Finite Group Databasebeta

← #11787698

Subgroups — #11787698

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic
2C2×#63831C211yesmaximal, characteristic
3#10592672C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591107C211yesmaximal, characteristic, complemented
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71666—31nomaximal
9#69004—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×C4×#67—22no—
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×#893—21no—
19C3×#892—21no—
20C3×D3×C4⋊C4—21no—
21C3×#887—21no—
22C2×#3719—21no—
23#63831—22no—
24#63831C414yescomplemented
25C2×#3716—21no—
26#63658—22no—
27#63568—22no—
28#63567—21no—
29#63567—21no—
30C3×#520—31no—
31C2×#951—31no—
32C2×#909—31no—
33#5504D311yescharacteristic
34C2×#837—31no—
35C2×#825—31no—
36#5120—31no—
37#5004—31no—
38#4973—31no—
39#4973—31no—
40#4973—61no—
41C3×#343—31no—
42#4555—31no—
43#4532—31no—
44#4530D311yescharacteristic, complemented
45C22×C32×C4D412yes—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634C2×C412yescomplemented
55C2×C3×#67—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235C2×C412yes—
59C3×#235D412yes—
60C2×C3×D12D411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—22no—
63C2×C3×Dic6D411yescharacteristic
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3—21no—
68C3×#217—21no—
69C3×(C2×D3)⋊C4—22no—
70C3×C4⋊Dic3D411yescharacteristic
71C3×C4⋊Dic3D411yescharacteristic
72C3×Dic3⋊C4—22no—
73C3×C4×Dic3—22no—
74C3×C4×Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208C2×C412yescomplemented
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81#3719—24no—
82#3716—24no—
83#1882—91noSylow
84C2×C3×#41—31no—
85C2×#235C2×D311yescharacteristic
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—61no—
89C2×C3×M16—31no—
90C2×C3×M16—31no—
91C3×C4×Q8—61no—
92C3×C4×D4—61no—
93C3×C4×D4—62no—
94C3×#117—31no—
95C3×#117—61no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—61no—
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C2×D311yescharacteristic
100#951—34no—
101#951—62no—
102C2×#216—61no—
103C2×#214—61no—
104C4×#67—22no—
105#926C2×D311yescharacteristic
106C2×C4×Dic3—31no—
107C2×C4×Dic3—31no—
108C2×C4×Dic3—61no—
109C2×#208C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111#909—34no—
112#909—62no—
113C2×Dic12—61no—
114C2×#204—61no—
115#893—21no—
116#892—21no—
117D3×C4⋊C4—21no—
118#887—21no—
119#837—62no—
120C3⋊#95—64no—
121C3⋊#95—62no—
122C3⋊#95—62no—
123#825—62no—
124#816—61no—
125#816—61no—
126#810—61no—
127#810—61no—
128C23×C32C2×D411yescharacteristic
129C22×C3×D3—21no—
130C2×C32×C4—22no—
131C2×C32×C4—42no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144#634—22no—
145#634—22no—
146#634—41no—
147#634—41no—
148C3×#67—22no—
149C3×#67—22no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C3×D12—21no—
154C3×D12C22⋊C412yes—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—82no—
158C3×Dic6—21no—
159C3×Dic6C22⋊C412yes—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C2×#137—91no—
163#520—31no—
164C2×#104—91no—
165#419—91no—
166#391—91no—
167#343—31no—
168#339—91no—
169C3×#41—32no—
170C3×#41—32no—
171C3×#41—61no—
172C3×#41—61no—
173C2×C3×Q8—31no—
174C2×C3×D4—31no—
175C2×C3×D4—61no—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—62no—
179C22×C3×C4—61no—
