Finite Group Databasebeta

← #11868536

Subgroups — #11868536

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic, complemented
2C4×#3828C211yesmaximal, characteristic
3#10592793C211yesmaximal, characteristic, complemented
4#10592790C211yesmaximal, characteristic, complemented
5#10592786C211yesmaximal, characteristic, complemented
6#10592783C211yesmaximal, characteristic, complemented
7#10592765C212yesmaximal, complemented
8#10592762C212yesmaximal, complemented
9#10592701C212yesmaximal
10#10592697C212yesmaximal, complemented
11C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
12#83349—34nomaximal
13C2×#3828C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C32×#125C2212yes—
17C32×C22⋊Q8—21no—
18C32×C22⋊Q8—21no—
19C32×C4×Q8—21no—
20C32×C4×Q8—21no—
21C32×#117C2212yes—
22C2×C32×C42C2211yescharacteristic
23C4×#638—21no—
24C4×#638—21no—
25#64135C2211yescharacteristic
26C22×C3⋊(C3⋊C8)C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64081—21no—
30C42×C3⋊D3—21no—
31C4×#634C2211yescharacteristic
32C4×#634C2211yescharacteristic
33#63637C2212yes—
34#63637C2212yes—
35#63636C2212yes—
36#63636C2212yes—
37#63635C2212yes—
38#63635C2212yes—
39#63634C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
43C4⋊(C3⋊(C3⋊C8))C2212yes—
44C3×#533D314yescomplemented
45C4×#235—34no—
46#5094—34no—
47#5091—34no—
48#5087—34no—
49#5084—34no—
50#5066—38no—
51#5063—38no—
52#5002—38no—
53#4998—38no—
54C2×C4⋊(C3⋊C8)—34no—
55C2×C32×Q8—21no—
56C2×C32×Q8—21no—
57C22×C32×C4D411yescharacteristic
58C22×C32×C4D411yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61#3828—22no—
62#3828Q814yescomplemented
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×#634C2311yescharacteristic
68C32×C4⋊C4—22no—
69C32×C4⋊C4—22no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73C32×C4⋊C4C2312yes—
74C32×C22⋊C4—22no—
75C32×C42—22no—
76C32×C42D411yescharacteristic
77C32×C42D411yescharacteristic
78C32×C42C2311yescharacteristic
79C32×C42C2311yescharacteristic
80#3757—21no—
81#3752—21no—
82#3752—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86#3750—21no—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3—21no—
90C2×C3⋊(C3⋊C8)—24no—
91C2×C3⋊(C3⋊C8)C2312yes—
92C2×C3⋊(C3⋊C8)C2312yes—
93#3076—91noSylow
94C2×#235—34no—
95C3×C4⋊Q8C2×D314yes—
96C3×C4⋊Q8C2×D314yes—
97C3×#125C2×D318yes—
98C3×C22⋊Q8—24no—
99C3×C22⋊Q8—24no—
100C3×C4×Q8—24no—
101C3×C4×Q8—24no—
102C3×#117C2×D318yes—
103C2×C3×C42C2×D314yes—
104C4×#67—64no—
105C4×#67—64no—
106#926—34no—
107C22×C3⋊C8—38no—
108C4×D12—34no—
109C4×D12—34no—
110#872—64no—
111C42×D3—64no—
112C4×Dic6—34no—
113C4×Dic6—34no—
114#810—38no—
115#810—38no—
116#809—38no—
117#809—38no—
118#808—38no—
119#808—38no—
120#807—38no—
121#807—38no—
122C4⋊(C3⋊C8)—38no—
123C4⋊(C3⋊C8)—34no—
124C4⋊(C3⋊C8)—34no—
125C23×C32C2×D411yescharacteristic
126C22×C3⋊D3—21no—
127C32×Q8—42no—
