Finite Group Databasebeta

← #11785472

Subgroups — #11785472

Order 1152.

474 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#63791C211yesmaximal, characteristic
2#10593771C211yesmaximal, characteristic, complemented
3#10593307C212yesmaximal
4#10590913C211yesmaximal, characteristic, complemented
5#10590050C212yesmaximal, complemented
6C2×C4×D32C2211yescharacteristic
7#64283C2212yes—
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×ΓL(1,𝔽25)—21no—
10C2×#3711—21no—
11#63818C2212yes—
12C2×#3710C2211yescharacteristic
13#63791—21no—
14#63791—21no—
15#63791C412yes—
16#63791C412yes—
17#63771—21no—
18#63770—21no—
19D32⋊C8—24no—
20C3×#819—21no—
21#63578—21no—
22C2×D3×M16—61no—
23D3×#108—61no—
24C22×D32Q811yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×C4×D3—21no—
27C2×#624Q811yescharacteristic
28C2×D3×Dic3—21no—
29C4×D32—21no—
30C4×D32—21no—
31C4×D32C2×C412yes—
32C4×D32D412yes—
33#3792—22no—
34#3788—22no—
35#3787—22no—
36C2×C32×C8D411yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C8×C3⋊D3C2×C411yescharacteristic
39C8×C3⋊D3C2×C411yescharacteristic
40C8×C3⋊D3D411yescharacteristic
41C8×C3⋊D3D411yescharacteristic
42C3×#208—22no—
43C2×C3×C3⋊C8—21no—
44C3×ΓL(1,𝔽25)—22no—
45C3×ΓL(1,𝔽25)—22no—
46#3712—22no—
47#3711—22no—
48#3711—22no—
49#3710—21no—
50#3710—22no—
51#3710C2×C412yes—
52#1811—91nomaximal, Sylow
53C22×C4×D3—61no—
54C2×C3×M16—61no—
55C2×#208—61no—
56D3×M16—62no—
57D3×M16—62no—
58D3×M16—62no—
59D3×M16—62no—
60D3×M16—62no—
61C2×ΓL(1,𝔽25)—21no—
62C2×ΓL(1,𝔽25)—61no—
63C2×D3×C8—61no—
64C2×D3×C8—61no—
65C2×D3×C8—61no—
66C3×#108—61no—
67#822—62no—
68#819—21no—
69C22×C3⋊D3C2×Q811yescharacteristic
70C22×C3×D3—21no—
71C2×D32—21no—
72C2×D32—42no—
73C2×D32C4⋊C412yes—
74C2×C32×C4C2×D411yescharacteristic
75C2×C3⋊Dic3#4111yescharacteristic
76C4×C3⋊D3C22×C411yescharacteristic
77C4×C3⋊D3C2×D411yescharacteristic
78C4×C3⋊D3C2×D411yescharacteristic
79C4×C3⋊D3#4111yescharacteristic
80C2×C3×Dic3—21no—
81C3×C4×D3—22no—
82C3×C4×D3—22no—
83#624—21no—
84#624C4⋊C412yes—
85D3×Dic3—22no—
86D3×Dic3—22no—
87#622—42no—
88C32×C8C22⋊C411yescharacteristic
89C32×C8C22⋊C411yescharacteristic
90C3⋊(C3⋊C8)C22⋊C411yescharacteristic
91C3⋊(C3⋊C8)C22⋊C411yescharacteristic
92C3×C3⋊C8—22no—
93C3×C3⋊C8—42no—
94C22×M16—91no—
95C2×#108—91no—
96C2×#108—91no—
97#407—92no—
98#341—92no—
99C23×D3—61no—
100C22×C3×C4—61no—
101C22×Dic3—61no—
102C2×C4×D3—21no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—61no—
111C3×M16—62no—
112C3×M16—62no—
113C3×M16—62no—
114C2×C3×C8—21no—
115C2×C3×C8—21no—
116C2×C3×C8—61no—
117#208—22no—
118#208—62no—
119#208—62no—
120C2×C3⋊C8—21no—
121C2×C3⋊C8—61no—
122C2×C3⋊C8—61no—
123ΓL(1,𝔽25)—22no—
124ΓL(1,𝔽25)—22no—
125ΓL(1,𝔽25)—62no—
126ΓL(1,𝔽25)—62no—
127ΓL(1,𝔽25)—122no—
128D3×C8—62no—
129D3×C8—61no—
130D3×C8—61no—
131D3×C8—61no—
132D3×C8—61no—
133D3×C8—61no—
134D3×C8—61no—
135D3×C8—61no—
136D3×C8—61no—
137D3×C8—62no—
138D3×C8—122no—
139C22×C32C22⋊Q811yescharacteristic
140C2×C3⋊D3—22no—
141C2×C3⋊D3C2×C4⋊C411yescharacteristic
142C2×C3⋊D3C22⋊Q811yescharacteristic
143C2×C3×D3—22no—
144C2×C3×D3—42no—
145D32—24no—
146D32—42no—
147C32×C4C2×C22⋊C411yescharacteristic
148C32×C4#12111yescharacteristic
149C3⋊Dic3#11711yescharacteristic
150C3⋊Dic3#12111yescharacteristic
151C3×Dic3—22no—
