Finite Group Databasebeta

← #11884253

Subgroups — #11884253

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×#5824C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×#63933C211yesmaximal, characteristic, complemented
4#10594886C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic, complemented
7#10591634C211yesmaximal, characteristic, complemented
8#10591605C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10591468C211yesmaximal, characteristic, complemented
11#10591450C211yesmaximal, characteristic, complemented
12#10591430C211yesmaximal, characteristic, complemented
13#10591169C211yesmaximal, characteristic, complemented
14#10591147C211yesmaximal, characteristic, complemented
15#10591121C211yesmaximal, characteristic, complemented
16#83954—31nomaximal
17#83522—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic, complemented
24#64133C2211yescharacteristic
25C3×#949—24no—
26C3×#946C2211yescharacteristic, complemented
27C3×#944C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C3×#939—21no—
31C3×#935—21no—
32C3×D4×Dic3C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic
34C2×C3×#213C2211yescharacteristic
35C3×#929—21no—
36C3×C4×#67C2211yescharacteristic
37C3×#924C2211yescharacteristic
38C2×C3×Dic3⋊C4—21no—
39C2×C3×#208C2211yescharacteristic
40#63976—21no—
41D3×#217—21no—
42#63933—24no—
43#63908C2211yescharacteristic
44Dic3×D12C2211yescharacteristic
45#63885—21no—
46#63884—21no—
47#63860C2211yescharacteristic
48C2×#3719C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63657C2211yescharacteristic
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C3×#547—31no—
65#5824D311yescharacteristic, complemented
66C2×#950—31no—
67C2×#949D311yescharacteristic, complemented
68#5806—31no—
69C2×#912—31no—
70#5550—31no—
71#5239—31no—
72#5239—31no—
73#5239—61no—
74#5238—31no—
75#5218—31no—
76#5173—31no—
77#5171—31no—
78#5167—31no—
79#5162—31no—
80#5158—31no—
81#5153—31no—
82#5152—31no—
83#5137—31no—
84#5127—31no—
85#5086—31no—
86#5083—31no—
87#5052—31no—
88#5048—31no—
89#5047—31no—
90#5046—31no—
91#5016—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×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C3×#237—22no—
108C3×#237—41no—
109C2×C3×D12—22no—
110C2×C3×D12—21no—
111C2×C3×D12—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#625—21no—
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×#217—21no—
131C3×#217D411yescharacteristic
132C3×#215—22no—
133C3×#215—22no—
134C3×#213—22no—
135C3×#213D414yescomplemented
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4D411yescharacteristic
144C3×C4×Dic3C2311yescharacteristic
145C3×#208—22no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—22no—
153#3715—22no—
154#3715—41no—
155D3×C3⋊C8—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×#237C2×D311yescharacteristic, complemented
164C2×#235—31no—
165C22×D12C2×D311yescharacteristic
166C3×AGL(1,ℤ/8)—64no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C2×C3×D8—31no—
171C2×C3×M16—31no—
172C3×C4⋊Q8—31no—
173C3×#123—61no—
174C3×#123—61no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8—31no—
177C3×#121—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C4⋊C4—61no—
181#953—61no—
182C2×#217—61no—
183#950—64no—
184#949—24no—
185#946C2×D311yescharacteristic, complemented
186#944C2×D311yescharacteristic, complemented
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—61no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215C2×D311yescharacteristic
194C2×#215C2×D311yescharacteristic
195#939—21no—
196#939—61no—
197#938—31no—
198#937—61no—
199#936—31no—
200#935—21no—
201#935—61no—
202D4×Dic3—31no—
203D4×Dic3C2×D311yescharacteristic, complemented
204C2×#214—31no—
205C2×#214—31no—
206C2×#214—31no—
207C2×#214—31no—
208C2×#214—61no—
209C2×#213C2×D311yescharacteristic
210C2×#213C2×D311yescharacteristic
211#930—31no—
212#929—21no—
213C4×#67C2×D311yescharacteristic
214#924—31no—
215#924—31no—
216#924—61no—
217#924C2×D311yescharacteristic
218C2×Dic3⋊C4—21no—
219C2×#208C2×D311yescharacteristic
220C22×C3⋊C8—31no—
221#912—64no—
222C2×Dic12—31no—
223C2×D3×C8—31no—
224#894—61no—
225#884—61no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—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(C2×D3)⋊C8—31no—
243#817—31no—
244#816—31no—
245#816—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#809—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—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—42no—
290C3×D12C2×D412yes—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#625—42no—
296#625—81no—
297D3×Dic3—42no—
298D3×Dic3—81no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—31no—
304C2×#135—91no—
305#547—31no—
306#546—91no—
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—62no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—121no—
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C22×D311yescharacteristic
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—41no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—21no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67#6711yescharacteristic
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364#237—22no—
365#237—41no—
366#237—62no—
367#237—121no—
368#235—62no—
369#235—121no—
370C2×D12—22no—
371C2×D12—21no—
372C2×D12—41no—
373C2×D12C22×D311yescharacteristic
374C2×D12C22×D311yescharacteristic
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×SD16—62no—
383C3×SD16—62no—
384C3×D8—34no—
