Finite Group Databasebeta

← #11869691

Subgroups — #11869691

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#117C211yesmaximal, characteristic, complemented
2#10595034C211yesmaximal, characteristic
3C3×#5002C211yesmaximal, characteristic, complemented
4C3×#4998C211yesmaximal, characteristic, complemented
5#10591122C211yesmaximal, characteristic, complemented
6#10591084C211yesmaximal, characteristic, complemented
7C2×#63557C211yesmaximal, characteristic, complemented
8#10590529C211yesmaximal, characteristic, complemented
9#10590528C211yesmaximal, characteristic, complemented
10#10590527C211yesmaximal, characteristic, complemented
11#10590526C211yesmaximal, characteristic, complemented
12#10590513C211yesmaximal, characteristic, complemented
13#10590512C211yesmaximal, characteristic, complemented
14#10590511C211yesmaximal, characteristic, complemented
15#10590510C211yesmaximal, characteristic, complemented
16#79185—31nomaximal
17#78842—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×#117C2211yescharacteristic
21#64135C2211yescharacteristic
22#64101C2211yescharacteristic
23#64101C2211yescharacteristic
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2211yescharacteristic
26C22⋊C4×C3⋊D3—21no—
27#64086—21no—
28#64081—21no—
29C42×C3⋊D3—21no—
30C3×#926C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33#63981—21no—
34#63962—21no—
35#63916C2211yescharacteristic
36#63916C2211yescharacteristic
37C4×#626—21no—
38C4×#626—21no—
39#63871C2211yescharacteristic
40#63871C2211yescharacteristic
41C3×#810C2211yescharacteristic, complemented
42C3×#810C2211yescharacteristic, complemented
43C3×#809C2211yescharacteristic, complemented
44C3×#809C2211yescharacteristic, complemented
45C3×#808C2211yescharacteristic, complemented
46C3×#808C2211yescharacteristic, complemented
47C3×#807C2211yescharacteristic, complemented
48C3×#807C2211yescharacteristic, complemented
49#63575C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63557C2211yescharacteristic
58#63557C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61#5828—31no—
62#5524—31no—
63D3×#117—31no—
64D3×#117—31no—
65D3×#117—61no—
66C3×#427—31no—
67C3×#416—31no—
68#5233—31no—
69#5113—31no—
70C2×(C2×D3)⋊C8—31no—
71C2×(C2×D3)⋊C8—31no—
72#5106—31no—
73#5002D311yescharacteristic, complemented
74#4998—31no—
75#4998D311yescharacteristic, complemented
76#4888—31no—
77#4885—31no—
78#4884—31no—
79#4882—31no—
80#4868—31no—
81#4866—31no—
82#4863—31no—
83#4862—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
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3D411yescharacteristic
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3D411yescharacteristic
100C2×C4×C3⋊D3D411yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×#67—21no—
104C3×#235—22no—
105C3×#235—22no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42—21no—
115#3757—21no—
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3—21no—
125C3×#217—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8—22no—
130C2×C3×C3⋊C8—22no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3091—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—61no—
147C22×C3×C8—31no—
148C22×C3×C8—31no—
149C3×#117—21no—
150C3×#117—31no—
151C3×#117C2×D311yescharacteristic
152C3×#117C2×D311yescharacteristic
153#946—31no—
154#946—31no—
155#938—31no—
156#938—31no—
157#937—61no—
158#935—61no—
159C4×#67—61no—
160C4×#67—61no—
161#926—31no—
162#926—31no—
163#926—61no—
164#926C2×D311yescharacteristic
165C22×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊C8C2×D311yescharacteristic
167#897—31no—
168#897—31no—
169#895—31no—
170#895—31no—
171#892—31no—
172#892—31no—
173#892—31no—
174#892—31no—
175#892—61no—
176#892—61no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—31no—
181D3×C4⋊C4—61no—
182D3×C4⋊C4—61no—
183#886—61no—
184#882—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—62no—
188#877—61no—
189#877—61no—
190#877—62no—
191C4×D12—61no—
192C4×D12—61no—
193#872—61no—
194#872—61no—
195#872—62no—
196C42×D3—61no—
197C42×D3—61no—
198C42×D3—62no—
199C3×#107—31no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#821—31no—
212#821—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#818—31no—
222#818—31no—
223#817—31no—
224#817—31no—
225#816—31no—
226#816—31no—
227#810C2×D311yescharacteristic, complemented
228#810C2×D311yescharacteristic, complemented
229#809C2×D311yescharacteristic, complemented
230#809C2×D311yescharacteristic, complemented
231#808—31no—
232#808—31no—
233#808C2×D311yescharacteristic, complemented
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237#807C2×D311yescharacteristic, complemented
238#807C2×D311yescharacteristic, complemented
