Finite Group Databasebeta

← C22×D32⋊C8 #11857343

Subgroups — C22×D32⋊C8 #11857343

Order 1152.

1922 conjugacy classes of subgroups; only the 287 normal subgroups are shown.

normal subgroups only

This group has 1922 conjugacy classes of subgroups — too many to draw. Only its 287 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
1C22×C4×D32C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic, complemented
3C22×#3710C211yesmaximal, characteristic, complemented
4C2×D32⋊C8C2112yesmaximal, direct product factor
5C23×D32C411yescharacteristic
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×C3×C4×D3—21no—
8C22×#624C411yescharacteristic
9C22×D3×Dic3—21no—
10C2×C4×D32—23no—
11C2×C4×D32—23no—
12C2×C4×D32C416yes—
13C2×C4×D32C2216yes—
14C22×#622—21no—
15C2×#3787—23no—
16C2×#3787C2216yescomplemented
17C22×C3×C3⋊C8—21no—
18C2×#3710—23no—
19C2×#3710C2216yescomplemented
20D32⋊C8C22116yesdirect product factor
21C23×C4×D3—61no—
22C22×D3×C8—61no—
23C23×C3⋊D3C2×C411yescharacteristic
24C23×C3×D3—21no—
25C22×D32—23no—
26C22×D32—24no—
27C22×D32C818yescomplemented
28C22×D32C2×C416yes—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C2×C4×C3⋊D3C2×C413yes—
32C2×C4×C3⋊D3D413yes—
33C2×C4×C3⋊D3D413yes—
34C2×C4×C3⋊D3C2313yes—
35C22×C3×Dic3—21no—
36C2×C3×C4×D3—26no—
37C2×C3×C4×D3—26no—
38C2×#624—23no—
39C2×#624C2×C416yes—
40C2×D3×Dic3—26no—
41C2×D3×Dic3—26no—
42C4×D32—212no—
43C4×D32—26no—
44C4×D32—26no—
45C4×D32C2×C4112yes—
46C4×D32C2314yes—
47C2×#622—26no—
48#3787—26no—
49#3787C2314yescomplemented
50C2×C3×C3⋊C8—26no—
51#3710—26no—
52#3710C2314yescomplemented
53C22×C22⋊C8—91nomaximal, Sylow
54C24×D3—61no—
55C23×C3×C4—61no—
56C23×Dic3—61no—
57C22×C4×D3—21no—
58C22×C4×D3—66no—
59C22×C4×D3—66no—
60C22×C4×D3—61no—
61C22×C4×D3—61no—
62C22×C4×D3—61no—
63C22×C4×D3—66no—
64C22×C4×D3—66no—
65C22×C4×D3—61no—
66C22×C3×C8—61no—
67C22×C3⋊C8—21no—
68C2×D3×C8—66no—
69C2×D3×C8—66no—
70C23×C32C22⋊C411yescharacteristic
71C22×C3⋊D3C22⋊C413yes—
72C22×C3⋊D3C2×C814yes—
73C22×C3⋊D3M1614yes—
74C22×C3⋊D3C22×C413yes—
75C22×C3×D3—28no—
76C22×C3×D3—26no—
77C2×D32—224no—
78C2×D32—26no—
79C2×D32—212no—
80C2×D32C2×C8124yescomplemented
81C2×D32C22×C414yes—
82C2×C32×C4C22⋊C413yes—
83C2×C32×C4C2×D413yes—
84C2×C3⋊Dic3C22⋊C413yes—
85C2×C3⋊Dic3C2×D413yes—
86C4×C3⋊D3C22⋊C416yes—
87C4×C3⋊D3C22×C413yes—
88C4×C3⋊D3C2×D413yes—
89C4×C3⋊D3C2×D413yes—
90C4×C3⋊D3C2411yescharacteristic
91C2×C3×Dic3—26no—
92C3×C4×D3—212no—
93C3×C4×D3—24no—
94#624—26no—
95#624C22×C414yes—
96D3×Dic3—212no—
97D3×Dic3—24no—
98#622—24no—
99C3×C3⋊C8—24no—
100C24×C4—91no—
101C23×C8—91no—
102C23×C8—91no—
103C2×C22⋊C8—912no—
104C24×C3—61no—
105C23×D3—21no—
106C23×D3—68no—
107C23×D3—66no—
108C23×D3—61no—
