Finite Group Databasebeta

← #11909764

Subgroups — #11909764

Order 1152.

2355 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic, complemented
2C3×#5834C211yesmaximal, characteristic, complemented
3C3×#5831C211yesmaximal, characteristic, complemented
4Q8×#627C211yesmaximal, characteristic, complemented
5#10595409C211yesmaximal, characteristic, complemented
6#10595394C211yesmaximal, characteristic, complemented
7D3×Q8×Dic3C211yesmaximal, characteristic, complemented
8#10595199C213yesmaximal, complemented
9#10595134C213yesmaximal, complemented
10#10595133C213yesmaximal, complemented
11#10595126C213yesmaximal, complemented
12#10594993C213yesmaximal, complemented
13#10594984C213yesmaximal, complemented
14#10594934C213yesmaximal, complemented
15#10594907C213yesmaximal, complemented
16#86776—31nomaximal
17#86722—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3805C2216yes—
22Q8×C3⋊Dic3C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2213yes—
25D4×C3⋊Dic3C2213yes—
26#64135C2213yes—
27C2×C4⋊(C3⋊Dic3)C2213yes—
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×#940C2213yes—
31C3×#938C2213yes—
32C3×#938C2213yes—
33C3×#936C2213yes—
34C3×#930C2213yes—
35C3×C4×#67C2213yes—
36C3×C4×#67C2213yes—
37C3×#924C2213yes—
38#63982C2216yes—
39#67⋊Dic3C2216yes—
40#63970C2213yes—
41#63969C2213yes—
42#63969C2216yes—
43#63962C2216yes—
44#63959C2216yes—
45#63959C2213yes—
46#63956C2213yes—
47#63919C2213yes—
48#63918C2213yes—
49#63918C2213yes—
50C4×#627C2213yes—
51#63908C2213yes—
52C4×#625C2213yes—
53#63898C2213yes—
54#63893C2216yes—
55#63893C2211yescharacteristic
56Dic3×D12C2213yes—
57#63891C2213yes—
58D3×C4⋊Dic3C2213yes—
59D3×C4⋊Dic3C2213yes—
60C4×D3×Dic3C2213yes—
61#63863C2213yes—
62#63861C2213yes—
63#63856C2213yes—
64#63855C2213yes—
65#63845C2213yes—
66#63843C2213yes—
67Dic3×Dic6C2213yes—
68C3×#550—31no—
69C3×#548—31no—
70#5834D311yescharacteristic, complemented
71#5831—31no—
72#5831D311yescharacteristic, complemented
73#5827—31no—
74#5827—31no—
75#5827—31no—
76#5827—61no—
77#5817—31no—
78C2×Q8×Dic3—31no—
79#5716—33no—
80#5713—33no—
81#5682—33no—
82#5681—33no—
83#5643—33no—
84#5635—33no—
85#5611—33no—
86#5611—33no—
87#5611—33no—
88#5603—33no—
89#5603—33no—
90#5596—33no—
91#5574—31no—
92C4×D3×Q8—31no—
93Q8×Dic6—31no—
94Q8×Dic6—31no—
95#5557—33no—
96#5555—33no—
97#5543—33no—
98#5538—33no—
99C32×#41—24no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2313yes—
102C22×C32×C4C2313yes—
103C22×C3⋊Dic3C2316yes—
104C2×C3×#67C2313yes—
105C2×C3×#67C2313yes—
106C2×C3×#67C2316yes—
107C3×#239—24no—
108C3×D3×Q8—24no—
109C2×C3×D12C2313yes—
110C2×C3×C4×D3C2313yes—
