Finite Group Databasebeta

← #11904216

Subgroups — #11904216

Order 1152.

2333 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596047C211yesmaximal, characteristic, complemented
2C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
3C3×#5569C211yesmaximal, characteristic, complemented
4Q8×#626C211yesmaximal, characteristic, complemented
5#10595386C211yesmaximal, characteristic, complemented
6Q8×#624C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10594553C213yesmaximal, complemented
9#10594517C213yesmaximal, complemented
10#10594464C213yesmaximal, complemented
11#10594397C213yesmaximal, complemented
12#10593976C213yesmaximal, complemented
13C4×#3799C213yesmaximal, complemented
14#10593947C213yesmaximal, complemented
15#10593850C213yesmaximal, complemented
16#87017—31nomaximal
17#85817—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3799C2213yes—
22C32×C4×Q8C2211yescharacteristic
23#64106C2213yes—
24#64104C2213yes—
25#64084C2213yes—
26C4×C4⋊(C3⋊D3)C2213yes—
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×D3×C4⋊C4C2213yes—
31C3×#890C2213yes—
32C3×#888C2213yes—
33C3×#887C2213yes—
34C3×C42×D3C2213yes—
35C3×#870C2213yes—
36C3×C4×Dic6C2213yes—
37C3×C4×Dic6C2213yes—
38#63909C2213yes—
39#63904C2211yescharacteristic
40#63904C2213yes—
41C4×#626C2213yes—
42C4×#626C2213yes—
43#63900C2213yes—
44#63897C2216yes—
45#63894C2213yes—
46#63894C2213yes—
47#63894C2213yes—
48#63888C2216yes—
49C4×#624C2213yes—
50C4×#624C2213yes—
51#63871C2213yes—
52#63871C2213yes—
53#63868C2216yes—
54#63866C2213yes—
55#63864C2213yes—
56#63857C2213yes—
57#63850C2216yes—
58#63849C2213yes—
59#63848C2216yes—
60#63845C2216yes—
61#63844C2213yes—
62#63844C2213yes—
63Dic3×Dic6C2213yes—
64#63841C2213yes—
65#63836C2213yes—
66#63836C2216yes—
67#63836C2213yes—
68C3×#557—31no—
69C2×C3×C4×Q8—31no—
70#5817—31no—
71Q8×#67—31no—
72#5728—33no—
73#5726—33no—
74#5694—33no—
75#5694—33no—
76#5691—33no—
77#5691—33no—
78#5584—33no—
79#5581—33no—
80#5580—33no—
81#5578—33no—
82#5576—31no—
83#5576—31no—
84#5576—31no—
85#5576—61no—
86Q8×D12—31no—
87C4×#239—31no—
88C4×#239—31no—
89C4×#239—33no—
90C4×D3×Q8—31no—
91C4×D3×Q8—31no—
92C4×D3×Q8D311yescharacteristic, complemented
93#5569D311yescharacteristic, complemented
94#5568—33no—
95#5513—33no—
96#5507—33no—
97#5479—33no—
98C4×#235—33no—
99C2×C32×Q8C2311yescharacteristic
100#3832—24no—
101Q8×C3⋊D3—24no—
102C2×C4⋊(C3⋊D3)C2313yes—
103C2×C4⋊(C3⋊D3)C2313yes—
104C2×C4×C3⋊D3C2313yes—
105C2×C4×C3⋊D3C2313yes—
106C2×#634C2313yes—
107C3×D3×Q8—24no—
108C2×C3×C4×D3C2313yes—
109C2×C3×C4×D3C2313yes—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2313yes—
112C2×C3×Dic6C2313yes—
