Finite Group Databasebeta

← #33994214

Subgroups — #33994214

Order 18688.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624024C213yesmaximal, complemented
2#22624022C211yesmaximal, characteristic, complemented
3#22624017C211yesmaximal, characteristic, complemented
4#22624015C213yesmaximal, complemented
5#22623925C212yesmaximal, complemented
6#22623921C216yesmaximal, complemented
7#22623797C213yesmaximal, complemented
8#22623794C213yesmaximal, complemented
9#22623740C211yesmaximal, characteristic, complemented
10#22623701C211yesmaximal, characteristic, complemented
11#22623639C216yesmaximal, complemented
12#22623581C212yesmaximal, complemented
13#22623549C216yesmaximal, complemented
14#22623548C212yesmaximal, complemented
15#22623526C211yesmaximal, characteristic, complemented
16#22623524C213yesmaximal, complemented
17#22623509C213yesmaximal, complemented
18#22623362C216yesmaximal, complemented
19#22623228C213yesmaximal, complemented
20#22623224C213yesmaximal, complemented
21C4×#14556639C212yesmaximal, complemented
22C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
23Q8×#41×C73C211yesmaximal, characteristic, complemented
24C2×#14556639C2212yes—
25C22×Q8×D73C2211yescharacteristic
26#17989322C2213yescomplemented
27#17989322C2213yescomplemented
28#17989320C2216yescomplemented
29#17989317C2213yescomplemented
30#17989316C2211yescharacteristic, complemented
31#17989315C2213yescomplemented
32#17989314C2216yescomplemented
33#17989313C2212yescomplemented
34#17989312C2213yescomplemented
35#17989312C2216yescomplemented
36#17989311C2216yescomplemented
37#17989310C2213yescomplemented
38#17989309C2216yescomplemented
39#17989309C2216yescomplemented
40#17989308C22112yescomplemented
41#17989307C2213yescomplemented
42#17989298C2213yescomplemented
43#17989295C2216yes—
44#17989293C2216yescomplemented
45#17989291C22112yes—
46#17989286C22112yes—
47#17989285C2216yes—
48#17989283C2216yes—
49#17989278C2216yes—
50#17989272C2216yescomplemented
51#17989271C2216yes—
52#17989271C2216yescomplemented
53#17989269C22112yes—
54#17989269C22112yescomplemented
55#17989259C2211yescharacteristic, complemented
56#17989258C2213yescomplemented
57#17989252C2216yes—
58#17989252C2213yescomplemented
59Q8×C22⋊D73C2212yes—
60#17989250C2216yes—
61#17989249C2212yes—
62#17989248C2212yes—
63#17989248C2212yescomplemented
64#17989247C2216yes—
65#17989247C2216yescomplemented
66#17989246C2216yes—
67#17989240C2216yes—
68#17989239C22112yes—
69#17989238C2216yes—
70#17989214C2216yes—
71#17989211C2216yescomplemented
72#17989210C2216yescomplemented
73#17989207C22112yescomplemented
74#17989198C2216yescomplemented
75#17989197C2216yescomplemented
76#17989196C22112yescomplemented
77#17989185C22112yes—
78#17989183C22112yes—
79#17989167C2216yes—
80#17989162C2216yes—
81#17989160C2216yes—
82#17989142C2213yes—
83#17989142C2213yes—
84#17989141C2213yes—
85#17989141C2213yes—
86#17989141C2216yescomplemented
87#17989141C22112yescomplemented
88#17989140C2213yes—
89#17989138C2213yes—
90#17989138C2213yes—
91#17989137C2213yes—
92#17989134C2213yes—
93#17989134C2213yes—
94#17989133C2213yes—
95#17989124C2213yes—
96#17989124C2213yes—
97#17989124C2216yes—
98#17989124C2216yes—
99#17989124C2216yescomplemented
100#17989123C2216yes—
101#17989123C2216yes—
102#17989122C2216yes—
103#17989122C2216yes—
104#17989121C2216yescomplemented
105#17989119C2213yes—
106#17989119C2213yes—
107#17989117C2216yes—
108#17989117C2216yes—
109#17989115C2216yes—
110#17989115C2216yes—
111#17989115C22112yescomplemented
112#17989100C2216yes—
113#17989100C2216yes—
114#17989099C2213yes—
115#17989096C2216yes—
116#17989096C2216yes—
117#17989094C2211yescharacteristic
118#17989069C2216yes—
119#17989069C2212yescomplemented
120#17989068C2216yes—
121#17989068C2216yescomplemented
122#17989065C2212yescomplemented
123#17989063C2212yes—
124#17989063C2216yescomplemented
125C4×#11924029C2216yes—