180C22×C3×C4D1212yes—
181C22×C3×C4#6712yes—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—21no—
185C22×Dic3—62no—
186C22×Dic3—62no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191#235—21no—
192#235—21no—
193#235C4×D312yes—
194#235D1212yes—
195C2×D12#6711yescharacteristic
196C2×C4×D3—21no—
197C2×C4×D3—22no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—62no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—121no—
213C2×Dic6—121no—
214C2×Dic6—121no—
215C2×Dic6—121no—
216C2×Dic6#6711yescharacteristic
217C3×M16—32no—
218C3×M16—61no—
219C3×M16—61no—
220C3×M16—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—41no—
231C3×C4⋊C4—62no—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—61no—
234C3×C42—62no—
235C3×C42—61no—
236#217—21no—
237#216—64no—
238#214—64no—
239(C2×D3)⋊C4—22no—
240C4⋊Dic3#6711yescharacteristic
241C4⋊Dic3#6711yescharacteristic
242Dic3⋊C4—22no—
243C4×Dic3—22no—
244C4×Dic3—21no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—121no—
250C4×Dic3—121no—
251#208—21no—
252#208—21no—
253#208—21no—
254#208C4×D312yescomplemented
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257Dic12—64no—
258#204—64no—
259C22×C32—21no—
260C22×C32—21no—
261C22×C32C4×D411yescharacteristic
262C22×C32#12011yescharacteristic
263C22×C32#12111yescharacteristic
264C2×C3×D3—22no—
265C2×C3×D3—41no—
266C2×C3×D3—41no—
267C32×C4—42no—
268C32×C4C2×C22⋊C411yescharacteristic
269C32×C4C4×D411yescharacteristic
270C32×C4#12111yescharacteristic
271C32×C4#12311yescharacteristic
272C3⋊Dic3—42no—
273C3⋊Dic3—42no—
274C3×Dic3—22no—
275C3×Dic3—41no—
276C3×Dic3—41no—
277C2×#41—31no—
278C22×Q8—91no—
279#137—94no—
280#137—182no—
281C2×Q16—181no—
282C2×SD16—181no—
283C2×M16—31no—
284C2×M16—31no—
285C4×Q8—61no—
286C4×D4—61no—
287C4×D4—62no—
288#117—31no—
289#117—61no—
290C2×C4⋊C4—61no—
291C2×C4⋊C4D3211yescharacteristic
292C2×C42—91no—
293#104—182no—
294#103—181no—
295#103—181no—
296#95—182no—
297C23×C3—21no—
298C23×C3—61no—
299C23×C3C2×D1211yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C22×D3—21no—
302C3×Q8—32no—
303C3×Q8—61no—
304C3×D4—32no—
305C3×D4—62no—
306C3×D4—62no—
307C3×D4—61no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—44no—
320C2×C3×C4—61no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—242no—
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4#23511yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23911yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338#67—22no—
339#67—22no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361D12—21no—
362D12(C2×D3)⋊C412yes—
363C4×D3—22no—
364C4×D3—22no—
365C4×D3—82no—
366Dic6—21no—
367Dic6—62no—
368Dic6—62no—
369Dic6—62no—
370Dic6—62no—
371Dic6—122no—
372Dic6—122no—
373Dic6—122no—
374Dic6—122no—
375Dic6—121no—
376Dic6—121no—
377Dic6—121no—
378Dic6—121no—
379Dic6(C2×D3)⋊C412yes—
380C3×C8—62no—
381C3×C8—121no—
382C3⋊C8—22no—
383C3⋊C8—41no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32#38611yescharacteristic
387C2×C32#45511yescharacteristic
388C2×C32#45611yescharacteristic
389C3×D3—42no—
390#41—32no—
391#41—32no—
392#41—61no—
393#41—61no—
394C2×Q8—31no—
395C2×Q8—92no—
396C2×Q8—181no—
397C2×Q8—181no—
398C2×Q8—181no—
399C2×Q8—181no—
400C2×Q8—181no—
401C2×D4—31no—
402C2×D4—61no—
403C22×C4—62no—
