Finite Group Databasebeta

← #11887462

Subgroups — #11887462

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5676C211yesmaximal, characteristic, complemented
2#10593923C211yesmaximal, characteristic, complemented
3#10592755C211yesmaximal, characteristic, complemented
4C3×#5057C211yesmaximal, characteristic, complemented
5#10591634C211yesmaximal, characteristic, complemented
6#10591586C211yesmaximal, characteristic, complemented
7#10591556C211yesmaximal, characteristic, complemented
8#10591551C211yesmaximal, characteristic, complemented
9#10591498C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11#10591422C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13C4×#3713C211yesmaximal, characteristic, complemented
14#10590329C211yesmaximal, characteristic, complemented
15#10590271C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#80559—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×#124C2211yescharacteristic
21#64079C2211yescharacteristic, complemented
22C3×#946C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic, complemented
24C3×#938C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#884—21no—
27C3×#883—21no—
28C3×#882—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33#63908C2211yescharacteristic
34#63908C2211yescharacteristic, complemented
35#63905—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63885—21no—
38#63879—21no—
39#63858—21no—
40#63841C2211yescharacteristic, complemented
41C2×#3713C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5676D311yescharacteristic, complemented
63#5565—31no—
64#5558—31no—
65C3×#463—31no—
66#5238—31no—
67#5233—31no—
68#5217—31no—
69C2×#832—31no—
70#5172—31no—
71#5171—31no—
72#5157—31no—
73#5156—31no—
74#5057D311yescharacteristic, complemented
75#5056—31no—
76#5056—31no—
77#5056—61no—
78#5048—31no—
79#5044—31no—
80#5038—31no—
81#5035—31no—
82C4×#213—31no—
83C4×#213—31no—
84D4×C3⋊C8—31no—
85#5009—31no—
86#4847—31no—
87#4834—31no—
88#4811—31no—
89#4804—31no—
90#4779—31no—
91D3×#102—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C3×#239—22no—
98C3×#239—41no—
99C3×D3×D4—22no—
100C3×D3×D4—41no—
101C2×C3×D12—21no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×#625—21no—
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#215—41no—
124C3×#213—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3713—22no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C3×#124—21no—
152C3×#124C2×D311yescharacteristic
153C3×#124C2×D311yescharacteristic
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C22⋊C4—61no—
163#946C2×D311yescharacteristic
164C2×#215C2×D311yescharacteristic, complemented
165#939—61no—
166#938—31no—
167#938—31no—
168#938C2×D311yescharacteristic
169C2×#213—31no—
170C2×#213—31no—
171C2×#213C2×D311yescharacteristic
172#930—31no—
173#930—31no—
174#929—61no—
175C4×#67—61no—
176#926—31no—
177C2×C4⋊Dic3—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—31no—
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182#898—61no—
183#892—31no—
184D3×C4⋊C4—31no—
185#884—21no—
186#884—61no—
187#883—21no—
188#883—61no—
189#882—21no—
190#67⋊C4—61no—
191D3×C22⋊C4—21no—
192#879—61no—
193C4×D12C2×D311yescharacteristic
194C4×D12C2×D311yescharacteristic
195C4×D12C2×D311yescharacteristic, complemented
196#870—31no—
197#870—31no—
198#870—61no—
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#102—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—61no—
207#835—61no—
208#835C2×D311yescharacteristic, complemented
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—61no—
218#832—61no—
219#832C2×D311yescharacteristic
220#830—31no—
221#830—31no—
222#821—31no—
223#821—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226#818—31no—
227#817—31no—
228#809—31no—
229#809—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C4×C3⋊C8—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×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C3×#67—42no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—42no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—42no—
273C3×C4×D3—81no—
274C3×C4×D3—81no—
275#625—42no—
276#625—81no—
277D3×Dic3—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—31no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—31no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—21no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4—121no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C22×Dic3—61no—
327#239—22no—
328#239—41no—
329D3×D4—22no—
330D3×D4—41no—
331C2×D12—21no—
332C2×D12#6711yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—61no—
339C2×C4×D3C22×D311yescharacteristic
340C2×C4×D3C22×D311yescharacteristic
341C3×SD16—121no—
342C3×D8—121no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4—41no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—21no—
362C3×C42C22×D311yescharacteristic
363C3×C42C22×D311yescharacteristic
364#217—21no—
365#217—61no—
366#217—61no—
367#217—61no—
368#215—41no—
369#213—41no—
370#213—62no—
371#213—62no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4#6711yescharacteristic
379(C2×D3)⋊C4#6711yescharacteristic
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3#6711yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397Dic3⋊C4—121no—
398C4×Dic3—61no—
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⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D3×C8—121no—
411D3×C8—121no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—22no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
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—21no—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
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—91no—
446C22×C8—91no—
447#126—181no—
448#125—91no—
449#124D3211yescharacteristic
450#123—61no—
