Finite Group Databasebeta

← #11911061

Subgroups — #11911061

Order 1152.

2545 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic, complemented
2C3×#5804C212yesmaximal, complemented
3#10595526C212yesmaximal, complemented
4#10595509C212yesmaximal, complemented
5#10595500C212yesmaximal, complemented
6#10595494C212yesmaximal, complemented
7#10595311C211yesmaximal, characteristic, complemented
8#10595294C212yesmaximal, complemented
9#10595280C211yesmaximal, characteristic, complemented
10#10595265C212yesmaximal, complemented
11#10595258C212yesmaximal, complemented
12#10595209C211yesmaximal, characteristic, complemented
13#10595197C212yesmaximal, complemented
14#10595195C212yesmaximal, complemented
15#10595185C212yesmaximal, complemented
16#10595140C211yesmaximal, characteristic, complemented
17#10595079C211yesmaximal, characteristic, complemented
18#10594994C212yesmaximal, complemented
19#10594920C211yesmaximal, characteristic, complemented
20#86311—32nomaximal
21C22×C32×D4C2211yescharacteristic, complemented
22C22×#638C2212yescomplemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2212yescomplemented
25C2×#3811C2211yescharacteristic
26C2×D3×#67C2212yescomplemented
27C2×#3805C2211yescharacteristic, complemented
28C2×#3804C2212yescomplemented
29C2×#3757C2212yescomplemented
30#64147C2211yescharacteristic
31#64147C2211yescharacteristic, complemented
32#64147C2211yescharacteristic, complemented
33#64147C2212yescomplemented
34#64147C2211yescharacteristic, complemented
35#64147C2212yescomplemented
36C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37C3×#953C2212yes—
38C3×#953C2212yescomplemented
39C2×C3×#217C2212yescomplemented
40C3×#939C2212yescomplemented
41C3×#939C2212yescomplemented
42C3×#939C2212yescomplemented
43C3×#939C2212yescomplemented
44C3×#937C2212yescomplemented
45C3×#937C2212yescomplemented
46C3×#935C2212yescomplemented
47C3×#935C2212yescomplemented
48C3×#929C2212yescomplemented
49C3×#929C2212yescomplemented
50#63983C2212yescomplemented
51#63982C2212yescomplemented
52#63981C2212yescomplemented
53#63980C2212yes—
54#63979C2212yescomplemented
55#63978C2212yescomplemented
56#63978C2212yescomplemented
57#63977C2212yescomplemented
58#63976C2212yescomplemented
59#63975C2212yescomplemented
60#63974C2211yescharacteristic, complemented
61#67⋊Dic3C2212yescomplemented
62#67⋊Dic3C2212yescomplemented
63Dic3×#67C2212yescomplemented
64Dic3×#67C2212yescomplemented
65#63971C2212yescomplemented
66#63971C2212yescomplemented
67#63970C2212yescomplemented
68#63970C2212yescomplemented
69#63969C2212yescomplemented
70#63969C2212yescomplemented
71D3×#217C2212yescomplemented
72#63966C2212yescomplemented
73#63964C2212yescomplemented
74#63964C2212yescomplemented
75#63962C2212yescomplemented
76#63961C2212yescomplemented
77#63959C2212yescomplemented
78#63959C2212yescomplemented
79#63958C2212yescomplemented
80#63958C2212yescomplemented
81#63957C2211yescharacteristic, complemented
82#63956C2212yescomplemented
83#63956C2212yescomplemented
84#63955C2212yescomplemented
85#63953C2212yescomplemented
86#63952C2212yescomplemented
87#63952C2212yescomplemented
88#63921C2211yescharacteristic, complemented
89#63921C2211yescharacteristic, complemented
90#63912C2211yescharacteristic, complemented
