Finite Group Databasebeta

← #11884283

Subgroups — #11884283

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×#63932C211yesmaximal, characteristic, complemented
4#10594887C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic, complemented
7#10591638C211yesmaximal, characteristic, complemented
8#10591627C211yesmaximal, characteristic, complemented
9#10591567C211yesmaximal, characteristic, complemented
10#10591489C211yesmaximal, characteristic, complemented
11#10591458C211yesmaximal, characteristic, complemented
12#10591430C211yesmaximal, characteristic, complemented
13#10591175C211yesmaximal, characteristic, complemented
14#10591161C211yesmaximal, characteristic, complemented
15#10591155C211yesmaximal, characteristic, complemented
16#83921—31nomaximal
17#83503—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×#3795C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic
24#64133C2211yescharacteristic, complemented
25C3×#950—24no—
26C3×#947C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#939—21no—
31C3×#937—21no—
32C3×D4×Dic3C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic
34C2×C3×#213C2211yescharacteristic
35C3×#930C2211yescharacteristic
36C3×#929—21no—
37C3×C4×#67C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4—21no—
39C22×C3×C3⋊C8C2211yescharacteristic, complemented
40#63970—21no—
41#63969—21no—
42#63932—24no—
43#63905—21no—
44Dic3×D12C2211yescharacteristic, complemented
45D3×Dic3⋊C4—21no—
46#63866C2211yescharacteristic, complemented
47#63856C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic
54#63657C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64C3×#546—31no—
65#5829D311yescharacteristic, complemented
66#5824—31no—
67C2×#950D311yescharacteristic, complemented
68C2×#932—31no—
69C2×#911—31no—
70#5551—31no—
71#5239—31no—
72#5239—31no—
73#5239—61no—
74#5238—31no—
75#5218—31no—
76#5190—31no—
77#5189—31no—
78#5173—31no—
79#5169—31no—
80#5165—31no—
81#5162—31no—
82#5152—31no—
83#5114—31no—
84#5111—31no—
85#5060—31no—
86#5057—31no—
87#5052—31no—
88#5047—31no—
89#5041—31no—
90#5037—31no—
91#5019—31no—
92#5014—31no—
93#5011—31no—
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C22×C3×Dic3—21no—
108C3×D3×D4—22no—
109C3×D3×D4—41no—
110C3×#235—22no—
111C3×#235—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#625—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120#3795—22no—
121#3795—41no—
122#3757—21no—
123#3756—41no—
124#3754—22no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—22no—
132C3×#215—22no—
133C3×#214—22no—
134C3×#213D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8—22no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3724—21no—
148Dic3⋊Dic3—21no—
149Dic3⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3716—22no—
153#3715—41no—
154#3713—22no—
155#3711—22no—
156#3267—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic
160C2×C3×#41C2×D311yescharacteristic
161C22×C3×D4—31no—
162C2×#237—31no—
163C2×D3×D4C2×D311yescharacteristic
164C2×#235—31no—
165C2×#235C2×D311yescharacteristic, complemented
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C22×C3×C8—31no—
172C3×#124—31no—
173C3×#123—61no—
174C3×C22⋊Q8—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#120—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C22⋊C4—61no—
181#950—24no—
182#947C2×D311yescharacteristic
183#946—31no—
184#946C2×D311yescharacteristic
185#944—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—61no—
189C2×#216C2×D311yescharacteristic, complemented
190C2×#215—31no—
191C2×#215C2×D311yescharacteristic, complemented
192#939—21no—
193#939—61no—
194#938—61no—
195#937—21no—
196#935—61no—
197D4×Dic3—31no—
198D4×Dic3C2×D311yescharacteristic
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—61no—
204C2×#214C2×D311yescharacteristic
205#932—64no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213C2×D311yescharacteristic
209#930C2×D311yescharacteristic
210#929—21no—
211#929—61no—
212C4×#67C2×D311yescharacteristic
213C2×(C2×D3)⋊C4—21no—
214#924—31no—
215#924—31no—
216#924—31no—
217#924—61no—
218C2×Dic3⋊C4—61no—
219C2×#208—31no—
220C22×C3⋊C8C2×D311yescharacteristic, complemented
221#911—64no—
222C2×#204—31no—
223C2×ΓL(1,𝔽25)—31no—
224D3×C4⋊C4—61no—
225#883—61no—
226#883—61no—
227C4×D12—31no—
228#869—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#830—31no—
240#830—31no—
241#830—61no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244#817—31no—
245#816—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#810—31no—
250#809—31no—
251#808—31no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×D4—21no—
265C32×D4—42no—
266C32×D4C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—42no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275#634—21no—
276#634—21no—
277C3×#67—41no—
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—81no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12C2×D412yes—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#625—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—31no—