113C2×#626C2313yes—
114C2×#626C2311yescharacteristic
115C2×#624C2313yes—
116C2×#624C2313yes—
117C2×#624C2313yes—
118C2×#624C2311yescharacteristic
119#3799—212no—
120C32×C4⋊C4C2313yes—
121C32×C42C2313yes—
122#3752C2311yescharacteristic
123#3752C2313yes—
124#3752C2316yes—
125C4⋊(C3⋊Dic3)C2313yes—
126C3×C4⋊Dic3C2313yes—
127C3×C4⋊Dic3C2313yes—
128C3×C4⋊Dic3C2313yes—
129C3×C4⋊Dic3C2313yes—
130C3×Dic3⋊C4C2316yes—
131C3×Dic3⋊C4C2316yes—
132C3×Dic3⋊C4C2311yescharacteristic
133C3×Dic3⋊C4C2313yes—
134C3×C4×Dic3C2313yes—
135C3×C4×Dic3C2313yes—
136C3×C4×Dic3C2313yes—
137C3×C4×Dic3C2313yes—
138C3×C4×Dic3C2313yes—
139#3724C2316yes—
140Dic3⋊Dic3C2313yes—
141Dic3⋊Dic3C2313yes—
142Dic3⋊Dic3C2316yes—
143#3722C2313yes—
144#3722C2316yes—
145#3722C2313yes—
146#3722C2316yes—
147(C2×D3)⋊Dic3C2311yescharacteristic
148(C2×D3)⋊Dic3C2313yes—
149Dic32C2313yes—
150Dic32C2313yes—
151Dic32C2313yes—
152Dic32C2311yescharacteristic
153#3482—91noSylow
154C22×C3×Q8—31no—
155C2×#239—31no—
156C2×#239—31no—
157C2×#239—33no—
158C2×#239—61no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8—61no—
162C2×D3×Q8C2×D311yescharacteristic
163C2×#235—33no—
164C3×C4⋊Q8—33no—
165C3×#125—33no—
166C3×#125—33no—
167C3×C4×Q8—21no—
168C3×C4×Q8—31no—
169C3×C4×Q8—31no—
170C3×C4×Q8—31no—
171C3×C4×Q8—33no—
172C3×C4×Q8—33no—
173C3×C4×Q8—33no—
174C3×C4×Q8C2×D311yescharacteristic
175C3×C4×Q8C2×D311yescharacteristic
176C2×C3×C4⋊C4—33no—
177C2×C3×C42—33no—
178#947—33no—
179#946—33no—
180#946—33no—
181#946—36no—
182Q8×Dic3—33no—
183Q8×Dic3C2×D311yescharacteristic
184Q8×Dic3C2×D311yescharacteristic
185Q8×Dic3C2×D311yescharacteristic
186#944—33no—
187#930—33no—
188#929—36no—
189C4×#67—31no—
190C4×#67—33no—
191C4×#67—33no—
192C4×#67—33no—
193#926—33no—
194#924—33no—
195#898—36no—
196#898—36no—
197#898—36no—
198#897—33no—
199#897—33no—
200#897—33no—
201#897—33no—
202#897—33no—
203#897—63no—
204#896—36no—
205#895—33no—
206#895—33no—
207#895—33no—
208#895—63no—
209#894—36no—
210#894—36no—
211#894—36no—
212#893—33no—
213#893—31no—
214#893—33no—
215#893—33no—
216#893—33no—
217#892—33no—
218#892—33no—
219#892—33no—
220#892—36no—
221#892—33no—
222#892—33no—
223D3×C4⋊C4—33no—
224D3×C4⋊C4—33no—
225D3×C4⋊C4C2×D313yes—
226#890—36no—
227#890C2×D313yes—
228#889—36no—
229#888C2×D313yes—
230#887—33no—
231#887—33no—
232#887C2×D313yes—
233#876—36no—
234#875—33no—
235#875—33no—
236#875—33no—
237#875—63no—
238C4×D12—33no—
239C4×D12—33no—
240C4×D12—33no—
241C4×D12—33no—
242C4×D12—33no—
243C4×D12—33no—
244C4×D12—33no—
245C4×D12—63no—
246#872—33no—
247#872—33no—
248#872—36no—
249C42×D3—33no—
250C42×D3—33no—
251C42×D3—33no—
252C42×D3—33no—
