Finite Group Databasebeta

← #11911054

Subgroups — #11911054

Order 1152.

2503 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic, complemented
2C3×D4×#67C212yesmaximal, complemented
3#10595518C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5#10595508C211yesmaximal, characteristic, complemented
6#10595501C211yesmaximal, characteristic, complemented
7#10595494C212yesmaximal, complemented
8#10595494C212yesmaximal, complemented
9#10595260C212yesmaximal, complemented
10#10595259C212yesmaximal, complemented
11#10595230C212yesmaximal, complemented
12#10595216C212yesmaximal, complemented
13#10595188C212yesmaximal, complemented
14#10595180C212yesmaximal, complemented
15#10595175C212yesmaximal, complemented
16#10595150C212yesmaximal, complemented
17#10595037C211yesmaximal, characteristic, complemented
18#10594962C212yesmaximal, complemented
19#10594930C211yesmaximal, characteristic, complemented
20#86613—32nomaximal
21C22×C32×D4C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×#67C2212yescomplemented
24C22×C3×#67C2212yescomplemented
25C2×C3×D3×D4C2212yescomplemented
26C22×#625C2211yescharacteristic, complemented
27C2×#3805C2211yescharacteristic, complemented
28C2×#3805C2212yescomplemented
29C2×#3757C2211yescharacteristic, complemented
30C2×#3757C2211yescharacteristic, complemented
31C2×#3757C2211yescharacteristic, complemented
32#64144C2212yescomplemented
33#64144C2212yescomplemented
34#64144C2212yescomplemented
35#64144C2212yescomplemented
36C2×#3750C2211yescharacteristic, complemented
37C2×#3750C2211yescharacteristic, complemented
38C3×#953C2212yescomplemented
39C3×#953C2212yescomplemented
40C3×#940C2212yescomplemented
41C3×#939C2212yes—
42C3×#939C2212yescomplemented
43C3×#938C2212yescomplemented
44C3×#937C2212yes—
45C3×#937C2212yescomplemented
46C3×D4×Dic3C2212yescomplemented
47C3×#930C2212yescomplemented
48C3×C4×#67C2212yescomplemented
49#63982C2211yescharacteristic, complemented
50#63982C2211yescharacteristic, complemented
51#63980C2211yescharacteristic
52#63980C2211yescharacteristic, complemented
53#63980C2211yescharacteristic, complemented
54#63980C2211yescharacteristic, complemented
55#63980C2211yescharacteristic, complemented
56#63980C2212yescomplemented
57#63980C2212yescomplemented
58#63980C2211yescharacteristic, complemented
59#63980C2212yescomplemented
60#63976C2212yescomplemented
61#63976C2212yescomplemented
62#63976C2212yescomplemented
63#63976C2212yescomplemented
64#67⋊Dic3C2212yescomplemented
65#67⋊Dic3C2212yescomplemented
66#67⋊Dic3C2212yescomplemented
67Dic3×#67C2212yescomplemented
68Dic3×#67C2212yescomplemented
69#63970C2212yescomplemented
70#63970C2212yescomplemented
71#63970C2212yescomplemented
72#63970C2212yescomplemented
73#63970C2212yescomplemented
74#63969C2212yescomplemented
75#63969C2212yescomplemented
76#63969C2212yescomplemented
77D3×#217C2212yescomplemented
78D3×#217C2212yescomplemented
79C2×#3724C2211yescharacteristic, complemented
80#63964C2212yescomplemented
81#63964C2212yescomplemented
82#63962C2212yescomplemented
83#63962C2212yescomplemented
84#63961C2212yescomplemented
85#63961C2212yescomplemented
86C2×(C2×D3)⋊Dic3C2212yescomplemented
87#63959C2212yescomplemented
88#63959C2212yescomplemented
89#63959C2212yescomplemented
90#63957C2211yescharacteristic, complemented
91#63956C2212yescomplemented
92#63905C2212yescomplemented
93#63905C2212yescomplemented
94#63899C2212yescomplemented
