Finite Group Databasebeta

← #11869698

Subgroups — #11869698

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×#5606C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic, complemented
3#10592734C211yesmaximal, characteristic, complemented
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591420C211yesmaximal, characteristic, complemented
6#10591420C211yesmaximal, characteristic, complemented
7#10591415C211yesmaximal, characteristic, complemented
8#10591413C211yesmaximal, characteristic, complemented
9D3×#830C211yesmaximal, characteristic, complemented
10#10591127C211yesmaximal, characteristic, complemented
11#10591102C211yesmaximal, characteristic, complemented
12#10590572C211yesmaximal, characteristic, complemented
13#10590571C211yesmaximal, characteristic, complemented
14#10590440C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#82913—31nomaximal
17#81371—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C32×#121C2211yescharacteristic
21#64135C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C3×#937—21no—
24C3×D4×Dic3—21no—
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#892C2211yescharacteristic
29C3×#883—21no—
30C3×#67⋊C4—21no—
31D3×#217—21no—
32#63955—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35C4×D3×Dic3—21no—
36#63855—21no—
37#63841C2211yescharacteristic
38#63841C2211yescharacteristic
39C2×D3×C3⋊C8C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41#63659C2211yescharacteristic, complemented
42#63659C2211yescharacteristic, complemented
43#63657C2211yescharacteristic
44#63635C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#525—31no—
62C2×#926—31no—
63#5606D311yescharacteristic
64D3×#117—31no—
65C3×#482—31no—
66#5233—31no—
67#5233—31no—
68C2×#830—31no—
69#5045—31no—
70#5045—31no—
71#5044—31no—
72#5043—31no—
73#5035—31no—
74#5035—31no—
75#5035—61no—
76#5035D311yescharacteristic, complemented
77#5034—31no—
78#5033—31no—
79#4998—31no—
80#4998—31no—
81#4996—31no—
82#4884—31no—
83#4880—31no—
84#4862—31no—
85#4860—31no—
86#4777—31no—
87#4774—31no—
88#4772—31no—
89#4772—31no—
90D3×C22⋊C8—31no—
91#4723—31no—
92C23×C3×D3D411yescharacteristic
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3D411yescharacteristic
100C3×#237—22no—
101C3×#237—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139D3×C3⋊C8—22no—
140D3×C3⋊C8—22no—
141#3091—91noSylow
142C2×C3×#41—31no—
143C23×C3×C4—31no—
144C2×#237C2×D311yescharacteristic
145C22×C4×D3C2×D311yescharacteristic
146C3×#123—61no—
147C3×C22⋊Q8—31no—
148C3×C22⋊Q8—31no—
149C3×#121—21no—
150C3×#121—31no—
151C3×#121C2×D311yescharacteristic
152C3×#121C2×D311yescharacteristic
153C3×#120—61no—
154C3×C4×D4—61no—
155C3×C4×D4—61no—
156C3×#117—31no—
157C3×#117—31no—
158C2×#217—61no—
159#938C2×D311yescharacteristic
160#937—21no—
161D4×Dic3—21no—
162#926—31no—
163#926—31no—
164#926—31no—
165#926—31no—
166#926—61no—
167#926—61no—
168#926—61no—
169#926C2×D311yescharacteristic
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172#924C2×D311yescharacteristic
173C2×C4×Dic3—61no—
174C22×C3⋊C8—31no—
175C22×C3⋊C8—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#897C2×D311yescharacteristic
179#892—31no—
180#892—31no—
181#892C2×D311yescharacteristic
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184#883—21no—
185#67⋊C4—21no—
186D3×C22⋊C4—61no—
187#877—61no—
188#872—61no—
189C42×D3—61no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#102—31no—
193C3×#102—31no—
194C3×C22⋊C8—31no—
195#835—31no—
196#835—31no—
197#835—31no—
198#835—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—61no—
204#832—61no—
205#832C2×D311yescharacteristic, complemented
206#832C2×D311yescharacteristic, complemented
207#830—31no—
208#830—31no—
209#830—31no—
210#830—31no—
211#830—61no—
212#830C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215#818—31no—
216#817—31no—
217#816—31no—
218#816—31no—
219#810—31no—
220#810—31no—
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×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3×D3—22no—
238C22×C3×D3—22no—
239C22×C3×D3—41no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—42no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C3×#67—42no—
253C3×#67—42no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—22no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—22no—
266C3×C4×D3#4112yes—
267C3×C4×D3#4112yes—
268C3×Dic6—21no—
269C3×Dic6—21no—
270D3×Dic3—42no—
271D3×Dic3—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#525—31no—
277C2×#117—91no—
278#485—91no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—31no—
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
293C3×#41—62no—
294C3×#41—62no—
295C2×C3×Q8—31no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—41no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—62no—
311C22×C3×C4—62no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—21no—
316C2×#67—21no—
317C22×Dic3—21no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3#6711yescharacteristic
321#237—22no—
322#237—22no—
323C2×C4×D3—22no—
324C2×C4×D3—22no—
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—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—41no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—61no—
351C3×C42—61no—
352#217—21no—
353#217—21no—
354#217—21no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364C4⋊Dic3—21no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379C4×Dic3—21no—
