Finite Group Databasebeta

← #33994597

Subgroups — #33994597

Order 18688.

7220 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624043C212yesmaximal, complemented
2#22624028C211yesmaximal, characteristic, complemented
3#22624017C211yesmaximal, characteristic, complemented
4#22624002C216yesmaximal, complemented
5#22623981C213yesmaximal, complemented
6#22623964C213yesmaximal, complemented
7#22623949C211yesmaximal, characteristic, complemented
8#22623938C211yesmaximal, characteristic, complemented
9#22623927C212yesmaximal, complemented
10#22623910C213yesmaximal, complemented
11#22623893C213yesmaximal, complemented
12#22623874C216yesmaximal, complemented
13#22623526C213yesmaximal, complemented
14#22623498C213yesmaximal, complemented
15#22623498C216yesmaximal, complemented
16#41×D292C212yesmaximal, complemented
17#41×D292C211yesmaximal, characteristic, complemented
18#22623323C216yesmaximal, complemented
19#22623228C213yesmaximal, complemented
20C2×#17989124C213yesmaximal, complemented
21#22623130C212yesmaximal, complemented
22C4×#41×D73C211yesmaximal, characteristic, complemented
23Q8×#41×C73C211yesmaximal, characteristic, complemented
24C2×#41×D73C2211yescharacteristic
25C2×#41×D73C2212yes—
26#17989322C2213yescomplemented
27#17989322C2216yescomplemented
28#17989316C2213yescomplemented
29#17989311C2216yescomplemented
30#17989311C2213yescomplemented
31#17989310C2216yescomplemented
32#17989310C2213yescomplemented
33#17989303C2216yescomplemented
34#17989303C2213yescomplemented
35#17989298C2213yescomplemented
36#17989298C2216yescomplemented
37#17989290C2216yescomplemented
38#17989290C2216yescomplemented
39#17989290C2216yescomplemented
40#17989285C22112yescomplemented
41#17989285C2216yescomplemented
42#17989279C22112yescomplemented
43#17989279C2216yescomplemented
44#17989275C2216yescomplemented
45#17989275C2216yescomplemented
46#17989275C2216yescomplemented
47#17989264C22112yescomplemented
48#17989264C22112yescomplemented
49#17989264C22112yescomplemented
50#17989259C2211yescharacteristic, complemented
51#17989259C2213yescomplemented
52#17989259C2212yescomplemented
53Q8×D292C2212yescomplemented
54Q8×D292C2211yescharacteristic, complemented
55#17989249C2212yescomplemented
56#17989249C2212yescomplemented
57#17989249C2212yescomplemented
58#17989248C2216yescomplemented
59#17989241C2216yescomplemented
60#17989241C2213yescomplemented
61#17989240C2216yescomplemented
62#17989240C2213yescomplemented
63#17989232C2216yescomplemented
64#17989232C2216yescomplemented
65#17989232C2216yescomplemented
66#17989228C22112yescomplemented
67#17989228C2216yescomplemented
68D4×D292C2216yescomplemented
69D4×D292C2213yescomplemented
70#17989211C2216yescomplemented
71#17989211C2216yescomplemented
72#17989211C2216yescomplemented
73#17989211C2216yescomplemented
74#17989200C2216yescomplemented
75#17989200C2216yescomplemented
76#17989193C2216yescomplemented
77#17989193C2216yescomplemented
78#17989186C22112yescomplemented
79#17989186C22112yescomplemented
80#17989177C22112yescomplemented
81#17989177C22112yescomplemented
82#17989142C2213yescomplemented
83#17989142C2213yescomplemented
84#17989138C2213yescomplemented
85#17989138C2213yescomplemented
86#17989137C2216yescomplemented
87#17989137C2213yescomplemented
88#17989124C2213yes—
89#17989124C2211yescharacteristic
90#17989124C2216yescomplemented
91#17989124C22112yescomplemented
92#17989124C2216yescomplemented
93#17989124C2213yescomplemented
94#17989124C22112yescomplemented
95#17989124C2213yescomplemented
96#17989124C2213yescomplemented
97#17989124C2216yescomplemented
98#17989124C2216yescomplemented
99#17989124C2216yescomplemented
100#17989124C2213yescomplemented
101#17989124C2213yescomplemented
102#17989124C2213yescomplemented
103#17989123C2216yescomplemented
104#17989123C2216yescomplemented
105#17989122C2216yescomplemented
106#17989122C2216yescomplemented
107C2×#14556586C2216yescomplemented
108C2×#14556582C2213yescomplemented
109C2×#14556580C2213yescomplemented
110#17989100C2216yescomplemented
111#17989100C2216yescomplemented
112#17989099C2216yescomplemented
113#17989099C2216yescomplemented
114#17989099C2216yescomplemented
115C2×#14556576C2216yescomplemented
116C2×#14556567C2213yescomplemented
117C2×#14556566C2213yes—
118#17989069C2212yescomplemented