111C2×C3×C4×D3C2313yes—
112C2×C3×Dic6C2313yes—
113C2×#627C2311yescharacteristic
114C2×#627C2316yes—
115C2×#625C2313yes—
116#3805—412no—
117C2×D3×Dic3C2313yes—
118C2×D3×Dic3C2311yescharacteristic
119C2×D3×Dic3C2316yes—
120#3757C2313yes—
121#3757C2313yes—
122C4⋊(C3⋊Dic3)C2313yes—
123C4⋊(C3⋊Dic3)C2313yes—
124C4⋊(C3⋊Dic3)C2313yes—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4×C3⋊Dic3C2313yes—
127C4×C3⋊Dic3C2313yes—
128C3×#217C2316yes—
129C3×#217C2313yes—
130C3×#217C2313yes—
131C3×(C2×D3)⋊C4C2311yescharacteristic
132C3×(C2×D3)⋊C4C2313yes—
133C3×C4⋊Dic3C2313yes—
134C3×C4⋊Dic3C2313yes—
135C3×Dic3⋊C4C2313yes—
136C3×Dic3⋊C4C2311yescharacteristic
137C3×C4×Dic3C2313yes—
138C3×C4×Dic3C2313yes—
139#3724C2313yes—
140#3724C2313yes—
141Dic3⋊Dic3C2316yes—
142Dic3⋊Dic3C2313yes—
143Dic3⋊Dic3C2313yes—
144Dic3⋊Dic3C2311yescharacteristic
145Dic3⋊Dic3C2313yes—
146(C2×D3)⋊Dic3C2313yes—
147(C2×D3)⋊Dic3C2313yes—
148(C2×D3)⋊Dic3C2316yes—
149(C2×D3)⋊Dic3C2313yes—
150(C2×D3)⋊Dic3C2311yescharacteristic
151Dic32C2313yes—
152Dic32C2313yes—
153#3522—91noSylow
154C2×C3×#41—21no—
155C2×C3×#41—31no—
156C2×C3×#41C2×D311yescharacteristic
157C2×C3×#41C2×D311yescharacteristic
158C22×C3×Q8—31no—
159C2×#239C2×D311yescharacteristic
160C2×D3×Q8C2×D311yescharacteristic
161C2×#237—36no—
162C2×#237—36no—
163C3×#127—33no—
164C3×#124—33no—
165C3×C22⋊Q8—33no—
166C3×#121—33no—
167C3×#121—33no—
168C3×#121—33no—
169C3×C4×Q8—31no—
170C3×C4×Q8—31no—
171C3×C4×D4—33no—
172C3×C4×D4—33no—
173#947—33no—
174#946—33no—
175Q8×Dic3—31no—
176Q8×Dic3—31no—
177Q8×Dic3—31no—
178Q8×Dic3—31no—
179Q8×Dic3—33no—
180Q8×Dic3—33no—
181Q8×Dic3—61no—
182Q8×Dic3—61no—
183Q8×Dic3C2×D311yescharacteristic
184Q8×Dic3C2×D311yescharacteristic
185#940C2×D313yes—
186#939—33no—
187#938—33no—
188#938—33no—
189#938C2×D313yes—
190#938C2×D313yes—
191#936—33no—
192#936—33no—
193#936—36no—
194#936C2×D313yes—
195#935—36no—
196#935—36no—
197#935—33no—
198D4×Dic3—33no—
199D4×Dic3—33no—
200D4×Dic3—33no—
201D4×Dic3—33no—
202D4×Dic3—36no—
203D4×Dic3—33no—
204D4×Dic3—33no—
205D4×Dic3—63no—
206D4×Dic3—63no—
207#930—33no—
208#930C2×D313yes—
209C4×#67—33no—
210C4×#67—33no—
211C4×#67C2×D313yes—
212C4×#67C2×D313yes—
213#926—33no—
214#926—33no—
215#926—33no—
216#926—63no—
217C2×C4⋊Dic3—33no—
218C2×C4⋊Dic3—33no—
219C2×C4⋊Dic3—33no—
220C2×C4⋊Dic3—33no—
221C2×C4⋊Dic3—63no—
222#924—33no—
223#924C2×D313yes—
224C2×C4×Dic3—33no—
225#898—33no—
226#897—36no—
227#897—31no—
228#893—33no—
229D3×C4⋊C4—33no—
230D3×C4⋊C4—33no—
231#890—33no—
232#889—33no—
233#888—33no—
234#888—33no—
235#888—33no—
236#888—33no—
237#887—33no—
238#886—36no—
239#886—33no—
