Finite Group Databasebeta

← #11909792

Subgroups — #11909792

Order 1152.

2363 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596187C211yesmaximal, characteristic, complemented
2C3×#5718C211yesmaximal, characteristic, complemented
3C3×#5713C211yesmaximal, characteristic, complemented
4#10595272C212yesmaximal, complemented
5#10595237C212yesmaximal, complemented
6#10595222C212yesmaximal, complemented
7#10595203C214yesmaximal, complemented
8#10595199C212yesmaximal, complemented
9#10595191C212yesmaximal, complemented
10#10595162C214yesmaximal, complemented
11#10595139C212yesmaximal, complemented
12#10595136C212yesmaximal, complemented
13#10595126C212yesmaximal, complemented
14#10593960C211yesmaximal, characteristic, complemented
15C4×#3797C211yesmaximal, characteristic, complemented
16#10593875C211yesmaximal, characteristic, complemented
17Dic62C211yesmaximal, characteristic, complemented
18#87055—31nomaximal
19#86776—31nomaximal
20C2×#3830C2212yes—
21C2×C3×#237C2212yes—
22C2×#3804C2214yes—
23C2×#3797C2211yescharacteristic
24C32×#127C2211yescharacteristic
25#64147C2212yes—
26#64147C2212yes—
27#64145C2212yes—
28D4×C3⋊Dic3C2212yes—
29D4×C3⋊Dic3C2212yes—
30C42×C3⋊D3C2211yescharacteristic
31#64078C2211yescharacteristic
32C3×#940C2212yes—
33C3×#939C2214yes—
34C3×#938C2212yes—
35C3×#936C2212yes—
36C3×#936C2212yes—
37C3×#935C2214yes—
38C3×D4×Dic3C2212yes—
39C3×D4×Dic3C2212yes—
40C3×D4×Dic3C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63982C2214yes—
46#63975C2214yes—
47#67⋊Dic3C2214yes—
48Dic3×#67C2214yes—
49#63969C2214yes—
50C2×Dic3⋊Dic3C2214yes—
51#63964C2214yes—
52#63964C2214yes—
53#63962C2214yes—
54#63959C2214yes—
55#63959C2214yes—
56#63958C2214yes—
57#63956C2214yes—
58#63955C2214yes—
59#63952C2214yes—
60#63918C2212yes—
61#63918C2212yes—
62C4×#627C2212yes—
63#63916C2211yescharacteristic
64C4×#626C2212yes—
65#63900C2211yescharacteristic
66#63896C2214yes—
67Dic3×D12C2212yes—
68D3×C4⋊Dic3C2212yes—
69#63883C2212yes—
70C4×#624C2212yes—
71#63872C2211yescharacteristic
72#63871C2211yescharacteristic
73#63869C2212yes—
74#63863C2211yescharacteristic
75#63862C2212yes—
76#63856C2212yes—
77#63855C2212yes—
78#63853C2212yes—
79#63843C2211yescharacteristic
80#63843C2211yescharacteristic
81Dic3×Dic6C2212yes—
82Dic3×Dic6C2212yes—
83#63840C2214yes—
84#63838C2212yes—
85C3×#559—31no—
86C3×#550—31no—
87#5831—32no—
88#5827—32no—
89#5718D311yescharacteristic, complemented
90#5716—31no—
91#5716—31no—
92#5716—32no—
93#5716—61no—
94#5713—32no—
95#5713D311yescharacteristic, complemented
96#5682—32no—
97#5681—32no—
98#5680—32no—
99#5677—32no—
100#5662—34no—
101#5655—34no—
102#5611—34no—
103#5611—32no—
104#5603—32no—
105#5603—34no—
106#5580—31no—
107#5579—31no—
108C4×D3×Q8—31no—
109C4×D3×Q8—31no—
110Q8×Dic6—31no—
111Q8×Dic6—31no—
112#5557—32no—
113#5557—31no—
114#5551—32no—
115#5548—32no—
116#5546—32no—
117#5543—32no—
118#5543—31no—
119#5539—32no—
120C2×C32×D4C2312yes—
121C2×C32×D4C2312yes—
122C2×C32×D4C2312yes—
123C2×#638C2314yes—