119#17989069C2212yescomplemented
120#17989066C2216yescomplemented
121#17989066C2216yescomplemented
122#17989063C2212yescomplemented
123#17989063C2212yescomplemented
124#17989059C2216yescomplemented
125#17989059C2216yescomplemented
126#41×Dic73C2211yescharacteristic
127C4×#11924029C2216yescomplemented
128C4×#11924029C2216yescomplemented
129C4×#11924029C2211yescharacteristic, complemented
130C4×#11924029C2211yescharacteristic, complemented
131C4×#11924028C2213yescomplemented
132C4×#11924028C2216yescomplemented
133#17989055C2213yescomplemented
134#17989055C2216yescomplemented
135C4×#11924027C2213yescomplemented
136C4×#11924027C2213yescomplemented
137C4×Q8×D73C2211yescharacteristic, complemented
138C4×Q8×D73C2211yescharacteristic, complemented
139C2×C4×D292C2213yescomplemented
140C2×C4×D292C2216yescomplemented
141C4×D4×D73C2213yescomplemented
142C4×D4×D73C2213yescomplemented
143C2×#14556548C2216yescomplemented
144#117×D73C2213yescomplemented
145#117×D73C2216yescomplemented
146C2×C42×D73C2213yescomplemented
147Q82×C73C2211yescharacteristic, complemented
148#557×C73C2211yescharacteristic, complemented
149#557×C73C2212yescomplemented
150#554×C73C2216yescomplemented
151#554×C73C2213yescomplemented
152D4×Q8×C73C2213yescomplemented
153#533×C73C2216yescomplemented
154#533×C73C2213yescomplemented
155C4×#41×C73C2211yescharacteristic
156C4×#41×C73C2212yes—
157C2×C4×Q8×C73C2213yescomplemented
158C2×#11924029C2311yescharacteristic
159C2×#11924029C2312yes—
160C2×#11924029C2316yes—
161C2×#11924029C2316yes—
162C2×#11924028C2313yes—
163C2×#11924028C2316yes—
164C2×#11924027C2313yes—
165C2×#11924027C2316yes—
166#41×D73—28no—
167#41×D73—216no—
168C2×Q8×D73C2311yescharacteristic
169C2×Q8×D73C2312yes—
170C22×D292C2316yes—
171C22×D292C2313yes—
172C2×D4×D73C2313yes—
173C2×D4×D73C2316yes—
174C22×C4×D73C2313yes—
175C22×C4×D73C2316yes—
176C22×C4×D73C2313yes—
177C22×C4×D73C2313yes—
178#14556591C2313yes—
179#14556591C2316yes—
180#14556588C2313yes—
181#14556588C2316yes—
182#14556586C2316yes—
183#14556586C23112yes—
184#14556586C2312yes—
185#14556586C2316yes—
186#14556586C2316yes—
187#14556586C2316yes—
188#14556586C2316yes—
189#14556586C2316yes—
190#14556586C2316yes—
191#14556586C23112yes—
192#14556586C23112yes—
193#14556586C23112yes—
194#14556586C23112yes—
195#14556582C2313yes—
196#14556582C2316yes—
197#14556582C2311yescharacteristic
198#14556582C2313yes—
199#14556582C2316yes—
200#14556582C2316yes—
201#14556582C2313yes—
202#14556582C23112yes—
203#14556582C23112yes—
204#14556580C2313yes—
205#14556580C2316yes—
206#14556580C2311yescharacteristic
207#14556580C2313yes—
208#14556580C2316yes—
209#14556580C2313yes—
210#14556580C2316yes—
211#14556580C23112yes—
212#14556580C23112yes—
213#14556579C2316yes—
214#14556579C2316yes—
215#14556579C2316yes—
216#14556576C2316yes—
217#14556576C23112yes—
218#14556576C2312yes—
219#14556576C2316yes—
220#14556576C2316yes—
221#14556576C2316yes—
222#14556576C2316yes—
223#14556576C2316yes—
224#14556576C2316yes—
225#14556576C23112yes—
226#14556576C23112yes—
227#14556576C23112yes—
228#14556576C23112yes—
229#14556575C23112yes—
230#14556575C23112yes—
231#14556575C23112yes—
232#14556571C2316yes—
233#14556571C2316yes—
234#14556571C2316yes—
235#14556571C2316yes—
236#14556571C2316yes—
237#14556571C2316yes—
238#14556567C2311yescharacteristic
239#14556567C2313yes—
240#14556567C2316yes—
241#14556567C2313yes—
242#14556567C2313yes—
243#14556567C2316yes—
244#14556567C2316yes—
245#14556567C23112yes—
246#14556567C23112yes—
247#14556566C2316yes—
248#14556566C2316yes—
249#14556566C2311yescharacteristic
250#14556566C2313yes—
251#14556566C2316yes—
252#14556566C2316yes—
253#14556566C2313yes—
254#14556566C2313yes—
255#14556566C2316yes—
256#14556566C23112yes—
257#14556566C23112yes—
258#14556566C2316yes—
259#14556566C2316yes—
260#14556566C2316yes—
261#14556566C2316yes—
262#14556565C2316yes—
263#14556565C2316yes—
264#14556565C23112yes—
265#14556565C23112yes—
266#14556561C23112yes—
267#14556561C23112yes—
268#14556561C23112yes—
269Q8×Dic73C2316yes—
270Q8×Dic73C2316yes—
271Q8×Dic73C2311yescharacteristic
272Q8×Dic73C2311yescharacteristic
273C4×Dic146C2313yes—
274C4×Dic146C2316yes—
275C4×Dic146C2313yes—
276C4×Dic146C2316yes—
277#14556556C2316yes—
278#14556556C2316yes—
279#14556556C2313yes—
280#14556556C2313yes—
281C4×D292C2311yescharacteristic