91#63912C2211yescharacteristic, complemented
92#63893C2212yescomplemented
93#63893C2212yescomplemented
94#63891C2212yescomplemented
95#63891C2212yescomplemented
96#63883C2211yescharacteristic, complemented
97#63883C2211yescharacteristic, complemented
98#63881C2212yescomplemented
99#63881C2212yescomplemented
100#63865C2211yescharacteristic, complemented
101#63865C2211yescharacteristic, complemented
102#63861C2212yescomplemented
103#63861C2212yescomplemented
104#63853C2212yescomplemented
105#63853C2212yescomplemented
106#63845C2212yescomplemented
107#63845C2212yescomplemented
108C3×#534—32no—
109#5806—32no—
110#5804D312yescomplemented
111D4×#67—32no—
112C2×#938—32no—
113C2×#938—61no—
114#5667—32no—
115#5665—32no—
116#5665—32no—
117#5661—32no—
118#5660—32no—
119#5657—32no—
120#5656—32no—
121D3×#123—32no—
122#5621—32no—
123#5620—32no—
124#5619—32no—
125#5615—32no—
126#5614—32no—
127#5613—32no—
128#5612—32no—
129#5608—32no—
130#5595—32no—
131#5593—32no—
132#5591—32no—
133#5591—32no—
134#5591—32no—
135#5590—32no—
136#5589—32no—
137#5587—32no—
138#5495—32no—
139#5490—32no—
140C24×C32C2312yes—
141C23×C3⋊D3C2311yescharacteristic
142C23×C3×D3C2312yes—
143C22×D32C2311yescharacteristic
144C2×C32×D4—42no—
145C2×C32×D4C2311yescharacteristic
146C2×C32×D4C2312yes—
147C2×C32×D4C2311yescharacteristic
148C22×C32×C4C2311yescharacteristic
149C2×#638—44no—
150C2×#638C2312yes—
151C2×#638C2312yes—
152C2×#638C2312yes—
153C2×#638C2312yes—
154C22×C3⋊Dic3C2311yescharacteristic
155C22×C3⋊Dic3C2312yes—
156C2×C4×C3⋊D3—42no—
157C2×C4×C3⋊D3C2311yescharacteristic
158C2×C4×C3⋊D3C2311yescharacteristic
159C2×C4×C3⋊D3C2311yescharacteristic
160C2×C4×C3⋊D3C2311yescharacteristic
161C2×C3×#67—44no—
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—
172C22×C3×Dic3C2312yes—
173#3811—42no—
174D3×#67—44no—
175C2×#627C2312yes—
176C2×#627C2311yescharacteristic
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#625C2311yescharacteristic
181C2×#625C2312yes—
182C2×#624C2311yescharacteristic
183C2×#624C2311yescharacteristic
184C2×#624C2311yescharacteristic
185#3805—42no—
186#3804—44no—
187C2×D3×Dic3C2312yes—
188C2×D3×Dic3C2312yes—
189C2×D3×Dic3C2312yes—
190#3757C2312yes—
191#3757C2312yes—
192#3757C2312yes—
193#3757C2312yes—
194C4⋊(C3⋊Dic3)C2311yescharacteristic
195C4⋊(C3⋊Dic3)C2312yes—
196C4⋊(C3⋊Dic3)C2311yescharacteristic
197C3×#217C2312yes—
198C3×#217C2312yes—
199C3×#217C2312yes—
200C3×#217C2312yes—
201C3×#217C2312yes—
202C3×#217C2312yes—
203C3×#217C2312yes—
204C3×#217C2312yes—
205C3×(C2×D3)⋊C4C2312yes—
206C3×(C2×D3)⋊C4C2312yes—
207C3×(C2×D3)⋊C4C2312yes—
208C3×(C2×D3)⋊C4C2312yes—
209C3×Dic3⋊C4C2312yes—
210C3×Dic3⋊C4C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×Dic3⋊C4C2312yes—
213#3724C2312yes—
214#3724C2312yes—
215#3724C2311yescharacteristic
216#3724C2311yescharacteristic
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221Dic3⋊Dic3C2312yes—
222Dic3⋊Dic3C2312yes—
223#3722C2312yes—
224#3722C2312yes—
225#3722C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231(C2×D3)⋊Dic3C2312yes—
232Dic32C2312yes—
233Dic32C2312yes—
234Dic32C2312yes—
235#3534—91noSylow
236C22×C3×D4—21no—
237C22×C3×D4—32no—
238C22×C3×D4C2×D312yescomplemented
239C22×#67—32no—
240C22×#67—32no—
241C22×#67—32no—
242C22×#67—62no—
