Finite Group Databasebeta

← C2×#10593373 #11868529

Subgroups — C2×#10593373 #11868529

Order 1152.

646 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 127 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×#63870C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic
3C2×C4⋊#622C211yesmaximal, characteristic
4C2×#63743C211yesmaximal, characteristic
5C2×#63742C211yesmaximal, characteristic
6C2×#63740C211yesmaximal, characteristic
7C2×#63740C211yesmaximal, characteristic
8#10593373C218yesmaximal, direct product factor
9C22×#627C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×Dic3⋊C4—21no—
14C2×C3×Dic3⋊C4—21no—
15C2×#3724C2211yescharacteristic
16C2×#3724C2211yescharacteristic
17C2×#3724C2211yescharacteristic
18C2×Dic3⋊Dic3—21no—
19C2×Dic32—21no—
20#63870—22no—
21#63870C2214yes—
22#63838—22no—
23#63838C2214yes—
24C4⋊#622C2214yes—
25#63743C2214yes—
26#63742C2214yes—
27#63740C2214yes—
28#63740C2214yes—
29C2×#889—61no—
30C2×#887—61no—
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3⋊Dic3C2311yescharacteristic
34C22×C3×Dic3—21no—
35C22×C3×Dic3—21no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C2×#627—21no—
39C2×#627—22no—
40C2×#627Q814yes—
41C2×#627C2312yes—
42C2×#622—22no—
43C2×#622—22no—
44C2×#622C2312yes—
45C2×#622C2312yes—
46C4×C3⋊Dic3D412yes—
47C4×C3⋊Dic3C2312yes—
48C3×Dic3⋊C4—24no—
49C3×Dic3⋊C4—24no—
50#3724—21no—
51#3724—21no—
52#3724—21no—
53#3724C2312yes—
54#3724C2312yes—
55#3724C2312yes—
56Dic3⋊Dic3—24no—
57Dic32—24no—
58C2×#479—91nomaximal, Sylow
59C22×Dic6—61no—
60C2×C3×C4⋊C4—61no—
61C2×C3×C4⋊C4—61no—
62C2×C4⋊Dic3—61no—
63C2×Dic3⋊C4—21no—
64C2×Dic3⋊C4—21no—
65C2×Dic3⋊C4—61no—
66C2×Dic3⋊C4—61no—
67C2×Dic3⋊C4—61no—
68C2×Dic3⋊C4—61no—
69C2×C4×Dic3—61no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—61no—
72C2×C4×Dic3—61no—
73#889—64no—
74#889—64no—
75#887—64no—
76#887—64no—
77C23×C32C2×D411yescharacteristic
78C2×C32×C4—22no—
79C2×C32×C4C2×D412yes—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3C2×D412yes—
82C2×C3⋊Dic3C2×D411yescharacteristic
83C2×C3⋊Dic3C2×Q812yes—
84C2×C3⋊Dic3#4112yes—
85C2×C3⋊Dic3C2411yescharacteristic
86C2×C3×Dic3—24no—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—42no—
94#627—24no—
95#627—22no—
96#627C2×Q814yes—
97#622—22no—
98#622—22no—
99C2×#125—91no—
100C2×C4×Q8—91no—
101#479—98no—
102C2×#107—91no—
103C2×#106—91no—
104C2×C4⋊C8—91no—
105C2×#103—91no—
106C2×#103—91no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—61no—
110C22×C3×C4—61no—
111C22×C3×C4—61no—
112C22×C3×C4—61no—
113C22×Dic3—21no—
114C22×Dic3—21no—
115C22×Dic3—21no—
116C22×Dic3—21no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C2×Dic6—62no—
122C2×Dic6—64no—
123C2×Dic6—62no—
124C2×Dic6—64no—
125C3×C4⋊C4—64no—
126C3×C4⋊C4—64no—
127C4⋊Dic3—64no—
128Dic3⋊C4—24no—
129Dic3⋊C4—24no—
130Dic3⋊C4—62no—
131Dic3⋊C4—62no—
132Dic3⋊C4—62no—
133Dic3⋊C4—62no—
134Dic3⋊C4—64no—
135Dic3⋊C4—62no—
136Dic3⋊C4—62no—
137C4×Dic3—62no—
138C4×Dic3—62no—
139C4×Dic3—62no—
140C4×Dic3—62no—
141C4×Dic3—64no—
142C4×Dic3—64no—
143C22×C32C22⋊Q812yes—
144C22×C32#13512yes—
145C22×C32#13712yes—
146C22×C32C22×D411yescharacteristic
147C32×C4—22no—
148C3⋊Dic3—22no—
149C3⋊Dic3C22⋊Q812yes—
150C3⋊Dic3C22×Q811yescharacteristic
