋊C4—712no—
706C22⋊C4—712no—
707C22⋊C4—74no—
708C22⋊C4—712no—
709C22⋊C4—712no—
710C22⋊C4—712no—
711C22⋊C4C23×D7112yes—
712C22⋊C4C23×D7112yes—
713C42—712no—
714C42C23×D7112yes—
715C2×C7—24no—
716C2×C7—42no—
717C2×C7#348914yescomplemented
718C2×C7C24×D411yescharacteristic
719C2×C7C22×2−1+411yescharacteristic
720C2×C7C2×#58511yescharacteristic
721D7—212no—
722D7—42no—
723D7—46no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—76no—
730C23—712no—
731C23—76no—
732C23—72no—
733C23—1424no—
734C23—146no—
735C23—146no—
736C23—142no—
737C23—146no—
738C23—142no—
739C23—146no—
740C23—1424no—
741C23—142no—
742C23—146no—
743C23—2812no—
744C23—2848no—
745C23#655114yescomplemented
746C23C24×D712yes—
747C23C24×D712yes—
748C23C24×D711yescharacteristic
749Q8—224no—
750Q8—224no—
751Q8—1424no—
752Q8—1424no—
753Q8C2×D4×D7116yes—
754D4—28no—
755D4—748no—
756D4—1448no—
757D4—1424no—
758D4—148no—
759D4—1424no—
760D4—148no—
761D4—1424no—
762D4—2812no—
763D4—2812no—
764C2×C4—26no—
765C2×C4—26no—
766C2×C4—22no—
767C2×C4—26no—
768C2×C4—224no—
769C2×C4—224no—
770C2×C4—72no—
771C2×C4—74no—
772C2×C4—748no—
773C2×C4—72no—
774C2×C4—76no—
775C2×C4—76no—
776C2×C4—72no—
777C2×C4—1424no—
778C2×C4—1424no—
779C2×C4—1448no—
780C2×C4—148no—
781C2×C4—142no—
782C2×C4—146no—
783C2×C4—142no—
784C2×C4—146no—
785C2×C4—1424no—
786C2×C4—1424no—
787C2×C4—2824no—
788C2×C4C2×D4×D7112yes—
789C2×C4C24×D712yes—
790C2×C4C24×D716yes—
791C2×C4C24×D716yes—
792C2×C4C24×D716yes—
793C2×C4C24×D716yes—
794C7C2×#348911yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—28no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—712no—
803C22—146no—
804C22—146no—
805C22—1424no—
806C22—142no—
807C22—146no—
808C22—142no—
809C22—146no—
810C22—142no—
811C22—146no—
812C22—2848no—
813C22—2812no—
814C22—284no—
815C22C22×D4×D712yes—
816C22C2×#655112yes—
817C22C2×#655114yescomplemented
818C22#9062012yes—
819C22C25×D711yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—74no—
825C4—142no—
826C4—146no—
827C4—142no—
828C4—146no—
829C4C22×D4×D7112yes—
830C2—24no—
831C2—42no—
832C2—1412no—
833C2—286no—
834C2—282no—
835C2#1174381314yesdirect product factor
836C2C23×D4×D711yescharacteristic
837C2C22×#655111yescharacteristic
838C2C2×#9062011yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×D4×Q8C2
socleC23×C7C25
hypercenterC2×D4×Q8D7
hypocenterC7C2×#3489
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×#1161C2semidirect
3. C2×C7×D4×Q8C2semidirect
4. C2×#90508C2semidirect
5. C2×Q8×C22⋊D7C2semidirect
6. #11743813C2direct (N × H)
7. C2×#90417C2semidirect
8. C2×#90415C2semidirect
9. C2×#90322C2semidirect
10. C2×#90321C2semidirect
11. C2×#90320C2semidirect
12. C2×D7×C22⋊Q8C2semidirect
13. C2×#90267C2semidirect
14. C2×#90265C2semidirect
15. C2×#90241C2semidirect