126C4×#11924029C2216yes—
127C4×#11924029C2212yescomplemented
128C4×#11924028C2213yes—
129C4×#11924028C2216yes—
130C4×#11924028C2216yes—
131C4×#11924028C2216yescomplemented
132#17989055C2216yes—
133C2×Q8×Dic73C2211yescharacteristic
134C2×C4×Dic146C2213yes—
135C2×#14556556C2213yes—
136C4×Q8×D73C2213yes—
137C4×Q8×D73C2211yescharacteristic
138C4×Q8×D73C2213yes—
139C4×Q8×D73C2211yescharacteristic
140C4×Q8×D73C2213yes—
141C4×Q8×D73C2213yes—
142C4×Q8×D73C2211yescharacteristic
143C4×Q8×D73C2211yescharacteristic
144C4×Q8×D73C2216yescomplemented
145C2×C4⋊C4×D73C2213yes—
146C2×C42×D73C2213yes—
147Q82×C73C2211yescharacteristic, complemented
148#557×C73C2213yescomplemented
149#554×C73C2216yes—
150#554×C73C2213yescomplemented
151D4×Q8×C73C2212yes—
152D4×Q8×C73C2211yescharacteristic, complemented
153#533×C73C2213yes—
154#533×C73C2216yescomplemented
155C4×#41×C73C2213yes—
156C2×C4×Q8×C73C2211yescharacteristic
157C2×C4×Q8×C73C2212yescomplemented
158#14556639—216no—
159C2×#11924029C2316yes—
160C2×#11924029C2312yes—
161C2×#11924029C2316yes—
162C2×#11924028C2313yes—
163C2×#11924028C2316yes—
164C2×#11924028C2316yes—
165C2×#11924028C2316yes—
166C22×Dic146C2313yes—
167C2×Q8×D73—28no—
168C2×Q8×D73C2313yes—
169C2×Q8×D73C2313yes—
170C2×Q8×D73C2311yescharacteristic
171C2×Q8×D73C2316yes—
172C2×Q8×D73C2311yescharacteristic
173C22×C4×D73C2313yes—
174C22×C4×D73C2311yescharacteristic
175C22×C4×D73C2313yes—
176#14556591C2313yes—
177#14556590C2313yes—
178#14556590C2313yes—
179#14556590C23112yes—
180#14556590C2316yes—
181#14556589C2313yes—
182#14556589C2316yes—
183#14556589C23112yes—
184#14556588C2313yes—
185#14556587C2313yes—
186#14556586C23112yes—
187#14556586C23112yes—
188#14556586C2316yes—
189#14556586C2316yes—
190#14556586C23112yes—
191#14556586C23112yes—
192#14556585C23112yes—
193#14556584C23112yes—
194#14556584C2316yes—
195#14556584C2316yes—
196#14556583C2316yes—
197#14556582C2316yes—
198#14556582C2316yes—
199#14556582C2313yes—
200#14556582C2313yes—
201#14556582C2316yes—
202#14556581C2316yes—
203#14556581C2316yes—
204#14556581C23112yes—
205#14556581C23112yes—
206#14556581C23112yes—
207#14556581C23112yes—
208#14556580C2316yes—
209#14556580C2316yes—
210#14556580C2313yes—
211#14556580C2316yes—
212#14556579C2316yes—
213#14556579C2316yes—
214#14556578C2313yes—
215#14556577C2316yes—
216#14556577C2316yes—
217#14556577C23112yes—
218#14556576C23112yes—
219#14556576C23112yes—
220#14556576C2316yes—
221#14556576C2316yes—
222#14556576C23112yes—
223#14556576C23112yes—
224#14556575C2316yes—
225#14556574C23112yes—
226#14556573C2316yes—
227#14556573C23112yes—
228#14556573C2316yes—
229#14556572C2312yes—
230#14556571C2313yes—
231#14556571C2313yes—
232#14556571C2316yes—
233#14556571C23112yes—
234#14556570C2316yes—
235#14556569C2316yes—
236#14556569C2316yes—
237#14556569C23112yes—
238#14556569C23112yes—
239#14556569C23112yes—
240#14556569C23112yes—
241#14556568C2316yes—
242#14556568C2316yes—
243#14556567C2311yescharacteristic
244#14556567C2311yescharacteristic
245#14556567C2316yes—
246#14556567C2316yes—
247#14556567C2316yes—
248#14556567C2316yes—
249#14556567C23112yes—
250#14556566C2313yes—
251#14556566C2313yes—
252#14556566C2316yes—
253#14556566C2316yes—
254#14556566C2316yes—
255#14556565C2316yes—
256#14556565C2316yes—
257#14556565C2316yes—
258#14556564C2316yes—
259#14556564C2316yes—
260#14556564C23112yes—
261#14556563C2316yes—
262#14556563C2316yes—
263#14556562C2311yescharacteristic
264#14556562C2311yescharacteristic
265#14556561C2316yes—
266#14556559C2312yes—
267Q8×Dic73C2316yes—
268Q8×Dic73C2316yes—
269Q8×Dic73C2313yes—
270Q8×Dic73C2312yes—
271Q8×Dic73C2311yescharacteristic
272Q8×Dic73C2316yes—
273Q8×Dic73C2313yes—
274Q8×Dic73C2311yescharacteristic
275C4×Dic146C2313yes—
276C4×Dic146C2316yes—
277C4×Dic146C2316yes—
278C4×Dic146C2316yes—
279C4×Dic146C2316yes—
280C4×Dic146C2313yes—
281C4×Dic146C2313yes—
282C4×Dic146C2316yes—
283C4×Dic146C2316yes—
