Finite Group Databasebeta

← #11903886

Subgroups — #11903886

Order 1152.

2379 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C3×#5834C211yesmaximal, characteristic, complemented
3C3×#5831C211yesmaximal, characteristic, complemented
4#10595422C211yesmaximal, characteristic, complemented
5#10595409C211yesmaximal, characteristic, complemented
6Dic3×#239C211yesmaximal, characteristic, complemented
7D3×Q8×Dic3C211yesmaximal, characteristic, complemented
8#10595245C213yesmaximal, complemented
9#10595199C213yesmaximal, complemented
10#10595173C213yesmaximal, complemented
11#10595133C213yesmaximal, complemented
12#10594965C213yesmaximal, complemented
13#10594945C213yesmaximal, complemented
14C4×#3805C213yesmaximal, complemented
15#10594841C213yesmaximal, complemented
16#86767—31nomaximal
17#86711—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3805C2213yes—
22Q8×C3⋊Dic3C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2213yes—
25D4×C3⋊Dic3C2213yes—
26#64135C2213yes—
27C2×C4×C3⋊Dic3C2213yes—
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#67⋊Dic3C2213yes—
39#67⋊Dic3C2213yes—
40#67⋊Dic3C2216yes—
41#63970C2216yes—
42#63969C2216yes—
43#63962C2216yes—
44#63959C2216yes—
45#63957C2213yes—
46#63956C2216yes—
47#63918C2213yes—
48C4×#627C2213yes—
49#63908C2213yes—
50#63902C2213yes—
51C4×#625C2213yes—
52#63898C2213yes—
53Dic3×D12C2213yes—
54D3×C4⋊Dic3C2213yes—
55#63878C2211yescharacteristic
56#63878C2213yes—
57C4×D3×Dic3C2213yes—
58C4×D3×Dic3C2213yes—
59#63872C2213yes—
60#63869C2213yes—
61#63863C2213yes—
62#63862C2216yes—
63#63856C2213yes—
64#63843C2213yes—
65Dic3×Dic6C2213yes—
66#63841C2213yes—
67#63838C2213yes—
68C3×#550—31no—
69C3×#548—31no—
70#5834D311yescharacteristic, complemented
71#5831—31no—
72#5831D311yescharacteristic, complemented
73Dic3×#41—31no—
74Dic3×#41—31no—
75Dic3×#41—31no—
76Dic3×#41—61no—
77#5817—31no—
78C2×Q8×Dic3—31no—
79#5716—33no—
80#5713—33no—
81#5681—33no—
82#5680—33no—
83#5641—33no—
84#5624—33no—
85#5618—33no—
86#5614—33no—
87#5614—33no—
88#5600—33no—
89#5600—33no—
90#5596—33no—
91C4×#239—31no—
92C4×D3×Q8—31no—
93#5570—31no—
94#5569—31no—
95#5565—33no—
96#5542—33no—
97C4×#237—33no—
98C4×#237—33no—
99C32×#41—24no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2313yes—
102C22×C32×C4C2313yes—
103C22×C3⋊Dic3C2313yes—
104C22×C3⋊Dic3C2313yes—
105C2×C3×#67C2313yes—
106C2×C3×#67C2313yes—
107C2×C3×#67C2316yes—
108C3×#239—24no—
109C3×D3×Q8—24no—
110C2×C3×D12C2313yes—
111C2×C3×C4×D3C2313yes—
112C2×C3×C4×D3C2313yes—
113C2×C3×Dic6C2313yes—
114C2×#627C2313yes—
115C2×#625C2313yes—
116#3805—212no—
117C2×D3×Dic3C2313yes—
118C2×D3×Dic3C2313yes—
119C2×D3×Dic3C2313yes—
120C2×D3×Dic3C2311yescharacteristic
121#3757C2316yes—
122C4⋊(C3⋊Dic3)C2313yes—
123C4⋊(C3⋊Dic3)C2313yes—
124C4×C3⋊Dic3C2313yes—
125C4×C3⋊Dic3C2313yes—
126C4×C3⋊Dic3C2313yes—
127C4×C3⋊Dic3C2311yescharacteristic