95#63899C2212yescomplemented
96#63885C2212yescomplemented
97#63885C2212yescomplemented
98#63885C2212yescomplemented
99#63884C2212yescomplemented
100#63879C2212yescomplemented
101#63877C2212yescomplemented
102#63867C2212yescomplemented
103#63859C2212yescomplemented
104#63859C2212yescomplemented
105#63858C2212yescomplemented
106#63851C2212yescomplemented
107#63847C2212yescomplemented
108C3×D42—32no—
109#5806—32no—
110#5806—32no—
111#5806—32no—
112#5804—32no—
113#5804—32no—
114C2×#939—32no—
115D4×#67D312yescomplemented
116C2×#935—32no—
117C2×#935—61no—
118#5720—32no—
119#5719—32no—
120#5621—32no—
121#5621—32no—
122#5615—32no—
123#5613—32no—
124#5610—32no—
125#5602—32no—
126#5601—32no—
127#5597—32no—
128#5595—32no—
129#5593—32no—
130#5593—32no—
131#5591—32no—
132#5591—32no—
133#5589—32no—
134#5587—32no—
135#5586—32no—
136#5564—32no—
137#5564—32no—
138#5556—32no—
139#5540—32no—
140C24×C32C2311yescharacteristic
141C24×C32C2311yescharacteristic
142C23×C3×D3C2312yes—
143C23×C3×D3C2312yes—
144C2×C32×D4—42no—
145C2×C32×D4C2312yes—
146C2×C32×D4C2312yes—
147C22×C32×C4C2311yescharacteristic
148C22×C3⋊Dic3—42no—
149C22×C3⋊Dic3C2311yescharacteristic
150C22×C3⋊Dic3C2311yescharacteristic
151C22×C3⋊Dic3C2311yescharacteristic
152C22×C3⋊Dic3C2311yescharacteristic
153C22×C3⋊Dic3C2311yescharacteristic
154C22×C3⋊Dic3C2311yescharacteristic
155C22×C3⋊Dic3C2311yescharacteristic
156C22×C3⋊Dic3C2311yescharacteristic
157C2×C3×#67—44no—
158C2×C3×#67—44no—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C2×C3×#67C2312yes—
165C2×C3×#67C2312yes—
166C2×C3×#67C2312yes—
167C2×C3×#67C2312yes—
168C2×C3×#67C2312yes—
169C2×C3×#67C2312yes—
170C22×C3×Dic3C2312yes—
171C22×C3×Dic3C2312yes—
172C3×D3×D4—44no—
173C2×C3×D12C2312yes—
174C2×C3×C4×D3C2312yes—
175C2×#627C2311yescharacteristic
176C2×#627C2312yes—
177C2×#625—42no—
178C2×#625C2312yes—
179C2×#625C2311yescharacteristic
180C2×#625C2311yescharacteristic
181C2×#625C2312yes—
182C2×#625C2311yescharacteristic
183C2×#625C2312yes—
184#3805—42no—
185#3805—44no—
186C2×D3×Dic3C2312yes—
187C2×D3×Dic3C2312yes—
188C2×D3×Dic3C2312yes—
189C2×D3×Dic3C2312yes—
190#3757C2312yes—
191#3757C2312yes—
192#3757C2312yes—
193#3757C2312yes—
194#3757C2312yes—
195#3757C2312yes—
196#3750C2312yes—
197#3750C2312yes—
198#3750C2312yes—
199#3750C2312yes—
200C3×#217C2312yes—
201C3×#217C2312yes—
202C3×#217C2312yes—
203C3×#217C2312yes—
204C3×#217C2312yes—
205C3×(C2×D3)⋊C4C2312yes—
206C3×(C2×D3)⋊C4C2312yes—
207C3×(C2×D3)⋊C4C2312yes—
208C3×C4⋊Dic3C2312yes—
209C3×Dic3⋊C4C2312yes—
210C3×C4×Dic3C2312yes—
211#3724C2312yes—
212#3724C2312yes—
213#3724C2311yescharacteristic
214#3724C2311yescharacteristic
215#3724C2311yescharacteristic
216#3724C2311yescharacteristic
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221Dic3⋊Dic3C2312yes—
222(C2×D3)⋊Dic3C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231(C2×D3)⋊Dic3C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233Dic32C2312yes—
234Dic32C2312yes—
235#3534—91noSylow
236C22×C3×D4—21no—
237C22×C3×D4—32no—
238C22×C3×D4—32no—
239C22×C3×D4—32no—
240C22×C3×D4C2×D312yes—
241C22×#67—32no—
242C22×#67C2×D312yescomplemented
243C22×#67C2×D312yescomplemented
244C23×Dic3—32no—
245C23×Dic3—61no—
246C2×#237—32no—
247C2×#237—32no—
248C2×#237—32no—
249C2×D3×D4C2×D312yescomplemented
250C3×#127—32no—
251C3×#121—32no—
252C3×#121—32no—
253C3×#121—32no—
254C3×#121—32no—
255C3×#120—32no—
256C3×#120—32no—
