Finite Group Databasebeta

← #11887379

Subgroups — #11887379

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#10595070C211yesmaximal, characteristic, complemented
2#10594967C211yesmaximal, characteristic, complemented
3#10592424C211yesmaximal, characteristic, complemented
4C3×#4737C211yesmaximal, characteristic, complemented
5C3×#4734C211yesmaximal, characteristic, complemented
6#10591166C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590945C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590868C211yesmaximal, characteristic, complemented
11#10590843C211yesmaximal, characteristic, complemented
12#10590782C211yesmaximal, characteristic, complemented
13#10590777C211yesmaximal, characteristic, complemented
14#10590750C211yesmaximal, characteristic, complemented
15#10590689C211yesmaximal, characteristic, complemented
16#81382—31nomaximal
17#80102—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C4×#638C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×#930C2211yescharacteristic, complemented
25C3×#926C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic, complemented
28#63983—21no—
29#63970—21no—
30#63969—21no—
31#63958—21no—
32D3×(C2×D3)⋊C4—21no—
33#63916C2211yescharacteristic
34#63905—21no—
35#63900C2211yescharacteristic
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic, complemented
38#63880—21no—
39#63872C2211yescharacteristic, complemented
40#63871C2211yescharacteristic
41#63863C2211yescharacteristic
42#63859—21no—
43C2×#3713C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63641C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61#5829—31no—
62#5614—31no—
63#5612—31no—
64#5530—31no—
65C3×#482—31no—
66C3×#449—31no—
67#5233—31no—
68#5171—31no—
69#5165—31no—
70#5156—31no—
71Dic3×D8—31no—
72#5038—31no—
73#5038—31no—
74#5002—31no—
75#4884—31no—
76#4872—31no—
77#4871—31no—
78#4864—31no—
79#4811—31no—
80#4800—31no—
81#4787—31no—
82#4773—31no—
83D3×#102—31no—
84D3×#102—31no—
85#4768—31no—
86#4763—31no—
87#4737D311yescharacteristic, complemented
88#4734D311yescharacteristic, complemented
89#67⋊C8—31no—
90#67⋊C8—31no—
91#67⋊C8—61no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638D411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C3×#235—22no—
100C3×#235—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#625—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3802—22no—
112#3802—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3757D411yescharacteristic
116#3752D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)—41no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C8×C3⋊D3—41no—
123C3×#217—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3—21no—
131C3×D24—22no—
132C3×#204—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3713—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×#235C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C3×#121—31no—
152C3×#121—31no—
153C3×#117—31no—
154#947—31no—
155#946—31no—
156#939—61no—
157#938—31no—
158#938—61no—
159#938—61no—
160#937—61no—
161#937—61no—
162#936—31no—
163#935—61no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166C2×#213—31no—
167C2×#213—31no—
168#930C2×D311yescharacteristic
169#930C2×D311yescharacteristic, complemented
170#929—61no—
171C4×#67—31no—
172C4×#67—31no—
173C4×#67—61no—
174C2×(C2×D3)⋊C4—61no—
175#926C2×D311yescharacteristic, complemented
176C22×C3⋊C8—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—61no—
179C2×D24C2×D311yescharacteristic
180C2×#204C2×D311yescharacteristic, complemented
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183C2×D3×C8—61no—
184#897—31no—
185#895—31no—
186#893—31no—
187#893—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190#890—31no—
191#890—31no—
192#884—61no—
193#883—61no—
194#883—61no—
195#67⋊C4—61no—
196D3×C22⋊C4—61no—
197#879—61no—
198#876—61no—
199C4×D12—61no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8C2×D311yescharacteristic, complemented
208C3×C22⋊C8C2×D311yescharacteristic, complemented
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—61no—
221#818C2×D311yescharacteristic, complemented
222#817C2×D311yescharacteristic, complemented
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230#810—31no—
231#810—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#807—31no—
237#807—31no—
238C23×C32C2×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×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—22no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C3×#67—42no—
257C3×#67—81no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12#4112yes—
270C3×C4×D3—42no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#626—42no—
274#625—42no—
275#624—81no—
276D3×Dic3—81no—
277D3×Dic3—81no—
278C32×C8—21no—
279C32×C8—21no—
280C3⋊(C3⋊C8)—21no—
281C3⋊(C3⋊C8)—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—31no—
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—91no—
297C23×D3—61no—
298C23×D3—61no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C22×C3×C4—21no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—31no—
316C2×#67—31no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323D3×D4—62no—
324D3×D4—62no—
325D3×D4—121no—
326D3×D4—121no—
327#235—22no—
328#235—41no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—21no—
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×SD16—121no—
343C3×D8—62no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—61no—
358#217—21no—
359#217—31no—
360#217—31no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#213—121no—
368#213—121no—
369(C2×D3)⋊C4—21no—
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—
380(C2×D3)⋊C4—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—21no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—61no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—122no—
409D24—22no—
410#204—41no—
411D3×C8—121no—
412D3×C8—121no—
413D3×C8—122no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32C22×D411yescharacteristic
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×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—31no—
