Finite Group Databasebeta

← C2×#10593355 #11865613

Subgroups — C2×#10593355 #11865613

Order 1152.

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

normal subgroups only

This group has 982 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
1C22×#3775C212yesmaximal, complemented
2C2×#63914C211yesmaximal, characteristic
3C2×#63838C211yesmaximal, characteristic, complemented
4C2×#63779C211yesmaximal, characteristic, complemented
5C2×#63739C212yesmaximal, complemented
6#10593355C218yesmaximal, direct product factor
7C22×C3×D12—21no—
8C22×#627C2211yescharacteristic
9C22×#625—21no—
10C22×#625C2212yes—
11C22×#622C2212yes—
12C2×#3775—28no—
13C2×#3775C2218yescomplemented
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16C2×#3724C2211yescharacteristic
17C2×Dic32—21no—
18#63914—22no—
19#63914C2214yes—
20#63838—22no—
21#63838C2214yescomplemented
22#63779C2214yescomplemented
23#63739C2218yescomplemented
24C2×#940—61no—
25C2×#887—61no—
26C23×C3×D3—22no—
27C22×C32×C4D411yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3C2311yescharacteristic
30C22×C3×Dic3—21no—
31C22×C3×Dic3—21no—
32C2×C3×D12—24no—
33C2×C3×D12—44no—
34C2×#627—21no—
35C2×#627—22no—
36C2×#627D414yescomplemented
37C2×#627C2312yes—
38C2×#625—24no—
39C2×#625—24no—
40C2×#625—24no—
41C2×#625—22no—
42C2×#625—44no—
43C2×#625C2314yes—
44C2×#622—24no—
45C2×#622C2314yes—
46#3775—216no—
47C4×C3⋊Dic3D412yes—
48C4×C3⋊Dic3C2312yes—
49C3×Dic3⋊C4—24no—
50#3724—21no—
51#3724C2312yes—
52Dic32—24no—
53C2×#460—91nomaximal, Sylow
54C22×C3×D4—61no—
55C22×#67—62no—
56C22×#67—62no—
57C22×D12—21no—
58C22×Dic6—61no—
59C2×C3×C4⋊C4—61no—
60#940—64no—
61#940—64no—
62C2×Dic3⋊C4—21no—
63C2×Dic3⋊C4—61no—
64C2×C4×Dic3—61no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—61no—
67C2×C4×Dic3—61no—
68#887—64no—
69#887—64no—
70C23×C32C2×D411yescharacteristic
71C22×C3×D3—24no—
72C22×C3×D3—44no—
73C22×C3×D3—44no—
74C22×C3×D3—44no—
75C2×C32×C4—22no—
76C2×C32×C4C2×D412yes—
77C2×C3⋊Dic3SD1614yescomplemented
78C2×C3⋊Dic3C2×D411yescharacteristic
79C2×C3⋊Dic3C2×D412yes—
80C2×C3⋊Dic3C2×D412yes—
81C2×C3⋊Dic3#4112yes—
82C2×C3⋊Dic3C2411yescharacteristic
83C2×C3×Dic3—24no—
84C2×C3×Dic3—22no—
85C2×C3×Dic3—22no—
86C2×C3×Dic3—42no—
87C3×D12—48no—
88#627—24no—
89#627—22no—
90#627C2×D414yescomplemented
91#625—24no—
92#625—24no—
93#625—44no—
94#625—48no—
95#622—24no—
96C22×SD16—92no—
97C2×#127—91no—
98C2×C4×Q8—91no—
99#460—98no—
100C2×C4⋊C8—91no—
101C2×#102—92no—
102C24×C3—62no—
103C23×D3—22no—
104C2×C3×D4—64no—
105C2×C3×D4—124no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—61no—
109C22×C3×C4—61no—
110C2×#67—64no—
111C2×#67—68no—
112C2×#67—64no—
113C2×#67—124no—
114C2×#67—124no—
115C2×#67—128no—
116C22×Dic3—21no—
117C22×Dic3—21no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C2×D12—24no—
123C2×D12—44no—
124C2×Dic6—62no—
125C2×Dic6—64no—
126C2×Dic6—62no—
127C2×Dic6—64no—
128C3×C4⋊C4—64no—
129Dic3⋊C4—24no—
130Dic3⋊C4—62no—
131Dic3⋊C4—62no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C4×Dic3—62no—
135C4×Dic3—62no—
136C4×Dic3—64no—
137C4×Dic3—64no—
138C22×C32#12112yes—
139C22×C32C2×SD1612yes—
140C22×C32AGL(1,ℤ/8)12yes—
141C22×C32C22×D411yescharacteristic
142C2×C3×D3—44no—
143C2×C3×D3—44no—
144C2×C3×D3—44no—
145C2×C3×D3—88no—
146C32×C4—22no—
147C3⋊Dic3#12112yes—
148C3⋊Dic3C2×SD1614yescomplemented
149C3⋊Dic3C22×D411yescharacteristic
150C3⋊Dic3C2×#4111yescharacteristic
151C3×Dic3—24no—
152C3×Dic3—42no—
153C22×Q8—91no—
154C22×D4—61no—
155C22×D4—92no—
156C22×D4—181no—
157C2×SD16—98no—
158C2×SD16—188no—
159C22×C8—92no—
160#127—94no—
161#127—182no—