253C42×D3C2×D313yes—
254#870C2×D313yes—
255#869—33no—
256C4×Dic6—33no—
257C4×Dic6—33no—
258C4×Dic6—33no—
259C4×Dic6C2×D313yes—
260C4×Dic6C2×D313yes—
261C22×C3⋊D3C2413yes—
262C22×C3⋊D3C2411yescharacteristic
263C22×C3×D3C2411yescharacteristic
264C32×Q8#4114yescomplemented
265C2×C32×C4C2411yescharacteristic
266C2×C32×C4C2413yes—
267C2×C32×C4C2413yes—
268C2×C3⋊Dic3C2411yescharacteristic
269C2×C3⋊Dic3C2413yes—
270C4⋊(C3⋊D3)—26no—
271C4⋊(C3⋊D3)—26no—
272C4×C3⋊D3—26no—
273C4×C3⋊D3—26no—
274#634—26no—
275C2×C3×Dic3C2411yescharacteristic
276C2×C3×Dic3C2413yes—
277C2×C3×Dic3C2413yes—
278C2×C3×Dic3C2413yes—
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2411yescharacteristic
281C2×C3×Dic3C2411yescharacteristic
282C3×C4×D3—26no—
283C3×C4×D3—26no—
284C3×C4×D3—22no—
285C3×Dic6—26no—
286C3×Dic6—26no—
287#626—26no—
288#626#4114yescomplemented
289#624—26no—
290#624—26no—
291#624—22no—
292#624—26no—
293#557—31no—
294#556—93no—
295#552—93no—
296#552—93no—
297D4×Q8—91no—
298#548—91no—
299#548—91no—
300#547—93no—
301#533—93no—
302#529—93no—
303#529—93no—
304C4×#41—93no—
305C4×#41—91no—
306C2×C4×Q8—31no—
307C2×C4×Q8—91no—
308C2×C3×Q8—21no—
309C2×C3×Q8—33no—
310C2×C3×Q8—33no—
311C2×C3×Q8—64no—
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×Q8C22×D311yescharacteristic
314C22×C3×C4—33no—
315C22×C3×C4—33no—
316C22×C3×C4—31no—
317C2×#67—31no—
318C2×#67—33no—
319#239—612no—
320#239—64no—
321#239—64no—
322#239—124no—
323D3×Q8—24no—
324D3×Q8—64no—
325D3×Q8—64no—
326D3×Q8—124no—
327#235—612no—
328C2×D12—31no—
329C2×D12—33no—
330C2×D12—33no—
331C2×D12—33no—
332C2×D12—33no—
333C2×D12—33no—
334C2×D12—63no—
335C2×D12—63no—
336C2×C4×D3—33no—
337C2×C4×D3—33no—
338C2×C4×D3—33no—
339C2×C4×D3—33no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—33no—
343C2×C4×D3—33no—
344C2×C4×D3—33no—
345C2×C4×D3—33no—
346C2×C4×D3—33no—
347C2×C4×D3—33no—
348C2×C4×D3—63no—
349C2×C4×D3—63no—
350C2×C4×D3C22×D311yescharacteristic
351C2×C4×D3C22×D313yes—
352C2×C4×D3C22×D313yes—
353C2×Dic6—33no—
354C2×Dic6—33no—
355C2×Dic6—63no—
356C2×Dic6C22×D313yes—
357C2×Dic6C22×D313yes—
358C3×C4⋊C4—23no—
359C3×C4⋊C4—33no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—36no—
362C3×C4⋊C4—36no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—33no—
365C3×C4⋊C4—33no—
366C3×C4⋊C4—33no—
367C3×C4⋊C4C22×D313yes—
368C3×C4⋊C4C22×D313yes—
369C3×C42—23no—
370C3×C42—33no—
371C3×C42—33no—
372C3×C42—33no—
373C3×C42—33no—
374C3×C42—33no—
375C3×C42C22×D313yes—
376C3×C42C22×D313yes—
377#217—33no—
378#217—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—33no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—33no—
