Finite Group Databasebeta

← #11790563

Subgroups — #11790563

Order 1152.

822 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 104 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×#64090C211yesmaximal, characteristic
2C2×C22⋊#622C212yesmaximal, complemented
3C2×#63779C211yesmaximal, characteristic, complemented
4C2×#63778C212yesmaximal, complemented
5C2×C4×#622C211yesmaximal, characteristic, complemented
6C22×#638C411yescharacteristic
7C23×C3⋊Dic3C2211yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#622C2212yes—
10C22×#622C2212yes—
11C2×C32×C22⋊C4C411yescharacteristic
12C2×#3752C411yescharacteristic
13C2×#3750C411yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64090—22no—
16#64090—22no—
17C22⋊#622—24no—
18#63779—22no—
19#63778—24no—
20C4×#622—22no—
21C2×#67⋊C4—62no—
22C24×C32C2×C411yescharacteristic
23C23×C3⋊D3C2×C411yescharacteristic
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C2×#638—22no—
27C2×#638—22no—
28C2×#638C814yescomplemented
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3—22no—
32C22×C3⋊Dic3—22no—
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2311yescharacteristic
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—22no—
39C2×C4×C3⋊D3—22no—
40C2×#622—22no—
41C2×#622—22no—
42C2×#622—22no—
43C2×#622—22no—
44C2×#622—22no—
45C2×#622D414yescomplemented
46C32×C22⋊C4—22no—
47#3752—22no—
48#3750—22no—
49C4×C3⋊Dic3D412yes—
50C4×C3⋊Dic3D412yes—
51#1954—91nomaximal, Sylow
52C22×#67—62no—
53C23×Dic3—62no—
54C22×C4×D3—62no—
55C2×C3×C22⋊C4—22no—
56C2×(C2×D3)⋊C4—62no—
57C2×Dic3⋊C4—62no—
58C2×C4×Dic3—62no—
59#67⋊C4—68no—
60#67⋊C4—68no—
61C23×C32—21no—
62C23×C32—21no—
63C23×C32—22no—
64C23×C32—22no—
65C23×C32C2×C812yes—
66C23×C32C22×C411yescharacteristic
67C22×C3⋊D3—21no—
68C22×C3⋊D3—21no—
69C22×C3⋊D3—22no—
70C22×C3⋊D3—22no—
71C22×C3⋊D3C2×C812yes—
72C2×C32×C4—21no—
73C2×C32×C4—22no—
74C2×C32×C4—22no—
75C2×C32×C4C22⋊C412yes—
76#638—28no—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—42no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3C22⋊C412yes—
83C2×C3⋊Dic3C2×C812yes—
84C2×C3⋊Dic3M1612yes—
85C2×C3⋊Dic3C2×D411yescharacteristic
86C2×C3⋊Dic3C2×D412yes—
87C2×C3⋊Dic3C2×D411yescharacteristic
88C2×C3⋊Dic3#4112yes—
89C4×C3⋊D3—42no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3—41no—
92#622—24no—
93#622—42no—
94C2×C4×D4—91no—
95C2×C4⋊C8—91no—
96C2×C22⋊C8—92no—
97C2×C22⋊C8—92no—
98C2×C4×C8—91no—
99C24×C3—22no—
100C23×D3—62no—
101C22×C3×C4—22no—
102C22×C3×C4—22no—
103C2×#67—68no—
104C2×#67—68no—
105C2×#67—68no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C22×Dic3—62no—
109C22×Dic3—64no—
110C22×Dic3—64no—
111C22×Dic3—124no—
112C22×Dic3—124no—
113C2×C4×D3—64no—
114C2×C4×D3—64no—
115C2×C4×D3—124no—
116C2×C4×D3—124no—
117C3×C22⋊C4—28no—
118(C2×D3)⋊C4—68no—
119Dic3⋊C4—68no—
120C4×Dic3—64no—
121C4×Dic3—64no—
122C22×C32—22no—
123C22×C32—24no—
124C22×C32—41no—
125C22×C32—41no—
126C22×C32—42no—
127C22×C32C2×C22⋊C411yescharacteristic
128C22×C32C4×D412yes—
129C22×C32C22×C811yescharacteristic
130C22×C32C2×M1611yescharacteristic
131C22×C32#13112yes—
132C2×C3⋊D3—22no—
133C2×C3⋊D3—24no—
134C2×C3⋊D3—41no—
135C2×C3⋊D3—41no—
136C2×C3⋊D3—42no—
137C32×C4—22no—
138C32×C4—41no—
139C3⋊Dic3—41no—
140C3⋊Dic3C22⋊C814yescomplemented
141C3⋊Dic3#12112yes—
142C3⋊Dic3#12411yescharacteristic
143C3⋊Dic3#12711yescharacteristic
144C22×D4—91no—
145C23×C4—91no—
146C23×C4—91no—
147C22×C8—92no—
148C22×C8—92no—
149C4×D4—182no—
150C4×D4—182no—
151C2×C4⋊C4—91no—
