Finite Group Databasebeta

← #11785305

Subgroups — #11785305

Order 1152.

936 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic
3#10592817C211yesmaximal, characteristic, complemented
4C4×#3750C211yesmaximal, characteristic, complemented
5C2×#63632C211yesmaximal, characteristic
6C32×#339C211yesmaximal, characteristic, complemented
7#10589398C211yesmaximal, characteristic, complemented
8#68770—34nomaximal
9C2×#3828C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3750—21no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17#64102C411yescharacteristic, complemented
18#64102C411yescharacteristic, complemented
19#64096C411yescharacteristic, complemented
20#64096C411yescharacteristic, complemented
21#64090—21no—
22#64090—21no—
23#64081—21no—
24C42×C3⋊D3—21no—
25#63658—21no—
26#63652—22no—
27#63641—21no—
28#63641—21no—
29#63632—22no—
30#5522—34no—
31C2×#825—34no—
32#5118—34no—
33C4×Dic3⋊C4—34no—
34C2×#805—34no—
35C3×#339D314yescomplemented
36#4532—34no—
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C2×#638—21no—
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43#3828—21no—
44#3828—21no—
45#3828D412yes—
46#3828Q812yes—
47C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×#634C2×C411yescharacteristic
52C32×M16—21no—
53C32×M16—21no—
54C2×C32×C8—21no—
55C32×C4⋊C4C2×C411yescharacteristic
56C32×C4⋊C4C2×C411yescharacteristic
57C32×C22⋊C4—21no—
58C32×C42—21no—
59C32×C42—21no—
60C32×C42—21no—
61#3752—21no—
62#3752—21no—
63#3750—24no—
64#3750—21no—
65#3750—21no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3C2×C411yescharacteristic
71C4×C3⋊Dic3C2×C411yescharacteristic
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74#3748—21no—
75#3748—21no—
76C2×C3⋊(C3⋊C8)—21no—
77#1806—91noSylow
78C2×#235—34no—
79C2×C3×M16C2×D314yes—
80C3×#117C2×D314yes—
81C2×C3×C42C2×D314yes—
82C2×Dic3⋊C4—64no—
83C2×C4×Dic3—34no—
84C2×C4×Dic3—34no—
85C2×#208—34no—
86#893—34no—
87#893—34no—
88#887—34no—
89#887—34no—
90#67⋊C4—64no—
91#67⋊C4—64no—
92#872—64no—
93C42×D3—64no—
94C3⋊#95—64no—
95#825—68no—
96Dic3⋊C8—64no—
97Dic3⋊C8—64no—
98#805—68no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—21no—
101C2×C32×C4—22no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×Q811yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112#638—22no—
113#638—22no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3C22⋊C411yescharacteristic
121C2×C3⋊Dic3C22⋊C411yescharacteristic
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C4⋊(C3⋊D3)—21no—
125C4⋊(C3⋊D3)C4⋊C412yescomplemented
126C4×C3⋊D3—22no—
127C4×C3⋊D3—22no—
128C4×C3⋊D3—42no—
129C4×C3⋊D3—42no—
130#634—21no—
131#634C4⋊C412yescomplemented
132C32×C8—41no—
133C3⋊(C3⋊C8)—41no—
134C4×#41—91no—
135#423—91no—
136C2×#104—91no—
