Finite Group Databasebeta

← C2×#10593367 #11868266

Subgroups — C2×#10593367 #11868266

Order 1152.

838 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 838 conjugacy classes of subgroups — too many to draw. Only its 135 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×#63919C211yesmaximal, characteristic, complemented
2C2×#63902C211yesmaximal, characteristic
3C2×#63779C211yesmaximal, characteristic, complemented
4C2×#63743C212yesmaximal, complemented
5C2×#63739C212yesmaximal
6#10593367C218yesmaximal, direct product factor
7C22×#627—21no—
8C22×#625C2211yescharacteristic
9C22×D3×Dic3—21no—
10C22×#622C2212yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×C4⋊Dic3—21no—
14C2×#3724C2211yescharacteristic
15C2×#3724C2212yes—
16#63919—22no—
17#63919C2214yescomplemented
18#63902—22no—
19#63902C2214yes—
20#63779C2214yescomplemented
21#63743C2218yescomplemented
22#63739C2218yes—
23C2×#888—61no—
24C2×#67⋊C4—61no—
25C23×C3×D3—21no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—22no—
30C22×C3×Dic3—21no—
31C2×#627—24no—
32C2×#627—44no—
33C2×#625—21no—
34C2×#625—22no—
35C2×#625Q814yescomplemented
36C2×#625C2312yes—
37C2×D3×Dic3—24no—
38C2×D3×Dic3—44no—
39C2×#622—24no—
40C2×#622C2314yes—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3C2312yes—
43C3×(C2×D3)⋊C4—24no—
44C3×C4⋊Dic3—24no—
45#3724—21no—
46#3724—22no—
47#3724C2312yes—
48#3724C2314yes—
49C2×#474—91nomaximal, Sylow
50C22×#67—61no—
51C23×Dic3—61no—
52C22×C4×D3—61no—
53C22×Dic6—62no—
54C2×C3×C4⋊C4—61no—
55C2×C3×C22⋊C4—61no—
56C2×(C2×D3)⋊C4—21no—
57C2×C4⋊Dic3—21no—
58C2×Dic3⋊C4—61no—
59C2×Dic3⋊C4—62no—
60C2×C4×Dic3—61no—
61C2×C4×Dic3—61no—
62#888—64no—
63#888—64no—
64#67⋊C4—64no—
65#67⋊C4—64no—
66C23×C32C2×D411yescharacteristic
67C22×C3×D3—24no—
68C22×C3×D3—22no—
69C22×C3×D3—42no—
70C22×C3×D3—42no—
71C2×C32×C4—22no—
72C2×C32×C4C2×D412yes—
73C2×C3⋊Dic3D814yes—
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3C2×D412yes—
76C2×C3⋊Dic3C2×Q812yes—
77C2×C3⋊Dic3#4112yes—
78C2×C3⋊Dic3C2411yescharacteristic
79C2×C3×Dic3—24no—
80C2×C3×Dic3—22no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—44no—
83#627—48no—
84#625—24no—
85#625—22no—
86#625C2×Q814yescomplemented
87D3×Dic3—48no—
88#622—24no—
89C2×C4⋊Q8—91no—
90C2×C4×D4—91no—
91#474—98no—
92C2×#107—92no—
93C2×C4⋊C8—91no—
94C2×#102—92no—
95C24×C3—61no—
96C23×D3—21no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—61no—
100C22×C3×C4—62no—
101C2×#67—62no—
102C2×#67—64no—
103C2×#67—62no—
104C2×#67—64no—
105C22×Dic3—22no—
106C22×Dic3—21no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111C22×Dic3—64no—
112C22×Dic3—124no—
113C2×C4×D3—64no—
114C2×C4×D3—124no—
115C2×Dic6—68no—
116C2×Dic6—128no—
117C3×C4⋊C4—64no—
118C3×C22⋊C4—64no—
119(C2×D3)⋊C4—24no—
120C4⋊Dic3—24no—
121Dic3⋊C4—62no—
122Dic3⋊C4—64no—
123Dic3⋊C4—62no—
124Dic3⋊C4—64no—
125C4×Dic3—62no—
126C4×Dic3—62no—
127C4×Dic3—62no—
128C4×Dic3—62no—
129C22×C32C22⋊Q812yes—
130C22×C32C2×D812yes—
131C22×C32#13712yes—
132C22×C32C22×D411yescharacteristic
133C2×C3×D3—24no—
134C2×C3×D3—42no—
135C2×C3×D3—42no—
136C2×C3×D3—48no—
137C32×C4—22no—
138C3⋊Dic3C22⋊Q812yes—
139C3⋊Dic3C2×D814yes—
140C3⋊Dic3C22×Q811yescharacteristic
141C3⋊Dic3C2×#4111yescharacteristic
142C3×Dic3—42no—
143C3×Dic3—44no—
144C22×Q8—181no—
145C22×D4—91no—
146C23×C4—181no—