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⋊Dic3C2316yes—
143Dic3⋊Dic3C2313yes—
144Dic3⋊Dic3C2311yescharacteristic
145(C2×D3)⋊Dic3C2316yes—
146(C2×D3)⋊Dic3C2316yes—
147(C2×D3)⋊Dic3C2313yes—
148(C2×D3)⋊Dic3C2311yescharacteristic
149Dic32C2313yes—
150Dic32C2313yes—
151Dic32C2313yes—
152Dic32C2311yescharacteristic
153#3480—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—33no—
162C2×#237—33no—
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—36no—
187#938—36no—
188#938—33no—
189#938C2×D313yes—
190#938C2×D313yes—
191#936—33no—
192#936—36no—
193#936C2×D313yes—
194#935—36no—
195#935—36no—
196D4×Dic3—33no—
197D4×Dic3—33no—
198D4×Dic3—33no—
199D4×Dic3—33no—
200D4×Dic3—33no—
201D4×Dic3—36no—
202D4×Dic3—33no—
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—
218#924—33no—
219#924C2×D313yes—
220C2×C4×Dic3—33no—
221C2×C4×Dic3—33no—
222C2×C4×Dic3—33no—
223C2×C4×Dic3—33no—
224C2×C4×Dic3—63no—
225#898—36no—
226#893—33no—
227#892—33no—
228#892—31no—
229#892—33no—
230D3×C4⋊C4—33no—
231#890—33no—
232#890—33no—
233#890—33no—
234#888—33no—
235#887—33no—
236#887—33no—
237#887—33no—
238#886—36no—
239#885—36no—
240#883—36no—
241#67⋊C4—36no—
242#67⋊C4—33no—
243#67⋊C4—33no—
244#67⋊C4—33no—
245#67⋊C4—33no—
246#879—36no—
247#879—36no—
248#879—36no—
249#877—33no—
250#877—33no—
251#877—31no—
252#877—33no—
253C4×D12—33no—
254C42×D3—33no—
255C42×D3—33no—
256#870—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—26no—
270C2×C3⋊Dic3—43no—
271C2×C3⋊Dic3C2413yes—
272C2×C3⋊Dic3C2411yescharacteristic
273C2×C3⋊Dic3C2413yes—
274C2×C3⋊Dic3C2411yescharacteristic
275C3×#67—26no—
276C3×#67—26no—
277C3×#67—46no—
278C2×C3×Dic3C2411yescharacteristic
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2413yes—
281C2×C3×Dic3C2413yes—
282C2×C3×Dic3C2411yescharacteristic
283C2×C3×Dic3C2411yescharacteristic
284C3×D12—26no—
285C3×C4×D3—26no—
286C3×C4×D3—26no—
287C3×Dic6—26no—
288#627—26no—
289#625—26no—
290D3×Dic3—26no—
291D3×Dic3—43no—
292D3×Dic3—43no—
293D3×Dic3#4114yescomplemented
294#559—93no—
295#557—91no—
296#556—93no—
297#553—93no—
298#553—93no—
299#550—31no—
300#548—31no—
301#548—91no—
302#532—93no—
303#529—93no—
304#529—93no—
305C4×#41—93no—
306C4×#41—91no—
307C4×#41—91no—
308C2×C4×Q8—91no—
309C3×#41—28no—
310C3×#41—24no—
311C3×#41—24no—
312C3×#41—64no—
313C2×C3×Q8—21no—
314C2×C3×Q8—33no—
315C2×C3×Q8—64no—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×D4—23no—
319C2×C3×D4—33no—
320C2×C3×D4—33no—
321C2×C3×D4—36no—
322C2×C3×D4—33no—
323C2×C3×D4C22×D313yes—
324C2×C3×D4C22×D313yes—
325C22×C3×C4—23no—
326C22×C3×C4—33no—
327C22×C3×C4—33no—
328C22×C3×C4C22×D313yes—
329C22×C3×C4C22×D313yes—
330C2×#67—33no—
331C2×#67—33no—
332C2×#67C22×D313yes—
333C2×#67C22×D313yes—
334C2×#67C22×D316yes—
335C22×Dic3—31no—
336C22×Dic3—33no—
337C22×Dic3—33no—
338C22×Dic3—33no—
339C22×Dic3—33no—
340C22×Dic3—33no—
341C22×Dic3—33no—
342C22×Dic3—33no—
