Finite Group Databasebeta

← #11884020

Subgroups — #11884020

Order 1152.

1306 conjugacy classes of subgroups.

The subgroup lattice has 985 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596080C211yesmaximal, characteristic, complemented
2C2×#63930C211yesmaximal, characteristic, complemented
3#10594830C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5042C211yesmaximal, characteristic, complemented
6C3×#5037C211yesmaximal, characteristic, complemented
7#10591475C211yesmaximal, characteristic, complemented
8#10591456C211yesmaximal, characteristic, complemented
9#10591444C211yesmaximal, characteristic, complemented
10#10591183C211yesmaximal, characteristic, complemented
11#10591149C211yesmaximal, characteristic, complemented
12#10590606C211yesmaximal, characteristic, complemented
13#10590540C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590484C211yesmaximal, characteristic, complemented
16#80834—31nomaximal
17#80121—31nomaximal
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic, complemented
22C2×#3797C2211yescharacteristic, complemented
23C32×#121C2211yescharacteristic
24#64149C2211yescharacteristic
25#64146—21no—
26C4×#638C2211yescharacteristic
27#64104C2211yescharacteristic
28#64102C2211yescharacteristic
29#64093—21no—
30#64091—21no—
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#214C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic, complemented
34C3×#924C2211yescharacteristic, complemented
35C2×C3×#208C2211yescharacteristic, complemented
36#63959—21no—
37#63958—21no—
38#63930—24no—
39#63916C2211yescharacteristic, complemented
40#63904—21no—
41#63863C2211yescharacteristic, complemented
42#63851—21no—
43#63843C2211yescharacteristic, complemented
44C2×#3717C2211yescharacteristic
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48#63825—24no—
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#830C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58#63572C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63#5831—31no—
64C2×#949—31no—
65C2×D3×SD16—31no—
66C2×D3×SD16—31no—
67C2×#908—31no—
68#5633—31no—
69#5609—31no—
70#5609—31no—
71#5609—61no—
72C3×#468—31no—
73C3×#449—31no—
74#5176—31no—
75#5163—31no—
76#5156—31no—
77#5154—31no—
78#5127—31no—
79#5046—31no—
80#5042D311yescharacteristic, complemented
81#5037D311yescharacteristic, complemented
82#4889—31no—
83#4883—31no—
84#4819—31no—
85#4817—31no—
86#4806—31no—
87#4806—31no—
88#4787—31no—
89#4775—31no—
90#4773—31no—
91#4762—31no—
92#4731—31no—
93#4728—31no—
94C23×C3⋊D3—21no—
95C23×C3⋊D3—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×#638—21no—
101C2×#638—21no—
102C2×#638D411yescharacteristic
103D4×C3⋊D3—22no—
104D4×C3⋊D3—41no—
105D4×C3⋊D3—44no—
106C2×C4⋊(C3⋊D3)—22no—
107C2×C4⋊(C3⋊D3)—21no—
108C2×C4⋊(C3⋊D3)—21no—
109C2×C4⋊(C3⋊D3)—41no—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4⋊(C3⋊D3)C2311yescharacteristic
112C2×C4×C3⋊D3—21no—
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C3×#67—21no—
115C3×#235—22no—
116C3×#235—41no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×#627—21no—
122C2×#626—21no—
123C2×#624—21no—
124#3797—22no—
125#3797—41no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128#3757D411yescharacteristic
129#3752—21no—
