Finite Group Databasebeta

← C2×#10593375 #11857763

Subgroups — C2×#10593375 #11857763

Order 1152.

1450 conjugacy classes of subgroups; only the 247 normal subgroups are shown.

normal subgroups only

This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 247 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×#3797C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic
3C2×#63900C211yesmaximal, characteristic
4C2×#63740C214yesmaximal, complemented
5#10593375C218yesmaximal, direct product factor
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×C3×Dic6—21no—
8C22×#627C2212yes—
9C22×#624—21no—
10C22×#624—21no—
11C2×#3797—22no—
12C2×#3797—24no—
13C2×#3797C418yescomplemented
14C2×#3797C2214yes—
15C22×#622C2212yes—
16C2×#3787—24no—
17C2×#3787C2214yes—
18C2×C3×C4⋊Dic3—21no—
19C2×#3724C2212yes—
20#63900—22no—
21#63900C2214yes—
22#63740C22116yescomplemented
23C22×D3×Q8—61no—
24C2×D3×C4⋊C4—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C2×C4×C3⋊D3C2×C414yes—
29C2×C4×C3⋊D3D412yes—
30C2×C4×C3⋊D3D414yes—
31C2×C4×C3⋊D3C2312yes—
32C22×C3×Dic3—22no—
33C22×C3×Dic3—22no—
34C2×C3×Dic6—28no—
35C2×C3×Dic6—24no—
36C2×#627—22no—
37C2×#627—24no—
38C2×#627C2×C418yescomplemented
39C2×#627C2314yes—
40C2×#624—28no—
41C2×#624—24no—
42C2×#624—24no—
43C2×#624—44no—
44#3797—216no—
45#3797—28no—
46#3797C2×C4116yescomplemented
47C2×#622—24no—
48C2×#622C2314yes—
49#3787—28no—
50C3×C4⋊Dic3—24no—
51#3724—22no—
52#3724C2314yes—
53C22×#103—91nomaximal, Sylow
54C22×C3×Q8—61no—
55C2×D3×Q8—68no—
56C2×D3×Q8—64no—
57C2×D3×Q8—64no—
58C2×D3×Q8—68no—
59C22×C4×D3—61no—
60C22×C4×D3—61no—
61C22×C4×D3—62no—
62C22×C4×D3—62no—
63C22×Dic6—21no—
64C22×Dic6—62no—
65C2×C3×C4⋊C4—61no—
66C2×C4⋊Dic3—21no—
67C2×Dic3⋊C4—62no—
68D3×C4⋊C4—64no—
69D3×C4⋊C4—64no—
70C23×C32C2×D411yescharacteristic
71C22×C3⋊D3C22⋊C414yes—
72C22×C3⋊D3SD1614yes—
73C22×C3⋊D3Q1614yes—
74C22×C3⋊D3C2×D412yes—
75C2×C32×C4C22⋊C414yes—
76C2×C32×C4C2×D412yes—
77C2×C3⋊Dic3C22×C412yes—
78C2×C3⋊Dic3C2×D411yescharacteristic
79C2×C3⋊Dic3C2×D412yes—
80C2×C3⋊Dic3C2411yescharacteristic
81C4×C3⋊D3C22⋊C418yes—
82C4×C3⋊D3C22×C414yes—
83C4×C3⋊D3C2×D414yes—
84C2×C3×Dic3—28no—
85C2×C3×Dic3—24no—
86C2×C3×Dic3—24no—
87C2×C3×Dic3—44no—
88C3×Dic6—216no—
89#627—28no—
90#627—24no—
91#627C22×C418yescomplemented
92#624—216no—
93#624—48no—
94#622—24no—
95C23×Q8—91no—
96C23×C8—91no—
97C22×C4⋊C4—91no—
98C2×#103—98no—
99C2×#103—94no—
100C23×D3—61no—
101C23×D3—61no—
102C2×C3×Q8—64no—
103C2×C3×Q8—68no—
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×C3×C4—62no—
107C22×C3×C4—62no—
108C22×Dic3—22no—
109C22×Dic3—22no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112D3×Q8—616no—
113D3×Q8—632no—
114D3×Q8—616no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×C4×D3—64no—
118C2×C4×D3—62no—
119C2×C4×D3—64no—
120C2×C4×D3—62no—
121C2×C4×D3—64no—
122C2×C4×D3—64no—
123C2×C4×D3—616no—
124C2×C4×D3—68no—
125C2×C4×D3—68no—
126C2×C4×D3—128no—
127C2×Dic6—24no—
128C2×Dic6—28no—
129C2×Dic6—68no—
130C2×Dic6—64no—
131C2×Dic6—64no—
132C2×Dic6—68no—
133C3×C4⋊C4—64no—
134C4⋊Dic3—24no—
135Dic3⋊C4—64no—
136Dic3⋊C4—64no—
137C22×C32C2×C22⋊C412yes—
138C22×C32C2×SD1612yes—
139C22×C32C2×Q1612yes—
140C22×C32C22×D411yescharacteristic
141C2×C3⋊D3#103116yescomplemented
142C2×C3⋊D3C2×C22⋊C414yes—
143C2×C3⋊D3C2×SD1614yes—
144C2×C3⋊D3C2×Q1614yes—
145C32×C4C2×C22⋊C414yes—
146C3⋊Dic3C2×C22⋊C412yes—
147C3⋊Dic3C23×C411yescharacteristic
148C3⋊Dic3C22×D411yescharacteristic
149C3×Dic3—28no—