124C22×C3⋊Dic3C2314yes—
125#3830—44no—
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×C4×C3⋊D3C2311yescharacteristic
128C2×C4×C3⋊D3C2311yescharacteristic
129C2×#634C2312yes—
130C2×C3×#67C2314yes—
131C2×C3×#67C2314yes—
132C22×C3×Dic3C2314yes—
133C22×C3×Dic3C2314yes—
134C3×#237—28no—
135C2×C3×D12C2311yescharacteristic
136C2×C3×C4×D3C2312yes—
137C2×C3×Dic6C2311yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139C2×C3×Dic6C2311yescharacteristic
140C2×#627C2312yes—
141C2×#627C2314yes—
142C2×#626C2312yes—
143C2×#624C2312yes—
144C2×#624C2312yes—
145#3804—48no—
146C2×D3×Dic3C2314yes—
147#3797—24no—
148C32×C42C2311yescharacteristic
149#3757C2314yes—
150#3757C2314yes—
151C4⋊(C3⋊Dic3)C2312yes—
152C4⋊(C3⋊Dic3)C2312yes—
153C4×C3⋊Dic3C2311yescharacteristic
154C4×C3⋊Dic3C2311yescharacteristic
155C4×C3⋊Dic3C2311yescharacteristic
156C3×#217C2314yes—
157C3×#217C2314yes—
158C3×#217C2314yes—
159C3×#217C2314yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2311yescharacteristic
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2312yes—
171#3724C2312yes—
172#3724C2314yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181#3722C2312yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2314yes—
189#3522—91noSylow
190C2×C3×#41—32no—
191C2×D3×Q8—31no—
192C2×D3×Q8—31no—
193C2×#237—32no—
194C2×#237—32no—
195C2×#237—34no—
196C2×#237—62no—
197C2×#237C2×D312yes—
198C2×#235—34no—
199C3×#127—21no—
200C3×#127—32no—
201C3×#127C2×D311yescharacteristic
202C3×#127C2×D311yescharacteristic
203C3×#124—32no—
204C3×#124—32no—
205C3×#123—34no—
206C3×#121—32no—
207C3×#121—34no—
208C3×C4×Q8—31no—
209C3×C4×Q8—31no—
210C3×C4×Q8—31no—
211C3×C4×D4—32no—
212C3×C4×D4—32no—
213C3×C4×D4—32no—
214C3×C4×D4—31no—
215#947—31no—
216#946—32no—
217#946—31no—
218Q8×Dic3—31no—
219Q8×Dic3—31no—
220Q8×Dic3—32no—
221Q8×Dic3—32no—
222#940C2×D312yes—
223#939C2×D314yes—
224#938—32no—
225#938—32no—
226#938—32no—
227#938—32no—
228#938—34no—
229#938—31no—
230#938—62no—
231#938—62no—
232#938C2×D312yes—
233#936—32no—
234#936—32no—
235#936—31no—
236#936—34no—
237#936—34no—
238#936—62no—
239#936C2×D312yes—
240#936C2×D312yes—
241#935—34no—
242#935—34no—
243#935C2×D314yes—
244D4×Dic3—32no—
245D4×Dic3—32no—
246D4×Dic3—32no—
247D4×Dic3—32no—
248D4×Dic3—34no—
249D4×Dic3—34no—
250D4×Dic3—32no—
251D4×Dic3—62no—
252D4×Dic3—62no—
253D4×Dic3C2×D312yes—
254D4×Dic3C2×D312yes—
255D4×Dic3C2×D312yes—
256C4×#67—34no—
257C4×#67—34no—
258C4×#67—32no—
259#926—34no—
260#926—32no—
261C2×C4⋊Dic3—34no—
262C2×C4⋊Dic3—32no—
263#924—32no—
264#924—34no—
265#924—34no—
266C2×Dic3⋊C4—34no—
267#898—32no—
268#897—31no—
269#896—34no—
270#895—31no—
271#894—32no—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—31no—
274D3×C4⋊C4—31no—
275D3×C4⋊C4—32no—
276D3×C4⋊C4—32no—
277#890—31no—
278#890—31no—
279#890—32no—
280#888—34no—
281#888—34no—
282#888—32no—
283#888—32no—
284#887—31no—
285#887—31no—
286#887—32no—
287#887—32no—
288#886—34no—
289#885—34no—
290#885—34no—
291#884—34no—
292#883—34no—
293#883—34no—
