Finite Group Databasebeta

← #14217777

Subgroups — #14217777

Order 1792.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D4×#41C211yesmaximal, characteristic
2C2×#90510C211yesmaximal, characteristic, complemented
3C22×#6511C211yesmaximal, characteristic, complemented
4#11741520C211yesmaximal, characteristic, complemented
5#11741520C211yesmaximal, characteristic, complemented
6#11740722C213yesmaximal, complemented
7#11740721C213yesmaximal, complemented
8#11740363C213yesmaximal, complemented
9#11740363C213yesmaximal, complemented
10#11740362C213yesmaximal, complemented
11#11740361C213yesmaximal, complemented
12#11739957C211yesmaximal, characteristic, complemented
13#11739956C211yesmaximal, characteristic, complemented
14D4×#1136C213yesmaximal, complemented
15C2×#89783C213yesmaximal, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C7×#550C411yescharacteristic
19C7×D4×Q8C411yescharacteristic
20C7×#548C411yescharacteristic
21C7×#548C411yescharacteristic
22C7×#547C413yes—
23C7×#546C413yes—
24C7×#546C413yes—
25C7×D42C413yes—
26C7×#532C2213yes—
27C7×#525C2213yes—
28C7×#525C2213yes—
29C4×C7×#41C2211yescharacteristic
30C2×C4×C7×D4C2213yes—
31#90510—28no—
32C2×#6511—28no—
33C2×#6511C2211yescharacteristic
34C2×#6511C2211yescharacteristic
35C2×#6511C2211yescharacteristic
36C2×#6511C2211yescharacteristic
37C2×#6511C2213yescomplemented
38C2×#6511C2213yescomplemented
39C2×#6511C2213yescomplemented
40C2×#6511C2213yescomplemented
41C22×#1136C2213yescomplemented
42C22×#1136C2213yescomplemented
43C22×#1136C2213yescomplemented
44C23×C7⋊C8C2213yescomplemented
45#90006C2213yescomplemented
46#90006C2213yescomplemented
47#90006C2213yescomplemented
48#90006C2213yescomplemented
49#89979C2213yescomplemented
50#89979C2213yescomplemented
51C2×C22⋊(C7⋊C8)C2213yescomplemented
52C2×C22⋊(C7⋊C8)C2213yescomplemented
53#89784C2216yescomplemented
54#89784C2216yescomplemented
55#89783C2211yescharacteristic
56#89783C2213yes—
57#89783C2213yescomplemented
58#89783C2216yescomplemented
59#89783C2216yescomplemented
60#89783C2216yescomplemented
61#89783C2213yescomplemented
62#89783C2213yescomplemented
63#89783C2213yescomplemented
64#89783C2213yescomplemented
65#89783C2213yescomplemented
66D4×C7⋊C8C2216yescomplemented
67D4×C7⋊C8C2216yescomplemented
68#89771C2213yescomplemented
69#89771C2213yescomplemented
70#89769C2213yescomplemented
71#89769C2213yescomplemented
72#89696C2213yescomplemented
73C2×C4⋊(C7⋊C8)C2213yescomplemented
74C4×#1136C2213yescomplemented
75C2×#6377C2213yescomplemented
76#60146—71nomaximal, Sylow
77C2×C7×#41—24no—
78C2×C7×#41—24no—