404C22×C4—61no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4#62612yes—
408C22×C4C2×D3211yescharacteristic
409Q16—184no—
410SD16—184no—
411M16—32no—
412M16—61no—
413M16—61no—
414M16—61no—
415C2×C8—61no—
416C2×C8—61no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—62no—
422C22⋊C4—62no—
423C22⋊C4—61no—
424C42—62no—
425C42—61no—
426C42—181no—
427C42—181no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—62no—
438C22×C3—121no—
439C22×C3—121no—
440C22×C3C4×D1211yescharacteristic
441C22×C3#88211yescharacteristic
442C22×C3#89511yescharacteristic
443C22×C3C4×#6711yescharacteristic
444C22×C3#93011yescharacteristic
445C22×C3#95311yescharacteristic
446C2×D3—22no—
447C2×D3—41no—
448C2×D3—41no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—62no—
456C3×C4—82no—
457C3×C4—121no—
458C3×C4—121no—
459C3×C4D3×C22⋊C411yescharacteristic
460C3×C4#88411yescharacteristic
461C3×C4#89311yescharacteristic
462C3×C4#89411yescharacteristic
463C3×C4C2×(C2×D3)⋊C411yescharacteristic
464C3×C4C4×#6711yescharacteristic
465C3×C4#92911yescharacteristic
466C3×C4#93011yescharacteristic
467Dic3—22no—
468Dic3—41no—
469Dic3—41no—
470Dic3—124no—
471Dic3—124no—
472Dic3—122no—
473Dic3—122no—
474Dic3—122no—
475Dic3—122no—
476C32#188211yescharacteristic, complemented, Sylow
477C23—61no—
478C23C2×#62611yescharacteristic
479Q8—32no—
480Q8—61no—
481Q8—182no—
482Q8—182no—
483Q8—361no—
484Q8—361no—
485D4—32no—
486D4—62no—
487D4—62no—
488D4—61no—
489C2×C4—22no—
490C2×C4—42no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—242no—
499C2×C4—361no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4—361no—
503C2×C4#379811yescharacteristic
504C2×C4#379911yescharacteristic
505C2×C4C4×D3211yescharacteristic
506C2×C4D3×D1211yescharacteristic
507C2×C4D3×#6711yescharacteristic
508C2×C4D3×#6711yescharacteristic
509C8—62no—
510C8—121no—
511C2×C3—22no—
512C2×C3—22no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—122no—
521C2×C3#466511yescharacteristic
522C2×C3#474611yescharacteristic
523C2×C3#475211yescharacteristic
524C2×C3#521311yescharacteristic
525C2×C3#524211yescharacteristic
526C2×C3#524611yescharacteristic
527D3—42no—
528C22—21no—
529C22—21no—
530C22—62no—
531C22—121no—
532C22—121no—
533C22C4×#62611yescharacteristic
534C22#6390911yescharacteristic
535C22#6397711yescharacteristic
536C4—42no—
537C4—62no—
538C4—121no—
539C4—121no—
540C4—362no—
541C4—362no—
542C4#6385011yescharacteristic
543C4#6390411yescharacteristic
544C4#6390611yescharacteristic
545C4D3×(C2×D3)⋊C411yescharacteristic
546C3—21no—
547C3#6900411yescharacteristic, complemented
548C3#7166611yescharacteristic, complemented
549C2—21no—
550C2—21no—
551C2—122no—
552C2#1059138211yescharacteristic
553C2#1059151311yescharacteristic
554C2#1059164911yescharacteristic
subgroupG/H
centerC22#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1882
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10592672C2semidirect
5. #10591107C2semidirect
6. C3×#4530C2semidirect
7. #10589160C2semidirect
24. #63831C4semidirect
44. #4530D3semidirect
54. C2×#634C2×C4semidirect
78. C3×#208C2×C4semidirect
254. #208C4×D3semidirect
476. C32#1882semidirect
547. C3#69004semidirect
548. C3#71666semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
C2×#638312
#105926722
C2×#635682
#105911072
C3×#45302
#105891602
#716663
#690043