Finite Group Databasebeta

← #11887123

Subgroups — #11887123

Order 1152.

1138 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#638C211yesmaximal, characteristic
2#10594991C211yesmaximal, characteristic, complemented
3C3×#5218C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591495C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7#10591465C211yesmaximal, characteristic, complemented
8#10591445C211yesmaximal, characteristic, complemented
9#10591444C211yesmaximal, characteristic, complemented
10#10591419C211yesmaximal, characteristic, complemented
11#10591416C211yesmaximal, characteristic, complemented
12#10591402C211yesmaximal, characteristic, complemented
13#10591177C211yesmaximal, characteristic, complemented
14#10591148C211yesmaximal, characteristic, complemented
15#10591125C211yesmaximal, characteristic, complemented
16#80158—31nomaximal
17#78758—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#63964—21no—
35#63952—21no—
36#63919C2211yescharacteristic, complemented
37#63900C2211yescharacteristic, complemented
38#63895—21no—
39#63871C2211yescharacteristic, complemented
40#63847—21no—
41#63843C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#830C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62D4×#67—31no—
63D4×#67—61no—
64#5635—31no—
65#5511—31no—
66C3×#450—31no—
67C2×C3×#102—31no—
68#5218D311yescharacteristic, complemented
69C2×#832D311yescharacteristic, complemented
70#5171—31no—
71#5169—31no—
72#5163—31no—
73Dic3×SD16—31no—
74#5114—31no—
75C8×#67—31no—
76#5048—31no—
77#4968—31no—
78#4778—31no—
79#4777—31no—
80#4777—31no—
81#4776—31no—
82D3×#102—31no—
83D3×#102—31no—
84#4762—31no—
85#4761—31no—
86#4761—31no—
87#4760—31no—
88#4760—31no—
89#4758—31no—
90#4735—31no—
91#67⋊C8—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
114C2×#627—21no—
115C2×#624—21no—
116#3757—21no—
117#3757—21no—
118#3757D411yescharacteristic
119#3752—21no—
120#3752D411yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750D411yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C3×#217—21no—
125C3×#214—22no—
126C3×#214—41no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138#3724—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142Dic32—21no—
143#3717—41no—
144#3710—41no—
145#3295—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—
186C4×#67—31no—
187C4×#67—31no—
188C4×#67—61no—
189C4×#67—61no—
190C2×C4⋊Dic3C2×D311yescharacteristic, complemented
191#924—61no—
192#924C2×D311yescharacteristic, complemented
193C22×C3⋊C8C2×D311yescharacteristic, complemented
194C2×#204—31no—
195C2×D3×C8—31no—
196C2×D3×C8—31no—
197#897—31no—
198#897—61no—
199#896—61no—
200D3×C4⋊C4—31no—
201D3×C4⋊C4—31no—
202#889—61no—
203#889—61no—
204#888—31no—
205#888—31no—
206#887—31no—
207#67⋊C4—61no—
208#878—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#817—31no—
230#817—31no—
231#817—31no—
232#816—31no—
233Dic3⋊C8—31no—
234Dic3⋊C8—31no—
235C8×Dic3—31no—
236C8×Dic3—31no—
237#809—31no—
238#809—31no—
239#809—31no—
240#808—31no—
241#808—31no—
242#808—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—42no—
264#638—42no—
265#638—42no—
266#638—42no—
267#638—81no—
268#638SD1614yescomplemented
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—81no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285#627—81no—
286#624—81no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#554—91no—
292D42—91no—
293#486—91no—
294#481—91no—
295#481—91no—
296#476—91no—
297#465—91no—
298#465—91no—
299#460—91no—
300#450—31no—
301#450—91no—
302C4×SD16—91no—
