Finite Group Databasebeta

← #11878513

Subgroups — #11878513

Order 1152.

856 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595044C211yesmaximal, characteristic, complemented
2#10595004C211yesmaximal, characteristic, complemented
3#10592421C211yesmaximal, characteristic, complemented
4C3×#4734C211yesmaximal, characteristic, complemented
5C3×#4727C211yesmaximal, characteristic, complemented
6#10591173C211yesmaximal, characteristic, complemented
7#10591094C211yesmaximal, characteristic, complemented
8#10590962C211yesmaximal, characteristic, complemented
9#10590960C211yesmaximal, characteristic, complemented
10#10590848C211yesmaximal, characteristic, complemented
11#10590833C211yesmaximal, characteristic, complemented
12#10590831C211yesmaximal, characteristic, complemented
13#10590828C211yesmaximal, characteristic, complemented
14#10590682C211yesmaximal, characteristic, complemented
15#10590680C211yesmaximal, characteristic, complemented
16#80095—31nomaximal
17#78676—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22#64133C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63980—21no—
29#63980—21no—
30#63970—21no—
31#63970—21no—
32#63908—21no—
33#63908C2211yescharacteristic
34#63908C2211yescharacteristic
35#63908C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63887—21no—
38#63885—21no—
39#63857C2211yescharacteristic
40#63856—21no—
41#63856C2211yescharacteristic
42#63856C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C2×#3716C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63645C2211yescharacteristic
47#63645C2211yescharacteristic
48#63643C2211yescharacteristic
49#63643C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63566C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5833—31no—
62#5833—31no—
63#5833—31no—
64#5608—31no—
65C3×#449—31no—
66C3×#408—31no—
67#5239—31no—
68#5174—31no—
69#5173—31no—
70#5158—31no—
71#5157—31no—
72#5134—31no—
73#5134—31no—
74#5116—31no—
75#5115—31no—
76#5033—31no—
77#4813—31no—
78#4811—31no—
79#4780—31no—
80#4774—31no—
81#4736—31no—
82#4736—31no—
83#4734—31no—
84#4734D311yescharacteristic, complemented
85#4733—31no—
86#4733—31no—
87#4727D311yescharacteristic, complemented
88#4722—31no—
89#4722—31no—
90#4722—31no—
91#4722—61no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C2×C3×#67D411yescharacteristic
99C3×#235—41no—
100C3×#235—41no—
101C3×#235—41no—
102C3×#235—41no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6D411yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3795—41no—
118#3795—41no—
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121#3757—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D24—41no—
132C3×#204—41no—
133C3×ΓL(1,𝔽25)—41no—
134C3×D3×C8—41no—
135#3724—21no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3719—41no—
146#3716—41no—
147#3203—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×#237—31no—
151C2×#235—31no—
152C2×#235C2×D311yescharacteristic
153C2×#235C2×D311yescharacteristic
154C2×C3×SD16—31no—
155C2×C3×D8—31no—
156C2×C3×M16—31no—
157C22×C3×C8—31no—
158C3×#121—31no—
159#946—31no—
160#946—31no—
161#946—61no—
162#946—61no—
163C2×#216—31no—
164#939—61no—
165#939—61no—
166#939—61no—
167#939—61no—
168#939—61no—
169#939—61no—
170#939—61no—
171#938—31no—
172#938—31no—
173#938—31no—
174#938—61no—
175#938—61no—
176#938—61no—
177C2×#214—31no—
178#930—31no—
179#930—31no—
180#930—31no—
181#930—61no—
182#930C2×D311yescharacteristic
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—61no—
187#924—31no—
188#924—31no—
189#924—31no—
190#924—31no—
191#924—31no—
192#924—61no—
193#924—61no—
194C2×Dic12—31no—
195C2×D24C2×D311yescharacteristic
196C2×#204—31no—
197C2×#204C2×D311yescharacteristic
198C2×ΓL(1,𝔽25)C2×D311yescharacteristic
199C2×D3×C8C2×D311yescharacteristic
200#897—31no—
201D3×C4⋊C4—31no—
202#884—61no—
203#878—61no—
204C3×#103—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8C2×D311yescharacteristic
211C3×C22⋊C8C2×D311yescharacteristic
212#835—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#830C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic
222(C2×D3)⋊C8C2×D311yescharacteristic
223#818—31no—
224#818—31no—
225#818—31no—
226#818—31no—
227#818—31no—
228#818—31no—
229#818—61no—
230#818—61no—
231#816—31no—
232#816—31no—
233#816—31no—
234#816—31no—
235#816—31no—