243C22×#67C2×D312yescomplemented
244C2×#237—32no—
245C2×#237—32no—
246C2×D3×D4—32no—
247C2×D3×D4—32no—
248C2×#235—32no—
249C22×C4×D3—32no—
250C22×C4×D3—61no—
251C3×#123—32no—
252C3×#123—32no—
253C3×#123—32no—
254C3×#123—32no—
255C3×#121—32no—
256C3×#121—32no—
257C3×#121—32no—
258C3×#121—32no—
259C3×#120—32no—
260C3×#120—32no—
261C3×#120—32no—
262C3×#120—32no—
263C2×C3×C22⋊C4—32no—
264#953—32no—
265#953—32no—
266#953C2×D312yes—
267#953C2×D312yescomplemented
268C2×#217—32no—
269C2×#217—32no—
270C2×#217—32no—
271C2×#217—62no—
272C2×#217C2×D312yescomplemented
273#940—32no—
274#940—32no—
275#939—32no—
276#939—32no—
277#939—32no—
278#939—32no—
279#939—32no—
280#939—32no—
281#939—32no—
282#939—32no—
283#939C2×D312yescomplemented
284#939C2×D312yescomplemented
285#939C2×D312yescomplemented
286#939C2×D312yescomplemented
287#938—32no—
288#938—32no—
289#938—32no—
290#938—32no—
291#938—32no—
292#938—32no—
293#938—32no—
294#938—32no—
295#938—32no—
296#938—32no—
297#938—32no—
298#938—32no—
299#938—61no—
300#938—61no—
301#938—61no—
302#938—61no—
303#938—62no—
304#938—62no—
305#937—32no—
306#937—32no—
307#937—32no—
308#937—32no—
309#937C2×D312yescomplemented
310#937C2×D312yescomplemented
311#936—32no—
312#936—32no—
313#935—32no—
314#935—32no—
315#935—32no—
316#935—32no—
317#935C2×D312yescomplemented
318#935C2×D312yescomplemented
319D4×Dic3—32no—
320D4×Dic3—32no—
321D4×Dic3—32no—
322D4×Dic3—32no—
323#930—32no—
324#930—32no—
325#929—32no—
326#929—32no—
327#929C2×D312yescomplemented
328#929C2×D312yescomplemented
329C4×#67—32no—
330C4×#67—32no—
331C4×#67—32no—
332C4×#67—32no—
333#926—32no—
334C2×C4⋊Dic3—32no—
335C2×C4⋊Dic3—61no—
336#924—32no—
337#924—32no—
338#898—32no—
339#898—32no—
340#897—32no—
341#897—32no—
342#896—32no—
343#896—32no—
344#894—32no—
345#894—32no—
346#893—32no—
347#893—32no—
348D3×C4⋊C4—32no—
349D3×C4⋊C4—32no—
350#890—32no—
351#890—32no—
352#889—32no—
353#889—32no—
354#886—32no—
355#886—32no—
356#886—32no—
357#886—32no—
358#885—32no—
359#885—32no—
360#885—32no—
361#885—32no—
362#884—32no—
363#884—32no—
364#884—32no—
365#884—32no—
366#884—32no—
367#884—32no—
368#883—32no—
369#883—32no—
370#883—32no—
371#883—32no—
372#883—32no—
373#883—32no—
374#883—32no—
375#883—32no—
376#882—32no—
377#882—32no—
378#67⋊C4—32no—
379#67⋊C4—32no—
380#67⋊C4—32no—
381#67⋊C4—32no—
382#67⋊C4—32no—
383#67⋊C4—32no—
384D3×C22⋊C4—32no—
385D3×C22⋊C4—32no—
386D3×C22⋊C4—32no—
387D3×C22⋊C4—32no—
388#879—32no—
389#879—32no—
390#879—32no—
391#879—32no—
392#879—32no—
393#879—32no—
394#878—32no—
395#878—32no—
396#878—32no—
397#878—32no—
398#878—32no—
399#878—32no—
400#877—32no—
401#877—32no—
402C23×C32—24no—
403C23×C32—42no—
404C23×C32—42no—
405C23×C32C2412yes—
406C23×C32C2412yes—
407C23×C32C2411yescharacteristic
408C22×C3⋊D3—22no—
409C22×C3⋊D3—22no—
410C22×C3⋊D3—41no—
411C22×C3⋊D3C2411yescharacteristic
412C22×C3⋊D3C2411yescharacteristic
413C22×C3×D3—42no—
414C22×C3×D3—42no—
415C22×C3×D3—42no—
416C22×C3×D3C2412yes—
417C22×C3×D3C2412yes—
418C2×D32—22no—
419C2×D32—41no—
420C2×D32—41no—
421C32×D4—41no—
422C32×D4—42no—
423C32×D4—41no—
424C2×C32×C4—22no—
425C2×C32×C4C2411yescharacteristic
426C2×C32×C4C2411yescharacteristic
427#638—24no—
428#638—24no—
429#638—42no—
430#638—42no—
431C2×C3⋊Dic3—22no—
432C2×C3⋊Dic3—42no—
