Finite Group Databasebeta

← #11889097

Subgroups — #11889097

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#638C211yesmaximal, characteristic
2#10594825C211yesmaximal, characteristic, complemented
3C3×#5218C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591480C211yesmaximal, characteristic, complemented
6#10591479C211yesmaximal, characteristic, complemented
7#10591467C211yesmaximal, characteristic, complemented
8#10591464C211yesmaximal, characteristic, complemented
9#10591446C211yesmaximal, characteristic, complemented
10#10591444C211yesmaximal, characteristic, complemented
11#10591426C211yesmaximal, characteristic, complemented
12#10591425C211yesmaximal, characteristic, complemented
13#10591177C211yesmaximal, characteristic, complemented
14#10591157C211yesmaximal, characteristic, complemented
15#10591133C211yesmaximal, characteristic, complemented
16#80160—31nomaximal
17#78762—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×#638—21no—
20C2×D4×C3⋊D3C2211yescharacteristic
21#64162—21no—
22#64149C2211yescharacteristic
23#64148—21no—
24#64147C2211yescharacteristic
25#64146—21no—
26D4×C3⋊Dic3C2211yescharacteristic
27#64139C2211yescharacteristic
28C4×#638C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic, complemented
31C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
32C3×#924C2211yescharacteristic, complemented
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34#63966—21no—
35#63955—21no—
36#63872C2211yescharacteristic, complemented
37#63871C2211yescharacteristic, complemented
38#63849C2211yescharacteristic, complemented
39#63848—21no—
40#63846—21no—
41#63843C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic, complemented
43C2×#3712C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#830C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61D4×#67—31no—
62D4×#67—31no—
63D4×#67—61no—
64#5642—31no—
65#5513—31no—
66C3×#450—31no—
67C2×C3×#102—31no—
68#5218D311yescharacteristic, complemented
69C2×#832D311yescharacteristic, complemented
70#5174—31no—
71#5169—31no—
72#5164—31no—
73#5163—31no—
74#5114—31no—
75#5111—31no—
76#5048—31no—
77#4967—31no—
78#4784—31no—
79#4780—31no—
80#4779—31no—
81#4776—31no—
82#4770—31no—
83#4770—31no—
84#4766—31no—
85#4764—31no—
86#4764—31no—
87#4763—31no—
88#4762—31no—
89#4757—31no—
90#4736—31no—
91#4730—31no—
92C24×C32—21no—
93C23×C3⋊D3—21no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4—41no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101C2×#638—21no—
102C2×#638—21no—
103C2×#638—21no—
104C2×#638—21no—
105C2×#638—44no—
106C2×#638D411yescharacteristic
107C22×C3⋊Dic3—21no—
108D4×C3⋊D3—22no—
109D4×C3⋊D3—41no—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C22×C3×Dic3—21no—
113C2×C3×Dic6C2311yescharacteristic
114#3757—21no—
115#3757—21no—
116#3757D411yescharacteristic
117#3752—21no—
118#3752D411yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750D411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C3×#217—21no—
123C3×#214—22no—
124C3×#214—41no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140#3722—21no—
141Dic32—21no—
142Dic32—21no—
143#3717—41no—
144#3712—41no—
145#3310—91noSylow
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C2×D311yescharacteristic
149C22×#67—61no—
150C22×#67—61no—
151C22×#67—62no—
152C2×D3×D4—31no—
153C2×D3×D4—31no—
154C2×D3×D4—61no—
155C2×C3×SD16—31no—
156C2×C3×SD16—31no—
157C22×C3×C8—31no—
158C3×C22⋊Q8—31no—
159C2×C3×C4⋊C4—31no—
160#953—61no—
161#953—61no—
162#953—62no—
163#946—31no—
164Q8×Dic3—31no—
165C2×#215—31no—
166#940—31no—
167#940—31no—
168#940—61no—
169#939—61no—
170#939—61no—
171#939—62no—
172#938—31no—
173#938—31no—
174#938—61no—
175#937—61no—
176#937—61no—
177#937—62no—
178D4×Dic3—31no—
179D4×Dic3—31no—
180D4×Dic3—61no—
181C2×#214C2×D311yescharacteristic
182C2×#214C2×D311yescharacteristic, complemented
183#930—31no—
184#930—31no—
185#930—61no—
186#929—61no—
187C4×#67—31no—
188C4×#67—31no—
189C4×#67—61no—
190#926—61no—
