Finite Group Databasebeta

← #11869686

Subgroups — #11869686

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5828C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic, complemented
3#10592932C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591559C211yesmaximal, characteristic, complemented
6#10591558C211yesmaximal, characteristic, complemented
7#10591551C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10591423C211yesmaximal, characteristic, complemented
10#10591422C211yesmaximal, characteristic, complemented
11#10591415C211yesmaximal, characteristic, complemented
12#10591413C211yesmaximal, characteristic, complemented
13#10591138C211yesmaximal, characteristic, complemented
14#10591122C211yesmaximal, characteristic, complemented
15C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
16#82913—31nomaximal
17#78842—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20#64135C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×#937—21no—
27C3×#935—21no—
28C3×C4×#67—21no—
29C3×C4×#67—21no—
30C3×#926C2211yescharacteristic
31C3×#926C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33D3×#217—21no—
34#63955—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37C4×D3×Dic3—21no—
38#63855—21no—
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic
41#63662C2211yescharacteristic, complemented
42#63662C2211yescharacteristic, complemented
43#63659C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45C3×#835C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49#63576C2211yescharacteristic, complemented
50#63576C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#525—31no—
62#5828D311yescharacteristic
63C2×#926—31no—
64D3×#117—31no—
65C3×#416—31no—
66#5233—31no—
67#5233—31no—
68#5233—61no—
69#5233D311yescharacteristic, complemented
70C2×#830—31no—
71C2×(C2×D3)⋊C8—31no—
72#5106—31no—
73#5045—31no—
74#5045—31no—
75#5044—31no—
76#5043—31no—
77#5035—31no—
78#5035—31no—
79#5034—31no—
80#5033—31no—
81#4998—31no—
82#4998—31no—
83#4998—31no—
84#4815—31no—
85#4814—31no—
86#4811—31no—
87#4805—31no—
88#4784—31no—
89#4779—31no—
90#4777—31no—
91#4774—31no—
92C23×C3×D3D411yescharacteristic
93C32×#41—22no—
94C32×#41—22no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3D411yescharacteristic
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3757—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)—22no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8—22no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3091—91noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C2×D311yescharacteristic
145C23×C3×C4—31no—
146C22×C4×D3C2×D311yescharacteristic
147C22×C3×C8—31no—
148C3×#123—61no—
149C3×C22⋊Q8—31no—
150C3×C22⋊Q8—31no—
151C3×#121—31no—
152C3×#121—31no—
153C3×#120—61no—
154C3×C4×D4—61no—
155C3×C4×D4—61no—
156C3×#117—31no—
157C3×#117—31no—
158C2×#217—61no—
159#946C2×D311yescharacteristic
160#946C2×D311yescharacteristic
161#938C2×D311yescharacteristic
162#938C2×D311yescharacteristic
163#937—21no—
164#935—21no—
165C4×#67—21no—
166C4×#67—21no—
167#926—31no—
168#926—31no—
169#926—31no—
170#926—31no—
171#926—61no—
172#926—61no—
173#926—61no—
174#926C2×D311yescharacteristic
175#926C2×D311yescharacteristic
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4×Dic3—61no—
179C22×C3⋊C8—31no—
180C22×C3⋊C8—31no—
181C22×C3⋊C8—61no—
182C22×C3⋊C8C2×D311yescharacteristic
183#892—31no—
184#892—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C22⋊C4—61no—
188#877—61no—
189#872—61no—
190C42×D3—61no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#102—31no—
194C3×#102—31no—
195#835—31no—
196#835—31no—
197#835—31no—
198#835—31no—
199#835—61no—
200#835—61no—
201#835C2×D311yescharacteristic, complemented
202#835C2×D311yescharacteristic, complemented
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—61no—
208#832—61no—
209#832C2×D311yescharacteristic, complemented
210#832C2×D311yescharacteristic, complemented
211#830—31no—
212#830—31no—
213#830—31no—
214#830—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219#818—31no—