343C22×Dic3—63no—
344C22×Dic3—63no—
345#239—24no—
346D3×Q8—24no—
347#237—612no—
348#237—612no—
349C2×D12C22×D313yes—
350C2×C4×D3—31no—
351C2×C4×D3—33no—
352C2×C4×D3—33no—
353C2×C4×D3—33no—
354C2×C4×D3C22×D313yes—
355C2×C4×D3C22×D313yes—
356C2×Dic6—33no—
357C2×Dic6—33no—
358C2×Dic6C22×D313yes—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—33no—
362C3×C4⋊C4—33no—
363C3×C22⋊C4—33no—
364C3×C22⋊C4—33no—
365C3×C22⋊C4—36no—
366C3×C22⋊C4—33no—
367C3×C22⋊C4—31no—
368C3×C42—33no—
369C3×C42—33no—
370#217—36no—
371#217—36no—
372#217—31no—
373#217—33no—
374#217—36no—
375#217—36no—
376#217—66no—
377#217C22×D313yes—
378#217C22×D313yes—
379#217C22×D316yes—
380(C2×D3)⋊C4—36no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—36no—
383(C2×D3)⋊C4—33no—
384(C2×D3)⋊C4C22×D311yescharacteristic
385(C2×D3)⋊C4C22×D313yes—
386C4⋊Dic3—33no—
387C4⋊Dic3—33no—
388C4⋊Dic3—33no—
389C4⋊Dic3—33no—
390C4⋊Dic3—31no—
391C4⋊Dic3—33no—
392C4⋊Dic3—36no—
393C4⋊Dic3—36no—
394C4⋊Dic3—63no—
395C4⋊Dic3—63no—
396C4⋊Dic3C22×D313yes—
397C4⋊Dic3C22×D313yes—
398Dic3⋊C4—31no—
399Dic3⋊C4—33no—
400Dic3⋊C4—33no—
401Dic3⋊C4—33no—
402Dic3⋊C4—36no—
403Dic3⋊C4—36no—
404Dic3⋊C4—33no—
405Dic3⋊C4—33no—
406Dic3⋊C4C22×D313yes—
407Dic3⋊C4C22×D311yescharacteristic
408C4×Dic3—33no—
409C4×Dic3—33no—
410C4×Dic3—33no—
411C4×Dic3—33no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—33no—
415C4×Dic3—33no—
416C4×Dic3—33no—
417C4×Dic3—31no—
418C4×Dic3—33no—
419C4×Dic3—33no—
420C4×Dic3—31no—
421C4×Dic3—33no—
422C4×Dic3—33no—
423C4×Dic3—33no—
424C4×Dic3—61no—
425C4×Dic3—63no—
426C4×Dic3—63no—
427C4×Dic3—63no—
428C4×Dic3C22×D313yes—
429C4×Dic3C22×D313yes—
430C22×C32—23no—
431C22×C32—23no—
432C22×C32—23no—
433C22×C32C2511yescharacteristic
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—23no—
437C2×C3×D3—23no—
438C2×C3×D3—23no—
439C2×C3×D3C2×#4112yes—
440C32×C4—21no—
441C32×C4C2×#4116yes—
442C3⋊Dic3—21no—
443C3⋊Dic3—23no—
444C3⋊Dic3—23no—
445C3⋊Dic3C2×#4112yes—
446C3×Dic3—23no—
447C3×Dic3—23no—
448C3×Dic3—21no—
449C3×Dic3—21no—
450C3×Dic3—23no—
451C3×Dic3C2×#4112yes—
452C2×#41—31no—
453C2×#41—93no—
454C2×#41D3211yescharacteristic
455C22×Q8—31no—
456C4⋊Q8—93no—
457#127—33no—
458#126—96no—
459#126—96no—
460#125—93no—
461#125—93no—
462#124—33no—
463#124—96no—
464#124—93no—
465#123—96no—
466#123—96no—
467C22⋊Q8—33no—
468C22⋊Q8—93no—
469#121—33no—
470#121—33no—
471#121—33no—
472#121—93no—
473#121—96no—
474C4×Q8—31no—
475C4×Q8—31no—
476C4×Q8—93no—
477C4×Q8—93no—
478C4×Q8—93no—
479C4×Q8—93no—
480C4×Q8—91no—
481C4×Q8—91no—
482C4×D4—33no—
483C4×D4—33no—
484C4×D4—93no—
485C4×D4—93no—
486C4×D4—93no—
487C4×D4—93no—
488C4×D4—96no—
489C4×D4—93no—
490C4×D4—93no—
491C4×D4—93no—
492C4×D4—93no—
493#117—93no—
494#117—91no—
495#117—93no—
496#117—93no—
497#117—93no—
498C2×C4⋊C4—93no—
499C2×C42—93no—
500C2×C42—93no—
501C2×C42—93no—
502C23×C3—23no—
503C23×C3—31no—
504C23×C3—33no—
