Finite Group Databasebeta

← #11887448

Subgroups — #11887448

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594005C211yesmaximal, characteristic, complemented
2#10593982C211yesmaximal, characteristic, complemented
3C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×#4697C211yesmaximal, characteristic, complemented
5C3×C4×D24C211yesmaximal, characteristic, complemented
6#10590963C211yesmaximal, characteristic, complemented
7#10590956C211yesmaximal, characteristic, complemented
8#10590945C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590841C211yesmaximal, characteristic, complemented
11#10590839C211yesmaximal, characteristic, complemented
12#10590689C211yesmaximal, characteristic, complemented
13#10590651C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#81653—31nomaximal
17#79609—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic, complemented
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×D24C2211yescharacteristic
24C3×#875C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic, complemented
27C3×#870C2211yescharacteristic, complemented
28#63923—21no—
29D3×(C2×D3)⋊C4—21no—
30#63916C2211yescharacteristic
31#63916C2211yescharacteristic
32#63916C2211yescharacteristic, complemented
33#63910—21no—
34#63906—21no—
35#63904—21no—
36#63900C2211yescharacteristic
37#63891—21no—
38#63871C2211yescharacteristic
39#63861—21no—
40#63850—21no—
41#63849C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic, complemented
43C2×#3713C2211yescharacteristic
44C32×C4×C8C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5695—31no—
62#5676—31no—
63#5558—31no—
64#5554—31no—
65C3×#488—31no—
66C3×C4×D8—31no—
67#5158—31no—
68#5156—31no—
69#5066—31no—
70#5057—31no—
71#5016—31no—
72#5009—31no—
73#4885—31no—
74#4884—31no—
75#4811—31no—
76#4810—31no—
77#4807—31no—
78#4804—31no—
79#4784—31no—
80#4778—31no—
81#4775—31no—
82#4775—31no—
83#4773—31no—
84#4772—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4697D311yescharacteristic, complemented
88C4×D24D311yescharacteristic, complemented
89C8×D12—31no—
90C8×D12—31no—
91C8×D12—61no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)D411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109#3802—22no—
110#3802—41no—
111#3796—22no—
112#3796—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752D411yescharacteristic
117#3752D411yescharacteristic
118C4⋊(C3⋊Dic3)D411yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C8×C3⋊D3—41no—
122C8×C3⋊D3—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×D24—22no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3715—41no—
143#3713—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×C3×D8—31no—
150C3×#125—31no—
151C3×#124—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154#946—31no—
155C2×#215—31no—
156#938—31no—
157#938—31no—
158#938—31no—
159C2×#214—31no—
160C2×#213—31no—
161C2×#213—31no—
162#930—61no—
163#929—61no—
164C4×#67—61no—
165C2×(C2×D3)⋊C4—61no—
166C2×D24C2×D311yescharacteristic
167C2×D3×C8—31no—
168C2×D3×C8—31no—
169C2×D3×C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8—61no—
172C2×D3×C8—61no—
173#898—61no—
174#897—31no—
175#895—31no—
176#895—31no—
177#895—31no—
178#895—61no—
179#894—61no—
180#893—61no—
181#892—31no—
182#892—31no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185#886—61no—
186#884—61no—
187#884—61no—
188#883—61no—
189#882—61no—
190#882—61no—
191D3×C22⋊C4—61no—
192#879—61no—
193#875C2×D311yescharacteristic
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197C4×D12C2×D311yescharacteristic
198C4×D12C2×D311yescharacteristic, complemented
199#870C2×D311yescharacteristic, complemented
200C3×#107—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C4×C8—21no—
208C3×C4×C8C2×D311yescharacteristic, complemented
209C3×C4×C8C2×D311yescharacteristic, complemented
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic, complemented
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—61no—
223(C2×D3)⋊C8—61no—
224#818C2×D311yescharacteristic, complemented
225#816C2×D311yescharacteristic, complemented