109C23×D3—61no—
110C23×D3—66no—
111C23×D3—68no—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—66no—
115C22×C3×C4—66no—
116C22×C3×C4—61no—
117C22×Dic3—21no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120C22×Dic3—66no—
121C22×Dic3—66no—
122C2×C4×D3—26no—
123C2×C4×D3—26no—
124C2×C4×D3—612no—
125C2×C4×D3—64no—
126C2×C4×D3—66no—
127C2×C4×D3—63no—
128C2×C4×D3—63no—
129C2×C4×D3—63no—
130C2×C4×D3—63no—
131C2×C4×D3—63no—
132C2×C4×D3—63no—
133C2×C4×D3—63no—
134C2×C4×D3—63no—
135C2×C4×D3—624no—
136C2×C4×D3—612no—
137C2×C4×D3—612no—
138C2×C4×D3—66no—
139C2×C4×D3—66no—
140C2×C4×D3—66no—
141C2×C3×C8—66no—
142C2×C3⋊C8—26no—
143D3×C8—64no—
144D3×C8—612no—
145C22×C32C22⋊C814yescomplemented
146C22×C32C2×C22⋊C413yes—
147C2×C3⋊D3C22⋊C8112yescomplemented
148C2×C3⋊D3C2×C22⋊C413yes—
149C2×C3⋊D3C22×C816yes—
150C2×C3⋊D3C2×M1616yes—
151C2×C3⋊D3C23×C411yescharacteristic
152C2×C3×D3—24no—
153C2×C3×D3—224no—
154D32—24no—
155D32—224no—
156D32C22×C818yescomplemented
157C32×C4C2×C22⋊C413yes—
158C32×C4C22×D411yescharacteristic
159C3⋊Dic3C2×C22⋊C413yes—
160C3⋊Dic3C22×D411yescharacteristic
161C3×Dic3—24no—
162C25—91no—
163C23×C4—61no—
164C23×C4—96no—
165C23×C4—91no—
166C23×C4—96no—
167C23×C4—91no—
168C23×C4—183no—
169C23×C4—183no—
170C23×C4—181no—
171C22×C8—61no—
172C22×C8—96no—
173C22×C8—96no—
174C22×C8—183no—
175C22×C8—183no—
176C22×C8—181no—
177C22⋊C8—916no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—66no—
181C23×C3—68no—
182C22×D3—26no—
183C22×D3—28no—
184C22×D3—624no—
185C22×D3—64no—
186C22×D3—63no—
187C22×D3—63no—
188C22×D3—64no—
189C22×D3—64no—
190C22×D3—64no—
191C22×D3—64no—
192C22×D3—63no—
193C22×D3—63no—
194C22×D3—612no—
195C22×D3—648no—
196C22×D3—624no—
197C2×C3×C4—23no—
198C2×C3×C4—23no—
199C2×C3×C4—23no—
200C2×C3×C4—23no—
201C2×C3×C4—64no—
202C2×C3×C4—612no—
203C2×C3×C4—66no—
204C2×Dic3—26no—
205C2×Dic3—63no—
206C2×Dic3—63no—
207C2×Dic3—63no—
208C2×Dic3—63no—
209C2×Dic3—612no—
210C2×Dic3—64no—
211C4×D3—24no—
212C4×D3—212no—
213C4×D3—64no—
214C4×D3—66no—
215C4×D3—66no—
216C4×D3—63no—
217C4×D3—63no—
218C4×D3—63no—
219C4×D3—63no—
220C4×D3—63no—
221C4×D3—63no—
222C4×D3—61no—
223C4×D3—61no—
224C4×D3—612no—
225C4×D3—612no—
226C4×D3—64no—
227C3×C8—64no—
228C3⋊C8—24no—
229C2×C32C2×C22⋊C816yescomplemented
230C2×C32C22×C22⋊C411yescharacteristic
231C3⋊D3C2×C22⋊C816yescomplemented
232C3⋊D3C23×C811yescharacteristic
233C3⋊D3C22×M1611yescharacteristic
234C3×D3—28no—
235C24—61no—
236C24—96no—
237C24—98no—
238C24—91no—
239C24—183no—
240C24—184no—
241C22×C4—61no—
242C22×C4—66no—
243C22×C4—66no—
244C22×C4—94no—
245C22×C4—96no—
246C22×C4—912no—
247C22×C4—91no—
248C22×C4—93no—
249C22×C4—93no—
250C22×C4—93no—
251C22×C4—93no—
252C22×C4—186no—