433C2×C3⋊Dic3C2411yescharacteristic
434C2×C3⋊Dic3C2412yes—
435C2×C3⋊Dic3C2412yes—
436C2×C3⋊Dic3C2411yescharacteristic
437C4×C3⋊D3—41no—
438C4×C3⋊D3—41no—
439C4×C3⋊D3—41no—
440C4×C3⋊D3—41no—
441C3×#67—24no—
442C3×#67—24no—
443C3×#67—42no—
444C3×#67—42no—
445C3×#67—42no—
446C3×#67—42no—
447C3×#67—42no—
448C3×#67—42no—
449C2×C3×Dic3—42no—
450C2×C3×Dic3—42no—
451C2×C3×Dic3—42no—
452C2×C3×Dic3C2412yes—
453C2×C3×Dic3C2412yes—
454C2×C3×Dic3C2412yes—
455C2×C3×Dic3C2412yes—
456C2×C3×Dic3C2412yes—
457C2×C3×Dic3C2412yes—
458#627—42no—
459#627—41no—
460#626—24no—
461#626—42no—
462#626—42no—
463#625—41no—
464#625—42no—
465#624—22no—
466#624—41no—
467#624—41no—
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—92no—
479#540—92no—
480#539—91no—
481#539—92no—
482#538—92no—
483#538—91no—
484#537—91no—
485#534—32no—
486#534—91no—
487#525—91no—
488C2×#123—91no—
489C2×#121—91no—
490C24×C3—22no—
491C24×C3—32no—
492C24×C3C22×D312yes—
493C24×C3C22×D312yes—
494C23×D3—32no—
495C23×D3—32no—
496C23×D3—61no—
497C23×D3C22×D312yes—
498C2×C3×D4—21no—
499C2×C3×D4—22no—
500C2×C3×D4—21no—
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—44no—
510C2×C3×D4—44no—
511C2×C3×D4—124no—
512C2×C3×D4C22×D312yes—
513C2×C3×D4C22×D312yes—
514C2×C3×D4C22×D312yes—
515C2×C3×D4C22×D312yes—
516C22×C3×C4—21no—
517C22×C3×C4—32no—
518C22×C3×C4—32no—
519C22×C3×C4—32no—
520C22×C3×C4C22×D312yes—
521C2×#67—32no—
522C2×#67—32no—
523C2×#67—32no—
524C2×#67—32no—
525C2×#67—32no—
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—62no—
537C2×#67—62no—
538C2×#67—62no—
539C2×#67—62no—
540C2×#67—124no—
541C2×#67—124no—
542C2×#67—124no—
543C2×#67—128no—
544C2×#67C22×D312yes—
545C2×#67C22×D312yes—
546C2×#67C22×D312yes—
547C2×#67C22×D312yes—
548C2×#67C22×D312yes—
549C2×#67C22×D312yes—
550C2×#67C22×D312yes—
551C2×#67C22×D312yes—
552C22×Dic3—32no—
553C22×Dic3—32no—
554C22×Dic3—32no—
555C22×Dic3—32no—
556C22×Dic3—32no—
557C22×Dic3—32no—
558C22×Dic3—62no—
559C22×Dic3—61no—
560C22×Dic3C22×D312yes—
561C22×Dic3C22×D312yes—
562C22×Dic3C22×D312yes—
563#237—124no—
564#237—124no—
565D3×D4—124no—
566D3×D4—124no—
567#235—124no—
568C2×D12—32no—
569C2×D12—32no—
570C2×D12—32no—
571C2×C4×D3—32no—
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
580C2×C4×D3—32no—
581C2×C4×D3—61no—
582C2×C4×D3—61no—
583C2×C4×D3—61no—
584C2×C4×D3—61no—
585C2×C4×D3—124no—
586C2×C4×D3—124no—
587C2×Dic6—32no—
588C2×Dic6—32no—
589C2×Dic6—32no—
590C3×C4⋊C4—32no—
591C3×C4⋊C4—32no—
592C3×C4⋊C4—32no—
593C3×C4⋊C4—32no—
594C3×C22⋊C4—32no—
595C3×C22⋊C4—32no—
596C3×C22⋊C4—32no—
597C3×C22⋊C4—32no—
598C3×C22⋊C4—32no—
599C3×C22⋊C4—32no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4—32no—
605C3×C22⋊C4—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#217C22×D312yes—
625#217C22×D312yes—
626#217C22×D312yes—
627#217C22×D312yes—
628#217C22×D312yes—
629#217C22×D312yes—
630#217C22×D312yes—
631#217C22×D312yes—
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)⋊C4—32no—
643(C2×D3)⋊C4—32no—
644(C2×D3)⋊C4C22×D312yes—
645(C2×D3)⋊C4C22×D312yes—
646(C2×D3)⋊C4C22×D312yes—
647(C2×D3)⋊C4C22×D312yes—
648C4⋊Dic3—32no—
649C4⋊Dic3—32no—
650C4⋊Dic3—32no—
651C4⋊Dic3—32no—
652C4⋊Dic3—32no—
653C4⋊Dic3—32no—
654C4⋊Dic3—32no—
655C4⋊Dic3—32no—
656C4⋊Dic3—32no—
657C4⋊Dic3—32no—
658C4⋊Dic3—61no—