137C2×#104—91no—
138C4×C4⋊C4—91no—
139#339—91no—
140#339C3⋊D311yescharacteristic, complemented
141C22×C3×C4—24no—
142C22×C3×C4C22×D314yes—
143C2×#67—64no—
144C22×Dic3—34no—
145C22×Dic3—34no—
146C22×Dic3—64no—
147#235—38no—
148#235—38no—
149#235—64no—
150#235—64no—
151C2×D12—34no—
152C2×C4×D3—64no—
153C2×C4×D3—64no—
154C2×C4×D3—64no—
155C2×Dic6—34no—
156C3×M16—24no—
157C3×M16—24no—
158C2×C3×C8—24no—
159C3×C4⋊C4C4×D314yes—
160C3×C4⋊C4C4×D314yes—
161C3×C22⋊C4—24no—
162C3×C42—24no—
163C3×C42—24no—
164C3×C42—24no—
165(C2×D3)⋊C4—64no—
166(C2×D3)⋊C4—64no—
167Dic3⋊C4—64no—
168Dic3⋊C4—64no—
169Dic3⋊C4—616no—
170C4×Dic3—34no—
171C4×Dic3—34no—
172C4×Dic3—34no—
173C4×Dic3—34no—
174C4×Dic3—64no—
175C4×Dic3—64no—
176C4×Dic3—64no—
177C4×Dic3—64no—
178#208—64no—
179#208—64no—
180C2×C3⋊C8—64no—
181C22×C32—21no—
182C22×C32—21no—
183C22×C32C2×C22⋊C411yescharacteristic
184C22×C32#12111yescharacteristic
185C22×C32C22⋊Q811yescharacteristic
186C2×C3⋊D3—22no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C32×C4—42no—
190C32×C4—41no—
191C32×C4—41no—
192C32×C4C2×C4⋊C411yescharacteristic
193C32×C4#11711yescharacteristic
194C32×C4#12111yescharacteristic
195C32×C4C22⋊Q811yescharacteristic
196C3⋊Dic3—22no—
197C3⋊Dic3—21no—
198C3⋊Dic3—21no—
199C3⋊Dic3—21no—
200C3⋊Dic3—42no—
201C3⋊Dic3#10412yescomplemented
202C2×#41—91no—
203C2×M16—91no—
204C2×M16C2×C3⋊D311yescharacteristic
205C4×Q8—91no—
206C4×Q8—91no—
207C4×D4—91no—
208C4×D4—91no—
209C4×D4—181no—
210C4×D4—181no—
211#117—181no—
212#117C2×C3⋊D311yescharacteristic
213C2×C4⋊C4—181no—
214C2×C42—91no—
215C2×C42—91no—
216C2×C42—181no—
217C2×C42C2×C3⋊D311yescharacteristic
218C4⋊C8—181no—
219C4⋊C8—181no—
220#104—182no—
221#104—182no—
222#95—181no—
223C23×C3D3×D414yes—
224C22×D3—64no—
225C2×C3×C4—28no—
226C2×C3×C4—24no—
227C2×C3×C4—24no—
228C2×C3×C4—44no—
229C2×C3×C4—44no—
230C2×C3×C4C2×C4×D314yes—
231C2×C3×C4#23514yes—
232C2×C3×C4#23514yes—
233C2×C3×C4D3×D414yes—
234C2×C3×C4D3×D414yes—
235C2×C3×C4D3×Q814yes—
236#67—68no—
237#67—68no—
238C2×Dic3—34no—
239C2×Dic3—34no—
240C2×Dic3—34no—
241C2×Dic3—34no—
242C2×Dic3—68no—
243C2×Dic3—64no—
244C2×Dic3—68no—
245C2×Dic3—124no—
246C2×Dic3—124no—
247C2×Dic3—124no—
248D12—38no—
249D12—64no—
250C4×D3—68no—
251C4×D3—68no—
252C4×D3—128no—
253C4×D3—128no—
254Dic6—38no—
255Dic6—64no—
256C3×C8—44no—
257C3⋊C8—124no—
258C2×C32—21no—
259C2×C32—21no—
260C2×C32#38011yescharacteristic
261C2×C32C2×#10411yescharacteristic
262C2×C32#42111yescharacteristic
263C3⋊D3—42no—
264#41—92no—
265#41—92no—
266#41—181no—
267#41—181no—
268C2×Q8—91no—
269C2×D4—91no—
270C2×D4—181no—
271C22×C4—21no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—181no—
275C22×C4—181no—
276C22×C4—181no—
277C22×C4—181no—
278C22×C4C22×C3⋊D311yescharacteristic