152C2×C22⋊C4—91no—
153C2×C22⋊C4#15711yescharacteristic
154C2×C42—91no—
155C4⋊C8—182no—
156C22⋊C8—184no—
157C22⋊C8—184no—
158C4×C8—182no—
159C23×C3—24no—
160C23×C3—24no—
161C23×C3—22no—
162C23×C3—24no—
163C23×C3—44no—
164C23×C3—44no—
165C22×D3—64no—
166C22×D3—64no—
167C22×D3—64no—
168C22×D3—124no—
169C22×D3—124no—
170C2×C3×C4—24no—
171C2×C3×C4—24no—
172C2×C3×C4—44no—
173C2×C3×C4—44no—
174#67—632no—
175C2×Dic3—64no—
176C2×Dic3—64no—
177C2×Dic3—64no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—64no—
181C2×Dic3—64no—
182C2×Dic3—64no—
183C2×Dic3—124no—
184C2×Dic3—128no—
185C2×Dic3—124no—
186C2×Dic3—124no—
187C4×D3—128no—
188C4×D3—124no—
189C4×D3—124no—
190C2×C32—42no—
191C2×C32#39011yescharacteristic
192C2×C32C2×C22⋊C811yescharacteristic
193C2×C32#40811yescharacteristic
194C2×C32C8×D412yes—
195C2×C32#43612yes—
196C3⋊D3—42no—
197C24—91no—
198C24C2×#15711yescharacteristic
199C2×D4—94no—
200C2×D4—182no—
201C2×D4—182no—
202C22×C4—91no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—182no—
206C22×C4—181no—
207C22×C4—181no—
208C22×C4—182no—
209C22×C4—182no—
210C22×C4—181no—
211C22×C4—181no—
212C22×C4—182no—
213C22×C4C2×#15711yescharacteristic
214C22×C4C2×#15711yescharacteristic
215C2×C8—94no—
216C2×C8—182no—
217C2×C8—182no—
218C2×C8—182no—
219C2×C8—182no—
220C2×C8—182no—
221C4⋊C4—182no—
222C22⋊C4—22no—
223C22⋊C4—182no—
224C42—92no—
225C42—92no—
226C22×C3—28no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3—24no—
230C22×C3—24no—
231C22×C3—22no—
232C22×C3—48no—
233C22×C3—44no—
234C22×C3—44no—
235C22×C3—48no—
236C2×D3—68no—
237C2×D3—128no—
238C2×D3—124no—
239C2×D3—124no—
240C2×D3—128no—
241C3×C4—44no—
242C3×C4—44no—
243Dic3—64no—
244Dic3—62no—
245Dic3—62no—
246Dic3—68no—
247Dic3—124no—
248C32#195411yescharacteristic, complemented, Sylow
249C23—21no—
250C23—22no—
251C23—22no—
252C23—21no—
253C23—92no—
254C23—181no—
255C23—182no—
256C23—182no—
257C23—181no—
258C23#378712yes—
259C23C22×#15711yescharacteristic
260D4—188no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—92no—
267C2×C4—92no—
268C2×C4—92no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—182no—
272C2×C4—181no—
273C2×C4—362no—
274C2×C4—361no—
275C2×C4—361no—
276C2×C4—362no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4C22⋊#15712yes—
280C8—184no—
281C8—362no—
282C2×C3—22no—
283C2×C3—22no—
284C2×C3—22no—
285C2×C3—24no—
286C2×C3—24no—
287C2×C3—48no—
288D3—128no—
289C22—22no—
290C22—24no—
291C22—41no—
292C22—41no—
293C22—42no—
294C22—182no—
295C22—184no—
296C22—361no—
297C22—361no—
298C22—362no—
299C22C2×#378711yescharacteristic
300C22#6428311yescharacteristic
301C22#6428712yes—
302C22D4×#15712yes—
303C22C2×C22⋊#15711yescharacteristic
304C4—22no—
305C4—41no—
306C4—94no—
307C4—92no—
308C4—91no—
309C4—91no—
310C4—361no—
311C3—22no—
312C2—42no—
313C2—362no—
314C2#1059373912yes—
315C2#1059374212yes—
316C2#1059380011yescharacteristic
317C2#1059382211yescharacteristic
318C2#1059382711yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C22×C8
FittingC2×C32×C22⋊C4C4
socleC23×C32C22×C4
prime radicalC22×#638C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32#1954
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#622C2semidirect
3. C2×#63779C2semidirect
4. C2×#63778C2semidirect
5. C2×C4×#622C2semidirect
28. C2×#638C8semidirect
45. C2×#622D4semidirect
140. C3⋊Dic3C22⋊C8semidirect
248. C32#1954semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×C22⋊#6222
C2×#637792
C2×#637782
C2×C4×#6222
#19549