282C4×D292C2312yes—
283C4×D292C2316yes—
284C4×D292C2313yes—
285C4×D292C2316yes—
286C4×D292C2316yes—
287C4×D292C2316yes—
288C4×D292C23112yes—
289C4×D292C2316yes—
290C4×D292C2313yes—
291C4×D292C2316yes—
292C4×D292C2316yes—
293C4×D292C2316yes—
294C4×D292C2313yes—
295C4×D292C2316yes—
296C4×D292C2316yes—
297C4×D292C2313yes—
298C4×D292C2316yes—
299C4×D292C2316yes—
300C4×D292C2313yes—
301D4×Dic73C2313yes—
302D4×Dic73C2313yes—
303#14556553C2316yes—
304#14556553C2316yes—
305#14556553C23112yes—
306#14556553C23112yes—
307#14556553C2316yes—
308#14556553C2316yes—
309#14556553C2313yes—
310#14556553C2313yes—
311C4×C22⋊D73C2316yes—
312C4×C22⋊D73C23112yes—
313C4×C22⋊D73C23112yes—
314C4×C22⋊D73C2316yes—
315#14556551C23112yes—
316#14556551C23112yes—
317#14556551C2316yes—
318#14556551C2316yes—
319#14556550C2313yes—
320#14556549C23112yes—
321#14556549C23112yes—
322#14556549C2316yes—
323#14556549C2316yes—
324#14556549C2313yes—
325#14556549C2316yes—
326#14556549C2316yes—
327#14556549C2313yes—
328#14556548C2312yes—
329#14556548C2316yes—
330#14556548C2316yes—
331#14556548C2316yes—
332#14556548C2316yes—
333#14556548C2316yes—
334#14556548C2316yes—
335#14556548C2316yes—
336#14556548C2316yes—
337#14556547C2316yes—
338#14556547C23112yes—
339C2×C4⋊Dic73C2313yes—
340C2×C4⋊Dic73C2316yes—
341C2×#11924007C2316yes—
342C2×#11924007C2316yes—
343C4⋊C4×D73C2313yes—
344C4⋊C4×D73C2316yes—
345C4⋊C4×D73C2316yes—
346C4⋊C4×D73C2313yes—
347C2×#11924005C2316yes—
348C2×#11924005C2316yes—
349C2×#11924005C2316yes—
350C2×#11924005C2316yes—
351C2×#11924005C2316yes—
352C22⋊C4×D73C2316yes—
353C22⋊C4×D73C23112yes—
354C2×C4×Dic73C2313yes—
355C2×C4×Dic73C2313yes—
356C2×C4×Dic73C2313yes—
357C42×D73C2313yes—
358C42×D73C2313yes—
359C42×D73C2311yescharacteristic
360C42×D73C2313yes—
361C42×D73C2313yes—
362C42×D73C2313yes—
363C42×D73C2313yes—
364C42×D73C2313yes—
365C42×D73C23112yes—
366C2×#41×C73C2311yescharacteristic
367C22×Q8×C73C2313yes—
368C4⋊Q8×C73C2313yes—
369C4⋊Q8×C73C2313yes—
370C4⋊Q8×C73C2316yes—
371C4⋊Q8×C73C2316yes—
372#125×C73C2316yes—
373#125×C73C2316yes—
374#125×C73C2316yes—
375C22⋊Q8×C73C2316yes—
376C22⋊Q8×C73C2316yes—
377C22⋊Q8×C73C23112yes—
378C22⋊Q8×C73C23112yes—
379C4×Q8×C73C2311yescharacteristic
380C4×Q8×C73C2313yes—
381C4×Q8×C73C2316yes—
382C4×Q8×C73C2316yes—
383C4×Q8×C73C2313yes—
384C4×Q8×C73C2313yes—
385C4×Q8×C73C2316yes—
386C4×Q8×C73C2311yescharacteristic
387C4×Q8×C73C2312yes—
388C4×Q8×C73C2312yes—
389C4×Q8×C73C2311yescharacteristic
390C4×D4×C73C2313yes—
391C4×D4×C73C2316yes—
392C4×D4×C73C2316yes—
393C4×D4×C73C2313yes—
394#117×C73C2313yes—
395#117×C73C2316yes—
396C2×C4⋊C4×C73C2313yes—
397C2×C4⋊C4×C73C2316yes—
398C2×C42×C73C2313yes—
399C2×C42×C73C2316yes—
400C23×D73C2413yes—
401C23×D73C2416yes—
402#11924029—24no—
403#11924029—28no—
404#11924029—412no—
405#11924029—412no—
406#11924028—212no—
407#11924028—224no—
408#11924027—212no—
409#11924027—224no—
410C2×Dic146C2416yes—
411C2×Dic146C2413yes—
412Q8×D73—24no—
413Q8×D73—28no—
414C2×D292—46no—
415C2×D292—412no—
416C2×D292C2416yes—
417C2×D292C2413yes—
418C2×D292C2416yes—
419C2×D292C2413yes—
420C2×D292C2412yes—
421C2×D292C2411yescharacteristic
422C2×D292C24112yes—
423C2×D292C2416yes—
424C2×D292C2416yes—
425C2×D292C2416yes—
426C2×D292C2416yes—
427C2×C22⋊D73C24112yes—
428C2×C22⋊D73C2416yes—
429D4×D73—212no—
430D4×D73—224no—
431C22×Dic73C2413yes—
432C22×Dic73C2416yes—
433C22×Dic73C2413yes—
434C22×Dic73C2413yes—
435C2×C4×D73—212no—
436C2×C4×D73—224no—
437C2×C4×D73—46no—
438C2×C4×D73—46no—
439C2×C4×D73C2411yescharacteristic
440C2×C4×D73C2411yescharacteristic
441C2×C4×D73C2411yescharacteristic
442C2×C4×D73C2413yes—
443C2×C4×D73C2413yes—
444C2×C4×D73C2413yes—
445C2×C4×D73C2416yes—
446C2×C4×D73C2413yes—
447C2×C4×D73C2413yes—
448C2×C4×D73C2416yes—
449C2×C4×D73C2412yes—
450C2×C4×D73C2416yes—
451C2×C4×D73C2413yes—
452C2×C4×D73C2413yes—
453C2×C4×D73C2413yes—
454C2×C4×D73C2413yes—
455C2×C4×D73C24112yes—
456C2×C4×D73C24112yes—
457C4⋊Dic73C2413yes—
458C4⋊Dic73C2413yes—
459C4⋊Dic73C2411yescharacteristic
460C4⋊Dic73C2412yes—
461C4⋊Dic73C2413yes—
462C4⋊Dic73C2416yes—
463C4⋊Dic73C2416yes—
464C4⋊Dic73C2416yes—
465C4⋊Dic73C2416yes—
466C4⋊Dic73C24112yes—
467C4⋊Dic73C2416yes—
468#11924007C2416yes—
469#11924007C2416yes—
470#11924007C2416yes—
471#11924007C2416yes—
472#11924007C2412yes—
