Finite Group Databasebeta

← #11887236

Subgroups — #11887236

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic
2#10594939C211yesmaximal, characteristic, complemented
3#10592938C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591614C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591577C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10591459C211yesmaximal, characteristic, complemented
10D3×#832C211yesmaximal, characteristic, complemented
11#10591409C211yesmaximal, characteristic, complemented
12#10591401C211yesmaximal, characteristic, complemented
13#10591175C211yesmaximal, characteristic, complemented
14C3⋊C8×#67C211yesmaximal, characteristic, complemented
15#10591090C211yesmaximal, characteristic, complemented
16#83494—31nomaximal
17#78845—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3756C2211yescharacteristic, complemented
21C2×#3754C2211yescharacteristic
22#64133C2211yescharacteristic, 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#63969—21no—
35#63956—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63877—21no—
38#63869C2211yescharacteristic, complemented
39#63867—21no—
40#63857C2211yescharacteristic
41#63844C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
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#63574C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5829D311yescharacteristic
63#5541—31no—
64#5529—31no—
65C3×#416—31no—
66#5239—31no—
67#5239—31no—
68#5239—61no—
69#5233D311yescharacteristic, complemented
70#5218—31no—
71C2×#832—31no—
72#5114—31no—
73C8×#67—31no—
74#5056—31no—
75#5054—31no—
76#5051—31no—
77#5043—31no—
78#5041—31no—
79#5035—31no—
80C4×#214—31no—
81D4×C3⋊C8—31no—
82#5009—31no—
83#5003—31no—
84#4813—31no—
85#4805—31no—
86#4800—31no—
87#4798—31no—
88#4776—31no—
89D3×#102—31no—
90#4763—31no—
91#4758—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×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C22×C3×Dic3—21no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×D3×Dic3—21no—
110#3757—21no—
111#3756—41no—
112#3754—22no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3716—41no—
143D3×C3⋊C8—41no—
144#3296—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×#216—31no—
164C2×#216—31no—
165C2×#216—61no—
166#939—21no—
167#937—21no—
168#935—61no—
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—61no—
174#930C2×D311yescharacteristic
175#929—21no—
176C4×#67C2×D311yescharacteristic
177C2×(C2×D3)⋊C4—21no—
178#926C2×D311yescharacteristic, complemented
179C2×C4⋊Dic3—31no—
180#924—31no—
181#924—31no—
182#924—31no—
183#924—61no—
184C22×C3⋊C8—31no—
185C22×C3⋊C8C2×D311yescharacteristic, complemented
186C2×#204—31no—
187C2×D3×C8—31no—
188#897—31no—
189D3×C4⋊C4—31no—
190#890—31no—
191#889—61no—
192#887—31no—
193#883—61no—
194#879—61no—
195#879—61no—
196#877—61no—
197#872—61no—
198#870—31no—
199#870—61no—
200C4×Dic6—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(C2×D3)⋊C8—31no—
224#817—31no—
225#816—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228#810—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#808—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—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—42no—
249C32×D4#4112yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258#634—21no—
259#634—21no—
260C3×#67—22no—
261C3×#67—42no—
262C3×#67—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—81no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274D3×Dic3—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—31no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—31no—
293C2×#102—91no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—22no—
297C3×#41—22no—
298C3×#41—42no—
299C3×#41—41no—
300C3×#41—41no—
301C3×#41—42no—
302C2×C3×Q8—21no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—41no—
311C2×C3×D4—61no—
312C2×C3×D4—62no—
313C2×C3×D4—61no—
314C2×C3×D4—121no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—41no—
322C22×C3×C4—61no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—21no—
326C2×#67—21no—
327C2×#67#6711yescharacteristic
328C22×Dic3—21no—
329C22×Dic3—61no—
330D3×D4—22no—
331D3×D4—41no—
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—61no—
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—121no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355C3×C42—61no—
356#217—21no—
357#217—21no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—121no—
362#217#6711yescharacteristic
363#216—121no—
364#216—121no—
365#216—122no—
366#214—62no—
367#214—62no—
368#214—122no—
369#214—121no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4#6711yescharacteristic
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—121no—
396Dic3⋊C4#6711yescharacteristic
397C4×Dic3—21no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—41no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—121no—
412D3×C8—121no—
413C22×C32—22no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—84no—
426C2×C3×D3#13512yes—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41D3211yescharacteristic
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—31no—
445C22×C8—91no—
446#126—181no—
447#125—91no—
448#125—181no—
449#124—31no—
450#123—61no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455#121—31no—
456#121—61no—
457#120—61no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—31no—
461#117—31no—
462#117—181no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—61no—
465#107—91no—
