Finite Group Databasebeta

← C2×#10593803 #11857358

Subgroups — C2×#10593803 #11857358

Order 1152.

2370 conjugacy classes of subgroups; only the 242 normal subgroups are shown.

normal subgroups only

This group has 2370 conjugacy classes of subgroups — too many to draw. Only its 242 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
1C23×C4×C3⋊D3C211yesmaximal, characteristic
2C22×#3788C212yesmaximal, complemented
3C2×C22⋊#622C212yesmaximal, complemented
4#10593803C218yesmaximal, direct product factor
5C2×#63778C212yesmaximal, complemented
6C24×C3⋊D3C411yescharacteristic
7C23×C32×C4C411yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C22×C4×C3⋊D3—28no—
10C22×C4×C3⋊D3C414yes—
11C22×C4×C3⋊D3C411yescharacteristic
12C22×C4×C3⋊D3C411yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2214yes—
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#622C2214yescomplemented
17C2×#3788—28no—
18C2×#3788C2218yescomplemented
19C22⋊#622C2218yescomplemented
20#63778C2218yescomplemented
21C23×C4×D3—62no—
22C24×C32C2×C411yescharacteristic
23C23×C3⋊D3—24no—
24C23×C3⋊D3—24no—
25C23×C3⋊D3—24no—
26C23×C3⋊D3C2×C414yes—
27C23×C3⋊D3C2×C411yescharacteristic
28C23×C3⋊D3C2×C411yescharacteristic
29C22×C32×C4—24no—
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4C2×C414yes—
32C22×C32×C4C2×C411yescharacteristic
33C22×C3⋊Dic3—24no—
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C412yes—
36C22×C3⋊Dic3C2312yes—
37C22×C3⋊Dic3C2311yescharacteristic
38C2×C4×C3⋊D3—24no—
39C2×C4×C3⋊D3—24no—
40C2×C4×C3⋊D3—24no—
41C2×C4×C3⋊D3—216no—
42C2×C4×C3⋊D3—216no—
43C2×C4×C3⋊D3C2×C414yes—
44C2×C4×C3⋊D3C2×C414yes—
45C2×C4×C3⋊D3C2×C412yes—
46C2×C4×C3⋊D3C2×C412yes—
47C2×C4×C3⋊D3D418yes—
48C2×C4×C3⋊D3C2312yes—
49C2×C4×C3⋊D3C2312yes—
50C2×#622—28no—
51C2×#622C2318yescomplemented
52#3788—216no—
53C2×#407—91nomaximal, Sylow
54C24×D3—62no—
55C23×C3×C4—22no—
56C23×Dic3—62no—
57C22×C4×D3—68no—
58C22×C4×D3—62no—
59C22×C4×D3—62no—
60C22×C4×D3—62no—
61C22×C4×D3—62no—
62C22×C4×D3—68no—
63C22×C4×D3—632no—
64C23×C32—22no—
65C23×C32—22no—
66C23×C32M1614yescomplemented
67C23×C32C22×C412yes—
68C23×C32C22×C411yescharacteristic
69C22×C3⋊D3—232no—
70C22×C3⋊D3—22no—
71C22×C3⋊D3—22no—
72C22×C3⋊D3—22no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3—28no—
75C22×C3⋊D3—28no—
76C22×C3⋊D3—28no—
77C22×C3⋊D3C22⋊C414yes—
78C22×C3⋊D3M1614yescomplemented
79C22×C3⋊D3C22×C412yes—
80C22×C3⋊D3C22×C412yes—
81C2×C32×C4—22no—
82C2×C32×C4—28no—
83C2×C32×C4C22⋊C414yes—
84C2×C32×C4C22×C412yes—
85C2×C32×C4C22×C412yes—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—24no—
88C2×C3⋊Dic3—24no—
89C2×C3⋊Dic3C22×C412yes—
90C2×C3⋊Dic3C22×C411yescharacteristic