257C3×#120—32no—
258C3×#120—32no—
259C3×C4×D4—32no—
260C3×C4×D4—32no—
261#953—32no—
262#953—32no—
263#953—32no—
264#953—32no—
265#953C2×D312yescomplemented
266#953C2×D312yescomplemented
267C2×#217—32no—
268C2×#217—32no—
269C2×#217—32no—
270C2×#217—32no—
271C2×#217—32no—
272C2×#217—32no—
273C2×#217—61no—
274C2×#217—61no—
275C2×#217—61no—
276#940C2×D312yescomplemented
277#939—32no—
278#939—32no—
279#939—32no—
280#939—32no—
281#939—32no—
282#939—32no—
283#939—32no—
284#939—32no—
285#939—32no—
286#939—32no—
287#939—32no—
288#939—32no—
289#939—32no—
290#939—32no—
291#939—32no—
292#939—32no—
293#939—32no—
294#939—32no—
295#939—32no—
296#939—32no—
297#939C2×D312yes—
298#939C2×D312yescomplemented
299#938—32no—
300#938—32no—
301#938—32no—
302#938—32no—
303#938—32no—
304#938C2×D312yescomplemented
305#937—32no—
306#937—32no—
307#937—32no—
308#937—32no—
309#937C2×D312yes—
310#937C2×D312yescomplemented
311#936—32no—
312#936—32no—
313#936—32no—
314#935—32no—
315#935—32no—
316#935—32no—
317#935—32no—
318#935—32no—
319#935—32no—
320#935—32no—
321#935—32no—
322#935—32no—
323#935—32no—
324#935—32no—
325#935—32no—
326#935—32no—
327#935—32no—
328#935—32no—
329#935—32no—
330#935—62no—
331#935—62no—
332#935—62no—
333#935—62no—
334D4×Dic3—32no—
335D4×Dic3—32no—
336D4×Dic3—32no—
337D4×Dic3—32no—
338D4×Dic3—32no—
339D4×Dic3C2×D312yescomplemented
340#930C2×D312yescomplemented
341#929—32no—
342#929—32no—
343#929—32no—
344#929—32no—
345C4×#67—32no—
346C4×#67—32no—
347C4×#67—32no—
348C4×#67C2×D312yescomplemented
349C2×(C2×D3)⋊C4—32no—
350#924—32no—
351#924—32no—
352#924—32no—
353C2×Dic3⋊C4—32no—
354C2×Dic3⋊C4—32no—
355C2×Dic3⋊C4—32no—
356C2×Dic3⋊C4—61no—
357C2×Dic3⋊C4—61no—
358#898—32no—
359#896—32no—
360#896—32no—
361#896—32no—
362#894—32no—
363#889—32no—
364#889—32no—
365#889—32no—
366#886—32no—
367#886—32no—
368#885—32no—
369#885—32no—
370#885—32no—
371#884—32no—
372#884—32no—
373#884—32no—
374#883—32no—
375#883—32no—
376#883—32no—
377#883—32no—
378#883—32no—
379#67⋊C4—32no—
380#67⋊C4—32no—
381#67⋊C4—32no—
382#67⋊C4—32no—
383D3×C22⋊C4—32no—
384D3×C22⋊C4—32no—
385#879—32no—
386#879—32no—
387#879—32no—
388#879—32no—
389#879—32no—
390#878—32no—
391#878—32no—
392#878—32no—
393#878—32no—
394#878—32no—
395#878—32no—
396#877—32no—
397#877—32no—
398#876—32no—
399#876—32no—
400#872—32no—
401#870—32no—
402C23×C32—22no—
403C23×C32—22no—
404C23×C32—22no—
405C23×C32—41no—
406C23×C32—41no—
407C23×C32—41no—
408C23×C32C2412yes—
409C23×C32C2411yescharacteristic
410C23×C32C2411yescharacteristic
411C23×C32C2411yescharacteristic
412C22×C3×D3—24no—
413C22×C3×D3—42no—
414C22×C3×D3—42no—
415C22×C3×D3—42no—
416C22×C3×D3—42no—
417C22×C3×D3—42no—
418C22×C3×D3C2412yes—
419C22×C3×D3C2412yes—
420C22×C3×D3C2412yes—
421C32×D4—24no—
422C32×D4—42no—
423C2×C32×C4—41no—
424C2×C32×C4C2412yes—
425C2×C3⋊Dic3—22no—
426C2×C3⋊Dic3—22no—
427C2×C3⋊Dic3—22no—
428C2×C3⋊Dic3—41no—
429C2×C3⋊Dic3—41no—
430C2×C3⋊Dic3—41no—
431C2×C3⋊Dic3—41no—
432C2×C3⋊Dic3—41no—
433C2×C3⋊Dic3C2411yescharacteristic
434C2×C3⋊Dic3C2412yes—
435C2×C3⋊Dic3C2411yescharacteristic
436C2×C3⋊Dic3C2411yescharacteristic
437C2×C3⋊Dic3C2411yescharacteristic
438C2×C3⋊Dic3C2412yes—
439C3×#67—24no—
440C3×#67—24no—
441C3×#67—24no—
442C3×#67—24no—
443C3×#67—42no—
444C3×#67—42no—
445C3×#67—42no—
446C3×#67—42no—
447C3×#67—42no—
448C3×#67—42no—
449C3×#67—42no—
450C2×C3×Dic3—42no—
451C2×C3×Dic3—42no—
452C2×C3×Dic3C2412yes—
453C2×C3×Dic3C2412yes—