473#11924007C2412yes—
474#11924007C2416yes—
475#11924007C2416yes—
476#11924007C2416yes—
477#11924007C2416yes—
478C22⋊Dic73C2416yes—
479#11924005C2416yes—
480#11924005C2416yes—
481#11924005C2416yes—
482#11924005C2416yes—
483#11924005C2412yes—
484#11924005C2412yes—
485#11924005C2412yes—
486#11924005C2412yes—
487#11924005C2412yes—
488#11924005C2416yes—
489#11924005C2416yes—
490#11924005C2416yes—
491#11924005C2416yes—
492#11924005C2416yes—
493#11924005C2416yes—
494#11924005C2416yes—
495#11924005C2416yes—
496#11924005C2416yes—
497#11924005C2416yes—
498#11924005C2416yes—
499#11924005C2416yes—
500#11924005C2416yes—
501#11924005C24112yes—
502#11924005C24112yes—
503#11924005C24112yes—
504C4×Dic73C2413yes—
505C4×Dic73C2411yescharacteristic
506C4×Dic73C2411yescharacteristic
507C4×Dic73C2411yescharacteristic
508C4×Dic73C2413yes—
509C4×Dic73C2413yes—
510C4×Dic73C2413yes—
511C4×Dic73C2413yes—
512C4×Dic73C2413yes—
513C4×Dic73C2413yes—
514C4×Dic73C2413yes—
515C4×Dic73C2413yes—
516C4×Dic73C24112yes—
517C4×Dic73C24112yes—
518#41×C73#4118yescomplemented
519C2×Q8×C73—46no—
520C2×Q8×C73C2411yescharacteristic
521C2×Q8×C73C2413yes—
522C2×Q8×C73C2416yes—
523C2×Q8×C73C2416yes—
524C2×Q8×C73C2411yescharacteristic
525C2×D4×C73C2413yes—
526C22×C4×C73C2413yes—
527C22×C4×C73C2413yes—
528C22×C4×C73C2416yes—
529C22×C4×C73C2416yes—
530C22×C4×C73C2413yes—
531C4⋊C4×C73C2411yescharacteristic
532C4⋊C4×C73C2412yes—
533C4⋊C4×C73C2416yes—
534C4⋊C4×C73C2416yes—
535C4⋊C4×C73C2416yes—
536C4⋊C4×C73C2413yes—
537C4⋊C4×C73C2416yes—
538C4⋊C4×C73C2413yes—
539C4⋊C4×C73C2416yes—
540C4⋊C4×C73C2416yes—
541C4⋊C4×C73C2413yes—
542C4⋊C4×C73C24112yes—
543C4⋊C4×C73C2416yes—
544C22⋊C4×C73C2416yes—
545C22⋊C4×C73C24112yes—
546C42×C73C2411yescharacteristic
547C42×C73C2412yes—
548C42×C73C2413yes—
549C42×C73C2416yes—
550C42×C73C2413yes—
551C42×C73C2416yes—
552C42×C73C2413yes—
553C42×C73C2416yes—
554C23×C73C2513yes—
555C22×D73—26no—
556C22×D73—212no—
557C22×D73—26no—
558C22×D73—43no—
559C22×D73—46no—
560C22×D73—46no—
561C22×D73C2512yes—
562C22×D73C2513yes—
563C22×D73C2516yes—
564C22×D73C2511yescharacteristic
565Q8×C73—22no—
566Q8×C73—26no—
567Q8×C73—46no—
568Q8×C73—46no—
569Q8×C73C2×#4114yes—
570D4×C73C2×#41112yes—
571C2×C4×C73—26no—
572C2×C4×C73—46no—
573C2×C4×C73—43no—
574C2×C4×C73—46no—
575C2×C4×C73C2×#41112yes—
576C2×C4×C73C2511yescharacteristic
577C2×C4×C73C2512yes—
578C2×C4×C73C2512yes—
579C2×C4×C73C2513yes—
580C2×C4×C73C2516yes—
581C2×C4×C73C2513yes—
582C2×C4×C73C2516yes—
583C2×C4×C73C2513yes—
584C2×C4×C73C2511yescharacteristic
585C2×C4×C73C2511yescharacteristic
586C22⋊D73—212no—
587C22⋊D73—224no—
588C2×Dic73—26no—
589C2×Dic73—212no—
590C2×Dic73—43no—
591C2×Dic73—43no—
592C2×Dic73C2511yescharacteristic
593C2×Dic73C2511yescharacteristic
594C2×Dic73C2511yescharacteristic
595C2×Dic73C2513yes—
596C2×Dic73C2513yes—
597C2×Dic73C2513yes—
598C2×Dic73C2516yes—
599C2×Dic73C2512yes—
600D292—24no—
601D292—212no—
602D292—26no—
603D292—212no—
604D292—22no—
605D292—26no—
606D292—46no—
607D292—46no—
608D292—46no—
609D292—46no—
610D292—412no—
611C4×D73—22no—
612C4×D73—26no—
613C4×D73—22no—
614C4×D73—24no—
615C4×D73—26no—
616C4×D73—212no—
617C4×D73—26no—
618C4×D73—212no—
619C4×D73—26no—
620C4×D73—212no—
621C4×D73—22no—
622C4×D73—26no—
623C4×D73—43no—
624C4×D73—43no—
625C4×D73—43no—
626C4×D73—43no—
627C4×D73—412no—
628C4×D73—412no—
629Dic146—26no—
630Dic146—212no—
631C22×C73—23no—
632C22×C73—23no—
633C22×C73C22×#4116yes—
634C22×C73C2611yescharacteristic
635C2×D73—21no—
636C2×D73—21no—
637C2×D73—22no—
638C2×D73—23no—
639C2×D73—26no—
640C2×D73—23no—
641C2×D73—26no—
642C2×D73—26no—
643C2×D73—23no—
644C2×D73—22no—
645C2×D73—22no—
646C2×D73—412no—
647C2×D73—812no—
648C2×D73#58512yes—
649C4×C73—21no—
650C4×C73—23no—
651C4×C73—26no—
652C4×C73—23no—
653C4×C73—26no—
654C4×C73—22no—
655C4×C73—22no—
656C4×C73C22×#4116yes—
657C4×C73C22×#4112yes—
658C4×C73#58512yes—
659Dic73—23no—
660Dic73—26no—
661Dic73—21no—
662Dic73—22no—
663Dic73—23no—
664Dic73—23no—
665Dic73—21no—
666Dic73—21no—
667#62816—731nomaximal, Sylow
668C2×C73—26no—
669C2×C73C23×#4111yescharacteristic
670C2×C73C2×#58511yescharacteristic
671C2×C73C2×#58511yescharacteristic
672D73—22no—
673D73—43no—
674D73—46no—
675D73—42no—
676#3524—732no—
677#3523—731no—
678#3522—731no—
679#3521—736no—
680#3520—733no—
