Finite Group Databasebeta

← #11887390

Subgroups — #11887390

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic, complemented
2#10594946C211yesmaximal, characteristic, complemented
3#10592937C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591614C211yesmaximal, characteristic, complemented
6#10591585C211yesmaximal, characteristic, complemented
7#10591568C211yesmaximal, characteristic, complemented
8#10591551C211yesmaximal, characteristic, complemented
9#10591448C211yesmaximal, characteristic, complemented
10D3×#832C211yesmaximal, characteristic, complemented
11#10591411C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14C3⋊C8×#67C211yesmaximal, characteristic, complemented
15#10591090C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#78846—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3755C2211yescharacteristic, complemented
21C2×#3753C2211yescharacteristic
22#64139C2211yescharacteristic, complemented
23C3×#947C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#939—21no—
26C3×#937—21no—
27C3×D4×Dic3C2211yescharacteristic
28C3×#930C2211yescharacteristic
29C3×#929—21no—
30C3×C4×#67C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4—21no—
32C3×#926C2211yescharacteristic, complemented
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34#63975—21no—
35#63971—21no—
36#63909C2211yescharacteristic
37#63894C2211yescharacteristic, complemented
38D3×C4⋊Dic3C2211yescharacteristic
39#63880—21no—
40#63869C2211yescharacteristic, complemented
41#63868—21no—
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic, complemented
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5829D311yescharacteristic, complemented
63#5565—31no—
64#5530—31no—
65C3×#416—31no—
66#5238—31no—
67#5238—31no—
68#5238—61no—
69#5233D311yescharacteristic, complemented
70#5217—31no—
71C2×#832—31no—
72#5115—31no—
73C8×#67—31no—
74#5057—31no—
75#5056—31no—
76#5048—31no—
77#5044—31no—
78#5038—31no—
79#5035—31no—
80C4×#213—31no—
81D4×C3⋊C8—31no—
82#5009—31no—
83#5003—31no—
84#4819—31no—
85#4811—31no—
86#4807—31no—
87#4800—31no—
88#4773—31no—
89D3×#102—31no—
90#4766—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C32×#41—22no—
94C32×#41—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×#626—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113#3755—41no—
114#3753—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141#3722—21no—
142#3714—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C2×D311yescharacteristic
148C22×C3×D4—31no—
149C2×D3×D4C2×D311yescharacteristic
150C22×C3×C8—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×#121—31no—
155C3×#121—61no—
156C3×#120—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160C2×C3×C22⋊C4—61no—
161#947C2×D311yescharacteristic
162#946C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—61no—
166#939—21no—
167#939—61no—
168#937—21no—
169D4×Dic3C2×D311yescharacteristic
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—61no—
174#930—31no—
175#930—31no—
176#930—31no—
177#930—61no—
178#930C2×D311yescharacteristic
179#929—21no—
180C4×#67C2×D311yescharacteristic
181C2×(C2×D3)⋊C4—21no—
182#926C2×D311yescharacteristic, complemented
183C2×C4⋊Dic3—31no—
184C22×C3⋊C8—31no—
185C22×C3⋊C8C2×D311yescharacteristic, complemented
186C2×D24—31no—
187C2×D3×C8—31no—
188#898—61no—
189#895—31no—
190#893—31no—
191D3×C4⋊C4—31no—
192#890—31no—
193#884—61no—
194#883—61no—
195#883—61no—
196#67⋊C4—61no—
197#876—61no—
198C4×D12—31no—
199C4×D12—61no—
200#870—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205#835—31no—
206#835—31no—
207#835—61no—
208#835C2×D311yescharacteristic, complemented
209#835C2×D311yescharacteristic, complemented
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222#821—31no—
223#821—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—42no—
250C32×D4#4112yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—42no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—81no—
258C2×C3⋊Dic3—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C3×#67—22no—
262C3×#67—42no—
263C3×#67—81no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—81no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×D12—21no—
272C3×D12—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275#626—42no—
