Finite Group Databasebeta

← #11889094

Subgroups — #11889094

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic, complemented
3C3×#5011C211yesmaximal, characteristic, complemented
4#10591183C211yesmaximal, characteristic, complemented
5#10591183C211yesmaximal, characteristic, complemented
6#10591178C211yesmaximal, characteristic, complemented
7#10591177C211yesmaximal, characteristic, complemented
8#10591136C211yesmaximal, characteristic, complemented
9#10591133C211yesmaximal, characteristic, complemented
10#10591096C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590367C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590282C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#79501—31nomaximal
18C2×D4×C3⋊D3—21no—
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22#64139C2211yescharacteristic
23#64139C2211yescharacteristic
24#64104—21no—
25#64091—21no—
26#64091—21no—
27#64083C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C3×#935—21no—
30C3×#926C2211yescharacteristic, complemented
31C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
32C3×#924C2211yescharacteristic, complemented
33C3×#924C2211yescharacteristic, complemented
34C2×C3×#208C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×#889—21no—
37C3×#879—21no—
38C3×#877—21no—
39C3×#870C2211yescharacteristic, complemented
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic, complemented
44C3×#830C2211yescharacteristic, complemented
45C3×#830C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#803C2211yescharacteristic, complemented
48#63575C2211yescharacteristic, complemented
49#63575C2211yescharacteristic, complemented
50#63573C2211yescharacteristic, complemented
51#63566C2211yescharacteristic, complemented
52#63564C2211yescharacteristic
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61C3×#552—31no—
62D4×D12—31no—
63D4×D12—31no—
64D4×D12—61no—
65#5541D311yescharacteristic, complemented
66C3×#435—31no—
67#5134—31no—
68#5131—31no—
69#5114—31no—
70C2×#821—31no—
71#5067—31no—
72#5066—31no—
73#5049—31no—
74#5048—31no—
75#5046—31no—
76#5046—31no—
77#5027—31no—
78#5026—31no—
79#5011D311yescharacteristic, complemented
80#5003—31no—
81#5001—31no—
82#4967—31no—
83C2×#809—31no—
84#4848—31no—
85#4847—31no—
86#4737—31no—
87#4736—31no—
88#4731—31no—
89#4731—31no—
90#4713—31no—
91#4710—31no—
92C23×C3⋊D3—21no—
93C23×C3⋊D3—21no—
94C2×C32×D4D411yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99D4×C3⋊D3—44no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)—21no—
106C2×C4⋊(C3⋊D3)—41no—
107C2×C4⋊(C3⋊D3)—41no—
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4⋊(C3⋊D3)C2311yescharacteristic
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3—21no—
112C22×C3×Dic3—21no—
113C2×C3×Dic6C2311yescharacteristic
114C32×C4⋊C4D411yescharacteristic
115C32×C22⋊C4D411yescharacteristic
116C32×C22⋊C4D411yescharacteristic
117C32×C42C2311yescharacteristic
118#3752—21no—
119#3752—21no—
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C3×#217—21no—
123C3×#217—21no—
124C3×#217—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×#208—41no—
137C2×C3×C3⋊C8—41no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142#3717—22no—
143#3717—41no—
144#3717—41no—
145#3310—91noSylow
146C2×D3×D4—62no—
147C2×D3×D4—61no—
148C2×D3×D4—61no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—31no—
153C22×D12—61no—
154C22×D12—61no—
155C2×C3×M16—31no—
156C22×C3×C8—31no—
157C3×#126—61no—
158C3×#125—31no—
159C3×#125—61no—
160C3×#123—61no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×D4—21no—
165C3×C4×D4C2×D311yescharacteristic
166C3×C4×D4C2×D311yescharacteristic
167C3×#117—31no—
168C3×#117—61no—
169C2×C3×C4⋊C4—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—31no—
173#935—21no—
174#930—31no—
175#930—31no—
176#930—31no—
177#930—31no—
178#930—61no—
179#930—61no—
180#926C2×D311yescharacteristic, complemented
181C2×C4⋊Dic3C2×D311yescharacteristic, complemented
182#924C2×D311yescharacteristic, complemented
183#924C2×D311yescharacteristic, complemented
184C2×#208C2×D311yescharacteristic, complemented
