Finite Group Databasebeta

← #11887398

Subgroups — #11887398

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595244C211yesmaximal, characteristic, complemented
2#10594559C211yesmaximal, characteristic, complemented
3#10592455C211yesmaximal, characteristic, complemented
4C3×#4772C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591479C211yesmaximal, characteristic, complemented
7#10591452C211yesmaximal, characteristic, complemented
8#10591448C211yesmaximal, characteristic, complemented
9#10590868C211yesmaximal, characteristic, complemented
10#10590847C211yesmaximal, characteristic, complemented
11#10590826C211yesmaximal, characteristic, complemented
12C8×#625C211yesmaximal, characteristic, complemented
13#10590540C211yesmaximal, characteristic, complemented
14#10590517C211yesmaximal, characteristic, complemented
15#10590502C211yesmaximal, characteristic, complemented
16#78846—31nomaximal
17#78760—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64102C2211yescharacteristic, complemented
23C2×C3×D3×C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#892C2211yescharacteristic, complemented
26C3×D3×C4⋊C4C2211yescharacteristic
27#63980—21no—
28#63976—21no—
29#63961—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63909C2211yescharacteristic
32#63909C2211yescharacteristic, complemented
33#63908C2211yescharacteristic
34#63906—21no—
35C4×#626—21no—
36C4×#625C2211yescharacteristic
37#63872C2211yescharacteristic, complemented
38#63868—21no—
39#63863C2211yescharacteristic
40#63856C2211yescharacteristic
41#63853—21no—
42C2×#3717C2211yescharacteristic, complemented
43C2×#3714C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63648C2211yescharacteristic, complemented
46C8×C3⋊Dic3C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5829—31no—
62#5806—31no—
63#5530—31no—
64#5514—31no—
65C3×#416—31no—
66C2×C3×#102—31no—
67#5238—31no—
68#5217—31no—
69#5115—31no—
70#5114—31no—
71C8×#67—31no—
72C8×#67—31no—
73#5003—31no—
74#4970—31no—
75#4819—31no—
76#4811—31no—
77#4807—31no—
78#4800—31no—
79#4787—31no—
80#4781—31no—
81#4779—31no—
82#4775—31no—
83#4773—31no—
84#4772D311yescharacteristic, complemented
85D3×#102D311yescharacteristic, complemented
86#4768—31no—
87#4766—31no—
88#4763—31no—
89#4756—31no—
90#4756—31no—
91#4756—61no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C3×#237—22no—
101C3×#237—41no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#625—21no—
112C2×#625D411yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116#3753—22no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×D3×C8—41no—
129C3×D3×C8—41no—
130#3724—21no—
131#3724D411yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—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#3717—41no—
143#3714—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C22×C3×C8—31no—
150C22×C3×C8—31no—
151C3×#117—31no—
152C2×C3×C4⋊C4—31no—
153#953—61no—
154C2×#217—61no—
155#947—31no—
156#946—31no—
157C2×#215—31no—
158#939—61no—
159#939—61no—
160#938—31no—
161#937—61no—
162#936—31no—
163#935—61no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—61no—
171#930—31no—
172#930—31no—
173#930—31no—
174#930—61no—
175#929—61no—
176C4×#67—31no—
177C4×#67—31no—
178C4×#67—61no—
179C2×(C2×D3)⋊C4—61no—
180#924—31no—
181C2×D24—31no—
182C2×#204—31no—
183C2×D3×C8C2×D311yescharacteristic
184C2×D3×C8C2×D311yescharacteristic, complemented
185#898—61no—
186#895—31no—
187#895—31no—
188#894—61no—
189#893—31no—
190#893—31no—
191#893—61no—
192#892C2×D311yescharacteristic, complemented
193D3×C4⋊C4C2×D311yescharacteristic
194#890—31no—
195#890—31no—
196#884—61no—
197#883—61no—
198#876—61no—
199C4×D12—61no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102C2×D311yescharacteristic
208C3×#102C2×D311yescharacteristic
209#835—31no—
210#832—31no—
211#832C2×D311yescharacteristic
212#832C2×D311yescharacteristic
213#830—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#818—31no—
222#817—31no—
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—61no—
229#810—31no—
230#810C2×D311yescharacteristic, complemented
231#809—31no—