383(C2×D3)⋊C4—36no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—33no—
386(C2×D3)⋊C4—36no—
387(C2×D3)⋊C4—33no—
388(C2×D3)⋊C4—33no—
389(C2×D3)⋊C4—36no—
390(C2×D3)⋊C4—33no—
391(C2×D3)⋊C4—36no—
392(C2×D3)⋊C4—33no—
393(C2×D3)⋊C4—36no—
394(C2×D3)⋊C4—36no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—63no—
397(C2×D3)⋊C4—66no—
398C4⋊Dic3—33no—
399C4⋊Dic3—33no—
400C4⋊Dic3—33no—
401C4⋊Dic3—36no—
402C4⋊Dic3—33no—
403C4⋊Dic3—63no—
404C4⋊Dic3C22×D313yes—
405C4⋊Dic3C22×D313yes—
406C4⋊Dic3C22×D313yes—
407C4⋊Dic3C22×D313yes—
408Dic3⋊C4—33no—
409Dic3⋊C4—33no—
410Dic3⋊C4—36no—
411Dic3⋊C4—36no—
412Dic3⋊C4—36no—
413Dic3⋊C4C22×D311yescharacteristic
414Dic3⋊C4C22×D313yes—
415Dic3⋊C4C22×D316yes—
416Dic3⋊C4C22×D316yes—
417C4×Dic3—31no—
418C4×Dic3—33no—
419C4×Dic3—33no—
420C4×Dic3—31no—
421C4×Dic3—33no—
422C4×Dic3—33no—
423C4×Dic3—33no—
424C4×Dic3—33no—
425C4×Dic3C22×D313yes—
426C4×Dic3C22×D313yes—
427C4×Dic3C22×D313yes—
428C4×Dic3C22×D313yes—
429C4×Dic3C22×D313yes—
430C22×C32C2511yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—23no—
434C2×C3⋊D3—23no—
435C2×C3⋊D3—23no—
436C2×C3⋊D3C2×#4112yes—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3C2×#4112yes—
440C32×C4—23no—
441C32×C4—21no—
442C32×C4C2×#4116yes—
443C3⋊Dic3—23no—
444C3⋊Dic3—21no—
445C3×Dic3—23no—
446C3×Dic3—23no—
447C3×Dic3—23no—
448C3×Dic3—21no—
449C3×Dic3—23no—
450C3×Dic3C2×#4112yes—
451C3×Dic32−1+412yes—
452C2×#41—93no—
453C2×#41—91no—
454C22×Q8—31no—
455C22×Q8—91no—
456C4⋊Q8—33no—
457C4⋊Q8—93no—
458#126—96no—
459#126—96no—
460#125—33no—
461#125—33no—
462#125—96no—
463#124—93no—
464#124—93no—
465#123—96no—
466#123—96no—
467C22⋊Q8—93no—
468C22⋊Q8—93no—
469C22⋊Q8—96no—
470C22⋊Q8—93no—
471C22⋊Q8—93no—
472#121—93no—
473#121—93no—
474C4×Q8—31no—
475C4×Q8—31no—
476C4×Q8—31no—
477C4×Q8—33no—
478C4×Q8—33no—
479C4×Q8—33no—
480C4×Q8—93no—
481C4×Q8—93no—
482C4×Q8—93no—
483C4×Q8D3211yescharacteristic
484C4×D4—93no—
485C4×D4—93no—
486C4×D4—93no—
487C4×D4—93no—
488C4×D4—93no—
489C4×D4—91no—
490C4×D4—93no—
491C4×D4—93no—
492#117—93no—
493#117—93no—
494#117—96no—
495#117—93no—
496#117—93no—
497C2×C4⋊C4—33no—
498C2×C4⋊C4—93no—
499C2×C42—33no—
500C2×C42—93no—
501C2×C42—93no—
502C23×C3—31no—
503C22×D3—31no—
504C22×D3—31no—
505C22×D3—33no—
506C22×D3—33no—
507C22×D3—61no—
508C22×D3—63no—
509C22×D3C23×D311yescharacteristic
510C3×Q8—24no—
511C3×Q8—66no—
512C3×Q8—66no—
513C3×Q8#23514yescomplemented
514C3×Q8#23914yescomplemented
515C2×C3×C4—23no—
516C2×C3×C4—23no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—33no—
522C2×C3×C4—33no—
523C2×C3×C4—33no—
524C2×C3×C4—33no—
525C2×C3×C4—62no—
526C2×C3×C4—66no—