380C4×Dic3—21no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—121no—
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×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C22×D411yescharacteristic
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×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3#12312yes—
426C2×#41—31no—
427C23×C4—31no—
428C22×C8—91no—
429C22×C8—91no—
430#123—61no—
431C22⋊Q8—31no—
432C22⋊Q8—31no—
433#121—31no—
434#121D3211yescharacteristic
435#120—61no—
436C4×D4—61no—
437C4×D4—61no—
438#117—31no—
439#117—31no—
440#117—91no—
441#117—91no—
442#117—91no—
443#117—181no—
444#117—181no—
445C2×C4⋊C4—91no—
446C2×C4⋊C4—91no—
447C2×C22⋊C4—181no—
448C2×C42—181no—
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—91no—
458#103—91no—
459#103—91no—
460#103—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—31no—
474C23×C3—41no—
475C23×C3—62no—
476C23×C3—62no—
477C23×C3—121no—
478C23×C3D3×D411yescharacteristic
479C23×C3C2×#6711yescharacteristic
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—41no—
483C22×D3C2×#6711yescharacteristic
484C22×D3C2×#6711yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—42no—
494C3×D4—42no—
495C3×D4—82no—
496C3×D4—122no—
497C3×D4—122no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—62no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—122no—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—42no—
528#67—42no—
529C2×Dic3—22no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—42no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—122no—
542C2×Dic3—122no—
543C2×Dic3C2×#6711yescharacteristic
544C2×Dic3C2×#6711yescharacteristic
545C4×D3—22no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—22no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3#23712yes—
552C4×D3#23712yes—
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×C32—81no—
567C2×C32C2×#12311yescharacteristic
568C2×C32C2×#13511yescharacteristic
569C2×C32#57511yescharacteristic
570C3×D3—22no—
571C3×D3—22no—
572C24—31no—
573#41—62no—
574#41—62no—
575C2×Q8—31no—
576C2×D4—21no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4C2×D3211yescharacteristic
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—181no—
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—91no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4C2×D3211yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—61no—
617C42—61no—
618C42—181no—
619C42—181no—
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—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—124no—
647C22×C3C2×D3×D411yescharacteristic
648C22×C3C22×#6711yescharacteristic
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—44no—
654C2×D3#93512yes—
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—61no—
665C3×C4—81no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C2×#23711yescharacteristic
671C3×C4C2×#23711yescharacteristic
672C3×C4D3×#4111yescharacteristic
673C3×C4D3×#4111yescharacteristic
674Dic3—21no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—241no—
684Dic3—241no—
685Dic3#93512yes—
686C32#309111yescharacteristic, complemented, Sylow
687C23—21no—
688C23—31no—
689C23—31no—
690C23—62no—
691C23—62no—
692C23—121no—
693C23D3×#6711yescharacteristic
694Q8—61no—
695Q8—61no—
696D4—21no—
697D4—21no—
698D4—42no—
699D4—122no—
700D4—122no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—31no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—122no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—362no—
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×C3—81no—
737C2×C3—81no—
738C2×C3—161no—
739C2×C3D3×#12311yescharacteristic
740C2×C3D3×#13511yescharacteristic
741C2×C3#577311yescharacteristic
742C2×C3C2×#93511yescharacteristic
743C2×C3C2×#95011yescharacteristic
744C2×C3#582211yescharacteristic
745D3—22no—
746D3—22no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—32no—
751C22—32no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—124no—
760C22C2×D3×#6711yescharacteristic
761C4—21no—
762C4—32no—
763C4—41no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—361no—
770C4—361no—
771C4D3×#23711yescharacteristic
772C4D3×#23711yescharacteristic
773C3—21no—
774C3#8137111yescharacteristic, complemented
775C3#8291311yescharacteristic, complemented
776C2—41no—
777C2—62no—
778C2—62no—
779C2—81no—
780C2#1059509511yescharacteristic
781C2D3×#93511yescharacteristic
782C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5606C2
hypercenter#121D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. D3×#926C2semidirect
3. #10592734C2semidirect
4. C3×#5035C2semidirect
5. #10591420C2semidirect
6. #10591420C2semidirect
7. #10591415C2semidirect
8. #10591413C2semidirect
9. D3×#830C2semidirect
10. #10591127C2semidirect
11. #10591102C2semidirect
12. #10590572C2semidirect
13. #10590571C2semidirect
14. #10590440C2semidirect
15. #10590439C2semidirect
41. #63659C22semidirect
42. #63659C22semidirect
44. #63635C22semidirect
45. #63634C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
76. #5035D3semidirect
205. #832C2×D3semidirect
206. #832C2×D3semidirect
227. #808C2×D3semidirect
234. #807C2×D3semidirect
686. C32#3091semidirect
774. C3#81371semidirect
775. C3#82913semidirect

Maximal subgroups

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

subgroupindex
C3×#56062
D3×#9262
#105927342
C3×#50352
#105914202
#105914152
#105914132
D3×#8302
#105911272
#105911022
#105905722
#105905712
#105904402
#105904392
#829133
#813713