454C2×C3×Dic3C2412yes—
455C2×C3×Dic3C2412yes—
456C2×C3×Dic3C2412yes—
457C3×D12—42no—
458C3×C4×D3—42no—
459#627—41no—
460#627—42no—
461#625—42no—
462#625—41no—
463#625—41no—
464#625—42no—
465#625—41no—
466#625—42no—
467D3×Dic3—42no—
468D3×Dic3—42no—
469D3×Dic3—42no—
470D3×Dic3—42no—
471#562—92no—
472#560—92no—
473#553—92no—
474#551—92no—
475#546—92no—
476#546—92no—
477#546—92no—
478D42—32no—
479#540—92no—
480#539—91no—
481#539—92no—
482#538—91no—
483#538—92no—
484#537—91no—
485#534—92no—
486#534—91no—
487#525—91no—
488C2×#123—91no—
489C2×#121—91no—
490C24×C3—21no—
491C24×C3—21no—
492C24×C3—32no—
493C24×C3—32no—
494C24×C3C22×D312yes—
495C24×C3C22×D312yes—
496C23×D3C22×D312yes—
497C23×D3C22×D312yes—
498C2×C3×D4—22no—
499C2×C3×D4—22no—
500C2×C3×D4—32no—
501C2×C3×D4—32no—
502C2×C3×D4—32no—
503C2×C3×D4—32no—
504C2×C3×D4—32no—
505C2×C3×D4—32no—
506C2×C3×D4—32no—
507C2×C3×D4—32no—
508C2×C3×D4—32no—
509C2×C3×D4—32no—
510C2×C3×D4—32no—
511C2×C3×D4—32no—
512C2×C3×D4—44no—
513C2×C3×D4—44no—
514C2×C3×D4—124no—
515C2×C3×D4—124no—
516C2×C3×D4—124no—
517C2×C3×D4C22×D312yes—
518C2×C3×D4C22×D312yes—
519C2×C3×D4C22×D312yes—
520C2×C3×D4C22×D312yes—
521C22×C3×C4—21no—
522C22×C3×C4—32no—
523C22×C3×C4—32no—
524C22×C3×C4—32no—
525C22×C3×C4C22×D312yes—
526C2×#67—32no—
527C2×#67—32no—
528C2×#67—32no—
529C2×#67—32no—
530C2×#67—32no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—44no—
536C2×#67—44no—
537C2×#67—124no—
538C2×#67C22×D312yes—
539C2×#67C22×D312yes—
540C2×#67C22×D312yes—
541C2×#67C22×D312yes—
542C2×#67C22×D312yes—
543C2×#67C22×D312yes—
544C2×#67C22×D312yes—
545C2×#67C22×D312yes—
546C2×#67C22×D312yes—
547C2×#67C22×D312yes—
548C2×#67C22×D312yes—
549C22×Dic3—32no—
550C22×Dic3—32no—
551C22×Dic3—32no—
552C22×Dic3—32no—
553C22×Dic3—32no—
554C22×Dic3—32no—
555C22×Dic3—32no—
556C22×Dic3—32no—
557C22×Dic3—32no—
558C22×Dic3—32no—
559C22×Dic3—32no—
560C22×Dic3—32no—
561C22×Dic3—61no—
562C22×Dic3—61no—
563C22×Dic3—61no—
564C22×Dic3—61no—
565C22×Dic3—61no—
566C22×Dic3—61no—
567C22×Dic3—61no—
568C22×Dic3—61no—
569C22×Dic3—124no—
570C22×Dic3—124no—
571C22×Dic3C22×D312yes—
572C22×Dic3C22×D312yes—
573#237—124no—
574#237—124no—
575#237—124no—
576D3×D4—44no—
577C2×D12C22×D312yes—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
580C2×C4×D3—32no—
581C2×C4×D3—32no—
582C2×C4×D3C22×D312yes—
583C2×Dic6—32no—
584C2×Dic6—32no—
585C2×Dic6—32no—
586C3×C4⋊C4—32no—
587C3×C4⋊C4—32no—
588C3×C22⋊C4—32no—
589C3×C22⋊C4—32no—
590C3×C22⋊C4—32no—
591C3×C22⋊C4—32no—
592C3×C22⋊C4—32no—
593C3×C22⋊C4—32no—
594C3×C22⋊C4—32no—
595C3×C22⋊C4—32no—
596C3×C42—32no—
597#217—32no—
598#217—32no—
599#217—32no—
600#217—32no—
601#217—32no—
602#217—32no—
603#217—32no—
604#217—32no—
605#217—32no—
606#217—32no—
607#217—32no—
608#217—32no—
609#217—32no—
610#217—32no—
611#217—32no—
612#217—32no—
613#217—32no—
614#217—32no—
615#217—32no—
616#217—32no—
617#217—32no—
618#217—32no—
619#217—32no—
620#217—62no—
621#217—62no—
622#217—62no—
623#217—62no—
624#217—62no—
625#217—62no—
626#217C22×D312yes—
627#217C22×D312yes—
628#217C22×D312yes—
629#217C22×D312yes—
630#217C22×D312yes—
631(C2×D3)⋊C4—32no—
632(C2×D3)⋊C4—32no—
633(C2×D3)⋊C4—32no—
634(C2×D3)⋊C4—32no—
635(C2×D3)⋊C4—32no—
636(C2×D3)⋊C4—32no—
637(C2×D3)⋊C4—32no—
638(C2×D3)⋊C4—32no—
639(C2×D3)⋊C4—32no—
640(C2×D3)⋊C4—32no—
641(C2×D3)⋊C4—32no—
642(C2×D3)⋊C4C22×D312yes—
643(C2×D3)⋊C4C22×D312yes—
644(C2×D3)⋊C4C22×D312yes—
645C4⋊Dic3—32no—
