Finite Group Databasebeta

← #11785566

Subgroups — #11785566

Order 1152.

442 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 67 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×#63805C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic, complemented
3#10593323C212yesmaximal
4#10590913C211yesmaximal, characteristic, complemented
5#10590055C212yesmaximal, complemented
6C2×#3798C2211yescharacteristic
7#64286C2212yes—
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×ΓL(1,𝔽25)—21no—
10C2×#3712C2211yescharacteristic
11#63818C2212yes—
12C2×D3×C3⋊C8—21no—
13#63805—21no—
14#63805—21no—
15#63805C412yescomplemented
16#63805C412yescomplemented
17#63769—21no—
18#63768—21no—
19#63731—24no—
20C3×#819—21no—
21#63578—21no—
22C2×#907—61no—
23D3×#108—61no—
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×C3×C4×D3—21no—
26C2×#627Q811yescharacteristic
27C2×#626—21no—
28C2×#625Q811yescharacteristic
29#3798—21no—
30#3798—21no—
31#3798C2×C412yes—
32#3798D412yes—
33C22⋊#157—22no—
34C4⋊#157—22no—
35C4×#157—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—21no—
47#3712—22no—
48#3712C2×C412yes—
49#3710—22no—
50D3×C3⋊C8—22no—
51D3×C3⋊C8—22no—
52#1814—91nomaximal, Sylow
53C2×#235—61no—
54C2×C3×M16—61no—
55C22×C3⋊C8—61no—
56#907—62no—
57#907—62no—
58#907—62no—
59#907—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⋊D3#4111yescharacteristic
70C22×C3×D3—21no—
71C2×#157—42no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C3⋊Dic3C2×Q811yescharacteristic
74C4×C3⋊D3C22×C411yescharacteristic
75C4×C3⋊D3C2×D411yescharacteristic
76C4×C3⋊D3C2×D411yescharacteristic
77C4×C3⋊D3#4111yescharacteristic
78C2×C3×Dic3—21no—
79C3×C4×D3—22no—
80C3×C4×D3—22no—
81#627—21no—
82#627C4⋊C412yes—
83#626—22no—
84#626—22no—
85#625—21no—
86#625C4⋊C412yes—
87C32×C8C22⋊C411yescharacteristic
88C32×C8C22⋊C411yescharacteristic
89C3⋊(C3⋊C8)C22⋊C411yescharacteristic
90C3⋊(C3⋊C8)C22⋊C411yescharacteristic
91C3×C3⋊C8—22no—
92C3×C3⋊C8—42no—
93C2×#131—91no—
94C2×#108—91no—
95#427—91no—
96#421—92no—
97#344—92no—
98C22×C3×C4—61no—
99C2×#67—61no—
100C2×#67—61no—
101#235—62no—
102#235—62no—
103#235—62no—
104#235—62no—
105C2×D12—61no—
106C2×C4×D3—21no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×Dic6—61no—
110C3×M16—62no—
111C3×M16—62no—
112C3×M16—62no—
113C2×C3×C8—21no—
114C2×C3×C8—21no—
115C2×C3×C8—61no—
116#208—22no—
117C2×C3⋊C8—21no—
118C2×C3⋊C8—61no—
119C2×C3⋊C8—61no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8—62no—
122ΓL(1,𝔽25)—22no—
123ΓL(1,𝔽25)—22no—
124ΓL(1,𝔽25)—62no—
125ΓL(1,𝔽25)—62no—
126ΓL(1,𝔽25)—122no—
127D3×C8—61no—
128D3×C8—61no—
129D3×C8—61no—
130D3×C8—61no—
131D3×C8—61no—
132D3×C8—61no—
133D3×C8—61no—
134D3×C8—61no—
135D3×C8—62no—
136D3×C8—62no—
137D3×C8—122no—
138C22×C32C22⋊Q811yescharacteristic
139C2×C3⋊D3—41no—
140C2×C3⋊D3#11711yescharacteristic
141C2×C3⋊D3#12111yescharacteristic
142C2×C3×D3—22no—
143C2×C3×D3—42no—
144#157—82no—
145C32×C4C2×C22⋊C411yescharacteristic
146C32×C4#12111yescharacteristic
147C3⋊Dic3C2×C4⋊C411yescharacteristic
148C3⋊Dic3C22⋊Q811yescharacteristic
149C3×Dic3—22no—
150C2×#41—91no—
151#131—92no—
152#131—92no—
153#131—181no—