185C22×C3⋊C8C2×D311yescharacteristic, complemented
186C2×#204—31no—
187C2×#204—31no—
188C2×#204—31no—
189#895—62no—
190#895—61no—
191#895—61no—
192#889—21no—
193#882—62no—
194#882—62no—
195#882—61no—
196#882—61no—
197#882—61no—
198#882—61no—
199#879—21no—
200#877—21no—
201#874—31no—
202#874—31no—
203#874—61no—
204C4×D12—31no—
205C4×D12—31no—
206C4×D12—61no—
207#870C2×D311yescharacteristic, complemented
208C4×Dic6C2×D311yescharacteristic, complemented
209C3×C4⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×C22⋊C8—31no—
212C3×#97—31no—
213#835—31no—
214#830C2×D311yescharacteristic, complemented
215#830C2×D311yescharacteristic, complemented
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223#821—31no—
224#821—31no—
225#818—31no—
226#818—31no—
227#817—31no—
228#816—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#808—31no—
239#807—31no—
240#807—31no—
241C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
242#803C2×D311yescharacteristic, complemented
243C23×C32C2×D411yescharacteristic
244C23×C32C2×D411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—42no—
249C22×C3⋊D3—42no—
250C22×C3⋊D3—42no—
251C22×C3⋊D3—42no—
252C22×C3⋊D3—81no—
253C22×C3⋊D3—81no—
254C32×D4—22no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264#638—42no—
265#638—42no—
266C2×C3⋊Dic3—21no—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4⋊(C3⋊D3)—42no—
274C4⋊(C3⋊D3)—42no—
275C4⋊(C3⋊D3)—81no—
276C4⋊(C3⋊D3)#4112yes—
277C4×C3⋊D3—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289#552—31no—
290D42—91no—
291#490—91no—
292#482—91no—
293#480—91no—
294#478—91no—
295#468—91no—
296#465—91no—
297#460—91no—
298#450—91no—
299#450—91no—
300#440—91no—
301#435—31no—
302#418—91no—
303C2×#102—91no—
304C23×D3—62no—
305C23×D3—62no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×Q8—31no—
311C2×C3×D4—21no—
312C2×C3×D4D1211yescharacteristic
313C2×C3×D4#6711yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—62no—
322C2×#67—62no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C22×Dic3—21no—
328D3×D4—128no—
329D3×D4—124no—
330D3×D4—124no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—62no—
341C2×D12—62no—
342C2×D12—62no—
343C2×D12—62no—
344C2×D12—62no—
345C2×D12—62no—
346C2×D12—62no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—62no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—122no—
357C2×D12—122no—
358C2×D12—121no—
359C2×D12—121no—
360C2×D12—121no—
361C2×D12—121no—
362C2×D12—122no—
363C2×D12—122no—
364C2×C4×D3—62no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×Dic6C22×D311yescharacteristic
368C3×M16—121no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8—121no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4—61no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4D1211yescharacteristic
385C3×C4⋊C4#6711yescharacteristic
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4D1211yescharacteristic
392C3×C22⋊C4D1211yescharacteristic
393C3×C22⋊C4#6711yescharacteristic
394C3×C22⋊C4#6711yescharacteristic
395C3×C42—21no—
396C3×C42—61no—
397C3×C42—61no—
398C3×C42C22×D311yescharacteristic
399C3×C42C22×D311yescharacteristic
400#217—21no—
401#217—21no—
402#217—21no—
403#215—62no—
404#215—121no—
405#215—121no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415C4⋊Dic3—21no—
416C4⋊Dic3—31no—
417C4⋊Dic3—31no—
418C4⋊Dic3—61no—
419C4⋊Dic3C22×D311yescharacteristic
420C4⋊Dic3C22×D311yescharacteristic
421C4⋊Dic3C22×D311yescharacteristic
422Dic3⋊C4—21no—
423Dic3⋊C4—21no—
424Dic3⋊C4—21no—
425Dic3⋊C4—21no—
426Dic3⋊C4—21no—
427C4×Dic3—21no—
428C4×Dic3—21no—
429#208—41no—
430C2×C3⋊C8—41no—
431C2×C3⋊C8C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434C2×C3⋊C8C22×D311yescharacteristic
435#204—62no—
436#204—121no—
437#204—121no—
438C22×C32—21no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32AGL(1,ℤ/8)12yes—
444C22×C32C22×D411yescharacteristic
445C2×C3⋊D3—22no—
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—84no—
455C2×C3⋊D3—84no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—21no—
459C32×C4—21no—
460C32×C4C2×#4111yescharacteristic
461C32×C4H(5,𝔽2)11yescharacteristic