646C4⋊Dic3—32no—
647C4⋊Dic3—32no—
648C4⋊Dic3—32no—
649C4⋊Dic3—32no—
650C4⋊Dic3C22×D312yes—
651Dic3⋊C4—32no—
652Dic3⋊C4—32no—
653Dic3⋊C4—32no—
654Dic3⋊C4—32no—
655Dic3⋊C4—32no—
656Dic3⋊C4—32no—
657Dic3⋊C4—32no—
658Dic3⋊C4—32no—
659Dic3⋊C4—32no—
660Dic3⋊C4—32no—
661Dic3⋊C4—32no—
662Dic3⋊C4—32no—
663Dic3⋊C4—32no—
664Dic3⋊C4—32no—
665Dic3⋊C4—32no—
666Dic3⋊C4—32no—
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—62no—
673Dic3⋊C4—62no—
674Dic3⋊C4—62no—
675Dic3⋊C4—62no—
676Dic3⋊C4C22×D312yes—
677C4×Dic3—32no—
678C4×Dic3—32no—
679C4×Dic3—32no—
680C4×Dic3—32no—
681C4×Dic3C22×D312yes—
682C22×C32—21no—
683C22×C32—21no—
684C22×C32—21no—
685C22×C32—21no—
686C22×C32—21no—
687C22×C32—22no—
688C22×C32—21no—
689C22×C32—22no—
690C22×C32—21no—
691C22×C32—22no—
692C22×C32—44no—
693C22×C32—82no—
694C22×C32H(5,𝔽2)12yes—
695C22×C32H(5,𝔽2)12yes—
696C22×C32C2511yescharacteristic
697C2×C3×D3—22no—
698C2×C3×D3—22no—
699C2×C3×D3—22no—
700C2×C3×D3—22no—
701C2×C3×D3—22no—
702C2×C3×D3—22no—
703C2×C3×D3—22no—
704C2×C3×D3—22no—
705C2×C3×D3—22no—
706C2×C3×D3—84no—
707C2×C3×D3—84no—
708C32×C4—22no—
709C3⋊Dic3—22no—
710C3⋊Dic3—21no—
711C3⋊Dic3—21no—
712C3⋊Dic3—21no—
713C3⋊Dic3—21no—
714C3⋊Dic3—22no—
715C3×Dic3—22no—
716C3×Dic3—22no—
717C3×Dic3—22no—
718C3×Dic3—22no—
719C3×Dic3—22no—
720C2×#41—91no—
721C2×#41—92no—
722C22×D4—32no—
723C22×D4—32no—
724C22×D4—32no—
725C22×D4—91no—
726C22×D4D3211yescharacteristic
727C23×C4—91no—
728#127—32no—
729#126—92no—
730#126—92no—
731#126—92no—
732#126—92no—
733#125—92no—
734#125—92no—
735#124—92no—
736#124—92no—
737#124—92no—
738#123—92no—
739#123—92no—
740#123—92no—
741#123—92no—
742#123—92no—
743#123—92no—
744#123—92no—
745#123—92no—
746#123—92no—
747#123—92no—
748#123—92no—
749#123—92no—
750#123—92no—
751#123—92no—
752C22⋊Q8—91no—
753C22⋊Q8—91no—
754C22⋊Q8—92no—
755C22⋊Q8—92no—
756C22⋊Q8—92no—
757C22⋊Q8—92no—
758C22⋊Q8—92no—
759#121—32no—
760#121—32no—
761#121—32no—
762#121—32no—
763#121—92no—
764#121—92no—
765#121—92no—
766#121—91no—
767#121—91no—
768#121—91no—
769#121—91no—
770#121—92no—
771#121—92no—
772#121—91no—
773#121—91no—
774#121—92no—
775#121—92no—
776#121—92no—
777#121—92no—
778#121—92no—
779#121—92no—
780#120—32no—
781#120—32no—
782#120—32no—
783#120—32no—
784#120—92no—
785#120—92no—
786#120—92no—
787#120—92no—
788C4×D4—32no—
789C4×D4—32no—
790C4×D4—92no—
791C4×D4—92no—
792C4×D4—92no—
793C4×D4—92no—
794C4×D4—92no—
795C4×D4—92no—
796#117—92no—
797#117—91no—
798C2×C4⋊C4—91no—
799C2×C4⋊C4—91no—
800C2×C4⋊C4—91no—
801C2×C22⋊C4—92no—
802C2×C22⋊C4—92no—
803C2×C22⋊C4—92no—
804C2×C22⋊C4—91no—
805C2×C22⋊C4—91no—
806C2×C22⋊C4—91no—
807C23×C3—24no—
808C23×C3—24no—
809C23×C3—24no—
810C23×C3—24no—
811C23×C3—21no—
812C23×C3—21no—
813C23×C3—21no—
814C23×C3—22no—
815C23×C3—32no—
816C23×C3—32no—
817C23×C3—32no—
818C23×C3—42no—
819C23×C3—42no—
820C23×C3—42no—
821C23×C3—42no—
822C23×C3—42no—
823C23×C3—42no—
824C23×C3—42no—
825C23×C3—42no—
826C23×C3—64no—
827C23×C3—122no—
828C23×C3—122no—
829C23×C3—122no—
830C23×C3—122no—
831C23×C3—122no—
832C23×C3C23×D312yes—
833C23×C3C23×D312yes—
834C23×C3C23×D312yes—
835C23×C3C23×D312yes—
836C23×C3C23×D312yes—
837C22×D3—24no—
838C22×D3—42no—
839C22×D3—42no—
840C22×D3—42no—
841C22×D3—42no—
842C22×D3—42no—
843C22×D3C23×D312yes—
844C22×D3C23×D312yes—
845C22×D3C23×D312yes—
846C3×D4—24no—
847C3×D4—24no—
848C3×D4—44no—
849C3×D4—42no—
850C3×D4—42no—
851C3×D4—44no—
852C3×D4—64no—
