Finite Group Databasebeta

← #11860916

Subgroups — #11860916

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic, complemented
2C2×#64159C211yesmaximal, characteristic
3#10595975C211yesmaximal, characteristic, complemented
4C32×#417C211yesmaximal, characteristic, complemented
5#10592832C211yesmaximal, characteristic, complemented
6#10592821C211yesmaximal, characteristic, complemented
7C2×#63635C211yesmaximal, characteristic, complemented
8#10592488C212yesmaximal, complemented
9#10592487C212yesmaximal, complemented
10#10592484C212yesmaximal, complemented
11#10592457C212yesmaximal, complemented
12#78869—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×#3828C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17#64159C418yescomplemented
18Q8×C3⋊Dic3C2212yes—
19C2×#3756C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21D4×C3⋊Dic3—22no—
22D4×C3⋊Dic3C2212yes—
23C2×#3754C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25C4×#638—22no—
26#64135—21no—
27#64135C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)—21no—
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C22×C3⋊(C3⋊C8)C2211yescharacteristic
31#64102C2212yes—
32#64101—21no—
33C4⋊C4×C3⋊D3—21no—
34#64096C2212yes—
35C32×#103C2212yes—
36C32×#102C2212yes—
37#63648C2212yes—
38#63643C2212yes—
39#63642C2212yes—
40C8×C3⋊Dic3C2212yes—
41#63635C2212yes—
42#63635C2212yes—
43#5827—34no—
44C2×#950—34no—
45#5504—34no—
46C3×#417D314yescomplemented
47#5133—34no—
48#5122—34no—
49C2×#808—34no—
50#4789—38no—
51#4788—38no—
52#4785—38no—
53#4758—38no—
54C32×#41—22no—
55C32×#41C2×C414yescomplemented
56C2×C32×Q8C2311yescharacteristic
57C2×C32×D4—21no—
58C2×C32×D4C2311yescharacteristic
59C22×C32×C4—21no—
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C2×#638—21no—
63C22×C3⋊Dic3—21no—
64C22×C3⋊Dic3—22no—
65#3828—22no—
66#3828C2×C414yescomplemented
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
70C2×#634C2311yescharacteristic
71C32×M16—22no—
72C2×C32×C8C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75#3757—22no—
76#3757D412yes—
77#3756C2×C414yescomplemented
78#3755C2×C414yescomplemented
79#3754C2×C414yescomplemented
80#3753C2×C414yescomplemented
81#3752—22no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)D411yescharacteristic
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C4⋊(C3⋊Dic3)C2312yes—
87#3750—22no—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3—22no—
90C4×C3⋊Dic3C2312yes—
91C2×C3⋊(C3⋊C8)C2×C414yescomplemented
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2311yescharacteristic
94#2952—91noSylow
95C2×C3×#41C2×D314yes—
96C2×#235—34no—
97C2×C3×M16C2×D314yes—
98C2×C3×C4⋊C4C2×D314yes—
99#950—332no—
100Q8×Dic3—38no—
101C2×#216—34no—
102C2×#215—34no—
103D4×Dic3—38no—
104D4×Dic3—68no—
105C2×#214—34no—
106C2×#213—34no—
107C4×#67—68no—
108#926—34no—
109#926—64no—
110C2×C4⋊Dic3—34no—
111C2×C4⋊Dic3—64no—
112C22×C3⋊C8—34no—
113#893—38no—
114#892—64no—
115D3×C4⋊C4—64no—
116#887—38no—
117C3×#103C2×D318yes—
118C3×#102C2×D318yes—
119#821—38no—
120#816—38no—
121#815—38no—
122C8×Dic3—38no—
123#808—38no—
124#808—38no—
125C23×C32—21no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C32×Q8—21no—
129C32×Q8C22×C412yes—
130C32×D4—24no—
