Finite Group Databasebeta

← #11775435

Subgroups — #11775435

Order 1152.

559 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 559 conjugacy classes of subgroups — too many to draw. Only its 90 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#10594929C211yesmaximal, characteristic
2#10592418C211yesmaximal, characteristic, complemented
3#10591229C211yesmaximal, characteristic, complemented
4C3×#4470C212yesmaximal, complemented
5#10589149C212yesmaximal, complemented
6#68281—32nomaximal
7C2×#3805—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×#930C2212yes—
10#63980—21no—
11#63919C411yescharacteristic, complemented
12#63915—21no—
13#63914C411yescharacteristic, complemented
14#63902—21no—
15#63898C412yescomplemented
16C32×C22⋊C8C2211yescharacteristic
17#63657C2211yescharacteristic
18#63642—21no—
19#63641—21no—
20C3×C3⋊#95C2212yes—
21#63579—21no—
22#63579—21no—
23#5596—32no—
24#4719—32no—
25#4719—61no—
26#4651—32no—
27C3×#327—32no—
28#4537—32no—
29#4470D312yescomplemented
30#4451—32no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C2×C3×#67—22no—
35C22×C3×Dic3—22no—
36C2×C3×D12C2×C412yes—
37C2×#627—21no—
38C2×#625—21no—
39C2×#625—21no—
40#3805—44no—
41C2×D3×Dic3—22no—
42C2×C32×C8—21no—
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C3×(C2×D3)⋊C4—22no—
49C3×C4⋊Dic3C2×C412yes—
50#3724—21no—
51(C2×D3)⋊Dic3—22no—
52#1514—91noSylow
53C2×#237—62no—
54C3×#121—32no—
55#940—32no—
56#939—62no—
57D4×Dic3—32no—
58#930C2×D312yes—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—61no—
61#893—32no—
62#888—32no—
63#885—62no—
64#67⋊C4—62no—
65C3×C22⋊C8—21no—
66C3×C22⋊C8C2×D312yes—
67C3×#95—32no—
68C3⋊#95—62no—
69C3⋊#95—62no—
70C3⋊#95C2×D312yes—
71#830—32no—
72#830—61no—
73#815—62no—
74#815—62no—
75Dic3⋊C8—62no—
76Dic3⋊C8—62no—
77C23×C32C2×D411yescharacteristic
78C22×C3×D3—22no—
79C2×C32×C4—41no—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C3×#67—42no—
89C3×#67—42no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—42no—
94C3×D12—42no—
95#627—42no—
96#625—42no—
97#625—42no—
98D3×Dic3—44no—
99C32×C8—41no—
100C3⋊(C3⋊C8)—41no—
101#532—91no—
102#432—91no—
103#383—91no—
104#327—32no—
105#327—92no—
106C2×C3×D4—32no—
107C2×C3×D4—62no—
108C22×C3×C4—21no—
109C22×C3×C4—62no—
110C22×C3×C4C22×D312yes—
111C2×#67—22no—
112C2×#67—62no—
113C2×#67—62no—
114C22×Dic3—22no—
115C22×Dic3—32no—
116C22×Dic3—32no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119C22×Dic3—62no—
120#237—124no—
121#237—124no—
122C2×D12C4×D312yes—
123C2×C4×D3—62no—
124C2×Dic6—62no—
125C2×C3×C8—22no—
126C2×C3×C8—22no—
127C3×C4⋊C4—32no—
128C3×C22⋊C4—62no—
129#217—62no—
130(C2×D3)⋊C4—22no—
131(C2×D3)⋊C4—62no—
132C4⋊Dic3C4×D312yes—
133Dic3⋊C4—62no—
134C4×Dic3—32no—
135C4×Dic3—32no—
136C4×Dic3—32no—
137C4×Dic3—32no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C2×C3⋊C8—62no—
143C2×C3⋊C8—62no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32C2×C22⋊C411yescharacteristic
147C22×C32AGL(1,ℤ/8)12yes—
148C2×C3×D3—42no—
149C2×C3×D3—42no—
150C2×C3×D3—42no—
151C32×C4—21no—
152C32×C4—21no—
153C3⋊Dic3—21no—
154C3⋊Dic3—21no—
155C3⋊Dic3—21no—
156C3⋊Dic3—21no—
157C3×Dic3—42no—
158C3×Dic3—82no—
159C2×#41—181no—
160C4⋊Q8—91no—
161#127—91no—
162#124—181no—
163#121—32no—
164#121—181no—
165C4×D4—92no—
166C4×D4—181no—