284C4×Dic146C2313yes—
285C4×Dic146C2316yes—
286C4×Dic146C2313yes—
287C4×Dic146C2313yes—
288#14556556C2316yes—
289#14556556C2316yes—
290#14556556C2316yes—
291#14556556C2313yes—
292#14556556C2316yes—
293#14556556C2313yes—
294#14556556C23112yes—
295#14556556C2316yes—
296#14556556C2313yes—
297#14556556C2313yes—
298C4×D292C2316yes—
299C4×D292C2316yes—
300C4×D292C2316yes—
301C4×D292C2316yes—
302C4×D292C2313yes—
303C4×D292C2313yes—
304C4×D292C2316yes—
305C4×D292C2316yes—
306C4×D292C2316yes—
307#14556553C2316yes—
308#14556553C2316yes—
309#14556553C23112yes—
310#14556553C23112yes—
311#14556553C2316yes—
312#14556553C2316yes—
313#14556553C2316yes—
314C4×C22⋊D73C2316yes—
315C4×C22⋊D73C2316yes—
316C4×C22⋊D73C2316yes—
317C4×C22⋊D73C2316yes—
318C4×C22⋊D73C2316yes—
319C4×C22⋊D73C2316yes—
320C4×C22⋊D73C23112yes—
321C4×C22⋊D73C2316yes—
322C4×C22⋊D73C2316yes—
323C4×C22⋊D73C2312yes—
324C4×C22⋊D73C2312yes—
325#14556551C23112yes—
326#14556551C23112yes—
327#14556550C2311yescharacteristic
328#14556550C2316yes—
329#14556550C2316yes—
330#14556550C2316yes—
331#14556549C23112yes—
332#14556549C23112yes—
333#14556549C2316yes—
334#14556549C2316yes—
335#14556549C2316yes—
336#14556548C23112yes—
337#14556548C2316yes—
338#14556548C2316yes—
339#14556548C2316yes—
340#14556548C2316yes—
341#14556548C2316yes—
342#14556548C23112yes—
343C2×C4⋊Dic73C2313yes—
344C2×#11924007C2316yes—
345C4⋊C4×D73C2313yes—
346C4⋊C4×D73C2316yes—
347C4⋊C4×D73C2313yes—
348C4⋊C4×D73C2316yes—
349C4⋊C4×D73C23112yes—
350C4⋊C4×D73C2313yes—
351C4⋊C4×D73C2316yes—
352C4⋊C4×D73C2313yes—
353C2×C4×Dic73C2313yes—
354C2×C4×Dic73C2313yes—
355C2×C4×Dic73C2313yes—
356C42×D73C2313yes—
357C42×D73C2313yes—
358C42×D73C2313yes—
359C42×D73C2313yes—
360C42×D73C2313yes—
361C42×D73C2316yes—
362C42×D73C2313yes—
363C42×D73C23112yes—
364C42×D73C2313yes—
365C42×D73C2313yes—
366C2×#41×C73C2311yescharacteristic
367C22×Q8×C73C2311yescharacteristic
368C22×Q8×C73C2312yes—
369C4⋊Q8×C73C2313yes—
370C4⋊Q8×C73C2313yes—
371C4⋊Q8×C73C2316yes—
372C4⋊Q8×C73C2316yes—
373#125×C73C2316yes—
374#125×C73C23112yes—
375C22⋊Q8×C73C2316yes—
376C22⋊Q8×C73C2316yes—
377C22⋊Q8×C73C2316yes—
378C22⋊Q8×C73C2316yes—
379C22⋊Q8×C73C23112yes—
380C4×Q8×C73C2313yes—
381C4×Q8×C73C2313yes—
382C4×Q8×C73C2316yes—
383C4×Q8×C73C2316yes—
384C4×Q8×C73C2313yes—
385C4×Q8×C73C2312yes—
386C4×Q8×C73C2311yescharacteristic
387C4×Q8×C73C2311yescharacteristic
388C4×Q8×C73C2313yes—
389C4×Q8×C73C2316yes—
390C4×D4×C73C2313yes—
391C4×D4×C73C2313yes—
392C4×D4×C73C2316yes—
393C4×D4×C73C2316yes—
394#117×C73C2313yes—
395#117×C73C2316yes—
396C2×C4⋊C4×C73C2316yes—
397C2×C4⋊C4×C73C2313yes—
398C2×C42×C73C2316yes—
399C2×C42×C73C2313yes—
400C23×D73C2411yescharacteristic
401#11924029—28no—
402#11924029—224no—
403#11924029—412no—
404#11924028—212no—
405#11924028—224no—
406#11924028—224no—
407#11924028—412no—
408C2×Dic146—212no—
409C2×Dic146C2413yes—
410C2×Dic146C2416yes—
411C2×Dic146C2416yes—
412C2×Dic146C2413yes—
413C2×Dic146C2416yes—
414C2×Dic146C2413yes—
415Q8×D73—24no—
416Q8×D73—212no—
417Q8×D73—212no—
418Q8×D73—224no—
419Q8×D73#4118yescomplemented
420C2×D292C2413yes—
421C2×D292C2416yes—
422C2×D292C2416yes—
423C2×D292C2416yes—
424C2×D292C2416yes—
425C2×C22⋊D73C2416yes—
426C2×C22⋊D73C2412yes—
427C2×C22⋊D73C2412yes—
428C2×C22⋊D73C2416yes—
429C2×C22⋊D73C2416yes—
430C22×Dic73C2411yescharacteristic
431C22×Dic73C2413yes—
432C22×Dic73C2413yes—
433C2×C4×D73—24no—
434C2×C4×D73—212no—
435C2×C4×D73—46no—
436C2×C4×D73C2411yescharacteristic
437C2×C4×D73C2411yescharacteristic
438C2×C4×D73C2411yescharacteristic
439C2×C4×D73C2411yescharacteristic
440C2×C4×D73C2416yes—
441C2×C4×D73C2413yes—
442C2×C4×D73C2413yes—
443C2×C4×D73C2413yes—
444C2×C4×D73C2413yes—
445C2×C4×D73C2413yes—
446C2×C4×D73C24112yes—
447C2×C4×D73C2416yes—
448C2×C4×D73C2413yes—
449C2×C4×D73C2413yes—
450C2×C4×D73C2416yes—
451C2×C4×D73C24112yes—
452C2×C4×D73C2413yes—
453C4⋊Dic73C2413yes—