150C3×Dic3—44no—
151C22×Q8—61no—
152C22×Q8—92no—
153C22×Q8—94no—
154C22×Q8—98no—
155C22×Q8—182no—
156C22×Q8—184no—
157C23×C4—91no—
158C23×C4—181no—
159C23×C4—181no—
160C22×C8—94no—
161C22×C8—92no—
162C22×C8—184no—
163C2×C4⋊C4—61no—
164C2×C4⋊C4—94no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—182no—
167#103—916no—
168C23×C3—21no—
169C23×C3—21no—
170C22×D3—64no—
171C22×D3—64no—
172C22×D3—64no—
173C22×D3—64no—
174C22×D3—64no—
175C22×D3—64no—
176C22×D3—62no—
177C22×D3—62no—
178C3×Q8—616no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—64no—
184C2×C3×C4—68no—
185C2×C3×C4—64no—
186C2×C3×C4—124no—
187C2×Dic3—24no—
188C2×Dic3—28no—
189C2×Dic3—24no—
190C2×Dic3—44no—
191C2×Dic3—62no—
192C2×Dic3—62no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C4×D3—68no—
200C4×D3—68no—
201C4×D3—64no—
202C4×D3—64no—
203C4×D3—64no—
204C4×D3—64no—
205C4×D3—632no—
206C4×D3—1216no—
207Dic6—216no—
208Dic6—68no—
209Dic6—616no—
210Dic6—68no—
211C2×C32C2×#10314yescomplemented
212C2×C32C22×C22⋊C411yescharacteristic
213C2×C32C22×SD1611yescharacteristic
214C2×C32C22×Q1611yescharacteristic
215C3⋊D3C2×#10318yescomplemented
216C24—91no—
217C2×Q8—64no—
218C2×Q8—68no—
219C2×Q8—94no—
220C2×Q8—98no—
221C2×Q8—916no—
222C2×Q8—182no—
223C2×Q8—184no—
224C2×Q8—188no—
225C2×Q8—1816no—
226C22×C4—62no—
227C22×C4—62no—
228C22×C4—91no—
229C22×C4—92no—
230C22×C4—92no—
231C22×C4—94no—
232C22×C4—94no—
233C22×C4—184no—
234C22×C4—188no—
235C22×C4—184no—
236C22×C4—364no—
237C22×C4GO+(4,𝔽2)11yescharacteristic
238C2×C8—94no—
239C2×C8—188no—
240C2×C8—184no—
241C4⋊C4—64no—
242C4⋊C4—94no—
243C4⋊C4—182no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—22no—
252C2×D3—64no—
253C2×D3—64no—
254C2×D3—64no—
255C2×D3—616no—
256C2×D3—616no—
257C2×D3—64no—
258C2×D3—64no—
259C2×D3—64no—
260C3×C4—24no—
261C3×C4—24no—
262C3×C4—68no—
263C3×C4—124no—
264Dic3—28no—
265Dic3—44no—
266Dic3—62no—
267Dic3—61no—
268Dic3—61no—
269Dic3—62no—
270Dic3—61no—
271Dic3—61no—
272C32C22×#10311yescharacteristic, complemented, Sylow
273C23—92no—
274C23—94no—
275C23—94no—
276C23—94no—
277C23C2×GO+(4,𝔽2)11yescharacteristic
278Q8—616no—
279Q8—98no—
280Q8—184no—
281Q8—188no—
282C2×C4—64no—
283C2×C4—68no—
284C2×C4—64no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—92no—
288C2×C4—92no—
289C2×C4—94no—
290C2×C4—94no—
291C2×C4—98no—
292C2×C4—124no—
293C2×C4—1816no—
294C2×C4—368no—
295C2×C4D32⋊C414yes—
296C2×C4C2×GO+(4,𝔽2)12yes—
297C8—184no—
298C2×C3—24no—
299C2×C3—24no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306D3—68no—
307D3—68no—
308C22—916no—
309C22—94no—
310C22—94no—
311C22—94no—
312C22#6422712yes—
313C22#6422812yes—
314C22C2×D32⋊C412yes—
315C22C22×GO+(4,𝔽2)11yescharacteristic
316C4—68no—
317C4—91no—
318C4—91no—
319C4—92no—
320C4—124no—
321C4C2×D32⋊C414yes—
322C3—21no—
323C3—21no—
324C2—98no—
325C2#1059337514yesdirect product factor
326C2C2×#6422711yescharacteristic
327C2C2×#6422811yescharacteristic
328C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C22×#103
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63740C2semidirect
5. #10593375C2direct (N × H)
13. C2×#3797C4semidirect
22. #63740C22semidirect
38. C2×#627C2×C4semidirect
46. #3797C2×C4semidirect
91. #627C22×C4semidirect
141. C2×C3⋊D3#103semidirect
211. C2×C32C2×#103semidirect
215. C3⋊D3C2×#103semidirect
272. C32C22×#103semidirect
325. C2#10593375direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×#37872
C2×#639002
C2×#637402
#105933752
C22×#1039