130#3752—21no—
131#3752D411yescharacteristic
132#3750D411yescharacteristic
133C4×C3⋊Dic3C2311yescharacteristic
134C3×#217—21no—
135C3×#214—22no—
136C3×#214—22no—
137C3×#213—41no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×#208—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149Dic32—21no—
150#3717—22no—
151#3717—22no—
152#3717—41no—
153#3717D414yescomplemented
154#3714—22no—
155#3714—22no—
156#3710—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—61no—
164C2×D3×D4—61no—
165C2×D3×D4—61no—
166C2×D3×D4—62no—
167C2×#235C2×D311yescharacteristic, complemented
168C22×D12—31no—
169C22×D12—31no—
170C22×D12—61no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×D8—31no—
174C2×C3×M16—31no—
175C3×C22⋊Q8—31no—
176C3×#121—21no—
177C3×#121C2×D311yescharacteristic
178C3×#121C2×D311yescharacteristic
179#949—64no—
180#947—31no—
181Q8×Dic3—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186#940—31no—
187#940—31no—
188#940—61no—
189#938—31no—
190#938—61no—
191#937—61no—
192#937—61no—
193#937—62no—
194#936—31no—
195#936—61no—
196C2×#214C2×D311yescharacteristic, complemented
197C2×#214C2×D311yescharacteristic, complemented
198C2×#213—31no—
199C2×#213—31no—
200C2×#213C2×D311yescharacteristic, complemented
201C4×#67—31no—
202C4×#67—31no—
203C4×#67—61no—
204C4×#67—61no—
205#924—61no—
206#924C2×D311yescharacteristic, complemented
207C2×#208C2×D311yescharacteristic, complemented
208D3×SD16—64no—
209D3×SD16—64no—
210#908—64no—
211C2×D24—31no—
212C2×D24—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—31no—
216C2×#204—31no—
217C2×D3×C8—31no—
218C2×D3×C8—31no—
219#896—61no—
220#895—31no—
221#895—31no—
222#895—31no—
223#895—61no—
224#893—31no—
225#893—31no—
226#893—61no—
227#893—61no—
228#887—31no—
229#885—61no—
230#884—61no—
231#884—61no—
232#884—62no—
233#884—61no—
234#882—61no—
235#882—61no—
236#882—62no—
237C3×#107—31no—
238C3×#103—31no—
239C3×#103—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×C22⋊C8—31no—
243#832C2×D311yescharacteristic, complemented
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246#821—31no—
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249#815—31no—
250#815—31no—
251Dic3⋊C8—31no—
252Dic3⋊C8—31no—
253#810C2×D311yescharacteristic, complemented
254#810C2×D311yescharacteristic, complemented
255#809—31no—
256#809—31no—
257#809C2×D311yescharacteristic, complemented
258#807C2×D311yescharacteristic, complemented
259C23×C32—21no—
260C23×C32C2×D411yescharacteristic
261C22×C3⋊D3—21no—
262C22×C3⋊D3—21no—
263C22×C3⋊D3—42no—
264C22×C3⋊D3—42no—
265C22×C3⋊D3—42no—
266C22×C3⋊D3—42no—
267C22×C3⋊D3—81no—
268C22×C3⋊D3—81no—
269C22×C3⋊D3C2×D411yescharacteristic
270C22×C3×D3—21no—
271C32×D4—21no—
272C32×D4—21no—
273C32×D4—42no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C2×D411yescharacteristic
278C2×C32×C4C2411yescharacteristic
279#638—22no—
280#638—42no—
281#638—42no—
282#638—81no—
283C2×C3⋊Dic3C2×D411yescharacteristic
284C2×C3⋊Dic3C2×D411yescharacteristic
285C2×C3⋊Dic3C2×D411yescharacteristic
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)—21no—
288C4⋊(C3⋊D3)—21no—
289C4⋊(C3⋊D3)—42no—
290C4⋊(C3⋊D3)—42no—
291C4⋊(C3⋊D3)C2×D412yes—
292C4×C3⋊D3—21no—
293C4×C3⋊D3—21no—
294C4×C3⋊D3—42no—
