Finite Group Databasebeta

← #11887401

Subgroups — #11887401

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5554C211yesmaximal, characteristic, complemented
2#10593925C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591452C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591420C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590577C211yesmaximal, characteristic, complemented
10#10590576C211yesmaximal, characteristic, complemented
11#10590449C211yesmaximal, characteristic, complemented
12#10590440C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590329C211yesmaximal, characteristic, complemented
15#10590278C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#81187—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C3×#930—21no—
24C2×C3×(C2×D3)⋊C4—21no—
25C3×#897C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×#886—21no—
28C3×#882—21no—
29C3×#875C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×#870C2211yescharacteristic, complemented
32#63909C2211yescharacteristic
33#63909C2211yescharacteristic, complemented
34D3×C4⋊Dic3C2211yescharacteristic
35#63886—21no—
36#63881—21no—
37#63853—21no—
38#63848—21no—
39#63841C2211yescharacteristic, complemented
40C2×#3717C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63636C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5695—31no—
63#5565—31no—
64#5554D311yescharacteristic, complemented
65C3×#478—31no—
66#5238—31no—
67#5233—31no—
68#5217—31no—
69C2×#832—31no—
70#5068—31no—
71#5057—31no—
72#5056—31no—
73#5048—31no—
74#5044—31no—
75#5038—31no—
76#5035—31no—
77C4×#213—31no—
78C4×#213—31no—
79C4×#213—61no—
80D4×C3⋊C8—31no—
81#5009D311yescharacteristic, complemented
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—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C3×#237—22no—
101C3×#237—41no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C2×C3×D12—21no—
105C2×C3×D12D411yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×D3×Dic3—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116#3753—22no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3717—41no—
141#3714—41no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C3×#125—31no—
150C3×#124—31no—
151C3×#123—61no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#120—61no—
156C3×C4×D4—21no—
157C3×C4×D4—31no—
158C3×C4×D4C2×D311yescharacteristic
159C3×C4×D4C2×D311yescharacteristic
160C2×C3×C22⋊C4—61no—
161C2×#215—31no—
162#939—61no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—61no—
167#930—21no—
168#930—31no—
169#930—31no—
170C2×(C2×D3)⋊C4—21no—
171#926—31no—
172C2×C4⋊Dic3—31no—
173C22×C3⋊C8—31no—
174C22×C3⋊C8—31no—
175C2×D24—31no—
176C2×#204—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179#898—61no—
180#898—61no—
181#897C2×D311yescharacteristic
182#895—31no—
183#895—31no—
184#895—61no—
185#895C2×D311yescharacteristic
186#894—61no—
187#893—61no—
188#892—31no—
189D3×C4⋊C4—31no—
190#886—21no—
191#883—61no—
192#882—21no—
193#67⋊C4—61no—
194#875C2×D311yescharacteristic
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199#870C2×D311yescharacteristic, complemented
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#102—31no—
204C3×#102—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#832C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218#821—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#816—31no—
222#810—31no—
223#810—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#808C2×D311yescharacteristic, complemented
230#807—31no—
231#807—31no—
232#807—61no—
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C4×C3⋊C8—61no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4×C3⋊D3—81no—
257C3×#67—42no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—22no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—81no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#626—42no—
276#626—81no—
277D3×Dic3—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—31no—
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—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—41no—
317C22×C3×C4—61no—
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—61no—
321C2×#67—61no—
322C22×Dic3—21no—
323C22×Dic3—61no—
324#237—22no—
325#237—41no—
326D3×D4—22no—
327D3×D4—41no—
328C2×D12—21no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12#6711yescharacteristic
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—121no—
340C2×C4×D3C22×D311yescharacteristic
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—21no—
364C3×C42C22×D311yescharacteristic
365C3×C42C22×D311yescharacteristic
366#217—61no—
367#215—121no—
368#213—64no—
369#213—62no—
370#213—62no—
371#213—121no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
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—61no—
383(C2×D3)⋊C4—121no—
384(C2×D3)⋊C4#6711yescharacteristic
385(C2×D3)⋊C4#6711yescharacteristic
386C4⋊Dic3—21no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3#6711yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—121no—
410#204—121no—
411D3×C8—121no—
412D3×C8—121no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—84no—
429C2×C3×D3#13512yes—
430C32×C4—21no—
431C32×C4—21no—
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—
440C3×Dic3—41no—
441C2×#41—31no—
442C22×D4—31no—
443C2×SD16—91no—
444C2×D8—91no—
445C2×D8—91no—
446C22×C8—91no—
447C22×C8—91no—
448#126—181no—
449#125—31no—
450#124—31no—
451#123—61no—
452#123—181no—
453C22⋊Q8—31no—
454#121—31no—
455#121—61no—
456#121—91no—
457#121—91no—
458#121—181no—
459#120—61no—
460C4×D4—31no—
461C4×D4—91no—
462C4×D4—181no—
463C4×D4D3211yescharacteristic
464#117—91no—
465C2×C4⋊C4—91no—
466C2×C22⋊C4—61no—
467#107—31no—
468#107—91no—
