Finite Group Databasebeta

← #11790014

Subgroups — #11790014

Order 1152.

358 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 57 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×#63767C211yesmaximal, characteristic, complemented
2#10593349C211yesmaximal, characteristic
3C2×#63731C211yesmaximal, characteristic
4#10590958C211yesmaximal, characteristic
5#10590701C211yesmaximal, characteristic, complemented
6#10590051C211yesmaximal, characteristic, complemented
7#10590047C211yesmaximal, characteristic, complemented
8C2×#3798C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C2×C8×C3⋊D3C2211yescharacteristic
12#63874C2211yescharacteristic
13C2×#3712C2211yescharacteristic
14C2×#3712C2211yescharacteristic
15#63767—22no—
16#63740C412yescomplemented
17#63739C412yescomplemented
18#63731—22no—
19C3×(C2×D3)⋊C8—21no—
20C3×Dic3⋊C8—21no—
21Dic3⋊(C3⋊C8)—21no—
22(C2×D3)⋊(C3⋊C8)—21no—
23#4839—61no—
24#4727—61no—
25C22×#157—21no—
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×C3×C4×D3—21no—
28C2×#627C2×C411yescharacteristic
29C2×#626—21no—
30C2×#625C2×C411yescharacteristic
31#3798—21no—
32#3798—21no—
33#3798—21no—
34#3798—21no—
35C2×#622C2×C412yes—
36C4×#157—21no—
37C4×#157D412yes—
38#3787—21no—
39#3787—21no—
40C2×C32×C8D411yescharacteristic
41C2×C3⋊(C3⋊C8)D411yescharacteristic
42C8×C3⋊D3—21no—
43C8×C3⋊D3—21no—
44C3×C4×Dic3—21no—
45C2×C3×C3⋊C8—21no—
46C2×C3×C3⋊C8—21no—
47#3724C2×C412yes—
48#3722—21no—
49#3712—21no—
50#3712—21no—
51#3712—21no—
52#3712—21no—
53#1938—91nomaximal, Sylow
54C2×#235—61no—
55C2×ΓL(1,𝔽25)—61no—
56C2×ΓL(1,𝔽25)—61no—
57C2×D3×C8—61no—
58C2×D3×C8—61no—
59#872—61no—
60C3×C4⋊C8—61no—
61C3×C22⋊C8—61no—
62#830—61no—
63(C2×D3)⋊C8—21no—
64(C2×D3)⋊C8—61no—
65Dic3⋊C8—21no—
66Dic3⋊C8—61no—
67C4⋊(C3⋊C8)—61no—
68C22×C3⋊D3#4111yescharacteristic
69C22×C3×D3—21no—
70C2×#157—22no—
71C2×#157—42no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C3⋊Dic3C22×C411yescharacteristic
74C4×C3⋊D3C2×D411yescharacteristic
75C4×C3⋊D3#4111yescharacteristic
76C4×C3⋊D3#4111yescharacteristic
77C4×C3⋊D3#4111yescharacteristic
78C2×C3×Dic3—22no—
79C2×C3×Dic3—21no—
80C3×C4×D3—41no—
81C3×C4×D3—41no—
82#627—21no—
83#627—21no—
84#626—41no—
85#626—41no—
86#625—21no—
87#625—21no—
88#622—22no—
89C32×C8—21no—
90C3⋊(C3⋊C8)—21no—
91C3×C3⋊C8—41no—
92C3×C3⋊C8—41no—
93#424—91no—
94C2×#104—91no—
95#416—91no—
96#408—91no—
97C2×#97—91no—
98#341—91no—
99#339—91no—
100C22×C3×C4—61no—
101C2×#67—61no—
102C2×#67—61no—
103#235—121no—
104#235—121no—
105#235—121no—
106#235—121no—
107C2×D12—61no—
108C2×C4×D3—21no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×Dic6—61no—
112C2×C3×C8—21no—
113C2×C3×C8—21no—
114C2×C3×C8—61no—
115C2×C3×C8—61no—
116C3×C42—61no—
117(C2×D3)⋊C4—62no—
118Dic3⋊C4—62no—
119C4×Dic3—21no—
120C2×C3⋊C8—21no—
121C2×C3⋊C8—21no—
122C2×C3⋊C8—61no—
123C2×C3⋊C8—61no—
124ΓL(1,𝔽25)—121no—
125ΓL(1,𝔽25)—121no—
126ΓL(1,𝔽25)—121no—
127ΓL(1,𝔽25)—121no—
128D3×C8—121no—
129D3×C8—121no—
130D3×C8—121no—
131D3×C8—121no—
132C22×C32C4×D411yescharacteristic
133C2×C3⋊D3—22no—
134C2×C3⋊D3#12311yescharacteristic
135C2×C3⋊D3#12611yescharacteristic
136C2×C3×D3—41no—
137C2×C3×D3—42no—
138#157—42no—
139C32×C4#12111yescharacteristic
140C32×C4#12411yescharacteristic
141C3⋊Dic3#11711yescharacteristic
142C3⋊Dic3C4×D411yescharacteristic
