Finite Group Databasebeta

← #11889247

Subgroups — #11889247

Order 1152.

910 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596013C211yesmaximal, characteristic, complemented
2C3×#5550C211yesmaximal, characteristic
3C3×#5011C211yesmaximal, characteristic, complemented
4#10591175C211yesmaximal, characteristic, complemented
5#10591173C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591127C211yesmaximal, characteristic, complemented
8#10591121C211yesmaximal, characteristic, complemented
9#10591093C211yesmaximal, characteristic, complemented
10#10591086C211yesmaximal, characteristic, complemented
11#10591084C211yesmaximal, characteristic, complemented
12#10590378C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590276C211yesmaximal, characteristic, complemented
15#10590268C211yesmaximal, characteristic, complemented
16#83497—31nomaximal
17#79502—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64145—21no—
22#64135C2211yescharacteristic
23#64135C2211yescharacteristic, complemented
24#64133C2211yescharacteristic
25#64133C2211yescharacteristic, complemented
26#64096—21no—
27#64088—21no—
28#64088—21no—
29#64078C2211yescharacteristic, complemented
30C4×#634C2211yescharacteristic, complemented
31C3×#937—21no—
32C3×#930C2211yescharacteristic
33C3×#924C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×#894—21no—
37C3×#884—21no—
38C3×D3×C22⋊C4—21no—
39C3×#875C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C2×#3719C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×#830C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#803C2211yescharacteristic, complemented
48#63575C2211yescharacteristic, complemented
49#63573C2211yescharacteristic, complemented
50#63573C2211yescharacteristic, complemented
51#63567C2211yescharacteristic, complemented
52#63566C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61C3×#546—31no—
62#5550D311yescharacteristic
63#5542—31no—
64#5542—31no—
65#5542—61no—
66C3×#435—31no—
67#5239—31no—
68#5233—31no—
69#5218—31no—
70#5215—31no—
71#5137—31no—
72#5131—31no—
73#5114—31no—
74#5113—31no—
75#5055—31no—
76#5054—31no—
77#5052—31no—
78#5045—31no—
79#5041—31no—
80#5035—31no—
81#5018—31no—
82#5011D311yescharacteristic, complemented
83#5008—31no—
84#4845—31no—
85#4842—31no—
86#4737—31no—
87#4733—31no—
88#4731—31no—
89#4723—31no—
90#4714—31no—
91#4710—31no—
92C23×C3×D3—21no—
93C2×C32×D4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#634—21no—
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C3×#235—22no—
101C3×#235—41no—
102C2×C3×D12—22no—
103C2×C3×D12—21no—
104C2×C3×D12—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×Dic6C2311yescharacteristic
110C32×C4⋊C4D411yescharacteristic
111C32×C22⋊C4D411yescharacteristic
112C32×C22⋊C4D411yescharacteristic
113C32×C42C2311yescharacteristic
114#3757—21no—
115#3757—21no—
116#3757—21no—
117#3757—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123#3750—21no—
124#3750—21no—
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3—21no—
128C3×#217—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×#208—41no—
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3719—41no—
142#3716—22no—
143#3716—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C2×C3×M16—31no—
150C22×C3×C8—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×#121—31no—
155C3×#121—61no—
156C3×#120—61no—
157C3×C4×D4—21no—
158C3×C4×D4—31no—
159C3×C4×D4C2×D311yescharacteristic
160C3×C4×D4C2×D311yescharacteristic
161C2×C3×C22⋊C4—61no—
162C2×#216—31no—
163#937—21no—
164#936—62no—
165#936—61no—
166#936—61no—
167C2×#214—31no—
168C2×#214—31no—
169#930C2×D311yescharacteristic
170#926—31no—
171#926—31no—
172#926—31no—
173#926—31no—
174#926—61no—
175#926—61no—
176#924—31no—
177#924—31no—
178#924—31no—
179#924—31no—
180#924—61no—
181#924—61no—
182#924C2×D311yescharacteristic
183C2×#208C2×D311yescharacteristic
184C22×C3⋊C8C2×D311yescharacteristic, complemented
185C2×Dic12—31no—
186C2×#204—31no—
187C2×#204—31no—
188#894—21no—
189#887—62no—
190#887—61no—
191#887—61no—
192#884—21no—
193D3×C22⋊C4—21no—
194#879—62no—
195#879—62no—
196#879—61no—
197#879—61no—
198#879—61no—
199#879—61no—
200#875C2×D311yescharacteristic
201C4×D12C2×D311yescharacteristic
202#869—31no—
203#869—31no—
204#869—61no—
205C4×Dic6—31no—
206C4×Dic6—31no—
207C4×Dic6—61no—
208C3×C4⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×#97—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#832—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#830C2×D311yescharacteristic
222#830C2×D311yescharacteristic, complemented
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#818—31no—
230#817—31no—
231#817—31no—
232#816—31no—
233#816—31no—
234#816—31no—
235#816—31no—