79C2×C7×#41—24no—
80C2×C7×#41—24no—
81C2×C7×#41C2×C413yes—
82C2×C7×#41C2×C413yes—
83C2×C7×#41C2×C411yescharacteristic
84C2×C7×#41C2×C411yescharacteristic
85C2×C7×#41C2313yes—
86C2×C7×#41C2313yes—
87C2×C7×#41C2311yescharacteristic
88C22×C7×Q8C2×C411yescharacteristic
89C22×C7×Q8C2×C411yescharacteristic
90C22×C7×D4C2×C413yes—
91C22×C7×D4C2×C413yes—
92C22×C7×D4C2×C413yes—
93C23×C4×C7C2313yes—
94C23×C4×C7C2313yes—
95C7×C4⋊Q8C2×C413yes—
96C7×#127C2×C413yes—
97C7×#124C2×C413yes—
98C7×#124C2×C413yes—
99C7×#123C2×C416yes—
100C7×#123C2×C416yes—
101C7×C22⋊Q8C2×C413yes—
102C7×C22⋊Q8C2×C413yes—
103C7×C22⋊Q8C2×C413yes—
104C7×C22⋊Q8C2×C413yes—
105C7×#121C2×C413yes—
106C7×#121C2×C413yes—
107C7×#121C2×C413yes—
108C7×#121C2×C413yes—
109C7×#121C2×C416yes—
110C7×#121C2×C416yes—
111C7×#120C2×C416yes—
112C7×#120C2×C416yes—
113C4×C7×Q8C2×C411yescharacteristic
114C4×C7×Q8C2×C411yescharacteristic
115C4×C7×D4C2×C413yes—
116C4×C7×D4C2×C413yes—
117C4×C7×D4C2×C413yes—
118C4×C7×D4C2×C413yes—
119C4×C7×D4C2×C413yes—
120C4×C7×D4C2×C413yes—
121C4×C7×D4C2311yescharacteristic
122C4×C7×D4C2313yes—
123C4×C7×D4C2313yes—
124C4×C7×D4C2313yes—
125C4×C7×D4C2316yes—
126C7×#117C2313yes—
127C2×C7×C4⋊C4C2×C413yes—
128C2×C7×C22⋊C4C2×C413yes—
129C2×C7×C22⋊C4C2×C413yes—
130C2×C42×C7C2313yes—
131#6511—24no—
132#6511—24no—
133#6511—24no—
134#6511—212no—
135#6511—212no—
136#6511—212no—
137#6511—212no—
138#6511D418yescomplemented
139C2×#1136—212no—
140C2×#1136—212no—
141C2×#1136—212no—
142C2×#1136C2313yes—
143C2×#1136C2313yes—
144C2×#1136C2313yes—
145C2×#1136C2311yescharacteristic
146C2×#1136C2313yes—
147C2×#1136C2313yes—
148C2×#1136C2316yes—
149C2×#1136C2313yes—
150C2×#1136C2313yes—
151C22×C7⋊C8—212no—
152C22×C7⋊C8C2313yes—
153C22×C7⋊C8C2313yes—
154C22×C7⋊C8C2313yes—
155C22×C7⋊C8C2311yescharacteristic
156C22×C7⋊C8C2313yes—
157C22×C7⋊C8C2313yes—
158C22×C7⋊C8C2313yes—
159C22×C7⋊C8C2316yes—
160C22×C7⋊C8C2313yes—
161C22⋊(C7⋊C8)C2311yescharacteristic
162C22⋊(C7⋊C8)C2311yescharacteristic
163C22⋊(C7⋊C8)C2313yes—
164C22⋊(C7⋊C8)C2313yes—
165C22⋊(C7⋊C8)C2313yes—
166C22⋊(C7⋊C8)C2313yes—
167C22⋊(C7⋊C8)C2313yes—
168C22⋊(C7⋊C8)C2313yes—
169C22⋊(C7⋊C8)C2316yes—
170C22⋊(C7⋊C8)C2316yes—
171C4⋊(C7⋊C8)C2311yescharacteristic
172C4⋊(C7⋊C8)C2313yes—
173C4⋊(C7⋊C8)C2313yes—
174C4⋊(C7⋊C8)C2313yes—
175C4⋊(C7⋊C8)C2316yes—
176#6377C2311yescharacteristic
177#6377C2313yes—
178#6377C2313yes—
179#6377C2313yes—
180C4×C7⋊C8C2316yes—
181C2×#568—71no—
182C22×#131—71no—
183D4×#41D711yescharacteristic
184#2935—73no—
185D4×M16—73no—
186#2933—73no—
187#2933—73no—
188#2932—73no—
189#2930—73no—
190#2929—73no—
191C2×#435—73no—