681#3519—733no—
682#3518—731no—
683#3517—731no—
684#3516—732no—
685#3515—733no—
686#3514—733no—
687#3513—736no—
688#3480—733no—
689Q8×#41D7311yescharacteristic, complemented
690#3475—736no—
691#3475—733no—
692D4×#41—731no—
693D4×#41—732no—
694#3455—736no—
695#3444—733no—
696C2×#529—733no—
697#3428—732no—
698C2×C4×#41—731no—
699C73#6281611yescharacteristic, complemented, Sylow
700C22×#41—731no—
701C22×#41—732no—
702#559—736no—
703#559—733no—
704Q82C2×D7311yescharacteristic, complemented
705#557—733no—
706#557C2×D7312yescomplemented
707#557C2×D7311yescharacteristic, complemented
708#556—733no—
709#556—736no—
710#556—736no—
711#556—733no—
712#555—736no—
713#555—733no—
714#554—733no—
715#554—736no—
716#554C2×D7316yescomplemented
717#554C2×D7313yescomplemented
718#553—736no—
719#553—736no—
720#553—736no—
721#553—7312no—
722#553—736no—
723#552—736no—
724#552—736no—
725#552—736no—
726#552—736no—
727#552—7312no—
728#551—7312no—
729#551—7312no—
730#551—7312no—
731#550—731no—
732#550—732no—
733#550—733no—
734D4×Q8—732no—
735D4×Q8—731no—
736D4×Q8C2×D7313yescomplemented
737#548—736no—
738#548—732no—
739#548—732no—
740#548—732no—
741#547—736no—
742#547—733no—
743#547—733no—
744#547—736no—
745#546—7312no—
746#546—736no—
747#546—736no—
748#546—736no—
749#546—736no—
750D42—736no—
751D42—733no—
752#542—736no—
753#542—736no—
754#542—736no—
755#542—736no—
756#541—736no—
757#541—736no—
758#540—736no—
759#540—736no—
760#539—7312no—
761#539—7312no—
762#538—7312no—
763#538—7312no—
764#533—733no—
765#533—733no—
766#533C2×D7313yescomplemented
767#533C2×D7316yescomplemented
768#532—733no—
769#532—733no—
770#532—733no—
771#532—736no—
772#529—736no—
773#529—736no—
774#529—736no—
775#529—736no—
776#529—731no—
777#529—733no—
778#529—733no—
779#529—736no—
780#529—736no—
781#529—733no—
782#529—733no—
783#529—736no—
784#529—733no—
785#529—733no—
786#529—733no—
787#529—736no—
788#529—736no—
789#529—7312no—
790#529—7312no—
791C2×#126—736no—
792C2×#125—733no—
793C2×#124—733no—
794#525—736no—
795#525—736no—
796#525—736no—
797#525—736no—
798#525—736no—
799C2×#123—736no—
800C2×C22⋊Q8—733no—
801C2×#121—733no—
802#520—732no—
803#520—732no—
804#520—736no—
805#520—736no—
806#519—732no—
807#519—732no—
808#518—736no—
809#518—736no—
810C4×#41—731no—
811C4×#41—731no—
812C4×#41—731no—
813C4×#41—736no—
814C4×#41—736no—
815C4×#41—733no—
816C4×#41—733no—
817C4×#41—733no—
818C4×#41—736no—
819C4×#41—733no—
820C4×#41—736no—
821C4×#41C2×D7311yescharacteristic
822C4×#41C2×D7312yes—
823C2×C4×Q8—731no—
824C2×C4×Q8—731no—
825C2×C4×Q8C2×D7313yescomplemented
826C2×C4×D4—733no—
827C2×C4×D4—733no—
828C2×C4×D4—736no—
829C2×C4×D4—733no—
830C2×#117—733no—
831C2×#117—736no—
832C2×#117—736no—
833C22×C42—733no—
834C2×#41—736no—
835C2×#41—736no—
836C2×#41—731no—
837C2×#41—732no—
838C2×#41—733no—
839C2×#41—736no—
840C2×#41—733no—
841C2×#41—736no—
842C2×#41—1468no—
843C2×#41—14616no—
844C2×#41C22×D7311yescharacteristic
845C22×Q8—731no—
846C22×Q8—732no—
847C22×Q8C22×D7313yes—
848C22×D4—733no—
849C22×D4—736no—
850C22×D4—736no—
851C22×D4—733no—
852C23×C4—733no—
853C23×C4—733no—
854C23×C4—736no—
855C23×C4—733no—
856C4⋊Q8—733no—
857C4⋊Q8—736no—
858C4⋊Q8C22×D7313yes—
859C4⋊Q8C22×D7313yes—
860C4⋊Q8C22×D7316yes—
861C4⋊Q8C22×D7316yes—
862#127—733no—
863#127—736no—
864#126—732no—
865#126—736no—
866#126—736no—
867#126—736no—
868#126—736no—
869#126—736no—
870#126—736no—
871#126—736no—
872#126—7312no—
873#126—7312no—
874#126—7312no—
875#126—7312no—
876#126—7312no—
877#125—731no—
878#125—733no—
879#125—736no—
880#125—736no—
881#125—733no—
882#125—733no—
883#125—736no—
884#125—7312no—
885#125—7312no—
886#125C22×D7316yes—
887#125C22×D7316yes—
888#125C22×D7316yes—
889#124—731no—
890#124—733no—
891#124—736no—
892#124—733no—
893#124—733no—
894#124—736no—
895#124—736no—
896#124—7312no—
897#124—7312no—
898#124—736no—
899#124—736no—
900#124—736no—
901#123—732no—
902#123—736no—
903#123—736no—
904#123—736no—
905#123—736no—
906#123—736no—
907#123—736no—
908#123—736no—
909#123—7312no—
910#123—7312no—
911#123—7312no—
912#123—7312no—
913#123—7312no—
914#123—7312no—
915#123—7312no—
916#123—7312no—
917C22⋊Q8—731no—
918C22⋊Q8—733no—
919C22⋊Q8—736no—
920C22⋊Q8—733no—
921C22⋊Q8—733no—
922C22⋊Q8—736no—
923C22⋊Q8—736no—
924C22⋊Q8—7312no—
925C22⋊Q8—7312no—
926C22⋊Q8—736no—
927C22⋊Q8—736no—
