Finite Group Databasebeta

← C8×D32⋊C4 #11783659

Subgroups — C8×D32⋊C4 #11783659

Order 1152.

634 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 119 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×D32×C8C211yesmaximal, characteristic
2C2×C8×#157C211yesmaximal, characteristic, complemented
3C4×D32⋊C4C211yesmaximal, characteristic
4C2×D32⋊C8C211yesmaximal, characteristic
5C8×#624C211yesmaximal, characteristic, complemented
6#10590044C211yesmaximal, characteristic, complemented
7#10590043C211yesmaximal, characteristic, complemented
8C2×C4×D32C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C2×D32⋊C4C412yes—
12C2×C8×C3⋊D3C2211yescharacteristic
13C2×C3×D3×C8—21no—
14C4×#624C2211yescharacteristic
15C2×#3710C2211yescharacteristic
16C2×#3710C2211yescharacteristic
17C2×D3×C3⋊C8—21no—
18D32×C8—22no—
19D32×C8C414yescomplemented
20C8×#157—22no—
21#63737C412yes—
22D32⋊C8C414yescomplemented
23C3×C8×Dic3—21no—
24Dic3×C3⋊C8—21no—
25C22×D3×C8—61no—
26C4×D3×C8—61no—
27C22×D32C2×C411yescharacteristic
28C22×#157C2×C412yes—
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×C3×C4×D3—21no—
31C2×#624C2×C411yescharacteristic
32C2×#624C2×C412yes—
33C2×D3×Dic3—21no—
34C4×D32—21no—
35C4×D32—21no—
36C4×D32C2×C412yes—
37C4×D32C2×C412yes—
38C2×#622—21no—
39C4×#157—21no—
40C4×#157—21no—
41#3787—21no—
42#3787C2×C412yes—
43D32⋊C4C818yesdirect product factor
44C2×C32×C8D411yescharacteristic
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C8×C3⋊D3C2×C412yes—
47C8×C3⋊D3D412yes—
48C3×C4×Dic3—21no—
49C2×C3×C3⋊C8—21no—
50C2×C3×C3⋊C8—21no—
51C3×D3×C8—24no—
52Dic32—21no—
53#3710—21no—
54#3710—21no—
55#3710C2×C412yes—
56#3710C2×C412yes—
57D3×C3⋊C8—24no—
58C8×C22⋊C4—91nomaximal, Sylow
59C22×C4×D3—61no—
60C22×C3×C8—61no—
61C22×C3⋊C8—61no—
62C2×D3×C8—21no—
63C2×D3×C8—64no—
64C2×D3×C8—61no—
65C2×D3×C8—61no—
66C2×D3×C8—61no—
67C2×D3×C8—61no—
68C2×D3×C8—64no—
69C2×D3×C8—61no—
70C42×D3—61no—
71C3×C4×C8—61no—
72C8×Dic3—21no—
73C8×Dic3—61no—
74C4×C3⋊C8—61no—
75C22×C3⋊D3C22×C411yescharacteristic
76C22×C3×D3—21no—
77C2×D32—21no—
78C2×D32—22no—
79C2×D32C4212yes—
80C2×D32C2×C814yes—
81C2×#157—22no—
82C2×#157—22no—
83C2×#157C2×C814yescomplemented
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3#4111yescharacteristic
86C4×C3⋊D3C22×C411yescharacteristic
87C4×C3⋊D3C22×C411yescharacteristic
88C4×C3⋊D3C2×D411yescharacteristic
89C4×C3⋊D3#4111yescharacteristic
90C2×C3×Dic3—22no—
91C2×C3×Dic3—21no—
92C3×C4×D3—22no—
93C3×C4×D3—22no—
94#624—21no—
95#624—22no—
96#624C4212yes—
97#624C2×C814yescomplemented
98D3×Dic3—22no—
99D3×Dic3—22no—