240#885—36no—
241#885—33no—
242#883—36no—
243#883—33no—
244#883—33no—
245#67⋊C4—36no—
246#879—33no—
247#879—33no—
248#879—33no—
249#878—36no—
250#878—36no—
251#878—31no—
252#878—36no—
253C4×D12—33no—
254#872—33no—
255C42×D3—33no—
256#869—33no—
257#869—33no—
258C4×Dic6—33no—
259C4×Dic6—33no—
260C4×Dic6—33no—
261C23×C32C2413yes—
262C22×C3×D3C2413yes—
263C22×C3×D3C2411yescharacteristic
264C32×Q8#4114yescomplemented
265C32×D4—26no—
266C2×C32×C4—26no—
267C2×C32×C4C2411yescharacteristic
268C2×C32×C4C2413yes—
269C2×C3⋊Dic3—46no—
270C2×C3⋊Dic3C2411yescharacteristic
271C2×C3⋊Dic3C2413yes—
272C2×C3⋊Dic3C2411yescharacteristic
273C2×C3⋊Dic3C2413yes—
274C3×#67—26no—
275C3×#67—26no—
276C3×#67—46no—
277C2×C3×Dic3C2413yes—
278C2×C3×Dic3C2413yes—
279C2×C3×Dic3C2411yescharacteristic
280C2×C3×Dic3C2411yescharacteristic
281C2×C3×Dic3C2413yes—
282C2×C3×Dic3C2411yescharacteristic
283C3×D12—26no—
284C3×C4×D3—26no—
285C3×C4×D3—26no—
286C3×Dic6—26no—
287#627—22no—
288#627—46no—
289#625—26no—
290D3×Dic3—26no—
291D3×Dic3—22no—
292D3×Dic3—46no—
293#559—93no—
294Q82—91no—
295#554—93no—
296#550—31no—
297#548—31no—
298#548—91no—
299#547—93no—
300#547—93no—
301#542—93no—
302#542—93no—
303#532—93no—
304#529—93no—
305#520—91no—
306#520—91no—
307C2×C4×Q8—91no—
308C3×#41—28no—
309C3×#41—24no—
310C3×#41—24no—
311C3×#41—64no—
312C2×C3×Q8—21no—
313C2×C3×Q8—33no—
314C2×C3×Q8—64no—
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×D4—23no—
318C2×C3×D4—33no—
319C2×C3×D4—33no—
320C2×C3×D4—36no—
321C2×C3×D4—33no—
322C2×C3×D4C22×D313yes—
323C2×C3×D4C22×D313yes—
324C22×C3×C4—23no—
325C22×C3×C4—33no—
326C22×C3×C4—33no—
327C22×C3×C4C22×D313yes—
328C22×C3×C4C22×D313yes—
329C2×#67—33no—
330C2×#67—33no—
331C2×#67C22×D313yes—
332C2×#67C22×D313yes—
333C2×#67C22×D316yes—
334C22×Dic3—36no—
335C22×Dic3—36no—
336C22×Dic3—31no—
337C22×Dic3—33no—
338C22×Dic3—36no—
339C22×Dic3—66no—
340#239—24no—
341D3×Q8—24no—
342#237—1212no—
343#237—1212no—
344C2×D12C22×D313yes—
345C2×C4×D3—31no—
346C2×C4×D3—33no—
347C2×C4×D3—36no—
348C2×C4×D3C22×D313yes—
349C2×C4×D3C22×D313yes—
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—36no—
353C2×Dic6—36no—
354C2×Dic6C22×D313yes—
355C3×C4⋊C4—33no—
356C3×C4⋊C4—33no—
357C3×C4⋊C4—33no—
358C3×C4⋊C4—31no—
359C3×C22⋊C4—33no—
360C3×C22⋊C4—36no—
361C3×C22⋊C4—33no—
362C3×C22⋊C4—33no—
363C3×C22⋊C4—31no—
364C3×C42—33no—
365C3×C42—33no—
366#217—33no—
367#217—33no—
368#217—33no—
369#217—33no—
370#217—36no—
371#217—31no—
372#217—33no—
373#217—33no—
374#217—33no—
375#217—63no—
376#217—63no—
377#217C22×D313yes—
378#217C22×D316yes—
379#217C22×D313yes—
380(C2×D3)⋊C4—33no—