462C3⋊Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C22×D4—91no—
468C22×D4—91no—
469C22×D4—181no—
470C2×SD16—91no—
471C2×SD16—91no—
472C2×SD16—91no—
473C2×M16—31no—
474C22×C8—31no—
475#127—91no—
476#126—61no—
477#125—31no—
478#125—61no—
479#123—61no—
480C22⋊Q8—31no—
481C22⋊Q8—31no—
482#121—91no—
483#121—91no—
484#121—181no—
485#120—181no—
486#120—181no—
487C4×Q8—31no—
488C4×D4—91no—
489C4×D4D3211yescharacteristic
490#117—31no—
491#117—61no—
492C2×C4⋊C4—31no—
493#107—91no—
494#107—91no—
495#106—91no—
496C4⋊C8—31no—
497#103—91no—
498#102—91no—
499#102—91no—
500#102—91no—
501#102—91no—
502#102—91no—
503#102—91no—
504#102—91no—
505#102—91no—
506#102—91no—
507C22⋊C8—31no—
508C22⋊C8—31no—
509#97—31no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3C2×D1211yescharacteristic
513C23×C3C2×D1211yescharacteristic
514C23×C3C2×#6711yescharacteristic
515C23×C3C2×#6711yescharacteristic
516C22×D3—62no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—62no—
520C22×D3—62no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C22×D3—124no—
530C22×D3—124no—
531C22×D3—124no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3—124no—
535C22×D3—122no—
536C22×D3—122no—
537C22×D3—241no—
538C22×D3—241no—
539C22×D3—241no—
540C22×D3—241no—
541C22×D3—242no—
542C22×D3—242no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×D4—24no—
546C3×D4—22no—
547C3×D4—22no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—122no—
570C2×C3×C4C2×D1211yescharacteristic
571C2×C3×C4C2×D1211yescharacteristic
572C2×C3×C4C2×D1211yescharacteristic
573C2×C3×C4C2×D1211yescharacteristic
574C2×C3×C4C2×#6711yescharacteristic
575C2×C3×C4C2×#6711yescharacteristic
576C2×C3×C4C2×#6711yescharacteristic
577C2×C3×C4C2×#6711yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580#67—124no—
581#67—122no—
582#67—122no—
583#67—124no—
584#67—122no—
585#67—122no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—42no—
591C2×Dic3—62no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594D12—32no—
595D12—32no—
596D12—62no—
597D12—62no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—121no—
609D12—121no—
610D12—121no—
611D12—121no—
612D12—122no—
613D12—122no—
614D12—122no—
615D12—122no—
616D12—124no—
617D12—122no—
618D12—122no—
619D12—124no—
620D12—124no—
621D12—241no—
622D12—241no—
623D12—242no—
624C4×D3—124no—
625C4×D3—122no—
626C4×D3—122no—
627Dic6—21no—
628Dic6—21no—
629C3×C8—61no—
630C3×C8—61no—
631C3×C8—61no—
632C3×C8—61no—
633C3⋊C8—21no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C2×C32—22no—
638C2×C32—41no—
639C2×C32#54611yescharacteristic
640C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
641C2×C32#57711yescharacteristic
642C3⋊D3—42no—
643C3⋊D3—81no—
644C3⋊D3—81no—
645C24—181no—
646C24—181no—
647C2×Q8—31no—
648C2×D4—91no—
649C2×D4—91no—
650C2×D4—91no—
651C2×D4—182no—
652C2×D4—182no—
653C2×D4—181no—
654C2×D4—181no—
655C2×D4—181no—
656C2×D4—181no—
657C2×D4—181no—
658C2×D4—181no—
659C2×D4—361no—
660C2×D4—361no—
661C2×D4—364no—
662C2×D4#62611yescharacteristic
663C22×C4—61no—
664C22×C4—181no—
665C22×C4C2×D3211yescharacteristic
666C22×C4C2×D3211yescharacteristic
667SD16—182no—
668SD16—361no—
669SD16—361no—
670M16—121no—
671C2×C8—31no—
672C2×C8—31no—
673C2×C8—31no—
674C2×C8—31no—
675C2×C8—121no—
676C4⋊C4—31no—
677C4⋊C4—31no—
678C4⋊C4—31no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—61no—
685C4⋊C4—91no—
686C4⋊C4#62611yescharacteristic
687C22⋊C4—61no—
688C22⋊C4—61no—
689C22⋊C4—61no—
690C22⋊C4—181no—
691C22⋊C4—181no—
692C22⋊C4—181no—
693C22⋊C4#62611yescharacteristic
694C22⋊C4#62611yescharacteristic
695C42—61no—
696C42—61no—
697C42C2×D3211yescharacteristic
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—22no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—22no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3#90812yes—
716C22×C3#94912yes—
717C22×C3C22×D1211yescharacteristic
718C22×C3C22×#6711yescharacteristic
719C2×D3—64no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—122no—
723C2×D3—122no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—122no—
729C2×D3—122no—
730C2×D3—122no—
731C2×D3—122no—