505C23×C3C23×D313yes—
506C23×C3C23×D313yes—
507C22×D3C23×D313yes—
508C22×D3C23×D311yescharacteristic
509C3×Q8—24no—
510C3×Q8—66no—
511C3×Q8#23714yescomplemented
512C3×Q8#23714yescomplemented
513C3×D4—212no—
514C3×D4—26no—
515C3×D4—26no—
516C3×D4—66no—
517C3×D4—66no—
518C3×D4—66no—
519C3×D4—126no—
520C2×C3×C4—212no—
521C2×C3×C4—26no—
522C2×C3×C4—26no—
523C2×C3×C4—21no—
524C2×C3×C4—23no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—33no—
528C2×C3×C4—33no—
529C2×C3×C4—31no—
530C2×C3×C4—33no—
531C2×C3×C4—66no—
532C2×C3×C4—66no—
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D313yes—
536C2×C3×C4C23×D313yes—
537#67—26no—
538#67—26no—
539#67—46no—
540#67—66no—
541#67—66no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—34no—
545C2×Dic3—31no—
546C2×Dic3—33no—
547C2×Dic3—31no—
548C2×Dic3—33no—
549C2×Dic3—33no—
550C2×Dic3—33no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—63no—
554C2×Dic3—63no—
555C2×Dic3—66no—
556C2×Dic3—66no—
557C2×Dic3—66no—
558C2×Dic3—126no—
559C2×Dic3—123no—
560C2×Dic3—123no—
561C2×Dic3—123no—
562C2×Dic3—123no—
563C2×Dic3—126no—
564C2×Dic3C23×D311yescharacteristic
565C2×Dic3C23×D313yes—
566C2×Dic3C23×D311yescharacteristic
567C2×Dic3C23×D313yes—
568C2×Dic3C23×D313yes—
569C2×Dic3C23×D311yescharacteristic
570D12—26no—
571C4×D3—26no—
572C4×D3—26no—
573C4×D3—34no—
574C4×D3—66no—
575C4×D3—123no—
576C4×D3—123no—
577Dic6—26no—
578Dic6—66no—
579Dic6—66no—
580C2×C32—43no—
581C2×C32C22×#4111yescharacteristic
582C2×C32C22×#4111yescharacteristic
583C2×C32#58511yescharacteristic
584C3×D3—22no—
585C3×D3—43no—
586#41—24no—
587#41—64no—
588#41—1812no—
589C2×Q8—33no—
590C2×Q8—64no—
591C2×Q8—93no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—33no—
594C2×D4—33no—
595C2×D4—36no—
596C2×D4—33no—
597C2×D4—93no—
598C2×D4C2×D3213yes—
599C22×C4—33no—
600C22×C4—33no—
601C22×C4—91no—
602C22×C4—93no—
603C22×C4—93no—
604C22×C4—93no—
605C22×C4—93no—
606C22×C4—93no—
607C22×C4C2×D3213yes—
608C4⋊C4—33no—
609C4⋊C4—31no—
610C4⋊C4—33no—
611C4⋊C4—33no—
612C4⋊C4—96no—
613C4⋊C4—91no—
614C4⋊C4—93no—
615C4⋊C4—93no—
616C4⋊C4—93no—
617C4⋊C4—96no—
618C4⋊C4—93no—
619C4⋊C4—93no—
620C22⋊C4—33no—
621C22⋊C4—33no—
622C22⋊C4—36no—
623C22⋊C4—31no—
624C22⋊C4—33no—
625C22⋊C4—91no—
626C22⋊C4—96no—
627C22⋊C4—93no—
628C22⋊C4—96no—
629C22⋊C4—96no—
630C42—33no—
631C42—33no—
632C42—91no—
633C42—93no—
634C42—93no—
635C42—93no—
636C42—91no—
637C42—93no—
638C42—93no—
639C42—93no—
640C22×C3—26no—
641C22×C3—23no—
642C22×C3—23no—
643C22×C3—23no—
644C22×C3—23no—
645C22×C3—23no—
646C22×C3—23no—
647C22×C3—21no—
648C22×C3—32no—
649C22×C3—43no—
650C22×C3—43no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—63no—
654C22×C3—63no—
655C22×C3—63no—
656C22×C3C24×D311yescharacteristic
657C22×C3C24×D311yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—23no—
661C2×D3—23no—
662C2×D3—23no—
663C2×D3D3×#4112yes—