443C22×D4—91no—
444C2×SD16—31no—
445C2×D8—31no—
446C2×D8—91no—
447C22×C8—91no—
448C22×C8—91no—
449#126—181no—
450#125—91no—
451#124—91no—
452#123—181no—
453#123—181no—
454C22⋊Q8—91no—
455#121—31no—
456#121—31no—
457#121—91no—
458#121—181no—
459#121—181no—
460#120—181no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—181no—
465#117—31no—
466C2×C4⋊C4—91no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—91no—
470#106—31no—
471C4⋊C8—91no—
472#103—31no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—91no—
483C22⋊C8D3211yescharacteristic, complemented
484C4×C8—91no—
485C23×C3—21no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3D3×D411yescharacteristic
490C23×C3D3×D411yescharacteristic
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—31no—
495C22×D3—31no—
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—
511C3×D4—122no—
512C3×D4—241no—
513C3×D4—241no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
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×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—42no—
533#67—62no—
534#67—62no—
535#67—64no—
536#67—81no—
537#67—81no—
538#67—122no—
539#67—122no—
540#67—122no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—241no—
556C2×Dic3—241no—
557D12—21no—
558D12—21no—
559D12—21no—
560D12—21no—
561D12—21no—
562D12—122no—
563D12#23712yes—
564C4×D3—42no—
565C4×D3—61no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—61no—
569C4×D3—121no—
570C4×D3—121no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575Dic6—21no—
576Dic6—21no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—41no—
582C3×C8—41no—
583C3⋊C8—62no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—121no—
589C2×C32—41no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13511yescharacteristic
592C2×C32#57611yescharacteristic
593C3⋊D3—22no—
594C3×D3—42no—
595C3×D3—81no—
596C3×D3—81no—
597C24—181no—
598#41—62no—
599#41—121no—
600C2×Q8—31no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—91no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—182no—
611C2×D4—361no—
612C22×C4—61no—
613C22×C4—91no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4C2×D3211yescharacteristic
618SD16—121no—
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—91no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—91no—
640C22⋊C4—91no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—61no—
648C42—91no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—62no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C2×D3×D411yescharacteristic
670C2×D3—22no—
671C2×D3—32no—
672C2×D3—32no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—62no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—244no—
689C2×D3—244no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×#23711yescharacteristic
701C3×C4#100411yescharacteristic
702C3×C4D3×#4111yescharacteristic
703C3×C4#100911yescharacteristic
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—41no—
708Dic3—41no—
709Dic3—62no—
710Dic3—61no—
711Dic3—61no—
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—362no—
724C23—362no—
725C23—721no—
726C23#380211yescharacteristic
727Q8—61no—
728Q8—61no—
729D4—32no—
730D4—61no—
731D4—61no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—122no—
736D4—182no—
737D4—241no—
738D4—241no—
739D4—362no—
740D4—362no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—91no—
749C2×C4—91no—
750C2×C4—91no—
751C2×C4—122no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—721no—
755C2×C4—721no—
756C2×C4—721no—
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—42no—
767C2×C3—41no—
768C2×C3—41no—
769C2×C3—122no—
770C2×C3—241no—
771C2×C3—241no—
772C2×C3#559111yescharacteristic
773C2×C3#565411yescharacteristic
774C2×C3D3×#13511yescharacteristic
775C2×C3D3×#13511yescharacteristic
776C2×C3#577411yescharacteristic
777C2×C3#577411yescharacteristic
778D3—42no—
779D3—62no—
780D3—62no—
781D3—81no—
782D3—81no—
783D3—122no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—62no—
788C22—92no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—181no—
798C22—181no—
799C22—724no—
800C22C2×#380211yescharacteristic
801C4—21no—
802C4—121no—
803C4—121no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—181no—
808C4—181no—
809C4—181no—
810C4D3×#23711yescharacteristic
811C4#6431411yescharacteristic
812C3—21no—
813C3#8010211yescharacteristic, complemented
814C3#8138211yescharacteristic, complemented
815C2—41no—
816C2—122no—
817C2—182no—
818C2—241no—
819C2—241no—
820C2#1059429411yescharacteristic
821C2#1059468411yescharacteristic
822C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595070C2semidirect
2. #10594967C2semidirect
3. #10592424C2semidirect
4. C3×#4737C2semidirect
5. C3×#4734C2semidirect
6. #10591166C2semidirect
7. #10591083C2semidirect
8. #10590945C2semidirect
9. #10590940C2semidirect
10. #10590868C2semidirect
11. #10590843C2semidirect
12. #10590782C2semidirect
13. #10590777C2semidirect
14. #10590750C2semidirect
15. #10590689C2semidirect
21. C22×C3⋊(C3⋊C8)C22semidirect
24. C3×#930C22semidirect
25. C3×#926C22semidirect
27. C2×C3×#204C22semidirect
37. #63898C22semidirect
39. #63872C22semidirect
44. C32×C22⋊C8C22semidirect
46. #63641C22semidirect
47. C8×C3⋊Dic3C22semidirect
51. C3×#818C22semidirect
52. C3×#817C22semidirect
53. C3×#816C22semidirect
54. #63576C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
60. #63562C22semidirect
87. #4737D3semidirect
88. #4734D3semidirect
169. #930C2×D3semidirect
175. #926C2×D3semidirect
180. C2×#204C2×D3semidirect
207. C3×C22⋊C8C2×D3semidirect
208. C3×C22⋊C8C2×D3semidirect
221. #818C2×D3semidirect
222. #817C2×D3semidirect
223. #816C2×D3semidirect
483. C22⋊C8D32semidirect
718. C32#3297semidirect
813. C3#80102semidirect
814. C3#81382semidirect

Maximal subgroups

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

subgroupindex
#105950702
#105949672
#105924242
C3×#47372
C3×#47342
#105911662
#105910832
#105909452
#105909402
#105908682
#105908432
#105907822
#105907772
#105907502
#105906892
#813823
#801023