451#123—181no—
452C22⋊Q8—31no—
453#121—31no—
454#121—61no—
455#121—91no—
456#121—91no—
457#121—181no—
458#120—61no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—181no—
463#117—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—61no—
466#107—91no—
467#107—91no—
468#106—91no—
469C4⋊C8—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—91no—
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×D3C2×#6711yescharacteristic
499C22×D3C2×#6711yescharacteristic
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—32no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—62no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—122no—
518C3×D4—122no—
519C3×D4—241no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—41no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4—241no—
536C2×C3×C4—241no—
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C2×#6711yescharacteristic
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543#67—42no—
544#67—81no—
545#67—122no—
546#67—122no—
547#67—241no—
548#67—241no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—241no—
558C2×Dic3C2×#6711yescharacteristic
559C2×Dic3C2×#6711yescharacteristic
560D12—22no—
561D12—21no—
562D12—21no—
563D12—21no—
564D12—42no—
565D12#23712yes—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—42no—
571C4×D3—81no—
572C4×D3—81no—
573C4×D3—241no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C3⋊C8—121no—
584C2×C32—81no—
585C2×C32#54611yescharacteristic
586C2×C32C2×#13511yescharacteristic
587C2×C32#57611yescharacteristic
588C3×D3—22no—
589C3×D3—41no—
590C3×D3—42no—
591C3×D3—81no—
592C24—61no—
593#41—62no—
594#41—121no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—62no—
602C2×D4—61no—
603C2×D4—121no—
604C2×D4—181no—
605C2×D4—181no—
606C2×D4C2×D3211yescharacteristic
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—181no—
613SD16—121no—
614D8—121no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—91no—
619C2×C8—91no—
620C2×C8—361no—
621C2×C8—361no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—61no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C42—181no—
643C42C2×D3211yescharacteristic
644C22×C3—21no—
645C22×C3—32no—
646C22×C3—41no—
647C22×C3—41no—
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—62no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C22×#6711yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—22no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—84no—
681C2×D3#95012yes—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—81no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4C2×#23711yescharacteristic
698C3×C4#100411yescharacteristic
699C3×C4#100411yescharacteristic
700C3×C4D3×#4111yescharacteristic
701Dic3—21no—
702Dic3—21no—
703Dic3—41no—
704Dic3—41no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—241no—
710Dic3—241no—
711C32#329711yescharacteristic, complemented, Sylow
712C23—21no—
713C23—31no—
714C23—31no—
715C23—61no—
716C23—61no—
717C23—122no—
718C23—122no—
719C23—241no—
720Q8—21no—
721Q8—21no—
722D4—21no—
723D4—21no—
724D4—32no—
725D4—62no—
726D4—61no—
727D4—61no—
728D4—61no—
729D4—122no—
730D4—122no—
731D4—241no—
732D4—362no—
733D4—721no—
734C2×C4—21no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—122no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—241no—
747C2×C4—241no—
748C2×C4—721no—
749C2×C4D3×#6711yescharacteristic
750C2×C4D3×#6711yescharacteristic
751C2×C4C22×D3211yescharacteristic
752C8—61no—
753C8—61no—
754C8—181no—
755C8—181no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—62no—
760C2×C3—81no—
761C2×C3—81no—
762C2×C3—121no—
763C2×C3—122no—
764C2×C3—161no—
765C2×C3—241no—
766C2×C3#561211yescharacteristic
767C2×C3D3×#13511yescharacteristic
768C2×C3#577411yescharacteristic
769C2×C3#580611yescharacteristic
770C2×C3C2×#95011yescharacteristic
771C2×C3#583511yescharacteristic
772D3—22no—
773D3—41no—
774D3—42no—
775D3—81no—
776C22—32no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—62no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—244no—
792C22C2×D3×#6711yescharacteristic
793C4—21no—
794C4—21no—
795C4—41no—
796C4—61no—
797C4—61no—
798C4—121no—
799C4—121no—
800C4—361no—
801C4—361no—
802C4D3×#23711yescharacteristic
803C4#6431311yescharacteristic
804C3—21no—
805C3#8055911yescharacteristic, complemented
806C3#8349511yescharacteristic, complemented
807C2—62no—
808C2—81no—
809C2—121no—
810C2—122no—
811C2—241no—
812C2#1059522811yescharacteristic
813C2D3×#95011yescharacteristic
814C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5676C2semidirect
2. #10593923C2semidirect
3. #10592755C2semidirect
4. C3×#5057C2semidirect
5. #10591634C2semidirect
6. #10591586C2semidirect
7. #10591556C2semidirect
8. #10591551C2semidirect
9. #10591498C2semidirect
10. #10591447C2semidirect
11. #10591422C2semidirect
12. D3×#832C2semidirect
13. C4×#3713C2semidirect
14. #10590329C2semidirect
15. #10590271C2semidirect
21. #64079C22semidirect
23. C2×C3×#215C22semidirect
32. C3×C4×D12C22semidirect
34. #63908C22semidirect
40. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
45. #63662C22semidirect
48. C4×C3⋊(C3⋊C8)C22semidirect
49. C3×#835C22semidirect
51. C3×C4⋊(C3⋊C8)C22semidirect
52. #63576C22semidirect
53. #63575C22semidirect
54. #63573C22semidirect
58. #63562C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5676D3semidirect
74. #5057D3semidirect
164. C2×#215C2×D3semidirect
195. C4×D12C2×D3semidirect
208. #835C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
711. C32#3297semidirect
805. C3#80559semidirect
806. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#56762
#105939232
#105927552
C3×#50572
#105916342
#105915862
#105915562
#105915512
#105914982
#105914472
#105914222
D3×#8322
C4×#37132
#105903292
#105902712
#834953
#805593