236#816—61no—
237#816—61no—
238#816C2×D311yescharacteristic
239#807—31no—
240#807—31no—
241C23×C32C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—81no—
255#634—21no—
256#634—21no—
257C3×#67—41no—
258C3×#67—41no—
259C3×#67—42no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—41no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—42no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6—41no—
278#625—42no—
279#625—81no—
280#625—81no—
281#625—81no—
282D3×Dic3—42no—
283D3×Dic3—81no—
284C32×C8—21no—
285C32×C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—91no—
289#537—91no—
290#484—91no—
291#484—91no—
292#480—91no—
293#480—91no—
294#468—91no—
295#468—91no—
296#467—91no—
297#466—91no—
298#452—91no—
299#452—91no—
300#449—31no—
301#449—91no—
302#408—31no—
303C3×#41—121no—
304C3×#41—121no—
305C3×#41—121no—
306C3×#41—121no—
307C2×C3×Q8—31no—
308C2×C3×Q8—31no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C2×#67—21no—
323C2×#67—21no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67D1211yescharacteristic
333C2×#67D1211yescharacteristic
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—121no—
339#237—121no—
340#237—121no—
341#235—41no—
342#235—41no—
343#235—41no—
344#235—41no—
345#235—121no—
346#235—121no—
347C2×D12D1211yescharacteristic
348C2×D12C22×D311yescharacteristic
349C2×D12C22×D311yescharacteristic
350C2×C4×D3—21no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3C22×D311yescharacteristic
354C2×C4×D3C22×D311yescharacteristic
355C2×Dic6—31no—
356C2×Dic6—31no—
357C2×Dic6—61no—
358C2×Dic6D1211yescharacteristic
359C2×Dic6C22×D311yescharacteristic
360C3×SD16—121no—
361C3×D8—121no—
362C3×M16—121no—
363C2×C3×C8—21no—
364C2×C3×C8—21no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—121no—
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C3×C4⋊C4—31no—
373C3×C22⋊C4—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—121no—
383#216—121no—
384#214—121no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—121no—
406C4⋊Dic3C22×D311yescharacteristic
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—121no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418Dic12—121no—
419D24—41no—
420#204—41no—
421#204—121no—
422ΓL(1,𝔽25)—41no—
423D3×C8—41no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32C22×D411yescharacteristic
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C32×C4—21no—
441C32×C4H(5,𝔽2)11yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
443C3⋊Dic3—41no—
444C3⋊Dic3—41no—
445C3⋊Dic3—41no—
446C3⋊Dic3—41no—
447C3×Dic3—21no—
448C3×Dic3—21no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—91no—
454C2×Q16—91no—
455C2×SD16—31no—
456C2×SD16—91no—
457C2×D8—31no—
458C2×M16—31no—
459C22×C8—31no—
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464C22⋊Q8—181no—
465C22⋊Q8—181no—
466#121—31no—
467#121—91no—
468#121—91no—
469#121—91no—
470#121—181no—
471#121—181no—
472#121—181no—
473#121—181no—
474#121—181no—
475#121—181no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478#107—91no—
479#107—91no—
480#107—91no—
481#107—91no—
482#103—31no—
483#103—91no—
484#103—91no—
485#103—91no—
486#102—31no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—31no—
491C22⋊C8—31no—
492C22⋊C8—31no—
493C22⋊C8D3211yescharacteristic
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—31no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3C2×D1211yescharacteristic
500C23×C3D3×D411yescharacteristic
501C22×D3—21no—
502C22×D3—21no—
503C22×D3C2×D1211yescharacteristic
504C22×D3C2×D1211yescharacteristic
505C3×Q8—61no—
506C3×Q8—61no—
507C3×Q8—121no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—121no—
513C3×D4—121no—
514C3×D4—121no—
515C3×D4—122no—
516C3×D4—241no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4C2×D1211yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538#67—41no—
539#67—41no—
540#67—42no—
541#67—81no—
542#67—122no—
543#67—122no—
544#67—241no—
545#67—241no—
546#67—241no—
547#67—241no—
548#67—241no—
549#67—241no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3—241no—
566C2×Dic3—241no—
567C2×Dic3—241no—
568C2×Dic3—242no—
569C2×Dic3C2×D1211yescharacteristic
570C2×Dic3C2×D1211yescharacteristic
571D12—21no—
572D12—21no—
573D12—21no—
574D12—21no—
575D12—41no—
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—42no—