128C32×Q8—42no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—41no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×Q812yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141#638—24no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C4⋊(C3⋊D3)—21no—
146C4⋊(C3⋊D3)C2×Q812yes—
147C4×C3⋊D3—24no—
148C4×C3⋊D3—42no—
149C4×C3⋊D3—42no—
150#634—21no—
151#634C2×Q812yes—
152C3⋊(C3⋊C8)—22no—
153C3⋊(C3⋊C8)—22no—
154#533C3⋊D311yescharacteristic, complemented
155C4×#41—91no—
156#479—92no—
157#478—92no—
158#477—91no—
159#476—91no—
160#475—91no—
161#474—91no—
162#427—92no—
163C2×C4⋊C8—91no—
164#416—92no—
165C2×C3×Q8—24no—
166C2×C3×Q8—24no—
167C22×C3×C4#6714yes—
168C22×C3×C4#6714yes—
169C22×C3×C4C22×D314yes—
170C2×#67—64no—
171#235—316no—
172#235—68no—
173C2×D12—34no—
174C2×C4×D3—64no—
175C2×C4×D3—64no—
176C2×C4×D3—64no—
177C2×Dic6—34no—
178C3×C4⋊C4—28no—
179C3×C4⋊C4—28no—
180C3×C4⋊C4—24no—
181C3×C4⋊C4—24no—
182C3×C4⋊C4C22×D318yes—
183C3×C4⋊C4C22×D318yes—
184C3×C22⋊C4—28no—
185C3×C42—28no—
186C3×C42#6714yes—
187C3×C42#6714yes—
188C3×C42C22×D314yes—
189C3×C42C22×D314yes—
190#217—64no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193C4⋊Dic3—34no—
194C4⋊Dic3—34no—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197C4×Dic3—64no—
198C4×Dic3—64no—
199C4×Dic3—64no—
200C2×C3⋊C8—38no—
201C2×C3⋊C8—38no—
202C2×C3⋊C8—616no—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32C22⋊Q812yes—
206C22×C32C22×D411yescharacteristic
207C2×C3⋊D3—22no—
208C2×C3⋊D3—41no—
209C2×C3⋊D3—41no—
210C32×C4—21no—
211C32×C4—21no—
212C32×C4—21no—
213C32×C4—42no—
214C32×C4—42no—
215C32×C4C22⋊Q812yes—
216C32×C4#13512yes—
217C32×C4C22×Q811yescharacteristic
218C32×C4C2×#4111yescharacteristic
219C3⋊Dic3—22no—
220C3⋊Dic3—41no—
221C3⋊Dic3—41no—
222C2×#41—91no—
223C22×C8—92no—
224C4⋊Q8C2×C3⋊D311yescharacteristic
225C4⋊Q8C2×C3⋊D311yescharacteristic
226#125C2×C3⋊D312yes—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—91no—
232C4×Q8—91no—
233C4×D4—91no—
234C4×D4—91no—
235C4×D4—181no—
236C4×D4—181no—
237#117—91no—
238#117—181no—
239#117C2×C3⋊D312yes—
240C2×C42—181no—
241C2×C42C2×C3⋊D311yescharacteristic
242#107—92no—
243#107—92no—
244#106—92no—
245#106—92no—
246C4⋊C8—91no—
247C4⋊C8—91no—
248C4⋊C8—92no—
249#103—92no—
250#103—92no—
251#102—92no—
252#102—92no—
253C23×C3C2×#6714yes—
254C22×D3—64no—
255C3×Q8—48no—
256C3×Q8—48no—
257C2×C3×C4—28no—
258C2×C3×C4—28no—
259C2×C3×C4—28no—
260C2×C3×C4—44no—
261C2×C3×C4D3×Q818yes—
262C2×C3×C4#23918yes—
263C2×C3×C4C2×#6714yes—
264C2×C3×C4C2×#6714yes—
265C2×C3×C4C2×#6714yes—
266C2×C3×C4C2×#6714yes—
267C2×C3×C4C2×#6714yes—
268C2×C3×C4C23×D314yes—
269#67—616no—
270C2×Dic3—64no—
271C2×Dic3—64no—
272C2×Dic3—64no—
273D12—38no—
274D12—64no—
275C4×D3—616no—
276C4×D3—128no—
277C4×D3—128no—
278Dic6—38no—
279Dic6—64no—
280C3⋊C8—68no—
281C3⋊C8—68no—
282C2×C32—22no—
283C2×C32C2×C22⋊Q811yescharacteristic
284C2×C32C2×#13511yescharacteristic
285C2×C32#57511yescharacteristic
286C3⋊D3—42no—
287#41—94no—