853C3×D4—64no—
854C3×D4—64no—
855C3×D4—64no—
856C3×D4—122no—
857C3×D4—122no—
858C3×D4—122no—
859C3×D4—122no—
860C3×D4—122no—
861C3×D4—122no—
862C3×D4—122no—
863C3×D4—122no—
864C2×C3×C4—22no—
865C2×C3×C4—32no—
866C2×C3×C4—32no—
867C2×C3×C4—32no—
868C2×C3×C4—32no—
869C2×C3×C4—32no—
870C2×C3×C4—42no—
871C2×C3×C4—42no—
872C2×C3×C4—122no—
873C2×C3×C4—122no—
874C2×C3×C4—122no—
875C2×C3×C4C23×D312yes—
876C2×C3×C4C23×D312yes—
877#67—24no—
878#67—24no—
879#67—24no—
880#67—24no—
881#67—42no—
882#67—42no—
883#67—42no—
884#67—42no—
885#67—42no—
886#67—42no—
887#67—42no—
888#67—122no—
889#67—122no—
890#67—122no—
891#67—122no—
892#67—122no—
893#67—122no—
894#67—122no—
895#67—122no—
896#67—122no—
897C2×Dic3—32no—
898C2×Dic3—32no—
899C2×Dic3—32no—
900C2×Dic3—32no—
901C2×Dic3—32no—
902C2×Dic3—32no—
903C2×Dic3—32no—
904C2×Dic3—32no—
905C2×Dic3—42no—
906C2×Dic3—42no—
907C2×Dic3—62no—
908C2×Dic3—62no—
909C2×Dic3—61no—
910C2×Dic3—61no—
911C2×Dic3—61no—
912C2×Dic3—61no—
913C2×Dic3—64no—
914C2×Dic3—64no—
915C2×Dic3—64no—
916C2×Dic3—122no—
917C2×Dic3—122no—
918C2×Dic3—122no—
919C2×Dic3—122no—
920C2×Dic3—122no—
921C2×Dic3—122no—
922C2×Dic3—122no—
923C2×Dic3—122no—
924C2×Dic3—122no—
925C2×Dic3—122no—
926C2×Dic3—122no—
927C2×Dic3—122no—
928C2×Dic3—122no—
929C2×Dic3—122no—
930C2×Dic3—122no—
931C2×Dic3—122no—
932C2×Dic3—122no—
933C2×Dic3C23×D312yes—
934C2×Dic3C23×D312yes—
935C2×Dic3C23×D312yes—
936C2×Dic3C23×D312yes—
937C2×Dic3C23×D312yes—
938D12—42no—
939C4×D3—42no—
940C4×D3—122no—
941C4×D3—122no—
942C4×D3—122no—
943C4×D3—122no—
944Dic6—122no—
945Dic6—122no—
946Dic6—122no—
947C2×C32—22no—
948C2×C32—22no—
949C2×C32—41no—
950C2×C32—42no—
951C2×C32C2×H(5,𝔽2)11yescharacteristic
952C2×C32C2×H(5,𝔽2)11yescharacteristic
953C2×C32#58511yescharacteristic
954C3×D3—42no—
955C3×D3—42no—
956C3×D3—42no—
957C24—32no—
958C24—32no—
959C24C2×D3211yescharacteristic
960C24C2×D3211yescharacteristic
961#41—364no—
962#41—362no—
963C2×Q8—91no—
964C2×Q8—92no—
965C2×D4—32no—
966C2×D4—32no—
967C2×D4—32no—
968C2×D4—32no—
969C2×D4—32no—
970C2×D4—32no—
971C2×D4—32no—
972C2×D4—32no—
973C2×D4—32no—
974C2×D4—32no—
975C2×D4—32no—
976C2×D4—32no—
977C2×D4—42no—
978C2×D4—92no—
979C2×D4—92no—
980C2×D4—91no—
981C2×D4—91no—
982C2×D4—92no—
983C2×D4—91no—
984C2×D4—124no—
985C2×D4—124no—
986C2×D4—124no—
987C2×D4—362no—
988C2×D4C2×D3212yes—
989C2×D4C2×D3212yes—
990C22×C4—32no—
991C22×C4—32no—
992C22×C4—32no—
993C22×C4—92no—
994C22×C4—92no—
995C22×C4—92no—
996C22×C4—92no—
997C22×C4—91no—
998C22×C4—91no—
999C22×C4—91no—
1000C22×C4—91no—
1001C22×C4—91no—
1002C22×C4—91no—
1003C22×C4—91no—
1004C22×C4—91no—
1005C22×C4—362no—
1006C22×C4C2×D3211yescharacteristic
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—91no—
1010C4⋊C4—92no—
1011C4⋊C4—91no—
1012C4⋊C4—91no—
1013C4⋊C4—92no—
1014C4⋊C4—91no—
1015C4⋊C4—92no—
1016C4⋊C4—92no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—92no—
1021C4⋊C4—92no—
1022C4⋊C4—92no—
1023C4⋊C4—92no—
1024C22⋊C4—32no—
1025C22⋊C4—32no—
1026C22⋊C4—32no—
1027C22⋊C4—32no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—92no—
1033C22⋊C4—92no—
1034C22⋊C4—92no—
1035C22⋊C4—92no—
1036C22⋊C4—92no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4—92no—
1047C22⋊C4—92no—
1048C22⋊C4—92no—
1049C42—32no—
1050C42—92no—
1051C42—92no—
1052C22×C3—22no—
1053C22×C3—22no—
1054C22×C3—22no—
1055C22×C3—22no—
1056C22×C3—22no—
1057C22×C3—22no—
1058C22×C3—22no—
1059C22×C3—22no—
1060C22×C3—22no—