162C4×Q8—94no—
163C4×Q8—182no—
164C2×C4⋊C4—61no—
165C2×C4⋊C4—91no—
166C2×C42—91no—
167C2×C42—181no—
168C4⋊C8—94no—
169#102—98no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—64no—
173C23×C3—124no—
174C23×C3—124no—
175C23×C3—124no—
176C22×D3—24no—
177C22×D3—44no—
178C22×D3—44no—
179C22×D3—44no—
180C3×D4—128no—
181C2×C3×C4—24no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—42no—
185C2×C3×C4—62no—
186C2×C3×C4—64no—
187C2×C3×C4—62no—
188C2×C3×C4—122no—
189#67—124no—
190#67—124no—
191#67—128no—
192#67—1216no—
193C2×Dic3—22no—
194C2×Dic3—24no—
195C2×Dic3—22no—
196C2×Dic3—42no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—62no—
200C2×Dic3—61no—
201C2×Dic3—62no—
202C2×Dic3—61no—
203C2×Dic3—62no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—62no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209D12—48no—
210Dic6—64no—
211Dic6—68no—
212Dic6—64no—
213C2×C32#46014yescomplemented
214C2×C32C2×#12111yescharacteristic
215C2×C32C22×SD1611yescharacteristic
216C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
217C3×D3—84no—
218C24—62no—
219C2×Q8—92no—
220C2×Q8—94no—
221C2×Q8—181no—
222C2×Q8—182no—
223C2×D4—64no—
224C2×D4—94no—
225C2×D4—124no—
226C2×D4—184no—
227C2×D4—184no—
228C2×D4—184no—
229C2×D4—182no—
230C2×D4—364no—
231C22×C4—61no—
232C22×C4—61no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4GO+(4,𝔽2)11yescharacteristic
236SD16—1816no—
237C2×C8—94no—
238C2×C8—184no—
239C4⋊C4—64no—
240C4⋊C4—92no—
241C4⋊C4—181no—
242C42—92no—
243C42—92no—
244C42—184no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—124no—
254C22×C3—124no—
255C22×C3—124no—
256C22×C3—248no—
257C2×D3—44no—
258C2×D3—44no—
259C2×D3—44no—
260C2×D3—88no—
261C3×C4—24no—
262C3×C4—42no—
263C3×C4—64no—
264C3×C4—122no—
265Dic3—24no—
266Dic3—42no—
267Dic3—62no—
268Dic3—61no—
269Dic3—61no—
270Dic3—62no—
271Dic3—64no—
272Dic3—61no—
273Dic3—61no—
274Dic3—64no—
275C32C2×#46011yescharacteristic, complemented, Sylow
276C23—64no—
277C23—124no—
278C23—124no—
279C23—124no—
280C23C2×GO+(4,𝔽2)11yescharacteristic
281Q8—94no—
282Q8—182no—
283Q8—184no—
284D4—128no—
285D4—184no—
286D4—184no—
287D4—364no—
288D4—368no—
289C2×C4—22no—
290C2×C4—62no—
291C2×C4—64no—
292C2×C4—62no—
293C2×C4—92no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—94no—
297C2×C4—92no—
298C2×C4—92no—
299C2×C4—122no—
300C2×C4C2×GO+(4,𝔽2)12yes—
301C8—184no—
302C2×C3—24no—
303C2×C3—24no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—244no—
311D3—84no—
312C22—124no—
313C22—124no—
314C22—124no—
315C22—248no—
316C22#6422712yes—
317C22#6423012yes—
318C22#6423612yes—
319C22C22×GO+(4,𝔽2)11yescharacteristic
320C4—22no—
321C4—64no—
322C4—94no—
323C4—91no—
324C4—91no—
325C4—92no—
326C4—122no—
327C3—21no—
328C3—21no—
329C2—244no—
330C2#1059335514yesdirect product factor
331C2C2×#6422711yescharacteristic
332C2C2×#6423011yescharacteristic
333C2C2×#6423611yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC2×#63914C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#460
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. C22×#3775C2semidirect
3. C2×#63838C2semidirect
4. C2×#63779C2semidirect
5. C2×#63739C2semidirect
6. #10593355C2direct (N × H)
13. C2×#3775C22semidirect
21. #63838C22semidirect
22. #63779C22semidirect
23. #63739C22semidirect
36. C2×#627D4semidirect
77. C2×C3⋊Dic3SD16semidirect
90. #627C2×D4semidirect
148. C3⋊Dic3C2×SD16semidirect
213. C2×C32#460semidirect
275. C32C2×#460semidirect
330. C2#10593355direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37752
C2×#639142
C2×#638382
C2×#637792
C2×#637392
#105933552
C2×#4609