226#816C2×D311yescharacteristic, complemented
227#810—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—31no—
237C4⋊(C3⋊C8)—61no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—22no—
252C4×C3⋊D3—21no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—42no—
273#626—81no—
274#626—81no—
275#625—42no—
276#624—81no—
277D3×Dic3—42no—
278C32×C8—21no—
279C32×C8—21no—
280C3⋊(C3⋊C8)—21no—
281C3⋊(C3⋊C8)—21no—
282#553—91no—
283#546—91no—
284#488—31no—
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—31no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×Q8—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312#239—62no—
313#239—121no—
314#237—62no—
315#237—121no—
316D3×D4—62no—
317D3×D4—62no—
318D3×D4—121no—
319D3×D4—121no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12C22×D311yescharacteristic
328C2×D12C22×D311yescharacteristic
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—31no—
333C2×C4×D3—31no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×Dic6C22×D311yescharacteristic
342C3×D8—62no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—21no—
360C3×C42C22×D311yescharacteristic
361C3×C42C22×D311yescharacteristic
362#217—61no—
363#217—61no—
364#217—61no—
365#215—121no—
366#214—121no—
367#213—121no—
368#213—121no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
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—61no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407D24—22no—
408D3×C8—121no—
409D3×C8—121no—
410D3×C8—121no—
411D3×C8—121no—
412D3×C8—122no—
413D3×C8—122no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3#13512yes—
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430D32—84no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C22×D4—91no—
444C2×SD16—91no—
445C2×D8—31no—
446C2×D8—91no—
447C22×C8—91no—
448C22×C8—91no—
449#126—181no—
450#125—31no—
451#124—31no—
452#123—181no—
453#123—181no—
454C22⋊Q8—91no—
455#121—91no—
456#121—91no—
457#121—91no—
458#121—181no—
459#121—181no—
460#120—181no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—181no—
465#117—91no—
466C2×C4⋊C4—91no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—91no—
470#106—91no—
471C4⋊C8—91no—
472#103—31no—
473#103—31no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—91no—
483C22⋊C8—91no—
484C4×C8D3211yescharacteristic, complemented
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—31no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—241no—
502C22×D3—241no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—32no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—241no—
520C2×C3×C4—241no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—122no—
528#67—122no—
529#67—122no—
530#67—122no—
531#67—241no—
532#67—241no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—122no—
545D12—21no—
546D12—21no—
547D12—21no—
548D12—21no—
549D12—21no—
550D12—62no—
551D12—62no—
552D12—64no—
553D12—122no—
554D12—122no—
555D12—241no—
556D12—241no—
557D12#23512yes—
558C4×D3—61no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—61no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—81no—
567C4×D3—81no—
568C4×D3—121no—
569C4×D3—121no—
570C4×D3—121no—
571C4×D3—121no—
572C4×D3—122no—
573C4×D3—241no—
574C4×D3—241no—
575Dic6—21no—
576Dic6—21no—
577C3×C8—22no—
578C3×C8—21no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—41no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—121no—
588C3⋊C8—121no—
589C2×C32#54611yescharacteristic
590C2×C32C2×#13511yescharacteristic
591C2×C32#57611yescharacteristic
592C3⋊D3—22no—
593C3⋊D3—41no—
594C3×D3—42no—
595C3×D3—81no—
596C3×D3—81no—
597C24—181no—
598#41—182no—
599#41—361no—
600C2×Q8—31no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—91no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—182no—
611C2×D4—361no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—91no—
615C22×C4—91no—
616C22×C4—181no—
617C22×C4—181no—
618SD16—361no—
619D8—62no—
620D8—361no—
621C2×C8—91no—
622C2×C8—91no—
623C2×C8—361no—
624C2×C8—361no—
625C2×C8C2×D3211yescharacteristic