469#106—31no—
470C4⋊C8—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—91no—
482C22⋊C8—91no—
483C4×C8—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—31no—
488C23×C3—41no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C22×D3—21no—
494C22×D3—42no—
495C22×D3—42no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—81no—
499C22×D3—121no—
500C22×D3C2×#6711yescharacteristic
501C22×D3C2×#6711yescharacteristic
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—41no—
508C3×D4—62no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—122no—
512C3×D4—122no—
513C3×D4—241no—
514C3×D4#23712yes—
515C3×D4#23912yes—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—81no—
532C2×C3×C4—81no—
533C2×C3×C4—82no—
534C2×C3×C4—122no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—42no—
542#67—42no—
543#67—122no—
544#67—241no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—42no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—121no—
552C2×Dic3—241no—
553C2×Dic3C2×#6711yescharacteristic
554C2×Dic3C2×#6711yescharacteristic
555D12—22no—
556D12—21no—
557D12—21no—
558D12—62no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—81no—
564D12—121no—
565D12—122no—
566D12—241no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—242no—
575Dic6—21no—
576Dic6—21no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—62no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—121no—
587C2×C32—42no—
588C2×C32#54611yescharacteristic
589C2×C32C2×#13511yescharacteristic
590C2×C32#57611yescharacteristic
591C3⋊D3—81no—
592C3×D3—22no—
593C3×D3—41no—
594C3×D3—81no—
595C24—61no—
596#41—62no—
597#41—121no—
598C2×Q8—31no—
599C2×D4—31no—
600C2×D4—31no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4—91no—
606C2×D4—121no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4C2×D3211yescharacteristic
610C22×C4—21no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—181no—
615C22×C4—181no—
616SD16—361no—
617D8—182no—
618D8—361no—
619C2×C8—31no—
620C2×C8—31no—
621C2×C8—91no—
622C2×C8—91no—
623C2×C8—361no—
624C2×C8—361no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4C2×D3211yescharacteristic
634C22⋊C4—21no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C42—181no—
646C42C2×D3211yescharacteristic
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—42no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C22×#6711yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—84no—
678C2×D3—122no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3#95012yes—
688C3×C4—22no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4—121no—
704C3×C4C2×#23711yescharacteristic
705C3×C4#100411yescharacteristic
706C3×C4C2×#23911yescharacteristic
707C3×C4#100911yescharacteristic
708Dic3—21no—
709Dic3—21no—
710Dic3—41no—
711Dic3—41no—
712Dic3—41no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716C32#329711yescharacteristic, complemented, Sylow
717C23—21no—
718C23—31no—
719C23—31no—
720C23—61no—
721C23—122no—
722C23—122no—
723C23—181no—
724C23—241no—
725Q8—61no—
726Q8—61no—
727D4—21no—
728D4—62no—
729D4—61no—
730D4—61no—
731D4—122no—
732D4—122no—
733D4—181no—
734D4—181no—
735D4—241no—
736D4—362no—
737D4—721no—
738D4#379612yes—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—81no—
750C2×C4—122no—
751C2×C4—181no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4D3×#6711yescharacteristic
755C2×C4D3×#6711yescharacteristic
756C2×C4C22×D3211yescharacteristic
757C8—61no—
758C8—61no—
759C8—181no—
760C8—181no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—62no—
767C2×C3—82no—
768C2×C3—121no—
769C2×C3—241no—
770C2×C3#563011yescharacteristic
771C2×C3D3×#13511yescharacteristic
772C2×C3#577411yescharacteristic
773C2×C3#580611yescharacteristic
774C2×C3C2×#95011yescharacteristic
775C2×C3#583511yescharacteristic
776D3—22no—
777D3—41no—
778D3—81no—
779D3—242no—
780D3—241no—
781D3—241no—
782C22—22no—
783C22—32no—
784C22—41no—
785C22—41no—
786C22—61no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—244no—
795C22—361no—
796C22—361no—
797C22—361no—
798C22C2×D3×#6711yescharacteristic
799C4—21no—
800C4—21no—
801C4—41no—
802C4—61no—
803C4—61no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—361no—
808C4C2×#379611yescharacteristic
809C4#6430711yescharacteristic
810C3—21no—
811C3#8118711yescharacteristic, complemented
812C3#8349511yescharacteristic, complemented
813C2—42no—
814C2—62no—
815C2—121no—
816C2—241no—
817C2—721no—
818C2#1059488911yescharacteristic
819C2#1059509711yescharacteristic
820C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5554C2semidirect
2. #10593925C2semidirect
3. C4×#3753C2semidirect
4. C3×#5009C2semidirect
5. #10591452C2semidirect
6. #10591448C2semidirect
7. #10591420C2semidirect
8. D3×#832C2semidirect
9. #10590577C2semidirect
10. #10590576C2semidirect
11. #10590449C2semidirect
12. #10590440C2semidirect
13. #10590356C2semidirect
14. #10590329C2semidirect
15. #10590278C2semidirect
22. C4×C4⋊(C3⋊D3)C22semidirect
31. C3×#870C22semidirect
33. #63909C22semidirect
39. #63841C22semidirect
40. C2×#3717C22semidirect
43. C2×D3×C3⋊C8C22semidirect
45. #63636C22semidirect
46. #63634C22semidirect
47. C4×C3⋊(C3⋊C8)C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
55. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
64. #5554D3semidirect
81. #5009D3semidirect
199. #870C2×D3semidirect
229. #808C2×D3semidirect
233. #807C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
716. C32#3297semidirect
811. C3#81187semidirect
812. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
#105939252
C4×#37532
C3×#50092
#105914522
#105914482
#105914202
D3×#8322
#105905772
#105905762
#105904492
#105904402
#105903562
#105903292
#105902782
#834953
#811873