220#818—31no—
221#817—31no—
222#817—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
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×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4—42no—
247C2×C32×C4—21no—
248C2×C32×C4—42no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4#4112yes—
251C2×C32×C4#4112yes—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C3×#67—42no—
256C3×#67—42no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×C4×D3—22no—
265C3×C4×D3—22no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—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—91no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—91no—
287#427—91no—
288#416—31no—
289#416—91no—
290C2×C22⋊C8—91no—
291C24×C3—31no—
292C23×D3#6711yescharacteristic
293C3×#41—24no—
294C3×#41—22no—
295C3×#41—22no—
296C3×#41—22no—
297C3×#41—22no—
298C3×#41—42no—
299C2×C3×Q8—21no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—41no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—41no—
319C22×C3×C4—62no—
320C22×C3×C4—62no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—21no—
324C2×#67—21no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3#6711yescharacteristic
328C2×C4×D3—22no—
329C2×C4×D3—22no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3#6711yescharacteristic
333C2×C4×D3#6711yescharacteristic
334C2×C4×D3C22×D311yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—62no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—61no—
352C3×C42—61no—
353#217—21no—
354#217—21no—
355#217—21no—
356#217—21no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—121no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—121no—
391C2×C3⋊C8—22no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—62no—
399C2×C3⋊C8—62no—
400C2×C3⋊C8—122no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32#12312yes—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—44no—
416C2×C3×D3#13512yes—
417C32×C4—41no—
418C32×C4#12312yes—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41D3211yescharacteristic
430C23×C4—31no—
431C22×C8—31no—
432C22×C8—91no—
433#123—61no—
434C22⋊Q8—31no—
435C22⋊Q8—31no—
436#121—31no—
437#121—31no—
438#120—61no—
439C4×D4—61no—
440C4×D4—61no—
441#117—31no—
442#117—31no—
443#117—91no—
444#117—91no—
445#117—91no—
446#117—181no—
447#117—181no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—91no—
450C2×C22⋊C4—181no—
451C2×C42—181no—
452#107—91no—
453#107—91no—
454#107—91no—
455#107—91no—
456#106—91no—
457#106—91no—
458#106—91no—
459#106—91no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#102—31no—
465#102—31no—
466#102—91no—
467#102—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—31no—
477C23×C3—41no—
478C23×C3—62no—
479C23×C3—62no—
480C23×C3—121no—
481C23×C3D3×D411yescharacteristic
482C23×C3C2×#6711yescharacteristic
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—41no—
486C22×D3C2×#6711yescharacteristic
487C22×D3C2×#6711yescharacteristic
488C3×Q8—22no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—41no—
494C3×D4—22no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—41no—
500C3×D4—44no—
501C3×D4—42no—
502C3×D4—42no—
503C3×D4—122no—
504C3×D4—122no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—44no—
515C2×C3×C4—42no—
516C2×C3×C4—42no—
517C2×C3×C4—62no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4#23512yes—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4#23712yes—
531C2×C3×C4#23712yes—
532C2×C3×C4#23712yes—
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—42no—
537#67—42no—
538C2×Dic3—22no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—122no—
550C2×Dic3—122no—
551C2×Dic3C2×#6711yescharacteristic
552C2×Dic3C2×#6711yescharacteristic
553C4×D3—22no—
554C4×D3—22no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—122no—
560C4×D3—122no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—121no—
570C3⋊C8—121no—
571C2×C32—22no—
572C2×C32—81no—
573C2×C32C2×#12311yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32#57511yescharacteristic