295C3×#67—42no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C3×D12—21no—
300C3×D12—21no—
301C3×C4×D3—42no—
302C3×Dic6—21no—
303C3×Dic6—21no—
304C3×Dic6—21no—
305C3×Dic6C2×D412yescomplemented
306#627—42no—
307#626—42no—
308#624—42no—
309C3×C3⋊C8—21no—
310C3×C3⋊C8—21no—
311C3×C3⋊C8—21no—
312C3×C3⋊C8C2×D412yescomplemented
313C2×AGL(1,ℤ/8)—91no—
314C22×SD16—91no—
315#548—91no—
316D42—91no—
317#496—91no—
318#468—31no—
319#466—91no—
320#463—91no—
321#460—91no—
322#450—91no—
323#449—31no—
324#448—91no—
325#447—91no—
326#440—91no—
327#435—91no—
328C23×D3—61no—
329C23×D3—61no—
330C23×D3—62no—
331C23×D3—62no—
332C23×D3—61no—
333C23×D3—61no—
334C3×#41—62no—
335C3×#41—121no—
336C2×C3×Q8—31no—
337C2×C3×Q8—31no—
338C2×C3×D4—22no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—21no—
342C2×C3×D4—31no—
343C2×C3×D4—61no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—21no—
351C2×#67—31no—
352C2×#67—31no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—62no—
362C2×#67—62no—
363C2×#67—62no—
364D3×Q8—62no—
365D3×Q8—62no—
366D3×Q8—121no—
367D3×Q8—121no—
368D3×D4—62no—
369D3×D4—62no—
370D3×D4—122no—
371D3×D4—121no—
372D3×D4—121no—
373D3×D4—122no—
374D3×D4—124no—
375D3×D4—124no—
376D3×D4—128no—
377#235—22no—
378#235—41no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—31no—
382C2×D12—31no—
383C2×D12—61no—
384C2×D12—61no—
385C2×D12—62no—
386C2×D12—62no—
387C2×D12—61no—
388C2×D12—61no—
389C2×D12—62no—
390C2×D12—62no—
391C2×D12—61no—
392C2×D12—61no—
393C2×D12—61no—
394C2×D12—122no—
395C2×D12—121no—
396C2×D12—121no—
397C2×D12—122no—
398C2×D12C22×D311yescharacteristic
399C2×C4×D3—21no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—61no—
403C2×C4×D3—61no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3—61no—
407C2×C4×D3—62no—
408C2×Dic6—61no—
409C2×Dic6—61no—
410C2×Dic6C22×D311yescharacteristic
411C2×Dic6C22×D311yescharacteristic
412C3×SD16—62no—
413C3×SD16—62no—
414C3×D8—121no—
415C3×M16—62no—
416C2×C3×C8—31no—
417C2×C3×C8—31no—
418C2×C3×C8—31no—
419C2×C3×C8—31no—
420C3×C4⋊C4—21no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4—61no—
423C3×C4⋊C4C22×D311yescharacteristic
424C3×C4⋊C4C22×D311yescharacteristic
425C3×C22⋊C4—22no—
426C3×C22⋊C4—21no—
427C3×C22⋊C4—21no—
428C3×C22⋊C4—61no—
429#217—21no—
430#217—31no—
431#217—31no—
432#217—61no—
433#217—61no—
434#217—61no—
435#217—61no—
436#215—34no—
437#215—62no—
438#215—62no—
439#215—121no—
440#214—22no—
441#214—22no—
442#213—41no—
443#213—62no—
444#213—62no—
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—31no—
447(C2×D3)⋊C4—61no—
448(C2×D3)⋊C4—61no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—61no—
455(C2×D3)⋊C4—62no—
456(C2×D3)⋊C4—62no—
457C4⋊Dic3—61no—
458C4⋊Dic3C22×D311yescharacteristic
459Dic3⋊C4—21no—
460Dic3⋊C4—31no—
461Dic3⋊C4—31no—
462Dic3⋊C4—61no—
463Dic3⋊C4—61no—
464C4×Dic3—31no—
465C4×Dic3—31no—
466C4×Dic3—61no—
467C4×Dic3—61no—
468C4×Dic3—61no—
469#208—22no—
470C2×C3⋊C8C22×D311yescharacteristic
471C2×C3⋊C8C22×D311yescharacteristic
472C2×C3⋊C8C22×D311yescharacteristic
473C2×C3⋊C8C22×D311yescharacteristic
474D24—62no—
475D24—62no—
476#204—34no—
477#204—62no—
478#204—62no—
479#204—121no—
480D3×C8—62no—
481D3×C8—62no—
482C22×C32—21no—
483C22×C32—21no—