131C32×D4—21no—
132C32×D4C22×C412yes—
133C2×C32×C4—21no—
134C2×C32×C4—24no—
135C2×C32×C4—22no—
136C2×C32×C4—81no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141#638—24no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—82no—
145C2×C3⋊Dic3—81no—
146C2×C3⋊Dic3C2×D412yes—
147C2×C3⋊Dic3C2×D412yes—
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)C22×C412yes—
150C4×C3⋊D3—24no—
151C4×C3⋊D3—82no—
152#634—21no—
153#634C22×C412yes—
154C32×C8—22no—
155C3⋊(C3⋊C8)C22×C412yes—
156C3⋊(C3⋊C8)C22×C412yes—
157C2×#135—91no—
158#520—91no—
159#520—91no—
160#442—92no—
161#441—92no—
162C4×SD16—92no—
163C4×SD16—92no—
164C2×#106—91no—
165#417—91no—
166#417C3⋊D311yescharacteristic, complemented
167#405—91no—
168C3×#41—28no—
169C3×#41C4×D3116yescomplemented
170C2×C3×Q8C22×D314yes—
171C2×C3×D4—24no—
172C2×C3×D4C22×D314yes—
173C22×C3×C4—24no—
174C22×C3×C4—24no—
175C22×C3×C4C22×D314yes—
176C2×#67—64no—
177C22×Dic3—68no—
178C22×Dic3—64no—
179#235—316no—
180#235—68no—
181C2×D12—34no—
182C2×C4×D3—64no—
183C2×C4×D3—68no—
184C2×Dic6—34no—
185C3×M16—28no—
186C2×C3×C8C22×D318yes—
187C3×C4⋊C4—24no—
188C3×C4⋊C4C22×D318yes—
189#217—38no—
190#217—68no—
191#216—316no—
192#215—316no—
193#214—316no—
194#213—316no—
195(C2×D3)⋊C4—68no—
196C4⋊Dic3—34no—
197C4⋊Dic3—34no—
198C4⋊Dic3—38no—
199C4⋊Dic3—68no—
200C4⋊Dic3—64no—
201Dic3⋊C4—68no—
202C4×Dic3—38no—
203C4×Dic3—68no—
204C4×Dic3—68no—
205C2×C3⋊C8—316no—
206C2×C3⋊C8—34no—
207C2×C3⋊C8—34no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—22no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32C4×D412yes—
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3—22no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—22no—
219C32×C4—42no—
220C32×C4C4×D412yes—
221C32×C4C23×C411yescharacteristic
222C32×C4C2×#4111yescharacteristic
223C3⋊Dic3—22no—
224C3⋊Dic3—22no—
225C3⋊Dic3—22no—
226C3⋊Dic3—42no—
227C2×#41—91no—
228C2×#41C2×C3⋊D311yescharacteristic
229#135—98no—
230C2×Q16—91no—
231C2×SD16—91no—
232C2×SD16—91no—
233C2×D8—91no—
234C2×M16C2×C3⋊D311yescharacteristic
235C22×C8—91no—
236C4×Q8—92no—
237C4×Q8—92no—
238C4×D4—92no—
239C4×D4—92no—
240C4×D4—182no—
241C4×D4—182no—
242#117—91no—
243#117—181no—
244#117—181no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—181no—
247C2×C4⋊C4—181no—
248C2×C4⋊C4C2×C3⋊D311yescharacteristic
249#106—92no—
250#106—92no—
251#103—92no—
252#103C2×C3⋊D312yes—
253#102—92no—
254#102C2×C3⋊D312yes—
255#97—92no—
256C4×C8—92no—
257C23×C3—24no—
258C23×C3D3×D414yes—
259C22×D3—64no—
260C3×Q8—24no—
261C3×Q8C2×C4×D318yes—
262C3×D4—216no—
263C3×D4—24no—
264C3×D4C2×C4×D318yes—
265C2×C3×C4—24no—
266C2×C3×C4—216no—
267C2×C3×C4—28no—
268C2×C3×C4—84no—
269C2×C3×C4C2×C4×D318yes—
270C2×C3×C4D3×D414yes—
271C2×C3×C4#23718yes—
272C2×C3×C4C23×D314yes—
273#67—616no—
274C2×Dic3—38no—
275C2×Dic3—38no—
276C2×Dic3—64no—
277C2×Dic3—68no—
278C2×Dic3—248no—
279C2×Dic3—244no—
280D12—38no—
281D12—64no—
282C4×D3—616no—
283C4×D3—248no—
284Dic6—38no—
285Dic6—64no—
286C3×C8—28no—
287C3⋊C8—38no—
288C3⋊C8—38no—
289C2×C32—22no—
290C2×C32—42no—
291C2×C32C2×C4×D411yescharacteristic
292C2×C32#57711yescharacteristic
293C2×C32#57711yescharacteristic
294C3⋊D3—42no—
295#41—22no—
296#41—94no—
297#41—182no—
298#41C4×C3⋊D314yescomplemented