192#2906—71no—
193#2880—71no—
194#2880—71no—
195#2875—71no—
196C24×C7C22×C413yes—
197C24×C7C22×C413yes—
198C7×#41—24no—
199C7×#41—24no—
200C7×#41—212no—
201C7×#41—212no—
202C7×#41—26no—
203C7×#41—26no—
204C7×#41—26no—
205C7×#41—26no—
206C7×#41C2×D414yes—
207C7×#41#4114yes—
208C2×C7×Q8—24no—
209C2×C7×Q8—24no—
210C2×C7×Q8C22×C413yes—
211C2×C7×Q8C22×C413yes—
212C2×C7×Q8C22×C411yescharacteristic
213C2×C7×D4—212no—
214C2×C7×D4—212no—
215C2×C7×D4—46no—
216C2×C7×D4C22×C411yescharacteristic
217C2×C7×D4C22×C413yes—
218C2×C7×D4C22×C416yes—
219C2×C7×D4C22×C416yes—
220C2×C7×D4C22×C413yes—
221C2×C7×D4C22×C413yes—
222C2×C7×D4C22×C413yes—
223C2×C7×D4C22×C413yes—
224C2×C7×D4C22×C416yes—
225C2×C7×D4C22×C413yes—
226C22×C4×C7—26no—
227C22×C4×C7—26no—
228C22×C4×C7—26no—
229C22×C4×C7—26no—
230C22×C4×C7C22×C413yes—
231C22×C4×C7C22×C413yes—
232C22×C4×C7C22×C413yes—
233C22×C4×C7C22×C413yes—
234C22×C4×C7C22×C413yes—
235C22×C4×C7C22×C413yes—
236C22×C4×C7C22×C413yes—
237C22×C4×C7C22×C413yes—
238C22×C4×C7C2411yescharacteristic
239C22×C4×C7C2413yes—
240C22×C4×C7C2413yes—
241C22×C4×C7C2411yescharacteristic
242C22×C4×C7C2413yes—
243C7×C4⋊C4C22×C411yescharacteristic
244C7×C4⋊C4C22×C413yes—
245C7×C4⋊C4C22×C413yes—
246C7×C4⋊C4C22×C413yes—
247C7×C4⋊C4C22×C413yes—
248C7×C4⋊C4C22×C413yes—
249C7×C4⋊C4C22×C416yes—
250C7×C22⋊C4C22×C411yescharacteristic
251C7×C22⋊C4C22×C411yescharacteristic
252C7×C22⋊C4C22×C413yes—
253C7×C22⋊C4C22×C413yes—
254C7×C22⋊C4C22×C413yes—
255C7×C22⋊C4C22×C413yes—
256C7×C22⋊C4C22×C413yes—
257C7×C22⋊C4C22×C413yes—
258C7×C22⋊C4C22×C416yes—
259C7×C22⋊C4C22×C416yes—
260C7×C22⋊C4C22×C416yes—
261C42×C7C22×C413yes—
262C42×C7C22×C413yes—
263C42×C7C2411yescharacteristic
264C42×C7C2413yes—
265#1136—26no—
266#1136—26no—
267#1136—26no—
268#1136—22no—
269#1136—26no—
270#1136—26no—
271#1136—212no—
272#1136—26no—
273#1136C2×D4112yescomplemented
274C2×C7⋊C8—26no—
275C2×C7⋊C8—26no—
276C2×C7⋊C8—26no—
277C2×C7⋊C8—22no—
278C2×C7⋊C8—26no—
279C2×C7⋊C8—26no—
280C2×C7⋊C8—26no—
281C2×C7⋊C8—212no—
282C2×C7⋊C8C2×D4112yescomplemented
283C2×C7⋊C8C2411yescharacteristic
284C2×C7⋊C8C2413yes—
285C2×C7⋊C8C2411yescharacteristic
286C2×C7⋊C8C2411yescharacteristic
287C2×C7⋊C8C2413yes—
288C2×C7⋊C8C2413yes—
289C2×C7⋊C8C2411yescharacteristic
290C2×C7⋊C8C2413yes—
291C22×#41C2×D711yescharacteristic
292C22×#41C2×D711yescharacteristic
293#568—148no—
294C2×#131—71no—
295C2×#131—71no—
296C2×#131—71no—
297C2×#131—71no—
298C2×#131—73no—
299C2×#131—73no—
300C2×#131—73no—
301C2×#131—73no—
302C2×#131—148no—
303C22×M16—73no—
304C22×M16—73no—
305C22×M16—73no—
306C23×C8—73no—