385C3×D8—62no—
386C3×M16—62no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C42—31no—
401#217—21no—
402#217—21no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—121no—
410#217#6711yescharacteristic
411#216—62no—
412#216—121no—
413#216—121no—
414#216—122no—
415#215—22no—
416#215—22no—
417#215—62no—
418#215—121no—
419#214—62no—
420#214—62no—
421#214—62no—
422#214—122no—
423#214—121no—
424#213—22no—
425#213#6714yescomplemented
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4#6711yescharacteristic
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434C4⋊Dic3—61no—
435C4⋊Dic3C22×D311yescharacteristic
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438Dic3⋊C4—21no—
439Dic3⋊C4—21no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—121no—
443Dic3⋊C4#6711yescharacteristic
444C4×Dic3C22×D311yescharacteristic
445#208—22no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—62no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455Dic12—62no—
456D3×C8—62no—
457C22×C32—22no—
458C22×C32—21no—
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)—64no—
490#135—184no—
491C2×Q16—91no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—31no—
500C2×M16—31no—
501C22×C8—91no—
502C4⋊Q8—31no—
503#124—91no—
504#123—61no—
505#123—61no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—31no—
509C22⋊Q8—91no—
510#121—61no—
511#121—91no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—91no—
517C2×C4⋊C4—61no—
518C2×C22⋊C4—181no—
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—122no—
568C3×D4—121no—
569C3×D4—122no—
570C3×D4D3×D412yes—
571C3×D4C2×#6712yes—
572C2×C3×C4—21no—
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—31no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—42no—
587C2×C3×C4—42no—
588C2×C3×C4—44no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
594C2×C3×C4—122no—
595C2×C3×C4D3×D411yescharacteristic
596C2×C3×C4C2×#6711yescharacteristic
597C2×C3×C4C23×D311yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599#67—41no—
600#67—42no—
601#67—122no—
602#67—122no—
603#67—241no—
604#67—241no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—42no—
608C2×Dic3—42no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—121no—
614C2×Dic3—121no—
615C2×Dic3—122no—
616C2×Dic3—241no—
617C2×Dic3C2×#6711yescharacteristic
618C2×Dic3C2×#6711yescharacteristic
619C2×Dic3C2×#6711yescharacteristic
620D12—21no—
621D12—21no—
622D12—21no—
623D12—42no—
624D12C2×#6712yes—
625C4×D3—21no—
626C4×D3—21no—
627C4×D3—122no—
628C4×D3—241no—
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—41no—
648C2×C32—42no—
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—62no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—121no—
673C2×D4—181no—
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—182no—
684Q16—361no—
685SD16—62no—
686SD16—62no—
687SD16—182no—
688SD16—182no—
689SD16—361no—
690D8—34no—
691D8—62no—
692M16—62no—
693C2×C8—31no—
694C2×C8—31no—
695C2×C8—91no—
696C2×C8—91no—
697C2×C8—182no—
698C4⋊C4—31no—
699C4⋊C4—31no—
700C4⋊C4—61no—
701C4⋊C4—61no—
702C4⋊C4—61no—
703C4⋊C4—61no—
704C4⋊C4—91no—
705C4⋊C4—181no—
706C22⋊C4—31no—
707C22⋊C4—31no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—31no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—22no—
720C22×C3—21no—
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—122no—
808D4—121no—
809D4—122no—
810D4—362no—
811D4—721no—
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—122no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—362no—
829C2×C4—721no—
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—41no—
840C2×C3—42no—
841C2×C3—41no—
842C2×C3—42no—
843C2×C3—81no—
844C2×C3—82no—
845C2×C3—122no—
846C2×C3—121no—
847C2×C3—241no—
848C2×C3#577311yescharacteristic
849C2×C3#577511yescharacteristic
850C2×C3D4×#6711yescharacteristic
851C2×C3D4×#6711yescharacteristic
852C2×C3#582211yescharacteristic
853C2×C3#583711yescharacteristic
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#8352211yescharacteristic, complemented
887C3#8395411yescharacteristic, complemented
888C2—41no—
889C2—42no—
890C2—121no—
891C2—122no—
892C2—241no—
893C2#1059545511yescharacteristic
894C2#1059546911yescharacteristic
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×#5824C2semidirect
2. C2×C3×#949C2semidirect
3. C2×#63933C2semidirect
4. #10594886C2semidirect
5. #10592938C2semidirect
6. #10591655C2semidirect
7. #10591634C2semidirect
8. #10591605C2semidirect
9. #10591564C2semidirect
10. #10591468C2semidirect
11. #10591450C2semidirect
12. #10591430C2semidirect
13. #10591169C2semidirect
14. #10591147C2semidirect
15. #10591121C2semidirect
19. C2×C3×#237C22semidirect
22. C2×#3756C22semidirect
23. C2×#3754C22semidirect
26. C3×#946C22semidirect
27. C3×#944C22semidirect
32. C3×D4×Dic3C22semidirect
48. C2×#3719C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
53. #63659C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
65. #5824D3semidirect
67. C2×#949D3semidirect
135. C3×#213D4semidirect
163. C2×#237C2×D3semidirect
185. #946C2×D3semidirect
186. #944C2×D3semidirect
203. D4×Dic3C2×D3semidirect
425. #213#67semidirect
786. C32#3267semidirect
886. C3#83522semidirect
887. C3#83954semidirect

Maximal subgroups

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

subgroupindex
C3×#58242
C2×C3×#9492
C2×#639332
#105948862
#105929382
#105916552
#105916342
#105916052
#105915642
#105914682
#105914502
#105914302
#105911692
#105911472
#105911212
#839543
#835223