659C4⋊Dic3—62no—
660C4⋊Dic3—61no—
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—32no—
673Dic3⋊C4C22×D312yes—
674Dic3⋊C4C22×D312yes—
675Dic3⋊C4C22×D312yes—
676Dic3⋊C4C22×D312yes—
677C4×Dic3—32no—
678C4×Dic3—32no—
679C4×Dic3—32no—
680C4×Dic3—32no—
681C4×Dic3—32no—
682C4×Dic3—32no—
683C22×C32—21no—
684C22×C32—21no—
685C22×C32—22no—
686C22×C32—22no—
687C22×C32—22no—
688C22×C32—22no—
689C22×C32—22no—
690C22×C32—22no—
691C22×C32—84no—
692C22×C32H(5,𝔽2)12yes—
693C22×C32C2511yescharacteristic
694C2×C3⋊D3—21no—
695C2×C3⋊D3—21no—
696C2×C3⋊D3—21no—
697C2×C3⋊D3—21no—
698C2×C3⋊D3—21no—
699C2×C3⋊D3—44no—
700C2×C3⋊D3H(5,𝔽2)12yes—
701C2×C3×D3—22no—
702C2×C3×D3—22no—
703C2×C3×D3—22no—
704C2×C3×D3—22no—
705C2×C3×D3—22no—
706C2×C3×D3—22no—
707C2×C3×D3—84no—
708D32—82no—
709C32×C4—21no—
710C32×C4—21no—
711C3⋊Dic3—21no—
712C3⋊Dic3—22no—
713C3⋊Dic3—22no—
714C3⋊Dic3—21no—
715C3×Dic3—22no—
716C3×Dic3—22no—
717C3×Dic3—22no—
718C3×Dic3—22no—
719C3×Dic3—22no—
720C3×Dic3—22no—
721C2×#41—92no—
722C2×#41—91no—
723C22×D4—32no—
724C22×D4—91no—
725C22×D4—92no—
726C22×D4—92no—
727C22×D4D3211yescharacteristic, complemented
728C23×C4—91no—
729#127—92no—
730#126—92no—
731#126—92no—
732#126—92no—
733#126—92no—
734#125—92no—
735#125—92no—
736#124—92no—
737#124—92no—
738#124—92no—
739#123—32no—
740#123—32no—
741#123—32no—
742#123—32no—
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—
752#123—92no—
753C22⋊Q8—92no—
754C22⋊Q8—92no—
755C22⋊Q8—92no—
756C22⋊Q8—92no—
757C22⋊Q8—92no—
758C22⋊Q8—91no—
759C22⋊Q8—91no—
760#121—32no—
761#121—32no—
762#121—32no—
763#121—32no—
764#121—91no—
765#121—91no—
766#121—92no—
767#121—92no—
768#121—92no—
769#121—92no—
770#121—92no—
771#121—92no—
772#121—92no—
773#121—92no—
774#121—92no—
775#121—91no—
776#121—91no—
777#121—91no—
778#121—91no—
779#121—92no—
780#121—92no—
781#120—32no—
782#120—32no—
783#120—32no—
784#120—32no—
785#120—92no—
786#120—92no—
787#120—92no—
788#120—92no—
789C4×D4—92no—
790C4×D4—92no—
791C4×D4—92no—
792C4×D4—92no—
793C4×D4—92no—
794C4×D4—92no—
795C4×D4—92no—
796C4×D4—92no—
797#117—91no—
798#117—92no—
799C2×C4⋊C4—91no—
800C2×C4⋊C4—91no—
801C2×C4⋊C4—91no—
802C2×C22⋊C4—32no—
803C2×C22⋊C4—91no—
804C2×C22⋊C4—91no—
805C2×C22⋊C4—91no—
806C2×C22⋊C4—92no—
807C2×C22⋊C4—92no—
808C23×C3—24no—
809C23×C3—24no—
810C23×C3—21no—
811C23×C3—22no—
812C23×C3—22no—
813C23×C3—32no—
814C23×C3—32no—
815C23×C3—44no—
816C23×C3—42no—
817C23×C3—42no—
818C23×C3—42no—
819C23×C3—42no—
820C23×C3—44no—
821C23×C3—44no—
822C23×C3—122no—
823C23×C3—122no—
824C23×C3—122no—
825C23×C3C23×D312yes—
826C23×C3C23×D312yes—
827C23×C3C23×D312yes—
828C23×C3C23×D312yes—
829C23×C3C23×D312yes—
830C22×D3—32no—
831C22×D3—32no—
832C22×D3—42no—
833C22×D3—42no—
834C22×D3—42no—
835C22×D3—61no—
836C22×D3—61no—
837C22×D3—64no—
838C22×D3—64no—
839C22×D3—64no—
840C22×D3—64no—
841C22×D3—122no—
842C22×D3—122no—
843C22×D3—122no—
844C22×D3—122no—
845C22×D3—122no—
846C22×D3C23×D312yes—
847C22×D3C23×D312yes—
848C3×D4—42no—
849C3×D4—42no—
850C3×D4—42no—
851C3×D4—42no—
852C3×D4—42no—
853C3×D4—44no—
854C3×D4—42no—
855C3×D4—64no—
856C3×D4—64no—
857C3×D4—122no—
858C3×D4—122no—
859C3×D4—122no—
860C3×D4—122no—
861C3×D4—122no—
862C3×D4—122no—
863C2×C3×C4—24no—
864C2×C3×C4—24no—
865C2×C3×C4—21no—
866C2×C3×C4—21no—