305#547—91no—
306#546—31no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—22no—
321C3×#41—22no—
322C3×#41—42no—
323C3×#41—41no—
324C3×#41—41no—
325C3×#41—42no—
326C3×#41—62no—
327C3×#41—121no—
328C2×C3×Q8—21no—
329C2×C3×Q8—31no—
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—41no—
339C2×C3×D4—61no—
340C2×C3×D4—62no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—121no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—41no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67#6711yescharacteristic
361C22×Dic3—21no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364#237—62no—
365#237—121no—
366D3×D4—22no—
367D3×D4—41no—
368#235—22no—
369#235—41no—
370#235—62no—
371#235—121no—
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×C4×D3—21no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—61no—
381C2×Dic6C22×D311yescharacteristic
382C3×Q16—62no—
383C3×SD16—62no—
384C3×SD16—62no—
385C3×D8—34no—
386C2×C3×C8—31no—
387C2×C3×C8—31no—
388C2×C3×C8—62no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—61no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—31no—
400#217—21no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—121no—
406#217#6711yescharacteristic
407#216—22no—
408#216—121no—
409#216—121no—
410#216—122no—
411#215—22no—
412#215—121no—
413#214—22no—
414#214—62no—
415#214—62no—
416#214—62no—
417#214—122no—
418#214—121no—
419#213—62no—
420#213—62no—
421#213#6714yescomplemented
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4#6711yescharacteristic
429C4⋊Dic3—31no—
430C4⋊Dic3—31no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—21no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—121no—
443Dic3⋊C4#6711yescharacteristic
444C4×Dic3C22×D311yescharacteristic
445#208—62no—
446C2×C3⋊C8—22no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455#204—62no—
456ΓL(1,𝔽25)—62no—
457C22×C32—21no—
458C22×C32—22no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—84no—
474C32×C4—21no—
475C32×C4—41no—
476C32×C4C22×D411yescharacteristic
477C32×C4H(5,𝔽2)11yescharacteristic
478C3⋊Dic3—41no—
479C3⋊Dic3—41no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—91no—
487C2×#41D3211yescharacteristic
488C22×D4—31no—
489AGL(1,ℤ/8)—184no—
490#135—64no—
491C2×Q16—31no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—91no—
500C2×M16—91no—
501C22×C8—31no—
502C4⋊Q8—91no—
503#124—31no—
504#123—61no—
505#123—181no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—31no—
511#121—61no—
512#121—181no—
513#120—61no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—91no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—61no—
519#106—91no—
520C4⋊C8—91no—
521#103—91no—
522#103—91no—
523#103—91no—
524#102—91no—
525#102—91no—
526#102—91no—
527C22⋊C8—91no—
528C22⋊C8—91no—
529#97—91no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—31no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—122no—
538C23×C3—122no—
539C23×C3—241no—
540C23×C3D3×D411yescharacteristic
541C23×C3C2×#6711yescharacteristic
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—42no—
545C22×D3—42no—
546C22×D3—81no—
547C22×D3C2×#6711yescharacteristic
548C3×Q8—22no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—41no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—22no—
559C3×D4—32no—
560C3×D4—41no—
561C3×D4—42no—
562C3×D4—42no—
563C3×D4—44no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—121no—
568C3×D4—122no—
569C3×D4—122no—
570C3×D4—241no—
571C3×D4D3×D412yes—
572C3×D4C2×#6712yes—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—44no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—122no—
595C2×C3×C4—241no—
596C2×C3×C4D3×D411yescharacteristic
597C2×C3×C4C2×#6711yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600#67—41no—
601#67—42no—
602#67—42no—
603#67—81no—
604#67—122no—
605#67—122no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—81no—
613C2×Dic3—121no—
614C2×Dic3—121no—
615C2×Dic3—122no—
616C2×Dic3—122no—
617C2×Dic3C2×#6711yescharacteristic
618C2×Dic3C2×#6711yescharacteristic
619C2×Dic3C2×#6711yescharacteristic
620D12—21no—
621D12—21no—
622D12—21no—
623D12C2×#6712yes—
624C4×D3—21no—
625C4×D3—21no—
626C4×D3—42no—
627C4×D3—122no—
628C4×D3—122no—
629Dic6—21no—
630Dic6—21no—
631Dic6—61no—
632Dic6—61no—
633Dic6—61no—
634Dic6—61no—
635Dic6—121no—
636Dic6—121no—
637C3×C8—32no—
638C3×C8—61no—
639C3⋊C8—21no—
640C3⋊C8—61no—
641C3⋊C8—61no—
642C3⋊C8—61no—
643C3⋊C8—61no—
644C3⋊C8—121no—
645C3⋊C8—121no—
646C3⋊C8C2×#6712yes—
647C2×C32—42no—
648C2×C32—41no—
649C2×C32D4211yescharacteristic
650C2×C32#57511yescharacteristic
651C2×C32#57711yescharacteristic
652C3×D3—41no—
653C3×D3—42no—
654C3×D3—81no—
655C24—61no—
656#41—22no—
657#41—41no—
658#41—62no—
659#41—121no—
660#41—182no—
661#41—361no—
662C2×Q8—31no—
663C2×Q8—91no—
664C2×Q8C2×D3211yescharacteristic