303C8×D4—91no—
304C2×#102—31no—
305C2×#102—91no—
306C24×C3—22no—
307C24×C3—21no—
308C24×C3—21no—
309C23×D3—61no—
310C23×D3—61no—
311C23×D3—62no—
312C2×C3×Q8—31no—
313C2×C3×D4—22no—
314C2×C3×D4—22no—
315C2×C3×D4—22no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—42no—
321C2×C3×D4—41no—
322C2×C3×D4—41no—
323C2×C3×D4—42no—
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C22×D311yescharacteristic
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—21no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—31no—
333C2×#67—31no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—62no—
350C2×#67—124no—
351C2×#67—124no—
352C2×#67—128no—
353C22×Dic3—21no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—62no—
357D3×D4—62no—
358D3×D4—62no—
359D3×D4—122no—
360D3×D4—121no—
361D3×D4—121no—
362D3×D4—122no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—61no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×Dic6—61no—
372C2×Dic6—61no—
373C2×Dic6C22×D311yescharacteristic
374C3×SD16—62no—
375C3×SD16—121no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C2×C3×C8—31no—
380C2×C3×C8—121no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C22⋊C4—61no—
387#217—21no—
388#217—31no—
389#217—31no—
390#217—61no—
391#217—61no—
392#217—61no—
393#217—61no—
394#217—61no—
395#217—62no—
396#217—62no—
397#215—121no—
398#214—22no—
399#214—41no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408C4⋊Dic3—21no—
409C4⋊Dic3—31no—
410C4⋊Dic3—31no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3—61no—
414C4⋊Dic3C22×D311yescharacteristic
415C4⋊Dic3C22×D311yescharacteristic
416C4⋊Dic3C22×D311yescharacteristic
417Dic3⋊C4—21no—
418Dic3⋊C4—31no—
419Dic3⋊C4—31no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—61no—
430C4×Dic3—61no—
431C4×Dic3—61no—
432C2×C3⋊C8—41no—
433C2×C3⋊C8C22×D311yescharacteristic
434C2×C3⋊C8C22×D311yescharacteristic
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437#204—121no—
438D3×C8—121no—
439D3×C8—121no—
440C22×C32—22no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—84no—
449C22×C32C2×SD1612yes—
450C22×C32C22×D411yescharacteristic
451C2×C3⋊D3—21no—
452C2×C3⋊D3—21no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—84no—
457C2×C3⋊D3C2×SD1612yes—
458C32×C4—21no—
459C32×C4C2×#4111yescharacteristic
460C32×C4H(5,𝔽2)11yescharacteristic
461C3⋊Dic3—21no—
462C3⋊Dic3—21no—
463C3⋊Dic3—41no—
464C3⋊Dic3C2×SD1612yes—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3—41no—
468C3×Dic3—41no—
469C22×D4—91no—
470C22×D4—181no—
471C22×D4D3211yescharacteristic
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—91no—
475C22×C8—31no—
476C22×C8—91no—
477C4⋊Q8—91no—
478#127—91no—
479#125—181no—
480C22⋊Q8—31no—
481C22⋊Q8—91no—
482C22⋊Q8—181no—
483C22⋊Q8—181no—
484#121—91no—
485#121—91no—
486#121—181no—
487#120—181no—
488#120—181no—
489C4×Q8—91no—
490C4×D4—91no—
491C4×D4—91no—
492C4×D4—181no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—91no—
495#106—91no—
496#106—91no—
497#106—91no—
498C4⋊C8—91no—
499#103—91no—
500#102—31no—
501#102—31no—
502#102—31no—
503#102—31no—
504#102—31no—
505#102—31no—
506#102—91no—
507#102—91no—
508#102—91no—
509C22⋊C8—31no—
510C22⋊C8—91no—
511C4×C8—91no—
512C23×C3—22no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—22no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—42no—
520C23×C3—42no—
521C23×C3—44no—
522C23×C3—44no—
523C23×C3—42no—
524C23×C3—42no—
525C23×C3—81no—
526C23×C3—81no—
527C23×C3—82no—
528C23×C3D3×D411yescharacteristic
529C23×C3D3×D411yescharacteristic