276#624—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—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—31no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—22no—
300C3×#41—22no—
301C3×#41—42no—
302C3×#41—41no—
303C3×#41—41no—
304C3×#41—42no—
305C2×C3×Q8—21no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—41no—
314C2×C3×D4—61no—
315C2×C3×D4—62no—
316C2×C3×D4—61no—
317C2×C3×D4—121no—
318C2×C3×D4C22×D311yescharacteristic
319C2×C3×D4C22×D311yescharacteristic
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—41no—
325C22×C3×C4—61no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C2×#67—21no—
329C2×#67—21no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—121no—
334C2×#67#6711yescharacteristic
335C22×Dic3—21no—
336C22×Dic3—61no—
337D3×D4—22no—
338D3×D4—41no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3C22×D311yescharacteristic
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—121no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365C3×C42—61no—
366#217—21no—
367#217—21no—
368#217#6711yescharacteristic
369#215—121no—
370#215—121no—
371#215—122no—
372#213—62no—
373#213—62no—
374#213—122no—
375#213—121no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
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—
386(C2×D3)⋊C4—121no—
387(C2×D3)⋊C4#6711yescharacteristic
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4#6711yescharacteristic
402C4×Dic3—21no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—41no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—121no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414D24—121no—
415D3×C8—121no—
416C22×C32—22no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—84no—
432C2×C3×D3#13512yes—
433C32×C4—21no—
434C32×C4—41no—
435C32×C4C2×#4111yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3⋊Dic3—41no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C2×#41D3211yescharacteristic
445C22×D4—31no—
446C2×SD16—91no—
447C2×D8—91no—
448C2×D8—91no—
449C22×C8—31no—
450C22×C8—91no—
451#126—181no—
452#125—91no—
453#124—31no—
454#123—61no—
455#123—181no—
456C22⋊Q8—31no—
457#121—31no—
458#121—61no—
459#121—91no—
460#121—91no—
461#121—181no—
462#120—61no—
463C4×D4—31no—
464C4×D4—31no—
465C4×D4—91no—
466C4×D4—181no—
467#117—31no—
468C2×C4⋊C4—91no—
469C2×C22⋊C4—61no—
470#107—91no—
471#107—91no—
472#106—91no—
473C4⋊C8—91no—
474#103—31no—
475#103—31no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484C22⋊C8—91no—
485C22⋊C8—91no—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—41no—
492C23×C3—61no—
493C23×C3—122no—
494C23×C3—122no—
495C23×C3—241no—
496C23×C3D3×D411yescharacteristic
497C23×C3C2×#6711yescharacteristic
498C22×D3—21no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—81no—
504C22×D3—121no—
505C22×D3C2×#6711yescharacteristic
506C3×Q8—22no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—41no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—22no—
515C3×D4—41no—
516C3×D4—42no—
517C3×D4—42no—
518C3×D4—44no—
519C3×D4—62no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—122no—
523C3×D4—241no—
524C3×D4#23512yes—
525C3×D4#23712yes—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—42no—
541C2×C3×C4—42no—
542C2×C3×C4—44no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—241no—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—22no—
554#67—42no—
555#67—81no—
556#67—122no—
557#67—241no—
558#67—241no—
559#67—242no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—81no—
566C2×Dic3—121no—
567C2×Dic3—241no—
568C2×Dic3C2×#6711yescharacteristic
569C2×Dic3C2×#6711yescharacteristic
570C2×Dic3C2×#6711yescharacteristic
571D12—21no—
572D12—21no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—121no—
578D12—121no—
579D12—122no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—241no—
583C4×D3—241no—
584C4×D3—241no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—121no—
594C3⋊C8—121no—
595C2×C32—42no—
596C2×C32—41no—
597C2×C32#54611yescharacteristic
598C2×C32C2×#13511yescharacteristic
599C2×C32#57611yescharacteristic
600C3⋊D3—81no—
601C3×D3—22no—
602C3×D3—81no—
603C24—61no—
604#41—22no—
605#41—41no—
606C2×Q8C2×D3211yescharacteristic
607C2×D4—21no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—61no—