1061C22×C3—22no—
1062C22×C3—22no—
1063C22×C3—22no—
1064C22×C3—22no—
1065C22×C3—22no—
1066C22×C3—22no—
1067C22×C3—22no—
1068C22×C3—22no—
1069C22×C3—22no—
1070C22×C3—21no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—42no—
1076C22×C3—42no—
1077C22×C3—42no—
1078C22×C3—48no—
1079C22×C3—48no—
1080C22×C3—62no—
1081C22×C3—62no—
1082C22×C3—62no—
1083C22×C3—62no—
1084C22×C3—62no—
1085C22×C3—62no—
1086C22×C3—62no—
1087C22×C3—62no—
1088C22×C3—62no—
1089C22×C3—84no—
1090C22×C3—84no—
1091C22×C3—244no—
1092C22×C3—244no—
1093C22×C3#100414yes—
1094C22×C3#100414yes—
1095C22×C3C24×D312yes—
1096C2×D3—22no—
1097C2×D3—22no—
1098C2×D3—22no—
1099C2×D3—22no—
1100C2×D3—22no—
1101C2×D3—22no—
1102C2×D3—22no—
1103C2×D3—22no—
1104C2×D3—22no—
1105C2×D3—84no—
1106C2×D3—84no—
1107C3×C4—22no—
1108C3×C4—22no—
1109C3×C4—42no—
1110C3×C4—62no—
1111C3×C4—62no—
1112C3×C4—62no—
1113C3×C4—62no—
1114C3×C4—62no—
1115Dic3—22no—
1116Dic3—22no—
1117Dic3—22no—
1118Dic3—22no—
1119Dic3—22no—
1120Dic3—62no—
1121Dic3—62no—
1122Dic3—62no—
1123Dic3—62no—
1124Dic3—62no—
1125Dic3—62no—
1126Dic3—62no—
1127Dic3—62no—
1128Dic3—121no—
1129Dic3—121no—
1130Dic3—121no—
1131Dic3—121no—
1132Dic3—122no—
1133Dic3—122no—
1134C32#353411yescharacteristic, complemented, Sylow
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—32no—
1139C23—32no—
1140C23—32no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—64no—
1145C23—122no—
1146C23—122no—
1147C23—122no—
1148C23—122no—
1149C23—122no—
1150C23C22×D3212yes—
1151C23C22×D3211yescharacteristic
1152C23C22×D3211yescharacteristic
1153C23C22×D3211yescharacteristic
1154Q8—362no—
1155Q8—361no—
1156D4—24no—
1157D4—42no—
1158D4—64no—
1159D4—64no—
1160D4—64no—
1161D4—64no—
1162D4—122no—
1163D4—122no—
1164D4—122no—
1165D4—122no—
1166D4—122no—
1167D4—122no—
1168D4—122no—
1169D4—122no—
1170D4—361no—
1171D4—362no—
1172D4—361no—
1173D4—362no—
1174D4—361no—
1175D4—362no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—32no—
1180C2×C4—32no—
1181C2×C4—41no—
1182C2×C4—91no—
1183C2×C4—92no—
1184C2×C4—92no—
1185C2×C4—91no—
1186C2×C4—91no—
1187C2×C4—91no—
1188C2×C4—122no—
1189C2×C4—122no—
1190C2×C4—122no—
1191C2×C4—182no—
1192C2×C4—182no—
1193C2×C4—182no—
1194C2×C4—362no—
1195C2×C4—362no—
1196C2×C4—362no—
1197C2×C4—362no—
1198C2×C4—361no—
1199C2×C4—361no—
1200C2×C4—361no—
1201C2×C4—361no—
1202C2×C4—361no—
1203C2×C4C22×D3212yes—
1204C2×C3—24no—
1205C2×C3—24no—
1206C2×C3—24no—
1207C2×C3—21no—
1208C2×C3—21no—
1209C2×C3—21no—
1210C2×C3—42no—
1211C2×C3—42no—
1212C2×C3—42no—
1213C2×C3—42no—
1214C2×C3—42no—
1215C2×C3—82no—
1216C2×C3—122no—
1217C2×C3—122no—
1218C2×C3—122no—
1219C2×C3C2×#100412yes—
1220C2×C3C2×#100412yes—
1221C2×C3#596612yes—
1222D3—42no—
1223D3—42no—
1224D3—42no—
1225C22—21no—
1226C22—21no—
1227C22—21no—
1228C22—21no—
1229C22—22no—
1230C22—21no—
1231C22—21no—
1232C22—22no—
1233C22—21no—
1234C22—22no—
1235C22—44no—
1236C22—62no—
1237C22—62no—
1238C22—62no—
1239C22—62no—
1240C22—62no—
1241C22—62no—
1242C22—62no—
1243C22—62no—
1244C22—62no—
1245C22—82no—
1246C22—244no—
1247C22—244no—
1248C22#6431312yes—
1249C22#6433012yes—
1250C22C23×D3211yescharacteristic
1251C4—22no—
1252C4—62no—
1253C4—62no—
1254C4—62no—
1255C4—62no—
1256C4—62no—
1257C4—182no—
1258C4—182no—
1259C4—181no—
1260C4—181no—
1261C4—181no—
1262C4—181no—
1263C3—21no—
1264C3#8661312yescomplemented
1265C2—22no—
1266C2—22no—
1267C2—41no—
1268C2—42no—
1269C2—122no—
1270C2—122no—