527C2×C3×C4—66no—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D313yes—
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D313yes—
532C2×C3×C4C23×D313yes—
533C2×C3×C4C23×D313yes—
534#67—34no—
535#67—66no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—33no—
539C2×Dic3—33no—
540C2×Dic3—61no—
541C2×Dic3—63no—
542C2×Dic3C23×D311yescharacteristic
543C2×Dic3C23×D313yes—
544C2×Dic3C23×D313yes—
545C2×Dic3C23×D313yes—
546C2×Dic3C23×D313yes—
547C2×Dic3C23×D311yescharacteristic
548C2×Dic3C23×D311yescharacteristic
549D12—34no—
550D12—66no—
551D12—66no—
552D12—66no—
553D12—66no—
554D12—66no—
555D12—126no—
556D12—126no—
557C4×D3—26no—
558C4×D3—26no—
559C4×D3—22no—
560C4×D3—62no—
561C4×D3—66no—
562C4×D3—66no—
563C4×D3—66no—
564C4×D3—66no—
565C4×D3—66no—
566C4×D3—66no—
567C4×D3—66no—
568C4×D3—66no—
569C4×D3—62no—
570C4×D3—66no—
571C4×D3—66no—
572C4×D3—126no—
573C4×D3—126no—
574Dic6—26no—
575Dic6—26no—
576Dic6—66no—
577Dic6—66no—
578Dic6—126no—
579C2×C32C22×#4111yescharacteristic
580C2×C32C22×#4111yescharacteristic
581C2×C32C2×2−1+411yescharacteristic
582C3⋊D3—22no—
583C3⋊D3—43no—
584C3×D3—22no—
585#41—1812no—
586#41—184no—
587C2×Q8—33no—
588C2×Q8—33no—
589C2×Q8—64no—
590C2×Q8—93no—
591C2×Q8—184no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—91no—
594C2×D4—93no—
595C2×D4—93no—
596C2×D4—93no—
597C22×C4—31no—
598C22×C4—33no—
599C22×C4—33no—
600C22×C4—91no—
601C22×C4—93no—
602C22×C4—93no—
603C22×C4—93no—
604C22×C4—93no—
605C22×C4—93no—
606C4⋊C4—33no—
607C4⋊C4—36no—
608C4⋊C4—33no—
609C4⋊C4—31no—
610C4⋊C4—33no—
611C4⋊C4—33no—
612C4⋊C4—33no—
613C4⋊C4—36no—
614C4⋊C4—96no—
615C4⋊C4—93no—
616C4⋊C4—93no—
617C4⋊C4—96no—
618C4⋊C4—93no—
619C4⋊C4C2×D3213yes—
620C22⋊C4—93no—
621C22⋊C4—96no—
622C22⋊C4—93no—
623C22⋊C4—96no—
624C22⋊C4—91no—
625C22⋊C4—93no—
626C22⋊C4—91no—
627C22⋊C4—93no—
628C22⋊C4—96no—
629C42—33no—
630C42—33no—
631C42—33no—
632C42—33no—
633C42—33no—
634C42—91no—
635C42—93no—
636C42—93no—
637C42—93no—
638C42C2×D3213yes—
639C22×C3—21no—
640C22×C3—32no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3C24×D311yescharacteristic
644C22×C3C24×D311yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—32no—
648C2×D3—32no—
649C2×D3—62no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—63no—
655C2×D3—63no—
656C2×D3—63no—
657C2×D3—63no—
658C2×D3—63no—
659C2×D3—63no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—123no—
663C2×D3—123no—
664C2×D3—123no—
665C2×D3D3×#4112yes—
666C3×C4—21no—
667C3×C4—23no—
668C3×C4—23no—
669C3×C4—21no—
670C3×C4—26no—
671C3×C4—32no—
672C3×C4—32no—
673C3×C4—43no—
674C3×C4—41no—
675C3×C4—63no—
676C3×C4—61no—
677C3×C4—63no—
678C3×C4—63no—
679C3×C4—63no—