91C2×C3⋊Dic3C2×D414yes—
92C2×C3⋊Dic3C2411yescharacteristic
93C4×C3⋊D3—28no—
94C4×C3⋊D3—28no—
95C4×C3⋊D3—24no—
96C4×C3⋊D3—24no—
97C4×C3⋊D3C22⋊C418yes—
98C4×C3⋊D3C2×D418yes—
99#622—28no—
100C24×C4—91no—
101C22×M16—92no—
102#407—98no—
103C2×C22⋊C8—92no—
104C2×C22⋊C8—92no—
105C24×C3—22no—
106C23×D3—62no—
107C23×D3—62no—
108C23×D3—68no—
109C23×D3—616no—
110C23×D3—616no—
111C23×D3—616no—
112C22×C3×C4—216no—
113C22×C3×C4—28no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×Dic3—64no—
117C22×Dic3—62no—
118C22×Dic3—62no—
119C22×Dic3—64no—
120C22×Dic3—616no—
121C2×C4×D3—64no—
122C2×C4×D3—64no—
123C2×C4×D3—68no—
124C2×C4×D3—68no—
125C2×C4×D3—616no—
126C2×C4×D3—64no—
127C2×C4×D3—64no—
128C2×C4×D3—664no—
129C2×C4×D3—664no—
130C2×C4×D3—616no—
131C2×C4×D3—616no—
132C2×C4×D3—616no—
133C22×C32—22no—
134C22×C32—22no—
135C22×C32—28no—
136C22×C32C2×C22⋊C412yes—
137C22×C32C2×M1612yes—
138C22×C32C2×M1612yes—
139C22×C32C2×M1614yescomplemented
140C22×C32C23×C411yescharacteristic
141C2×C3⋊D3—232no—
142C2×C3⋊D3—22no—
143C2×C3⋊D3—22no—
144C2×C3⋊D3—22no—
145C2×C3⋊D3—22no—
146C2×C3⋊D3—28no—
147C2×C3⋊D3—28no—
148C2×C3⋊D3C2×C22⋊C414yes—
149C2×C3⋊D3C2×M1614yescomplemented
150C32×C4—22no—
151C32×C4C2×C22⋊C414yes—
152C3⋊Dic3—22no—
153C3⋊Dic3C2×C22⋊C412yes—
154C3⋊Dic3C22×D412yes—
155C25—91no—
156C23×C4—91no—
157C23×C4—91no—
158C23×C4—91no—
159C23×C4—94no—
160C23×C4—94no—
161C23×C4—91no—
162C23×C4—91no—
163C23×C4—188no—
164C23×C4#15711yescharacteristic
165C2×M16—98no—
166C2×M16—188no—
167C22×C8—94no—
168C22⋊C8—98no—
169C22⋊C8—98no—
170C23×C3—28no—
171C23×C3—28no—
172C23×C3—24no—
173C23×C3—22no—
174C23×C3—28no—
175C22×D3—68no—
176C22×D3—68no—
177C22×D3—64no—
178C22×D3—64no—
179C22×D3—632no—
180C22×D3—68no—
181C22×D3—632no—
182C22×D3—6128no—
183C22×D3—68no—
184C22×D3—68no—
185C22×D3—632no—
186C22×D3—68no—
187C2×C3×C4—28no—
188C2×C3×C4—232no—
189C2×C3×C4—24no—
190C2×C3×C4—24no—
191C2×C3×C4—28no—
192C2×Dic3—62no—
193C2×Dic3—64no—
194C2×Dic3—68no—
195C2×Dic3—62no—
196C2×Dic3—616no—
197C2×Dic3—616no—
198C2×Dic3—68no—
199C4×D3—616no—
200C4×D3—616no—
201C4×D3—616no—
202C4×D3—616no—
203C4×D3—632no—
204C4×D3—632no—
205C2×C32—24no—
206C2×C32#40714yescomplemented
207C2×C32C22×C22⋊C411yescharacteristic
208C2×C32C22×M1611yescharacteristic
209C2×C32C22×M1611yescharacteristic
210C3⋊D3—24no—
211C3⋊D3—24no—
212C24—91no—
213C24—91no—
214C24—94no—
215C24—184no—
216C24—184no—
217C24—184no—
218C24C2×#15711yescharacteristic
219C22×C4—24no—
220C22×C4—91no—
221C22×C4—92no—
222C22×C4—92no—
223C22×C4—98no—
224C22×C4—92no—
225C22×C4—92no—
226C22×C4—91no—
227C22×C4—92no—
228C22×C4—92no—
229C22×C4—94no—
230C22×C4—94no—
231C22×C4—184no—
232C22×C4—1816no—
