Finite Group Databasebeta

← #11784106

Subgroups — #11784106

Order 1152.

514 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594669C211yesmaximal, characteristic
2#10593765C211yesmaximal, characteristic, complemented
3#10593380C211yesmaximal, characteristic
4#10593317C211yesmaximal, characteristic
5C8×#624C211yesmaximal, characteristic, complemented
6#10590050C211yesmaximal, characteristic, complemented
7#10590048C211yesmaximal, characteristic, complemented
8#64306C2211yescharacteristic
9#64286C2211yescharacteristic
10#64283C2211yescharacteristic
11C2×C8×C3⋊D3C2211yescharacteristic
12C3×#901—21no—
13C4×#624C2211yescharacteristic
14#63818C2211yescharacteristic
15C2×#3710C2211yescharacteristic
16#63815—21no—
17#63805C412yescomplemented
18#63803C412yescomplemented
19#63791—21no—
20D32×C8—21no—
21#63767—21no—
22C8×#157—21no—
23#63741C414yescomplemented
24#63730C412yescomplemented
25#63729C412yescomplemented
26C3×C8×Dic3—21no—
27Dic3×C3⋊C8—21no—
28D3×#131—61no—
29C4×D3×C8—61no—
30C2×C4×C3⋊D3C2311yescharacteristic
31C3×#235—21no—
32#3811—21no—
33C2×#624—21no—
34#3805C2×C412yes—
35#3802C2×C411yescharacteristic
36C4×D32—21no—
37#3798C2×C412yes—
38#3797C2×C411yescharacteristic
39#3796—21no—
40C22⋊#157—21no—
41#3792C2×C412yes—
42C4⋊#157C2×C412yes—
43C4×#157—21no—
44#3788—21no—
45#3787—21no—
46C2×C32×C8D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C8×C3⋊D3C2×C411yescharacteristic
49C8×C3⋊D3C2×C411yescharacteristic
50C8×C3⋊D3D411yescharacteristic
51C8×C3⋊D3D411yescharacteristic
52C3×C4×Dic3—21no—
53C3×#208—21no—
54C2×C3×C3⋊C8—21no—
55C3×ΓL(1,𝔽25)—22no—
56C3×D3×C8—22no—
57Dic32C2×C412yes—
58#3712C2×C412yes—
59#3711—22no—
60#3710—21no—
61#3710—21no—
62#3710C2×C412yes—
63D3×C3⋊C8—22no—
64#1764—91nomaximal, Sylow
65D3×#41—61no—
66C3×#131—61no—
67#948—61no—
68#907—62no—
69#907—61no—
70D3×M16—61no—
71D3×M16—62no—
72#901—21no—
73#901—62no—
74C2×D3×C8—61no—
75C2×D3×C8—61no—
76C2×D3×C8—61no—
77C2×D3×C8—62no—
78C42×D3—61no—
79C3×C4×C8—61no—
80C8×Dic3—21no—
81C8×Dic3—61no—
82C4×C3⋊C8—61no—
83C22×C3⋊D3#4111yescharacteristic
84C2×D32—21no—
85C2×#157—22no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C3⋊Dic3C22×C411yescharacteristic
88C4×C3⋊D3C22×C411yescharacteristic
89C4×C3⋊D3C22×C411yescharacteristic
90C4×C3⋊D3C2×D411yescharacteristic
91C4×C3⋊D3#4111yescharacteristic
92C3×#67—22no—
93C2×C3×Dic3—22no—
94C3×D12—21no—
95C3×C4×D3—22no—
96C3×Dic6—21no—
97#627C4212yes—
98#626—22no—
99#625C4212yes—
100#624—24no—
101#624—21no—
102D3×Dic3—22no—
103#622—22no—
104C32×C8C22⋊C411yescharacteristic
105C32×C8C22⋊C411yescharacteristic
106C3⋊(C3⋊C8)C22⋊C411yescharacteristic
107C3⋊(C3⋊C8)C22⋊C411yescharacteristic
108C3×C3⋊C8—22no—
109C3×C3⋊C8—22no—
110C2×#131—91no—
111C2×#104—91no—
112#416—91no—
113#405—91no—
114C2×C4×C8—91no—
115#341—91no—
116#339—91no—
117C3×#41—61no—
118#239—61no—
119D3×Q8—61no—
120#237—62no—
121#237—61no—
122D3×D4—61no—
123D3×D4—62no—
124#235—21no—
125#235—62no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C3×M16—62no—
131C3×M16—61no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—62no—
135C2×C3×C8—61no—
136C3×C42—61no—
137C4×Dic3—21no—
138C4×Dic3—62no—
139#208—21no—
140#208—62no—
141C2×C3⋊C8—21no—
142C2×C3⋊C8—61no—
143C2×C3⋊C8—61no—
144C2×C3⋊C8—62no—
145ΓL(1,𝔽25)—22no—
146ΓL(1,𝔽25)—62no—
147ΓL(1,𝔽25)—62no—
148D3×C8—22no—
149D3×C8—62no—
150D3×C8—61no—
151D3×C8—61no—
152D3×C8—61no—
153D3×C8—61no—
154D3×C8—61no—
155D3×C8—61no—
156D3×C8—61no—
157D3×C8—61no—
158D3×C8—62no—
159D3×C8—62no—
160D3×C8—62no—
161C22×C32C4×D411yescharacteristic
162C2×C3⋊D3—22no—
163C2×C3⋊D3#11711yescharacteristic
164C2×C3⋊D3C4×D411yescharacteristic
165C2×C3×D3—22no—
166D32—42no—
167#157—42no—
168C32×C4C2×C22⋊C411yescharacteristic
169C32×C4C4×D411yescharacteristic
