Finite Group Databasebeta

← C2×#10590163 #11783235

Subgroups — C2×#10590163 #11783235

Order 1152.

930 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#157C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic
3C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
4#10590163C214yesmaximal, direct product factor
5C23×#157—21no—
6C22×C4×C3⋊D3—21no—
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#622—21no—
9C2×C4⋊#157—22no—
10C2×C4⋊#157—21no—
11C2×C4⋊#157C414yescomplemented
12C2×C4⋊#157C2212yes—
13C2×#3787—21no—
14C2×#3787—22no—
15C2×#3787C414yescomplemented
16C2×#3787C2212yes—
17C2×C32×C4⋊C4C411yescharacteristic, complemented
18C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
19C2×#3750—21no—
20C4⋊C4×C3⋊D3—21no—
21C4⋊C4×C3⋊D3—21no—
22C4⋊C4×C3⋊D3C412yescomplemented
23C4⋊C4×C3⋊D3C2212yes—
24C2×D3×C4⋊C4—62no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—24no—
27C22×#157—22no—
28C22×#157—42no—
29C22×#157—42no—
30C22×C32×C4—21no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3—42no—
37C2×C4×C3⋊D3—42no—
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3C2×C412yes—
40C2×C4×C3⋊D3C2×C412yes—
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D412yes—
44C2×C4×C3⋊D3Q812yes—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×#622—24no—
47C2×#622—22no—
48C4⋊#157—24no—
49C4⋊#157—22no—
50C4⋊#157C2×C414yescomplemented
51#3787—24no—
52#3787—22no—
53#3787C2×C414yescomplemented
54C32×C4⋊C4—21no—
55C32×C4⋊C4C2×C412yescomplemented
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)C2×C412yescomplemented
58#3750—22no—
59#3750—22no—
60C2×#340—91nomaximal, Sylow
61C22×C4×D3—62no—
62C22×C4×D3—64no—
63C2×C3×C4⋊C4—22no—
64C2×C4⋊Dic3—62no—
65C2×Dic3⋊C4—64no—
66D3×C4⋊C4—64no—
67D3×C4⋊C4—64no—
68D3×C4⋊C4—64no—
69D3×C4⋊C4—64no—
70C23×C32C22⋊C411yescharacteristic
71C22×C3⋊D3C22⋊C411yescharacteristic
72C22×C3⋊D3C22⋊C412yes—
73C22×C3⋊D3C4⋊C412yes—
74C22×C3⋊D3D812yes—
75C22×C3⋊D3SD1612yes—
76C22×C3⋊D3SD1612yes—
77C22×C3⋊D3Q1612yes—
78C22×C3⋊D3C2×D411yescharacteristic
79C2×#157—24no—
80C2×#157—48no—
81C2×#157—42no—
82C2×#157—42no—
83C2×C32×C4—22no—
84C2×C32×C4—42no—
85C2×C32×C4C4212yes—
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C32×C4C4⋊C412yes—
88C2×C32×C4C22×C411yescharacteristic
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—42no—
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C22⋊C412yes—
93C2×C3⋊Dic3C4⋊C412yes—
94C2×C3⋊Dic3C2×D411yescharacteristic
95C4×C3⋊D3—44no—
96C4×C3⋊D3—42no—
97C4×C3⋊D3—42no—
98C4×C3⋊D3C4212yes—
99C4×C3⋊D3C22⋊C412yes—
100C4×C3⋊D3C22⋊C412yes—
101C4×C3⋊D3C4⋊C412yes—
102C4×C3⋊D3C4⋊C412yes—
103C4×C3⋊D3C4⋊C412yes—
104C4×C3⋊D3C22×C411yescharacteristic
105C4×C3⋊D3C22×C411yescharacteristic
106C4×C3⋊D3C2×D411yescharacteristic
107C4×C3⋊D3C2×Q811yescharacteristic
108#622—24no—