665C2×D4—21no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—31no—
669C2×D4—61no—
670C2×D4—62no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—121no—
674C2×D4—181no—
675C2×D4C2×D3211yescharacteristic
676C22×C4—21no—
677C22×C4—31no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—181no—
681C22×C4—181no—
682C22×C4C2×D3211yescharacteristic
683Q16—62no—
684Q16—361no—
685SD16—62no—
686SD16—62no—
687SD16—182no—
688SD16—182no—
689SD16—361no—
690D8—34no—
691D8—182no—
692M16—182no—
693C2×C8—31no—
694C2×C8—31no—
695C2×C8—62no—
696C2×C8—91no—
697C2×C8—91no—
698C4⋊C4—31no—
699C4⋊C4—31no—
700C4⋊C4—61no—
701C4⋊C4—91no—
702C4⋊C4—181no—
703C4⋊C4—181no—
704C4⋊C4—181no—
705C4⋊C4—181no—
706C22⋊C4—31no—
707C22⋊C4—31no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—31no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—22no—
721C22×C3—21no—
722C22×C3—22no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—42no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—62no—
737C22×C3—61no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—244no—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C22×#6711yescharacteristic
748C2×D3—21no—
749C2×D3—22no—
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—84no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—41no—
763C3×C4—42no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—61no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—121no—
770C3×C4—121no—
771C3×C4C2×D3×D411yescharacteristic
772C3×C4#100411yescharacteristic
773C3×C4#100411yescharacteristic
774C3×C4C22×#6711yescharacteristic
775Dic3—21no—
776Dic3—21no—
777Dic3—21no—
778Dic3—41no—
779Dic3—41no—
780Dic3—121no—
781Dic3—121no—
782Dic3—121no—
783Dic3—121no—
784Dic3—241no—
785Dic3—241no—
786C32#326711yescharacteristic, complemented, Sylow
787C23—21no—
788C23—31no—
789C23—61no—
790C23—61no—
791C23—122no—
792C23—122no—
793C23—241no—
794C23D3×#6711yescharacteristic
795Q8—21no—
796Q8—21no—
797Q8—61no—
798Q8—61no—
799Q8—181no—
800Q8—181no—
801D4—21no—
802D4—32no—
803D4—42no—
804D4—61no—
805D4—61no—
806D4—61no—
807D4—121no—
808D4—122no—
809D4—122no—
810D4—241no—
811D4—362no—
812D4D3×#6712yes—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—31no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—42no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—122no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—241no—
828C2×C4—362no—
829C2×C4—362no—
830C2×C4D3×#6711yescharacteristic
831C2×C4C22×D3211yescharacteristic
832C8—32no—
833C8—61no—
834C8—181no—
835C8—181no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—42no—
840C2×C3—41no—
841C2×C3—41no—
842C2×C3—42no—
843C2×C3—81no—
844C2×C3—82no—
845C2×C3—122no—
846C2×C3—121no—
847C2×C3—241no—
848C2×C3#576811yescharacteristic
849C2×C3#577011yescharacteristic
850C2×C3D4×#6711yescharacteristic
851C2×C3D4×#6711yescharacteristic
852C2×C3#582211yescharacteristic
853C2×C3#583611yescharacteristic
854D3—41no—
855D3—42no—
856D3—81no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—22no—
861C22—41no—
862C22—41no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—62no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—244no—
873C22C2×D3×#6711yescharacteristic
874C4—21no—
875C4—41no—
876C4—61no—
877C4—61no—
878C4—61no—
879C4—121no—
880C4—121no—
881C4—361no—
882C4—361no—
883C4C2×D3×#6711yescharacteristic
884C4#6433011yescharacteristic
885C3—21no—
886C3#8350311yescharacteristic, complemented
887C3#8392111yescharacteristic, complemented
888C2—41no—
889C2—42no—
890C2—121no—
891C2—122no—
892C2—241no—
893C2#1059545311yescharacteristic
894C2#1059546611yescharacteristic
895C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3267
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. C2×C3×#950C2semidirect
3. C2×#63932C2semidirect
4. #10594887C2semidirect
5. #10592938C2semidirect
6. #10591655C2semidirect
7. #10591638C2semidirect
8. #10591627C2semidirect
9. #10591567C2semidirect
10. #10591489C2semidirect
11. #10591458C2semidirect
12. #10591430C2semidirect
13. #10591175C2semidirect
14. #10591161C2semidirect
15. #10591155C2semidirect
20. C2×C3×#235C22semidirect
22. C2×#3756C22semidirect
24. #64133C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#215C22semidirect
39. C22×C3×C3⋊C8C22semidirect
44. Dic3×D12C22semidirect
46. #63866C22semidirect
52. #63662C22semidirect
54. #63657C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
60. #63562C22semidirect
62. #63554C22semidirect
65. #5829D3semidirect
67. C2×#950D3semidirect
134. C3×#213D4semidirect
165. C2×#235C2×D3semidirect
189. C2×#216C2×D3semidirect
191. C2×#215C2×D3semidirect
220. C22×C3⋊C8C2×D3semidirect
421. #213#67semidirect
786. C32#3267semidirect
886. C3#83503semidirect
887. C3#83921semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
C2×C3×#9502
C2×#639322
#105948872
#105929382
#105916552
#105916382
#105916272
#105915672
#105914892
#105914582
#105914302
#105911752
#105911612
#105911552
#839213
#835033