Finite Group Databasebeta

← #11774178

Subgroups — #11774178

Order 1152.

757 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 757 conjugacy classes of subgroups — too many to draw. Only its 132 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
2C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
3C4×#3710C211yesmaximal, characteristic, complemented
4C3×#4483C212yesmaximal, complemented
5#10589081C212yesmaximal, complemented
6D3×D4⋊C8—32nomaximal
7C2×#3802C411yescharacteristic
8C2×C4×D32—21no—
9C2×C8×C3⋊D3—21no—
10C42×C3⋊D3C2211yescharacteristic
11C3×C4×D12C2212yes—
12#63921—21no—
13#63902—21no—
14C4×#625—21no—
15#63900C411yescharacteristic
16#63898C412yes—
17C2×#3710—21no—
18C32×C4⋊C8C2211yescharacteristic, complemented
19#63641—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
21C3×C4×C3⋊C8C2212yescomplemented
22#63553—21no—
23C4×D3×D4—32no—
24D3×C4⋊C8—32no—
25D3×C4⋊C8—61no—
26C4×D3×C8—32no—
27C3×D4⋊C8—32no—
28D4⋊(C3⋊C8)—32no—
29#4483D312yescomplemented
30#4459—32no—
31C22×D32—21no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C3×D12C2×C412yes—
36C2×C3×C4×D3—22no—
37C2×#625—21no—
38C2×#624—21no—
39C2×D3×Dic3—22no—
40#3802—22no—
41#3802C814yescomplemented
42C4×D32—42no—
43C4×D32—42no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C2×C3⋊(C3⋊C8)—21no—
50C8×C3⋊D3—42no—
51C3×(C2×D3)⋊C4—22no—
52C3×C4⋊Dic3C2×C412yes—
53C2×C3×C3⋊C8—22no—
54#3724—21no—
55(C2×D3)⋊Dic3—22no—
56#3710—24no—
57C2×D4⋊C8—91noSylow
58C2×D3×D4—32no—
59C22×C4×D3—62no—
60C3×C4×D4—32no—
61D4×Dic3—32no—
62C4×#67—62no—
63C2×D3×C8—62no—
64C2×D3×C8—62no—
65C2×D3×C8—62no—
66#893—32no—
67D3×C4⋊C4—32no—
68#67⋊C4—62no—
69D3×C22⋊C4—62no—
70C4×D12C2×D312yes—
71C42×D3—32no—
72C42×D3—61no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8C2×D312yescomplemented
75C3×C4×C8—32no—
76Dic3⋊C8—62no—
77Dic3⋊C8—62no—
78C8×Dic3—62no—
79C4⋊(C3⋊C8)—32no—
80C4⋊(C3⋊C8)—61no—
81C4×C3⋊C8C2×D312yescomplemented
82C22×C3⋊D3C22⋊C411yescharacteristic
83C22×C3×D3—22no—
84C2×D32—24no—
85C2×D32—42no—
86C2×D32—42no—
87C2×C32×C4C22×C411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C4×C3⋊D3—22no—
94C4×C3⋊D3C2×C812yes—
95C4×C3⋊D3M1612yes—
96C4×C3⋊D3D812yes—
97C4×C3⋊D3SD1612yes—
98C2×C3×Dic3—22no—
99C3×D12—22no—
100C3×D12C2×C814yescomplemented
101C3×C4×D3—42no—
102C3×C4×D3—42no—
103#625—24no—
104#624—42no—
105D3×Dic3—44no—
106C32×C8—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—24no—
109C2×C4×D4—91no—
110C2×C4⋊C8—91no—
111C2×C4×C8—91no—
112D4⋊C8—32no—
113D4⋊C8—92no—
114C23×D3—62no—
115C2×C3×D4—32no—
116C22×C3×C4—62no—
117C2×#67—62no—
118C22×Dic3—62no—
119D3×D4—38no—
120D3×D4—64no—
121C2×D12C4×D312yes—
122C2×C4×D3—22no—
123C2×C4×D3—32no—
124C2×C4×D3—32no—
125C2×C4×D3—32no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—124no—
132C2×C4×D3—124no—
133C2×C3×C8—22no—
134C2×C3×C8—22no—
135C2×C3×C8—62no—
136C3×C4⋊C4—32no—
137C3×C22⋊C4—62no—
138C3×C42—21no—
139C3×C42C22×D312yes—
140#217—62no—
141(C2×D3)⋊C4—22no—
142(C2×D3)⋊C4—62no—
143C4⋊Dic3C4×D312yes—
144Dic3⋊C4—62no—
145C4×Dic3—32no—
146C4×Dic3—32no—
147C4×Dic3—32no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C2×C3⋊C8—22no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—62no—
154D3×C8—68no—
155D3×C8—124no—
156D3×C8—124no—
157C22×C32C2×C22⋊C411yescharacteristic
158C2×C3⋊D3C22⋊C812yes—
159C2×C3⋊D3#10212yes—
160C2×C3⋊D3#10412yes—
161C2×C3×D3—24no—
162C2×C3×D3—42no—
163C2×C3×D3—42no—
164D32—48no—
165C32×C4—21no—
166C32×C4C22×C811yescharacteristic
167C32×C4C2×M1611yescharacteristic
168C32×C4C2×D811yescharacteristic
169C32×C4C2×SD1611yescharacteristic
170C3⋊Dic3—21no—
171C3⋊Dic3C22⋊C812yes—
172C3⋊Dic3#10212yes—
173C3×Dic3—42no—
174C22×D4—91no—
175C23×C4—181no—
176C22×C8—181no—
177C22×C8—181no—
178C4×D4—32no—
179C4×D4—92no—
180C4×D4—181no—
181C4×D4—181no—
182C2×C4⋊C4—91no—
183C2×C22⋊C4—181no—