109C23×C8—91no—
110C22×C4⋊C4—91no—
111C22×C4⋊C4—91no—
112#340—94no—
113C23×D3—62no—
114C22×C3×C4—24no—
115C22×C3×C4—22no—
116C22×Dic3—62no—
117C22×Dic3—64no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—64no—
123C2×C4×D3—64no—
124C2×C4×D3—64no—
125C2×C4×D3—64no—
126C2×C4×D3—68no—
127C2×C4×D3—68no—
128C2×C4×D3—128no—
129C2×C4×D3—128no—
130C3×C4⋊C4—24no—
131C3×C4⋊C4—24no—
132C4⋊Dic3—64no—
133C4⋊Dic3—64no—
134Dic3⋊C4—68no—
135Dic3⋊C4—68no—
136C22×C32#9512yes—
137C22×C32#10212yes—
138C22×C32#10312yes—
139C22×C32C2×C22⋊C411yescharacteristic
140C2×C3⋊D3#9512yes—
141C2×C3⋊D3#10212yes—
142C2×C3⋊D3#10214yes—
143C2×C3⋊D3#10312yes—
144C2×C3⋊D3#10314yes—
145C2×C3⋊D3#10614yes—
146C2×C3⋊D3#10714yes—
147C2×C3⋊D3C2×C22⋊C411yescharacteristic
148C2×C3⋊D3C2×C4⋊C411yescharacteristic
149C2×C3⋊D3C2×D811yescharacteristic
150C2×C3⋊D3C2×SD1611yescharacteristic
151C2×C3⋊D3C2×SD1611yescharacteristic
152C2×C3⋊D3C2×Q1611yescharacteristic
153#157—44no—
154C32×C4—42no—
155C32×C4#9512yes—
156C32×C4C2×C4211yescharacteristic
157C32×C4C2×C4⋊C411yescharacteristic
158C3⋊Dic3—42no—
159C3⋊Dic3#9512yes—
160C3⋊Dic3C2×C22⋊C411yescharacteristic
161C3⋊Dic3C2×C4⋊C411yescharacteristic
162C23×C4—91no—
163C23×C4—181no—
164C23×C4—181no—
165C22×C8—94no—
166C22×C8—92no—
167C22×C8—182no—
168C22×C8—181no—
169C22×C8—181no—
170C2×C4⋊C4—94no—
171C2×C4⋊C4—92no—
172C2×C4⋊C4—91no—
173C2×C4⋊C4—92no—
174C2×C4⋊C4—92no—
175C2×C4⋊C4—181no—
176C2×C4⋊C4—181no—
177C2×C4⋊C4—181no—
178C2×C4⋊C4—182no—
179C2×C4⋊C4—181no—
180C2×C4⋊C4#15711yescharacteristic, complemented
181C23×C3—22no—
182C22×D3—62no—
183C22×D3—64no—
184C22×D3—64no—
185C22×D3—64no—
186C22×D3—64no—
187C22×D3—64no—
188C22×D3—64no—
189C22×D3—62no—
190C2×C3×C4—28no—
191C2×C3×C4—22no—
192C2×C3×C4—24no—
193C2×C3×C4—24no—
194C2×C3×C4—22no—
195C2×C3×C4—48no—
196C2×Dic3—62no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—62no—
200C2×Dic3—68no—
201C2×Dic3—128no—
202C4×D3—64no—
203C4×D3—64no—
204C4×D3—64no—
205C4×D3—64no—
206C4×D3—64no—
207C4×D3—64no—
208C4×D3—62no—
209C4×D3—62no—
210C4×D3—62no—
211C4×D3—62no—
212C4×D3—1216no—
213C4×D3—128no—
214C4×D3—128no—
215C2×C32#34014yescomplemented
216C2×C32C2×#9511yescharacteristic
217C2×C32C2×#10211yescharacteristic
218C2×C32C2×#10311yescharacteristic
219C3⋊D3#34014yescomplemented
220C3⋊D3C2×#10211yescharacteristic
221C3⋊D3C2×#10311yescharacteristic
222C3⋊D3C2×#10611yescharacteristic
223C3⋊D3C2×#10711yescharacteristic
224C24—91no—
225C22×C4—21no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—92no—
230C22×C4—92no—
231C22×C4—92no—
232C22×C4—92no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4—182no—
236C22×C4—182no—
237C22×C4—184no—
238C22×C4—182no—
239C22×C4—181no—
240C22×C4—362no—
241C22×C4—362no—
242C22×C4—362no—
243C22×C4—362no—
244C22×C4C2×#15711yescharacteristic
