Finite Group Databasebeta

← #11887148

Subgroups — #11887148

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic
2#10594537C211yesmaximal, characteristic, complemented
3#10592477C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591439C211yesmaximal, characteristic, complemented
8#10591419C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590825C211yesmaximal, characteristic, complemented
11#10590744C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590500C211yesmaximal, characteristic, complemented
15#10590465C211yesmaximal, characteristic, complemented
16#81577—31nomaximal
17#78758—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21#64147C2211yescharacteristic
22C2×#3754C2211yescharacteristic, complemented
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24#64106C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28C3×#888C2211yescharacteristic, complemented
29#63983—21no—
30#63976—21no—
31#63970—21no—
32#63908C2211yescharacteristic
33#63904—21no—
34C4×#626C2211yescharacteristic
35#63900C2211yescharacteristic, complemented
36Dic3×D12C2211yescharacteristic
37#63888—21no—
38#63857C2211yescharacteristic, complemented
39#63856—21no—
40#63845—21no—
41#63844C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63643C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61D4×#67—31no—
62#5730—31no—
63#5717—31no—
64#5511—31no—
65C3×#486—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5114—31no—
69C8×#67—31no—
70#5084—31no—
71#5075—31no—
72#4968—31no—
73#4778—31no—
74#4778—31no—
75#4778—31no—
76#4778—61no—
77#4777—31no—
78#4777—31no—
79#4777—31no—
80#4776—31no—
81#4776—31no—
82#4776—31no—
83D3×#102—31no—
84D3×#102—31no—
85D3×#102D311yescharacteristic, complemented
86#4762—31no—
87#4761—31no—
88#4760D311yescharacteristic, complemented
89#4758—31no—
90C4×#204—31no—
91C8×D12—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108D3×#67—44no—
109C2×#626D411yescharacteristic
110C2×#625—21no—
111C2×#625—21no—
112C2×#624—21no—
113C2×D3×Dic3—21no—
114#3802—22no—
115#3802—41no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3757—21no—
119#3754—41no—
120#3752—21no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C8×C3⋊D3—41no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3716—22no—
144#3716—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4C2×D311yescharacteristic
152C22×C3×C8—31no—
153C3×C4⋊Q8—31no—
154C3×#127—31no—
155C2×C3×C4⋊C4—31no—
156#953—61no—
157#946—61no—
158#946—61no—
159#940C2×D311yescharacteristic
160#939—61no—
161#938—31no—
162#938—31no—
163#938—31no—
164#938—61no—
165#938—61no—
166#937—61no—
167#937—61no—
168#937—61no—
169D4×Dic3—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—31no—
174C2×#214—61no—
175#930—31no—
176C4×#67—31no—
177C4×#67—61no—
178#924—31no—
179#924—61no—
180C2×#204—31no—
181C2×#204—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184C2×D3×C8—61no—
185C2×D3×C8C2×D311yescharacteristic, complemented
186#897—31no—
187#897—31no—
188#897—31no—
189#897—61no—
190#896—61no—
191#893—61no—
192D3×C4⋊C4—31no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4C2×D311yescharacteristic, complemented
195#890—61no—
196#889—61no—
197#888C2×D311yescharacteristic, complemented
198#887—31no—
199C4×D12—31no—
200C4×D12—31no—
201C4×Dic6—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic, complemented
210C3×#102C2×D311yescharacteristic, complemented
211C3×C4×C8—31no—
212#832—31no—
213#832—31no—
214#832C2×D311yescharacteristic, complemented
215#832C2×D311yescharacteristic, complemented
216#830—31no—
217#821C2×D311yescharacteristic
218#821C2×D311yescharacteristic, complemented
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#817—31no—
223#817—31no—
224#816—31no—
225#816—31no—
226#816—61no—
227Dic3⋊C8—31no—
228C8×Dic3C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic, complemented
233#808—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237#808—61no—
238C4⋊(C3⋊C8)—31no—
239C23×C32—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260#634—21no—
261#634—21no—
262C3×#67—42no—
263C3×#67—42no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12#4112yes—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—81no—
277C3×Dic6—81no—
278#626SD1614yescomplemented
279#625—42no—
280#625—42no—
281#624—81no—
282D3×Dic3—42no—
283C32×C8—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—91no—
289#486—31no—
290#481—91no—
291#481—91no—
292#476—91no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—31no—
301C2×#102—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—61no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—62no—
