Finite Group Databasebeta

← #11794293

Subgroups — #11794293

Order 1152.

392 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 55 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#10594351C211yesmaximal, characteristic
2#10593394C211yesmaximal, characteristic
3#10593344C211yesmaximal, characteristic
4#10590584C211yesmaximal, characteristic
5#10590164C211yesmaximal, characteristic
6#10590052C211yesmaximal, characteristic
7#10590047C211yesmaximal, characteristic
8C2×C4×#157C2211yescharacteristic
9C2×#3788C2211yescharacteristic
10#64101C2211yescharacteristic
11C3×#888—21no—
12#63900C2211yescharacteristic
13#63900C2211yescharacteristic
14#63888—22no—
15#63874C2211yescharacteristic
16#63873—21no—
17#63870—21no—
18#63869—21no—
19C2×#3712C2211yescharacteristic
20#63743—21no—
21#63742—21no—
22#63737—22no—
23C3×#808—21no—
24#63575—21no—
25#5729—61no—
26#4861—61no—
27C22×#157—21no—
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×C3×Dic6—22no—
30C2×#624—21no—
31C2×#624D412yes—
32C2×#622—21no—
33C4×#157—21no—
34C4×#157Q812yescomplemented
35#3788—21no—
36#3788Q812yescomplemented
37C32×C4⋊C4D411yescharacteristic
38#3752—21no—
39C4⋊(C3⋊Dic3)D411yescharacteristic
40C4×C3⋊Dic3—21no—
41C3×C4⋊Dic3—21no—
42C3×C4⋊Dic3—21no—
43C3×Dic3⋊C4—22no—
44C3×C4×Dic3—21no—
45C2×C3×C3⋊C8—21no—
46#3724—22no—
47#3724—21no—
48#3724—21no—
49#3724D411yescharacteristic
50#3724D411yescharacteristic
51Dic3⋊Dic3—22no—
52#3722—21no—
53#3712—21no—
54#3712Q812yescomplemented
55#2061—91nomaximal, Sylow
56C3×C4⋊Q8—61no—
57#946—62no—
58#944—62no—
59C2×ΓL(1,𝔽25)—61no—
60#896—62no—
61#892—61no—
62#892—61no—
63D3×C4⋊C4—61no—
64D3×C4⋊C4—61no—
65#890—61no—
66#889—62no—
67#888—21no—
68#872—61no—
69#870—61no—
70C3×#106—61no—
71#818—61no—
72#808—21no—
73#807—61no—
74C22×C3⋊D3C2×D411yescharacteristic
75C2×#157—22no—
76C2×#157—41no—
77C2×#157—41no—
78C2×C32×C4—21no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3C2×D411yescharacteristic
82C4×C3⋊D3C2×Q811yescharacteristic
83C4×C3⋊D3C2×Q811yescharacteristic
84C4×C3⋊D3C2×Q811yescharacteristic
85C4×C3⋊D3#4111yescharacteristic
86C2×C3×Dic3—21no—
87C2×C3×Dic3—21no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—41no—
90C3×Dic6—82no—
91#624—42no—
92#624—42no—
93#622—22no—
94C3×C3⋊C8—22no—
95#544—91no—
96#428—91no—
97#428—91no—
98#382—91no—
99#343—91no—
100#339—91no—
101#339—91no—
102C2×C3×Q8—62no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—62no—
106C2×C4×D3—121no—
107C2×Dic6—22no—
108C2×C3×C8—61no—
109C3×C4⋊C4—21no—
110C3×C4⋊C4—21no—
111C3×C4⋊C4—62no—
112C3×C4⋊C4—61no—
113C3×C4⋊C4—61no—
114C3×C42—61no—
115(C2×D3)⋊C4—61no—
116(C2×D3)⋊C4—61no—
117(C2×D3)⋊C4—62no—
118(C2×D3)⋊C4—121no—
119C4⋊Dic3—21no—
120C4⋊Dic3—21no—
121C4⋊Dic3—61no—
122C4⋊Dic3—61no—
123C4⋊Dic3—62no—
124Dic3⋊C4—22no—
125Dic3⋊C4—61no—
126Dic3⋊C4—61no—
127Dic3⋊C4—62no—
128Dic3⋊C4—62no—
129Dic3⋊C4—62no—
130Dic3⋊C4—62no—
131Dic3⋊C4—121no—
132C4×Dic3—21no—
133C4×Dic3—62no—
134C4×Dic3—121no—
135C2×C3⋊C8—21no—
136ΓL(1,𝔽25)—62no—
137ΓL(1,𝔽25)—62no—
138C22×C32#12011yescharacteristic
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3C22⋊Q811yescharacteristic
142C2×C3⋊D3C4⋊Q811yescharacteristic
143#157—42no—
144C32×C4—41no—
145C32×C4C22⋊Q811yescharacteristic
146C32×C4C4⋊Q811yescharacteristic
147C3⋊Dic3—41no—
148C3⋊Dic3C22⋊Q811yescharacteristic