154#131—181no—
155C2×M16—61no—
156C2×M16—91no—
157C2×M16—92no—
158C22×C8—91no—
159C22×C8—181no—
160#117—92no—
161#108—61no—
162#108—181no—
163#107—181no—
164#106—181no—
165#104—184no—
166C23×C3—61no—
167C22×D3—21no—
168C22×D3—61no—
169C22×D3—61no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—62no—
173C2×C3×C4—62no—
174C2×C3×C4—61no—
175#67—62no—
176#67—62no—
177#67—62no—
178#67—62no—
179C2×Dic3—21no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182D12—62no—
183D12—62no—
184C4×D3—22no—
185C4×D3—22no—
186C4×D3—61no—
187C4×D3—61no—
188C4×D3—61no—
189C4×D3—61no—
190C4×D3—61no—
191C4×D3—61no—
192C4×D3—61no—
193C4×D3—61no—
194Dic6—62no—
195Dic6—62no—
196C3×C8—21no—
197C3×C8—21no—
198C3×C8—21no—
199C3×C8—21no—
200C3×C8—62no—
201C3×C8—122no—
202C3⋊C8—22no—
203C3⋊C8—42no—
204C3⋊C8—61no—
205C3⋊C8—61no—
206C3⋊C8—61no—
207C3⋊C8—61no—
208C2×C32—21no—
209C2×C32#38011yescharacteristic
210C3⋊D3—21no—
211C3⋊D3—21no—
212C3×D3—42no—
213#41—92no—
214#41—92no—
215#41—181no—
216#41—181no—
217C2×Q8—91no—
218C2×D4—91no—
219C2×D4—181no—
220C22×C4—61no—
221C22×C4—91no—
222M16—62no—
223M16—62no—
224M16—62no—
225M16—92no—
226M16—181no—
227M16—182no—
228C2×C8—61no—
229C2×C8—91no—
230C2×C8—91no—
231C2×C8—91no—
232C2×C8—91no—
233C2×C8—91no—
234C2×C8—182no—
235C2×C8—182no—
236C2×C8—182no—
237C2×C8GO+(4,𝔽2)11yescharacteristic
238C4⋊C4—182no—
239C22⋊C4—182no—
240C42—182no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—62no—
244C22×C3—122no—
245C2×D3—22no—
246C2×D3—42no—
247C2×D3—61no—
248C2×D3—61no—
249C2×D3—61no—
250C2×D3—61no—
251C2×D3—122no—
252C2×D3—122no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—62no—
258Dic3—22no—
259Dic3—61no—
260Dic3—61no—
261Dic3—61no—
262Dic3—61no—
263C32#181411yescharacteristic, complemented, Sylow
264C23—61no—
265C23—91no—
266Q8—92no—
267Q8—181no—
268D4—92no—
269D4—182no—
270D4—182no—
271D4—181no—
272C2×C4—61no—
273C2×C4—62no—
274C2×C4—62no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—362no—
281C2×C4C2×GO+(4,𝔽2)11yescharacteristic
282C8—62no—
283C8—91no—
284C8—91no—
285C8—122no—
286C8D32⋊C411yescharacteristic
287C8D32⋊C411yescharacteristic
288C2×C3—22no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—41no—
292C2×C3—122no—
293D3—42no—
294D3—62no—
295D3—121no—
296D3—121no—
297D3—121no—
298C22—62no—
299C22—91no—
300C22—91no—
301C22—122no—
302C22—361no—
303C22D32⋊Q811yescharacteristic
304C4—62no—
305C4—91no—
306C4—91no—
307C4—722no—
308C4#6423011yescharacteristic
309C4C2×D32⋊C411yescharacteristic
310C3—21no—
311C3—21no—
312C2—21no—
313C2—122no—
314C2—181no—
315C2—181no—
316C2#1059340311yescharacteristic
subgroupG/H
centerC4#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#380
prime radicalC2×#3798C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1814
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. #10593768C2semidirect
4. #10590913C2semidirect
5. #10590055C2semidirect
15. #63805C4semidirect
16. #63805C4semidirect
263. C32#1814semidirect

Maximal subgroups

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

subgroupindex
C2×#638052
#105937682
#105933232
#105909132
#105900552
#18149