294#883—34no—
295#883—32no—
296#67⋊C4—34no—
297#67⋊C4—34no—
298#879—34no—
299#879—34no—
300#879—32no—
301#878—34no—
302#878—34no—
303#878—34no—
304#878—34no—
305#878—34no—
306#877—34no—
307C4×D12—32no—
308C4×D12—32no—
309C4×D12C2×D311yescharacteristic
310#872—32no—
311C42×D3—31no—
312C42×D3—31no—
313C42×D3—32no—
314C42×D3—32no—
315C42×D3—61no—
316#870—32no—
317#869—31no—
318#869—31no—
319#869—32no—
320#869—32no—
321#869—61no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C4×Dic6C2×D311yescharacteristic
329C23×C32C2414yes—
330C22×C3⋊D3C2411yescharacteristic
331C22×C3×D3C2412yes—
332C32×D4—24no—
333C32×D4—24no—
334C32×D4—42no—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338#638—28no—
339C2×C3⋊Dic3—44no—
340C2×C3⋊Dic3C2411yescharacteristic
341C2×C3⋊Dic3C2414yes—
342C2×C3⋊Dic3C2411yescharacteristic
343C2×C3⋊Dic3C2411yescharacteristic
344C4×C3⋊D3—22no—
345C4×C3⋊D3—22no—
346C4×C3⋊D3—22no—
347#634—42no—
348C3×#67—28no—
349C3×#67—44no—
350C2×C3×Dic3—28no—
351C2×C3×Dic3—44no—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2412yes—
358C2×C3×Dic3C2412yes—
359C3×D12—22no—
360C3×C4×D3—24no—
361C3×Dic6—22no—
362C3×Dic6—22no—
363C3×Dic6#4114yescomplemented
364#627—24no—
365#627—44no—
366#626—24no—
367#624—24no—
368#624—24no—
369D3×Dic3—44no—
370#559—31no—
371#559—92no—
372Q82—91no—
373#554—92no—
374#554—91no—
375#550—31no—
376#548—92no—
377#547—92no—
378#547—94no—
379#542—94no—
380#542—92no—
381#532—92no—
382#532—91no—
383#529—91no—
384#529—92no—
385#520—92no—
386C2×C4×Q8—91no—
387C3×#41—68no—
388C2×C3×Q8—31no—
389C2×C3×Q8—31no—
390C2×C3×Q8—31no—
391C2×C3×D4—22no—
392C2×C3×D4—22no—
393C2×C3×D4—22no—
394C2×C3×D4—34no—
395C2×C3×D4—34no—
396C2×C3×D4—31no—
397C2×C3×D4C22×D312yes—
398C2×C3×D4C22×D312yes—
399C2×C3×D4C22×D312yes—
400C2×C3×D4C22×D312yes—
401C2×C3×D4C22×D312yes—
402C2×C3×D4C22×D312yes—
403C22×C3×C4—34no—
404C22×C3×C4—34no—
405C22×C3×C4—32no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—32no—
409C2×#67—64no—
410C2×#67C22×D314yes—
411C2×#67C22×D314yes—
412C22×Dic3—34no—
413C22×Dic3—34no—
414C22×Dic3—34no—
415C22×Dic3—64no—
416C22×Dic3C22×D314yes—
417C22×Dic3C22×D314yes—
418D3×Q8—64no—
419D3×Q8—64no—
420#237—28no—
421#237—128no—
422#237—124no—
423#237—124no—
424#237—128no—
425#235—128no—
426C2×D12—32no—
427C2×D12C22×D311yescharacteristic
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—32no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—32no—
438C2×C4×D3—34no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3C22×D312yes—
443C2×Dic6—32no—
444C2×Dic6—32no—
445C2×Dic6—32no—
446C2×Dic6—32no—
447C2×Dic6—34no—
448C2×Dic6—34no—
449C2×Dic6—62no—
450C2×Dic6C22×D311yescharacteristic
451C2×Dic6C22×D311yescharacteristic
452C2×Dic6C22×D311yescharacteristic
453C3×C4⋊C4—32no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—31no—
456C3×C4⋊C4—32no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4—31no—
460C3×C22⋊C4—34no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—34no—
463C3×C22⋊C4—34no—