191C2×C4⋊Dic3C2×D311yescharacteristic, complemented
192#924C2×D311yescharacteristic, complemented
193C22×C3⋊C8C2×D311yescharacteristic, complemented
194C2×#204—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197#898—61no—
198#898—61no—
199#897—31no—
200#892—31no—
201#892—31no—
202#890—31no—
203#890—31no—
204#890—61no—
205#889—61no—
206#887—31no—
207#886—61no—
208#877—61no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×C22⋊C8—31no—
216#835—31no—
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic, complemented
221#832C2×D311yescharacteristic, complemented
222#832C2×D311yescharacteristic, complemented
223#830C2×D311yescharacteristic, complemented
224#821—31no—
225#821—31no—
226#821—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229#818—31no—
230#818—31no—
231#817—31no—
232#816—31no—
233#815—31no—
234#815—31no—
235Dic3⋊C8—31no—
236Dic3⋊C8—31no—
237#809—31no—
238#809—31no—
239#809—31no—
240#808—31no—
241#807—31no—
242#807—31no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—42no—
246C23×C32—42no—
247C23×C32—81no—
248C23×C32C2×D411yescharacteristic
249C22×C3⋊D3—21no—
250C22×C3⋊D3—42no—
251C22×C3⋊D3—42no—
252C22×C3⋊D3—81no—
253C22×C3⋊D3C2×D411yescharacteristic
254C32×D4—21no—
255C32×D4—21no—
256C32×D4—21no—
257C32×D4—42no—
258C32×D4#4112yes—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263#638—22no—
264#638—42no—
265#638—42no—
266#638—42no—
267#638—42no—
268#638—81no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—42no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4×C3⋊D3—21no—
277C4×C3⋊D3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289#552—91no—
290D42—91no—
291#490—91no—
292#482—91no—
293#480—91no—
294#478—91no—
295#468—91no—
296#465—91no—
297#460—91no—
298#450—31no—
299#450—91no—
300#440—91no—
301#435—91no—
302#418—91no—
303C2×#102—31no—
304C24×C3—22no—
305C24×C3—21no—
306C24×C3—21no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—62no—
310C2×C3×Q8—31no—
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4—22no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—42no—
319C2×C3×D4—41no—
320C2×C3×D4—41no—
321C2×C3×D4—42no—
322C2×C3×D4C22×D311yescharacteristic
323C2×C3×D4C22×D311yescharacteristic
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C22×D311yescharacteristic
326C22×C3×C4—21no—
327C22×C3×C4—61no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—31no—
331C2×#67—31no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—62no—
348C2×#67—128no—
349C2×#67—124no—
350C2×#67—124no—
351C22×Dic3—21no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—62no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—122no—
358D3×D4—121no—
359D3×D4—121no—
360D3×D4—122no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—61no—
367C2×Dic6C22×D311yescharacteristic
368C3×SD16—62no—
369C3×SD16—121no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C2×C3×C8—121no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4—61no—
380C3×C22⋊C4—61no—
381#217—21no—
382#217—31no—
383#217—31no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#217—62no—
390#217—62no—
391#215—121no—
392#214—22no—
393#214—41no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404C4⋊Dic3—21no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3C22×D311yescharacteristic
413C4⋊Dic3C22×D311yescharacteristic
414C4⋊Dic3C22×D311yescharacteristic
415Dic3⋊C4—21no—
416Dic3⋊C4—31no—
417Dic3⋊C4—31no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423C4×Dic3—31no—
424C4×Dic3—31no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C2×C3⋊C8—41no—
431C2×C3⋊C8C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434C2×C3⋊C8C22×D311yescharacteristic
435#204—121no—
436ΓL(1,𝔽25)—121no—
437ΓL(1,𝔽25)—121no—
438C22×C32—22no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—84no—
447C22×C32AGL(1,ℤ/8)12yes—
448C22×C32C22×D411yescharacteristic
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—84no—
456C32×C4—21no—
457C32×C4C2×#4111yescharacteristic