143C3×Dic3—41no—
144C3×Dic3—42no—
145C2×#41—91no—
146C2×M16—91no—
147C2×M16—91no—
148C22×C8—91no—
149C22×C8—91no—
150#117—91no—
151C2×C42—91no—
152C4⋊C8—61no—
153C4⋊C8—181no—
154#104—182no—
155#103—92no—
156#102—92no—
157C22⋊C8—61no—
158C22⋊C8—181no—
159#97—182no—
160C23×C3—61no—
161C22×D3—21no—
162C22×D3—61no—
163C22×D3—61no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—62no—
167C2×C3×C4—61no—
168C2×C3×C4—121no—
169C2×C3×C4—121no—
170#67—121no—
171#67—121no—
172#67—121no—
173#67—121no—
174C2×Dic3—22no—
175C2×Dic3—21no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178D12—121no—
179D12—121no—
180C4×D3—41no—
181C4×D3—41no—
182C4×D3—61no—
183C4×D3—61no—
184C4×D3—61no—
185C4×D3—61no—
186C4×D3—61no—
187C4×D3—61no—
188C4×D3—61no—
189C4×D3—61no—
190Dic6—121no—
191Dic6—121no—
192C3×C8—41no—
193C3×C8—41no—
194C3×C8—121no—
195C3×C8—121no—
196C3⋊C8—41no—
197C3⋊C8—41no—
198C3⋊C8—121no—
199C3⋊C8—121no—
200C2×C32#38811yescharacteristic
201C2×C32#44412yes—
202C3⋊D3—21no—
203C3⋊D3—21no—
204C3×D3—81no—
205#41—181no—
206#41—181no—
207#41—181no—
208#41—181no—
209C2×Q8—91no—
210C2×D4—91no—
211C2×D4—181no—
212C22×C4—61no—
213C22×C4—91no—
214C22×C4—181no—
215M16—181no—
216M16—181no—
217M16—181no—
218M16—181no—
219C2×C8—61no—
220C2×C8—61no—
221C2×C8—92no—
222C2×C8—91no—
223C2×C8—181no—
224C2×C8—181no—
225C2×C8—181no—
226C2×C8—181no—
227C2×C8GO+(4,𝔽2)11yescharacteristic
228C4⋊C4—92no—
229C22⋊C4—181no—
230C42—61no—
231C42—92no—
232C42—181no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—121no—
236C22×C3—122no—
237C2×D3—41no—
238C2×D3—42no—
239C2×D3—61no—
240C2×D3—61no—
241C2×D3—61no—
242C2×D3—61no—
243C2×D3—122no—
244C2×D3—122no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—121no—
250C3×C4—122no—
251Dic3—41no—
252Dic3—42no—
253Dic3—61no—
254Dic3—61no—
255Dic3—61no—
256Dic3—61no—
257C32#193811yescharacteristic, complemented, Sylow
258C23—61no—
259C23—91no—
260Q8—181no—
261Q8—181no—
262D4—181no—
263D4—181no—
264D4—361no—
265D4—361no—
266C2×C4—62no—
267C2×C4—61no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—91no—
272C2×C4—91no—
273C2×C4—121no—
274C2×C4—121no—
275C2×C4—182no—
276C2×C4—362no—
277C2×C4C2×GO+(4,𝔽2)11yescharacteristic
278C8—21no—
279C8—121no—
280C8—121no—
281C8—182no—
282C8—181no—
283C2×C3—22no—
284C2×C3—22no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—241no—
288D3—81no—
289D3—121no—
290D3—121no—
291D3—121no—
292D3—121no—
293C22—91no—
294C22—91no—
295C22—122no—
296C22—121no—
297C22—182no—
298C22C4×GO+(4,𝔽2)11yescharacteristic
299C4—91no—
300C4—91no—
301C4—122no—
302C4—121no—
303C4—362no—
304C4#6422111yescharacteristic
305C4#6424211yescharacteristic
306C3—21no—
307C3—21no—
308C2—181no—
309C2—181no—
310C2—241no—
311C2#1059329812yes—
312C2#1059340011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC2×#3798C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1938
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63767C2semidirect
5. #10590701C2semidirect
6. #10590051C2semidirect
7. #10590047C2semidirect
16. #63740C4semidirect
17. #63739C4semidirect
257. C32#1938semidirect

Maximal subgroups

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

subgroupindex
C2×#637672
#105933492
C2×#637312
#105909582
#105907012
#105900512
#105900472
#19389