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—61no—
533C22×D3—62no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—124no—
541C22×D3—124no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3—242no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×D4—22no—
548C3×D4—21no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—22no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—42no—
558C3×D4—42no—
559C3×D4—44no—
560C3×D4#23512yes—
561C3×D4#23712yes—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—241no—
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579#67—34no—
580#67—34no—
581#67—64no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—122no—
586#67—124no—
587#67—122no—
588#67—122no—
589#67—124no—
590#67—124no—
591#67—124no—
592#67—122no—
593#67—122no—
594#67—241no—
595#67—241no—
596#67—242no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—62no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—81no—
614C2×Dic3—122no—
615C2×Dic3—122no—
616C2×Dic3—124no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—121no—
622D12—121no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—61no—
626C4×D3—61no—
627C4×D3—121no—
628C4×D3—121no—
629C4×D3—241no—
630C4×D3—241no—
631Dic6—21no—
632Dic6—21no—
633Dic6—241no—
634Dic6—241no—
635C3×C8—61no—
636C3×C8—61no—
637C3×C8—61no—
638C3×C8—61no—
639C3⋊C8—21no—
640C3⋊C8—21no—
641C3⋊C8—21no—
642C3⋊C8—21no—
643C2×C32—22no—
644C2×C32—42no—
645C2×C32—81no—
646C2×C32#54611yescharacteristic
647C2×C32C22×SD1611yescharacteristic
648C2×C32#57611yescharacteristic
649C3⋊D3—22no—
650C3⋊D3—81no—
651C24—21no—
652C24—181no—
653C2×Q8—31no—
654C2×Q8—181no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—41no—
658C2×D4—91no—
659C2×D4—91no—
660C2×D4—181no—
661C2×D4—181no—
662C2×D4—181no—
663C2×D4—182no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—361no—
667C2×D4—364no—
668C2×D4C2×D3211yescharacteristic
669C2×D4C2×D3211yescharacteristic
670C22×C4—61no—
671C22×C4—91no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4C2×D3211yescharacteristic
675SD16—62no—
676SD16—121no—
677SD16—361no—
678C2×C8—31no—
679C2×C8—31no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—121no—
683C2×C8—361no—
684C4⋊C4—31no—
685C4⋊C4—31no—
686C4⋊C4—31no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—91no—
690C4⋊C4—91no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4—181no—
695C22⋊C4—61no—
696C22⋊C4—91no—
697C22⋊C4—91no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C42—91no—
703C42—181no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—24no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—21no—
712C22×C3—22no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—84no—
731C22×C3—84no—
732C22×C3—88no—
733C22×C3D3×SD1612yes—
734C22×C3D3×SD1612yes—
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C2×D3×D411yescharacteristic
737C2×D3—32no—
738C2×D3—32no—
739C2×D3—62no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—122no—
747C2×D3—122no—
748C2×D3—122no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—244no—
756C2×D3—244no—
757C2×D3—248no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—41no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4—121no—
767C3×C4C2×#23511yescharacteristic
768C3×C4C2×#23711yescharacteristic
769C3×C4#100411yescharacteristic
770C3×C4#100411yescharacteristic
771Dic3—32no—
772Dic3—32no—
773Dic3—41no—
774Dic3—41no—
775Dic3—41no—
776Dic3—41no—
777Dic3—62no—
778Dic3—61no—
779Dic3—61no—
780Dic3—61no—
781Dic3—61no—
782Dic3—121no—
783Dic3—121no—