484C22×C32—21no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32C22×D411yescharacteristic
489C2×C3⋊D3—22no—
490C2×C3⋊D3—21no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—41no—
493C2×C3⋊D3—41no—
494C2×C3⋊D3—41no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—84no—
498C2×C3⋊D3—84no—
499C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C32×C4—21no—
504C32×C4—41no—
505C32×C4C22×D411yescharacteristic
506C32×C4H(5,𝔽2)11yescharacteristic
507C3⋊Dic3—21no—
508C3⋊Dic3—21no—
509C3⋊Dic3—21no—
510C3×Dic3—22no—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C2×#41—31no—
514C22×Q8—91no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—181no—
518AGL(1,ℤ/8)—184no—
519C2×SD16—31no—
520C2×SD16—31no—
521C2×SD16—91no—
522C2×SD16—91no—
523C2×SD16—91no—
524C2×SD16—91no—
525C2×SD16—184no—
526C2×D8—31no—
527C2×D8—91no—
528C2×D8—91no—
529C2×M16—31no—
530C22×C8—91no—
531#127—91no—
532#124—91no—
533#124—181no—
534C22⋊Q8—31no—
535C22⋊Q8—181no—
536#121—91no—
537#121—91no—
538#121—181no—
539#121—181no—
540#121D3211yescharacteristic
541#120—181no—
542#120—181no—
543C4×Q8—91no—
544C4×D4—91no—
545C4×D4—91no—
546C4×D4—181no—
547#107—31no—
548C4⋊C8—91no—
549#103—31no—
550#103—31no—
551#102—31no—
552#102—31no—
553#102—91no—
554#102—91no—
555C22⋊C8—31no—
556C22⋊C8—91no—
557#97—91no—
558C23×C3—22no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—61no—
563C23×C3D3×D411yescharacteristic
564C23×C3D3×D411yescharacteristic
565C22×D3—21no—
566C22×D3—31no—
567C22×D3—31no—
568C22×D3—61no—
569C22×D3—62no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—62no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3—122no—
580C22×D3—122no—
581C22×D3—124no—
582C22×D3—124no—
583C22×D3—124no—
584C22×D3—124no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3—241no—
588C22×D3—241no—
589C22×D3—241no—
590C22×D3—241no—
591C22×D3—242no—
592C22×D3—242no—
593C3×Q8—32no—
594C3×Q8—61no—
595C3×Q8—61no—
596C3×Q8—61no—
597C3×D4—21no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—41no—
602C3×D4—41no—
603C3×D4—44no—
604C3×D4—42no—
605C3×D4—42no—
606C3×D4—61no—
607C3×D4—61no—
608C3×D4—122no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—22no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—122no—
624C2×C3×C4D3×D411yescharacteristic
625C2×C3×C4D3×D411yescharacteristic
626C2×C3×C4C23×D311yescharacteristic
627C2×C3×C4C23×D311yescharacteristic
628#67—42no—
629#67—62no—
630#67—62no—
631#67—64no—
632#67—122no—
633#67—122no—
634#67—122no—
635#67—124no—
636#67—122no—
637#67—122no—
638#67—124no—
639#67—241no—
640#67—241no—
641#67—242no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—31no—
646C2×Dic3—31no—
647C2×Dic3—31no—
648C2×Dic3—31no—
649C2×Dic3—31no—
650C2×Dic3—31no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654D12—21no—
655D12—21no—
656D12—32no—
657D12—32no—
658D12—62no—
659D12—62no—
660D12—61no—
661D12—61no—
662D12—61no—
663D12—61no—
664D12—61no—
665D12—61no—
666D12—121no—
667D12—121no—
668D12—122no—
669D12—122no—
670D12—122no—
671D12—122no—
672D12—124no—
673D12—124no—
674D12—122no—
675C4×D3—42no—
676C4×D3—61no—
677C4×D3—61no—
678C4×D3—61no—
679C4×D3—61no—
680C4×D3—121no—
681C4×D3—121no—
682C4×D3—122no—
683C4×D3—122no—
684C4×D3—124no—
685C4×D3—122no—
686C4×D3—122no—
687Dic6—21no—
688Dic6—21no—