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—22no—
241C22×C3⋊D3—22no—
242C22×C3⋊D3—41no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4#4112yes—
250C2×C32×C4#4112yes—
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—22no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4×C3⋊D3—22no—
258C4×C3⋊D3—22no—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—42no—
264C4×C3⋊D3—42no—
265C3×#67—42no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×C4×D3—42no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#626—42no—
275#626—42no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280#525—91no—
281C2×#117—91no—
282#485—91no—
283#485—91no—
284#484—91no—
285#483—91no—
286#482—91no—
287#482—91no—
288#481—91no—
289#480—91no—
290#427—31no—
291#427—91no—
292#416—31no—
293#416—91no—
294C2×C22⋊C8—91no—
295C23×D3—31no—
296C23×D3—31no—
297C23×D3—61no—
298C3×#41—62no—
299C3×#41—62no—
300C2×C3×Q8—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C22×C3×C4—21no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—61no—
313#235—22no—
314#235—22no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12C22×D311yescharacteristic
318C2×C4×D3—21no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—64no—
332C2×C4×D3—64no—
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—62no—
342C2×C4×D3—62no—
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—62no—
349C2×C3×C8—62no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—22no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—61no—
362C3×C42—22no—
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—61no—
366#217—21no—
367#217—61no—
368#217—61no—
369#217—62no—
370#217—61no—
371#217—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—62no—
383(C2×D3)⋊C4—62no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—62no—
401Dic3⋊C4—62no—
402C4×Dic3—21no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—62no—
408C4×Dic3—62no—
409C4×Dic3—62no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C2×C3⋊C8—22no—
413C2×C3⋊C8—22no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418C22×C32—21no—
419C22×C32—21no—
420C22×C32#12312yes—
421C22×C32C22×D411yescharacteristic
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—44no—
428C2×C3⋊D3#13512yes—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4#12312yes—
435C32×C4C2×#4111yescharacteristic
436C32×C4C2×#4111yescharacteristic
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C2×#41—31no—
445C23×C4—91no—
446C22×C8—31no—
447C22×C8—31no—
448#123—181no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—91no—
452#121—91no—
453#120—181no—
454C4×D4—181no—
455C4×D4—181no—
456#117—31no—
457#117—91no—
458#117—91no—
459#117—91no—
460#117—181no—
461#117—181no—
462#117D3211yescharacteristic
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—181no—
466C2×C42—181no—
467#107—31no—
468#107—31no—
469#107—91no—
470#107—91no—
471#106—31no—
472#106—31no—
473#106—91no—
474#106—91no—
475#103—31no—
476#103—31no—
477#103—91no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483C22⋊C8—91no—
484C22⋊C8—91no—
485C22⋊C8—91no—
486C22⋊C8—91no—
487C23×C3—21no—
488C23×C3—61no—
489C23×C3D3×D411yescharacteristic
490C23×C3D3×D411yescharacteristic
491C22×D3—21no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—62no—
499C22×D3—62no—
500C22×D3—64no—
501C22×D3—62no—
502C22×D3—62no—
503C22×D3—122no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—122no—
507C3×Q8—61no—
508C3×Q8—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—122no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—122no—
526C2×C3×C4#23512yes—
527C2×C3×C4#23512yes—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4#23712yes—
531C2×C3×C4#23912yes—
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—42no—
535#67—122no—
536#67—122no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—64no—
547C2×Dic3—62no—
548C2×Dic3—62no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555D12—21no—
556D12—21no—
557D12—122no—
558D12—122no—
559C4×D3—42no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—62no—
563C4×D3—62no—
564C4×D3—64no—
565C4×D3—64no—
566C4×D3—62no—
567C4×D3—62no—
568C4×D3—62no—
569C4×D3—62no—
570C4×D3—61no—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—61no—
574C4×D3—61no—
575C4×D3—61no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—124no—
581C4×D3—124no—
582C4×D3—122no—
583C4×D3—122no—
584Dic6—21no—
585Dic6—21no—
586C3×C8—61no—
587C3×C8—61no—
588C3×C8—61no—
589C3×C8—61no—
590C3⋊C8—21no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C2×C32—22no—
595C2×C32C2×#12311yescharacteristic
596C2×C32C2×#13511yescharacteristic
597C2×C32#57511yescharacteristic
598C3⋊D3—22no—
599C3⋊D3—41no—
600C3×D3—81no—
601C24—91no—