867C2×C3×C4—32no—
868C2×C3×C4—32no—
869C2×C3×C4—32no—
870C2×C3×C4—32no—
871C2×C3×C4—32no—
872C2×C3×C4—32no—
873C2×C3×C4—122no—
874C2×C3×C4—122no—
875C2×C3×C4—122no—
876C2×C3×C4C23×D312yes—
877C2×C3×C4C23×D312yes—
878#67—24no—
879#67—24no—
880#67—42no—
881#67—42no—
882#67—42no—
883#67—42no—
884#67—42no—
885#67—42no—
886#67—64no—
887#67—64no—
888#67—64no—
889#67—64no—
890#67—64no—
891#67—124no—
892#67—124no—
893#67—122no—
894#67—122no—
895#67—122no—
896#67—122no—
897#67—122no—
898#67—122no—
899#67—122no—
900#67—122no—
901#67—122no—
902#67—124no—
903#67—124no—
904C2×Dic3—32no—
905C2×Dic3—32no—
906C2×Dic3—32no—
907C2×Dic3—32no—
908C2×Dic3—32no—
909C2×Dic3—32no—
910C2×Dic3—42no—
911C2×Dic3—42no—
912C2×Dic3—42no—
913C2×Dic3—62no—
914C2×Dic3—62no—
915C2×Dic3—61no—
916C2×Dic3—61no—
917C2×Dic3—64no—
918C2×Dic3—122no—
919C2×Dic3—122no—
920C2×Dic3—122no—
921C2×Dic3—122no—
922C2×Dic3—122no—
923C2×Dic3—122no—
924C2×Dic3—124no—
925C2×Dic3C23×D312yes—
926C2×Dic3C23×D312yes—
927C2×Dic3C23×D312yes—
928C2×Dic3C23×D312yes—
929C2×Dic3C23×D312yes—
930C2×Dic3C23×D312yes—
931D12—64no—
932D12—122no—
933D12—122no—
934C4×D3—64no—
935C4×D3—122no—
936C4×D3—122no—
937C4×D3—122no—
938C4×D3—122no—
939C4×D3—122no—
940C4×D3—122no—
941C4×D3—122no—
942C4×D3—122no—
943C4×D3—122no—
944C4×D3—122no—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—122no—
948Dic6—122no—
949Dic6—122no—
950Dic6—122no—
951C2×C32—22no—
952C2×C32—42no—
953C2×C32—42no—
954C2×C32C2×H(5,𝔽2)11yescharacteristic
955C2×C32C2×H(5,𝔽2)11yescharacteristic
956C2×C32#58511yescharacteristic
957C3⋊D3—22no—
958C3⋊D3—41no—
959C3×D3—42no—
960C3×D3—42no—
961C24—32no—
962C24—91no—
963C24—91no—
964C24C2×D3212yes—
965#41—364no—
966#41—362no—
967C2×Q8—92no—
968C2×Q8—91no—
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—92no—
981C2×D4—92no—
982C2×D4—92no—
983C2×D4—91no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—92no—
987C2×D4—124no—
988C2×D4—362no—
989C2×D4—364no—
990C2×D4—364no—
991C2×D4C2×D3211yescharacteristic
992C2×D4C2×D3212yes—
993C2×D4C2×D3211yescharacteristic
994C22×C4—32no—
995C22×C4—32no—
996C22×C4—32no—
997C22×C4—91no—
998C22×C4—91no—
999C22×C4—91no—
1000C22×C4—92no—
1001C22×C4—92no—
1002C22×C4—92no—
1003C22×C4—91no—
1004C22×C4—92no—
1005C22×C4—91no—
1006C22×C4—91no—
1007C22×C4—91no—
1008C22×C4—91no—
1009C22×C4—362no—
1010C22×C4C2×D3211yescharacteristic
1011C4⋊C4—32no—
1012C4⋊C4—32no—
1013C4⋊C4—32no—
1014C4⋊C4—32no—
1015C4⋊C4—92no—
1016C4⋊C4—92no—
1017C4⋊C4—91no—
1018C4⋊C4—92no—
1019C4⋊C4—91no—
1020C4⋊C4—92no—
1021C4⋊C4—92no—
1022C4⋊C4—92no—
1023C4⋊C4—92no—
1024C4⋊C4—92no—
1025C4⋊C4—91no—
1026C4⋊C4—92no—
1027C4⋊C4—91no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—32no—
1035C22⋊C4—32no—
1036C22⋊C4—32no—
1037C22⋊C4—32no—
1038C22⋊C4—32no—
1039C22⋊C4—32no—
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—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4—92no—
1052C22⋊C4—92no—
1053C42—92no—
1054C42—92no—
1055C42—92no—
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—22no—
1071C22×C3—22no—
1072C22×C3—22no—
1073C22×C3—21no—
1074C22×C3—42no—
1075C22×C3—42no—
1076C22×C3—42no—
1077C22×C3—42no—
1078C22×C3—42no—
1079C22×C3—42no—
1080C22×C3—62no—
1081C22×C3—62no—
1082C22×C3—62no—
1083C22×C3—62no—
1084C22×C3—62no—