784Dic3—122no—
785Dic3—121no—
786Dic3—121no—
787C32#329511yescharacteristic, complemented, Sylow
788C23—21no—
789C23—21no—
790C23—42no—
791C23—42no—
792C23—81no—
793C23—91no—
794C23—181no—
795C23—362no—
796C23—362no—
797C23—721no—
798C23#381111yescharacteristic
799Q8—61no—
800Q8—61no—
801Q8—721no—
802D4—21no—
803D4—21no—
804D4—21no—
805D4—42no—
806D4—94no—
807D4—181no—
808D4—181no—
809D4—362no—
810D4—362no—
811D4—362no—
812D4—362no—
813D4—721no—
814D4#380412yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—91no—
822C2×C4—91no—
823C2×C4—91no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—241no—
828C2×C4—362no—
829C2×C4—721no—
830C2×C4#381111yescharacteristic
831C2×C4C22×D3211yescharacteristic
832C8—61no—
833C8—61no—
834C8—61no—
835C8—61no—
836C2×C3—22no—
837C2×C3—22no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—42no—
842C2×C3—44no—
843C2×C3—42no—
844C2×C3—42no—
845C2×C3—82no—
846C2×C3—81no—
847C2×C3—81no—
848C2×C3#549011yescharacteristic
849C2×C3#559111yescharacteristic
850C2×C3#575711yescharacteristic
851C2×C3C2×D3×SD1611yescharacteristic
852C2×C3C2×D3×SD1611yescharacteristic
853C2×C3#577411yescharacteristic
854D3—62no—
855D3—62no—
856D3—122no—
857D3—242no—
858D3—241no—
859D3—241no—
860C22—21no—
861C22—21no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—84no—
869C22—92no—
870C22—181no—
871C22—181no—
872C22—361no—
873C22—361no—
874C22—361no—
875C22—724no—
876C22#6393012yes—
877C22C2×#381111yescharacteristic
878C4—21no—
879C4—92no—
880C4—121no—
881C4—121no—
882C4—121no—
883C4—121no—
884C4—181no—
885C4—181no—
886C4—361no—
887C4C2×#380411yescharacteristic
888C4#6433011yescharacteristic
889C3—21no—
890C3#7875811yescharacteristic, complemented
891C3#8015811yescharacteristic, complemented
892C2—22no—
893C2—42no—
894C2—81no—
895C2—182no—
896C2—721no—
897C2#1059510211yescharacteristic
898C2C2×#6393011yescharacteristic
899C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalD4×#638C2
hypercenterC22×D4D32
hypocenterC32#3295
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. #10594991C2semidirect
3. C3×#5218C2semidirect
4. C2×C3×#832C2semidirect
5. #10591495C2semidirect
6. #10591467C2semidirect
7. #10591465C2semidirect
8. #10591445C2semidirect
9. #10591444C2semidirect
10. #10591419C2semidirect
11. #10591416C2semidirect
12. #10591402C2semidirect
13. #10591177C2semidirect
14. #10591148C2semidirect
15. #10591125C2semidirect
30. C2×C3×#214C22semidirect
31. C2×C3×C4⋊Dic3C22semidirect
32. C3×#924C22semidirect
33. C22×C3×C3⋊C8C22semidirect
36. #63919C22semidirect
37. #63900C22semidirect
39. #63871C22semidirect
41. #63843C22semidirect
42. C2×#3717C22semidirect
43. C2×#3710C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
50. C3×#830C22semidirect
51. #63573C22semidirect
52. #63573C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
55. #63566C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
68. #5218D3semidirect
69. C2×#832D3semidirect
182. C2×#214C2×D3semidirect
190. C2×C4⋊Dic3C2×D3semidirect
192. #924C2×D3semidirect
193. C22×C3⋊C8C2×D3semidirect
220. #832C2×D3semidirect
221. #832C2×D3semidirect
222. #832C2×D3semidirect
223. #830C2×D3semidirect
268. #638SD16semidirect
787. C32#3295semidirect
890. C3#78758semidirect
891. C3#80158semidirect

Maximal subgroups

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

subgroupindex
D4×#6382
#105949912
C3×#52182
C2×C3×#8322
#105914952
#105914672
#105914652
#105914452
#105914442
#105914192
#105914162
#105914022
#105911772
#105911482
#105911252
#801583
#787583