602#41—62no—
603#41—62no—
604C2×Q8—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—181no—
608C2×D4—181no—
609C22×C4—61no—
610C22×C4—91no—
611C22×C4—91no—
612C22×C4—91no—
613C22×C4—91no—
614C22×C4—91no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—182no—
618C22×C4—182no—
619C22×C4C2×D3211yescharacteristic
620C2×C8—31no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—62no—
625C2×C8—62no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—91no—
629C4⋊C4—91no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4C2×D3211yescharacteristic
635C4⋊C4C2×D3211yescharacteristic
636C22⋊C4—21no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C42—21no—
646C42—61no—
647C42—181no—
648C42—181no—
649C42—181no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—22no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3#88312yes—
662C22×C3#89412yes—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C2×D3—32no—
666C2×D3—32no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—62no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—124no—
687C2×D3—124no—
688C2×D3—128no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—22no—
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4#88312yes—
702C3×C4#89412yes—
703C3×C4C2×#23511yescharacteristic
704C3×C4C2×#23511yescharacteristic
705C3×C4C2×#23711yescharacteristic
706C3×C4C2×#23911yescharacteristic
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710Dic3—62no—
711Dic3—62no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—61no—
716Dic3—122no—
717Dic3—122no—
718Dic3—121no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722C32#309111yescharacteristic, complemented, Sylow
723C23—61no—
724C23—91no—
725C23—91no—
726C23—182no—
727C23—182no—
728C23—361no—
729C23#381111yescharacteristic
730Q8—61no—
731Q8—61no—
732D4—61no—
733D4—61no—
734D4—122no—
735D4—362no—
736D4—362no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—122no—
745C2×C4—182no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—182no—
751C2×C4—182no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—362no—
755C2×C4—362no—
756C2×C4#379612yes—
757C2×C4#379812yes—
758C2×C4#381111yescharacteristic
759C2×C4C22×D3211yescharacteristic
760C8—61no—
761C8—61no—
762C8—61no—
763C8—61no—
764C2×C3—22no—
765C2×C3—22no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—241no—
771C2×C3C2×#88311yescharacteristic
772C2×C3C2×#89411yescharacteristic
773C2×C3D3×#13511yescharacteristic
774C2×C3D3×#13511yescharacteristic
775C2×C3#576811yescharacteristic
776C2×C3#576811yescharacteristic
777D3—64no—
778D3—62no—
779D3—62no—
780D3—81no—
781D3—122no—
782D3—121no—
783D3—121no—
784C22—21no—
785C22—21no—
786C22—92no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—181no—
791C22—181no—
792C22—181no—
793C22—181no—
794C22—181no—
795C22—364no—
796C22#6385312yes—
797C22C2×#381111yescharacteristic
798C4—41no—
799C4—41no—
800C4—121no—
801C4—121no—
802C4—121no—
803C4—181no—
804C4—181no—
805C4—361no—
806C4—361no—
807C4#6385312yes—
808C4C2×#379611yescharacteristic
809C4C2×#379811yescharacteristic
810C3—21no—
811C3#7884211yescharacteristic, complemented
812C3#7918511yescharacteristic, complemented
813C2—22no—
814C2—182no—
815C2—241no—
816C2—361no—
817C2C2×#6385311yescharacteristic
818C2#1059545911yescharacteristic
819C2#1059546011yescharacteristic
subgroupG/H
centerC2×C4#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595034C2
hypercenter#117D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#117C2semidirect
3. C3×#5002C2semidirect
4. C3×#4998C2semidirect
5. #10591122C2semidirect
6. #10591084C2semidirect
7. C2×#63557C2semidirect
8. #10590529C2semidirect
9. #10590528C2semidirect
10. #10590527C2semidirect
11. #10590526C2semidirect
12. #10590513C2semidirect
13. #10590512C2semidirect
14. #10590511C2semidirect
15. #10590510C2semidirect
41. C3×#810C22semidirect
42. C3×#810C22semidirect
43. C3×#809C22semidirect
44. C3×#809C22semidirect
45. C3×#808C22semidirect
46. C3×#808C22semidirect
47. C3×#807C22semidirect
48. C3×#807C22semidirect
49. #63575C22semidirect
50. #63575C22semidirect
51. #63573C22semidirect
52. #63573C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
73. #5002D3semidirect
75. #4998D3semidirect
227. #810C2×D3semidirect
228. #810C2×D3semidirect
229. #809C2×D3semidirect
230. #809C2×D3semidirect
233. #808C2×D3semidirect
234. #808C2×D3semidirect
237. #807C2×D3semidirect
238. #807C2×D3semidirect
722. C32#3091semidirect
811. C3#78842semidirect
812. C3#79185semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
#105950342
C3×#50022
C3×#49982
#105911222
#105910842
C2×#635572
#105905292
#105905282
#105905272
#105905262
#105905132
#105905122
#105905112
#105905102
#791853
#788423