581C4×D3—122no—
582C4×D3—241no—
583Dic6—21no—
584Dic6—21no—
585Dic6—41no—
586Dic6—61no—
587Dic6—61no—
588Dic6—61no—
589Dic6—61no—
590Dic6—121no—
591Dic6—121no—
592C3×C8—21no—
593C3×C8—21no—
594C3×C8—21no—
595C3×C8—21no—
596C3×C8—41no—
597C3×C8—41no—
598C3×C8—61no—
599C3×C8—61no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C2×C32—41no—
603C2×C32#53411yescharacteristic
604C2×C32#57611yescharacteristic
605C2×C32#57811yescharacteristic
606C3×D3—41no—
607C3×D3—41no—
608C3×D3—81no—
609C3×D3—81no—
610#41—121no—
611#41—121no—
612#41—121no—
613#41—121no—
614#41—361no—
615#41—361no—
616C2×Q8—31no—
617C2×Q8—31no—
618C2×Q8—91no—
619C2×D4—31no—
620C2×D4—31no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—31no—
624C2×D4—61no—
625C2×D4—61no—
626C2×D4—181no—
627C2×D4—181no—
628C2×D4—181no—
629C2×D4—181no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—61no—
633C22×C4—181no—
634C22×C4—181no—
635C22×C4—181no—
636C22×C4C2×D3211yescharacteristic
637Q16—361no—
638SD16—121no—
639SD16—361no—
640D8—121no—
641M16—121no—
642C2×C8—31no—
643C2×C8—31no—
644C2×C8—121no—
645C2×C8C2×D3211yescharacteristic
646C2×C8C2×D3211yescharacteristic
647C4⋊C4—31no—
648C4⋊C4—91no—
649C4⋊C4—91no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4—181no—
657C22⋊C4—61no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22×C3—22no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3C22×D1211yescharacteristic
688C22×C3C2×D3×D411yescharacteristic
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—41no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4#100411yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4#100411yescharacteristic
713C3×C4#100411yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—41no—
717Dic3—41no—
718Dic3—121no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—121no—
725Dic3—121no—
726Dic3—241no—
727Dic3—241no—
728Dic3—241no—
729Dic3—241no—
730C32#320311yescharacteristic, complemented, Sylow
731C23—31no—
732C23—31no—
733C23—61no—
734C23—61no—
735C23D3×D1211yescharacteristic
736Q8—61no—
737Q8—61no—
738Q8—121no—
739Q8—181no—
740Q8—181no—
741D4—61no—
742D4—61no—
743D4—61no—
744D4—61no—
745D4—121no—
746D4—121no—
747D4—121no—
748D4—122no—
749D4—241no—
750D4—362no—
751D4—721no—
752D4—721no—
753D4—721no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—122no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—362no—
770C2×C4—721no—
771C2×C4—721no—
772C2×C4D3×D1211yescharacteristic
773C2×C4C22×D3211yescharacteristic
774C8—21no—
775C8—21no—
776C8—61no—
777C8—61no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—42no—
782C2×C3—41no—
783C2×C3—41no—
784C2×C3—121no—
785C2×C3—121no—
786C2×C3—241no—
787C2×C3—241no—
788C2×C3#549311yescharacteristic
789C2×C3#558911yescharacteristic
790C2×C3#575211yescharacteristic
791C2×C3#575311yescharacteristic
792C2×C3#577111yescharacteristic
793C2×C3#577411yescharacteristic
794D3—41no—
795D3—41no—
796D3—81no—
797D3—81no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22C2×D3×D1211yescharacteristic
814C4—21no—
815C4—61no—
816C4—61no—
817C4—121no—
818C4—121no—
819C4—361no—
820C4—361no—
821C4—361no—
822C4—361no—
823C4#6431311yescharacteristic
824C4#6431311yescharacteristic
825C3—21no—
826C3#7867611yescharacteristic, complemented
827C3#8009511yescharacteristic, complemented
828C2—41no—
829C2—121no—
830C2—121no—
831C2—241no—
832C2—241no—
833C2#1059429011yescharacteristic
834C2#1059469211yescharacteristic
835C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3203
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595044C2semidirect
2. #10595004C2semidirect
3. #10592421C2semidirect
4. C3×#4734C2semidirect
5. C3×#4727C2semidirect
6. #10591173C2semidirect
7. #10591094C2semidirect
8. #10590962C2semidirect
9. #10590960C2semidirect
10. #10590848C2semidirect
11. #10590833C2semidirect
12. #10590831C2semidirect
13. #10590828C2semidirect
14. #10590682C2semidirect
15. #10590680C2semidirect
84. #4734D3semidirect
87. #4727D3semidirect
730. C32#3203semidirect
826. C3#78676semidirect
827. C3#80095semidirect

Maximal subgroups

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

subgroupindex
#105950442
#105950042
#105924212
C3×#47342
C3×#47272
#105911732
#105910942
#105909622
#105909602
#105908482
#105908332
#105908312
#105908282
#105906822
#105906802
#800953
#786763