307#550Dic711yescharacteristic
308D4×Q8Dic711yescharacteristic
309#548Dic711yescharacteristic
310#548Dic711yescharacteristic
311#547Dic713yes—
312#546Dic713yes—
313#546Dic713yes—
314D42Dic713yes—
315#532C2×D713yes—
316#525C2×D713yes—
317#525C2×D713yes—
318C4×#41C2×D711yescharacteristic
319C2×C4×D4C2×D713yes—
320#436—76no—
321#436—76no—
322#435—71no—
323#435—73no—
324#435—73no—
325#435—73no—
326#435—73no—
327#435—73no—
328#435—73no—
329#435—73no—
330#435—76no—
331#435—76no—
332#435—76no—
333C8×D4—76no—
334C8×D4—76no—
335#424—73no—
336#424—73no—
337#423—73no—
338C2×C4⋊C8—73no—
339#408—73no—
340#408—73no—
341#408—73no—
342#408—73no—
343#407—73no—
344#407—73no—
345C2×C22⋊C8—73no—
346C2×C22⋊C8—73no—
347#405—73no—
348#405—73no—
349C4×M16—73no—
350C2×#97—73no—
351C23×C7—26no—
352C23×C7—26no—
353C23×C7—26no—
354C23×C7—43no—
355C23×C7—43no—
356C23×C7—43no—
357C23×C7C23×C411yescharacteristic
358C23×C7C23×C413yes—
359C23×C7C23×C413yes—
360C23×C7C23×C413yes—
361C23×C7C23×C411yescharacteristic
362C7×Q8—26no—
363C7×Q8—26no—
364C7×Q8C4×D414yes—
365C7×D4—212no—
366C7×D4—212no—
367C7×D4—22no—
368C7×D4—26no—
369C7×D4—26no—
370C7×D4—26no—
371C7×D4—43no—
372C7×D4—43no—
373C7×D4—46no—
374C7×D4C4×D4112yes—
375C2×C4×C7—26no—
376C2×C4×C7—26no—
377C2×C4×C7—26no—
378C2×C4×C7—26no—
379C2×C4×C7—26no—
380C2×C4×C7—26no—
381C2×C4×C7—21no—
382C2×C4×C7—23no—
383C2×C4×C7—23no—
384C2×C4×C7—21no—
385C2×C4×C7—21no—
386C2×C4×C7—21no—
387C2×C4×C7—23no—
388C2×C4×C7—23no—
389C2×C4×C7—43no—
390C2×C4×C7—43no—
391C2×C4×C7C23×C411yescharacteristic
392C2×C4×C7C23×C411yescharacteristic
393C2×C4×C7C23×C413yes—
394C2×C4×C7C23×C413yes—
395C2×C4×C7C23×C411yescharacteristic
396C2×C4×C7C23×C411yescharacteristic
397C2×C4×C7C23×C413yes—
398C2×C4×C7C23×C413yes—
399C2×C4×C7C23×C413yes—
400C2×C4×C7C22×D416yes—
401C2×C4×C7C2×#4116yes—
402C2×C4×C7C2511yescharacteristic
403C7⋊C8—21no—
404C7⋊C8—23no—
405C7⋊C8—21no—
406C7⋊C8—23no—
407C7⋊C8—21no—
408C7⋊C8—23no—
409C7⋊C8C22×D412yes—
410C7⋊C8C22×D416yes—
411C2×#41—24no—
412C2×#41—24no—
413C2×#41—24no—
414C2×#41—24no—
415C2×#41C2×Dic713yes—
416C2×#41C2×Dic713yes—
417C2×#41C2×Dic711yescharacteristic
418C2×#41C2×Dic711yescharacteristic
419C2×#41C22×D713yes—
420C2×#41C22×D713yes—
421C2×#41C22×D711yescharacteristic
422C22×Q8C2×Dic711yescharacteristic
423C22×Q8C2×Dic711yescharacteristic
424C22×D4C2×Dic713yes—
425C22×D4C2×Dic713yes—
426C22×D4C2×Dic713yes—
427C23×C4C22×D713yes—
428C23×C4C22×D713yes—
429#131—78no—
430#131—1412no—
431#131—1412no—
432#131—1412no—
433#131—1412no—
434#131—144no—
435#131—144no—
436#131—144no—
437C2×M16—73no—
438C2×M16—71no—
