Finite Group Databasebeta

← #11869679

Subgroups — #11869679

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#117C211yesmaximal, characteristic, complemented
2#10595005C211yesmaximal, characteristic
3#10592702C211yesmaximal, characteristic, complemented
4C3×#4996C211yesmaximal, characteristic, complemented
5D3×#830C211yesmaximal, characteristic, complemented
6#10591136C211yesmaximal, characteristic, complemented
7#10591102C211yesmaximal, characteristic, complemented
8#10590610C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590572C211yesmaximal, characteristic, complemented
11#10590571C211yesmaximal, characteristic, complemented
12#10590517C211yesmaximal, characteristic, complemented
13#10590516C211yesmaximal, characteristic, complemented
14#10590423C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#82215—31nomaximal
17#81515—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×#117C2211yescharacteristic
21#64139C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×D3×C22⋊C4—21no—
29C3×#877—21no—
30C3×#872—21no—
31C3×C42×D3—21no—
32#63977—21no—
33#63952—21no—
34#63909C2211yescharacteristic
35#63904—21no—
36#63856C2211yescharacteristic
37#63850—21no—
38#63841C2211yescharacteristic
39C2×D3×C3⋊C8C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41#63657C2211yescharacteristic
42#63636C2211yescharacteristic, complemented
43#63636C2211yescharacteristic, complemented
44#63635C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46C3×#830C2211yescharacteristic
47C3×#810C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C2×C3×#117—31no—
62#5791—31no—
63#5627—31no—
64D3×#117D311yescharacteristic, complemented
65C3×#485—31no—
66C2×#830—31no—
67#5045—31no—
68#5003—31no—
69#5003—31no—
70#5003—31no—
71#5003—61no—
72#5002—31no—
73#5002—31no—
74#4998—31no—
75#4998—31no—
76#4996—31no—
77#4996D311yescharacteristic, complemented
78#4971—31no—
79#4970—31no—
80#4968—31no—
81#4967—31no—
82#4882—31no—
83#4880—31no—
84#4863—31no—
85#4860—31no—
86#4811—31no—
87#4805—31no—
88#4804—31no—
89#4804—31no—
90#4737—31no—
91D3×C22⋊C8—31no—
92C23×C3×D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C22×C3×Dic3D411yescharacteristic
97C2×C3×C4×D3—22no—
98C2×C3×C4×D3—22no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3D411yescharacteristic
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109#3799—22no—
110#3799—22no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139D3×C3⋊C8—22no—
140D3×C3⋊C8—22no—
141#3091—91noSylow
142C23×C3×C4—31no—
143C2×#239—31no—
144C2×#235—31no—
145C22×C4×D3C2×D311yescharacteristic
146C3×C22⋊Q8—31no—
147C3×#117—21no—
148C3×#117—31no—
149C3×#117—31no—
150C3×#117—31no—
151C3×#117—61no—
152C3×#117—61no—
153C3×#117C2×D311yescharacteristic
154C3×#117C2×D311yescharacteristic
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C22⋊C4—61no—
158C2×C3×C42—61no—
159#953—61no—
160#946—31no—
161#930—31no—
162#930—31no—
163#930—31no—
164#930—61no—
165#929—61no—
166C4×#67—61no—
167C4×#67—61no—
168#926—31no—
169#926C2×D311yescharacteristic
170#924—31no—
171#924C2×D311yescharacteristic
172C22×C3⋊C8—31no—
173C22×C3⋊C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176#895—31no—
177#894—61no—
178#893—61no—
179#892—31no—
180#892C2×D311yescharacteristic
181#892C2×D311yescharacteristic
182D3×C4⋊C4C2×D311yescharacteristic
183D3×C4⋊C4C2×D311yescharacteristic
184#882—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—21no—
187#877—21no—
188#872—21no—
189C42×D3—21no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×C22⋊C8—31no—
195#835—31no—
196#835—31no—
197#830—31no—
198#830—31no—
199#830—31no—
200#830—31no—
201#830—61no—
202#830C2×D311yescharacteristic
203#821—31no—
204#821—31no—
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207#818—31no—
208#817—31no—
209#810—31no—
210#810—31no—
211#810C2×D311yescharacteristic, complemented
212#810C2×D311yescharacteristic, complemented
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—61no—
220#809—61no—
221#808—31no—
222#808—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#808C2×D311yescharacteristic, complemented
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic, complemented
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3—22no—
238C22×C3×D3—22no—
239C22×C3×D3—41no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248#638—42no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—22no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—22no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×C4×D3#4112yes—
266C3×C4×D3#4112yes—
267C3×Dic6—21no—
268C3×Dic6—21no—
269#626—42no—
270#626—42no—
271#624—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#525—91no—
277C2×#117—31no—
278#485—31no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—91no—
287#427—91no—
288#416—91no—
289#416—91no—
290C2×C22⋊C8—91no—
291C24×C3—31no—
292C23×D3#6711yescharacteristic
293C2×C3×Q8—31no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—62no—
301C22×C3×C4—62no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—121no—
311C22×Dic3#6711yescharacteristic
312#239—62no—
313#239—62no—
314#235—62no—
315#235—62no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×C4×D3—22no—
322C2×C4×D3—22no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3#6711yescharacteristic
328C2×C4×D3#6711yescharacteristic
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—41no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42—61no—
359#217—21no—
360#217—21no—
361#217—61no—
362#217—61no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—62no—
395C2×C3⋊C8—62no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D3×C8—62no—