149C3⋊Dic3C4⋊Q811yescharacteristic
150C3×Dic3—41no—
151C3×Dic3—42no—
152C3×Dic3—41no—
153C3×Dic3—81no—
154C2×M16—91no—
155C2×M16—91no—
156C4⋊Q8—61no—
157C4⋊Q8—181no—
158#125—181no—
159#125—181no—
160C22⋊Q8—182no—
161#117—91no—
162#117—91no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—91no—
165C2×C42—91no—
166#107—181no—
167#107—181no—
168#106—61no—
169#106—181no—
170#95—182no—
171C22×D3—61no—
172C22×D3—61no—
173C3×Q8—242no—
174C2×C3×C4—22no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—41no—
178C2×C3×C4—61no—
179C2×C3×C4—61no—
180C2×C3×C4—62no—
181C2×C3×C4—121no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—22no—
185C2×Dic3—41no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—62no—
189C2×Dic3—121no—
190C4×D3—61no—
191C4×D3—61no—
192C4×D3—61no—
193C4×D3—61no—
194C4×D3—61no—
195C4×D3—61no—
196C4×D3—61no—
197C4×D3—61no—
198C4×D3—242no—
199C4×D3—242no—
200Dic6—82no—
201C3×C8—62no—
202C3⋊C8—22no—
203C2×C32#39511yescharacteristic
204C2×C32#45411yescharacteristic
205C2×C32#45511yescharacteristic
206C3⋊D3—21no—
207C3⋊D3—21no—
208C2×Q8—62no—
209C22×C4—92no—
210C22×C4—91no—
211C22×C4—181no—
212C22×C4—181no—
213M16—92no—
214M16—92no—
215M16—181no—
216M16—181no—
217C2×C8—61no—
218C2×C8—181no—
219C4⋊C4—62no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C4⋊C4—91no—
223C4⋊C4—91no—
224C4⋊C4—91no—
225C4⋊C4—181no—
226C4⋊C4—182no—
227C4⋊C4—182no—
228C4⋊C4—181no—
229C4⋊C4GO+(4,𝔽2)11yescharacteristic
230C22⋊C4—181no—
231C22⋊C4—181no—
232C42—61no—
233C42—92no—
234C42—181no—
235C42—181no—
236C22×C3—21no—
237C22×C3—21no—
238C2×D3—61no—
239C2×D3—61no—
240C2×D3—61no—
241C2×D3—61no—
242C2×D3—121no—
243C2×D3—121no—
244C2×D3—121no—
245C2×D3—121no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—42no—
251C3×C4—81no—
252C3×C4—122no—
253C3×C4—121no—
254C3×C4—121no—
255C3×C4—241no—
256Dic3—41no—
257Dic3—42no—
258Dic3—41no—
259Dic3—61no—
260Dic3—61no—
261Dic3—61no—
262Dic3—61no—
263Dic3—81no—
264Dic3—122no—
265Dic3—241no—
266C32#206111yescharacteristic, complemented, Sylow
267C23—91no—
268Q8—242no—
269C2×C4—21no—
270C2×C4—61no—
271C2×C4—61no—
272C2×C4—62no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—121no—
279C2×C4—182no—
280C2×C4—181no—
281C2×C4—362no—
282C2×C4—362no—
283C2×C4—361no—
284C2×C4—361no—
285C2×C4C2×GO+(4,𝔽2)11yescharacteristic
286C8—62no—
287C8—182no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294D3—121no—
295D3—121no—
296D3—121no—
297D3—121no—
298C22—91no—
299C22—91no—
300C22—181no—
301C22—181no—
302C22#6424111yescharacteristic
303C4—41no—
304C4—91no—
305C4—91no—
306C4—122no—
307C4—121no—
308C4—121no—
309C4—241no—
310C4—362no—
311C4—361no—
312C4D32⋊Q811yescharacteristic
313C4#6422211yescharacteristic
314C3—21no—
315C3—21no—
316C2—181no—
317C2—181no—
318C2#1059341111yescharacteristic
319C2#1059346111yescharacteristic
320C2#1059348311yescharacteristic
subgroupG/H
centerC22#64241
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#120
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2061
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
34. C4×#157Q8semidirect
36. #3788Q8semidirect
54. #3712Q8semidirect
266. C32#2061semidirect

Maximal subgroups

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

subgroupindex
#105943512
#105933942
#105933442
#105905842
#105901642
#105900522
#105900472
#20619