245C2×C8—94no—
246C2×C8—182no—
247C2×C8—184no—
248C2×C8—184no—
249C2×C8—182no—
250C4⋊C4—21no—
251C4⋊C4—94no—
252C4⋊C4—92no—
253C4⋊C4—182no—
254C4⋊C4—182no—
255C4⋊C4—182no—
256C4⋊C4—184no—
257C4⋊C4—181no—
258C4⋊C4C2×#15712yescomplemented
259C22×C3—24no—
260C22×C3—22no—
261C22×C3—24no—
262C22×C3—24no—
263C2×D3—64no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—64no—
267C2×D3—62no—
268C2×D3—62no—
269C2×D3—68no—
270C2×D3—64no—
271C2×D3—68no—
272C2×D3—68no—
273C2×D3—68no—
274C2×D3—62no—
275C2×D3—62no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—24no—
279C3×C4—48no—
280Dic3—64no—
281Dic3—62no—
282Dic3—62no—
283Dic3—128no—
284C32C2×#34011yescharacteristic, complemented, Sylow
285C23—92no—
286C23—92no—
287C23—91no—
288C23—91no—
289C23—92no—
290C23—92no—
291C23—92no—
292C23—92no—
293C23C22⋊#15711yescharacteristic
294C2×C4—22no—
295C2×C4—42no—
296C2×C4—92no—
297C2×C4—92no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—92no—
303C2×C4—91no—
304C2×C4—91no—
305C2×C4—92no—
306C2×C4—92no—
307C2×C4—92no—
308C2×C4—92no—
309C2×C4—92no—
310C2×C4—184no—
311C2×C4—182no—
312C2×C4—362no—
313C2×C4—362no—
314C2×C4—364no—
315C2×C4—362no—
316C2×C4—362no—
317C2×C4—368no—
318C2×C4—362no—
319C2×C4C4×#15712yes—
320C2×C4C4⋊#15712yes—
321C2×C4C22⋊#15711yescharacteristic
322C2×C4C22×#15711yescharacteristic
323C8—184no—
324C2×C3—22no—
325C2×C3—22no—
326C2×C3—22no—
327C2×C3—28no—
328D3—68no—
329D3—62no—
330D3—62no—
331D3—62no—
332D3—62no—
333C22—91no—
334C22—91no—
335C22—92no—
336C22—91no—
337C22—91no—
338C22—92no—
339C22—91no—
340C22—91no—
341C22—92no—
342C22—94no—
343C22—94no—
344C22—94no—
345C22—94no—
346C22#6378112yes—
347C22#6378212yes—
348C22#6378412yes—
349C22C2×C22⋊#15711yescharacteristic
350C4—42no—
351C4—91no—
352C4—92no—
353C4—91no—
354C4—364no—
355C4—362no—
356C4#6378112yes—
357C4C2×C4×#15711yescharacteristic
358C4C2×C4⋊#15711yescharacteristic
359C3—22no—
360C2—91no—
361C2—91no—
362C2—91no—
363C2—91no—
364C2—94no—
365C2#1059016314yesdirect product factor
366C2C2×#6378111yescharacteristic
367C2C2×#6378211yescharacteristic
368C2C2×#6378411yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC23×C32C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32C2×#340
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590163C2direct (N × H)
11. C2×C4⋊#157C4semidirect
15. C2×#3787C4semidirect
17. C2×C32×C4⋊C4C4semidirect
18. C2×C4⋊(C3⋊Dic3)C4semidirect
22. C4⋊C4×C3⋊D3C4semidirect
50. C4⋊#157C2×C4semidirect
53. #3787C2×C4semidirect
55. C32×C4⋊C4C2×C4semidirect
57. C4⋊(C3⋊Dic3)C2×C4semidirect
180. C2×C4⋊C4#157semidirect
215. C2×C32#340semidirect
219. C3⋊D3#340semidirect
258. C4⋊C4C2×#157semidirect
284. C32C2×#340semidirect
365. C2#10590163direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C22×#37872
C2×C4⋊C4×C3⋊D32
#105901632
C2×#3409