454C4⋊Dic73C2413yes—
455C4⋊Dic73C2416yes—
456C4⋊Dic73C2416yes—
457C4⋊Dic73C2416yes—
458C4⋊Dic73C2416yes—
459C4⋊Dic73C2416yes—
460C4⋊Dic73C2416yes—
461C4⋊Dic73C2411yescharacteristic
462C4⋊Dic73C2411yescharacteristic
463C4⋊Dic73C2416yes—
464#11924007C2416yes—
465#11924007C2416yes—
466#11924007C2416yes—
467#11924007C2416yes—
468#11924007C2416yes—
469#11924007C2416yes—
470#11924007C2416yes—
471#11924007C2412yes—
472#11924007C2412yes—
473#11924007C24112yes—
474#11924007C24112yes—
475#11924007C2416yes—
476#11924007C2416yes—
477#11924007C2416yes—
478#11924007C2416yes—
479#11924007C2416yes—
480C22⋊Dic73C2412yes—
481C22⋊Dic73C2412yes—
482C22⋊Dic73C2416yes—
483C22⋊Dic73C2412yes—
484C22⋊Dic73C2416yes—
485#11924005C2412yes—
486#11924005C2412yes—
487#11924005C2416yes—
488#11924005C2416yes—
489#11924005C2416yes—
490#11924005C24112yes—
491#11924005C2416yes—
492#11924005C2416yes—
493#11924005C24112yes—
494#11924005C24112yes—
495#11924005C2416yes—
496#11924005C2416yes—
497#11924005C2416yes—
498#11924005C24112yes—
499C4×Dic73C2413yes—
500C4×Dic73C2412yes—
501C4×Dic73C2413yes—
502C4×Dic73C2413yes—
503C4×Dic73C2413yes—
504C4×Dic73C2413yes—
505C4×Dic73C2413yes—
506C4×Dic73C2413yes—
507C4×Dic73C2413yes—
508C4×Dic73C2413yes—
509C4×Dic73C2413yes—
510C4×Dic73C2413yes—
511C4×Dic73C2413yes—
512C4×Dic73C24112yes—
513C4×Dic73C2416yes—
514C4×Dic73C2416yes—
515C4×Dic73C24112yes—
516#41×C73—24no—
517C2×Q8×C73—24no—
518C2×Q8×C73—28no—
519C2×Q8×C73C2411yescharacteristic
520C2×Q8×C73C2413yes—
521C2×Q8×C73C2416yes—
522C2×Q8×C73C2416yes—
523C2×Q8×C73C2411yescharacteristic
524C2×D4×C73C2412yes—
525C2×D4×C73C2411yescharacteristic
526C22×C4×C73C2412yes—
527C22×C4×C73C2413yes—
528C22×C4×C73C2416yes—
529C22×C4×C73C2413yes—
530C22×C4×C73C2416yes—
531C22×C4×C73C2411yescharacteristic
532C4⋊C4×C73C2413yes—
533C4⋊C4×C73C2416yes—
534C4⋊C4×C73C24112yes—
535C4⋊C4×C73C2413yes—
536C4⋊C4×C73C2416yes—
537C4⋊C4×C73C2413yes—
538C4⋊C4×C73C2413yes—
539C4⋊C4×C73C2416yes—
540C4⋊C4×C73C2416yes—
541C4⋊C4×C73C2416yes—
542C4⋊C4×C73C24112yes—
543C22⋊C4×C73C2416yes—
544C22⋊C4×C73C2416yes—
545C22⋊C4×C73C2416yes—
546C42×C73C2413yes—
547C42×C73C2413yes—
548C42×C73C2416yes—
549C42×C73C2413yes—
550C42×C73C2416yes—
551C42×C73C2413yes—
552C42×C73C2416yes—
553C23×C73C2512yes—
554C23×C73C2511yescharacteristic
555C22×D73—22no—
556C22×D73—22no—
557C22×D73—22no—
558C22×D73C2516yes—
559C22×D73C2511yescharacteristic
560C22×D73C2511yescharacteristic
561Q8×C73—26no—
562Q8×C73—212no—
563Q8×C73—22no—
564Q8×C73—46no—
565Q8×C73C2×#4114yes—
566D4×C73—24no—
567D4×C73—22no—
568C2×C4×C73—26no—
569C2×C4×C73—212no—
570C2×C4×C73—24no—
571C2×C4×C73—43no—
572C2×C4×C73—46no—
573C2×C4×C732−1+414yescomplemented
574C2×C4×C73C2512yes—
575C2×C4×C73C2513yes—
576C2×C4×C73C2513yes—
577C2×C4×C73C2516yes—
578C2×C4×C73C2516yes—
579C2×C4×C73C2513yes—
580C2×C4×C73C2513yes—
581C2×C4×C73C2511yescharacteristic
582C2×C4×C73C2511yescharacteristic
583C22⋊D73—212no—
584C22⋊D73—24no—
585C22⋊D73—24no—
586C22⋊D73—212no—
587C22⋊D73—46no—
588C2×Dic73—22no—
589C2×Dic73—26no—
590C2×Dic73—43no—
591C2×Dic73C2511yescharacteristic
592C2×Dic73C2511yescharacteristic
593C2×Dic73C2513yes—
594C2×Dic73C2516yes—
595C2×Dic73C2513yes—
596C2×Dic73C2512yes—
597C2×Dic73C2512yes—
598C2×Dic73C2513yes—
599C2×Dic73C2513yes—
600D292—212no—
601D292—212no—
602D292—212no—
603D292—26no—
604D292—46no—
605C4×D73—26no—
606C4×D73—26no—
607C4×D73—26no—
608C4×D73—26no—
609C4×D73—212no—
610C4×D73—22no—
611C4×D73—22no—
612C4×D73—22no—
613C4×D73—22no—
614C4×D73—212no—
615C4×D73—26no—
616C4×D73—224no—
617C4×D73—43no—
618C4×D73—43no—
619C4×D73—46no—
620C4×D73—412no—
621C4×D73C2×#41112yes—
622Dic146—26no—
623Dic146—26no—
624Dic146—212no—
625Dic146—212no—
626Dic146—46no—
627Dic146C2×#41112yes—
628C22×C73—21no—
629C22×C73—21no—
630C22×C73—22no—
631C22×C73—22no—
632C22×C73—22no—
633C22×C73C2×2−1+412yes—
634C22×C73C2611yescharacteristic
635C2×D73—28no—
