Finite Group Databasebeta

← C2×#10593822 #11857388

Subgroups — C2×#10593822 #11857388

Order 1152.

1682 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 1682 conjugacy classes of subgroups — too many to draw. Only its 218 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×#3830C211yesmaximal, characteristic
2C22×#3792C211yesmaximal, characteristic, complemented
3C23×#622C211yesmaximal, characteristic, complemented
4C2×C22⋊#622C212yesmaximal, complemented
5#10593822C218yesmaximal, direct product factor
6C2×#63778C212yesmaximal, complemented
7C22×C32×D4C411yescharacteristic
8C22×#638C411yescharacteristic
9C22×#638C411yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C2×#3830—24no—
13C2×#3830—24no—
14C2×#3830C414yes—
15C2×#3830C2214yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#634C411yescharacteristic
18C2×#3792—24no—
19C2×#3792C2214yescomplemented
20C22×#622—24no—
21C22×#622C2212yes—
22C22×#622C2212yes—
23C22×#622C2214yescomplemented
24C22⋊#622C2218yescomplemented
25#63778C2218yescomplemented
26C22×#237—62no—
27C24×C32C2×C411yescharacteristic
28C24×C32C2×C411yescharacteristic
29C23×C3⋊D3C2×C411yescharacteristic
30C2×C32×D4—24no—
31C2×C32×D4C2×C414yes—
32C22×C32×C4C2×C411yescharacteristic
33C2×#638—24no—
34C2×#638—24no—
35C2×#638C2×C414yes—
36C2×#638C2×C414yes—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3C2×C411yescharacteristic
40C22×C3⋊Dic3C2×C412yes—
41C22×C3⋊Dic3C2×C411yescharacteristic
42C22×C3⋊Dic3C2×C412yes—
43C22×C3⋊Dic3D414yes—
44C22×C3⋊Dic3D414yes—
45C22×C3⋊Dic3C2312yes—
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3⋊Dic3C2312yes—
48#3830—216no—
49#3830—28no—
50#3830—28no—
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3C2×C412yes—
54C2×C4×C3⋊D3C2312yes—
55C2×#634—24no—
56C2×#634C2×C414yes—
57#3792—28no—
58C2×#622—24no—
59C2×#622—28no—
60C2×#622—24no—
61C2×#622C2314yes—
62C2×#622C2314yes—
63C2×#408—91nomaximal, Sylow
64C22×C3×D4—22no—
65C22×#67—62no—
66C22×#67—62no—
67C23×Dic3—62no—
68C23×Dic3—62no—
69C2×#237—68no—
70C2×#237—68no—
71C2×#237—616no—
72C2×#237—616no—
73C22×C4×D3—62no—
74C22×Dic6—62no—
75C23×C32—22no—
76C23×C32—24no—
77C23×C32—24no—
78C23×C32C22⋊C414yes—
79C23×C32C22×C412yes—
80C23×C32C22×C412yes—
81C23×C32C22×C411yescharacteristic
82C22×C3⋊D3—22no—
83C22×C3⋊D3—24no—
84C22×C3⋊D3C22×C412yes—
85C32×D4—28no—
86C2×C32×C4—22no—
87C2×C32×C4C22×C412yes—
88#638—28no—
89#638—28no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3C22⋊C414yes—
95C2×C3⋊Dic3C22⋊C418yes—
96C2×C3⋊Dic3C22×C412yes—
97C2×C3⋊Dic3C22×C412yes—
98C2×C3⋊Dic3C22×C411yescharacteristic
99C2×C3⋊Dic3C2×D412yes—
100C2×C3⋊Dic3C2×D412yes—
101C2×C3⋊Dic3C2×D414yes—
102C2×C3⋊Dic3C2×D414yes—
103C2×C3⋊Dic3C2411yescharacteristic
104C4×C3⋊D3—24no—
105C4×C3⋊D3—22no—
106C4×C3⋊D3—22no—
107#634—28no—
108#622—24no—
109#622—24no—
110C22×#41—91no—
111C22×M16—91no—
112C23×C8—91no—
113#408—98no—
114C2×C22⋊C8—92no—
115C2×C22⋊C8—92no—
116C24×C3—22no—
117C24×C3—22no—
118C23×D3—62no—
119C2×C3×D4—216no—
120C2×C3×D4—28no—
121C22×C3×C4—22no—
122C2×#67—68no—
123C2×#67—68no—
124C2×#67—616no—
125C2×#67—616no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128C22×Dic3—62no—
129C22×Dic3—64no—
130C22×Dic3—64no—
131C22×Dic3—68no—
132C22×Dic3—68no—
133C22×Dic3—64no—
134C22×Dic3—64no—
135C22×Dic3—68no—
136C22×Dic3—68no—
137#237—664no—
138#237—632no—
139#237—632no—
140C2×C4×D3—64no—
141C2×C4×D3—64no—
142C2×C4×D3—68no—
143C2×C4×D3—68no—
144C2×Dic6—68no—
145C2×Dic6—616no—
146C22×C32—22no—
147C22×C32—24no—
148C22×C32—28no—
149C22×C32—24no—
150C22×C32—44no—
151C22×C32C2×C22⋊C414yes—
152C22×C32C2×C22⋊C412yes—
153C22×C32#13114yes—
154C22×C32C23×C411yescharacteristic
155C2×C3⋊D3—22no—
156C2×C3⋊D3—24no—
157C2×C3⋊D3—44no—
158C32×C4—22no—
159C3⋊Dic3—22no—
160C3⋊Dic3C2×C22⋊C414yes—
161C3⋊Dic3C2×C22⋊C412yes—