184C2×C42—91no—
185C4⋊C8—91no—
186C4⋊C8—181no—
187C4⋊C8D3211yescharacteristic, complemented
188C4×C8—32no—
189C4×C8—181no—
190C23×C3—62no—
191C22×D3—22no—
192C22×D3—32no—
193C22×D3—61no—
194C22×D3—68no—
195C22×D3—124no—
196C22×D3—124no—
197C3×D4—34no—
198C3×D4—62no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—62no—
203C2×C3×C4—122no—
204C2×C3×C4—122no—
205C2×C3×C4C2×C4×D312yes—
206C2×C3×C4D3×D412yes—
207C2×C3×C4D3×D412yes—
208#67—68no—
209C2×Dic3—22no—
210C2×Dic3—32no—
211C2×Dic3—32no—
212C2×Dic3—32no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—124no—
217D12—22no—
218D12D3×C814yescomplemented
219C4×D3—34no—
220C4×D3—34no—
221C4×D3—34no—
222C4×D3—34no—
223C4×D3—42no—
224C4×D3—42no—
225C4×D3—62no—
226C4×D3—62no—
227C4×D3—62no—
228C4×D3—62no—
229C4×D3—64no—
230C4×D3—122no—
231C4×D3—124no—
232C4×D3—124no—
233C3×C8—42no—
234C3×C8—42no—
235C3×C8—64no—
236C3⋊C8—24no—
237C3⋊C8—122no—
238C3⋊C8—122no—
239C2×C32C2×C22⋊C811yescharacteristic
240C2×C32C2×#10211yescharacteristic
241C2×C32C2×#10411yescharacteristic
242C3⋊D3D4⋊C814yescomplemented
243C3×D3—44no—
244C24—181no—
245C2×D4—32no—
246C2×D4—94no—
247C2×D4—182no—
248C2×D4—181no—
249C22×C4—62no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—91no—
253C22×C4—181no—
254C22×C4—182no—
255C22×C4—362no—
256C22×C4—362no—
257C2×C8—21no—
258C2×C8—62no—
259C2×C8—184no—
260C2×C8—181no—
261C2×C8—362no—
262C4⋊C4—32no—
263C4⋊C4—181no—
264C22⋊C4—62no—
265C22⋊C4—182no—
266C42—91no—
267C42—91no—
268C42—91no—
269C42C2×D3211yescharacteristic
270C22×C3—21no—
271C22×C3—64no—
272C22×C3—122no—
273C22×C3—122no—
274C22×C3D3×C22⋊C412yes—
275C2×D3—24no—
276C2×D3—34no—
277C2×D3—34no—
278C2×D3—34no—
279C2×D3—42no—
280C2×D3—42no—
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—1216no—
285C3×C4—22no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—41no—
291C3×C4—122no—
292C3×C4C2×D3×C812yes—
293C3×C4D3×M1612yes—
294C3×C4D3×D812yes—
295C3×C4D3×SD1612yes—
296Dic3—34no—
297Dic3—34no—
298Dic3—42no—
299Dic3—62no—
300Dic3—62no—
301Dic3—62no—
302Dic3—121no—
303C32C2×D4⋊C811yescharacteristic, complemented, Sylow
304C23—62no—
305C23—91no—
306C23—184no—
307C23—362no—
308C23—362no—
309D4—34no—
310D4—62no—
311D4—184no—
312C2×C4—62no—
313C2×C4—91no—
314C2×C4—91no—
315C2×C4—92no—
316C2×C4—92no—
317C2×C4—92no—
318C2×C4—92no—
319C2×C4—91no—
320C2×C4—122no—
321C2×C4—122no—
322C2×C4—182no—
323C2×C4—364no—
324C2×C4—362no—
325C2×C4C4×D3211yescharacteristic
326C2×C4#380211yescharacteristic
327C2×C4#381111yescharacteristic
328C8—41no—
329C8—64no—
330C8—361no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—124no—
335C2×C3D3×C22⋊C812yes—
336C2×C3D3×#10212yes—
337C2×C3D3×#10412yes—
338D3—38no—
339D3—44no—
340D3—64no—
341C22—64no—
342C22—92no—
343C22—92no—
344C22—92no—
345C22—122no—
346C22—122no—
347C22—368no—
348C22#6392111yescharacteristic
349C4—21no—
350C4—92no—
351C4—92no—
352C4—122no—
353C4—181no—
354C4D32×C811yescharacteristic
355C4#6379111yescharacteristic
356C4#6392611yescharacteristic
357C4#6394011yescharacteristic
358C3—21no—
359C3D3×D4⋊C812yescomplemented
360C2—94no—
361C2—124no—
362C2#1059059311yescharacteristic
363C2#1059093511yescharacteristic
364C2#1059100811yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32C2×D4⋊C8
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C4⋊C8C2semidirect
3. C4×#3710C2semidirect
4. C3×#4483C2semidirect
5. #10589081C2semidirect
18. C32×C4⋊C8C22semidirect
20. C4⋊(C3⋊(C3⋊C8))C22semidirect
21. C3×C4×C3⋊C8C22semidirect
29. #4483D3semidirect
41. #3802C8semidirect
74. C3×C4⋊C8C2×D3semidirect
81. C4×C3⋊C8C2×D3semidirect
100. C3×D12C2×C8semidirect
187. C4⋊C8D32semidirect
218. D12D3×C8semidirect
242. C3⋊D3D4⋊C8semidirect
303. C32C2×D4⋊C8semidirect
359. C3D3×D4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
C3⋊D3×C4⋊C82
C4×#37102
C3×#44832
#105890812
D3×D4⋊C83