439C2×M16—73no—
440C2×M16—73no—
441C2×M16—73no—
442C2×M16—73no—
443C2×M16—73no—
444C2×M16—76no—
445C2×M16—73no—
446C2×M16—1412no—
447C2×M16—1412no—
448C2×M16—1412no—
449C22×C8—73no—
450C22×C8—71no—
451C22×C8—73no—
452C22×C8—73no—
453C22×C8—73no—
454C22×C8—73no—
455C22×C8—73no—
456C22×C8—76no—
457C22×C8—73no—
458C22×C8—1412no—
459C4⋊Q8C2×Dic713yes—
460#127C2×Dic713yes—
461#124C2×Dic713yes—
462#124C2×Dic713yes—
463#123C2×Dic716yes—
464#123C2×Dic716yes—
465C22⋊Q8C2×Dic713yes—
466C22⋊Q8C2×Dic713yes—
467C22⋊Q8C2×Dic713yes—
468C22⋊Q8C2×Dic713yes—
469#121C2×Dic713yes—
470#121C2×Dic713yes—
471#121C2×Dic713yes—
472#121C2×Dic713yes—
473#121C2×Dic716yes—
474#121C2×Dic716yes—
475#120C2×Dic716yes—
476#120C2×Dic716yes—
477C4×Q8C2×Dic711yescharacteristic
478C4×Q8C2×Dic711yescharacteristic
479C4×D4C2×Dic713yes—
480C4×D4C2×Dic713yes—
481C4×D4C2×Dic713yes—
482C4×D4C2×Dic713yes—
483C4×D4C2×Dic713yes—
484C4×D4C2×Dic713yes—
485C4×D4C22×D711yescharacteristic
486C4×D4C22×D713yes—
487C4×D4C22×D713yes—
488C4×D4C22×D713yes—
489C4×D4C22×D716yes—
490#117C22×D713yes—
491C2×C4⋊C4C2×Dic713yes—
492C2×C22⋊C4C2×Dic713yes—
493C2×C22⋊C4C2×Dic713yes—
494C2×C42C22×D713yes—
495C4⋊C8—71no—
496C4⋊C8—73no—
497C4⋊C8—73no—
498C4⋊C8—73no—
499C4⋊C8—76no—
500C22⋊C8—71no—
501C22⋊C8—71no—
502C22⋊C8—73no—
503C22⋊C8—73no—
504C22⋊C8—73no—
505C22⋊C8—73no—
506C22⋊C8—73no—
507C22⋊C8—73no—
508C22⋊C8—76no—
509C22⋊C8—76no—
510#97—71no—
511#97—73no—
512#97—73no—
513#97—73no—
514C4×C8—76no—
515C22×C7—21no—
516C22×C7—23no—
517C22×C7—23no—
518C22×C7—21no—
519C22×C7—21no—
520C22×C7—23no—
521C22×C7—23no—
522C22×C7—21no—
523C22×C7—23no—
524C22×C7—23no—
525C22×C7—23no—
526C22×C7—23no—
527C22×C7—21no—
528C22×C7—412no—
529C22×C7—86no—
530C22×C7C2×C4×D416yes—
531C22×C7#56812yescomplemented
532C22×C7C24×C411yescharacteristic
533C4×C7—21no—
534C4×C7—21no—
535C4×C7—23no—
536C4×C7—23no—
537C4×C7—21no—
538C4×C7—23no—
539C4×C7—21no—
540C4×C7—23no—
541C4×C7C2×C4×D416yes—
542C4×C7C23×D411yescharacteristic
543C4×C7C22×#4111yescharacteristic
544C24C22×Dic713yes—
545C24C22×Dic713yes—
546#41—24no—
547#41—24no—
548#41—212no—
549#41—212no—
550#41—26no—
551#41—26no—
552#41—26no—
553#41—26no—
554#41D4×D714yes—
555#41#115914yes—
556C2×Q8—24no—
557C2×Q8—24no—
558C2×Q8C22×Dic713yes—
559C2×Q8C22×Dic713yes—
560C2×Q8C22×Dic711yescharacteristic
561C2×D4—212no—
562C2×D4—212no—
563C2×D4—46no—
564C2×D4C22×Dic711yescharacteristic
565C2×D4C22×Dic713yes—
566C2×D4C22×Dic716yes—
567C2×D4C22×Dic716yes—
568C2×D4C22×Dic713yes—
569C2×D4C22×Dic713yes—
570C2×D4C22×Dic713yes—
571C2×D4C22×Dic713yes—
572C2×D4C22×Dic716yes—
573C2×D4C22×Dic713yes—