689Dic6—21no—
690Dic6—122no—
691Dic6—122no—
692Dic6D3×D412yescomplemented
693C3×C8—32no—
694C3×C8—61no—
695C3×C8—61no—
696C3×C8—61no—
697C3⋊C8—21no—
698C3⋊C8—21no—
699C3⋊C8—21no—
700C3⋊C8D3×D412yescomplemented
701C2×C32—41no—
702C2×C32—81no—
703C2×C32D4211yescharacteristic
704C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
705C2×C32#57711yescharacteristic
706C3⋊D3—22no—
707C3⋊D3—42no—
708C3⋊D3—81no—
709C3×D3—81no—
710C24—181no—
711C24—181no—
712#41—62no—
713#41—121no—
714C2×Q8—31no—
715C2×Q8—31no—
716C2×Q8—181no—
717C2×Q8—182no—
718C2×Q8—361no—
719C2×D4—21no—
720C2×D4—31no—
721C2×D4—61no—
722C2×D4—91no—
723C2×D4—91no—
724C2×D4—91no—
725C2×D4—182no—
726C2×D4—181no—
727C2×D4—181no—
728C2×D4—181no—
729C2×D4—181no—
730C2×D4—181no—
731C2×D4—182no—
732C2×D4—181no—
733C2×D4—361no—
734C2×D4—361no—
735C2×D4—364no—
736C2×D4C2×D3211yescharacteristic
737C22×C4—61no—
738C22×C4—91no—
739C22×C4—181no—
740C22×C4—181no—
741C22×C4C2×D3211yescharacteristic
742SD16—62no—
743SD16—62no—
744SD16—94no—
745SD16—182no—
746SD16—182no—
747SD16—361no—
748D8—121no—
749D8—182no—
750D8—182no—
751M16—62no—
752C2×C8—31no—
753C2×C8—31no—
754C2×C8—31no—
755C2×C8—31no—
756C2×C8—182no—
757C4⋊C4—31no—
758C4⋊C4—61no—
759C4⋊C4—91no—
760C4⋊C4—181no—
761C4⋊C4C2×D3211yescharacteristic
762C22⋊C4—21no—
763C22⋊C4—61no—
764C22⋊C4—91no—
765C22⋊C4—91no—
766C22⋊C4—181no—
767C22⋊C4—181no—
768C22⋊C4—181no—
769C22⋊C4—181no—
770C22⋊C4—181no—
771C42—91no—
772C42—181no—
773C22×C3—22no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3C2×D3×D411yescharacteristic
796C22×C3C2×D3×D411yescharacteristic
797C2×D3—32no—
798C2×D3—32no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—62no—
803C2×D3—61no—
804C2×D3—61no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3—64no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—122no—
813C2×D3—122no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—121no—
818C2×D3—122no—
819C2×D3—122no—
820C2×D3—122no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—244no—
828C2×D3—244no—
829C2×D3—248no—
830C2×D3—248no—
831C2×D3—244no—
832C2×D3—244no—
833C3×C4—21no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—41no—
838C3×C4—42no—
839C3×C4—41no—
840C3×C4—41no—
841C3×C4—62no—
842C3×C4—121no—
843C3×C4—121no—
844C3×C4C2×D3×D411yescharacteristic
845C3×C4C2×D3×D411yescharacteristic
846C3×C4#100411yescharacteristic
847C3×C4#100911yescharacteristic
848Dic3—22no—
849Dic3—41no—
850Dic3—41no—
851Dic3—62no—
852Dic3—61no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—121no—
859Dic3—121no—
860C32#326511yescharacteristic, complemented, Sylow
861C23—21no—
862C23—61no—
863C23—91no—
864C23—181no—
865C23—181no—
866C23—362no—
867C23—362no—
868C23—362no—
869C23—362no—
870C23—721no—
871C23—721no—
872C23#381111yescharacteristic
873Q8—32no—
874Q8—61no—
875Q8—61no—
876Q8—61no—
877Q8—362no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—61no—
882D4—61no—
883D4—92no—
884D4—122no—
885D4—182no—
886D4—181no—
887D4—181no—
888D4—181no—
889D4—362no—
890D4—362no—
891D4—362no—
892D4—362no—
893D4—362no—
894D4—721no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—122no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—362no—
908C2×C4—362no—
909C2×C4#381111yescharacteristic