381(C2×D3)⋊C4—33no—
382(C2×D3)⋊C4—36no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—33no—
385(C2×D3)⋊C4C22×D311yescharacteristic
386(C2×D3)⋊C4C22×D313yes—
387C4⋊Dic3—33no—
388C4⋊Dic3—33no—
389C4⋊Dic3—33no—
390C4⋊Dic3—33no—
391C4⋊Dic3—33no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—33no—
395C4⋊Dic3—33no—
396C4⋊Dic3—33no—
397C4⋊Dic3—33no—
398C4⋊Dic3—36no—
399C4⋊Dic3—31no—
400C4⋊Dic3—63no—
401C4⋊Dic3—63no—
402C4⋊Dic3—63no—
403C4⋊Dic3—61no—
404C4⋊Dic3C22×D313yes—
405C4⋊Dic3C22×D313yes—
406Dic3⋊C4—36no—
407Dic3⋊C4—33no—
408Dic3⋊C4—33no—
409Dic3⋊C4—33no—
410Dic3⋊C4—33no—
411Dic3⋊C4—31no—
412Dic3⋊C4—33no—
413Dic3⋊C4—33no—
414Dic3⋊C4—33no—
415Dic3⋊C4C22×D313yes—
416Dic3⋊C4C22×D311yescharacteristic
417C4×Dic3—33no—
418C4×Dic3—33no—
419C4×Dic3—33no—
420C4×Dic3—33no—
421C4×Dic3—33no—
422C4×Dic3—33no—
423C4×Dic3—33no—
424C4×Dic3—33no—
425C4×Dic3—63no—
426C4×Dic3—63no—
427C4×Dic3C22×D313yes—
428C4×Dic3C22×D313yes—
429C22×C32—23no—
430C22×C32—23no—
431C22×C32—23no—
432C22×C32C2511yescharacteristic
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—23no—
436C2×C3×D3—23no—
437C2×C3×D3—23no—
438C2×C3×D3H(5,𝔽2)12yes—
439C32×C4—21no—
440C32×C4C2×#4116yes—
441C3⋊Dic3—23no—
442C3⋊Dic3—23no—
443C3⋊Dic3—21no—
444C3⋊Dic3—21no—
445C3×Dic3—23no—
446C3×Dic3—21no—
447C3×Dic3—23no—
448C3×Dic3—23no—
449C3×Dic3—21no—
450C3×Dic32−1+412yes—
451C2×#41—31no—
452C2×#41—96no—
453C2×#41D3211yescharacteristic
454C22×Q8—31no—
455C4⋊Q8—93no—
456C4⋊Q8—93no—
457C4⋊Q8—93no—
458#127—33no—
459#126—93no—
460#126—93no—
461#125—93no—
462#124—33no—
463#124—93no—
464#124—96no—
465#124—93no—
466#123—93no—
467#123—93no—
468#123—96no—
469#123—96no—
470C22⋊Q8—33no—
471C22⋊Q8—96no—
472C22⋊Q8—91no—
473C22⋊Q8—96no—
474C22⋊Q8—93no—
475#121—33no—
476#121—33no—
477#121—33no—
478#121—93no—
479#121—93no—
480C4×Q8—31no—
481C4×Q8—31no—
482C4×Q8—93no—
483C4×Q8—93no—
484C4×Q8—93no—
485C4×Q8—91no—
486C4×Q8—91no—
487C4×D4—33no—
488C4×D4—33no—
489C4×D4—93no—
490C4×D4—96no—
491C4×D4—93no—
492C4×D4—93no—
493C4×D4—93no—
494C4×D4—93no—
495#117—93no—
496#117—93no—
497C2×C4⋊C4—93no—
498C2×C4⋊C4—93no—
499C2×C4⋊C4—93no—
500C2×C42—93no—
501C23×C3—23no—
502C23×C3—31no—
503C23×C3—33no—
504C23×C3C23×D313yes—
505C23×C3C23×D313yes—
506C22×D3C23×D313yes—
507C22×D3C23×D311yescharacteristic
508C3×Q8—24no—
509C3×Q8—66no—
510C3×Q8#23714yescomplemented
511C3×Q8#23714yescomplemented
512C3×D4—212no—
513C3×D4—26no—
514C3×D4—26no—
515C3×D4—66no—
516C3×D4—66no—
517C3×D4—66no—
518C3×D4—126no—
519C2×C3×C4—212no—
520C2×C3×C4—26no—
521C2×C3×C4—26no—
522C2×C3×C4—23no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—33no—