574C22×C4—26no—
575C22×C4—26no—
576C22×C4—26no—
577C22×C4—26no—
578C22×C4C22×Dic713yes—
579C22×C4C22×Dic713yes—
580C22×C4C22×Dic713yes—
581C22×C4C22×Dic713yes—
582C22×C4C22×Dic713yes—
583C22×C4C22×Dic713yes—
584C22×C4C22×Dic713yes—
585C22×C4C22×Dic713yes—
586C22×C4C23×D711yescharacteristic
587C22×C4C23×D713yes—
588C22×C4C23×D713yes—
589C22×C4C23×D711yescharacteristic
590C22×C4C23×D713yes—
591M16—712no—
592M16—142no—
593M16—146no—
594M16—146no—
595M16—146no—
596M16—1412no—
597M16—146no—
598M16—146no—
599M16—146no—
600C2×C8—712no—
601C2×C8—73no—
602C2×C8—71no—
603C2×C8—73no—
604C2×C8—71no—
605C2×C8—71no—
606C2×C8—71no—
607C2×C8—73no—
608C2×C8—73no—
609C2×C8—142no—
610C2×C8—146no—
611C2×C8—146no—
612C2×C8—146no—
613C2×C8—1412no—
614C2×C8—146no—
615C2×C8—146no—
616C2×C8—146no—
617C4⋊C4C22×Dic711yescharacteristic
618C4⋊C4C22×Dic713yes—
619C4⋊C4C22×Dic713yes—
620C4⋊C4C22×Dic713yes—
621C4⋊C4C22×Dic713yes—
622C4⋊C4C22×Dic713yes—
623C4⋊C4C22×Dic716yes—
624C22⋊C4C22×Dic711yescharacteristic
625C22⋊C4C22×Dic711yescharacteristic
626C22⋊C4C22×Dic713yes—
627C22⋊C4C22×Dic713yes—
628C22⋊C4C22×Dic713yes—
629C22⋊C4C22×Dic713yes—
630C22⋊C4C22×Dic713yes—
631C22⋊C4C22×Dic713yes—
632C22⋊C4C22×Dic716yes—
633C22⋊C4C22×Dic716yes—
634C22⋊C4C22×Dic716yes—
635C42C22×Dic713yes—
636C42C22×Dic713yes—
637C42C23×D713yes—
638C42C23×D711yescharacteristic
639C2×C7—22no—
640C2×C7—26no—
641C2×C7—43no—
642C2×C7—43no—
643C2×C7—41no—
644C2×C7C22×C4×D411yescharacteristic
645C2×C7C2×#56811yescharacteristic
646C2×C7#357311yescharacteristic
647C23—26no—
648C23—26no—
649C23—26no—
650C23—43no—
651C23—43no—
652C23—43no—
653C23C23×Dic711yescharacteristic
654C23C23×Dic713yes—
655C23C23×Dic713yes—
656C23C23×Dic713yes—
657C23C23×Dic711yescharacteristic
658Q8—26no—
659Q8—26no—
660Q8D4×Dic714yes—
661D4—212no—
662D4—212no—
663D4—22no—
664D4—26no—
665D4—26no—
666D4—26no—
667D4—43no—
668D4—43no—
669D4—46no—
670D4D4×Dic7112yes—
671C2×C4—26no—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—26no—
676C2×C4—26no—
677C2×C4—21no—
678C2×C4—23no—
679C2×C4—23no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—23no—
684C2×C4—23no—
685C2×C4—43no—
686C2×C4—43no—
687C2×C4C2×D4×D716yes—
688C2×C4C2×#115916yes—
689C2×C4C23×Dic711yescharacteristic
690C2×C4C23×Dic711yescharacteristic
691C2×C4C23×Dic713yes—
692C2×C4C23×Dic713yes—
693C2×C4C23×Dic711yescharacteristic
694C2×C4C23×Dic711yescharacteristic
695C2×C4C23×Dic713yes—
696C2×C4C23×Dic713yes—
697C2×C4C23×Dic713yes—
698C2×C4C24×D711yescharacteristic
699C8—72no—
700C8—76no—
701C8—141no—
702C8—143no—
703C8—143no—
704C8—141no—