253C22×C4—186no—
254C22×C4—1812no—
255C22×C4—183no—
256C22×C4—186no—
257C22×C4—186no—
258C22×C4GO+(4,𝔽2)11yescharacteristic
259C2×C8—66no—
260C2×C8—94no—
261C2×C8—94no—
262C2×C8—186no—
263C2×C8—186no—
264C2×C8—186no—
265C22×C3—23no—
266C22×C3—23no—
267C22×C3—24no—
268C22×C3—24no—
269C22×C3—64no—
270C22×C3—624no—
271C2×D3—24no—
272C2×D3—224no—
273C2×D3—68no—
274C2×D3—63no—
275C2×D3—61no—
276C2×D3—63no—
277C2×D3—61no—
278C2×D3—612no—
279C2×D3—66no—
280C2×D3—66no—
281C2×D3—612no—
282C2×D3—66no—
283C2×D3—66no—
284C2×D3—68no—
285C2×D3—648no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—23no—
289C3×C4—23no—
290C3×C4—64no—
291Dic3—24no—
292Dic3—63no—
293Dic3—61no—
294Dic3—63no—
295Dic3—61no—
296C32C22×C22⋊C811yescharacteristic, complemented, Sylow
297C23—66no—
298C23—68no—
299C23—94no—
300C23—924no—
301C23—93no—
302C23—93no—
303C23—94no—
304C23—94no—
305C23—186no—
306C23—1812no—
307C23—1824no—
308C23D32⋊C411yescharacteristic
309C2×C4—66no—
310C2×C4—64no—
311C2×C4—612no—
312C2×C4—94no—
313C2×C4—93no—
314C2×C4—93no—
315C2×C4—91no—
316C2×C4—93no—
317C2×C4—93no—
318C2×C4—93no—
319C2×C4—96no—
320C2×C4—186no—
321C2×C4—184no—
322C2×C4—1812no—
323C2×C4D32⋊C413yes—
324C2×C4C2×GO+(4,𝔽2)13yes—
325C8—64no—
326C8—184no—
327C2×C3—26no—
328C2×C3—26no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—68no—
332D3—28no—
333D3—61no—
334D3—61no—
335D3—66no—
336D3—61no—
337D3—61no—
338D3—66no—
339C22—624no—
340C22—64no—
341C22—98no—
342C22—96no—
343C22—96no—
344C22—912no—
345C22—91no—
346C22—93no—
347C22—184no—
348C22—1824no—
349C22D32⋊C814yesdirect product factor
350C22C2×D32⋊C413yes—
351C4—64no—
352C4—91no—
353C4—93no—
354C4C2×D32⋊C413yes—
355C4C22×GO+(4,𝔽2)11yescharacteristic
356C3—21no—
357C3—21no—
358C2—68no—
359C2—91no—
360C2—96no—
361C2—91no—
362C2C2×D32⋊C816yesdirect product factor
363C2C22×D32⋊C411yescharacteristic
subgroupG/H
center, hypercenterC22×C4GO+(4,𝔽2)
commutatorC3⋊D3C23×C8
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C22⋊C4
prime radicalC23×D32C4
cosocleC4×C3⋊D3C24
hypocenterC32C22×C22⋊C8
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3787C2semidirect
3. C22×#3710C2semidirect
4. C2×D32⋊C8C2direct (N × H)
16. C2×#3787C22semidirect
19. C2×#3710C22semidirect
20. D32⋊C8C22direct (N × H)
27. C22×D32C8semidirect
49. #3787C23semidirect
52. #3710C23semidirect
80. C2×D32C2×C8semidirect
145. C22×C32C22⋊C8semidirect
147. C2×C3⋊D3C22⋊C8semidirect
156. D32C22×C8semidirect
229. C2×C32C2×C22⋊C8semidirect
231. C3⋊D3C2×C22⋊C8semidirect
296. C32C22×C22⋊C8semidirect
349. C22D32⋊C8direct (N × H)
362. C2C2×D32⋊C8direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D322
C22×#37872
C22×#37102
C2×D32⋊C82
C22×C22⋊C89