458C32×C4H(5,𝔽2)11yescharacteristic
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C22×D4—91no—
468C22×D4—181no—
469C22×D4D3211yescharacteristic
470C2×SD16—31no—
471C2×SD16—31no—
472C2×SD16—91no—
473C2×M16—91no—
474C22×C8—31no—
475#127—91no—
476#126—181no—
477#125—91no—
478#125—181no—
479#123—181no—
480C22⋊Q8—31no—
481C22⋊Q8—91no—
482#121—91no—
483#121—91no—
484#121—181no—
485#120—181no—
486#120—181no—
487C4×Q8—91no—
488C4×D4—91no—
489C4×D4—91no—
490#117—91no—
491#117—181no—
492C2×C4⋊C4—31no—
493#107—91no—
494#107—91no—
495#106—91no—
496C4⋊C8—91no—
497#103—91no—
498#102—31no—
499#102—31no—
500#102—31no—
501#102—31no—
502#102—31no—
503#102—31no—
504#102—91no—
505#102—91no—
506#102—91no—
507C22⋊C8—31no—
508C22⋊C8—91no—
509#97—91no—
510C23×C3—22no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—22no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—42no—
518C23×C3—42no—
519C23×C3—44no—
520C23×C3—44no—
521C23×C3—42no—
522C23×C3—42no—
523C23×C3—81no—
524C23×C3—81no—
525C23×C3—82no—
526C23×C3D3×D411yescharacteristic
527C23×C3D3×D411yescharacteristic
528C22×D3—31no—
529C22×D3—31no—
530C22×D3—61no—
531C22×D3—62no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—124no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—124no—
540C22×D3—241no—
541C22×D3—241no—
542C22×D3—242no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×D4—22no—
546C3×D4—21no—
547C3×D4—21no—
548C3×D4—21no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—22no—
553C3×D4—41no—
554C3×D4—41no—
555C3×D4—42no—
556C3×D4—42no—
557C3×D4—44no—
558C3×D4#23512yes—
559C3×D4#23712yes—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—122no—
573C2×C3×C4D3×D411yescharacteristic
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—64no—
578#67—62no—
579#67—62no—
580#67—122no—
581#67—122no—
582#67—124no—
583#67—122no—
584#67—122no—
585#67—124no—
586#67—122no—
587#67—122no—
588#67—124no—
589#67—124no—
590#67—122no—
591#67—122no—
592#67—241no—
593#67—241no—
594#67—242no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—31no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—42no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—62no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—124no—
613C2×Dic3—122no—
614C2×Dic3—122no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—121no—
620D12—121no—
621C4×D3—61no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—121no—
626C4×D3—121no—
627Dic6—21no—
628Dic6—21no—
629C3×C8—61no—
630C3×C8—61no—
631C3×C8—61no—
632C3×C8—61no—
633C3⋊C8—21no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C2×C32—22no—
638C2×C32—42no—
639C2×C32—81no—
640C2×C32#54611yescharacteristic
641C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
642C2×C32#57711yescharacteristic
643C3⋊D3—41no—
644C3⋊D3—81no—
645C24—21no—
646C24—181no—
647C2×Q8—31no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—41no—
651C2×D4—91no—
652C2×D4—91no—
653C2×D4—181no—
654C2×D4—181no—
655C2×D4—181no—
656C2×D4—182no—
657C2×D4—181no—
658C2×D4—181no—
659C2×D4—361no—
660C2×D4—364no—
661C2×D4C2×D3211yescharacteristic
662C2×D4C2×D3211yescharacteristic
663C22×C4—61no—
664C22×C4—91no—
665C22×C4—181no—
666C22×C4C2×D3211yescharacteristic
667SD16—62no—
668SD16—121no—
669SD16—361no—
670M16—361no—
671C2×C8—31no—
672C2×C8—31no—
673C2×C8—31no—
674C2×C8—31no—
675C2×C8—121no—
676C4⋊C4—31no—
677C4⋊C4—31no—
678C4⋊C4—31no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—91no—
682C4⋊C4—91no—
683C4⋊C4—181no—
684C4⋊C4—181no—
685C4⋊C4—181no—
686C4⋊C4—181no—
687C22⋊C4—61no—
688C22⋊C4—91no—
689C22⋊C4—91no—
690C22⋊C4—181no—
691C22⋊C4—181no—
692C22⋊C4—181no—
693C22⋊C4—181no—
694C22⋊C4—181no—
695C42—91no—
696C42—181no—
697C42—181no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—24no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—22no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—84no—
725C22×C3—84no—
726C22×C3—88no—
727C22×C3#91112yes—
728C22×C3#91412yes—
729C22×C3C2×D3×D411yescharacteristic