236#810—31no—
237#808—31no—
238#808—31no—
239#807—31no—
240C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
241#803C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C23×C32C2×D411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C32×D4—41no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263#634—21no—
264#634—21no—
265#634—42no—
266C3×#67—42no—
267C3×#67—81no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—42no—
274C3×D12#4112yes—
275C3×C4×D3—42no—
276C3×C4×D3—81no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#556—91no—
284#546—31no—
285#489—91no—
286#485—91no—
287#482—91no—
288#476—91no—
289#470—91no—
290#465—91no—
291#464—91no—
292#452—91no—
293#450—91no—
294#440—91no—
295#435—31no—
296#418—91no—
297#416—91no—
298C24×C3—61no—
299C23×D3—21no—
300C3×#41—62no—
301C3×#41—121no—
302C2×C3×Q8—31no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—62no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—121no—
311C2×C3×D4D1211yescharacteristic
312C2×C3×D4#6711yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—21no—
322C2×#67—21no—
323#235—22no—
324#235—41no—
325C2×D12—22no—
326C2×D12—21no—
327C2×D12—41no—
328C2×D12C22×D311yescharacteristic
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C2×Dic6—62no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C3×M16—121no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4D1211yescharacteristic
349C3×C4⋊C4#6711yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4D1211yescharacteristic
358C3×C22⋊C4D1211yescharacteristic
359C3×C22⋊C4#6711yescharacteristic
360C3×C22⋊C4#6711yescharacteristic
361C3×C42—21no—
362C3×C42C22×D311yescharacteristic
363C3×C42C22×D311yescharacteristic
364#217—21no—
365#217—62no—
366#217—62no—
367#217—62no—
368#217—62no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#216—121no—
378#214—62no—
379#214—121no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—62no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—62no—
399Dic3⋊C4—62no—
400Dic3⋊C4—62no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407C4×Dic3—62no—
408C4×Dic3—62no—
409C4×Dic3—62no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416#208—41no—
417C2×C3⋊C8—41no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422Dic12—121no—
423#204—62no—
424#204—121no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32C22×D411yescharacteristic
432C2×C3×D3—22no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—84no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4C2×#4111yescharacteristic
444C32×C4H(5,𝔽2)11yescharacteristic
445C3⋊Dic3—41no—
446C3⋊Dic3—41no—
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—31no—
452C22×D4—31no—
453C2×Q16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C2×M16—31no—
457C22×C8—31no—
458C4⋊Q8—91no—
459#126—181no—
460#126—181no—
461#124—31no—
462#124—181no—
463#123—61no—
464C22⋊Q8—31no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467#121—31no—
468#121—61no—
469#120—61no—
470C4×Q8—91no—
471C4×Q8—181no—
472C4×D4—31no—
473C4×D4D3211yescharacteristic
474#117—91no—
475#117—91no—
476C2×C22⋊C4—61no—
477#107—91no—
478#106—91no—
479#106—91no—
480C4⋊C8—31no—
481#103—91no—
482#103—91no—
483#103—91no—
484#103—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490#102—91no—
491C22⋊C8—31no—
492C22⋊C8—31no—
493#97—31no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—61no—
497C23×C3—61no—
498C23×C3—122no—
499C23×C3—122no—
500C23×C3—241no—
501C23×C3C2×D1211yescharacteristic
502C23×C3C2×D1211yescharacteristic
503C23×C3C2×#6711yescharacteristic
504C23×C3C2×#6711yescharacteristic
505C22×D3—21no—
506C22×D3—21no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—81no—
510C3×Q8—61no—
511C3×Q8—61no—
512C3×D4—32no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—42no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—122no—
520C3×D4—122no—
521C3×D4—241no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—122no—
542C2×C3×C4—241no—
543C2×C3×C4C2×D1211yescharacteristic
544C2×C3×C4C2×D1211yescharacteristic
545C2×C3×C4C2×D1211yescharacteristic
546C2×C3×C4C2×D1211yescharacteristic
547C2×C3×C4C2×#6711yescharacteristic
548C2×C3×C4C2×#6711yescharacteristic
549C2×C3×C4C2×#6711yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—42no—
554#67—81no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—62no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—62no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569D12—21no—
570D12—21no—
571D12—21no—
572D12—42no—
573D12#23712yes—
574C4×D3—42no—
575C4×D3—81no—
576Dic6—21no—
577Dic6—21no—
578Dic6—61no—
579Dic6—61no—
580Dic6—61no—
581Dic6—61no—
582Dic6—121no—
583Dic6—121no—
584Dic6—124no—
585Dic6—122no—
586Dic6—122no—
587C3×C8—61no—