147C22×C8—92no—
148C4⋊Q8—94no—
149C4⋊Q8—182no—
150C4×D4—94no—
151C4×D4—182no—
152C2×C4⋊C4—61no—
153C2×C4⋊C4—91no—
154C2×C4⋊C4—92no—
155C2×C22⋊C4—61no—
156C2×C42—91no—
157#107—98no—
158C4⋊C8—94no—
159#102—98no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—62no—
163C23×C3—64no—
164C23×C3—122no—
165C23×C3—122no—
166C22×D3—22no—
167C22×D3—24no—
168C22×D3—42no—
169C22×D3—42no—
170C2×C3×C4—24no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—42no—
174C2×C3×C4—62no—
175C2×C3×C4—64no—
176C2×C3×C4—124no—
177C2×C3×C4—122no—
178#67—64no—
179#67—68no—
180#67—64no—
181C2×Dic3—24no—
182C2×Dic3—22no—
183C2×Dic3—44no—
184C2×Dic3—42no—
185C2×Dic3—64no—
186C2×Dic3—64no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—62no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—128no—
198C4×D3—128no—
199Dic6—1216no—
200C2×C32#47414yescomplemented
201C2×C32C2×C22⋊Q811yescharacteristic
202C2×C32C22×D811yescharacteristic
203C2×C32C2×#13711yescharacteristic
204C3×D3—44no—
205C24—61no—
206C2×Q8—184no—
207C2×Q8—364no—
208C2×D4—92no—
209C2×D4—94no—
210C2×D4—181no—
211C2×D4—182no—
212C22×C4—61no—
213C22×C4—62no—
214C22×C4—91no—
215C22×C4—91no—
216C22×C4—184no—
217C22×C4—364no—
218C22×C4GO+(4,𝔽2)11yescharacteristic
219C2×C8—94no—
220C2×C8—184no—
221C4⋊C4—64no—
222C4⋊C4—94no—
223C4⋊C4—92no—
224C4⋊C4—181no—
225C4⋊C4—182no—
226C22⋊C4—64no—
227C42—92no—
228C42—92no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—22no—
232C22×C3—22no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—64no—
238C22×C3—122no—
239C22×C3—128no—
240C22×C3—122no—
241C2×D3—24no—
242C2×D3—42no—
243C2×D3—48no—
244C2×D3—42no—
245C3×C4—24no—
246C3×C4—42no—
247C3×C4—124no—
248C3×C4—122no—
249Dic3—44no—
250Dic3—42no—
251Dic3—64no—
252Dic3—64no—
253Dic3—62no—
254Dic3—61no—
255Dic3—61no—
256Dic3—62no—
257Dic3—61no—
258Dic3—61no—
259C32C2×#47411yescharacteristic, complemented, Sylow
260C23—62no—
261C23—64no—
262C23—122no—
263C23—122no—
264C23C2×GO+(4,𝔽2)11yescharacteristic
265Q8—368no—
266D4—94no—
267D4—182no—
268D4—184no—
269C2×C4—22no—
270C2×C4—62no—
271C2×C4—64no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—92no—
275C2×C4—92no—
276C2×C4—92no—
277C2×C4—94no—
278C2×C4—122no—
279C2×C4—124no—
280C2×C4—368no—
281C2×C4C2×GO+(4,𝔽2)12yes—
282C8—184no—
283C2×C3—24no—
284C2×C3—24no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—124no—
292D3—44no—
293C22—64no—
294C22—128no—
295C22—122no—
296C22—122no—
297C22D32⋊Q812yes—
298C22#6422512yes—
299C22#6423912yes—
300C22C22×GO+(4,𝔽2)11yescharacteristic
301C4—22no—
302C4—91no—
303C4—91no—
304C4—92no—
305C4—94no—
306C4—122no—
307C4—124no—
308C3—21no—
309C3—21no—
310C2—124no—
311C2#1059336714yesdirect product factor
312C2C2×D32⋊Q811yescharacteristic
313C2C2×#6422511yescharacteristic
314C2C2×#6423911yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#474
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#63919C2semidirect
3. C2×#63779C2semidirect
4. C2×#63743C2semidirect
6. #10593367C2direct (N × H)
17. #63919C22semidirect
20. #63779C22semidirect
21. #63743C22semidirect
35. C2×#625Q8semidirect
86. #625C2×Q8semidirect
200. C2×C32#474semidirect
259. C32C2×#474semidirect
311. C2#10593367direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#639022
C2×#637792
C2×#637432
C2×#637392
#105933672
C2×#4749