1271C2—122no—
1272C2C2×#6431311yescharacteristic
1273C2#1059667911yescharacteristic
1274C2C2×#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64144C2semidirect
2. C3×D4×#67C2semidirect
3. #10595518C2semidirect
4. C2×#63980C2semidirect
5. #10595508C2semidirect
6. #10595501C2semidirect
7. #10595494C2semidirect
8. #10595494C2semidirect
9. #10595260C2semidirect
10. #10595259C2semidirect
11. #10595230C2semidirect
12. #10595216C2semidirect
13. #10595188C2semidirect
14. #10595180C2semidirect
15. #10595175C2semidirect
16. #10595150C2semidirect
17. #10595037C2semidirect
18. #10594962C2semidirect
19. #10594930C2semidirect
22. C23×C3⋊Dic3C22semidirect
23. C22×C3×#67C22semidirect
24. C22×C3×#67C22semidirect
25. C2×C3×D3×D4C22semidirect
26. C22×#625C22semidirect
27. C2×#3805C22semidirect
28. C2×#3805C22semidirect
29. C2×#3757C22semidirect
30. C2×#3757C22semidirect
31. C2×#3757C22semidirect
32. #64144C22semidirect
33. #64144C22semidirect
34. #64144C22semidirect
35. #64144C22semidirect
36. C2×#3750C22semidirect
37. C2×#3750C22semidirect
38. C3×#953C22semidirect
39. C3×#953C22semidirect
40. C3×#940C22semidirect
42. C3×#939C22semidirect
43. C3×#938C22semidirect
45. C3×#937C22semidirect
46. C3×D4×Dic3C22semidirect
47. C3×#930C22semidirect
48. C3×C4×#67C22semidirect
49. #63982C22semidirect
50. #63982C22semidirect
52. #63980C22semidirect
53. #63980C22semidirect
54. #63980C22semidirect
55. #63980C22semidirect
56. #63980C22semidirect
57. #63980C22semidirect
58. #63980C22semidirect
59. #63980C22semidirect
60. #63976C22semidirect
61. #63976C22semidirect
62. #63976C22semidirect
63. #63976C22semidirect
64. #67⋊Dic3C22semidirect
65. #67⋊Dic3C22semidirect
66. #67⋊Dic3C22semidirect
67. Dic3×#67C22semidirect
68. Dic3×#67C22semidirect
69. #63970C22semidirect
70. #63970C22semidirect
71. #63970C22semidirect
72. #63970C22semidirect
73. #63970C22semidirect
74. #63969C22semidirect
75. #63969C22semidirect
76. #63969C22semidirect
77. D3×#217C22semidirect
78. D3×#217C22semidirect
79. C2×#3724C22semidirect
80. #63964C22semidirect
81. #63964C22semidirect
82. #63962C22semidirect
83. #63962C22semidirect
84. #63961C22semidirect
85. #63961C22semidirect
86. C2×(C2×D3)⋊Dic3C22semidirect
87. #63959C22semidirect
88. #63959C22semidirect
89. #63959C22semidirect
90. #63957C22semidirect
91. #63956C22semidirect
92. #63905C22semidirect
93. #63905C22semidirect
94. #63899C22semidirect
95. #63899C22semidirect
96. #63885C22semidirect
97. #63885C22semidirect
98. #63885C22semidirect
99. #63884C22semidirect
100. #63879C22semidirect
101. #63877C22semidirect
102. #63867C22semidirect
103. #63859C22semidirect
104. #63859C22semidirect
105. #63858C22semidirect
106. #63851C22semidirect
107. #63847C22semidirect
115. D4×#67D3semidirect
242. C22×#67C2×D3semidirect
243. C22×#67C2×D3semidirect
249. C2×D3×D4C2×D3semidirect
265. #953C2×D3semidirect
266. #953C2×D3semidirect
276. #940C2×D3semidirect
298. #939C2×D3semidirect
304. #938C2×D3semidirect
310. #937C2×D3semidirect
339. D4×Dic3C2×D3semidirect
340. #930C2×D3semidirect
348. C4×#67C2×D3semidirect
1134. C32#3534semidirect
1264. C3#86613semidirect

Maximal subgroups

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

subgroupindex
C2×#641442
C3×D4×#672
#105955182
C2×#639802
#105955082
#105955012
#105954942
#105952602
#105952592
#105952302
#105952162
#105951882
#105951802
#105951752
#105951502
#105950372
#105949622
#105949302
#866133