732C2×D3—122no—
733C2×D3—122no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—244no—
747C2×D3—244no—
748C2×D3—248no—
749C2×D3—248no—
750C2×D3—244no—
751C2×D3—244no—
752C3×C4—22no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—41no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—121no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4#100411yescharacteristic
771C3×C4D3×#4111yescharacteristic
772C3×C4D3×#4111yescharacteristic
773C3×C4#100911yescharacteristic
774Dic3—41no—
775Dic3—41no—
776Dic3—41no—
777Dic3—41no—
778Dic3—122no—
779Dic3—121no—
780Dic3—121no—
781C32#331011yescharacteristic, complemented, Sylow
782C23—181no—
783C23—181no—
784C23—181no—
785C23—362no—
786C23—362no—
787C23—362no—
788C23—362no—
789C23—721no—
790C23—721no—
791C23C2×#62611yescharacteristic
792C23C2×#62611yescharacteristic
793Q8—61no—
794Q8—61no—
795D4—22no—
796D4—92no—
797D4—181no—
798D4—181no—
799D4—181no—
800D4—181no—
801D4—181no—
802D4—362no—
803D4—362no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—721no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—122no—
817C2×C4—181no—
818C2×C4—362no—
819C2×C4C2×#62611yescharacteristic
820C2×C4C2×#62611yescharacteristic
821C2×C4C2×#62611yescharacteristic
822C2×C4C2×#62611yescharacteristic
823C2×C4C22×D3211yescharacteristic
824C8—61no—
825C8—61no—
826C8—61no—
827C8—61no—
828C2×C3—22no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—42no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3#555411yescharacteristic
838C2×C3C2×#90811yescharacteristic
839C2×C3#575111yescharacteristic
840C2×C3C2×#94911yescharacteristic
841C2×C3#582911yescharacteristic
842C2×C3#583711yescharacteristic
843D3—124no—
844D3—122no—
845D3—122no—
846D3—242no—
847D3—242no—
848D3—241no—
849D3—241no—
850D3—241no—
851D3—241no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—182no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22—361no—
864C22—361no—
865C22—361no—
866C22—724no—
867C22—724no—
868C22#6382512yes—
869C22C22×#62611yescharacteristic
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—121no—
875C4—121no—
876C4—121no—
877C4—121no—
878C4—361no—
879C4#6431211yescharacteristic
880C4#6431411yescharacteristic
881C3—21no—
882C3#7950111yescharacteristic, complemented
883C3#8359911yescharacteristic, complemented
884C2—22no—
885C2—41no—
886C2—362no—
887C2—721no—
888C2—721no—
889C2C2×#6382511yescharacteristic
890C2#1059525411yescharacteristic
891C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalD4×C4⋊(C3⋊D3)C2
hypercenterC4×D4D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5541C2semidirect
3. C3×#5011C2semidirect
4. #10591183C2semidirect
5. #10591183C2semidirect
6. #10591178C2semidirect
7. #10591177C2semidirect
8. #10591136C2semidirect
9. #10591133C2semidirect
10. #10591096C2semidirect
11. C2×#63564C2semidirect
12. #10590367C2semidirect
13. #10590362C2semidirect
14. #10590308C2semidirect
15. #10590282C2semidirect
30. C3×#926C22semidirect
31. C2×C3×C4⋊Dic3C22semidirect
32. C3×#924C22semidirect
33. C3×#924C22semidirect
34. C2×C3×#208C22semidirect
35. C22×C3×C3⋊C8C22semidirect
39. C3×#870C22semidirect
40. C3×C4×Dic6C22semidirect
42. C2×#3717C22semidirect
43. C2×#3717C22semidirect
44. C3×#830C22semidirect
45. C3×#830C22semidirect
46. C3×C4⋊(C3⋊C8)C22semidirect
47. C3×#803C22semidirect
48. #63575C22semidirect
49. #63575C22semidirect
50. #63573C22semidirect
51. #63566C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
65. #5541D3semidirect
79. #5011D3semidirect
180. #926C2×D3semidirect
181. C2×C4⋊Dic3C2×D3semidirect
182. #924C2×D3semidirect
183. #924C2×D3semidirect
184. C2×#208C2×D3semidirect
185. C22×C3⋊C8C2×D3semidirect
207. #870C2×D3semidirect
208. C4×Dic6C2×D3semidirect
214. #830C2×D3semidirect
215. #830C2×D3semidirect
241. C4⋊(C3⋊C8)C2×D3semidirect
242. #803C2×D3semidirect
781. C32#3310semidirect
882. C3#79501semidirect
883. C3#83599semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊(C3⋊D3)2
C3×#55412
C3×#50112
#105911832
#105911782
#105911772
#105911362
#105911332
#105910962
C2×#635642
#105903672
#105903622
#105903082
#105902822
#835993
#795013