611C2×D4—62no—
612C2×D4—61no—
613C2×D4—91no—
614C2×D4—121no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4C2×D3211yescharacteristic
618C22×C4—21no—
619C22×C4—31no—
620C22×C4—61no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4C2×D3211yescharacteristic
624SD16—361no—
625D8—182no—
626D8—361no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—91no—
630C2×C8—91no—
631C2×C8—121no—
632C2×C8—361no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C22⋊C4—31no—
643C22⋊C4—31no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C42—31no—
654C42—61no—
655C22×C3—21no—
656C22×C3—22no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—32no—
665C22×C3—41no—
666C22×C3—42no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—244no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C22×#6711yescharacteristic
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—84no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—241no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3#95012yes—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—41no—
704C3×C4—42no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4C2×#23511yescharacteristic
714C3×C4C2×#23711yescharacteristic
715C3×C4#100411yescharacteristic
716C3×C4#100411yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—41no—
721Dic3—41no—
722Dic3—41no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726C32#329711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—31no—
729C23—61no—
730C23—122no—
731C23—122no—
732C23—181no—
733C23—241no—
734C23D3×#6711yescharacteristic
735Q8—21no—
736Q8—21no—
737D4—21no—
738D4—42no—
739D4—62no—
740D4—61no—
741D4—61no—
742D4—122no—
743D4—181no—
744D4—181no—
745D4—241no—
746D4—362no—
747D4—721no—
748D4#380412yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—31no—
755C2×C4—42no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—181no—
762C2×C4—241no—
763C2×C4—721no—
764C2×C4—721no—
765C2×C4D3×#6711yescharacteristic
766C2×C4C22×D3211yescharacteristic
767C8—61no—
768C8—61no—
769C8—181no—
770C8—181no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—42no—
775C2×C3—41no—
776C2×C3—41no—
777C2×C3—42no—
778C2×C3—62no—
779C2×C3—81no—
780C2×C3—82no—
781C2×C3—241no—
782C2×C3#549011yescharacteristic
783C2×C3D3×#13511yescharacteristic
784C2×C3#576911yescharacteristic
785C2×C3#580611yescharacteristic
786C2×C3C2×#95011yescharacteristic
787C2×C3#583511yescharacteristic
788D3—22no—
789D3—81no—
790D3—241no—
791D3—241no—
792D3—481no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—22no—
797C22—32no—
798C22—41no—
799C22—41no—
800C22—61no—
801C22—61no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—244no—
806C22—361no—
807C22—361no—
808C22—361no—
809C22C2×D3×#6711yescharacteristic
810C4—21no—
811C4—41no—
812C4—61no—
813C4—61no—
814C4—61no—
815C4—121no—
816C4—121no—
817C4—121no—
818C4—361no—
819C4C2×#380411yescharacteristic
820C4#6433011yescharacteristic
821C3—21no—
822C3#7884611yescharacteristic, complemented
823C3#8349511yescharacteristic, complemented
824C2—41no—
825C2—42no—
826C2—62no—
827C2—241no—
828C2—721no—
829C2D3×#95011yescharacteristic
830C2#1059545611yescharacteristic
831C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5829C2semidirect
2. #10594946C2semidirect
3. #10592937C2semidirect
4. C3×#5233C2semidirect
5. #10591614C2semidirect
6. #10591585C2semidirect
7. #10591568C2semidirect
8. #10591551C2semidirect
9. #10591448C2semidirect
10. D3×#832C2semidirect
11. #10591411C2semidirect
12. #10591400C2semidirect
13. #10591164C2semidirect
14. C3⋊C8×#67C2semidirect
15. #10591090C2semidirect
20. C2×#3755C22semidirect
22. #64139C22semidirect
32. C3×#926C22semidirect
33. C22×C3×C3⋊C8C22semidirect
37. #63894C22semidirect
40. #63869C22semidirect
44. #63662C22semidirect
46. #63657C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5829D3semidirect
69. #5233D3semidirect
182. #926C2×D3semidirect
185. C22×C3⋊C8C2×D3semidirect
208. #835C2×D3semidirect
209. #835C2×D3semidirect
726. C32#3297semidirect
822. C3#78846semidirect
823. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
#105949462
#105929372
C3×#52332
#105916142
#105915852
#105915682
#105915512
#105914482
D3×#8322
#105914112
#105914002
#105911642
C3⋊C8×#672
#105910902
#834953
#788463