928C22⋊Q8—736no—
929C22⋊Q8—736no—
930C22⋊Q8—736no—
931C22⋊Q8—736no—
932C22⋊Q8C22×D7316yes—
933C22⋊Q8C22×D7316yes—
934C22⋊Q8C22×D73112yes—
935C22⋊Q8C22×D73112yes—
936#121—736no—
937#121—736no—
938#121—7312no—
939#121—7312no—
940#121—731no—
941#121—733no—
942#121—736no—
943#121—736no—
944#121—733no—
945#121—733no—
946#121—736no—
947#121—736no—
948#121—736no—
949#121—736no—
950#121—736no—
951#121—736no—
952#121—736no—
953#121—7312no—
954#121—7312no—
955#120—7312no—
956#120—7312no—
957#120—7312no—
958C4×Q8—731no—
959C4×Q8—731no—
960C4×Q8—736no—
961C4×Q8—736no—
962C4×Q8—733no—
963C4×Q8—733no—
964C4×Q8—736no—
965C4×Q8—736no—
966C4×Q8—733no—
967C4×Q8—733no—
968C4×Q8—736no—
969C4×Q8—736no—
970C4×Q8C22×D7311yescharacteristic
971C4×Q8C22×D7311yescharacteristic
972C4×Q8C22×D7311yescharacteristic
973C4×Q8C22×D7313yes—
974C4×Q8C22×D7316yes—
975C4×Q8C22×D7313yes—
976C4×Q8C22×D7313yes—
977C4×Q8C22×D7316yes—
978C4×Q8C22×D7316yes—
979C4×Q8C22×D7312yes—
980C4×Q8C22×D7312yes—
981C4×D4—733no—
982C4×D4—733no—
983C4×D4—736no—
984C4×D4—736no—
985C4×D4—7312no—
986C4×D4—7312no—
987C4×D4—733no—
988C4×D4—733no—
989C4×D4—736no—
990C4×D4—736no—
991C4×D4—7312no—
992C4×D4—7312no—
993C4×D4—736no—
994C4×D4—736no—
995C4×D4—736no—
996C4×D4—736no—
997C4×D4—7312no—
998C4×D4—7312no—
999C4×D4—731no—
1000C4×D4—732no—
1001C4×D4—736no—
1002C4×D4—733no—
1003C4×D4—733no—
1004C4×D4—733no—
1005C4×D4—736no—
1006C4×D4—736no—
1007C4×D4—736no—
1008C4×D4—736no—
1009C4×D4—733no—
1010C4×D4—736no—
1011C4×D4—736no—
1012C4×D4—736no—
1013C4×D4—733no—
1014C4×D4—736no—
1015C4×D4—736no—
1016C4×D4—736no—
1017C4×D4—736no—
1018C4×D4—7312no—
1019C4×D4C22×D7313yes—
1020C4×D4C22×D7313yes—
1021C4×D4C22×D7316yes—
1022C4×D4C22×D7316yes—
1023#117—733no—
1024#117—733no—
1025#117—733no—
1026#117—736no—
1027#117—736no—
1028#117—736no—
1029#117—736no—
1030#117—7312no—
1031#117—7312no—
1032#117—736no—
1033#117—7312no—
1034#117—736no—
1035#117—732no—
1036#117—736no—
1037#117—736no—
1038#117—736no—
1039#117—736no—
1040#117—736no—
1041#117—736no—
1042#117—736no—
1043#117C22×D7313yes—
1044#117C22×D7316yes—
1045C2×C4⋊C4—736no—
1046C2×C4⋊C4—736no—
1047C2×C4⋊C4—733no—
1048C2×C4⋊C4—736no—
1049C2×C4⋊C4—733no—
1050C2×C4⋊C4—733no—
1051C2×C4⋊C4—736no—
1052C2×C4⋊C4—736no—
1053C2×C4⋊C4C22×D7313yes—
1054C2×C4⋊C4C22×D7316yes—
1055C2×C22⋊C4—736no—
1056C2×C22⋊C4—736no—
1057C2×C22⋊C4—736no—
1058C2×C22⋊C4—736no—
1059C2×C22⋊C4—736no—
1060C2×C22⋊C4—736no—
1061C2×C22⋊C4—7312no—
1062C2×C42—733no—
1063C2×C42—733no—
1064C2×C42—733no—
1065C2×C42—733no—
1066C2×C42—7312no—
1067C2×C42—733no—
1068C2×C42—733no—
1069C2×C42—733no—
1070C2×C42—733no—
1071C2×C42—733no—
1072C2×C42—733no—
1073C2×C42—731no—
1074C2×C42C22×D7316yes—
1075C2×C42C22×D7313yes—
1076C24—736no—
1077C24—733no—
1078#41—29212no—
1079#41—29212no—
1080#41—1464no—
1081#41—1468no—
1082#41—14612no—
1083#41—14624no—
1084#41—14612no—
1085#41—14624no—
1086#41#1192402918yescomplemented
1087C2×Q8—46no—
1088C2×Q8—733no—
1089C2×Q8—736no—
1090C2×Q8—1464no—
1091C2×Q8—1468no—
1092C2×Q8C23×D7313yes—
1093C2×Q8C23×D7311yescharacteristic
1094C2×Q8C23×D7316yes—
1095C2×Q8C23×D7316yes—
1096C2×Q8C23×D7311yescharacteristic
1097C2×D4—2926no—
1098C2×D4—29212no—
1099C2×D4—736no—
1100C2×D4—7312no—
1101C2×D4—736no—
1102C2×D4—736no—
1103C2×D4—7312no—
1104C2×D4—736no—
1105C2×D4—736no—
1106C2×D4—736no—
1107C2×D4—732no—
1108C2×D4—731no—
1109C2×D4—733no—
1110C2×D4—736no—
1111C2×D4—733no—
1112C2×D4—14612no—
1113C2×D4—14624no—
1114C2×D4C23×D7313yes—
1115C22×C4—2926no—
1116C22×C4—2926no—
1117C22×C4—733no—
1118C22×C4—733no—
1119C22×C4—733no—
1120C22×C4—733no—
1121C22×C4—733no—
1122C22×C4—733no—
1123C22×C4—7312no—
1124C22×C4—7312no—
1125C22×C4—733no—
1126C22×C4—736no—
1127C22×C4—731no—
1128C22×C4—731no—
1129C22×C4—733no—
1130C22×C4—733no—
1131C22×C4—733no—
1132C22×C4—733no—
1133C22×C4—736no—
1134C22×C4—736no—
1135C22×C4—731no—
1136C22×C4—736no—
1137C22×C4—733no—
1138C22×C4—732no—
1139C22×C4—14612no—
1140C22×C4—14624no—
1141C22×C4C23×D7313yes—
1142C22×C4C23×D7313yes—
1143C22×C4C23×D7316yes—
1144C22×C4C23×D7316yes—
1145C22×C4C23×D7313yes—
1146C4⋊C4—732no—
1147C4⋊C4—736no—
1148C4⋊C4—736no—
1149C4⋊C4—732no—
1150C4⋊C4—736no—
1151C4⋊C4—736no—
1152C4⋊C4—736no—
1153C4⋊C4—736no—
1154C4⋊C4—736no—
1155C4⋊C4—736no—
1156C4⋊C4—733no—
1157C4⋊C4—733no—
1158C4⋊C4—731no—
