Finite Group Databasebeta

← #11887440

Subgroups — #11887440

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5695C211yesmaximal, characteristic, complemented
2#10594003C211yesmaximal, characteristic, complemented
3#10592767C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5#10590613C211yesmaximal, characteristic, complemented
6#10590608C211yesmaximal, characteristic, complemented
7#10590595C211yesmaximal, characteristic, complemented
8D3×#809C211yesmaximal, characteristic, complemented
9#10590578C211yesmaximal, characteristic, complemented
10#10590576C211yesmaximal, characteristic, complemented
11#10590427C211yesmaximal, characteristic, complemented
12#10590425C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14C4×#3713C211yesmaximal, characteristic, complemented
15#10590329C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#81187—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×#125C2211yescharacteristic, complemented
21#64084C2211yescharacteristic
22C3×#898—21no—
23C3×#895—21no—
24C3×#895C2211yescharacteristic
25C3×#895C2211yescharacteristic, complemented
26C3×#894—21no—
27C3×#893—21no—
28C3×#892C2211yescharacteristic, complemented
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33#63922—21no—
34D3×(C2×D3)⋊C4—21no—
35#63909C2211yescharacteristic
36#63906—21no—
37#63890—21no—
38#63857C2211yescharacteristic
39C2×#3716C2211yescharacteristic, complemented
40C2×#3714C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63637C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#553—31no—
62#5695D311yescharacteristic, complemented
63#5554—31no—
64#5550—31no—
65C3×#478—31no—
66#5068—31no—
67#5068—31no—
68#5068—61no—
69#5066D311yescharacteristic, complemented
70#5041—31no—
71#5038—31no—
72#5037—31no—
73#5036—31no—
74#5016—31no—
75C4×#213—31no—
76C4×#213—31no—
77D4×C3⋊C8—31no—
78#5003—31no—
79#5002—31no—
80#4970—31no—
81C2×#809—31no—
82#4884—31no—
83#4883—31no—
84#4866—31no—
85#4864—31no—
86#4844—31no—
87#4834—31no—
88#4781—31no—
89#4773—31no—
90#4772—31no—
91D3×#102—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12D411yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—41no—
111#3795—22no—
112#3795—41no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C42C2311yescharacteristic
118#3752—21no—
119#3752—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3716—41no—
140#3714—41no—
141#3713—22no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C3×#126—61no—
150C3×#125—21no—
151C3×#125C2×D311yescharacteristic, complemented
152C3×#125C2×D311yescharacteristic, complemented
153C3×#123—61no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161C3×#117—31no—
162C2×C3×C4⋊C4—31no—
163#937—61no—
164C2×#214—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—31no—
168#930—31no—
169#930—61no—
170C2×(C2×D3)⋊C4—61no—
171#924—31no—
172C22×C3⋊C8—31no—
173C22×C3⋊C8—31no—
174C2×D24—31no—
175C2×#204—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#898—21no—
179#897—31no—
180#895—21no—
181#895—31no—
182#895C2×D311yescharacteristic
183#895C2×D311yescharacteristic, complemented
184#894—21no—
185#894—61no—
186#893—21no—
187#892C2×D311yescharacteristic, complemented
188D3×C4⋊C4C2×D311yescharacteristic
189#886—61no—
190#884—61no—
191#882—61no—
192D3×C22⋊C4—61no—
193#875—31no—
194#875—31no—
195#875—61no—
196C4×D12C2×D311yescharacteristic
197C4×D12C2×D311yescharacteristic
198C4×D12C2×D311yescharacteristic, complemented
199C3×#107—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×#102—31no—
203C3×#102—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#816—31no—
212#810—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—61no—
218#810—61no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—61no—
227#809—61no—
228#809C2×D311yescharacteristic
229#809C2×D311yescharacteristic
230#808C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C4×C3⋊C8—61no—
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254#634—21no—
255#634—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—22no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—42no—
265C3×D12—81no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272C3×C4×D3—81no—
273C3×C4×D3—81no—
274#626—42no—
275#626—81no—
276#625—42no—
277D3×Dic3—42no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—31no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314#237—62no—
315#237—121no—
316D3×D4—62no—
317D3×D4—121no—
318#235—62no—
319#235—121no—
320C2×D12—21no—
321C2×D12—21no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—62no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—121no—
329C2×D12#6711yescharacteristic
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—21no—
367C3×C42—61no—
368C3×C42C22×D311yescharacteristic
369C3×C42C22×D311yescharacteristic
370#217—61no—
371#214—121no—
372#213—62no—
373#213—62no—
374#213—121no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—121no—
388(C2×D3)⋊C4—121no—
389(C2×D3)⋊C4#6711yescharacteristic
390(C2×D3)⋊C4#6711yescharacteristic
391C4⋊Dic3—61no—
392C4⋊Dic3#6711yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—61no—
397C4×Dic3—21no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—121no—
409#204—121no—
410D3×C8—121no—
411D3×C8—121no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3#13512yes—
428D32—84no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—91no—
442C2×SD16—91no—
443C2×D8—91no—
444C2×D8—91no—
445C22×C8—91no—
446C22×C8—91no—
447#126—61no—
448#125D3211yescharacteristic, complemented
449#124—91no—
450#123—61no—
451#123—181no—
452C22⋊Q8—91no—
453#121—31no—
454#121—31no—
455#121—61no—
456#121—91no—
457#121—181no—
458#120—181no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—61no—
463#117—31no—
464C2×C4⋊C4—31no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#106—31no—
469C4⋊C8—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482C4×C8—91no—