730C22×C3C2×D3×D411yescharacteristic
731C2×D3—62no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—122no—
741C2×D3—122no—
742C2×D3—122no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—248no—
750C2×D3—244no—
751C2×D3—244no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—41no—
757C3×C4—121no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4C2×#23511yescharacteristic
762C3×C4C2×#23711yescharacteristic
763C3×C4#100411yescharacteristic
764C3×C4#100411yescharacteristic
765Dic3—41no—
766Dic3—41no—
767Dic3—41no—
768Dic3—41no—
769Dic3—62no—
770Dic3—61no—
771Dic3—61no—
772Dic3—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—121no—
777Dic3—121no—
778Dic3—122no—
779Dic3—121no—
780Dic3—121no—
781C32#331011yescharacteristic, complemented, Sylow
782C23—21no—
783C23—21no—
784C23—42no—
785C23—42no—
786C23—81no—
787C23—91no—
788C23—181no—
789C23—362no—
790C23—362no—
791C23—721no—
792C23#381111yescharacteristic
793Q8—61no—
794Q8—61no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—42no—
799D4—182no—
800D4—181no—
801D4—181no—
802D4—362no—
803D4—362no—
804D4—362no—
805D4—362no—
806D4—721no—
807D4#380412yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—122no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—362no—
822C2×C4#381111yescharacteristic
823C2×C4C22×D3211yescharacteristic
824C8—61no—
825C8—61no—
826C8—61no—
827C8—61no—
828C2×C3—22no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—42no—
834C2×C3—44no—
835C2×C3—42no—
836C2×C3—42no—
837C2×C3—82no—
838C2×C3—81no—
839C2×C3—81no—
840C2×C3#549011yescharacteristic
841C2×C3#559111yescharacteristic
842C2×C3C2×#91111yescharacteristic
843C2×C3C2×#91411yescharacteristic
844C2×C3#576211yescharacteristic
845C2×C3#577511yescharacteristic
846D3—122no—
847D3—121no—
848D3—121no—
849D3—242no—
850D3—241no—
851D3—241no—
852C22—21no—
853C22—21no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22#6393712yes—
869C22C2×#381111yescharacteristic
870C4—21no—
871C4—121no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4—181no—
877C4—181no—
878C4—361no—
879C4C2×#380411yescharacteristic
880C4#6433011yescharacteristic
881C3—21no—
882C3#7876211yescharacteristic, complemented
883C3#8016011yescharacteristic, complemented
884C2—22no—
885C2—42no—
886C2—81no—
887C2—361no—
888C2—721no—
889C2C2×#6393711yescharacteristic
890C2#1059511511yescharacteristic
891C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalD4×#638C2
hypercenterC22×D4D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594825C2semidirect
3. C3×#5218C2semidirect
4. C2×C3×#832C2semidirect
5. #10591480C2semidirect
6. #10591479C2semidirect
7. #10591467C2semidirect
8. #10591464C2semidirect
9. #10591446C2semidirect
10. #10591444C2semidirect
11. #10591426C2semidirect
12. #10591425C2semidirect
13. #10591177C2semidirect
14. #10591157C2semidirect
15. #10591133C2semidirect
30. C2×C3×#214C22semidirect
31. C2×C3×C4⋊Dic3C22semidirect
32. C3×#924C22semidirect
33. C22×C3×C3⋊C8C22semidirect
36. #63872C22semidirect
37. #63871C22semidirect
38. #63849C22semidirect
41. #63843C22semidirect
42. C2×#3717C22semidirect
43. C2×#3712C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
50. C3×#830C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
55. #63566C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
59. #63557C22semidirect
60. #63555C22semidirect
68. #5218D3semidirect
69. C2×#832D3semidirect
182. C2×#214C2×D3semidirect
191. C2×C4⋊Dic3C2×D3semidirect
192. #924C2×D3semidirect
193. C22×C3⋊C8C2×D3semidirect
220. #832C2×D3semidirect
221. #832C2×D3semidirect
222. #832C2×D3semidirect
223. #830C2×D3semidirect
781. C32#3310semidirect
882. C3#78762semidirect
883. C3#80160semidirect

Maximal subgroups

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

subgroupindex
D4×#6382
#105948252
C3×#52182
C2×C3×#8322
#105914802
#105914792
#105914672
#105914642
#105914462
#105914442
#105914262
#105914252
#105911772
#105911572
#105911332
#801603
#787623