464C3×C22⋊C4—32no—
465C3×C42—21no—
466C3×C42—32no—
467C3×C42—32no—
468C3×C42—32no—
469C3×C42C22×D311yescharacteristic
470C3×C42C22×D311yescharacteristic
471#217—34no—
472#217—34no—
473#217—34no—
474#217—34no—
475#217—34no—
476#217—32no—
477#217—32no—
478#217—32no—
479#217—64no—
480#217—64no—
481#217C22×D314yes—
482#217C22×D314yes—
483#217C22×D314yes—
484#217C22×D314yes—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4C22×D312yes—
492C4⋊Dic3—32no—
493C4⋊Dic3—32no—
494C4⋊Dic3—32no—
495C4⋊Dic3—32no—
496C4⋊Dic3—32no—
497C4⋊Dic3—32no—
498C4⋊Dic3—34no—
499C4⋊Dic3—34no—
500C4⋊Dic3—32no—
501C4⋊Dic3—32no—
502C4⋊Dic3—34no—
503C4⋊Dic3—32no—
504C4⋊Dic3—62no—
505C4⋊Dic3—62no—
506C4⋊Dic3C22×D311yescharacteristic
507C4⋊Dic3C22×D311yescharacteristic
508C4⋊Dic3C22×D311yescharacteristic
509C4⋊Dic3C22×D311yescharacteristic
510Dic3⋊C4—32no—
511Dic3⋊C4—32no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—34no—
522Dic3⋊C4C22×D312yes—
523Dic3⋊C4C22×D312yes—
524Dic3⋊C4C22×D312yes—
525C4×Dic3—31no—
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—34no—
532C4×Dic3—34no—
533C4×Dic3—32no—
534C4×Dic3—32no—
535C4×Dic3—32no—
536C4×Dic3—32no—
537C4×Dic3—61no—
538C4×Dic3—61no—
539C4×Dic3—61no—
540C4×Dic3C22×D312yes—
541C4×Dic3C22×D312yes—
542C4×Dic3C22×D312yes—
543C22×C32—24no—
544C22×C32—24no—
545C22×C32—24no—
546C22×C32C2511yescharacteristic
547C2×C3⋊D3—21no—
548C2×C3⋊D3—21no—
549C2×C3⋊D3H(5,𝔽2)12yes—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3—22no—
553C32×C4—21no—
554C32×C4C2×#4112yes—
555C32×C42−1+412yes—
556C3⋊Dic3—21no—
557C3⋊Dic3—21no—
558C3⋊Dic3—24no—
559C3⋊Dic3—21no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3—22no—
563C3×Dic3—22no—
564C3×Dic3—22no—
565C3×Dic3—22no—
566C3×Dic3C2×#4114yes—
567C2×#41—32no—
568C2×#41—94no—
569C2×#41—92no—
570C22×Q8—91no—
571C4⋊Q8—92no—
572C4⋊Q8—92no—
573C4⋊Q8—94no—
574C4⋊Q8—91no—
575#127—32no—
576#127D3211yescharacteristic
577#126—94no—
578#126—92no—
579#125—92no—
580#125—91no—
581#124—32no—
582#124—32no—
583#124—94no—
584#124—94no—
585#124—91no—
586#124—92no—
587#123—34no—
588#123—94no—
589#123—92no—
590#123—94no—
591#123—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C22⋊Q8—94no—
596C22⋊Q8—91no—
597C22⋊Q8—92no—
598#121—32no—
599#121—34no—
600#121—94no—
601#121—91no—
602#121—92no—
603#121—92no—
604C4×Q8—31no—
605C4×Q8—31no—
606C4×Q8—31no—
607C4×Q8—92no—
608C4×Q8—92no—
609C4×Q8—92no—
610C4×Q8—92no—
611C4×Q8—91no—
612C4×Q8—91no—
613C4×D4—32no—
614C4×D4—32no—
615C4×D4—32no—
616C4×D4—31no—
617C4×D4—92no—
618C4×D4—92no—
619C4×D4—94no—
620C4×D4—94no—
621C4×D4—94no—
622C4×D4—92no—
623C4×D4—92no—
624#117—92no—
625#117—94no—
626C2×C4⋊C4—91no—
627C2×C4⋊C4—92no—
628C2×C4⋊C4—92no—
629C2×C4⋊C4—94no—
630C2×C42—92no—
631C2×C42—91no—
632C23×C3—24no—
633C23×C3—32no—
634C23×C3C23×D314yes—
635C23×C3C23×D314yes—
636C22×D3—31no—
637C22×D3—31no—
638C22×D3—61no—
639C22×D3C23×D312yes—
640C3×Q8—34no—
641C3×Q8—62no—
642C3×Q8—62no—
643C3×D4—24no—
644C3×D4—24no—
645C3×D4—24no—
646C3×D4—24no—
647C3×D4—44no—