170C3⋊Dic3C2×C4211yescharacteristic
171C3⋊Dic3C4×D411yescharacteristic
172C3×Dic3—24no—
173C3×Dic3—22no—
174C2×#41—91no—
175#131—61no—
176#131—92no—
177#131—92no—
178#131—181no—
179C2×M16—91no—
180C2×M16—91no—
181C2×M16—181no—
182C22×C8—91no—
183C22×C8—91no—
184C22×C8—181no—
185#117—91no—
186C2×C42—91no—
187#104—94no—
188#103—92no—
189#102—92no—
190#97—181no—
191C4×C8—61no—
192C4×C8—181no—
193C4×C8—181no—
194C22×D3—61no—
195C22×D3—61no—
196C22×D3—62no—
197C3×Q8—61no—
198C3×D4—61no—
199C3×D4—62no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—62no—
203C2×C3×C4—62no—
204#67—22no—
205#67—62no—
206#67—62no—
207C2×Dic3—22no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—62no—
211D12—21no—
212D12—62no—
213C4×D3—22no—
214C4×D3—61no—
215C4×D3—61no—
216C4×D3—61no—
217C4×D3—61no—
218C4×D3—61no—
219C4×D3—61no—
220C4×D3—61no—
221C4×D3—61no—
222C4×D3—68no—
223C4×D3—62no—
224C4×D3—62no—
225Dic6—21no—
226Dic6—62no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8—21no—
230C3×C8—21no—
231C3×C8—62no—
232C3×C8—62no—
233C3⋊C8—22no—
234C3⋊C8—22no—
235C3⋊C8—61no—
236C3⋊C8—61no—
237C3⋊C8—61no—
238C3⋊C8—61no—
239C2×C32—21no—
240C2×C32C4×C22⋊C411yescharacteristic
241C3⋊D3—21no—
242C3⋊D3#44312yes—
243C3×D3—42no—
244#41—61no—
245#41—92no—
246#41—92no—
247#41—181no—
248C2×Q8—91no—
249C2×D4—91no—
250C2×D4—181no—
251C22×C4—91no—
252C22×C4—181no—
253C22×C4—181no—
254M16—61no—
255M16—62no—
256M16—92no—
257M16—92no—
258M16—182no—
259M16—181no—
260C2×C8—61no—
261C2×C8—62no—
262C2×C8—92no—
263C2×C8—91no—
264C2×C8—91no—
265C2×C8—91no—
266C2×C8—91no—
267C2×C8—91no—
268C2×C8—181no—
269C2×C8—181no—
270C2×C8—182no—
271C2×C8—181no—
272C2×C8GO+(4,𝔽2)11yescharacteristic
273C4⋊C4—92no—
274C22⋊C4—181no—
275C42—61no—
276C42—92no—
277C42—181no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—62no—
281C2×D3—22no—
282C2×D3—61no—
283C2×D3—61no—
284C2×D3—61no—
285C2×D3—61no—
286C2×D3—64no—
287C2×D3—122no—
288C2×D3—124no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—62no—
294C3×C4—64no—
295Dic3—22no—
296Dic3—24no—
297Dic3—61no—
298Dic3—61no—
299Dic3—61no—
300Dic3—61no—
301C32#176411yescharacteristic, complemented, Sylow
302C23—91no—
303C23—181no—
304Q8—61no—
305Q8—92no—
306D4—62no—
307D4—61no—
308D4—92no—
309D4—182no—
310C2×C4—62no—
311C2×C4—62no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—91no—
315C2×C4—91no—
316C2×C4—91no—
317C2×C4—181no—
318C2×C4—184no—
319C2×C4—182no—
320C2×C4—182no—
321C2×C4C2×GO+(4,𝔽2)11yescharacteristic
322C8—62no—
323C8—62no—
324C8—91no—
325C8—91no—
326C8—182no—
327C8D32⋊C411yescharacteristic
328C8D32⋊C411yescharacteristic
329C2×C3—22no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—41no—
333C2×C3—122no—
334D3—42no—
335D3—62no—
336D3—62no—
337D3—62no—
338D3—121no—
339C22—62no—
340C22—91no—
341C22—91no—
342C22—182no—
343C22—362no—
344C22C4×GO+(4,𝔽2)11yescharacteristic
345C4—64no—
346C4—62no—
347C4—91no—
348C4—91no—
349C4—362no—
350C4C4×GO+(4,𝔽2)11yescharacteristic
351C4C2×D32⋊C411yescharacteristic
352C3—21no—
353C3—21no—
354C2—21no—
355C2—92no—
356C2—122no—
357C2—181no—
358C2C4×D32⋊C411yescharacteristic
subgroupG/H
centerC8D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C4×C22⋊C4
prime radical#64306C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1764
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593765C2semidirect
5. C8×#624C2semidirect
6. #10590050C2semidirect
7. #10590048C2semidirect
17. #63805C4semidirect
18. #63803C4semidirect
23. #63741C4semidirect
24. #63730C4semidirect
25. #63729C4semidirect
301. C32#1764semidirect

Maximal subgroups

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

subgroupindex
#105946692
#105937652
#105933802
#105933172
C8×#6242
#105900502
#105900482
#17649