636C2×D73—21no—
637C2×D73—21no—
638C2×D73—21no—
639C2×D73—21no—
640C2×D73—26no—
641C2×D73—26no—
642C2×D73—26no—
643C2×D73C22×#4112yes—
644C2×D73#58512yes—
645C4×C73—23no—
646C4×C73—26no—
647C4×C73—22no—
648C4×C73—26no—
649C4×C73—23no—
650C4×C73—23no—
651C4×C73C22×#4116yes—
652C4×C73C2×2−1+412yes—
653C4×C73C2×2−1+412yes—
654Dic73—23no—
655Dic73—22no—
656Dic73—26no—
657Dic73—21no—
658Dic73—21no—
659Dic73—22no—
660Dic73—23no—
661Dic73—23no—
662Dic73C22×#4116yes—
663#62788—731nomaximal, Sylow
664C2×C73—22no—
665C2×C73—42no—
666C2×C73C23×#4111yescharacteristic
667C2×C73C22×2−1+411yescharacteristic
668C2×C73C2×#58511yescharacteristic
669D73—22no—
670D73—22no—
671D73—46no—
672#3523—733no—
673#3523—731no—
674#3522—731no—
675#3522—733no—
676#3516—736no—
677#3516—732no—
678#3507—733no—
679#3507—733no—
680#3502—731no—
681#3497—731no—
682#3492—736no—
683#3486—732no—
684#3482—736no—
685#3482—732no—
686#3480—733no—
687#3480—731no—
688Q8×#41—733no—
689Q8×#41D7311yescharacteristic, complemented
690#3461—736no—
691#3444—733no—
692#3444—733no—
693C4×2−1+4—732no—
694C22×C4×Q8—731no—
695C73#6278811yescharacteristic, complemented, Sylow
696C2×2−1+4—732no—
697C23×Q8—731no—
698#559—733no—
699#559—733no—
700#559—736no—
701Q82—733no—
702Q82C2×D7311yescharacteristic, complemented
703#557—733no—
704#557—736no—
705#557—736no—
706#557—733no—
707#557—731no—
708#557—732no—
709#557C2×D7313yescomplemented
710#556—736no—
711#556—7312no—
712#556—736no—
713#556—733no—
714#556—736no—
715#556—733no—
716#554—733no—
717#554—736no—
718#554—7312no—
719#554—736no—
720#554C2×D7316yes—
721#554C2×D7313yescomplemented
722#553—736no—
723#553—7312no—
724#553—736no—
725#552—7312no—
726#552—7312no—
727#552—736no—
728#552—736no—
729#552—736no—
730#552—736no—
731#550—731no—
732#550—733no—
733D4×Q8—732no—
734D4×Q8—736no—
735D4×Q8—733no—
736D4×Q8—736no—
737D4×Q8C2×D7312yes—
738D4×Q8C2×D7311yescharacteristic, complemented
739#548—732no—
740#548—732no—
741#548—736no—
742#548—736no—
743#548—732no—
744#548—736no—
745#547—736no—
746#547—7312no—
747#547—736no—
748#544—736no—
749#542—736no—
750#542—7312no—
751#542—736no—
752#541—736no—
753#541—7312no—
754#541—736no—
755#539—7312no—
756#539—7312no—
757#537—736no—
758#536—736no—
759#536—736no—
760#533—733no—
761#533—733no—
762#533—733no—
763#533—733no—
764#533—7312no—
765#533—736no—
766#533—733no—
767#533C2×D7313yes—
768#533C2×D7316yescomplemented
769#532—733no—
770#532—733no—
771#532—733no—
772#532—733no—
773#532—733no—
774#532—733no—
775#529—736no—
776#529—736no—
777#529—736no—
778#529—736no—
779#529—736no—
780#529—736no—
781#529—733no—
782#529—733no—
783#529—736no—
784#529—733no—
785#529—736no—
786#529—736no—
787#529—733no—
788#529—736no—
789#529—736no—
790#529—7312no—
791#529—736no—
792#525—731no—
793#525—736no—
794#525—736no—
795#525—736no—
796#525—736no—
797#525—733no—
798#520—736no—
799#520—732no—
800#520—736no—
801#520—736no—
802#519—732no—
803#519—732no—
804#519—736no—
805C4×#41—736no—
806C4×#41—732no—
807C4×#41—736no—
808C4×#41—736no—
809C4×#41—736no—
810C4×#41—736no—
811C4×#41—733no—
812C4×#41—736no—
813C4×#41C2×D7313yes—
814C2×C4×Q8—731no—
815C2×C4×Q8—731no—
816C2×C4×Q8—733no—
817C2×C4×Q8—731no—
818C2×C4×Q8—733no—
819C2×C4×Q8—731no—
820C2×C4×Q8—733no—
821C2×C4×Q8—731no—
822C2×C4×Q8—733no—
823C2×C4×Q8—736no—
824C2×C4×Q8—733no—
825C2×C4×Q8—733no—
826C2×C4×Q8C2×D7311yescharacteristic
827C2×C4×Q8C2×D7312yescomplemented
828C22×C4⋊C4—733no—
829C22×C42—733no—
8302−1+4—14616no—
831C2×#41—736no—
832C2×#41—736no—
833C2×#41—732no—
834C2×#41—736no—
835C2×#41—733no—
836C2×#41—736no—
837C2×#41—736no—
838C2×#41C22×D7311yescharacteristic
839C22×Q8—731no—
840C22×Q8—733no—
841C22×Q8—733no—
842C22×Q8—731no—
843C22×Q8—736no—
844C22×Q8—733no—
845C22×Q8—1468no—
846C22×Q8C22×D7311yescharacteristic
847C22×Q8C22×D7312yes—
848C23×C4—733no—
849C23×C4—733no—
850C23×C4—731no—
851C4⋊Q8—733no—
852C4⋊Q8—736no—
853C4⋊Q8—7312no—