483C23×C3—31no—
484C23×C3—31no—
485C23×C3—61no—
486C23×C3—61no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—121no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—241no—
497C22×D3—241no—
498C22×D3C2×#6711yescharacteristic
499C22×D3C2×#6711yescharacteristic
500C3×D4—32no—
501C3×D4—62no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—122no—
506C3×D4—241no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—241no—
525C2×C3×C4—241no—
526C2×C3×C4—241no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—122no—
534#67—122no—
535#67—122no—
536#67—241no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—121no—
542C2×Dic3—122no—
543C2×Dic3C2×#6711yescharacteristic
544C2×Dic3C2×#6711yescharacteristic
545D12—22no—
546D12—21no—
547D12—21no—
548D12—21no—
549D12—42no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—81no—
555D12—121no—
556D12—121no—
557D12—122no—
558D12—241no—
559D12#23912yes—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—21no—
564C4×D3—81no—
565C4×D3—81no—
566C4×D3—81no—
567C4×D3—122no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—121no—
573Dic6—121no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C3⋊C8—121no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13511yescharacteristic
586C2×C32#57611yescharacteristic
587C3⋊D3—81no—
588C3×D3—22no—
589C3×D3—42no—
590C3×D3—41no—
591C3×D3—81no—
592C24—181no—
593#41—182no—
594#41—361no—
595C2×Q8—91no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—91no—
602C2×D4—181no—
603C2×D4—182no—
604C2×D4—181no—
605C2×D4—181no—
606C2×D4—361no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—181no—
613SD16—361no—
614D8—182no—
615D8—361no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—91no—
619C2×C8—91no—
620C2×C8—361no—
621C2×C8—361no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—61no—
628C4⋊C4—181no—
629C4⋊C4C2×D3211yescharacteristic
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C42—61no—
643C42C2×D3211yescharacteristic
644C22×C3—21no—
645C22×C3—32no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—61no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3C2×D3×D411yescharacteristic
658C22×C3C22×#6711yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—22no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—241no—
679C2×D3—244no—
680C2×D3—244no—
681C2×D3#95012yes—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×#23911yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4#100911yescharacteristic
703C3×C4#100911yescharacteristic
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3—41no—
708Dic3—121no—
709Dic3—121no—
710Dic3—241no—
711C32#329711yescharacteristic, complemented, Sylow
712C23—31no—
713C23—31no—
714C23—61no—
715C23—61no—
716C23—181no—
717C23—362no—
718C23—362no—
719C23—721no—
720Q8—181no—
721Q8—181no—
722D4—32no—
723D4—62no—
724D4—61no—
725D4—61no—
726D4—61no—
727D4—122no—
728D4—181no—
729D4—181no—
730D4—241no—
731D4—362no—
732D4—362no—
733D4—721no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—181no—
745C2×C4—241no—
746C2×C4—241no—
747C2×C4—241no—
748C2×C4—362no—
749C2×C4D3×#6711yescharacteristic
750C2×C4D3×#6711yescharacteristic
751C2×C4C22×D3211yescharacteristic
752C8—61no—
753C8—61no—
754C8—181no—
755C8—181no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—62no—
760C2×C3—121no—
761C2×C3—122no—
762C2×C3—241no—
763C2×C3#563011yescharacteristic
764C2×C3D3×#13511yescharacteristic
765C2×C3#577411yescharacteristic
766C2×C3C2×#95011yescharacteristic
767C2×C3#582911yescharacteristic
768C2×C3#583511yescharacteristic
769D3—22no—
770D3—42no—
771D3—41no—
772D3—81no—
773D3—241no—
774D3—241no—
775D3—481no—
776C22—32no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—62no—
781C22—61no—
782C22—61no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—361no—
789C22—361no—
790C22—361no—
791C22—724no—
792C22C2×D3×#6711yescharacteristic
793C4—21no—
794C4—21no—
795C4—41no—
796C4—41no—
797C4—61no—
798C4—61no—
799C4—121no—
800C4—121no—
801C4—361no—
802C4D3×#23911yescharacteristic
803C4#6432011yescharacteristic
804C3—21no—
805C3#8118711yescharacteristic, complemented
806C3#8361411yescharacteristic, complemented
807C2—62no—
808C2—121no—
809C2—122no—
810C2—241no—
811C2—721no—
812C2#1059542711yescharacteristic
813C2D3×#95011yescharacteristic
814C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
hypercenter#125D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5695C2semidirect
2. #10594003C2semidirect
3. #10592767C2semidirect
4. C3×#5066C2semidirect
5. #10590613C2semidirect
6. #10590608C2semidirect
7. #10590595C2semidirect
8. D3×#809C2semidirect
9. #10590578C2semidirect
10. #10590576C2semidirect
11. #10590427C2semidirect
12. #10590425C2semidirect
13. #10590366C2semidirect
14. C4×#3713C2semidirect
15. #10590329C2semidirect
20. C32×#125C22semidirect
25. C3×#895C22semidirect
28. C3×#892C22semidirect
32. C3×C4×D12C22semidirect
39. C2×#3716C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63637C22semidirect
45. #63637C22semidirect
48. C4×C3⋊(C3⋊C8)C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. C3×C4⋊(C3⋊C8)C22semidirect
54. #63576C22semidirect
55. #63567C22semidirect
58. #63562C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5695D3semidirect
69. #5066D3semidirect
151. C3×#125C2×D3semidirect
152. C3×#125C2×D3semidirect
183. #895C2×D3semidirect
187. #892C2×D3semidirect
198. C4×D12C2×D3semidirect
230. #808C2×D3semidirect
233. #807C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
448. #125D32semidirect
711. C32#3297semidirect
805. C3#81187semidirect
806. C3#83614semidirect

Maximal subgroups

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

subgroupindex
C3×#56952
#105940032
#105927672
C3×#50662
#105906132
#105906082
#105905952
D3×#8092
#105905782
#105905762
#105904272
#105904252
#105903662
C4×#37132
#105903292
#836143
#811873