705C8—141no—
706C8—143no—
707C7#6014611yescharacteristic, complemented, Sylow
708C22—21no—
709C22—23no—
710C22—23no—
711C22—21no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—23no—
717C22—23no—
718C22—23no—
719C22—23no—
720C22—21no—
721C22—412no—
722C22—86no—
723C22C2×D4×Dic716yes—
724C22#9051012yescomplemented
725C22C24×Dic711yescharacteristic
726C4—21no—
727C4—21no—
728C4—23no—
729C4—23no—
730C4—21no—
731C4—23no—
732C4—21no—
733C4—23no—
734C4C2×D4×Dic716yes—
735C4C22×D4×D711yescharacteristic
736C4C22×#115911yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×D4×Dic711yescharacteristic
743C2C2×#9051011yescharacteristic
744C2#1174436411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D7
commutator, socleC22×C7C24×C4
Fitting, prime radicalC7×D4×#41C2
cosocleC2×C4×C7C25
hypercenterD4×#41D7
hypocenterC7#60146
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
2. C2×#90510C2semidirect
3. C22×#6511C2semidirect
4. #11741520C2semidirect
5. #11741520C2semidirect
6. #11740722C2semidirect
7. #11740721C2semidirect
8. #11740363C2semidirect
9. #11740363C2semidirect
10. #11740362C2semidirect
11. #11740361C2semidirect
12. #11739957C2semidirect
13. #11739956C2semidirect
14. D4×#1136C2semidirect
15. C2×#89783C2semidirect
37. C2×#6511C22semidirect
38. C2×#6511C22semidirect
39. C2×#6511C22semidirect
40. C2×#6511C22semidirect
41. C22×#1136C22semidirect
42. C22×#1136C22semidirect
43. C22×#1136C22semidirect
44. C23×C7⋊C8C22semidirect
45. #90006C22semidirect
46. #90006C22semidirect
47. #90006C22semidirect
48. #90006C22semidirect
49. #89979C22semidirect
50. #89979C22semidirect
51. C2×C22⋊(C7⋊C8)C22semidirect
52. C2×C22⋊(C7⋊C8)C22semidirect
53. #89784C22semidirect
54. #89784C22semidirect
57. #89783C22semidirect
58. #89783C22semidirect
59. #89783C22semidirect
60. #89783C22semidirect
61. #89783C22semidirect
62. #89783C22semidirect
63. #89783C22semidirect
64. #89783C22semidirect
65. #89783C22semidirect
66. D4×C7⋊C8C22semidirect
67. D4×C7⋊C8C22semidirect
68. #89771C22semidirect
69. #89771C22semidirect
70. #89769C22semidirect
71. #89769C22semidirect
72. #89696C22semidirect
73. C2×C4⋊(C7⋊C8)C22semidirect
74. C4×#1136C22semidirect
75. C2×#6377C22semidirect
138. #6511D4semidirect
273. #1136C2×D4semidirect
282. C2×C7⋊C8C2×D4semidirect
531. C22×C7#568semidirect
707. C7#60146semidirect
724. C22#90510semidirect

Maximal subgroups

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

subgroupindex
C7×D4×#412
C2×#905102
C22×#65112
#117415202
#117407222
#117407212
#117403632
#117403622
#117403612
#117399572
#117399562
D4×#11362
C2×#897832
#601467