854C4⋊Q8—733no—
855C4⋊Q8—733no—
856C4⋊Q8—7312no—
857C4⋊Q8—736no—
858C4⋊Q8—733no—
859C4⋊Q8C22×D7313yes—
860C4⋊Q8C22×D7313yes—
861C4⋊Q8C22×D7316yes—
862C4⋊Q8C22×D7316yes—
863#127—733no—
864#127—733no—
865#126—736no—
866#126—7312no—
867#126—736no—
868#126—7312no—
869#126—7312no—
870#126—7312no—
871#126—736no—
872#126—736no—
873#126—7312no—
874#126—7312no—
875#125—736no—
876#125—736no—
877#125—736no—
878#125—736no—
879#125—733no—
880#125—733no—
881#125—7312no—
882#125—736no—
883#125—7312no—
884#125—7312no—
885#125—7312no—
886#125—736no—
887#125C22×D7316yes—
888#125C22×D73112yes—
889#124—736no—
890#124—736no—
891#124—733no—
892#124—736no—
893#124—733no—
894#124—736no—
895#124—736no—
896#124—7312no—
897#124—736no—
898#124—736no—
899#123—732no—
900#123—7312no—
901#123—736no—
902#123—7312no—
903#123—736no—
904#123—7312no—
905#123—7312no—
906#123—7312no—
907#123—736no—
908#123—736no—
909#123—736no—
910#123—7312no—
911C22⋊Q8—731no—
912C22⋊Q8—731no—
913C22⋊Q8—736no—
914C22⋊Q8—736no—
915C22⋊Q8—736no—
916C22⋊Q8—736no—
917C22⋊Q8—7312no—
918C22⋊Q8—736no—
919C22⋊Q8—733no—
920C22⋊Q8—733no—
921C22⋊Q8—736no—
922C22⋊Q8—736no—
923C22⋊Q8—7312no—
924C22⋊Q8—7312no—
925C22⋊Q8—736no—
926C22⋊Q8—7312no—
927C22⋊Q8—7312no—
928C22⋊Q8—7312no—
929C22⋊Q8—736no—
930C22⋊Q8—736no—
931C22⋊Q8C22×D7316yes—
932C22⋊Q8C22×D7316yes—
933C22⋊Q8C22×D7316yes—
934C22⋊Q8C22×D7316yes—
935C22⋊Q8C22×D73112yes—
936#121—731no—
937#121—731no—
938#121—736no—
939#121—736no—
940#121—736no—
941#121—736no—
942#121—736no—
943#121—733no—
944#121—733no—
945#121—736no—
946#121—736no—
947#121—736no—
948#121—736no—
949#121—736no—
950#121—7312no—
951#120—732no—
952#120—736no—
953C4×Q8—731no—
954C4×Q8—733no—
955C4×Q8—731no—
956C4×Q8—733no—
957C4×Q8—736no—
958C4×Q8—736no—
959C4×Q8—732no—
960C4×Q8—736no—
961C4×Q8—733no—
962C4×Q8—736no—
963C4×Q8—733no—
964C4×Q8—733no—
965C4×Q8—736no—
966C4×Q8—733no—
967C4×Q8—736no—
968C4×Q8—7312no—
969C4×Q8—736no—
970C4×Q8—736no—
971C4×Q8—733no—
972C4×Q8—736no—
973C4×Q8—733no—
974C4×Q8—733no—
975C4×Q8—733no—
976C4×Q8—736no—
977C4×Q8—736no—
978C4×Q8—736no—
979C4×Q8—736no—
980C4×Q8—736no—
981C4×Q8—736no—
982C4×Q8—733no—
983C4×Q8—733no—
984C4×Q8C22×D7311yescharacteristic
985C4×Q8C22×D7313yes—
986C4×Q8C22×D7311yescharacteristic
987C4×Q8C22×D7313yes—
988C4×Q8C22×D7316yes—
989C4×Q8C22×D7312yes—
990C4×Q8C22×D7316yes—
991C4×Q8C22×D7316yes—
992C4×Q8C22×D7313yes—
993C4×Q8C22×D7313yes—
994C4×D4—732no—
995C4×D4—732no—
996C4×D4—736no—
997C4×D4—736no—
998C4×D4—736no—
999C4×D4—7312no—
1000C4×D4—736no—
1001C4×D4—736no—
1002C4×D4—736no—
1003C4×D4—736no—
1004C4×D4—736no—
1005C4×D4—7312no—
1006C4×D4—736no—
1007C4×D4—736no—
1008C4×D4—7312no—
1009C4×D4—736no—
1010C4×D4—736no—
1011C4×D4—736no—
1012C4×D4—7312no—
1013C4×D4—7312no—
1014C4×D4—736no—
1015C4×D4—736no—
1016C4×D4—736no—
1017C4×D4—736no—
1018C4×D4—736no—
1019C4×D4—736no—
1020C4×D4—736no—
1021C4×D4—733no—
1022C4×D4—733no—
1023C4×D4C22×D7316yes—
1024C4×D4C22×D7316yes—
1025C4×D4C22×D7313yes—
1026C4×D4C22×D7313yes—
1027#117—731no—
1028#117—736no—
1029#117—736no—
1030#117—736no—
1031#117—736no—
1032#117—7312no—
1033#117—736no—
1034#117—736no—
1035#117—7312no—
1036#117—736no—
1037#117—736no—
1038#117—7312no—
1039#117—736no—
1040#117—7312no—
1041#117—736no—
1042#117—736no—
1043#117C22×D7313yes—
1044#117C22×D7316yes—
1045C2×C4⋊C4—736no—
1046C2×C4⋊C4—733no—
1047C2×C4⋊C4—733no—
1048C2×C4⋊C4—733no—
1049C2×C4⋊C4—736no—
1050C2×C4⋊C4—736no—
1051C2×C4⋊C4—733no—
1052C2×C4⋊C4—733no—
1053C2×C4⋊C4—7312no—
1054C2×C4⋊C4—736no—
1055C2×C4⋊C4C22×D7313yes—
1056C2×C4⋊C4C22×D7316yes—
1057C2×C42—733no—
1058C2×C42—733no—
1059C2×C42—733no—
1060C2×C42—733no—
1061C2×C42—733no—
1062C2×C42—733no—
1063C2×C42—733no—
1064C2×C42—733no—
1065C2×C42—733no—
1066C2×C42—733no—
1067C2×C42—733no—
1068C2×C42—7312no—
1069C2×C42—736no—
1070C2×C42C22×D7313yes—
1071C2×C42C22×D7316yes—
1072C24—731no—
1073#41—24no—
1074#41—29212no—