1159C4⋊C4—732no—
1160C4⋊C4—733no—
1161C4⋊C4—736no—
1162C4⋊C4—736no—
1163C4⋊C4—736no—
1164C4⋊C4—736no—
1165C4⋊C4—736no—
1166C4⋊C4—7312no—
1167C4⋊C4C23×D7313yes—
1168C4⋊C4C23×D7313yes—
1169C4⋊C4C23×D7316yes—
1170C4⋊C4C23×D7316yes—
1171C4⋊C4C23×D7311yescharacteristic
1172C4⋊C4C23×D7312yes—
1173C4⋊C4C23×D7313yes—
1174C4⋊C4C23×D7316yes—
1175C4⋊C4C23×D7316yes—
1176C4⋊C4C23×D7316yes—
1177C4⋊C4C23×D7316yes—
1178C4⋊C4C23×D7316yes—
1179C4⋊C4C23×D73112yes—
1180C22⋊C4—736no—
1181C22⋊C4—732no—
1182C22⋊C4—736no—
1183C22⋊C4—736no—
1184C22⋊C4—732no—
1185C22⋊C4—732no—
1186C22⋊C4—732no—
1187C22⋊C4—732no—
1188C22⋊C4—736no—
1189C22⋊C4—736no—
1190C22⋊C4—736no—
1191C22⋊C4—736no—
1192C22⋊C4—736no—
1193C22⋊C4—736no—
1194C22⋊C4—736no—
1195C22⋊C4—736no—
1196C22⋊C4—736no—
1197C22⋊C4—736no—
1198C22⋊C4—736no—
1199C22⋊C4—736no—
1200C22⋊C4—736no—
1201C22⋊C4—736no—
1202C22⋊C4—736no—
1203C22⋊C4—7312no—
1204C22⋊C4—7312no—
1205C22⋊C4—7312no—
1206C22⋊C4C23×D7316yes—
1207C22⋊C4C23×D73112yes—
1208C42—731no—
1209C42—731no—
1210C42—733no—
1211C42—733no—
1212C42—733no—
1213C42—733no—
1214C42—733no—
1215C42—733no—
1216C42—733no—
1217C42—733no—
1218C42—7312no—
1219C42—7312no—
1220C42—733no—
1221C42—731no—
1222C42C23×D7313yes—
1223C42C23×D7313yes—
1224C42C23×D7316yes—
1225C42C23×D7316yes—
1226C42C23×D7311yescharacteristic
1227C42C23×D7313yes—
1228C42C23×D7316yes—
1229C42C23×D7312yes—
1230C23—2923no—
1231C23—2926no—
1232C23—2926no—
1233C23—731no—
1234C23—732no—
1235C23—733no—
1236C23—736no—
1237C23—1466no—
1238C23—1466no—
1239C23—14612no—
1240C23C24×D7313yes—
1241Q8—22no—
1242Q8—26no—
1243Q8—46no—
1244Q8—46no—
1245Q8—1466no—
1246Q8—14612no—
1247Q8C2×#1192402914yes—
1248D4—2926no—
1249D4—2926no—
1250D4—2926no—
1251D4—2926no—
1252D4—29212no—
1253D4—1464no—
1254D4—14612no—
1255D4—14612no—
1256D4—14624no—
1257D4—1466no—
1258D4—14612no—
1259D4—1462no—
1260D4—1466no—
1261D4C2×#11924029112yes—
1262C2×C4—26no—
1263C2×C4—43no—
1264C2×C4—46no—
1265C2×C4—46no—
1266C2×C4—2923no—
1267C2×C4—2923no—
1268C2×C4—2923no—
1269C2×C4—2923no—
1270C2×C4—29212no—
1271C2×C4—29212no—
1272C2×C4—2923no—
1273C2×C4—2923no—
1274C2×C4—731no—
1275C2×C4—731no—
1276C2×C4—733no—
1277C2×C4—731no—
1278C2×C4—733no—
1279C2×C4—733no—
1280C2×C4—736no—
1281C2×C4—732no—
1282C2×C4—1462no—
1283C2×C4—1466no—
1284C2×C4—1466no—
1285C2×C4—14612no—
1286C2×C4—1464no—
1287C2×C4—1462no—
1288C2×C4—14612no—
1289C2×C4—1466no—
1290C2×C4—1466no—
1291C2×C4—14612no—
1292C2×C4—1466no—
1293C2×C4—14612no—
1294C2×C4—1462no—
1295C2×C4—1466no—
1296C2×C4C2×#11924029112yes—
1297C2×C4C24×D7311yescharacteristic
1298C2×C4C24×D7316yes—
1299C2×C4C24×D7313yes—
1300C2×C4C24×D7313yes—
1301C2×C4C24×D7316yes—
1302C2×C4C24×D7312yes—
1303C2×C4C24×D7312yes—
1304C2×C4C24×D7313yes—
1305C2×C4C24×D7311yescharacteristic
1306C2×C4C24×D7311yescharacteristic
1307C22—23no—
1308C22—23no—
1309C22—29212no—
1310C22—58412no—
1311C22—732no—
1312C22—1462no—
1313C22—1463no—
1314C22—1466no—
1315C22—1463no—
1316C22—1466no—
1317C22—1462no—
1318C22—1466no—
1319C22—1463no—
1320C22—1462no—
1321C22—1461no—
1322C22—1461no—
1323C22C22×#1192402916yes—
1324C22C25×D7311yescharacteristic
1325C4—21no—
1326C4—22no—
1327C4—26no—
1328C4—23no—
1329C4—23no—
1330C4—22no—
1331C4—26no—
1332C4—1461no—
1333C4—1462no—
1334C4—1463no—
1335C4—1466no—
1336C4—1461no—
1337C4—1463no—
1338C4—1461no—
1339C4—1463no—
1340C4C22×#1192402912yes—
1341C4C22×#1192402916yes—
1342C4#1798942312yes—
1343C2—26no—
1344C2—2923no—
1345C2—2922no—
1346C2—2926no—
1347C2—1462no—
1348C2C23×#1192402911yescharacteristic
1349C2#585×D7311yescharacteristic
1350C2C2×#1798942311yescharacteristic
subgroupG/H
centerC2×C4C24×D73
commutator, socle, cosocleC22×C73C26
FrattiniC22C25×D73
FittingQ8×#41×C73C2
hypercenterQ8×#41D73
hypocenterC73#62816
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #22624043C2semidirect
2. #22624028C2semidirect
3. #22624017C2semidirect
4. #22624002C2semidirect
5. #22623981C2semidirect
6. #22623964C2semidirect
7. #22623949C2semidirect
8. #22623938C2semidirect
9. #22623927C2semidirect
10. #22623910C2semidirect
11. #22623893C2semidirect
12. #22623874C2semidirect
13. #22623526C2semidirect
14. #22623498C2semidirect
15. #22623498C2semidirect
16. #41×D292C2semidirect
17. #41×D292C2semidirect
18. #22623323C2semidirect
19. #22623228C2semidirect