588C3×C8—61no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—21no—
595C2×C32—41no—
596C2×C32—41no—
597C2×C32#54611yescharacteristic
598C2×C32#57511yescharacteristic
599C2×C32#57711yescharacteristic
600C3×D3—42no—
601C3×D3—81no—
602C24—61no—
603#41—62no—
604#41—121no—
605C2×Q8—31no—
606C2×Q8—91no—
607C2×Q8—181no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—62no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—121no—
615C2×D4#62611yescharacteristic
616C22×C4—61no—
617C22×C4—61no—
618C22×C4C2×D3211yescharacteristic
619C22×C4C2×D3211yescharacteristic
620Q16—361no—
621SD16—182no—
622SD16—361no—
623M16—121no—
624C2×C8—31no—
625C2×C8—31no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—121no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—91no—
632C4⋊C4—91no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4#62611yescharacteristic
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4#62611yescharacteristic
649C22⋊C4#62611yescharacteristic
650C42—181no—
651C42—181no—
652C42—181no—
653C42C2×D3211yescharacteristic
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—62no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—244no—
680C22×C3C22×D1211yescharacteristic
681C22×C3C22×#6711yescharacteristic
682C2×D3—22no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—84no—
689C3×C4—22no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4C2×#23711yescharacteristic
706C3×C4#100411yescharacteristic
707C3×C4#100411yescharacteristic
708C3×C4D3×#4111yescharacteristic
709Dic3—41no—
710Dic3—41no—
711Dic3—122no—
712Dic3—122no—
713Dic3—122no—
714Dic3—122no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723C32#331111yescharacteristic, complemented, Sylow
724C23—61no—
725C23—61no—
726C23—122no—
727C23—122no—
728C23—241no—
729C23C2×#62611yescharacteristic
730C23C2×#62611yescharacteristic
731Q8—61no—
732Q8—61no—
733Q8—181no—
734Q8—181no—
735Q8—362no—
736D4—32no—
737D4—41no—
738D4—61no—
739D4—61no—
740D4—61no—
741D4—122no—
742D4—122no—
743D4—241no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—122no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—241no—
756C2×C4C2×#62611yescharacteristic
757C2×C4C2×#62611yescharacteristic
758C2×C4C2×#62611yescharacteristic
759C2×C4C2×#62611yescharacteristic
760C2×C4C22×D3211yescharacteristic
761C8—61no—
762C8—61no—
763C8—61no—
764C8—61no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—41no—
769C2×C3—41no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—81no—
773C2×C3—81no—
774C2×C3—122no—
775C2×C3—241no—
776C2×C3#555411yescharacteristic
777C2×C3#574811yescharacteristic
778C2×C3#575111yescharacteristic
779C2×C3#580611yescharacteristic
780C2×C3#582211yescharacteristic
781C2×C3#583611yescharacteristic
782D3—42no—
783D3—81no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—62no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—244no—
797C22C22×#62611yescharacteristic
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—121no—
803C4—121no—
804C4—361no—
805C4—361no—
806C4—361no—
807C4—361no—
808C4D3×#23711yescharacteristic
809C4#6431311yescharacteristic
810C3—21no—
811C3#7950211yescharacteristic, complemented
812C3#8349711yescharacteristic, complemented
813C2—41no—
814C2—41no—
815C2—122no—
816C2—241no—
817C2#1059479511yescharacteristic
818C2#1059524611yescharacteristic
819C2#1059544711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5550C2
hypercenterC4×D4D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596013C2semidirect
3. C3×#5011C2semidirect
4. #10591175C2semidirect
5. #10591173C2semidirect
6. #10591172C2semidirect
7. #10591127C2semidirect
8. #10591121C2semidirect
9. #10591093C2semidirect
10. #10591086C2semidirect
11. #10591084C2semidirect
12. #10590378C2semidirect
13. #10590360C2semidirect
14. #10590276C2semidirect
15. #10590268C2semidirect
23. #64135C22semidirect
25. #64133C22semidirect
29. #64078C22semidirect
30. C4×#634C22semidirect
35. C22×C3×C3⋊C8C22semidirect
41. C2×#3719C22semidirect
45. C3×#830C22semidirect
46. C3×C4⋊(C3⋊C8)C22semidirect
47. C3×#803C22semidirect
48. #63575C22semidirect
49. #63573C22semidirect
50. #63573C22semidirect
51. #63567C22semidirect
52. #63566C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
82. #5011D3semidirect
184. C22×C3⋊C8C2×D3semidirect
222. #830C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. #803C2×D3semidirect
723. C32#3311semidirect
811. C3#79502semidirect
812. C3#83497semidirect

Maximal subgroups

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

subgroupindex
#105960132
C3×#55502
C3×#50112
#105911752
#105911732
#105911722
#105911272
#105911212
#105910932
#105910862
#105910842
#105903782
#105903602
#105902762
#105902682
#834973
#795023