314C2×C3×D4—121no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C2×#67—21no—
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—31no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—121no—
330C2×#67—124no—
331C22×Dic3—61no—
332D3×D4—22no—
333D3×D4—41no—
334D3×D4—62no—
335D3×D4—62no—
336D3×D4—121no—
337D3×D4—121no—
338D3×D4—124no—
339C2×D12—31no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3C22×D311yescharacteristic
350C2×Dic6—21no—
351C2×Dic6—31no—
352C2×Dic6—31no—
353C2×Dic6—61no—
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8—121no—
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C42—31no—
368#217—31no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—121no—
375#214—62no—
376#214—121no—
377#214—121no—
378#214—121no—
379#214—122no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—121no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—121no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—31no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415#204—62no—
416#204—121no—
417D3×C8—41no—
418D3×C8—121no—
419D3×C8—121no—
420D3×C8—122no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3C2×SD1612yes—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—22no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—84no—
437C2×C3×D3C2×SD1612yes—
438D32—84no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—21no—
443C3⋊Dic3—41no—
444C3⋊Dic3—41no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3C2×SD1612yes—
450C22×D4—31no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C22×C8—31no—
457C22×C8—91no—
458C4⋊Q8—31no—
459#127—31no—
460#125—181no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—181no—
464C22⋊Q8—181no—
465#121—91no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—91no—
471C4×D4—91no—
472C4×D4—91no—
473C4×D4—181no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—91no—
476#106—91no—
477#106—91no—
478#106—91no—
479C4⋊C8—91no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—31no—
486#102—31no—
487#102—91no—
488#102—91no—
489#102D3211yescharacteristic, complemented
490C22⋊C8—91no—
491C22⋊C8—91no—
492C4×C8—31no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—41no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C23×C3—241no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—31no—
505C22×D3—31no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—61no—
509C22×D3—81no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3D3×D411yescharacteristic
517C3×Q8—241no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—21no—
522C3×D4—32no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—61no—
526C3×D4—61no—
527C3×D4—61no—
528C3×D4—122no—
529C3×D4—122no—
530C3×D4—241no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—41no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—241no—
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—34no—
546#67—42no—
547#67—42no—
548#67—81no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—242no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—122no—
568C2×Dic3D3×D411yescharacteristic
569C2×Dic3D3×D411yescharacteristic
570C2×Dic3D3×D411yescharacteristic
571D12—21no—
572D12—21no—
573D12—21no—
574D12—34no—
575D12#23512yes—
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—81no—
583C4×D3—121no—
584C4×D3—121no—
585C4×D3—122no—
586C4×D3—241no—
587C4×D3—241no—
588Dic6—61no—
589Dic6—61no—
590Dic6—61no—
591Dic6—61no—
592Dic6—81no—
593Dic6—121no—
594Dic6—121no—
595C3×C8—21no—
596C3×C8—21no—
597C3×C8—41no—
598C3×C8—61no—
599C3×C8—61no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C3⋊C8—62no—
603C3⋊C8—61no—
604C3⋊C8—61no—
605C2×C32—81no—
606C2×C32#54611yescharacteristic
607C2×C32C22×SD1611yescharacteristic
608C2×C32#57611yescharacteristic
609C3⋊D3—22no—
610C3×D3—22no—
611C3×D3—42no—
612C3×D3—81no—
613C24—61no—
614C24—181no—
615C2×Q8—61no—
616C2×Q8—91no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—62no—
623C2×D4—91no—
624C2×D4—121no—
625C2×D4—181no—
626C2×D4—182no—
627C2×D4—181no—
628C2×D4—181no—
629C2×D4—361no—
630C2×D4—364no—
631C2×D4C2×D3211yescharacteristic
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—91no—
635C22×C4—181no—
636C22×C4—181no—
637SD16—182no—
638SD16—361no—
639SD16—361no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8—121no—
644C2×C8—361no—
645C2×C8C2×D3211yescharacteristic
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—91no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4C2×D3211yescharacteristic
657C22⋊C4—91no—
