Finite Group Databasebeta

← #11889762

Subgroups — #11889762

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595228C211yesmaximal, characteristic
2#10594531C211yesmaximal, characteristic, complemented
3#10592466C211yesmaximal, characteristic, complemented
4C3×#4774C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591496C211yesmaximal, characteristic, complemented
7#10591462C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10590969C211yesmaximal, characteristic, complemented
10#10590852C211yesmaximal, characteristic, complemented
11#10590778C211yesmaximal, characteristic, complemented
12#10590723C211yesmaximal, characteristic, complemented
13#10590607C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#81289—31nomaximal
17#78763—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64145C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C2×#3746C2211yescharacteristic, complemented
23#64096C2211yescharacteristic, complemented
24C3×#938C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28#63976—21no—
29#63970—21no—
30#63969—21no—
31D3×#217—21no—
32#63919C2211yescharacteristic, complemented
33C4×#625—21no—
34C4×#625C2211yescharacteristic
35#63898C2211yescharacteristic
36#63870—21no—
37#63857C2211yescharacteristic
38#63857C2211yescharacteristic
39#63857C2211yescharacteristic, complemented
40#63851—21no—
41#63851—21no—
42C2×#3716C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63641C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5806—31no—
62#5612—31no—
63#5511—31no—
64#5511—31no—
65C3×#480—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5116—31no—
69#5111—31no—
70#5042—31no—
71#4970—31no—
72#4966—31no—
73#4890—31no—
74#4889—31no—
75#4887—31no—
76#4884—31no—
77#4783—31no—
78#4780—31no—
79#4776—31no—
80#4774D311yescharacteristic, complemented
81#4771—31no—
82D3×#102D311yescharacteristic, complemented
83#4767—31no—
84#4767—31no—
85#4767—61no—
86#4765—31no—
87#4765—31no—
88#4759—31no—
89#4757—31no—
90#4733—31no—
91#4728—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×D3×D4—22no—
99C3×D3×D4—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#627—21no—
106C2×#625—21no—
107C2×#625D411yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3757—21no—
115#3757—21no—
116#3754—41no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3746—41no—
122C3×#217—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131#3724—21no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3716—22no—
143#3711—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235—31no—
149C22×C3×C8—31no—
150C3×#121—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153#953—61no—
154C2×#217—61no—
155#939—61no—
156#938—61no—
157#938C2×D311yescharacteristic
158#937—61no—
159#936—31no—
160#936—31no—
161#936—61no—
162#935—61no—
163D4×Dic3—31no—
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—61no—
168C4×#67—31no—
169C4×#67—31no—
170C4×#67—61no—
171C4×#67—61no—
172#924—31no—
173#924—31no—
174#924—31no—
175#924—61no—
176#924—61no—
177C2×#208—31no—
178C2×Dic12—31no—
179C2×Dic12—31no—
180C2×Dic12—61no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×D3×C8C2×D311yescharacteristic
184#897—31no—
185#897—31no—
186#897—31no—
187#896—61no—
188#896—61no—
189#893—31no—
190D3×C4⋊C4C2×D311yescharacteristic
191D3×C4⋊C4C2×D311yescharacteristic, complemented
192#889—61no—
193#889—61no—
194#888—31no—
195#888—31no—
196#887—31no—
197#887—31no—
198#887—61no—
199#883—61no—
200D3×C22⋊C4—61no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×C22⋊C8—31no—
211#832—31no—
212#832C2×D311yescharacteristic
213#832C2×D311yescharacteristic
214#830—31no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic, complemented
218#818C2×D311yescharacteristic, complemented
219#816—31no—
220#816—31no—
221#816—31no—
222#815—31no—
223#815—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—61no—
233#809—31no—
234#809C2×D311yescharacteristic
235#807—31no—
236#807—31no—
237#807C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634—21no—
255#634—21no—
256#634—21no—
257C3×#67—42no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272#627—81no—
273#625—22no—
274#625—42no—
275D3×Dic3—42no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—31no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—31no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×D4—21no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C2×C3×D4—62no—
302C2×C3×D4—61no—
303C2×C3×D4—121no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—21no—
312C2×#67—31no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#237—62no—
319#237—121no—
320D3×D4—22no—
321D3×D4—41no—
322#235—62no—
323#235—121no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—121no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
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⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354#217—21no—
355#217—31no—
356#217—31no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—121no—
366#217—121no—
367#214—62no—
368#214—121no—
369#214—121no—
370#214—122no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401#208—121no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—121no—
408Dic12—121no—
409Dic12—122no—
410#204—62no—
411ΓL(1,𝔽25)—121no—
412D3×C8—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—22no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—84no—