151C3⋊Dic3C2×#4111yescharacteristic
152C3×Dic3—24no—
153C3×Dic3—42no—
154C3×Dic3—42no—
155C3×Dic3—42no—
156C22×Q8—91no—
157C22×C8—91no—
158C22×C8—91no—
159#125—94no—
160#125—182no—
161C4×Q8—94no—
162C4×Q8—182no—
163C2×C4⋊C4—61no—
164C2×C4⋊C4—61no—
165C2×C4⋊C4—91no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—91no—
168C2×C4⋊C4—181no—
169C2×C42—91no—
170C2×C42—181no—
171#107—94no—
172#106—94no—
173C4⋊C8—94no—
174#103—94no—
175#103—94no—
176C23×C3—21no—
177C23×C3—21no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—62no—
183C2×C3×C4—64no—
184C2×C3×C4—62no—
185C2×C3×C4—62no—
186C2×C3×C4—62no—
187C2×C3×C4—122no—
188C2×C3×C4—122no—
189C2×C3×C4—122no—
190C2×Dic3—22no—
191C2×Dic3—24no—
192C2×Dic3—22no—
193C2×Dic3—22no—
194C2×Dic3—22no—
195C2×Dic3—42no—
196C2×Dic3—42no—
197C2×Dic3—42no—
198C2×Dic3—62no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—62no—
202C2×Dic3—62no—
203C2×Dic3—62no—
204C2×Dic3—62no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—62no—
208C2×Dic3—64no—
209C2×Dic3—122no—
210Dic6—64no—
211Dic6—68no—
212Dic6—64no—
213C2×C32#47914yescomplemented
214C2×C32C2×C22⋊Q811yescharacteristic
215C2×C32C2×#13511yescharacteristic
216C2×C32C2×#13711yescharacteristic
217C2×Q8—92no—
218C2×Q8—94no—
219C2×Q8—181no—
220C2×Q8—182no—
221C22×C4—61no—
222C22×C4—61no—
223C22×C4—61no—
224C22×C4—61no—
225C22×C4—91no—
226C22×C4—91no—
227C22×C4GO+(4,𝔽2)11yescharacteristic
228C2×C8—92no—
229C2×C8—92no—
230C2×C8—182no—
231C2×C8—182no—
232C4⋊C4—64no—
233C4⋊C4—64no—
234C4⋊C4—92no—
235C4⋊C4—92no—
236C4⋊C4—92no—
237C4⋊C4—181no—
238C4⋊C4—181no—
239C4⋊C4—181no—
240C4⋊C4—184no—
241C42—92no—
242C42—92no—
243C42—184no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—22no—
252C3×C4—42no—
253C3×C4—42no—
254C3×C4—64no—
255C3×C4—122no—
256C3×C4—122no—
257C3×C4—122no—
258Dic3—24no—
259Dic3—42no—
260Dic3—42no—
261Dic3—42no—
262Dic3—62no—
263Dic3—61no—
264Dic3—61no—
265Dic3—62no—
266Dic3—61no—
267Dic3—61no—
268Dic3—64no—
269Dic3—122no—
270C32C2×#47911yescharacteristic, complemented, Sylow
271C23C2×GO+(4,𝔽2)11yescharacteristic
272Q8—94no—
273Q8—182no—
274Q8—184no—
275C2×C4—22no—
276C2×C4—62no—
277C2×C4—64no—
278C2×C4—62no—
279C2×C4—62no—
280C2×C4—62no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—92no—
284C2×C4—92no—
285C2×C4—92no—
286C2×C4—122no—
287C2×C4—122no—
288C2×C4—122no—
289C2×C4—182no—
290C2×C4C2×GO+(4,𝔽2)12yes—
291C8—182no—
292C8—182no—
293C2×C3—24no—
294C2×C3—24no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C22D32⋊Q812yes—
302C22#6422612yes—
303C22#6423712yes—
304C22C22×GO+(4,𝔽2)11yescharacteristic
305C4—22no—
306C4—64no—
307C4—91no—
308C4—91no—
309C4—92no—
310C4—122no—
311C4—122no—
312C4—122no—
313C4—182no—
314C3—21no—
315C3—21no—
316C2#1059337314yesdirect product factor
317C2C2×D32⋊Q811yescharacteristic
318C2C2×#6422611yescharacteristic
319C2C2×#6423711yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#479
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
8. #10593373C2direct (N × H)
213. C2×C32#479semidirect
270. C32C2×#479semidirect
316. C2#10593373direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638702
C2×#638382
C2×C4⋊#6222
C2×#637432
C2×#637422
C2×#637402
#105933732
C2×#4799