Finite Group Databasebeta

← #11785601

Subgroups — #11785601

Order 1152.

462 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 71 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×#63803C211yesmaximal, characteristic
2C2×#63770C211yesmaximal, characteristic, complemented
3#10593360C212yesmaximal
4#10590685C211yesmaximal, characteristic, complemented
5#10590052C212yesmaximal, complemented
6C2×#3798C2211yescharacteristic
7C2×#3788C2212yes—
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×D3×C8—21no—
10#63900C2212yes—
11C2×#3712C2211yescharacteristic
12C2×#3711—21no—
13#63803—22no—
14#63803C414yescomplemented
15#63770—22no—
16#63740—22no—
17#63739—22no—
18C3×#817—21no—
19#63574—21no—
20C2×#901—61no—
21D3×#106—61no—
22C2×C4×C3⋊D3C2311yescharacteristic
23C2×C3×C4×D3—21no—
24C2×#627D411yescharacteristic
25C2×#626—21no—
26C2×#625D411yescharacteristic
27C2×#624—22no—
28#3798—21no—
29#3798—21no—
30#3798C2×C412yes—
31#3798Q812yes—
32C2×#622—22no—
33#3788—22no—
34#3788—22no—
35C2×C32×C8D411yescharacteristic
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37C8×C3⋊D3C2×C412yes—
38C8×C3⋊D3D412yes—
39C3×C4⋊Dic3—22no—
40C2×C3×C3⋊C8—21no—
41C3×D3×C8—24no—
42#3724—22no—
43#3712—21no—
44#3712C2×C412yes—
45#3711—24no—
46#1815—91nomaximal, Sylow
47C2×#235—61no—
48C22×C3×C8—61no—
49C2×#208—61no—
50#901—64no—
51#901—64no—
52C2×ΓL(1,𝔽25)—61no—
53C2×ΓL(1,𝔽25)—61no—
54C2×D3×C8—21no—
55C2×D3×C8—61no—
56C2×D3×C8—61no—
57D3×C4⋊C4—62no—
58C3×#106—61no—
59#817—21no—
60#808—62no—
61C22×C3⋊D3#4111yescharacteristic
62C22×C3×D3—21no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3C2×D411yescharacteristic
65C4×C3⋊D3C22×C411yescharacteristic
66C4×C3⋊D3C2×D411yescharacteristic
67C4×C3⋊D3C2×Q811yescharacteristic
68C4×C3⋊D3#4111yescharacteristic
69C2×C3×Dic3—21no—
70C2×C3×Dic3—42no—
71C3×C4×D3—22no—
72C3×C4×D3—22no—
73#627—21no—
74#627C4⋊C412yes—
75#626—22no—
76#626—22no—
77#625—21no—
78#625C4⋊C412yes—
79#624—82no—
80#622—42no—
81C32×C8C22⋊C412yes—
82C3⋊(C3⋊C8)C22⋊C412yes—
83C3×C3⋊C8—22no—
84C2×#131—91no—
85C2×#108—91no—
86C2×#106—91no—
87#417—92no—
88#343—92no—
89C22×C3×C4—61no—
90C2×#67—61no—
91C2×#67—61no—
92#235—62no—
93#235—62no—
94#235—62no—
95#235—62no—
96C2×D12—61no—
97C2×C4×D3—21no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C4×D3—122no—
101C2×Dic6—61no—
102C2×C3×C8—21no—
103C2×C3×C8—21no—
104C2×C3×C8—64no—
105C2×C3×C8—61no—
106C3×C4⋊C4—62no—
107C4⋊Dic3—22no—
108Dic3⋊C4—122no—
109#208—64no—
110C2×C3⋊C8—21no—
111C2×C3⋊C8—61no—
112C2×C3⋊C8—61no—
113ΓL(1,𝔽25)—62no—
114ΓL(1,𝔽25)—62no—
115ΓL(1,𝔽25)—64no—
116D3×C8—24no—
117D3×C8—62no—
118D3×C8—62no—
119D3×C8—62no—
120D3×C8—62no—
121C22×C32#12111yescharacteristic
122C2×C3⋊D3—22no—
123C2×C3⋊D3#11711yescharacteristic
124C2×C3⋊D3C22⋊Q811yescharacteristic
125C2×C3×D3—22no—
126C2×C3×D3—42no—
127C32×C4C2×C22⋊C411yescharacteristic
128C32×C4C22⋊Q811yescharacteristic
129C3⋊Dic3C2×C4⋊C411yescharacteristic
130C3⋊Dic3#12111yescharacteristic
131C3×Dic3—22no—
132C3×Dic3—82no—
133C2×#41—91no—
134#131—94no—