16. C2×#90238C2semidirect
18. C23×C7×Q8C22semidirect
20. C2×#6551C22semidirect
26. C22×#1161C22semidirect
27. C22×#1161C22semidirect
28. C22×Q8×D7C22semidirect
29. C22×Q8×D7C22semidirect
30. C22×#1157C22semidirect
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
43. C2×#6509C22semidirect
44. C2×#6509C22semidirect
45. C2×Q8×Dic7C22semidirect
46. C2×#6507C22semidirect
49. C2×#6493C22semidirect
51. C2×C4×C22⋊D7C22semidirect
53. #90417C22semidirect
54. #90415C22semidirect
55. #90322C22semidirect
56. #90321C22semidirect
57. #90320C22semidirect
58. D7×C22⋊Q8C22semidirect
59. #90267C22semidirect
60. #90265C22semidirect
61. #90241C22semidirect
62. #90238C22semidirect
63. C2×#6460C22semidirect
64. C2×#6459C22semidirect
65. C2×#6459C22semidirect
66. C2×#6458C22semidirect
67. C2×#6458C22semidirect
68. C2×#6457C22semidirect
69. C2×#6457C22semidirect
70. C2×#6457C22semidirect
71. C2×#6456C22semidirect
72. C2×D7×C4⋊C4C22semidirect
73. C2×D7×C4⋊C4C22semidirect
74. C2×#6447C22semidirect
75. C2×#6447C22semidirect
76. C2×#6446C22semidirect
80. C2×#6438C22semidirect
81. C2×C4×D28C22semidirect
82. C2×C4×D28C22semidirect
83. C2×#6435C22semidirect
92. C22×C7×Q8C23semidirect
107. C2×#1161D4semidirect
112. C2×#1161C23semidirect
115. C2×Q8×D7C23semidirect
116. C2×Q8×D7C23semidirect
119. C2×#1157C23semidirect
120. C2×#1157C23semidirect
139. C7×C4⋊Q8C23semidirect
141. C7×C22⋊Q8C23semidirect
142. C4×C7×Q8C23semidirect
152. #6510C23semidirect
153. #6509C23semidirect
154. #6509C23semidirect
155. Q8×Dic7C23semidirect
156. #6507C23semidirect
159. #6493C23semidirect
161. C4×C22⋊D7C23semidirect
179. #6460C23semidirect
180. #6459C23semidirect
181. #6459C23semidirect
182. #6458C23semidirect
183. #6458C23semidirect
184. #6457C23semidirect
185. #6457C23semidirect
186. #6457C23semidirect
187. #6456C23semidirect
188. D7×C4⋊C4C23semidirect
189. D7×C4⋊C4C23semidirect
190. #6447C23semidirect
191. #6447C23semidirect
192. #6446C23semidirect
196. #6438C23semidirect
197. C4×D28C23semidirect
198. C4×D28C23semidirect
199. #6435C23semidirect
204. C2×D4×Q8D7semidirect
263. #1161C2×D4semidirect
336. C23×Q8C2×D7semidirect
340. D4×Q8C2×D7semidirect
350. C2×C4⋊Q8C2×D7semidirect
367. C2×C22⋊Q8C2×D7semidirect
378. C2×C4×Q8C2×D7semidirect
394. C23×C72−1+4semidirect
488. C22×Q8C22×D7semidirect
514. C4⋊Q8C22×D7semidirect
529. C22⋊Q8C22×D7semidirect
539. C4×Q8C22×D7semidirect
583. C22×C7C2×2−1+4semidirect
717. C2×C7#3489semidirect
745. C23#6551semidirect
794. C7C2×#3489semidirect
817. C22C2×#6551semidirect
835. C2#11743813direct (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×#11612
C2×C7×D4×Q82
C2×#905082
C2×Q8×C22⋊D72
#117438132
C2×#904172
C2×#904152
C2×#903222
C2×#903212
C2×#903202
C2×D7×C22⋊Q82
C2×#902672
C2×#902652
C2×#902412
C2×#902382
C2×#34897