648C3×D4—44no—
649C3×D4—42no—
650C3×D4—42no—
651C3×D4—44no—
652C3×D4—68no—
653C3×D4—62no—
654C3×D4—124no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—68no—
666C2×C3×C4—64no—
667C2×C3×C4—124no—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673C2×C3×C4C23×D311yescharacteristic
674#67—28no—
675#67—44no—
676#67—64no—
677#67—68no—
678#67—68no—
679#67—128no—
680C2×Dic3—28no—
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—34no—
688C2×Dic3—34no—
689C2×Dic3—44no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—64no—
694C2×Dic3—124no—
695C2×Dic3—124no—
696C2×Dic3—124no—
697C2×Dic3—128no—
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701C2×Dic3C23×D312yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705D12—22no—
706D12—64no—
707C4×D3—24no—
708C4×D3—64no—
709C4×D3—64no—
710C4×D3—64no—
711C4×D3—62no—
712C4×D3—62no—
713C4×D3—64no—
714C4×D3—62no—
715C4×D3—62no—
716C4×D3—62no—
717C4×D3—62no—
718C4×D3—64no—
719C4×D3—122no—
720C4×D3—122no—
721C4×D3—124no—
722Dic6—22no—
723Dic6—22no—
724Dic6—64no—
725Dic6—64no—
726Dic6—124no—
727Dic6—124no—
728Dic6—122no—
729Dic6—122no—
730Dic6—124no—
731Dic6#23714yescomplemented
732C2×C32—44no—
733C2×C32C22×#4111yescharacteristic
734C2×C32C2×H(5,𝔽2)11yescharacteristic
735C2×C32C2×2−1+411yescharacteristic
736C3⋊D3—22no—
737C3×D3—42no—
738#41—68no—
739#41—368no—
740#41—364no—
741C2×Q8—31no—
742C2×Q8—31no—
743C2×Q8—31no—
744C2×Q8—92no—
745C2×Q8—94no—
746C2×Q8—92no—
747C2×Q8—184no—
748C2×D4—34no—
749C2×D4—34no—
750C2×D4—31no—
751C2×D4—92no—
752C2×D4—94no—
753C2×D4C2×D3212yes—
754C2×D4C2×D3212yes—
755C2×D4C2×D3212yes—
756C22×C4—34no—
757C22×C4—34no—
758C22×C4—32no—
759C22×C4—92no—
760C22×C4—92no—
761C22×C4—94no—
762C22×C4—94no—
763C22×C4—91no—
764C22×C4—91no—
765C22×C4—91no—
766C4⋊C4—31no—
767C4⋊C4—32no—
768C4⋊C4—31no—
769C4⋊C4—32no—
770C4⋊C4—31no—
771C4⋊C4—31no—
772C4⋊C4—32no—
773C4⋊C4—92no—
774C4⋊C4—94no—
775C4⋊C4—92no—
776C4⋊C4—94no—
777C4⋊C4—92no—
778C4⋊C4—92no—
779C4⋊C4—92no—
780C4⋊C4—94no—
781C4⋊C4—92no—
782C4⋊C4—94no—
783C4⋊C4—92no—
784C4⋊C4—92no—
785C22⋊C4—34no—
786C22⋊C4—34no—
787C22⋊C4—34no—
788C22⋊C4—34no—
789C22⋊C4—32no—
790C22⋊C4—92no—
791C22⋊C4—92no—
792C22⋊C4—92no—
793C22⋊C4—94no—
794C22⋊C4—92no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C42—32no—
798C42—32no—
799C42—32no—
800C42—92no—
801C42—92no—
802C42—94no—
803C42—91no—
804C42—91no—
805C42—91no—
806C42C2×D3211yescharacteristic
807C22×C3—24no—
808C22×C3—24no—
809C22×C3—24no—
810C22×C3—24no—
811C22×C3—24no—
812C22×C3—24no—
813C22×C3—21no—
814C22×C3—44no—
815C22×C3—44no—
816C22×C3—44no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3C24×D311yescharacteristic
821C22×C3C24×D311yescharacteristic
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—32no—
826C2×D3—32no—
827C2×D3—62no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—121no—
833C2×D3—121no—
834C3×C4—22no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—22no—
838C3×C4—22no—
839C3×C4—34no—
840C3×C4—62no—
841C3×C4—62no—