232#809C2×D311yescharacteristic
233#808—31no—
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—81no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4×C3⋊D3—81no—
257C3×#67—42no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
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#626—42no—
275#626—81no—
276#625—22no—
277#625—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—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—31no—
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—61no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4—121no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—31no—
317C2×#67—31no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C22×Dic3—21no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—121no—
326#237—22no—
327#237—41no—
328D3×D4—22no—
329D3×D4—41no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—21no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—121no—
340C2×C4×D3C22×D311yescharacteristic
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C2×C3×C8—121no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—61no—
357C3×C42—61no—
358#217—31no—
359#217—31no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—121no—
367#215—121no—
368#213—64no—
369#213—62no—
370#213—62no—
371#213—121no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
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—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—121no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400C4×Dic3—21no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—61no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—121no—
410#204—121no—
411D3×C8—41no—
412D3×C8—41no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—84no—
429C2×C3×D3#13512yes—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—31no—
442C22×D4—31no—
443C2×SD16—91no—
444C2×D8—91no—
445C2×D8—91no—
446C22×C8—31no—
447C22×C8—31no—
448#126—181no—
449#125—91no—
450#124—91no—
451#123—181no—
452#123—181no—
453C22⋊Q8—91no—
454#121—91no—
455#121—91no—
456#121—91no—
457#121—181no—
458#121—181no—
459#120—181no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—181no—
464#117—31no—
465C2×C4⋊C4—31no—
466C2×C22⋊C4—181no—
467#107—91no—
468#107—91no—
469#106—91no—
470C4⋊C8—91no—
471#103—31no—
472#103—31no—
473#103—91no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102D3211yescharacteristic
481C22⋊C8—91no—
482C22⋊C8—91no—
483C4×C8—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—31no—
488C23×C3—41no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C22×D3—21no—
494C22×D3—42no—
495C22×D3—42no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—81no—
499C22×D3—121no—
500C22×D3D3×D411yescharacteristic
501C22×D3D3×D411yescharacteristic
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—41no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—122no—
511C3×D4—122no—
512C3×D4#23512yes—
513C3×D4#23512yes—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
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—241no—
537#67—241no—
538#67—241no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—42no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—121no—
552C2×Dic3—241no—
553C2×Dic3—241no—
554C2×Dic3—242no—
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557D12—21no—
558D12—21no—
559D12—62no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—122no—
566D12—241no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—81no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—242no—
575Dic6—21no—
576Dic6—21no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—41no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C3⋊C8—62no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C2×C32—42no—
588C2×C32#54611yescharacteristic
589C2×C32C2×#13511yescharacteristic
590C2×C32#57611yescharacteristic
591C3⋊D3—81no—
592C3×D3—22no—
593C3×D3—41no—
594C3×D3—81no—
595C24—61no—
596#41—62no—
597#41—121no—
598C2×Q8—31no—
599C2×D4—31no—
600C2×D4—61no—
601C2×D4—62no—
602C2×D4—61no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—121no—