680C3×C4C2×#23516yes—
681C3×C4C2×#23916yes—
682Dic3—23no—
683Dic3—23no—
684Dic3—23no—
685Dic3—21no—
686Dic3—23no—
687Dic3—63no—
688Dic3—61no—
689Dic3—63no—
690Dic3—61no—
691Dic3—123no—
692Dic3—121no—
693Dic3#100712yes—
694Dic3D3×#4112yes—
695C32#348211yescharacteristic, complemented, Sylow
696C23—31no—
697C23—91no—
698C23—93no—
699Q8—66no—
700Q8—66no—
701Q8—186no—
702Q8#379914yescomplemented
703D4—94no—
704D4—186no—
705D4—186no—
706D4—186no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—33no—
711C2×C4—33no—
712C2×C4—33no—
713C2×C4—33no—
714C2×C4—62no—
715C2×C4—66no—
716C2×C4—66no—
717C2×C4—91no—
718C2×C4—93no—
719C2×C4—186no—
720C2×C4—182no—
721C2×C4—186no—
722C2×C4—186no—
723C2×C4—186no—
724C2×C4—186no—
725C2×C4C22×D3211yescharacteristic
726C2×C4C22×D3213yes—
727C2×C4C22×D3213yes—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—62no—
732C2×C3C22×#23511yescharacteristic
733C2×C3C22×#23911yescharacteristic
734C2×C3C2×#100711yescharacteristic
735C2×C3C2×D3×#4111yescharacteristic
736C2×C3C2×D3×#4111yescharacteristic
737C2×C3D3×2−1+411yescharacteristic
738D3—22no—
739D3—62no—
740D3—62no—
741D3—122no—
742D3—123no—
743D3—123no—
744D3—243no—
745C22—32no—
746C22—61no—
747C22—61no—
748C22—92no—
749C22—181no—
750C22—181no—
751C22—183no—
752C22—183no—
753C22—183no—
754C22C23×D3211yescharacteristic
755C4—21no—
756C4—23no—
757C4—32no—
758C4—32no—
759C4—63no—
760C4—61no—
761C4—63no—
762C4—63no—
763C4—63no—
764C4—181no—
765C4—183no—
766C4C2×#379916yes—
767C3—21no—
768C3#8581711yescharacteristic, complemented
769C3#8701711yescharacteristic, complemented
770C2—62no—
771C2—182no—
772C2—363no—
773C2C22×#379911yescharacteristic
774C2D3×#100711yescharacteristic
775C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596047C2semidirect
2. C3×C4×D3×Q8C2semidirect
3. C3×#5569C2semidirect
4. Q8×#626C2semidirect
5. #10595386C2semidirect
6. Q8×#624C2semidirect
7. #10595342C2semidirect
8. #10594553C2semidirect
9. #10594517C2semidirect
10. #10594464C2semidirect
11. #10594397C2semidirect
12. #10593976C2semidirect
13. C4×#3799C2semidirect
14. #10593947C2semidirect
15. #10593850C2semidirect
92. C4×D3×Q8D3semidirect
93. #5569D3semidirect
264. C32×Q8#41semidirect
288. #626#41semidirect
513. C3×Q8#235semidirect
514. C3×Q8#239semidirect
695. C32#3482semidirect
702. Q8#3799semidirect
768. C3#85817semidirect
769. C3#87017semidirect

Maximal subgroups

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

subgroupindex
#105960472
C3×C4×D3×Q82
C3×#55692
Q8×#6262
#105953862
Q8×#6242
#105953422
#105945532
#105945172
#105944642
#105943972
#105939762
C4×#37992
#105939472
#105938502
#870173
#858173