Finite Group Databasebeta

← #11790576

Subgroups — #11790576

Order 1152.

678 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C4×#3802C211yesmaximal, characteristic
2C4×#3787C211yesmaximal, characteristic, complemented
3C2×D32⋊C8C214yesmaximal, complemented
4#10590331C211yesmaximal, characteristic, complemented
5C2×#3802C411yescharacteristic
6C2×C4×D32C2212yes—
7C2×#3787C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×D12—21no—
10#63921C412yes—
11#63902—21no—
12C4×#625—21no—
13#63900C411yescharacteristic
14#63898—21no—
15C2×#3710C2212yes—
16C4×#622—21no—
17C4×#622—21no—
18D32⋊C8—28no—
19C3×C4⋊(C3⋊C8)—21no—
20#63572—21no—
21C4×D3×D4—61no—
22D3×C4⋊C8—61no—
23C22×D32C2×C412yes—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×C3×D12—21no—
28C2×C3×C4×D3—22no—
29C2×#625—21no—
30C2×#624C2×C412yes—
31C2×D3×Dic3—22no—
32#3802—22no—
33#3802C814yescomplemented
34C4×D32—24no—
35C4×D32—24no—
36C2×#622—22no—
37#3787—22no—
38#3787D414yescomplemented
39C32×C42D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C3×(C2×D3)⋊C4—22no—
44C3×C4⋊Dic3—21no—
45C2×C3×C3⋊C8—22no—
46#3724—21no—
47(C2×D3)⋊Dic3—22no—
48#3710—24no—
49#1954—91nomaximal, Sylow
50C2×D3×D4—61no—
51C22×C4×D3—62no—
52C3×C4×D4—61no—
53D4×Dic3—61no—
54C4×#67—62no—
55C2×D3×C8—62no—
56#893—61no—
57D3×C4⋊C4—61no—
58#67⋊C4—62no—
59D3×C22⋊C4—62no—
60C4×D12—21no—
61C42×D3—61no—
62C42×D3—61no—
63C3×C4⋊C8—61no—
64Dic3⋊C8—62no—
65C4⋊(C3⋊C8)—21no—
66C22×C3⋊D3C22×C411yescharacteristic
67C22×C3×D3—22no—
68C2×D32—22no—
69C2×D32—24no—
70C2×D32—24no—
71C2×D32C2×C814yes—
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C22⋊C411yescharacteristic
74C2×C32×C4C2×D411yescharacteristic
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C4×C3⋊D3—22no—
79C4×C3⋊D3C2×C812yes—
80C4×C3⋊D3M1612yes—
81C4×C3⋊D3C2×D412yes—
82C4×C3⋊D3#4112yes—
83C2×C3×Dic3—22no—
84C3×D12—24no—
85C3×C4×D3—42no—
86C3×C4×D3—42no—
87#625—24no—
88#624—24no—
89D3×Dic3—44no—
90#622—24no—
91C3×C3⋊C8—42no—
92C2×C4×D4—91no—
93C2×C4⋊C8—91no—
94C2×C22⋊C8—94no—
95C2×C4×C8—91no—
96C23×D3—62no—
97C2×C3×D4—61no—
98C22×C3×C4—62no—
99C2×#67—62no—
100C22×Dic3—62no—
101D3×D4—64no—
102D3×D4—64no—
103C2×D12—21no—
104C2×C4×D3—22no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—62no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—62no—
113C2×C4×D3—124no—
114C2×C4×D3—124no—
115C2×C3×C8—62no—
116C3×C4⋊C4—61no—
117C3×C22⋊C4—62no—
118C3×C42—21no—
119C3×C42—21no—
120#217—62no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—62no—
123C4⋊Dic3—21no—
124Dic3⋊C4—62no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C2×C3⋊C8—22no—
132D3×C8—124no—
133C22×C32C2×C22⋊C411yescharacteristic
134C2×C3⋊D3C4×D412yes—
135C2×C3⋊D3C22×C811yescharacteristic
136C2×C3⋊D3C2×M1611yescharacteristic
137C2×C3⋊D3#13112yes—
138C2×C3×D3—24no—
139C2×C3×D3—42no—
140C2×C3×D3—42no—
141D32—28no—
142D32—44no—
143C32×C4—21no—
144C32×C4C22⋊C812yescomplemented
145C32×C4#12411yescharacteristic
146C32×C4#12711yescharacteristic
147C3⋊Dic3—21no—
148C3⋊Dic3C22⋊C812yescomplemented
149C3⋊Dic3#12112yes—
150C3×Dic3—42no—
151C22×D4—91no—
152C23×C4—92no—
153C22×C8—92no—
154C22×C8—92no—
155C4×D4—61no—
156C4×D4—181no—
157C4×D4—181no—
158C4×D4—181no—
159C2×C4⋊C4—91no—
160C2×C22⋊C4—92no—
161C2×C42—91no—
162C4⋊C8—61no—
