Finite Group Databasebeta

← #11887389

Subgroups — #11887389

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595244C211yesmaximal, characteristic, complemented
2#10594560C211yesmaximal, characteristic, complemented
3#10592462C211yesmaximal, characteristic, complemented
4C3×#4781C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591447C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591420C211yesmaximal, characteristic, complemented
9#10590837C211yesmaximal, characteristic, complemented
10#10590829C211yesmaximal, characteristic, complemented
11#10590750C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic, complemented
13#10590539C211yesmaximal, characteristic, complemented
14#10590517C211yesmaximal, characteristic, complemented
15#10590499C211yesmaximal, characteristic, complemented
16#80102—31nomaximal
17#78760—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21#64099C2211yescharacteristic, complemented
22C2×C3×#213C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic, complemented
24C2×C3×D3×C8C2211yescharacteristic
25C3×#895C2211yescharacteristic, complemented
26C3×D3×C4⋊C4C2211yescharacteristic
27#63980—21no—
28#63976—21no—
29#63961—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63908—21no—
32#63908C2211yescharacteristic
33#63908C2211yescharacteristic
34C4×#625C2211yescharacteristic
35#63898C2211yescharacteristic, complemented
36#63884—21no—
37#63879—21no—
38#63863C2211yescharacteristic
39#63861—21no—
40#63856C2211yescharacteristic
41#63841C2211yescharacteristic, complemented
42C2×#3713C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63644C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5829—31no—
62#5806—31no—
63#5614—31no—
64#5514—31no—
65C3×#449—31no—
66C2×C3×#102—31no—
67#5233—31no—
68#5217—31no—
69#5171—31no—
70#5165—31no—
71#5156—31no—
72Dic3×D8—31no—
73#5114—31no—
74C8×#67—31no—
75#5038—31no—
76#4970—31no—
77#4811—31no—
78#4800—31no—
79#4787—31no—
80#4781D311yescharacteristic, complemented
81#4779—31no—
82#4775—31no—
83#4772—31no—
84D3×#102D311yescharacteristic, complemented
85#4768—31no—
86#4763—31no—
87#4763—31no—
88#4763—61no—
89#4756—31no—
90#4737—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×#237—22no—
99C3×#237—41no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#625—21no—
110C2×#625—21no—
111C2×#625D411yescharacteristic
112C2×D3×Dic3—21no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—41no—
129C3×D3×C8—41no—
130#3724—21no—
131#3724D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3713—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C22×C3×C8—31no—
152C3×#121—31no—
153C2×C3×C4⋊C4—31no—
154#953—61no—
155C2×#217—61no—
156#947—31no—
157#946—31no—
158#939—61no—
159#939—61no—
160#938—31no—
161#938—31no—
162#938—61no—
163#937—61no—
164#936—31no—
165#935—61no—
166#935—61no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—61no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213C2×D311yescharacteristic
174#930—31no—
175#930—31no—
176#930—61no—
177#929—61no—
178C4×#67—31no—
179C4×#67—31no—
180C4×#67—61no—
181C2×(C2×D3)⋊C4—61no—
182#926—31no—
183#924—31no—
184C22×C3⋊C8—31no—
185C2×#204C2×D311yescharacteristic, complemented
186C2×D3×C8—31no—
187C2×D3×C8C2×D311yescharacteristic
188#898—61no—
189#895C2×D311yescharacteristic, complemented
190#894—61no—
191#893—31no—
192#892—31no—
193D3×C4⋊C4C2×D311yescharacteristic
194#890—31no—
195#890—31no—
196#890—61no—
197#67⋊C4—61no—
198#879—61no—
199C3×#103—31no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic
205C3×#102C2×D311yescharacteristic
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8C2×D311yescharacteristic, complemented
221#818—31no—
222#817—31no—
223#817—31no—
224#817—61no—
225#816—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—61no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810—31no—
232#810C2×D311yescharacteristic, complemented
233#809C2×D311yescharacteristic
234#807—31no—
235#807—31no—
236#807—31no—
237#807—61no—
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—81no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C3×#67—42no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—81no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#625—22no—
275#625—42no—
276#625—81no—
277D3×Dic3—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—31no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—31no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—21no—
317C2×#67—21no—
318C2×#67—31no—
319C2×#67—31no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C22×Dic3—21no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—121no—
329#237—22no—
330#237—41no—
331D3×D4—22no—
332D3×D4—41no—
333C2×D12—21no—
334C2×D12C22×D311yescharacteristic
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—21no—
337C2×C4×D3—61no—
338C2×C4×D3C22×D311yescharacteristic
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6C22×D311yescharacteristic
341C3×SD16—121no—
342C3×D8—62no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—61no—
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—61no—
366#217—121no—
367#213—22no—
368#213—121no—
369#213—121no—
370(C2×D3)⋊C4—21no—
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—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—121no—
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—41no—
410D3×C8—41no—
411D3×C8—121no—
412C22×C32—22no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—84no—
428C2×C3×D3#13512yes—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—31no—
441C22×D4—31no—
442C2×SD16—31no—
443C2×D8—31no—
444C2×D8—91no—
445C22×C8—31no—
446C22×C8—91no—
447#126—181no—
448#125—91no—
449#124—91no—
450#123—181no—
451#123—181no—