526C2×C3×C4—33no—
527C2×C3×C4—31no—
528C2×C3×C4—33no—
529C2×C3×C4—31no—
530C2×C3×C4—66no—
531C2×C3×C4—66no—
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D313yes—
535C2×C3×C4C23×D313yes—
536#67—26no—
537#67—26no—
538#67—46no—
539#67—66no—
540#67—66no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—33no—
546C2×Dic3—33no—
547C2×Dic3—33no—
548C2×Dic3—33no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—63no—
552C2×Dic3—63no—
553C2×Dic3—66no—
554C2×Dic3—62no—
555C2×Dic3—126no—
556C2×Dic3—126no—
557C2×Dic3—126no—
558C2×Dic3—246no—
559C2×Dic3C23×D313yes—
560C2×Dic3C23×D313yes—
561C2×Dic3C23×D311yescharacteristic
562C2×Dic3C23×D313yes—
563C2×Dic3C23×D311yescharacteristic
564C2×Dic3C23×D311yescharacteristic
565D12—26no—
566C4×D3—26no—
567C4×D3—26no—
568C4×D3—62no—
569C4×D3—66no—
570C4×D3—126no—
571Dic6—26no—
572Dic6—62no—
573Dic6—62no—
574Dic6—126no—
575Dic6—126no—
576C2×C32—43no—
577C2×C32C22×#4111yescharacteristic
578C2×C32C2×H(5,𝔽2)11yescharacteristic
579C2×C32C2×2−1+411yescharacteristic
580C3×D3—22no—
581C3×D3—43no—
582#41—24no—
583#41—64no—
584#41—3612no—
585C2×Q8—33no—
586C2×Q8—64no—
587C2×Q8—91no—
588C2×Q8—96no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—33no—
591C2×D4—33no—
592C2×D4—36no—
593C2×D4—33no—
594C2×D4—93no—
595C2×D4C2×D3213yes—
596C22×C4—33no—
597C22×C4—33no—
598C22×C4—91no—
599C22×C4—93no—
600C22×C4—96no—
601C22×C4—96no—
602C22×C4C2×D3213yes—
603C4⋊C4—33no—
604C4⋊C4—33no—
605C4⋊C4—31no—
606C4⋊C4—33no—
607C4⋊C4—93no—
608C4⋊C4—96no—
609C4⋊C4—91no—
610C4⋊C4—93no—
611C4⋊C4—93no—
612C4⋊C4—93no—
613C4⋊C4—93no—
614C4⋊C4—93no—
615C4⋊C4—93no—
616C4⋊C4—93no—
617C4⋊C4—91no—
618C22⋊C4—33no—
619C22⋊C4—33no—
620C22⋊C4—36no—
621C22⋊C4—31no—
622C22⋊C4—33no—
623C22⋊C4—93no—
624C22⋊C4—93no—
625C22⋊C4—91no—
626C22⋊C4—96no—
627C22⋊C4—93no—
628C22⋊C4—93no—
629C22⋊C4—93no—
630C42—33no—
631C42—33no—
632C42—93no—
633C42—93no—
634C42—93no—
635C42—93no—
636C22×C3—26no—
637C22×C3—23no—
638C22×C3—23no—
639C22×C3—23no—
640C22×C3—23no—
641C22×C3—23no—
642C22×C3—23no—
643C22×C3—21no—
644C22×C3—32no—
645C22×C3—43no—
646C22×C3—43no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—63no—
650C22×C3—63no—
651C22×C3—63no—
652C22×C3C24×D311yescharacteristic
653C22×C3C24×D311yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—23no—
657C2×D3—23no—
658C2×D3—23no—
659C2×D3#100912yes—
660C3×C4—22no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—26no—
664C3×C4—32no—
665C3×C4—61no—
666C3×C4—63no—
667C3×C4—63no—
668C3×C4—61no—
669C3×C4—63no—
670C3×C4C2×#23716yes—
671C3×C4C2×#23716yes—
672Dic3—23no—
673Dic3—21no—
674Dic3—23no—
675Dic3—23no—