1085C22×C3—62no—
1086C22×C3—84no—
1087C22×C3—84no—
1088C22×C3—88no—
1089C22×C3—244no—
1090C22×C3#100414yes—
1091C22×C3C24×D312yes—
1092C2×D3—22no—
1093C2×D3—22no—
1094C2×D3—22no—
1095C2×D3—22no—
1096C2×D3—22no—
1097C2×D3—22no—
1098C2×D3—34no—
1099C2×D3—62no—
1100C2×D3—62no—
1101C2×D3—62no—
1102C2×D3—62no—
1103C2×D3—62no—
1104C2×D3—62no—
1105C2×D3—62no—
1106C2×D3—84no—
1107C2×D3—121no—
1108C2×D3—121no—
1109C2×D3—121no—
1110C2×D3—121no—
1111C2×D3—128no—
1112C2×D3—128no—
1113C2×D3—244no—
1114C3×C4—22no—
1115C3×C4—22no—
1116C3×C4—22no—
1117C3×C4—22no—
1118C3×C4—62no—
1119C3×C4—62no—
1120C3×C4—62no—
1121C3×C4—62no—
1122C3×C4—62no—
1123C3×C4—62no—
1124Dic3—22no—
1125Dic3—22no—
1126Dic3—22no—
1127Dic3—22no—
1128Dic3—22no—
1129Dic3—22no—
1130Dic3—62no—
1131Dic3—62no—
1132Dic3—62no—
1133Dic3—62no—
1134Dic3—62no—
1135Dic3—62no—
1136Dic3—121no—
1137Dic3—121no—
1138Dic3—122no—
1139Dic3—122no—
1140C32#353411yescharacteristic, complemented, Sylow
1141C23—24no—
1142C23—32no—
1143C23—32no—
1144C23—42no—
1145C23—42no—
1146C23—91no—
1147C23—91no—
1148C23—122no—
1149C23—122no—
1150C23—122no—
1151C23—182no—
1152C23—182no—
1153C23—182no—
1154C23—361no—
1155C23—361no—
1156C23—361no—
1157C23C22×D3212yes—
1158C23C22×D3212yes—
1159C23C22×D3211yescharacteristic
1160Q8—362no—
1161Q8—361no—
1162D4—41no—
1163D4—42no—
1164D4—41no—
1165D4—64no—
1166D4—64no—
1167D4—122no—
1168D4—122no—
1169D4—122no—
1170D4—122no—
1171D4—122no—
1172D4—122no—
1173D4—184no—
1174D4—184no—
1175D4—184no—
1176D4—362no—
1177D4—362no—
1178D4—362no—
1179D4—362no—
1180D4—362no—
1181D4—361no—
1182C2×C4—22no—
1183C2×C4—32no—
1184C2×C4—32no—
1185C2×C4—32no—
1186C2×C4—32no—
1187C2×C4—32no—
1188C2×C4—32no—
1189C2×C4—91no—
1190C2×C4—92no—
1191C2×C4—92no—
1192C2×C4—91no—
1193C2×C4—122no—
1194C2×C4—122no—
1195C2×C4—122no—
1196C2×C4—182no—
1197C2×C4—182no—
1198C2×C4—361no—
1199C2×C4—361no—
1200C2×C4—361no—
1201C2×C4—361no—
1202C2×C4—361no—
1203C2×C4—361no—
1204C2×C4—362no—
1205C2×C4—362no—
1206C2×C4—362no—
1207C2×C4—362no—
1208C2×C4C22×D3211yescharacteristic
1209C2×C4C22×D3211yescharacteristic
1210C2×C3—24no—
1211C2×C3—24no—
1212C2×C3—21no—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—42no—
1216C2×C3—42no—
1217C2×C3—42no—
1218C2×C3—42no—
1219C2×C3—82no—
1220C2×C3—82no—
1221C2×C3—122no—
1222C2×C3—122no—
1223C2×C3C2×#100412yes—
1224C2×C3D3×H(5,𝔽2)12yes—
1225C2×C3#596612yes—
1226D3—42no—
1227D3—42no—
1228D3—64no—
1229D3—122no—
1230D3—122no—
1231D3—122no—
1232C22—21no—
1233C22—21no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—62no—
1241C22—62no—
1242C22—62no—
1243C22—62no—
1244C22—62no—
1245C22—62no—
1246C22—84no—
1247C22—92no—
1248C22—181no—
1249C22—181no—
1250C22—181no—
1251C22—181no—
1252C22—181no—
1253C22—244no—
1254C22—364no—
1255C22—722no—
1256C22#6433012yes—
1257C22C23×D3211yescharacteristic
1258C4—21no—
1259C4—21no—
1260C4—62no—
1261C4—62no—
1262C4—62no—
1263C4—62no—
1264C4—62no—
1265C4—62no—
1266C4—182no—
1267C4—182no—
1268C4—181no—
1269C4—181no—
1270C3—21no—
1271C3#8631112yescomplemented
1272C2—22no—
1273C2—42no—
1274C2—42no—
1275C2—122no—
1276C2—122no—
1277C2—182no—
1278C2—361no—
1279C2#1059667511yescharacteristic
1280C2#1059667911yescharacteristic
1281C2C2×#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×#64147C2semidirect