152C23×C4—91no—
153C2×M16—61no—
154C2×M16—92no—
155C2×M16—92no—
156C2×M16—92no—
157C2×M16—92no—
158C2×M16—181no—
159C2×M16—181no—
160C2×M16—181no—
161C22×C8—91no—
162C22×C8—91no—
163#108—61no—
164#108—181no—
165#108—181no—
166#108—181no—
167C22⋊C8—184no—
168C23×C3—61no—
169C22×D3—21no—
170C22×D3—62no—
171C22×D3—61no—
172C22×D3—61no—
173C22×D3—62no—
174C22×D3—124no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—62no—
178C2×C3×C4—62no—
179C2×C3×C4—61no—
180C2×Dic3—21no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C4×D3—22no—
186C4×D3—22no—
187C4×D3—62no—
188C4×D3—61no—
189C4×D3—61no—
190C4×D3—61no—
191C4×D3—61no—
192C4×D3—61no—
193C4×D3—61no—
194C4×D3—61no—
195C4×D3—61no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—62no—
199C3×C8—21no—
200C3×C8—21no—
201C3×C8—21no—
202C3×C8—21no—
203C3×C8—62no—
204C3×C8—122no—
205C3⋊C8—22no—
206C3⋊C8—42no—
207C3⋊C8—61no—
208C3⋊C8—61no—
209C3⋊C8—61no—
210C3⋊C8—61no—
211C2×C32—21no—
212C2×C32#38011yescharacteristic
213C3⋊D3—21no—
214C3⋊D3#43012yes—
215C3×D3—42no—
216C24—91no—
217C22×C4—61no—
218C22×C4—92no—
219C22×C4—92no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4—181no—
223C22×C4—181no—
224C22×C4—181no—
225M16—62no—
226M16—62no—
227M16—62no—
228M16—182no—
229M16—182no—
230M16—182no—
231M16—182no—
232M16—182no—
233C2×C8—61no—
234C2×C8—92no—
235C2×C8—91no—
236C2×C8—91no—
237C2×C8—91no—
238C2×C8—91no—
239C2×C8—91no—
240C2×C8—181no—
241C2×C8—182no—
242C2×C8—182no—
243C2×C8GO+(4,𝔽2)11yescharacteristic
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—62no—
247C22×C3—122no—
248C2×D3—22no—
249C2×D3—42no—
250C2×D3—61no—
251C2×D3—61no—
252C2×D3—61no—
253C2×D3—61no—
254C2×D3—64no—
255C2×D3—124no—
256C2×D3—122no—
257C2×D3—124no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—62no—
263Dic3—22no—
264Dic3—61no—
265Dic3—61no—
266Dic3—61no—
267Dic3—61no—
268C32#181111yescharacteristic, complemented, Sylow
269C23—61no—
270C23—92no—
271C23—91no—
272C23—181no—
273C23—362no—
274C2×C4—61no—
275C2×C4—62no—
276C2×C4—62no—
277C2×C4—92no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—181no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4C2×GO+(4,𝔽2)11yescharacteristic
287C8—62no—
288C8—91no—
289C8—91no—
290C8—122no—
291C8—362no—
292C8D32⋊C411yescharacteristic
293C8D32⋊C411yescharacteristic
294C2×C3—22no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—41no—
298C2×C3—122no—
299D3—42no—
300D3—62no—
301D3—62no—
302D3—62no—
303D3—121no—
304C22—62no—
305C22—91no—
306C22—91no—
307C22—122no—
308C22—182no—
309C22—184no—
310C22—362no—
311C22D32⋊Q811yescharacteristic
312C4—62no—
313C4—91no—
314C4—91no—
315C4#6423011yescharacteristic
316C4C2×D32⋊C411yescharacteristic
317C3—21no—
318C3—21no—
319C2—21no—
320C2—92no—
321C2—122no—
322C2—181no—
323C2#1059340311yescharacteristic
subgroupG/H
centerC4#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#380
prime radicalC22×D32Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1811
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593771C2semidirect
4. #10590913C2semidirect
5. #10590050C2semidirect
268. C32#1811semidirect

Maximal subgroups

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

subgroupindex
C2×#637912
#105937712
#105933072
#105909132
#105900502
#18119