Finite Group Databasebeta

← #11790575

Subgroups — #11790575

Order 1152.

598 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 89 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×C4×GO+(4,𝔽2)C211yesmaximal, characteristic
2C2×C8×#157C211yesmaximal, characteristic, complemented
3C2×#63732C211yesmaximal, characteristic, complemented
4C2×D32⋊C8C212yesmaximal, complemented
5#10590935C212yesmaximal, complemented
6C22×GO+(4,𝔽2)C411yescharacteristic
7C2×C4×D32C2212yes—
8C2×C4×#157C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10C2×#3773C411yescharacteristic
11C2×D32⋊C4C412yes—
12C4×GO+(4,𝔽2)—22no—
13C4×GO+(4,𝔽2)—22no—
14C2×C8×C3⋊D3C2211yescharacteristic
15C2×#3710C2212yes—
16C8×#157—22no—
17#63732—22no—
18D32⋊C8—24no—
19C3×(C2×D3)⋊C8—22no—
20(C2×D3)⋊(C3⋊C8)—22no—
21D3×C22⋊C8—62no—
22C22×D32C2×C412yes—
23C22×#157C2×C411yescharacteristic
24C22×#157C2×C411yescharacteristic
25C2×GO+(4,𝔽2)—22no—
26C2×GO+(4,𝔽2)—22no—
27C2×GO+(4,𝔽2)C814yescomplemented
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×C3×C4×D3—22no—
30C2×#624C2×C412yes—
31C2×D3×Dic3—22no—
32C4×D32—22no—
33C4×D32—22no—
34C4×D32—22no—
35C4×D32—22no—
36C2×#622—21no—
37C4×#157D412yes—
38C4×#157D412yes—
39#3787—21no—
40#3787D412yescomplemented
41#3773—22no—
42D32⋊C4—24no—
43C2×C32×C8D411yescharacteristic, complemented
44C2×C3⋊(C3⋊C8)D411yescharacteristic, complemented
45C8×C3⋊D3—21no—
46C8×C3⋊D3—21no—
47C2×C3×C3⋊C8—22no—
48#3710—22no—
49#3710—22no—
50#1954—91nomaximal, Sylow
51C22×C4×D3—62no—
52C2×D3×C8—62no—
53C2×D3×C8—62no—
54C3×C22⋊C8—62no—
55#830—62no—
56(C2×D3)⋊C8—22no—
57(C2×D3)⋊C8—62no—
58C22×C3⋊D3C22×C411yescharacteristic
59C22×C3×D3—22no—
60C2×D32—22no—
61C2×D32—22no—
62C2×D32—22no—
63C2×D32—22no—
64C2×D32—22no—
65C2×D32C2×C814yes—
66C2×#157—21no—
67C2×#157—21no—
68C2×#157C22⋊C412yes—
69C2×#157C22⋊C412yes—
70C2×#157C2×C812yes—
71C2×#157M1612yes—
72GO+(4,𝔽2)—28no—
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3#4111yescharacteristic
75C4×C3⋊D3C2×D411yescharacteristic
76C4×C3⋊D3C2×D411yescharacteristic
77C4×C3⋊D3C2×D411yescharacteristic
78C4×C3⋊D3#4111yescharacteristic
79C2×C3×Dic3—22no—
80C3×C4×D3—42no—
81C3×C4×D3—42no—
82#624—22no—
83#624—22no—
84D3×Dic3—42no—
85D3×Dic3—42no—
86#622—22no—
87C32×C8—21no—
88C3⋊(C3⋊C8)—21no—
89C3×C3⋊C8—42no—
90C2×C4×D4—91no—
91C2×C4⋊C8—91no—
92C2×C22⋊C8—92no—
93C2×C22⋊C8—92no—
94C2×C4×C8—91no—
95C23×D3—62no—
96C22×C3×C4—62no—
97C22×Dic3—62no—
98C2×C4×D3—22no—
99C2×C4×D3—62no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—122no—
103C2×C4×D3—122no—
104C2×C4×D3—122no—
105C2×C4×D3—122no—
106C2×C3×C8—22no—
107C2×C3×C8—62no—
108C2×C3⋊C8—22no—
109C2×C3⋊C8—62no—
110D3×C8—122no—
111D3×C8—122no—
112D3×C8—122no—
113D3×C8—122no—
114C22×C32C4×D411yescharacteristic
115C2×C3⋊D3C2×C22⋊C411yescharacteristic
116C2×C3⋊D3C4×D411yescharacteristic
117C2×C3⋊D3C22×C811yescharacteristic
118C2×C3⋊D3C2×M1611yescharacteristic
119C2×C3⋊D3#13111yescharacteristic
120C2×C3⋊D3#13111yescharacteristic
121C2×C3×D3—24no—
122C2×C3×D3—42no—
123C2×C3×D3—42no—
124D32—24no—
125D32—24no—
126D32—42no—
127D32—42no—
128#157—22no—
129#157C22⋊C814yescomplemented
130C32×C4#12111yescharacteristic
131C32×C4#12711yescharacteristic
132C3⋊Dic3#12111yescharacteristic
133C3⋊Dic3#12411yescharacteristic
134C3×Dic3—42no—
135C22×D4—91no—
136C23×C4—92no—
137C22×C8—92no—
138C22×C8—91no—
139C22×C8—91no—
140C4×D4—182no—
141C4×D4—182no—
142C2×C4⋊C4—91no—
143C2×C22⋊C4—92no—
144C2×C42—91no—
145C4⋊C8—182no—
146C22⋊C8—62no—