288#41—182no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—91no—
292C2×D4—91no—
293C2×D4—181no—
294C22×C4—181no—
295C22×C4—181no—
296C22×C4—181no—
297C22×C4#63811yescharacteristic
298C22×C4#63811yescharacteristic
299C22×C4C22×C3⋊D311yescharacteristic
300C2×C8—92no—
301C2×C8—92no—
302C2×C8—184no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—91no—
308C4⋊C4—91no—
309C4⋊C4—181no—
310C4⋊C4—181no—
311C4⋊C4C22×C3⋊D312yes—
312C4⋊C4C22×C3⋊D312yes—
313C22⋊C4—22no—
314C22⋊C4—181no—
315C22⋊C4—181no—
316C22⋊C4—181no—
317C42—22no—
318C42—181no—
319C42—181no—
320C42—181no—
321C42#63811yescharacteristic
322C42#63811yescharacteristic
323C42C22×C3⋊D311yescharacteristic
324C42C22×C3⋊D311yescharacteristic
325C22×C3—24no—
326C22×C3—24no—
327C22×C3#94618yes—
328C22×C3C22×#6714yes—
329C2×D3—68no—
330C2×D3—124no—
331C2×D3—124no—
332C3×C4—24no—
333C3×C4—24no—
334C3×C4—24no—
335C3×C4—48no—
336C3×C4—48no—
337C3×C4#94618yes—
338C3×C4#95018yes—
339C3×C4C2×D3×Q814yes—
340C3×C4C2×#23914yes—
341Dic3—68no—
342Dic3—124no—
343Dic3—124no—
344C32#307611yescharacteristic, complemented, Sylow
345C23—181no—
346C23C2×#63811yescharacteristic
347Q8—42no—
348Q8—42no—
349Q8—92no—
350Q8—181no—
351D4—92no—
352D4—184no—
353D4—181no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—181no—
359C2×C4—184no—
360C2×C4—181no—
361C2×C4—181no—
362C2×C4—362no—
363C2×C4—362no—
364C2×C4Q8×C3⋊D312yes—
365C2×C4#383212yes—
366C2×C4C2×#63811yescharacteristic
367C2×C4C2×#63811yescharacteristic
368C2×C4C2×#63811yescharacteristic
369C2×C4C2×#63811yescharacteristic
370C2×C4C2×#63811yescharacteristic
371C2×C4C23×C3⋊D311yescharacteristic
372C8—182no—
373C8—182no—
374C2×C3—28no—
375C2×C3C2×#94614yes—
376C2×C3C2×#95014yes—
377C2×C3#582214yes—
378D3—128no—
379C22—21no—
380C22—21no—
381C22—182no—
382C22—361no—
383C22—361no—
384C22#6415512yes—
385C22C22×#63811yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—42no—
391C4—182no—
392C4—361no—
393C4—361no—
394C4#6415512yes—
395C4#6415912yes—
396C4C2×Q8×C3⋊D311yescharacteristic
397C4C2×#383211yescharacteristic
398C3#8334914yescomplemented
399C2—22no—
400C2—362no—
401C2C2×#6415511yescharacteristic
402C2C2×#6415911yescharacteristic
403C2#1059629311yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#533C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenter#533C3⋊D3
hypocenterC32#3076
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C32×#533C2semidirect
3. #10592793C2semidirect
4. #10592790C2semidirect
5. #10592786C2semidirect
6. #10592783C2semidirect
7. #10592765C2semidirect
8. #10592762C2semidirect
10. #10592697C2semidirect
11. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
44. C3×#533D3semidirect
62. #3828Q8semidirect
154. #533C3⋊D3semidirect
344. C32#3076semidirect
398. C3#83349semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
C4×#38282
#105927932
#105927902
#105927862
#105927832
#105927652
#105927622
#105927012
#105926972
C2×C4⋊(C3⋊(C3⋊C8))2
#833493