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—91no—
641C22⋊C4—91no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—181no—
648C42C2×D3211yescharacteristic
649C22×C3—21no—
650C22×C3—62no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—22no—
662C2×D3—32no—
663C2×D3—32no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—62no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—62no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—244no—
689C2×D3—244no—
690C3×C4—22no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—41no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4C2×#23511yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4#100911yescharacteristic
706C3×C4#100911yescharacteristic
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710Dic3—41no—
711Dic3—41no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—61no—
716Dic3—121no—
717Dic3—121no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—61no—
720C23—61no—
721C23—61no—
722C23—91no—
723C23—91no—
724C23—362no—
725C23—362no—
726C23—721no—
727Q8—61no—
728Q8—61no—
729D4—32no—
730D4—61no—
731D4—61no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—182no—
736D4—362no—
737D4—362no—
738D4—362no—
739D4—721no—
740D4—721no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—91no—
747C2×C4—91no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—241no—
753C2×C4—241no—
754C2×C4—362no—
755C2×C4—721no—
756C2×C4#380211yescharacteristic
757C2×C4#380211yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—21no—
760C8—21no—
761C8—181no—
762C8—181no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—122no—
767C2×C3—241no—
768C2×C3—241no—
769C2×C3#555011yescharacteristic
770C2×C3#567611yescharacteristic
771C2×C3#575711yescharacteristic
772C2×C3D3×#13511yescharacteristic
773C2×C3D3×#13511yescharacteristic
774C2×C3#576911yescharacteristic
775D3—42no—
776D3—62no—
777D3—62no—
778D3—81no—
779D3—81no—
780D3—122no—
781D3—122no—
782D3—121no—
783D3—121no—
784C22—62no—
785C22—92no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—181no—
795C22—181no—
796C22—181no—
797C22—181no—
798C22—181no—
799C22—724no—
800C22C2×#380211yescharacteristic
801C4—21no—
802C4—21no—
803C4—121no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—181no—
809C4—181no—
810C4D3×#23511yescharacteristic
811C4#6430811yescharacteristic
812C3—21no—
813C3#7960911yescharacteristic, complemented
814C3#8165311yescharacteristic, complemented
815C2—122no—
816C2—182no—
817C2—241no—
818C2—241no—
819C2—361no—
820C2#1059400711yescharacteristic
821C2#1059468411yescharacteristic
822C2#1059468711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10594005C2semidirect
2. #10593982C2semidirect
3. C8×C4⋊(C3⋊D3)C2semidirect
4. C3×#4697C2semidirect
5. C3×C4×D24C2semidirect
6. #10590963C2semidirect
7. #10590956C2semidirect
8. #10590945C2semidirect
9. #10590940C2semidirect
10. #10590841C2semidirect
11. #10590839C2semidirect
12. #10590689C2semidirect
13. #10590651C2semidirect
14. #10590348C2semidirect
15. #10590270C2semidirect
21. C2×C8×C3⋊D3C22semidirect
26. C3×C4×D12C22semidirect
27. C3×#870C22semidirect
32. #63916C22semidirect
41. #63849C22semidirect
42. C2×#3715C22semidirect
44. C32×C4×C8C22semidirect
46. #63647C22semidirect
47. C4⋊(C3⋊(C3⋊C8))C22semidirect
51. C3×#821C22semidirect
52. C3×#818C22semidirect
53. C3×#816C22semidirect
54. C3×#816C22semidirect
55. #63576C22semidirect
56. #63574C22semidirect
57. #63565C22semidirect
87. #4697D3semidirect
88. C4×D24D3semidirect
198. C4×D12C2×D3semidirect
199. #870C2×D3semidirect
208. C3×C4×C8C2×D3semidirect
209. C3×C4×C8C2×D3semidirect
217. #821C2×D3semidirect
224. #818C2×D3semidirect
225. #816C2×D3semidirect
226. #816C2×D3semidirect
484. C4×C8D32semidirect
718. C32#3297semidirect
813. C3#79609semidirect
814. C3#81653semidirect

Maximal subgroups

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

subgroupindex
#105940052
#105939822
C8×C4⋊(C3⋊D3)2
C3×#46972
C3×C4×D242
#105909632
#105909562
#105909452
#105909402
#105908412
#105908392
#105906892
#105906512
#105903482
#105902702
#816533
#796093