399D3×C8—62no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—44no—
412C2×C3×D3#12312yes—
413C2×C3×D3#13512yes—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3#12312yes—
426C2×#41—91no—
427C23×C4—31no—
428C22×C8—91no—
429C22×C8—91no—
430#123—181no—
431C22⋊Q8—31no—
432C22⋊Q8—91no—
433#121—91no—
434#121—91no—
435#120—181no—
436C4×D4—181no—
437C4×D4—181no—
438#117—31no—
439#117—31no—
440#117—31no—
441#117—61no—
442#117—61no—
443#117—91no—
444#117D3211yescharacteristic
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C22⋊C4—61no—
448C2×C42—61no—
449#107—31no—
450#107—91no—
451#107—91no—
452#107—91no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457#103—31no—
458#103—31no—
459#103—91no—
460#103—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—62no—
473C23×C3—62no—
474C23×C3—121no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×#6711yescharacteristic
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—41no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—121no—
483C22×D3C2×#6711yescharacteristic
484C22×D3C2×#6711yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—122no—
521#67—122no—
522#67—122no—
523#67—122no—
524#67—242no—
525C2×Dic3—22no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3C2×#6711yescharacteristic
534C2×Dic3C2×#6711yescharacteristic
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12—121no—
541D12—122no—
542D12—122no—
543C4×D3—22no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—22no—
547C4×D3—42no—
548C4×D3—42no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3#23512yes—
552C4×D3#23512yes—
553Dic6—21no—
554Dic6—21no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—121no—
564C3⋊C8—121no—
565C2×C32—41no—
566C2×C32C2×#12311yescharacteristic
567C2×C32C2×#13511yescharacteristic
568C2×C32#57511yescharacteristic
569C3⋊D3—81no—
570C3×D3—22no—
571C3×D3—22no—
572C24—31no—
573#41—182no—
574#41—182no—
575C2×Q8—31no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4—181no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—181no—
590C22×C4C2×D3211yescharacteristic
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C2×C8—182no—
596C2×C8—182no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C4⋊C4C2×D3211yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—21no—
617C42—61no—
618C42—61no—
619C42—61no—
620C42—181no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—32no—
629C22×C3—32no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—124no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C22×#6711yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—44no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3—241no—
654C2×D3#92912yes—
655C2×D3#95012yes—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—32no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4C2×#23511yescharacteristic
674C3×C4C2×#23511yescharacteristic
675C3×C4D3×#4111yescharacteristic
676C3×C4D3×#4111yescharacteristic
677Dic3—21no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685Dic3#92912yes—
686C32#309111yescharacteristic, complemented, Sylow
687C23—31no—
688C23—31no—
689C23—62no—
690C23—62no—
691C23—121no—
692C23—181no—
693C23D3×#6711yescharacteristic
694Q8—61no—
695Q8—61no—
696D4—181no—
697D4—181no—
698D4—362no—
699D4—362no—
700D4—362no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—31no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—181no—
721C2×C4—362no—
722C2×C4D3×#6711yescharacteristic
723C2×C4C22×D3211yescharacteristic
724C8—61no—
725C8—61no—
726C8—181no—
727C8—181no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—41no—
732C2×C3—41no—
733C2×C3—62no—
734C2×C3—62no—
735C2×C3—81no—
736C2×C3D3×#12311yescharacteristic
737C2×C3D3×#13511yescharacteristic
738C2×C3#577711yescharacteristic
739C2×C3C2×#92911yescharacteristic
740C2×C3C2×#95011yescharacteristic
741C2×C3#582211yescharacteristic
742D3—22no—
743D3—22no—
744D3—241no—
745D3—241no—
746D3—481no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—32no—
751C22—32no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—61no—
756C22—124no—
757C22—361no—
758C22—361no—
759C22—361no—
760C22C2×D3×#6711yescharacteristic
761C4—21no—
762C4—32no—
763C4—41no—
764C4—41no—
765C4—61no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—361no—
771C4D3×#23511yescharacteristic
772C4D3×#23511yescharacteristic
773C3—21no—
774C3#8151511yescharacteristic, complemented
775C3#8221511yescharacteristic, complemented
776C2—41no—
777C2—62no—
778C2—62no—
779C2—721no—
780C2D3×#92911yescharacteristic
781C2D3×#95011yescharacteristic
782C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595005C2
hypercenter#117D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×D3×#117C2semidirect
3. #10592702C2semidirect
4. C3×#4996C2semidirect
5. D3×#830C2semidirect
6. #10591136C2semidirect
7. #10591102C2semidirect
8. #10590610C2semidirect
9. #10590610C2semidirect
10. #10590572C2semidirect
11. #10590571C2semidirect
12. #10590517C2semidirect
13. #10590516C2semidirect
14. #10590423C2semidirect
15. #10590422C2semidirect
42. #63636C22semidirect
43. #63636C22semidirect
44. #63635C22semidirect
45. #63634C22semidirect
47. C3×#810C22semidirect
48. C3×#810C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
64. D3×#117D3semidirect
77. #4996D3semidirect
211. #810C2×D3semidirect
212. #810C2×D3semidirect
227. #808C2×D3semidirect
234. #807C2×D3semidirect
686. C32#3091semidirect
774. C3#81515semidirect
775. C3#82215semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1172
#105950052
#105927022
C3×#49962
D3×#8302
#105911362
#105911022
#105906102
#105905722
#105905712
#105905172
#105905162
#105904232
#105904222
#822153
#815153