426C2×C3×D3#13712yes—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×M16—91no—
445C22×C8—31no—
446C4⋊Q8—91no—
447#125—181no—
448#124—91no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—31no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—181no—
465#107—31no—
466#107—31no—
467#107—91no—
468C4⋊C8—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102D3211yescharacteristic
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—31no—
486C23×C3—41no—
487C23×C3—61no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—241no—
491C22×D3—21no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—81no—
495C22×D3D3×D411yescharacteristic
496C22×D3D3×D411yescharacteristic
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—32no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—61no—
505C3×D4—122no—
506C3×D4—241no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—42no—
525#67—62no—
526#67—62no—
527#67—81no—
528#67—122no—
529#67—122no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—122no—
546C2×Dic3—241no—
547C2×Dic3D3×D411yescharacteristic
548C2×Dic3D3×D411yescharacteristic
549D12—21no—
550D12#23512yes—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—81no—
556C4×D3—81no—
557C4×D3—122no—
558C4×D3—241no—
559Dic6—62no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—121no—
569Dic6—121no—
570Dic6—121no—
571Dic6—241no—
572Dic6—241no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32—81no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13711yescharacteristic
586C2×C32#57611yescharacteristic
587C3×D3—22no—
588C3×D3—41no—
589C3×D3—42no—
590C24—61no—
591#41—182no—
592#41—361no—
593C2×Q8—91no—
594C2×Q8—91no—
595C2×Q8—181no—
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—62no—
599C2×D4—61no—
600C2×D4—91no—
601C2×D4—121no—
602C2×D4—181no—
603C2×D4C2×D3211yescharacteristic
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—181no—
609C22×C4—181no—
610Q16—361no—
611SD16—182no—
612SD16—361no—
613M16—361no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—121no—
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—91no—
641C42—181no—
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—62no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—244no—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—22no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—84no—
673C2×D3#91512yes—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4C2×#23511yescharacteristic
685C3×C4#100411yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4#100911yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—121no—
698Dic3—121no—
699Dic3—122no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—21no—
707C23—31no—
708C23—31no—
709C23—61no—
710C23—122no—
711C23—122no—
712C23—241no—
713Q8—181no—
714Q8—181no—
715Q8—181no—
716Q8—181no—
717Q8—721no—
718D4—21no—
719D4—21no—
720D4—32no—
721D4—61no—
722D4—122no—
723D4—182no—
724D4—241no—
725D4—362no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—362no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—62no—
753C2×C3—81no—
754C2×C3—81no—
755C2×C3—122no—
756C2×C3—121no—
757C2×C3—161no—
758C2×C3#549011yescharacteristic
759C2×C3#565411yescharacteristic
760C2×C3#575711yescharacteristic
761C2×C3#575711yescharacteristic
762C2×C3C2×#91511yescharacteristic
763C2×C3D3×#13711yescharacteristic
764D3—22no—
765D3—41no—
766D3—42no—
767C22—32no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—61no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—244no—
780C22D32×D411yescharacteristic
781C4—41no—
782C4—61no—
783C4—61no—
784C4—121no—
785C4—121no—
786C4—121no—
787C4—181no—
788C4—181no—
789C4—361no—
790C4—361no—
791C4D3×#23511yescharacteristic
792C4#6431411yescharacteristic
793C3—21no—
794C3#7876311yescharacteristic, complemented
795C3#8128911yescharacteristic, complemented
796C2—62no—
797C2—81no—
798C2—121no—
799C2—122no—
800C2#1059427211yescharacteristic
801C2#1059473111yescharacteristic
802C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595228C2
hypercenter#102D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594531C2semidirect
3. #10592466C2semidirect
4. C3×#4774C2semidirect
5. C3×D3×#102C2semidirect
6. #10591496C2semidirect
7. #10591462C2semidirect
8. #10591459C2semidirect
9. #10590969C2semidirect
10. #10590852C2semidirect
11. #10590778C2semidirect
12. #10590723C2semidirect
13. #10590607C2semidirect
14. #10590461C2semidirect
15. #10590427C2semidirect
22. C2×#3746C22semidirect
23. #64096C22semidirect
27. C3×D3×C4⋊C4C22semidirect
32. #63919C22semidirect
39. #63857C22semidirect
43. C2×#3711C22semidirect
45. #63641C22semidirect
46. #63637C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#818C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
60. #63555C22semidirect
80. #4774D3semidirect
82. D3×#102D3semidirect
191. D3×C4⋊C4C2×D3semidirect
217. (C2×D3)⋊C8C2×D3semidirect
218. #818C2×D3semidirect
237. #807C2×D3semidirect
705. C32#3314semidirect
794. C3#78763semidirect
795. C3#81289semidirect

Maximal subgroups

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

subgroupindex
#105952282
#105945312
#105924662
C3×#47742
C3×D3×#1022
#105914962
#105914622
#105914592
#105909692
#105908522
#105907782
#105907232
#105906072
#105904612
#105904272
#812893
#787633