Finite Group Databasebeta

← C2×#10593500 #11869619

Subgroups — C2×#10593500 #11869619

Order 1152.

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

normal subgroups only

This group has 830 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×#63982C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic
3C2×C22⋊#622C211yesmaximal, characteristic
4C2×#63743C212yesmaximal, complemented
5C2×#63740C212yesmaximal, complemented
6#10593500C218yesmaximal, direct product factor
7C23×C3⋊Dic3C2211yescharacteristic
8C23×C3×Dic3—21no—
9C22×#627C2211yescharacteristic
10C22×#622C2212yes—
11C2×C3×#217—21no—
12#63982—22no—
13#63982C2214yes—
14C2×#3724—21no—
15C2×#3724—22no—
16C2×#3724C2214yes—
17C2×#3724C2212yes—
18C2×#3724C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C22⋊#622C2214yes—
21#63743C2218yescomplemented
22#63740C2218yescomplemented
23C22×Dic3⋊C4—61no—
24C2×#878—61no—
25C24×C32D411yescharacteristic
26C22×C3⋊Dic3—24no—
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3D412yes—
29C22×C3⋊Dic3C2312yes—
30C22×C3⋊Dic3C2311yescharacteristic
31C22×C3×Dic3—21no—
32C22×C3×Dic3—21no—
33C22×C3×Dic3—24no—
34C22×C3×Dic3—22no—
35C22×C3×Dic3—44no—
36C2×#627—24no—
37C2×#627—21no—
38C2×#627C2312yes—
39C2×#622—24no—
40C2×#622C2314yes—
41C3×#217—24no—
42#3724—24no—
43#3724—22no—
44#3724—21no—
45#3724C2314yes—
46#3724C2312yes—
47Dic3⋊Dic3—24no—
48C2×#484—91nomaximal, Sylow
49C23×C3×C4—61no—
50C23×Dic3—21no—
51C23×Dic3—61no—
52C23×Dic3—61no—
53C22×Dic6—61no—
54C2×C3×C22⋊C4—61no—
55C2×#217—21no—
56C2×C4⋊Dic3—61no—
57C2×Dic3⋊C4—61no—
58C2×Dic3⋊C4—62no—
59C2×Dic3⋊C4—64no—
60C2×Dic3⋊C4—61no—
61C2×Dic3⋊C4—64no—
62C2×Dic3⋊C4—62no—
63#878—64no—
64#878—64no—
65C23×C32—22no—
66C23×C32—22no—
67C23×C32Q1614yes—
68C23×C32C2×D412yes—
69C23×C32C2×D411yescharacteristic
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—24no—
72C2×C3⋊Dic3—24no—
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3#4114yes—
76C2×C3⋊Dic3C2411yescharacteristic
77C2×C3×Dic3—22no—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—24no—
80C2×C3×Dic3—48no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C2×C3×Dic3—44no—
84#627—24no—
85#627—42no—
86#622—24no—
87C2×C22⋊Q8—91no—
88C22×C4⋊C4—91no—
89#484—98no—
90C2×#107—92no—
91C2×#103—92no—
92C2×C22⋊C8—91no—
93C24×C3—21no—
94C24×C3—21no—
95C22×C3×C4—64no—
96C22×C3×C4—62no—
97C22×C3×C4—61no—
98C22×C3×C4—61no—
99C22×C3×C4—124no—
100C22×Dic3—21no—
101C22×Dic3—24no—
102C22×Dic3—22no—
103C22×Dic3—21no—
104C22×Dic3—44no—
105C22×Dic3—62no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3—62no—
109C22×Dic3—61no—
110C22×Dic3—62no—
111C22×Dic3—62no—
112C22×Dic3—61no—
113C22×Dic3—68no—
114C22×Dic3—124no—
115C2×Dic6—62no—
116C2×Dic6—62no—
117C2×Dic6—124no—
118C3×C22⋊C4—64no—
119#217—24no—
120C4⋊Dic3—64no—
121Dic3⋊C4—62no—
122Dic3⋊C4—64no—
123Dic3⋊C4—64no—
124Dic3⋊C4—62no—
125Dic3⋊C4—64no—
126Dic3⋊C4—68no—
127C22×C32—22no—
128C22×C32—22no—
129C22×C32—28no—
130C22×C32#12312yes—
131C22×C32C2×Q1614yes—
132C22×C32C2×Q1612yes—
133C22×C32AGL(1,ℤ/8)12yes—
134C22×C32C22×D411yescharacteristic
135C3⋊Dic3—22no—
136C3⋊Dic3#12312yes—
137C3⋊Dic3C2×#4112yes—
138C3×Dic3—42no—
139C3×Dic3—42no—
140C3×Dic3—44no—
141C22×Q8—91no—
142C23×C4—61no—
143C23×C4—91no—
144C22×C8—92no—
145C22⋊Q8—94no—
146C22⋊Q8—182no—