167C2×C42—91no—
168C4⋊C8—181no—
169C22⋊C8—91no—
170C22⋊C8D3211yescharacteristic
171#97—181no—
172#95—32no—
173#95—181no—
174#95—181no—
175C23×C3—21no—
176C23×C3—62no—
177C23×C3D3×D412yes—
178C22×D3—22no—
179C3×D4—122no—
180C3×D4—122no—
181C3×D4—122no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—62no—
187C2×C3×C4—122no—
188C2×C3×C4—122no—
189C2×C3×C4—122no—
190C2×C3×C4C2×C4×D312yes—
191C2×C3×C4D3×D412yes—
192#67—42no—
193#67—42no—
194#67—124no—
195#67—124no—
196C2×Dic3—22no—
197C2×Dic3—32no—
198C2×Dic3—32no—
199C2×Dic3—32no—
200C2×Dic3—32no—
201C2×Dic3—42no—
202C2×Dic3—42no—
203C2×Dic3—42no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—122no—
211C2×Dic3—124no—
212C2×Dic3—122no—
213C2×Dic3—122no—
214D12—42no—
215C4×D3—124no—
216Dic6—124no—
217C3×C8—42no—
218C3×C8—42no—
219C3⋊C8—122no—
220C3⋊C8—122no—
221C2×C32—22no—
222C2×C32#41011yescharacteristic
223C2×C32#41811yescharacteristic
224C2×C32#42111yescharacteristic
225C3×D3—82no—
226#41—364no—
227C2×Q8—181no—
228C2×D4—32no—
229C2×D4—62no—
230C2×D4—181no—
231C2×D4—181no—
232C22×C4—62no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4—182no—
236C22×C4C2×D3211yescharacteristic
237C2×C8—21no—
238C2×C8—181no—
239C4⋊C4—32no—
240C4⋊C4—181no—
241C22⋊C4—62no—
242C22⋊C4—182no—
243C42—91no—
244C42—91no—
245C42—91no—
246C42—91no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—21no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—122no—
254C22×C3—122no—
255C22×C3—122no—
256C22×C3D3×C22⋊C412yes—
257C22×C3#91112yes—
258C22×C3#91412yes—
259C2×D3—42no—
260C2×D3—42no—
261C2×D3—42no—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—41no—
266C3×C4—122no—
267C3×C4—242no—
268Dic3—42no—
269Dic3—62no—
270Dic3—62no—
271Dic3—62no—
272Dic3—62no—
273Dic3—62no—
274Dic3—82no—
275Dic3—121no—
276Dic3—121no—
277Dic3—121no—
278C32#151411yescharacteristic, complemented, Sylow
279C23—62no—
280C23#380211yescharacteristic
281Q8—362no—
282D4—122no—
283D4—122no—
284D4—122no—
285D4—362no—
286D4—362no—
287C2×C4—41no—
288C2×C4—62no—
289C2×C4—91no—
290C2×C4—91no—
291C2×C4—91no—
292C2×C4—91no—
293C2×C4—122no—
294C2×C4—122no—
295C2×C4—122no—
296C2×C4—182no—
297C2×C4—364no—
298C2×C4—361no—
299C2×C4C4×D3211yescharacteristic
300C2×C4#381111yescharacteristic
301C8—41no—
302C8—361no—
303C2×C3—22no—
304C2×C3—22no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—42no—
309C2×C3—242no—
310C2×C3#474012yes—
311C2×C3#477012yes—
312C2×C3#482112yes—
313D3—82no—
314C22—21no—
315C22—21no—
316C22—122no—
317C22—122no—
318C22—122no—
319C22#6379812yes—
320C22#6392111yescharacteristic
321C4—21no—
322C4—21no—
323C4—122no—
324C4—181no—
325C4—181no—
326C4—181no—
327C4—181no—
328C4—242no—
329C3—21no—
330C3#6828112yescomplemented
331C2—22no—
332C2—242no—
333C2#1059040611yescharacteristic
334C2#1059094111yescharacteristic
335C2#1059100911yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1514
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592418C2semidirect
3. #10591229C2semidirect
4. C3×#4470C2semidirect
5. #10589149C2semidirect
11. #63919C4semidirect
13. #63914C4semidirect
15. #63898C4semidirect
29. #4470D3semidirect
278. C32#1514semidirect
330. C3#68281semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105924182
#105912292
C3×#44702
#105891492
#682813