147C22⋊C8—182no—
148C22⋊C8—184no—
149C4×C8—182no—
150C23×C3—62no—
151C22×D3—22no—
152C22×D3—64no—
153C22×D3—62no—
154C22×D3—64no—
155C22×D3—122no—
156C22×D3—122no—
157C22×D3—122no—
158C22×D3—122no—
159C2×C3×C4—22no—
160C2×C3×C4—62no—
161C2×C3×C4—122no—
162C2×C3×C4—122no—
163C2×Dic3—22no—
164C2×Dic3—62no—
165C2×Dic3—122no—
166C2×Dic3—122no—
167C4×D3—42no—
168C4×D3—42no—
169C4×D3—62no—
170C4×D3—62no—
171C4×D3—62no—
172C4×D3—62no—
173C4×D3—122no—
174C4×D3—122no—
175C4×D3—122no—
176C4×D3—122no—
177C3×C8—42no—
178C3×C8—122no—
179C3⋊C8—42no—
180C3⋊C8—122no—
181C2×C32#39011yescharacteristic
182C2×C32C8×D411yescharacteristic
183C2×C32#43611yescharacteristic
184C3⋊D3C2×C22⋊C811yescharacteristic
185C3⋊D3#40811yescharacteristic
186C3⋊D3C8×D411yescharacteristic
187C3⋊D3#43611yescharacteristic
188C3×D3—44no—
189C24—92no—
190C2×D4—94no—
191C2×D4—182no—
192C2×D4—182no—
193C22×C4—62no—
194C22×C4—92no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—182no—
199C22×C4—182no—
200C22×C4—182no—
201C22×C4—182no—
202C22×C4—182no—
203C2×C8—62no—
204C2×C8—92no—
205C2×C8—91no—
206C2×C8—181no—
207C2×C8—181no—
208C2×C8—182no—
209C2×C8—182no—
210C2×C8—181no—
211C2×C8—181no—
212C2×C8GO+(4,𝔽2)11yescharacteristic, complemented
213C4⋊C4—182no—
214C22⋊C4—184no—
215C42—92no—
216C42—92no—
217C22×C3—22no—
218C22×C3—64no—
219C22×C3—122no—
220C22×C3—122no—
221C2×D3—24no—
222C2×D3—42no—
223C2×D3—42no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—62no—
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—124no—
231C2×D3—124no—
232C2×D3—124no—
233C2×D3—124no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—122no—
237Dic3—42no—
238Dic3—62no—
239Dic3—62no—
240C32#195411yescharacteristic, complemented, Sylow
241C23—62no—
242C23—94no—
243C23—91no—
244C23—182no—
245C23—182no—
246C23—182no—
247C23—182no—
248C23—182no—
249D4—188no—
250C2×C4—62no—
251C2×C4—92no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—92no—
260C2×C4—122no—
261C2×C4—122no—
262C2×C4—182no—
263C2×C4—182no—
264C2×C4—181no—
265C2×C4—181no—
266C2×C4—362no—
267C2×C4—362no—
268C2×C4C2×GO+(4,𝔽2)11yescharacteristic
269C8—21no—
270C8—122no—
271C8—182no—
272C8—181no—
273C2×C3—22no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—124no—
277D3—44no—
278D3—62no—
279D3—62no—
280D3—62no—
281D3—62no—
282C22—64no—
283C22—91no—
284C22—91no—
285C22—91no—
286C22—91no—
287C22—91no—
288C22—91no—
289C22—122no—
290C22—122no—
291C22—184no—
292C22—184no—
293C22—362no—
294C22—362no—
295C22C4×GO+(4,𝔽2)11yescharacteristic
296C4—94no—
297C4—91no—
298C4—91no—
299C4—122no—
300C4—182no—
301C4#6423111yescharacteristic
302C4#6424211yescharacteristic
303C3—22no—
304C2—91no—
305C2—91no—
306C2—91no—
307C2—91no—
308C2—124no—
309C2C8×GO+(4,𝔽2)11yescharacteristic
310C2#1059328311yescharacteristic
311C2#1059345411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C22×C8
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC22×GO+(4,𝔽2)C4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1954
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×#157C2semidirect
3. C2×#63732C2semidirect
4. C2×D32⋊C8C2semidirect
5. #10590935C2semidirect
27. C2×GO+(4,𝔽2)C8semidirect
40. #3787D4semidirect
43. C2×C32×C8D4semidirect
44. C2×C3⋊(C3⋊C8)D4semidirect
129. #157C22⋊C8semidirect
212. C2×C8GO+(4,𝔽2)semidirect
240. C32#1954semidirect

Maximal subgroups

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

subgroupindex
C2×C4×GO+(4,𝔽2)2
C2×C8×#1572
C2×#637322
C2×D32⋊C82
#105909352
#19549