279M16—21no—
280M16—21no—
281M16—181no—
282M16—181no—
283C2×C8—21no—
284C2×C8—181no—
285C4⋊C4—181no—
286C4⋊C4—181no—
287C4⋊C4—184no—
288C4⋊C4C4×C3⋊D311yescharacteristic
289C4⋊C4C4×C3⋊D311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—181no—
292C22⋊C4—181no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—91no—
297C42—91no—
298C42—91no—
299C42—91no—
300C42—181no—
301C42—181no—
302C42—181no—
303C42—181no—
304C22×C3—24no—
305C22×C3—24no—
306C22×C3D3×C22⋊C414yes—
307C22×C3#88414yes—
308C22×C3#89614yes—
309C2×D3—68no—
310C2×D3—124no—
311C2×D3—124no—
312C3×C4—48no—
313C3×C4—44no—
314C3×C4—44no—
315C3×C4#87214yes—
316C3×C4#88414yes—
317C3×C4D3×C4⋊C414yes—
318C3×C4#89614yes—
319Dic3—38no—
320Dic3—68no—
321Dic3—64no—
322Dic3—64no—
323Dic3—64no—
324Dic3—128no—
325C32#180611yescharacteristic, complemented, Sylow
326C23—181no—
327C23D4×C3⋊D311yescharacteristic
328Q8—92no—
329Q8—181no—
330D4—92no—
331D4—182no—
332D4—182no—
333D4—181no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—91no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—182no—
344C2×C4—181no—
345C2×C4—182no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—362no—
349C2×C4—362no—
350C2×C4—361no—
351C2×C4—361no—
352C2×C4—361no—
353C2×C4C2×C4×C3⋊D311yescharacteristic
354C2×C4#382811yescharacteristic
355C2×C4#382811yescharacteristic
356C2×C4D4×C3⋊D311yescharacteristic
357C2×C4D4×C3⋊D311yescharacteristic
358C2×C4Q8×C3⋊D311yescharacteristic
359C8—41no—
360C8—361no—
361C2×C3—24no—
362C2×C3—24no—
363C2×C3#466714yes—
364C2×C3D3×#10414yes—
365C2×C3#482114yes—
366D3—128no—
367C22—21no—
368C22—21no—
369C22—182no—
370C22—361no—
371C22—361no—
372C22C22⋊C4×C3⋊D311yescharacteristic
373C22#6409311yescharacteristic
374C22#6410511yescharacteristic
375C4—42no—
376C4—41no—
377C4—41no—
378C4—92no—
379C4—181no—
380C4—181no—
381C4—181no—
382C4—182no—
383C4—362no—
384C4#6408111yescharacteristic
385C4#6409311yescharacteristic
386C4C4⋊C4×C3⋊D311yescharacteristic
387C4#6410511yescharacteristic
388C3#6877014yescomplemented
389C2—21no—
390C2—21no—
391C2—362no—
392C2#1059236611yescharacteristic
393C2C3⋊D3×#10411yescharacteristic
394C2#1059252011yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
3. #10592817C2semidirect
4. C4×#3750C2semidirect
6. C32×#339C2semidirect
7. #10589398C2semidirect
17. #64102C4semidirect
18. #64102C4semidirect
19. #64096C4semidirect
20. #64096C4semidirect
35. C3×#339D3semidirect
125. C4⋊(C3⋊D3)C4⋊C4semidirect
131. #634C4⋊C4semidirect
140. #339C3⋊D3semidirect
201. C3⋊Dic3#104semidirect
325. C32#1806semidirect
388. C3#68770semidirect

Maximal subgroups

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

subgroupindex
#105959932
C2×#636522
#105928172
C4×#37502
C2×#636322
C32×#3392
#105893982
#687703