606C2×D4—181no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4C2×D3211yescharacteristic
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—181no—
615C22×C4—181no—
616SD16—361no—
617D8—182no—
618D8—361no—
619C2×C8—31no—
620C2×C8—31no—
621C2×C8—91no—
622C2×C8—121no—
623C2×C8—121no—
624C2×C8C2×D3211yescharacteristic
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—61no—
628C4⋊C4—91no—
629C4⋊C4—91no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4C2×D3211yescharacteristic
634C22⋊C4—61no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C42—61no—
646C42—91no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—42no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C2×D3×D411yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—84no—
678C2×D3—122no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3#91612yes—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—81no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4C2×#23511yescharacteristic
699C3×C4C2×#23511yescharacteristic
700C3×C4#100411yescharacteristic
701C3×C4#100411yescharacteristic
702Dic3—21no—
703Dic3—21no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—62no—
708Dic3—61no—
709Dic3—61no—
710Dic3—61no—
711Dic3—61no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716C32#329711yescharacteristic, complemented, Sylow
717C23—21no—
718C23—31no—
719C23—31no—
720C23—61no—
721C23—122no—
722C23—122no—
723C23—181no—
724C23—241no—
725Q8—61no—
726Q8—61no—
727D4—21no—
728D4—61no—
729D4—61no—
730D4—122no—
731D4—122no—
732D4—182no—
733D4—181no—
734D4—181no—
735D4—362no—
736D4—721no—
737D4—721no—
738D4#379812yes—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—91no—
750C2×C4—91no—
751C2×C4—122no—
752C2×C4—181no—
753C2×C4—241no—
754C2×C4—721no—
755C2×C4—721no—
756C2×C4C22×D3211yescharacteristic
757C8—21no—
758C8—61no—
759C8—61no—
760C8—181no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—62no—
767C2×C3—82no—
768C2×C3—121no—
769C2×C3—241no—
770C2×C3#549011yescharacteristic
771C2×C3#549011yescharacteristic
772C2×C3#575711yescharacteristic
773C2×C3C2×#91611yescharacteristic
774C2×C3D3×#13511yescharacteristic
775C2×C3#576911yescharacteristic
776D3—22no—
777D3—41no—
778D3—81no—
779D3—242no—
780D3—241no—
781D3—241no—
782C22—22no—
783C22—32no—
784C22—41no—
785C22—41no—
786C22—61no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—244no—
795C22—361no—
796C22—361no—
797C22—361no—
798C22D32×D411yescharacteristic
799C4—41no—
800C4—61no—
801C4—61no—
802C4—121no—
803C4—121no—
804C4—121no—
805C4—181no—
806C4—181no—
807C4—361no—
808C4C2×#379811yescharacteristic
809C4#6431311yescharacteristic
810C3—21no—
811C3#7876011yescharacteristic, complemented
812C3#7884611yescharacteristic, complemented
813C2—42no—
814C2—62no—
815C2—121no—
816C2—241no—
817C2—721no—
818C2#1059418311yescharacteristic
819C2#1059473411yescharacteristic
820C2D3×#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. #10594559C2semidirect
3. #10592455C2semidirect
4. C3×#4772C2semidirect
5. C3×D3×#102C2semidirect
6. #10591479C2semidirect
7. #10591452C2semidirect
8. #10591448C2semidirect
9. #10590868C2semidirect
10. #10590847C2semidirect
11. #10590826C2semidirect
12. C8×#625C2semidirect
13. #10590540C2semidirect
14. #10590517C2semidirect
15. #10590502C2semidirect
22. #64102C22semidirect
24. C2×C3×D3×C8C22semidirect
25. C3×#892C22semidirect
32. #63909C22semidirect
37. #63872C22semidirect
42. C2×#3717C22semidirect
45. #63648C22semidirect
46. C8×C3⋊Dic3C22semidirect
47. #63634C22semidirect
51. C3×#816C22semidirect
52. C3×#810C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4772D3semidirect
85. D3×#102D3semidirect
184. C2×D3×C8C2×D3semidirect
192. #892C2×D3semidirect
223. #816C2×D3semidirect
230. #810C2×D3semidirect
716. C32#3297semidirect
811. C3#78760semidirect
812. C3#78846semidirect

Maximal subgroups

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

subgroupindex
#105952442
#105945592
#105924552
C3×#47722
C3×D3×#1022
#105914792
#105914522
#105914482
#105908682
#105908472
#105908262
C8×#6252
#105905402
#105905172
#105905022
#788463
#787603