1075#41—29212no—
1076#41—14624no—
1077#41—14624no—
1078#41—14624no—
1079#41—1468no—
1080#41—14612no—
1081C2×Q8—24no—
1082C2×Q8—28no—
1083C2×Q8—738no—
1084C2×Q8—736no—
1085C2×Q8—733no—
1086C2×Q8—733no—
1087C2×Q8—736no—
1088C2×Q8—733no—
1089C2×Q8—736no—
1090C2×Q8—14612no—
1091C2×Q8—14612no—
1092C2×Q8—14612no—
1093C2×Q8—14624no—
1094C2×Q8—1464no—
1095C2×Q8C23×D7313yes—
1096C2×Q8C23×D7316yes—
1097C2×Q8C23×D7311yescharacteristic
1098C2×Q8C23×D7316yes—
1099C2×Q8C23×D7311yescharacteristic
1100C2×D4—736no—
1101C2×D4—736no—
1102C2×D4—732no—
1103C2×D4—732no—
1104C2×D4—736no—
1105C2×D4—736no—
1106C2×D4—733no—
1107C2×D4—736no—
1108C2×D4—736no—
1109C2×D4—736no—
1110C2×D4C23×D7312yes—
1111C2×D4C23×D7311yescharacteristic
1112C22×C4—2926no—
1113C22×C4—733no—
1114C22×C4—733no—
1115C22×C4—733no—
1116C22×C4—7312no—
1117C22×C4—736no—
1118C22×C4—733no—
1119C22×C4—731no—
1120C22×C4—733no—
1121C22×C4—731no—
1122C22×C4—731no—
1123C22×C4—733no—
1124C22×C4—733no—
1125C22×C4—733no—
1126C22×C4—733no—
1127C22×C4—733no—
1128C22×C4—7312no—
1129C22×C4—736no—
1130C22×C4—731no—
1131C22×C4—731no—
1132C22×C4—736no—
1133C22×C4—14612no—
1134C22×C4—1464no—
1135C22×C4C23×D7313yes—
1136C22×C4C23×D7316yes—
1137C22×C4C23×D7312yes—
1138C22×C4C23×D7313yes—
1139C22×C4C23×D7316yes—
1140C22×C4C23×D7311yescharacteristic
1141C4⋊C4—736no—
1142C4⋊C4—736no—
1143C4⋊C4—736no—
1144C4⋊C4—736no—
1145C4⋊C4—736no—
1146C4⋊C4—736no—
1147C4⋊C4—736no—
1148C4⋊C4—732no—
1149C4⋊C4—732no—
1150C4⋊C4—736no—
1151C4⋊C4—736no—
1152C4⋊C4—736no—
1153C4⋊C4—7312no—
1154C4⋊C4—736no—
1155C4⋊C4—736no—
1156C4⋊C4—7312no—
1157C4⋊C4—733no—
1158C4⋊C4—733no—
1159C4⋊C4—736no—
1160C4⋊C4—736no—
1161C4⋊C4—736no—
1162C4⋊C4—736no—
1163C4⋊C4—736no—
1164C4⋊C4—731no—
1165C4⋊C4—731no—
1166C4⋊C4—736no—
1167C4⋊C4—736no—
1168C4⋊C4C23×D7313yes—
1169C4⋊C4C23×D7313yes—
1170C4⋊C4C23×D7316yes—
1171C4⋊C4C23×D7316yes—
1172C4⋊C4C23×D73112yes—
1173C4⋊C4C23×D7316yes—
1174C4⋊C4C23×D73112yes—
1175C4⋊C4C23×D7313yes—
1176C4⋊C4C23×D7313yes—
1177C4⋊C4C23×D7316yes—
1178C4⋊C4C23×D7316yes—
1179C22⋊C4—736no—
1180C22⋊C4—732no—
1181C22⋊C4—732no—
1182C22⋊C4—732no—
1183C22⋊C4—736no—
1184C22⋊C4—736no—
1185C22⋊C4—736no—
1186C22⋊C4—732no—
1187C22⋊C4—732no—
1188C22⋊C4—736no—
1189C22⋊C4—7312no—
1190C22⋊C4—736no—
1191C22⋊C4—736no—
1192C22⋊C4—736no—
1193C22⋊C4—7312no—
1194C22⋊C4—7312no—
1195C22⋊C4—736no—
1196C22⋊C4—7312no—
1197C22⋊C4—736no—
1198C22⋊C4C23×D7316yes—
1199C22⋊C4C23×D7316yes—
1200C22⋊C4C23×D7316yes—
1201C42—733no—
1202C42—733no—
1203C42—733no—
1204C42—733no—
1205C42—733no—
1206C42—733no—
1207C42—733no—
1208C42—733no—
1209C42—733no—
1210C42—733no—
1211C42—7312no—
1212C42—736no—
1213C42—7312no—
1214C42—736no—
1215C42—733no—
1216C42—733no—
1217C42—732no—
1218C42C23×D7313yes—
1219C42C23×D7313yes—
1220C42C23×D7316yes—
1221C42C23×D7316yes—
1222C42C23×D7313yes—
1223C42C23×D7313yes—
1224C42C23×D7316yes—
1225C23—731no—
1226C23—731no—
1227C23—736no—
1228C23—1462no—
1229C23—1462no—
1230C23—1462no—
1231C23C24×D7312yes—
1232C23C24×D7311yescharacteristic
1233Q8—26no—
1234Q8—212no—
1235Q8—22no—
1236Q8—46no—
1237Q8—2926no—
1238Q8—7312no—
1239Q8—14612no—
1240Q8—14612no—
1241Q8—1466no—
1242Q8—1466no—
1243Q8#41×D7314yes—
1244D4—24no—
1245D4—22no—
1246D4—2926no—
1247D4—2926no—
1248D4—14612no—
1249D4—14612no—
1250D4—14612no—
1251D4—1464no—
1252D4—1464no—
1253D4—14612no—
1254D4—14612no—
1255D4—1466no—
1256C2×C4—26no—
1257C2×C4—212no—
1258C2×C4—24no—
1259C2×C4—43no—
1260C2×C4—46no—
1261C2×C4—2923no—
1262C2×C4—2923no—
1263C2×C4—2926no—
1264C2×C4—29212no—
1265C2×C4—2923no—
1266C2×C4—733no—
1267C2×C4—7312no—
1268C2×C4—731no—
1269C2×C4—731no—
1270C2×C4—733no—
1271C2×C4—736no—
1272C2×C4—733no—
1273C2×C4—732no—
1274C2×C4—732no—
1275C2×C4—733no—
1276C2×C4—1466no—
1277C2×C4—14624no—
1278C2×C4—1466no—
1279C2×C4—1466no—
1280C2×C4—1466no—
1281C2×C4—1466no—
1282C2×C4—1462no—
1283C2×C4—1466no—
1284C2×C4—14612no—
1285C2×C4—1462no—
1286C2×C4—1462no—