100#622—22no—
101C32×C8C22⋊C412yescomplemented
102C3⋊(C3⋊C8)C22⋊C412yescomplemented
103C3×C3⋊C8—22no—
104C3×C3⋊C8—22no—
105C23×C8—91no—
106C2×C22⋊C8—91no—
107C2×C4×C8—91no—
108C2×C4×C8—91no—
109C4×C22⋊C4—91no—
110#336—91no—
111#336—91no—
112C23×D3—61no—
113C22×C3×C4—61no—
114C22×Dic3—61no—
115C2×C4×D3—21no—
116C2×C4×D3—62no—
117C2×C4×D3—62no—
118C2×C4×D3—62no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—61no—
125C2×C3×C8—21no—
126C2×C3×C8—21no—
127C2×C3×C8—64no—
128C2×C3×C8—61no—
129C2×C3×C8—61no—
130C3×C42—61no—
131C4×Dic3—21no—
132C4×Dic3—62no—
133C2×C3⋊C8—21no—
134C2×C3⋊C8—21no—
135C2×C3⋊C8—61no—
136C2×C3⋊C8—61no—
137C2×C3⋊C8—64no—
138D3×C8—24no—
139D3×C8—62no—
140D3×C8—62no—
141D3×C8—62no—
142D3×C8—62no—
143D3×C8—62no—
144D3×C8—62no—
145D3×C8—62no—
146D3×C8—62no—
147D3×C8—64no—
148C22×C32C4×D411yescharacteristic
149C2×C3⋊D3C2×C4211yescharacteristic
150C2×C3⋊D3C4×D411yescharacteristic
151C2×C3⋊D3C22×C812yes—
152C2×C3⋊D3#13112yes—
153C2×C3×D3—22no—
154C2×C3×D3—24no—
155D32—22no—
156D32—24no—
157D32C4×C814yescomplemented
158#157—24no—
159C32×C4C2×C22⋊C411yescharacteristic
160C32×C4C4×D411yescharacteristic
161C3⋊Dic3#11711yescharacteristic
162C3⋊Dic3C4×D411yescharacteristic
163C3×Dic3—22no—
164C3×Dic3—24no—
165C23×C4—91no—
166C22×C8—61no—
167C22×C8—91no—
168C22×C8—94no—
169C22×C8—91no—
170C22×C8—91no—
171C22×C8—91no—
172C22×C8—182no—
173C22×C8—181no—
174C2×C22⋊C4—92no—
175C2×C42—91no—
176C2×C42—91no—
177C22⋊C8—94no—
178C4×C8—61no—
179C4×C8—181no—
180C4×C8—182no—
181#95—92no—
182C23×C3—61no—
183C22×D3—21no—
184C22×D3—62no—
185C22×D3—64no—
186C22×D3—61no—
187C22×D3—61no—
188C22×D3—62no—
189C22×D3—64no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—62no—
193C2×C3×C4—62no—
194C2×C3×C4—62no—
195C2×C3×C4—61no—
196C2×Dic3—22no—
197C2×Dic3—21no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C4×D3—22no—
203C4×D3—22no—
204C4×D3—62no—
205C4×D3—64no—
206C4×D3—61no—
207C4×D3—61no—
208C4×D3—61no—
209C4×D3—61no—
210C4×D3—61no—
211C4×D3—61no—
212C4×D3—61no—
213C4×D3—61no—
214C4×D3—64no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—62no—
218C3×C8—22no—
219C3×C8—22no—
220C3×C8—62no—
221C3×C8—62no—
222C3⋊C8—22no—
223C3⋊C8—22no—
224C3⋊C8—62no—
225C3⋊C8—62no—
226C2×C32C4×C22⋊C411yescharacteristic
227C2×C32C8×D412yes—
228C3⋊D3C2×C4×C811yescharacteristic
229C3⋊D3#40511yescharacteristic
230C3⋊D3C8×D412yes—
231C3×D3—24no—
232C24—91no—
233C22×C4—61no—
234C22×C4—91no—
235C22×C4—92no—
236C22×C4—92no—
237C22×C4—92no—
238C22×C4—91no—
239C22×C4—92no—
240C22×C4—181no—
241C22×C4—181no—
242C22×C4—181no—