842C3×C4—62no—
843C3×C4—62no—
844C3×C4—62no—
845C3×C4—62no—
846C3×C4C2×#23712yes—
847C3×C4D3×#4112yes—
848C3×C4#101012yes—
849C3×C4#101012yes—
850Dic3—22no—
851Dic3—22no—
852Dic3—22no—
853Dic3—22no—
854Dic3—22no—
855Dic3—22no—
856Dic3—62no—
857Dic3—61no—
858Dic3—61no—
859Dic3—61no—
860Dic3—61no—
861Dic3—64no—
862Dic3—64no—
863Dic3—61no—
864Dic3—61no—
865Dic3—124no—
866Dic3—121no—
867Dic3—121no—
868Dic3C2×#23714yes—
869C32#352211yescharacteristic, complemented, Sylow
870C23—32no—
871C23—91no—
872C23C22×D3214yes—
873Q8—34no—
874Q8—62no—
875Q8—62no—
876Q8—184no—
877Q8—362no—
878Q8—364no—
879D4—24no—
880D4—24no—
881D4—42no—
882D4—68no—
883D4—62no—
884D4—124no—
885D4—184no—
886D4—188no—
887C2×C4—32no—
888C2×C4—32no—
889C2×C4—32no—
890C2×C4—32no—
891C2×C4—32no—
892C2×C4—32no—
893C2×C4—32no—
894C2×C4—68no—
895C2×C4—64no—
896C2×C4—91no—
897C2×C4—91no—
898C2×C4—91no—
899C2×C4—94no—
900C2×C4—124no—
901C2×C4—182no—
902C2×C4—184no—
903C2×C4—184no—
904C2×C4—182no—
905C2×C4—182no—
906C2×C4—364no—
907C2×C4—364no—
908C2×C4C22×D3211yescharacteristic
909C2×C4C22×D3211yescharacteristic
910C2×C4C22×D3211yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—44no—
915C2×C3—44no—
916C2×C3—84no—
917C2×C3—122no—
918C2×C3C22×#23711yescharacteristic
919C2×C3C2×D3×#4111yescharacteristic
920C2×C3C2×#101011yescharacteristic
921C2×C3C2×#101011yescharacteristic
922C2×C3D3×H(5,𝔽2)11yescharacteristic
923C2×C3D3×H(5,𝔽2)11yescharacteristic
924D3—42no—
925D3—62no—
926D3—62no—
927D3—122no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—62no—
932C22—62no—
933C22—62no—
934C22—92no—
935C22—181no—
936C22—181no—
937C22C23×D3211yescharacteristic
938C4—21no—
939C4—34no—
940C4—62no—
941C4—62no—
942C4—62no—
943C4—62no—
944C4—62no—
945C4—62no—
946C4—181no—
947C4—181no—
948C4—181no—
949C4—184no—
950C4#6430912yes—
951C4D3×#23712yes—
952C3—21no—
953C3#8677611yescharacteristic, complemented
954C3#8705511yescharacteristic, complemented
955C2—44no—
956C2—122no—
957C2—182no—
958C2C2×#6430911yescharacteristic
959C2C2×D3×#23711yescharacteristic
960C2#1059667511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596187C2semidirect
2. C3×#5718C2semidirect
3. C3×#5713C2semidirect
4. #10595272C2semidirect
5. #10595237C2semidirect
6. #10595222C2semidirect
7. #10595203C2semidirect
8. #10595199C2semidirect
9. #10595191C2semidirect
10. #10595162C2semidirect
11. #10595139C2semidirect
12. #10595136C2semidirect
13. #10595126C2semidirect
14. #10593960C2semidirect
15. C4×#3797C2semidirect
16. #10593875C2semidirect
17. Dic62C2semidirect
89. #5718D3semidirect
95. #5713D3semidirect
363. C3×Dic6#41semidirect
731. Dic6#237semidirect
869. C32#3522semidirect
953. C3#86776semidirect
954. C3#87055semidirect

Maximal subgroups

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

subgroupindex
#105961872
C3×#57182
C3×#57132
#105952722
#105952372
#105952222
#105952032
#105951992
#105951912
#105951622
#105951392
#105951362
#105951262
#105939602
C4×#37972
#105938752
Dic622
#870553
#867763