147C2×C4⋊C4—92no—
148C2×C4⋊C4—94no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—182no—
151C2×C4⋊C4—181no—
152C2×C4⋊C4—181no—
153C2×C22⋊C4—61no—
154#107—98no—
155#103—98no—
156C22⋊C8—94no—
157C23×C3—24no—
158C23×C3—24no—
159C23×C3—22no—
160C23×C3—22no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—24no—
164C23×C3—24no—
165C23×C3—42no—
166C23×C3—42no—
167C2×C3×C4—64no—
168C2×C3×C4—62no—
169C2×C3×C4—62no—
170C2×C3×C4—122no—
171C2×C3×C4—122no—
172C2×C3×C4—128no—
173C2×C3×C4—124no—
174C2×Dic3—22no—
175C2×Dic3—24no—
176C2×Dic3—22no—
177C2×Dic3—42no—
178C2×Dic3—42no—
179C2×Dic3—48no—
180C2×Dic3—44no—
181C2×Dic3—61no—
182C2×Dic3—62no—
183C2×Dic3—61no—
184C2×Dic3—64no—
185C2×Dic3—64no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—62no—
189C2×Dic3—68no—
190C2×Dic3—68no—
191C2×Dic3—64no—
192C2×Dic3—124no—
193C2×Dic3—124no—
194C2×Dic3—122no—
195Dic6—124no—
196Dic6—124no—
197C2×C32—24no—
198C2×C32#48414yescomplemented
199C2×C32C2×#12311yescharacteristic
200C2×C32C22×Q1611yescharacteristic
201C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
202C24GO+(4,𝔽2)11yescharacteristic
203C2×Q8—92no—
204C2×Q8—181no—
205C2×Q8—184no—
206C22×C4—64no—
207C22×C4—61no—
208C22×C4—61no—
209C22×C4—62no—
210C22×C4—91no—
211C22×C4—92no—
212C22×C4—92no—
213C22×C4—91no—
214C22×C4—124no—
215C22×C4—184no—
216C2×C8—94no—
217C2×C8—184no—
218C4⋊C4—94no—
219C4⋊C4—92no—
220C4⋊C4—182no—
221C4⋊C4—184no—
222C4⋊C4—181no—
223C4⋊C4—184no—
224C22⋊C4—64no—
225C22×C3—24no—
226C22×C3—24no—
227C22×C3—216no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—22no—
231C22×C3—22no—
232C22×C3—22no—
233C22×C3—22no—
234C22×C3—24no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—24no—
238C22×C3—42no—
239C22×C3—42no—
240C22×C3—48no—
241C3×C4—122no—
242C3×C4—124no—
243C3×C4—122no—
244Dic3—42no—
245Dic3—44no—
246Dic3—42no—
247Dic3—62no—
248Dic3—62no—
249Dic3—62no—
250Dic3—62no—
251Dic3—64no—
252Dic3—122no—
253C32C2×#48411yescharacteristic, complemented, Sylow
254C23—22no—
255C23—22no—
256C23#377614yes—
257C23C2×GO+(4,𝔽2)12yes—
258C23C2×GO+(4,𝔽2)11yescharacteristic
259Q8—184no—
260Q8—362no—
261C2×C4—62no—
262C2×C4—62no—
263C2×C4—64no—
264C2×C4—91no—
265C2×C4—91no—
266C2×C4—94no—
267C2×C4—92no—
268C2×C4—128no—
269C2×C4—122no—
270C2×C4—124no—
271C2×C4—122no—
272C2×C4—184no—
273C2×C4—184no—
274C2×C4—182no—
275C8—184no—
276C2×C3—28no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—24no—
284C2×C3—24no—
285C2×C3—44no—
286C22—22no—
287C22—22no—
288C22—28no—
289C22#6423312yes—
290C22#6423612yes—
291C22C2×#377614yes—
292C22C2×#377612yes—
293C22C22×GO+(4,𝔽2)11yescharacteristic
294C4—92no—
295C4—92no—
296C4—122no—
297C4—124no—
298C4—122no—
299C4—182no—
300C3—21no—
301C3—21no—
302C2—24no—
303C2#1059350014yesdirect product factor
304C2C2×#6423311yescharacteristic
305C2C2×#6423611yescharacteristic
306C2C22×#377611yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#484
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
4. C2×#63743C2semidirect
5. C2×#63740C2semidirect
6. #10593500C2direct (N × H)
21. #63743C22semidirect
22. #63740C22semidirect
198. C2×C32#484semidirect
253. C32C2×#484semidirect
303. C2#10593500direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639822
C22×#37242
C2×C22⋊#6222
C2×#637432
C2×#637402
#105935002
C2×#4849