299C2×Q8—91no—
300C2×Q8C22×C3⋊D311yescharacteristic
301C2×D4—21no—
302C2×D4—91no—
303C2×D4—181no—
304C2×D4C22×C3⋊D311yescharacteristic
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—182no—
308C22×C4—182no—
309C22×C4—181no—
310C22×C4—181no—
311C22×C4C22×C3⋊D311yescharacteristic
312Q16—94no—
313SD16—94no—
314SD16—94no—
315D8—94no—
316M16—22no—
317C2×C8—91no—
318C2×C8—91no—
319C2×C8—94no—
320C2×C8C22×C3⋊D312yes—
321C4⋊C4—21no—
322C4⋊C4—91no—
323C4⋊C4—91no—
324C4⋊C4—92no—
325C4⋊C4—182no—
326C4⋊C4—182no—
327C4⋊C4—181no—
328C4⋊C4C22×C3⋊D312yes—
329C22⋊C4—92no—
330C22⋊C4—182no—
331C22⋊C4—182no—
332C42—92no—
333C42—182no—
334C42—182no—
335C22×C3—24no—
336C22×C3—24no—
337C22×C3—28no—
338C22×C3—44no—
339C22×C3—44no—
340C22×C3#67⋊C418yes—
341C22×C3C2×D3×D414yes—
342C2×D3—68no—
343C2×D3—124no—
344C2×D3—124no—
345C3×C4—28no—
346C3×C4—48no—
347C3×C4#67⋊C418yes—
348C3×C4C22×C4×D314yes—
349C3×C4C2×#23714yes—
350Dic3—68no—
351Dic3—68no—
352Dic3—68no—
353Dic3—128no—
354C32#295211yescharacteristic, complemented, Sylow
355C23—21no—
356C23—181no—
357C23D4×C3⋊D311yescharacteristic
358Q8—21no—
359Q8—92no—
360Q8—181no—
361Q8C2×C4×C3⋊D312yes—
362D4—24no—
363D4—21no—
364D4—92no—
365D4—184no—
366D4—181no—
367D4C2×C4×C3⋊D312yes—
368C2×C4—21no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—81no—
372C2×C4—92no—
373C2×C4—92no—
374C2×C4—181no—
375C2×C4—184no—
376C2×C4—182no—
377C2×C4—722no—
378C2×C4—722no—
379C2×C4—721no—
380C2×C4C2×C4×C3⋊D312yes—
381C2×C4D4×C3⋊D311yescharacteristic
382C2×C4#383012yes—
383C2×C4C23×C3⋊D311yescharacteristic
384C8—22no—
385C8—92no—
386C8—92no—
387C2×C3—28no—
388C2×C3—48no—
389C2×C3C2×#67⋊C414yes—
390C2×C3#577514yes—
391C2×C3#577814yes—
392D3—128no—
393C22—21no—
394C22—21no—
395C22—22no—
396C22—41no—
397C22—41no—
398C22—182no—
399C22—361no—
400C22—361no—
401C22#6409012yes—
402C22C2×D4×C3⋊D311yescharacteristic
403C4—22no—
404C4—42no—
405C4—182no—
406C4—182no—
407C4—182no—
408C4—362no—
409C4#6409012yes—
410C4C22×C4×C3⋊D311yescharacteristic
411C4C2×#383011yescharacteristic
412C3#7886914yescomplemented
413C2—22no—
414C2—42no—
415C2—362no—
416C2C2×#6409011yescharacteristic
417C2#1059624611yescharacteristic
418C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#417C2
socleC22×C32C22×D4
prime radicalC2×#64159C2
cosocleC2×C32×C4C24
hypercenter#417C3⋊D3
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #10596298C2semidirect
3. #10595975C2semidirect
4. C32×#417C2semidirect
5. #10592832C2semidirect
6. #10592821C2semidirect
7. C2×#63635C2semidirect
8. #10592488C2semidirect
9. #10592487C2semidirect
10. #10592484C2semidirect
11. #10592457C2semidirect
17. #64159C4semidirect
46. C3×#417D3semidirect
55. C32×#41C2×C4semidirect
66. #3828C2×C4semidirect
77. #3756C2×C4semidirect
78. #3755C2×C4semidirect
79. #3754C2×C4semidirect
80. #3753C2×C4semidirect
91. C2×C3⋊(C3⋊C8)C2×C4semidirect
166. #417C3⋊D3semidirect
169. C3×#41C4×D3semidirect
298. #41C4×C3⋊D3semidirect
354. C32#2952semidirect
412. C3#78869semidirect

Maximal subgroups

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

subgroupindex
#105962982
C2×#641592
#105959752
C32×#4172
#105928322
#105928212
C2×#636352
#105924882
#105924872
#105924842
#105924572
#788693