452C22⋊Q8—91no—
453#121—31no—
454#121—91no—
455#121—91no—
456#121—181no—
457#121—181no—
458#120—181no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463#117—91no—
464C2×C4⋊C4—31no—
465C2×C22⋊C4—181no—
466#107—91no—
467#107—91no—
468#106—91no—
469C4⋊C8—91no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102D3211yescharacteristic
480C22⋊C8—31no—
481C22⋊C8—91no—
482C4×C8—91no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—81no—
498C22×D3D3×D411yescharacteristic
499C22×D3D3×D411yescharacteristic
500C3×Q8—61no—
501C3×Q8—61no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—22no—
505C3×D4—41no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—122no—
511C3×D4—122no—
512C3×D4—241no—
513C3×D4#23512yes—
514C3×D4#23712yes—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—122no—
528C2×C3×C4—241no—
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—42no—
532#67—42no—
533#67—62no—
534#67—62no—
535#67—122no—
536#67—122no—
537#67—241no—
538#67—241no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—42no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—241no—
555C2×Dic3—241no—
556C2×Dic3—241no—
557C2×Dic3—242no—
558C2×Dic3D3×D411yescharacteristic
559C2×Dic3D3×D411yescharacteristic
560D12—21no—
561D12—21no—
562D12—21no—
563D12—21no—
564D12—81no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—81no—
570C4×D3—241no—
571Dic6—21no—
572Dic6—21no—
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—42no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13511yescharacteristic
586C2×C32#57611yescharacteristic
587C3×D3—22no—
588C3×D3—41no—
589C3×D3—81no—
590C3×D3—81no—
591C24—61no—
592#41—62no—
593#41—121no—
594C2×Q8—31no—
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—91no—
602C2×D4—121no—
603C2×D4—181no—
604C2×D4—181no—
605C2×D4C2×D3211yescharacteristic
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—181no—
611C22×C4—181no—
612SD16—121no—
613D8—62no—
614D8—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—121no—
619C2×C8—361no—
620C2×C8C2×D3211yescharacteristic
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4C2×D3211yescharacteristic
630C22⋊C4—61no—
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—91no—
642C42—181no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—32no—
647C22×C3—42no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—244no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C2×D3×D411yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—84no—
680C2×D3#91612yes—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4C2×#23511yescharacteristic
691C3×C4C2×#23711yescharacteristic
692C3×C4#100411yescharacteristic
693C3×C4#100411yescharacteristic
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—241no—
709Dic3—241no—
710C32#329711yescharacteristic, complemented, Sylow
711C23—21no—
712C23—31no—
713C23—31no—
714C23—61no—
715C23—61no—
716C23—122no—
717C23—122no—
718C23—241no—
719Q8—61no—
720Q8—61no—
721D4—21no—
722D4—61no—
723D4—61no—
724D4—61no—
725D4—61no—
726D4—122no—
727D4—122no—
728D4—182no—
729D4—241no—
730D4—362no—
731D4—721no—
732D4#379512yes—
733C2×C4—21no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—122no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—241no—
748C2×C4—721no—
749C2×C4—721no—
750C2×C4C22×D3211yescharacteristic
751C8—21no—
752C8—61no—
753C8—61no—
754C8—181no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—42no—
759C2×C3—42no—
760C2×C3—62no—
761C2×C3—82no—
762C2×C3—121no—
763C2×C3—241no—
764C2×C3—241no—
765C2×C3#549011yescharacteristic
766C2×C3#559111yescharacteristic
767C2×C3#575711yescharacteristic
768C2×C3C2×#91611yescharacteristic
769C2×C3D3×#13511yescharacteristic
770C2×C3#577411yescharacteristic
771D3—22no—
772D3—41no—
773D3—81no—
774D3—81no—
775C22—22no—
776C22—32no—
777C22—41no—
778C22—41no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—244no—
791C22D32×D411yescharacteristic
792C4—41no—
793C4—61no—
794C4—61no—
795C4—121no—
796C4—121no—
797C4—181no—
798C4—181no—
799C4—361no—
800C4—361no—
801C4C2×#379511yescharacteristic
802C4#6431311yescharacteristic
803C3—21no—
804C3#7876011yescharacteristic, complemented
805C3#8010211yescharacteristic, complemented
806C2—42no—
807C2—62no—
808C2—121no—
809C2—241no—
810C2—241no—
811C2#1059418411yescharacteristic
812C2#1059473211yescharacteristic
813C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3297
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
1. #10595244C2semidirect
2. #10594560C2semidirect
3. #10592462C2semidirect
4. C3×#4781C2semidirect
5. C3×D3×#102C2semidirect
6. #10591447C2semidirect
7. #10591435C2semidirect
8. #10591420C2semidirect
9. #10590837C2semidirect
10. #10590829C2semidirect
11. #10590750C2semidirect
12. #10590717C2semidirect
13. #10590539C2semidirect
14. #10590517C2semidirect
15. #10590499C2semidirect
21. #64099C22semidirect
23. C2×C3×#204C22semidirect
25. C3×#895C22semidirect
35. #63898C22semidirect
41. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63644C22semidirect
47. #63641C22semidirect
48. #63634C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#810C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
58. #63563C22semidirect
60. #63553C22semidirect
80. #4781D3semidirect
84. D3×#102D3semidirect
185. C2×#204C2×D3semidirect
189. #895C2×D3semidirect
220. (C2×D3)⋊C8C2×D3semidirect
232. #810C2×D3semidirect
710. C32#3297semidirect
804. C3#78760semidirect
805. C3#80102semidirect

Maximal subgroups

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

subgroupindex
#105952442
#105945602
#105924622
C3×#47812
C3×D3×#1022
#105914472
#105914352
#105914202
#105908372
#105908292
#105907502
#105907172
#105905392
#105905172
#105904992
#801023
#787603