243C2×C8—61no—
244C2×C8—61no—
245C2×C8—64no—
246C2×C8—92no—
247C2×C8—92no—
248C2×C8—91no—
249C2×C8—92no—
250C2×C8—92no—
251C2×C8—92no—
252C2×C8—181no—
253C2×C8—181no—
254C2×C8—184no—
255C2×C8—181no—
256C2×C8—181no—
257C2×C8GO+(4,𝔽2)11yescharacteristic
258C22⋊C4—98no—
259C42—61no—
260C42—181no—
261C42—181no—
262C42—181no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—62no—
266C22×C3—64no—
267C2×D3—22no—
268C2×D3—24no—
269C2×D3—64no—
270C2×D3—61no—
271C2×D3—61no—
272C2×D3—61no—
273C2×D3—61no—
274C2×D3—62no—
275C2×D3—62no—
276C2×D3—62no—
277C2×D3—62no—
278C2×D3—64no—
279C2×D3—68no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—62no—
285C3×C4—64no—
286Dic3—22no—
287Dic3—24no—
288Dic3—61no—
289Dic3—61no—
290Dic3—61no—
291Dic3—61no—
292C32C8×C22⋊C411yescharacteristic, complemented, Sylow
293C23—61no—
294C23—94no—
295C23—92no—
296C23—91no—
297C23—181no—
298C23—182no—
299C2×C4—62no—
300C2×C4—61no—
301C2×C4—62no—
302C2×C4—62no—
303C2×C4—94no—
304C2×C4—92no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—94no—
311C2×C4—181no—
312C2×C4—182no—
313C2×C4—182no—
314C2×C4—182no—
315C2×C4—182no—
316C2×C4—182no—
317C2×C4C2×GO+(4,𝔽2)11yescharacteristic
318C8—62no—
319C8—62no—
320C8—92no—
321C8—182no—
322C8D32⋊C412yesdirect product factor
323C2×C3—22no—
324C2×C3—22no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—64no—
328D3—24no—
329D3—61no—
330D3—61no—
331D3—62no—
332D3—61no—
333D3—61no—
334D3—62no—
335C22—64no—
336C22—62no—
337C22—94no—
338C22—92no—
339C22—92no—
340C22—91no—
341C22—91no—
342C22—184no—
343C22—182no—
344C22C4×GO+(4,𝔽2)11yescharacteristic
345C4—64no—
346C4—62no—
347C4—91no—
348C4—91no—
349C4—184no—
350C4C4×GO+(4,𝔽2)11yescharacteristic
351C4C2×D32⋊C411yescharacteristic
352C3—21no—
353C3—21no—
354C2—64no—
355C2—92no—
356C2—91no—
357C2—91no—
358C2C8×GO+(4,𝔽2)12yes—
359C2C4×D32⋊C411yescharacteristic
subgroupG/H
center, hypercenterC2×C8GO+(4,𝔽2)
commutatorC3⋊D3C2×C4×C8
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC22×D32C2×C4
cosocleC2×C4×C3⋊D3C23
hypocenterC32C8×C22⋊C4
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×#157C2semidirect
5. C8×#624C2semidirect
6. #10590044C2semidirect
7. #10590043C2semidirect
19. D32×C8C4semidirect
22. D32⋊C8C4semidirect
43. D32⋊C4C8direct (N × H)
83. C2×#157C2×C8semidirect
97. #624C2×C8semidirect
101. C32×C8C22⋊C4semidirect
102. C3⋊(C3⋊C8)C22⋊C4semidirect
157. D32C4×C8semidirect
292. C32C8×C22⋊C4semidirect
322. C8D32⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D32×C82
C2×C8×#1572
C4×D32⋊C42
C2×D32⋊C82
C8×#6242
#105900442
#105900432
C8×C22⋊C49