233C22×C4—1816no—
234C22×C4—184no—
235C22×C4—184no—
236C22×C4—184no—
237C22×C4C2×#15714yes—
238C22×C4C2×#15711yescharacteristic
239C22×C4C2×#15711yescharacteristic
240M16—1816no—
241C2×C8—98no—
242C2×C8—188no—
243C22×C3—28no—
244C22×C3—232no—
245C22×C3—28no—
246C22×C3—24no—
247C22×C3—28no—
248C22×C3—24no—
249C22×C3—24no—
250C22×C3—22no—
251C2×D3—68no—
252C2×D3—68no—
253C2×D3—68no—
254C2×D3—6128no—
255C2×D3—632no—
256C2×D3—632no—
257C2×D3—68no—
258C2×D3—68no—
259C2×D3—68no—
260C3×C4—28no—
261C3×C4—28no—
262Dic3—64no—
263Dic3—64no—
264Dic3—68no—
265C32C2×#40711yescharacteristic, complemented, Sylow
266C23—22no—
267C23—22no—
268C23—94no—
269C23—94no—
270C23—92no—
271C23—92no—
272C23—188no—
273C23—188no—
274C23—1832no—
275C23—182no—
276C23—182no—
277C23—188no—
278C23—182no—
279C23—182no—
280C23#378814yescomplemented
281C23C22×#15712yes—
282C23C22×#15711yescharacteristic
283C2×C4—22no—
284C2×C4—28no—
285C2×C4—94no—
286C2×C4—91no—
287C2×C4—91no—
288C2×C4—98no—
289C2×C4—98no—
290C2×C4—92no—
291C2×C4—184no—
292C2×C4—184no—
293C2×C4—188no—
294C2×C4—184no—
295C2×C4—184no—
296C2×C4—182no—
297C2×C4—188no—
298C2×C4C22⋊#15714yes—
299C2×C4C22×#15712yes—
300C2×C4C22×#15712yes—
301C8—188no—
302C2×C3—216no—
303C2×C3—28no—
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—22no—
307D3—616no—
308D3—616no—
309C22—28no—
310C22—22no—
311C22—22no—
312C22—94no—
313C22—94no—
314C22—1832no—
315C22—188no—
316C22—188no—
317C22—182no—
318C22—182no—
319C22—182no—
320C22—182no—
321C22C2×#378812yes—
322C22C2×#378814yescomplemented
323C22#6428312yes—
324C22C2×C22⋊#15712yes—
325C22C23×#15711yescharacteristic
326C4—22no—
327C4—92no—
328C4—92no—
329C4—182no—
330C4C2×C22⋊#15714yes—
331C3—22no—
332C2—24no—
333C2—184no—
334C2—184no—
335C2#1059380314yesdirect product factor
336C2C22×#378811yescharacteristic
337C2C2×#6428311yescharacteristic
338C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC23×C32×C4C4
socleC23×C32C22×C4
prime radicalC24×C3⋊D3C4
cosocleC2×C3⋊Dic3C24
hypercenterC23×C4#157
hypocenterC32C2×#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3788C2semidirect
3. C2×C22⋊#622C2semidirect
4. #10593803C2direct (N × H)
5. C2×#63778C2semidirect
16. C22×#622C22semidirect
18. C2×#3788C22semidirect
19. C22⋊#622C22semidirect
20. #63778C22semidirect
51. C2×#622C23semidirect
66. C23×C32M16semidirect
78. C22×C3⋊D3M16semidirect
139. C22×C32C2×M16semidirect
149. C2×C3⋊D3C2×M16semidirect
206. C2×C32#407semidirect
265. C32C2×#407semidirect
280. C23#3788semidirect
322. C22C2×#3788semidirect
335. C2#10593803direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C22×#37882
C2×C22⋊#6222
#105938032
C2×#637782
C2×#4079