162C3⋊Dic3C22×D411yescharacteristic
163C3⋊Dic3C22×D411yescharacteristic
164C2×#41—94no—
165C2×#41—94no—
166C2×#41—184no—
167C2×#41—184no—
168C22×Q8—91no—
169C22×D4—91no—
170C22×D4—91no—
171C22×D4#15711yescharacteristic
172C23×C4—91no—
173C23×C4—91no—
174C23×C4—91no—
175C2×M16—94no—
176C2×M16—184no—
177C22×C8—92no—
178C22×C8—92no—
179C22×C8—94no—
180C22×C8—184no—
181C22⋊C8—98no—
182C22⋊C8—98no—
183C23×C3—28no—
184C23×C3—24no—
185C23×C3—24no—
186C23×C3—22no—
187C23×C3—28no—
188C23×C3—48no—
189C23×C3—48no—
190C22×D3—64no—
191C22×D3—68no—
192C22×D3—128no—
193C3×D4—232no—
194C2×C3×C4—28no—
195C2×C3×C4—24no—
196#67—632no—
197#67—632no—
198C2×Dic3—68no—
199C2×Dic3—616no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—62no—
203C2×Dic3—64no—
204C2×Dic3—64no—
205C2×Dic3—68no—
206C2×Dic3—68no—
207C2×Dic3—62no—
208C2×Dic3—68no—
209C2×Dic3—616no—
210C2×Dic3—68no—
211C2×Dic3—68no—
212C4×D3—616no—
213C4×D3—68no—
214C4×D3—68no—
215Dic6—632no—
216C2×C32—24no—
217C2×C32—42no—
218C2×C32#40814yescomplemented
219C2×C32C22×C22⋊C411yescharacteristic
220C2×C32C2×#13112yes—
221C3⋊D3—42no—
222C24—91no—
223C24C2×#15711yescharacteristic
224C24C2×#15711yescharacteristic
225#41—188no—
226#41—188no—
227#41—1816no—
228C2×Q8—94no—
229C2×Q8—184no—
230C2×D4—24no—
231C2×D4—94no—
232C2×D4—94no—
233C2×D4—184no—
234C2×D4—184no—
235C2×D4C2×#15714yes—
236C22×C4—92no—
237C22×C4—92no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—94no—
241C22×C4—94no—
242C22×C4—92no—
243C22×C4—92no—
244C22×C4—91no—
245C22×C4—92no—
246C22×C4—92no—
247C22×C4—182no—
248C22×C4—182no—
249C22×C4—182no—
250C22×C4—182no—
251C22×C4C2×#15711yescharacteristic
252M16—188no—
253C2×C8—94no—
254C2×C8—94no—
255C2×C8—184no—
256C2×C8—188no—
257C2×C8—184no—
258C22×C3—28no—
259C22×C3—28no—
260C22×C3—24no—
261C22×C3—28no—
262C22×C3—22no—
263C22×C3—416no—
264C22×C3—48no—
265C22×C3—48no—
266C22×C3—416no—
267C2×D3—68no—
268C2×D3—128no—
269C2×D3—1216no—
270C3×C4—28no—
271Dic3—68no—
272Dic3—64no—
273Dic3—62no—
274Dic3—62no—
275Dic3—68no—
276C32C2×#40811yescharacteristic, complemented, Sylow
277C23—24no—
278C23—24no—
279C23—22no—
280C23—92no—
281C23—184no—
282C23—182no—
283C23C22⋊#15714yes—
284C23C22×#15712yes—
285C23C22×#15712yes—
286C23C22×#15711yescharacteristic
287Q8—188no—
288D4—28no—
289D4—188no—
290D4—188no—
291C2×C4—22no—
292C2×C4—92no—
293C2×C4—92no—
294C2×C4—94no—
295C2×C4—94no—
296C2×C4—94no—
297C2×C4—98no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—92no—
301C2×C4—92no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4—184no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—184no—
308C2×C4—182no—
309C2×C4C22×#15712yes—
310C8—184no—
311C8—184no—
312C2×C3—28no—
313C2×C3—24no—
314C2×C3—22no—
315C2×C3—48no—
316C2×C3—48no—
317D3—128no—
318C22—28no—
319C22—24no—
320C22—24no—
321C22—22no—
322C22—44no—
323C22—184no—
324C22—182no—
325C22—364no—
326C22#6428714yes—
327C22C2×C22⋊#15714yes—
328C22C2×C22⋊#15712yes—
329C22C23×#15711yescharacteristic
330C4—22no—
331C4—91no—
332C4—91no—
333C4—92no—
334C4—94no—
335C4—182no—
336C3—22no—
337C2—24no—
338C2—42no—
339C2—362no—
340C2#1059382214yesdirect product factor
341C2C2×#6428712yes—
342C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC22×C32×D4C4
socleC23×C32C22×C4
prime radicalC22×#3830C2
cosocleC2×C3⋊Dic3C24
hypercenterC22×D4#157
hypocenterC32C2×#408
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×#3792C2semidirect
3. C23×#622C2semidirect
4. C2×C22⋊#622C2semidirect
5. #10593822C2direct (N × H)
6. C2×#63778C2semidirect
19. C2×#3792C22semidirect
23. C22×#622C22semidirect
24. C22⋊#622C22semidirect
25. #63778C22semidirect
218. C2×C32#408semidirect
276. C32C2×#408semidirect
340. C2#10593822direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×#37922
C23×#6222
C2×C22⋊#6222
#105938222
C2×#637782
C2×#4089