658C22⋊C4—91no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—181no—
666C22×C3—21no—
667C22×C3—32no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—62no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—244no—
686C22×C3C2×D3×D411yescharacteristic
687C22×C3C2×D3×D411yescharacteristic
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—22no—
691C2×D3—32no—
692C2×D3—32no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—62no—
699C2×D3—61no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—84no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—244no—
707C2×D3—244no—
708C2×D3D3×SD1612yes—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—32no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—81no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4C2×#23511yescharacteristic
720C3×C4#100411yescharacteristic
721C3×C4D3×#4111yescharacteristic
722C3×C4#100911yescharacteristic
723Dic3—21no—
724Dic3—21no—
725Dic3—41no—
726Dic3—41no—
727Dic3—61no—
728Dic3—61no—
729Dic3—121no—
730Dic3—121no—
731Dic3—121no—
732Dic3—121no—
733Dic3—121no—
734Dic3—241no—
735Dic3—241no—
736Dic3D3×SD1612yes—
737C32#329511yescharacteristic, complemented, Sylow
738C23—21no—
739C23—31no—
740C23—61no—
741C23—61no—
742C23—91no—
743C23—122no—
744C23—122no—
745C23—241no—
746C23—362no—
747C23—362no—
748C23—721no—
749Q8—181no—
750Q8—181no—
751Q8—241no—
752D4—21no—
753D4—21no—
754D4—32no—
755D4—61no—
756D4—61no—
757D4—61no—
758D4—94no—
759D4—122no—
760D4—122no—
761D4—241no—
762D4—362no—
763D4—362no—
764D4—362no—
765C2×C4—21no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—91no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—241no—
779C2×C4—362no—
780C2×C4—721no—
781C2×C4C22×D3211yescharacteristic
782C8—21no—
783C8—61no—
784C8—61no—
785C8—181no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—62no—
790C2×C3—81no—
791C2×C3—81no—
792C2×C3—122no—
793C2×C3—161no—
794C2×C3—241no—
795C2×C3#549011yescharacteristic
796C2×C3#567611yescharacteristic
797C2×C3#575711yescharacteristic
798C2×C3#575711yescharacteristic
799C2×C3C2×D3×SD1611yescharacteristic
800C2×C3C2×D3×SD1611yescharacteristic
801D3—22no—
802D3—42no—
803D3—62no—
804D3—62no—
805D3—81no—
806D3—122no—
807C22—32no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—61no—
812C22—61no—
813C22—62no—
814C22—92no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—181no—
821C22—181no—
822C22—244no—
823C22—724no—
824C22D32×D411yescharacteristic
825C4—32no—
826C4—41no—
827C4—61no—
828C4—61no—
829C4—121no—
830C4—121no—
831C4—181no—
832C4—361no—
833C4—361no—
834C4D3×#23511yescharacteristic
835C4#6431411yescharacteristic
836C3—21no—
837C3#7875811yescharacteristic, complemented
838C3#8157711yescharacteristic, complemented
839C2—62no—
840C2—81no—
841C2—122no—
842C2—182no—
843C2—241no—
844C2#1059428011yescharacteristic
845C2#1059473111yescharacteristic
846C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595293C2
hypercenter#102D32
hypocenterC32#3295
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. #10594537C2semidirect
3. #10592477C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4760C2semidirect
6. #10591459C2semidirect
7. #10591439C2semidirect
8. #10591419C2semidirect
9. #10590940C2semidirect
10. #10590825C2semidirect
11. #10590744C2semidirect
12. C8×#626C2semidirect
13. #10590597C2semidirect
14. #10590500C2semidirect
15. #10590465C2semidirect
22. C2×#3754C22semidirect
23. C2×C8×C3⋊D3C22semidirect
24. #64106C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×D3×C4⋊C4C22semidirect
28. C3×#888C22semidirect
35. #63900C22semidirect
38. #63857C22semidirect
41. #63844C22semidirect
43. C2×#3716C22semidirect
44. C32×#102C22semidirect
45. #63643C22semidirect
46. #63635C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
50. C3×#821C22semidirect
51. C3×C8×Dic3C22semidirect
53. C3×#809C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
85. D3×#102D3semidirect
88. #4760D3semidirect
185. C2×D3×C8C2×D3semidirect
194. D3×C4⋊C4C2×D3semidirect
197. #888C2×D3semidirect
209. C3×#102C2×D3semidirect
210. C3×#102C2×D3semidirect
214. #832C2×D3semidirect
215. #832C2×D3semidirect
218. #821C2×D3semidirect
228. C8×Dic3C2×D3semidirect
232. #809C2×D3semidirect
278. #626SD16semidirect
489. #102D32semidirect
737. C32#3295semidirect
837. C3#78758semidirect
838. C3#81577semidirect

Maximal subgroups

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

subgroupindex
#105952932
#105945372
#105924772
C3×D3×#1022
C3×#47602
#105914592
#105914392
#105914192
#105909402
#105908252
#105907442
C8×#6262
#105905972
#105905002
#105904652
#815773
#787583