1287C2×C4—1462no—
1288C2×C4—1462no—
1289C2×C4—14612no—
1290C2×C4#1455663914yescomplemented
1291C2×C4C24×D7313yes—
1292C2×C4C24×D7313yes—
1293C2×C4C24×D7316yes—
1294C2×C4C24×D7316yes—
1295C2×C4C24×D7313yes—
1296C2×C4C24×D7312yes—
1297C2×C4C24×D7313yes—
1298C2×C4C24×D7311yescharacteristic
1299C2×C4C24×D7311yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—732no—
1306C22—732no—
1307C22—1468no—
1308C22—1466no—
1309C22—1466no—
1310C22—1466no—
1311C22—1461no—
1312C22—1461no—
1313C22—1461no—
1314C22—1461no—
1315C22C2×#1455663912yes—
1316C22C25×D7311yescharacteristic
1317C4—26no—
1318C4—23no—
1319C4—22no—
1320C4—23no—
1321C4—26no—
1322C4—23no—
1323C4—736no—
1324C4—1462no—
1325C4—1463no—
1326C4—1461no—
1327C4—1461no—
1328C4—1466no—
1329C4—1463no—
1330C4—1462no—
1331C4—1463no—
1332C4C2×#41×D7316yes—
1333C4C2×#1455663912yes—
1334C4C2×#1455663912yes—
1335C2—22no—
1336C2—42no—
1337C2—2926no—
1338C2—1462no—
1339C2—1462no—
1340C2C22×#41×D7311yescharacteristic
1341C2C22×#1455663911yescharacteristic
1342C2#585×D7311yescharacteristic
subgroupG/H
centerC2×C4C24×D73
commutator, socle, cosocleC22×C73C26
FrattiniC22C25×D73
FittingQ8×#41×C73C2
hypercenterQ8×#41D73
hypocenterC73#62788
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #22624024C2semidirect
2. #22624022C2semidirect
3. #22624017C2semidirect
4. #22624015C2semidirect
5. #22623925C2semidirect
6. #22623921C2semidirect
7. #22623797C2semidirect
8. #22623794C2semidirect
9. #22623740C2semidirect
10. #22623701C2semidirect
11. #22623639C2semidirect
12. #22623581C2semidirect
13. #22623549C2semidirect
14. #22623548C2semidirect
15. #22623526C2semidirect
16. #22623524C2semidirect
17. #22623509C2semidirect
18. #22623362C2semidirect
19. #22623228C2semidirect
20. #22623224C2semidirect
21. C4×#14556639C2semidirect
22. C2×C4×Q8×D73C2semidirect
23. Q8×#41×C73C2semidirect
26. #17989322C22semidirect
27. #17989322C22semidirect
28. #17989320C22semidirect
29. #17989317C22semidirect
30. #17989316C22semidirect
31. #17989315C22semidirect
32. #17989314C22semidirect
33. #17989313C22semidirect
34. #17989312C22semidirect
35. #17989312C22semidirect
36. #17989311C22semidirect
37. #17989310C22semidirect
38. #17989309C22semidirect
39. #17989309C22semidirect
40. #17989308C22semidirect
41. #17989307C22semidirect
42. #17989298C22semidirect
44. #17989293C22semidirect
50. #17989272C22semidirect
52. #17989271C22semidirect
54. #17989269C22semidirect
55. #17989259C22semidirect
56. #17989258C22semidirect
58. #17989252C22semidirect
63. #17989248C22semidirect
65. #17989247C22semidirect
71. #17989211C22semidirect
72. #17989210C22semidirect
73. #17989207C22semidirect
74. #17989198C22semidirect
75. #17989197C22semidirect
76. #17989196C22semidirect
86. #17989141C22semidirect
87. #17989141C22semidirect
99. #17989124C22semidirect
104. #17989121C22semidirect
111. #17989115C22semidirect
119. #17989069C22semidirect
121. #17989068C22semidirect
122. #17989065C22semidirect
124. #17989063C22semidirect
127. C4×#11924029C22semidirect
131. C4×#11924028C22semidirect
144. C4×Q8×D73C22semidirect
147. Q82×C73C22semidirect
148. #557×C73C22semidirect
150. #554×C73C22semidirect
152. D4×Q8×C73C22semidirect
154. #533×C73C22semidirect
157. C2×C4×Q8×C73C22semidirect
419. Q8×D73#41semidirect
573. C2×C4×C732−1+4semidirect
689. Q8×#41D73semidirect
695. C73#62788semidirect
702. Q82C2×D73semidirect
709. #557C2×D73semidirect
721. #554C2×D73semidirect
738. D4×Q8C2×D73semidirect
768. #533C2×D73semidirect
827. C2×C4×Q8C2×D73semidirect
1290. C2×C4#14556639semidirect

Maximal subgroups

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

subgroupindex
#226240242
#226240222
#226240172
#226240152
#226239252
#226239212
#226237972
#226237942
#226237402
#226237012
#226236392
#226235812
#226235492
#226235482
#226235262
#226235242
#226235092
#226233622
#226232282
#226232242
C4×#145566392
C2×C4×Q8×D732
Q8×#41×C732
#6278873