676Dic3—21no—
677Dic3—63no—
678Dic3—63no—
679Dic3—61no—
680Dic3—61no—
681Dic3—63no—
682Dic3—63no—
683Dic3—61no—
684Dic3—61no—
685Dic3—123no—
686Dic3—123no—
687Dic3—121no—
688Dic3—121no—
689Dic3#101012yes—
690C32#352211yescharacteristic, complemented, Sylow
691C23—31no—
692C23—33no—
693C23C22×D3213yes—
694Q8—66no—
695Q8—182no—
696Q8—366no—
697Q8#380514yescomplemented
698D4—26no—
699D4—66no—
700D4—66no—
701D4—66no—
702D4—126no—
703D4—186no—
704C2×C4—26no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—33no—
708C2×C4—33no—
709C2×C4—33no—
710C2×C4—31no—
711C2×C4—66no—
712C2×C4—66no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—93no—
716C2×C4—93no—
717C2×C4—182no—
718C2×C4—186no—
719C2×C4—366no—
720C2×C4—366no—
721C2×C4C22×D3211yescharacteristic
722C2×C4C22×D3213yes—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—46no—
727C2×C3—43no—
728C2×C3—43no—
729C2×C3—62no—
730C2×C3—123no—
731C2×C3C22×#23711yescharacteristic
732C2×C3C22×#23711yescharacteristic
733C2×C3C2×#100911yescharacteristic
734C2×C3C2×#101011yescharacteristic
735C2×C3D3×H(5,𝔽2)11yescharacteristic
736C2×C3D3×2−1+411yescharacteristic
737D3—22no—
738D3—43no—
739C22—23no—
740C22—23no—
741C22—23no—
742C22—32no—
743C22—61no—
744C22—61no—
745C22—63no—
746C22—63no—
747C22—63no—
748C22C23×D3211yescharacteristic
749C4—21no—
750C4—32no—
751C4—63no—
752C4—63no—
753C4—61no—
754C4—61no—
755C4—63no—
756C4—183no—
757C4—183no—
758C4—181no—
759C4—181no—
760C4C2×#380516yes—
761C3—21no—
762C3#8672211yescharacteristic, complemented
763C3#8677611yescharacteristic, complemented
764C2—43no—
765C2—62no—
766C2—123no—
767C2D3×#100911yescharacteristic
768C2D3×#101011yescharacteristic
769C2C22×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596298C2semidirect
2. C3×#5834C2semidirect
3. C3×#5831C2semidirect
4. Q8×#627C2semidirect
5. #10595409C2semidirect
6. #10595394C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10595199C2semidirect
9. #10595134C2semidirect
10. #10595133C2semidirect
11. #10595126C2semidirect
12. #10594993C2semidirect
13. #10594984C2semidirect
14. #10594934C2semidirect
15. #10594907C2semidirect
70. #5834D3semidirect
72. #5831D3semidirect
264. C32×Q8#41semidirect
510. C3×Q8#237semidirect
511. C3×Q8#237semidirect
690. C32#3522semidirect
697. Q8#3805semidirect
762. C3#86722semidirect
763. C3#86776semidirect

Maximal subgroups

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

subgroupindex
#105962982
C3×#58342
C3×#58312
Q8×#6272
#105954092
#105953942
D3×Q8×Dic32
#105951992
#105951342
#105951332
#105951262
#105949932
#105949842
#105949342
#105949072
#867763
#867223