20. C2×#17989124C2semidirect
21. #22623130C2semidirect
22. C4×#41×D73C2semidirect
23. Q8×#41×C73C2semidirect
26. #17989322C22semidirect
27. #17989322C22semidirect
28. #17989316C22semidirect
29. #17989311C22semidirect
30. #17989311C22semidirect
31. #17989310C22semidirect
32. #17989310C22semidirect
33. #17989303C22semidirect
34. #17989303C22semidirect
35. #17989298C22semidirect
36. #17989298C22semidirect
37. #17989290C22semidirect
38. #17989290C22semidirect
39. #17989290C22semidirect
40. #17989285C22semidirect
41. #17989285C22semidirect
42. #17989279C22semidirect
43. #17989279C22semidirect
44. #17989275C22semidirect
45. #17989275C22semidirect
46. #17989275C22semidirect
47. #17989264C22semidirect
48. #17989264C22semidirect
49. #17989264C22semidirect
50. #17989259C22semidirect
51. #17989259C22semidirect
52. #17989259C22semidirect
53. Q8×D292C22semidirect
54. Q8×D292C22semidirect
55. #17989249C22semidirect
56. #17989249C22semidirect
57. #17989249C22semidirect
58. #17989248C22semidirect
59. #17989241C22semidirect
60. #17989241C22semidirect
61. #17989240C22semidirect
62. #17989240C22semidirect
63. #17989232C22semidirect
64. #17989232C22semidirect
65. #17989232C22semidirect
66. #17989228C22semidirect
67. #17989228C22semidirect
68. D4×D292C22semidirect
69. D4×D292C22semidirect
70. #17989211C22semidirect
71. #17989211C22semidirect
72. #17989211C22semidirect
73. #17989211C22semidirect
74. #17989200C22semidirect
75. #17989200C22semidirect
76. #17989193C22semidirect
77. #17989193C22semidirect
78. #17989186C22semidirect
79. #17989186C22semidirect
80. #17989177C22semidirect
81. #17989177C22semidirect
82. #17989142C22semidirect
83. #17989142C22semidirect
84. #17989138C22semidirect
85. #17989138C22semidirect
86. #17989137C22semidirect
87. #17989137C22semidirect
90. #17989124C22semidirect
91. #17989124C22semidirect
92. #17989124C22semidirect
93. #17989124C22semidirect
94. #17989124C22semidirect
95. #17989124C22semidirect
96. #17989124C22semidirect
97. #17989124C22semidirect
98. #17989124C22semidirect
99. #17989124C22semidirect
100. #17989124C22semidirect
101. #17989124C22semidirect
102. #17989124C22semidirect
103. #17989123C22semidirect
104. #17989123C22semidirect
105. #17989122C22semidirect
106. #17989122C22semidirect
107. C2×#14556586C22semidirect
108. C2×#14556582C22semidirect
109. C2×#14556580C22semidirect
110. #17989100C22semidirect
111. #17989100C22semidirect
112. #17989099C22semidirect
113. #17989099C22semidirect
114. #17989099C22semidirect
115. C2×#14556576C22semidirect
116. C2×#14556567C22semidirect
118. #17989069C22semidirect
119. #17989069C22semidirect
120. #17989066C22semidirect
121. #17989066C22semidirect
122. #17989063C22semidirect
123. #17989063C22semidirect
124. #17989059C22semidirect
125. #17989059C22semidirect
127. C4×#11924029C22semidirect
128. C4×#11924029C22semidirect
129. C4×#11924029C22semidirect
130. C4×#11924029C22semidirect
131. C4×#11924028C22semidirect
132. C4×#11924028C22semidirect
133. #17989055C22semidirect
134. #17989055C22semidirect
135. C4×#11924027C22semidirect
136. C4×#11924027C22semidirect
137. C4×Q8×D73C22semidirect
138. C4×Q8×D73C22semidirect
139. C2×C4×D292C22semidirect
140. C2×C4×D292C22semidirect
141. C4×D4×D73C22semidirect
142. C4×D4×D73C22semidirect
143. C2×#14556548C22semidirect
144. #117×D73C22semidirect
145. #117×D73C22semidirect
146. C2×C42×D73C22semidirect
147. Q82×C73C22semidirect
148. #557×C73C22semidirect
149. #557×C73C22semidirect
150. #554×C73C22semidirect
151. #554×C73C22semidirect
152. D4×Q8×C73C22semidirect
153. #533×C73C22semidirect
154. #533×C73C22semidirect
157. C2×C4×Q8×C73C22semidirect
518. #41×C73#41semidirect
689. Q8×#41D73semidirect
699. C73#62816semidirect
704. Q82C2×D73semidirect
706. #557C2×D73semidirect
707. #557C2×D73semidirect
716. #554C2×D73semidirect
717. #554C2×D73semidirect
736. D4×Q8C2×D73semidirect
766. #533C2×D73semidirect
767. #533C2×D73semidirect
825. C2×C4×Q8C2×D73semidirect
1086. #41#11924029semidirect

Maximal subgroups

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

subgroupindex
#226240432
#226240282
#226240172
#226240022
#226239812
#226239642
#226239492
#226239382
#226239272
#226239102
#226238932
#226238742
#226235262
#226234982
#41×D2922
#226233232
#226232282
C2×#179891242
#226231302
C4×#41×D732
Q8×#41×C732
#6281673