664C3×C4—22no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—26no—
668C3×C4—32no—
669C3×C4—61no—
670C3×C4—63no—
671C3×C4—63no—
672C3×C4—61no—
673C3×C4—63no—
674C3×C4C2×#23716yes—
675C3×C4C2×#23716yes—
676Dic3—23no—
677Dic3—21no—
678Dic3—23no—
679Dic3—23no—
680Dic3—21no—
681Dic3—32no—
682Dic3—32no—
683Dic3—62no—
684Dic3—62no—
685Dic3—63no—
686Dic3—63no—
687Dic3—63no—
688Dic3—61no—
689Dic3—63no—
690Dic3—61no—
691Dic3—123no—
692Dic3—123no—
693Dic3D3×#4112yes—
694C32#348011yescharacteristic, complemented, Sylow
695C23—31no—
696C23—33no—
697C23C22×D3213yes—
698Q8—66no—
699Q8—186no—
700Q8#380514yescomplemented
701D4—26no—
702D4—66no—
703D4—66no—
704D4—66no—
705D4—126no—
706D4—186no—
707C2×C4—26no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—33no—
711C2×C4—33no—
712C2×C4—31no—
713C2×C4—33no—
714C2×C4—66no—
715C2×C4—66no—
716C2×C4—94no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—93no—
720C2×C4—93no—
721C2×C4—186no—
722C2×C4—186no—
723C2×C4—363no—
724C2×C4—363no—
725C2×C4—363no—
726C2×C4C22×D3211yescharacteristic
727C2×C4C22×D3213yes—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—46no—
732C2×C3—43no—
733C2×C3—43no—
734C2×C3—62no—
735C2×C3—123no—
736C2×C3C22×#23711yescharacteristic
737C2×C3C22×#23711yescharacteristic
738C2×C3C2×D3×#4111yescharacteristic
739C2×C3C2×D3×#4111yescharacteristic
740C2×C3#596611yescharacteristic
741C2×C3#596811yescharacteristic
742D3—22no—
743D3—43no—
744C22—23no—
745C22—23no—
746C22—23no—
747C22—32no—
748C22—61no—
749C22—61no—
750C22—63no—
751C22—63no—
752C22—63no—
753C22C23×D3211yescharacteristic
754C4—21no—
755C4—32no—
756C4—63no—
757C4—61no—
758C4—63no—
759C4—61no—
760C4—63no—
761C4—92no—
762C4—183no—
763C4—181no—
764C4—183no—
765C4C2×#380516yes—
766C3—21no—
767C3#8671111yescharacteristic, complemented
768C3#8676711yescharacteristic, complemented
769C2—43no—
770C2—62no—
771C2—123no—
772C2D32×#4111yescharacteristic
773C2#1059669811yescharacteristic
774C2C22×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3480
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊Dic3C2semidirect
2. C3×#5834C2semidirect
3. C3×#5831C2semidirect
4. #10595422C2semidirect
5. #10595409C2semidirect
6. Dic3×#239C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10595245C2semidirect
9. #10595199C2semidirect
10. #10595173C2semidirect
11. #10595133C2semidirect
12. #10594965C2semidirect
13. #10594945C2semidirect
14. C4×#3805C2semidirect
15. #10594841C2semidirect
70. #5834D3semidirect
72. #5831D3semidirect
264. C32×Q8#41semidirect
293. D3×Dic3#41semidirect
511. C3×Q8#237semidirect
512. C3×Q8#237semidirect
694. C32#3480semidirect
700. Q8#3805semidirect
767. C3#86711semidirect
768. C3#86767semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C3×#58342
C3×#58312
#105954222
#105954092
Dic3×#2392
D3×Q8×Dic32
#105952452
#105951992
#105951732
#105951332
#105949652
#105949452
C4×#38052
#105948412
#867673
#867113