135#131—182no—
136C2×M16—91no—
137C2×M16—92no—
138C2×M16—181no—
139C22×C8—61no—
140C22×C8—91no—
141C2×C4⋊C4—92no—
142#108—182no—
143#106—61no—
144#106—181no—
145#103—182no—
146#102—182no—
147C23×C3—61no—
148C22×D3—21no—
149C22×D3—61no—
150C22×D3—61no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—62no—
154C2×C3×C4—62no—
155C2×C3×C4—61no—
156C2×C3×C4—122no—
157#67—62no—
158#67—62no—
159#67—62no—
160#67—62no—
161C2×Dic3—21no—
162C2×Dic3—42no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165D12—62no—
166D12—62no—
167C4×D3—22no—
168C4×D3—22no—
169C4×D3—61no—
170C4×D3—61no—
171C4×D3—61no—
172C4×D3—61no—
173C4×D3—61no—
174C4×D3—61no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—244no—
178Dic6—62no—
179Dic6—62no—
180C3×C8—22no—
181C3×C8—22no—
182C3×C8—62no—
183C3⋊C8—22no—
184C3⋊C8—62no—
185C3⋊C8—62no—
186C2×C32#38011yescharacteristic
187C2×C32#47112yes—
188C3⋊D3—21no—
189C3⋊D3—21no—
190C3×D3—42no—
191#41—92no—
192#41—92no—
193#41—181no—
194#41—181no—
195C2×Q8—91no—
196C2×D4—91no—
197C2×D4—181no—
198C22×C4—61no—
199C22×C4—91no—
200C22×C4—182no—
201M16—92no—
202M16—181no—
203M16—184no—
204M16—182no—
205M16—182no—
206C2×C8—61no—
207C2×C8—64no—
208C2×C8—91no—
209C2×C8—92no—
210C2×C8—92no—
211C2×C8—182no—
212C2×C8GO+(4,𝔽2)11yescharacteristic
213C4⋊C4—62no—
214C4⋊C4—182no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—62no—
218C22×C3—122no—
219C2×D3—22no—
220C2×D3—42no—
221C2×D3—61no—
222C2×D3—61no—
223C2×D3—61no—
224C2×D3—61no—
225C2×D3—64no—
226C2×D3—122no—
227C3×C4—21no—
228C3×C4—21no—
229C3×C4—21no—
230C3×C4—21no—
231C3×C4—62no—
232C3×C4—242no—
233Dic3—22no—
234Dic3—61no—
235Dic3—61no—
236Dic3—61no—
237Dic3—61no—
238Dic3—82no—
239C32#181511yescharacteristic, complemented, Sylow
240C23—61no—
241C23—91no—
242Q8—92no—
243Q8—181no—
244D4—92no—
245D4—182no—
246D4—182no—
247D4—181no—
248C2×C4—61no—
249C2×C4—62no—
250C2×C4—62no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—122no—
257C2×C4—722no—
258C2×C4C2×GO+(4,𝔽2)11yescharacteristic
259C8—62no—
260C8—92no—
261C8—362no—
262C8D32⋊C412yes—
263C2×C3—22no—
264C2×C3—22no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—122no—
268D3—42no—
269D3—62no—
270D3—62no—
271D3—121no—
272D3—121no—
273C22—62no—
274C22—91no—
275C22—91no—
276C22—122no—
277C22—182no—
278C22#6423011yescharacteristic
279C4—62no—
280C4—91no—
281C4—91no—
282C4—242no—
283C4D32⋊Q811yescharacteristic
284C4C2×D32⋊C411yescharacteristic
285C3—21no—
286C3—21no—
287C2—122no—
288C2—181no—
289C2—181no—
290C2#1059330012yes—
291C2#1059340311yescharacteristic
subgroupG/H
centerC22#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC2×#3798C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1815
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63770C2semidirect
4. #10590685C2semidirect
5. #10590052C2semidirect
14. #63803C4semidirect
239. C32#1815semidirect

Maximal subgroups

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

subgroupindex
C2×#638032
C2×#637702
#105933602
#105906852
#105900522
#18159