576C3×D3—22no—
577C3×D3—41no—
578C24—31no—
579#41—22no—
580#41—22no—
581C2×Q8C2×D3211yescharacteristic
582C2×D4—21no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4C2×D3211yescharacteristic
586C22×C4—21no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4C2×D3211yescharacteristic
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—62no—
600C2×C8—91no—
601C2×C8—91no—
602C2×C8—182no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C42—61no—
623C42—61no—
624C42—181no—
625C42—181no—
626C42—181no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—32no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—124no—
651C22×C3#88312yes—
652C22×C3#93512yes—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C22×#6711yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—44no—
661C2×D3#95012yes—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—22no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4#88312yes—
675C3×C4#93512yes—
676C3×C4C2×#23511yescharacteristic
677C3×C4C2×#23711yescharacteristic
678C3×C4C2×#23711yescharacteristic
679C3×C4C2×#23711yescharacteristic
680Dic3—21no—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3—241no—
692C32#309111yescharacteristic, complemented, Sylow
693C23—21no—
694C23—31no—
695C23—31no—
696C23—62no—
697C23—62no—
698C23—121no—
699C23D3×#6711yescharacteristic
700Q8—21no—
701Q8—21no—
702D4—21no—
703D4—21no—
704D4—42no—
705D4—122no—
706D4—122no—
707C2×C4—21no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—42no—
711C2×C4—62no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—362no—
725C2×C4—362no—
726C2×C4#380412yes—
727C2×C4#380512yes—
728C2×C4D3×#6711yescharacteristic
729C2×C4C22×D3211yescharacteristic
730C8—61no—
731C8—61no—
732C8—181no—
733C8—181no—
734C2×C3—22no—
735C2×C3—22no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—42no—
740C2×C3—62no—
741C2×C3—82no—
742C2×C3—81no—
743C2×C3—81no—
744C2×C3—121no—
745C2×C3C2×#88311yescharacteristic
746C2×C3D3×#13511yescharacteristic
747C2×C3#576811yescharacteristic
748C2×C3C2×#93511yescharacteristic
749C2×C3C2×#95011yescharacteristic
750C2×C3#582211yescharacteristic
751D3—22no—
752D3—41no—
753C22—21no—
754C22—21no—
755C22—32no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—124no—
765C22#6396912yes—
766C22C2×D3×#6711yescharacteristic
767C4—41no—
768C4—61no—
769C4—61no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—121no—
774C4—361no—
775C4—361no—
776C4#6396912yes—
777C4C2×#380411yescharacteristic
778C4C2×#380511yescharacteristic
779C3—21no—
780C3#7884211yescharacteristic, complemented
781C3#8291311yescharacteristic, complemented
782C2—22no—
783C2—62no—
784C2—81no—
785C2—121no—
786C2D3×#95011yescharacteristic
787C2#1059545311yescharacteristic
788C2C2×#6396911yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5828C2
hypercenterC2×#41D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. D3×#926C2semidirect
3. #10592932C2semidirect
4. C3×#5233C2semidirect
5. #10591559C2semidirect
6. #10591558C2semidirect
7. #10591551C2semidirect
8. #10591549C2semidirect
9. #10591423C2semidirect
10. #10591422C2semidirect
11. #10591415C2semidirect
12. #10591413C2semidirect
13. #10591138C2semidirect
14. #10591122C2semidirect
15. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
41. #63662C22semidirect
42. #63662C22semidirect
43. #63659C22semidirect
44. #63659C22semidirect
45. C3×#835C22semidirect
46. C3×#835C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. #63576C22semidirect
50. #63576C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
69. #5233D3semidirect
201. #835C2×D3semidirect
202. #835C2×D3semidirect
209. #832C2×D3semidirect
210. #832C2×D3semidirect
692. C32#3091semidirect
780. C3#78842semidirect
781. C3#82913semidirect

Maximal subgroups

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

subgroupindex
C3×#58282
D3×#9262
#105929322
C3×#52332
#105915592
#105915582
#105915512
#105915492
#105914232
#105914222
#105914152
#105914132
#105911382
#105911222
C2×(C2×D3)⋊(C3⋊C8)2
#829133
#788423