163C4⋊C8—181no—
164C22⋊C8—188no—
165C4×C8—181no—
166C4×C8—181no—
167C23×C3—62no—
168C22×D3—22no—
169C22×D3—64no—
170C22×D3—61no—
171C22×D3—61no—
172C22×D3—64no—
173C22×D3—124no—
174C22×D3—124no—
175C3×D4—64no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—62no—
183C2×C3×C4—122no—
184C2×C3×C4—122no—
185#67—68no—
186C2×Dic3—22no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—124no—
194D12—24no—
195C4×D3—42no—
196C4×D3—42no—
197C4×D3—62no—
198C4×D3—62no—
199C4×D3—62no—
200C4×D3—62no—
201C4×D3—62no—
202C4×D3—62no—
203C4×D3—62no—
204C4×D3—62no—
205C4×D3—124no—
206C4×D3—122no—
207C4×D3—122no—
208C4×D3—124no—
209C3×C8—122no—
210C3⋊C8—42no—
211C2×C32#39011yescharacteristic
212C2×C32C2×C22⋊C811yescharacteristic
213C2×C32#40811yescharacteristic
214C3⋊D3C8×D412yes—
215C3⋊D3#43612yes—
216C3×D3—44no—
217C24—92no—
218C2×D4—61no—
219C2×D4—94no—
220C2×D4—182no—
221C2×D4—181no—
222C22×C4—62no—
223C22×C4—92no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—91no—
227C22×C4—182no—
228C22×C4—184no—
229C22×C4—184no—
230C2×C8—62no—
231C2×C8—94no—
232C2×C8—184no—
233C2×C8—182no—
234C2×C8—182no—
235C4⋊C4—61no—
236C4⋊C4—181no—
237C22⋊C4—62no—
238C22⋊C4—182no—
239C42—91no—
240C42—91no—
241C42—91no—
242C42GO+(4,𝔽2)11yescharacteristic
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—64no—
246C22×C3—122no—
247C22×C3—122no—
248C2×D3—24no—
249C2×D3—42no—
250C2×D3—42no—
251C2×D3—62no—
252C2×D3—61no—
253C2×D3—61no—
254C2×D3—62no—
255C2×D3—61no—
256C2×D3—61no—
257C2×D3—62no—
258C2×D3—62no—
259C2×D3—128no—
260C2×D3—128no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4—122no—
270Dic3—42no—
271Dic3—62no—
272Dic3—62no—
273Dic3—62no—
274Dic3—62no—
275Dic3—121no—
276Dic3—121no—
277C32#195411yescharacteristic, complemented, Sylow
278C23—62no—
279C23—94no—
280C23—91no—
281C23—182no—
282C23—184no—
283C23—184no—
284D4—64no—
285D4—184no—
286C2×C4—62no—
287C2×C4—91no—
288C2×C4—91no—
289C2×C4—92no—
290C2×C4—92no—
291C2×C4—92no—
292C2×C4—92no—
293C2×C4—91no—
294C2×C4—122no—
295C2×C4—122no—
296C2×C4—182no—
297C2×C4—184no—
298C2×C4—364no—
299C2×C4D32⋊C411yescharacteristic
300C2×C4D32⋊C411yescharacteristic
301C2×C4C2×GO+(4,𝔽2)11yescharacteristic
302C8—122no—
303C8—184no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—124no—
311D3—44no—
312D3—62no—
313D3—62no—
314D3—62no—
315D3—62no—
316C22—64no—
317C22—91no—
318C22—91no—
319C22—92no—
320C22—92no—
321C22—122no—
322C22—122no—
323C22—188no—
324C22—364no—
325C22C2×D32⋊C411yescharacteristic
326C4—21no—
327C4—92no—
328C4—92no—
329C4—122no—
330C4—181no—
331C4D32⋊C812yescomplemented
332C4#6422111yescharacteristic
333C4#6423111yescharacteristic
334C3—21no—
335C3—21no—
336C2—92no—
337C2—92no—
338C2—124no—
339C2C2×D32⋊C811yescharacteristic
340C2#1059330911yescharacteristic
341C2#1059340711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C22×C8
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1954
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#3787C2semidirect
3. C2×D32⋊C8C2semidirect
4. #10590331C2semidirect
33. #3802C8semidirect
38. #3787D4semidirect
144. C32×C4C22⋊C8semidirect
148. C3⋊Dic3C22⋊C8semidirect
277. C32#1954semidirect
331. C4D32⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
C4×#37872
C2×D32⋊C82
#105903312
#19549