466#106—91no—
467#106—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—41no—
487C23×C3—61no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—241no—
491C23×C3D3×D411yescharacteristic
492C23×C3C2×#6711yescharacteristic
493C22×D3—21no—
494C22×D3—42no—
495C22×D3—42no—
496C22×D3—81no—
497C22×D3C2×#6711yescharacteristic
498C3×Q8—22no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—41no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—41no—
508C3×D4—42no—
509C3×D4—42no—
510C3×D4—44no—
511C3×D4—62no—
512C3×D4—61no—
513C3×D4—61no—
514C3×D4—122no—
515C3×D4—241no—
516C3×D4#23512yes—
517C3×D4#23712yes—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—42no—
533C2×C3×C4—42no—
534C2×C3×C4—44no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—241no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—22no—
546#67—42no—
547#67—81no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—81no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—122no—
559C2×Dic3C2×#6711yescharacteristic
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562D12—21no—
563D12—21no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—122no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—121no—
572Dic6—121no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C3⋊C8—121no—
583C2×C32—42no—
584C2×C32—41no—
585C2×C32#54611yescharacteristic
586C2×C32C2×#13511yescharacteristic
587C2×C32#57711yescharacteristic
588C3×D3—22no—
589C3×D3—81no—
590C24—61no—
591#41—22no—
592#41—41no—
593C2×Q8—91no—
594C2×Q8C2×D3211yescharacteristic
595C2×D4—21no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—121no—
602C2×D4C2×D3211yescharacteristic
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—181no—
607C22×C4C2×D3211yescharacteristic
608Q16—361no—
609SD16—182no—
610SD16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—121no—
616C2×C8—361no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—61no—
641C42—181no—
642C22×C3—21no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—22no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—32no—
652C22×C3—42no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—244no—
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C22×#6711yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—84no—
676C2×D3#95012yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—41no—
682C3×C4—42no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4C2×#23511yescharacteristic
692C3×C4C2×#23711yescharacteristic
693C3×C4#100411yescharacteristic
694C3×C4#100411yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—21no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—241no—
706Dic3—241no—
707C32#329611yescharacteristic, complemented, Sylow
708C23—21no—
709C23—31no—
710C23—61no—
711C23—122no—
712C23—122no—
713C23—241no—
714C23D3×#6711yescharacteristic
715Q8—21no—
716Q8—21no—
717Q8—181no—
718Q8—181no—
719D4—21no—
720D4—42no—
721D4—62no—
722D4—61no—
723D4—61no—
724D4—122no—
725D4—241no—
726D4#380412yes—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—42no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—241no—
742C2×C4—362no—
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—181no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—42no—
753C2×C3—41no—
754C2×C3—41no—
755C2×C3—42no—
756C2×C3—62no—
757C2×C3—81no—
758C2×C3—82no—
759C2×C3—241no—
760C2×C3#549011yescharacteristic
761C2×C3D3×#13511yescharacteristic
762C2×C3#577011yescharacteristic
763C2×C3#580611yescharacteristic
764C2×C3C2×#95011yescharacteristic
765C2×C3#583611yescharacteristic
766D3—22no—
767D3—81no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—22no—
772C22—32no—
773C22—41no—
774C22—41no—
775C22—61no—
776C22—61no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—244no—
781C22C2×D3×#6711yescharacteristic
782C4—21no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—361no—
791C4—361no—
792C4C2×#380411yescharacteristic
793C4#6433011yescharacteristic
794C3—21no—
795C3#7884511yescharacteristic, complemented
796C3#8349411yescharacteristic, complemented
797C2—41no—
798C2—42no—
799C2—62no—
800C2—241no—
801C2D3×#95011yescharacteristic
802C2#1059546611yescharacteristic
803C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5829C2
hypercenterC2×#41D32
hypocenterC32#3296
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
2. #10594939C2semidirect
3. #10592938C2semidirect
4. C3×#5233C2semidirect
5. #10591614C2semidirect
6. #10591596C2semidirect
7. #10591577C2semidirect
8. #10591549C2semidirect
9. #10591459C2semidirect
10. D3×#832C2semidirect
11. #10591409C2semidirect
12. #10591401C2semidirect
13. #10591175C2semidirect
14. C3⋊C8×#67C2semidirect
15. #10591090C2semidirect
20. C2×#3756C22semidirect
22. #64133C22semidirect
32. C3×#926C22semidirect
33. C22×C3×C3⋊C8C22semidirect
38. #63869C22semidirect
41. #63844C22semidirect
44. #63662C22semidirect
46. #63657C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. #63576C22semidirect
52. #63574C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
60. Dic3×C3⋊C8C22semidirect
69. #5233D3semidirect
178. #926C2×D3semidirect
185. C22×C3⋊C8C2×D3semidirect
208. #835C2×D3semidirect
209. #835C2×D3semidirect
707. C32#3296semidirect
795. C3#78845semidirect
796. C3#83494semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
#105949392
#105929382
C3×#52332
#105916142
#105915962
#105915772
#105915492
#105914592
D3×#8322
#105914092
#105914012
#105911752
C3⋊C8×#672
#105910902
#834943
#788453