910C2×C4C22×D3211yescharacteristic
911C8—32no—
912C8—61no—
913C8—61no—
914C8—61no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—42no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—82no—
922C2×C3—81no—
923C2×C3—81no—
924C2×C3—241no—
925C2×C3#559011yescharacteristic
926C2×C3#560911yescharacteristic
927C2×C3#577011yescharacteristic
928C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
929C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
930C2×C3#577811yescharacteristic
931D3—62no—
932D3—62no—
933D3—81no—
934D3—122no—
935D3—124no—
936D3—122no—
937D3—122no—
938D3—242no—
939D3—241no—
940D3—241no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—92no—
948C22—121no—
949C22—121no—
950C22—121no—
951C22—181no—
952C22—181no—
953C22—182no—
954C22—361no—
955C22—361no—
956C22—361no—
957C22—361no—
958C22—361no—
959C22—724no—
960C22—724no—
961C22C2×#381111yescharacteristic
962C4—21no—
963C4—41no—
964C4—62no—
965C4—121no—
966C4—121no—
967C4—181no—
968C4—181no—
969C4—181no—
970C4D32×D411yescharacteristic
971C4#6431411yescharacteristic
972C3—21no—
973C3#8012111yescharacteristic, complemented
974C3#8083411yescharacteristic, complemented
975C2—41no—
976C2—81no—
977C2—182no—
978C2—241no—
979C2—362no—
980C2—721no—
981C2#1059510011yescharacteristic
982C2#1059529211yescharacteristic
983C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596080C2semidirect
2. C2×#63930C2semidirect
3. #10594830C2semidirect
4. C2×#63825C2semidirect
5. C3×#5042C2semidirect
6. C3×#5037C2semidirect
7. #10591475C2semidirect
8. #10591456C2semidirect
9. #10591444C2semidirect
10. #10591183C2semidirect
11. #10591149C2semidirect
12. #10590606C2semidirect
13. #10590540C2semidirect
14. #10590509C2semidirect
15. #10590484C2semidirect
21. C2×C3×#235C22semidirect
22. C2×#3797C22semidirect
31. C2×C3×#214C22semidirect
32. C2×C3×#214C22semidirect
33. C2×C3×#213C22semidirect
34. C3×#924C22semidirect
35. C2×C3×#208C22semidirect
39. #63916C22semidirect
41. #63863C22semidirect
43. #63843C22semidirect
46. C2×#3717C22semidirect
47. C2×#3717C22semidirect
50. C2×#3714C22semidirect
51. C2×#3710C22semidirect
52. C3×#832C22semidirect
53. C3×#830C22semidirect
54. C3×#810C22semidirect
55. C3×#810C22semidirect
56. C3×#809C22semidirect
57. C3×#807C22semidirect
58. #63572C22semidirect
60. #63564C22semidirect
61. #63557C22semidirect
62. #63555C22semidirect
80. #5042D3semidirect
81. #5037D3semidirect
153. #3717D4semidirect
167. C2×#235C2×D3semidirect
196. C2×#214C2×D3semidirect
197. C2×#214C2×D3semidirect
200. C2×#213C2×D3semidirect
206. #924C2×D3semidirect
207. C2×#208C2×D3semidirect
243. #832C2×D3semidirect
244. #830C2×D3semidirect
253. #810C2×D3semidirect
254. #810C2×D3semidirect
257. #809C2×D3semidirect
258. #807C2×D3semidirect
305. C3×Dic6C2×D4semidirect
312. C3×C3⋊C8C2×D4semidirect
499. C2×C3⋊D3AGL(1,ℤ/8)semidirect
692. Dic6D3×D4semidirect
700. C3⋊C8D3×D4semidirect
860. C32#3265semidirect
973. C3#80121semidirect
974. C3#80834semidirect

Maximal subgroups

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

subgroupindex
#105960802
C2×#639302
#105948302
C2×#638252
C3×#50422
C3×#50372
#105914752
#105914562
#105914442
#105911832
#105911492
#105906062
#105905402
#105905092
#105904842
#808343
#801213