2. C3×#5804C2semidirect
3. #10595526C2semidirect
4. #10595509C2semidirect
5. #10595500C2semidirect
6. #10595494C2semidirect
7. #10595311C2semidirect
8. #10595294C2semidirect
9. #10595280C2semidirect
10. #10595265C2semidirect
11. #10595258C2semidirect
12. #10595209C2semidirect
13. #10595197C2semidirect
14. #10595195C2semidirect
15. #10595185C2semidirect
16. #10595140C2semidirect
17. #10595079C2semidirect
18. #10594994C2semidirect
19. #10594920C2semidirect
21. C22×C32×D4C22semidirect
22. C22×#638C22semidirect
23. C22×C4×C3⋊D3C22semidirect
24. C22×C3×#67C22semidirect
26. C2×D3×#67C22semidirect
27. C2×#3805C22semidirect
28. C2×#3804C22semidirect
29. C2×#3757C22semidirect
31. #64147C22semidirect
32. #64147C22semidirect
33. #64147C22semidirect
34. #64147C22semidirect
35. #64147C22semidirect
36. C2×C4⋊(C3⋊Dic3)C22semidirect
38. C3×#953C22semidirect
39. C2×C3×#217C22semidirect
40. C3×#939C22semidirect
41. C3×#939C22semidirect
42. C3×#939C22semidirect
43. C3×#939C22semidirect
44. C3×#937C22semidirect
45. C3×#937C22semidirect
46. C3×#935C22semidirect
47. C3×#935C22semidirect
48. C3×#929C22semidirect
49. C3×#929C22semidirect
50. #63983C22semidirect
51. #63982C22semidirect
52. #63981C22semidirect
54. #63979C22semidirect
55. #63978C22semidirect
56. #63978C22semidirect
57. #63977C22semidirect
58. #63976C22semidirect
59. #63975C22semidirect
60. #63974C22semidirect
61. #67⋊Dic3C22semidirect
62. #67⋊Dic3C22semidirect
63. Dic3×#67C22semidirect
64. Dic3×#67C22semidirect
65. #63971C22semidirect
66. #63971C22semidirect
67. #63970C22semidirect
68. #63970C22semidirect
69. #63969C22semidirect
70. #63969C22semidirect
71. D3×#217C22semidirect
72. #63966C22semidirect
73. #63964C22semidirect
74. #63964C22semidirect
75. #63962C22semidirect
76. #63961C22semidirect
77. #63959C22semidirect
78. #63959C22semidirect
79. #63958C22semidirect
80. #63958C22semidirect
81. #63957C22semidirect
82. #63956C22semidirect
83. #63956C22semidirect
84. #63955C22semidirect
85. #63953C22semidirect
86. #63952C22semidirect
87. #63952C22semidirect
88. #63921C22semidirect
89. #63921C22semidirect
90. #63912C22semidirect
91. #63912C22semidirect
92. #63893C22semidirect
93. #63893C22semidirect
94. #63891C22semidirect
95. #63891C22semidirect
96. #63883C22semidirect
97. #63883C22semidirect
98. #63881C22semidirect
99. #63881C22semidirect
100. #63865C22semidirect
101. #63865C22semidirect
102. #63861C22semidirect
103. #63861C22semidirect
104. #63853C22semidirect
105. #63853C22semidirect
106. #63845C22semidirect
107. #63845C22semidirect
110. #5804D3semidirect
238. C22×C3×D4C2×D3semidirect
243. C22×#67C2×D3semidirect
267. #953C2×D3semidirect
272. C2×#217C2×D3semidirect
283. #939C2×D3semidirect
284. #939C2×D3semidirect
285. #939C2×D3semidirect
286. #939C2×D3semidirect
309. #937C2×D3semidirect
310. #937C2×D3semidirect
317. #935C2×D3semidirect
318. #935C2×D3semidirect
327. #929C2×D3semidirect
328. #929C2×D3semidirect
727. C22×D4D32semidirect
1140. C32#3534semidirect
1271. C3#86311semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C3×#58042
#105955262
#105955092
#105955002
#105954942
#105953112
#105952942
#105952802
#105952652
#105952582
#105952092
#105951972
#105951952
#105951852
#105951402
#105950792
#105949942
#105949202
#863113