Finite Group Databasebeta

← C2×#10593369 #11860134

Subgroups — C2×#10593369 #11860134

Order 1152.

778 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 167 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×#3776C211yesmaximal, characteristic
2C2×C4×#627C211yesmaximal, characteristic
3C2×#63838C211yesmaximal, characteristic
4C2×#63777C211yesmaximal, characteristic
5C2×#63742C211yesmaximal, characteristic
6C2×#63740C211yesmaximal, characteristic
7C2×#63740C211yesmaximal, characteristic
8#10593369C218yesmaximal, direct product factor
9C22×#627C2211yescharacteristic
10C22×#627C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C2×#3776C418yescomplemented
14C2×#3776C2214yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C2×C3×C4×Dic3—21no—
18C2×#3724C2211yescharacteristic
19C2×#3724C2211yescharacteristic
20C2×Dic3⋊Dic3—21no—
21C2×Dic32—21no—
22C4×#627—22no—
23C4×#627C2214yes—
24#63838—22no—
25#63838C2214yes—
26#63777C2214yes—
27#63742C2214yes—
28#63740C2214yes—
29#63740C2214yes—
30C2×#887—61no—
31C2×C4×Dic6—61no—
32C22×C32×C4D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3C2311yescharacteristic
35C22×C3×Dic3—21no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C2×#627—21no—
40C2×#627—21no—
41C2×#627—22no—
42C2×#627—22no—
43C2×#627C2×C414yes—
44C2×#627C2×C414yes—
45C2×#627C2312yes—
46C2×#627C2312yes—
47C2×#622—22no—
48C2×#622C2×C414yes—
49C2×#622C2312yes—
50C2×#622C2312yes—
51#3776C2×C4116yescomplemented
52C4×C3⋊Dic3D412yes—
53C4×C3⋊Dic3C2312yes—
54C3×Dic3⋊C4—24no—
55C3×C4×Dic3—24no—
56#3724—21no—
57#3724—21no—
58#3724C2312yes—
59#3724C2312yes—
60Dic3⋊Dic3—24no—
61Dic32—24no—
62C2×#441—91nomaximal, Sylow
63C22×Dic6—61no—
64C22×Dic6—61no—
65C2×C3×C4⋊C4—61no—
66C2×C3×C42—61no—
67C2×C4⋊Dic3—61no—
68C2×Dic3⋊C4—21no—
69C2×Dic3⋊C4—61no—
70C2×Dic3⋊C4—61no—
71C2×Dic3⋊C4—61no—
72C2×C4×Dic3—21no—
73C2×C4×Dic3—61no—
74C2×C4×Dic3—61no—
75C2×C4×Dic3—61no—
76C2×C4×Dic3—61no—
77#887—64no—
78#887—64no—
79C4×Dic6—64no—
80C4×Dic6—64no—
81C23×C32C2×D411yescharacteristic
82C2×C32×C4—22no—
83C2×C32×C4C2×D412yes—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3C22×C412yes—
86C2×C3⋊Dic3C2×D412yes—
87C2×C3⋊Dic3C2×D411yescharacteristic
88C2×C3⋊Dic3#4112yes—
89C2×C3⋊Dic3C2411yescharacteristic
90C2×C3×Dic3—24no—
91C2×C3×Dic3—24no—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—22no—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—42no—
98#627—24no—
99#627—24no—
100#627—22no—
101#627—22no—
102#627C22×C414yes—
103#627C22×C414yes—
104#622—22no—
105#622C22×C414yes—
106C22×Q16—91no—
107C2×C4×Q8—91no—
108C2×C4×Q8—91no—
109#441—98no—
110C2×#106—91no—
111C2×#103—91no—
112C2×#103—91no—
113C2×#97—91no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—61no—
117C22×C3×C4—61no—
118C22×C3×C4—61no—
119C22×C3×C4—61no—
120C22×Dic3—21no—
121C22×Dic3—21no—
122C22×Dic3—21no—
123C22×Dic3—21no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C2×Dic6—62no—
129C2×Dic6—62no—
130C2×Dic6—64no—
131C2×Dic6—64no—
132C2×Dic6—62no—
133C2×Dic6—62no—
134C2×Dic6—64no—
135C2×Dic6—64no—
136C3×C4⋊C4—64no—
137C3×C42—64no—
138C4⋊Dic3—64no—
139Dic3⋊C4—24no—
140Dic3⋊C4—62no—
141Dic3⋊C4—62no—
142Dic3⋊C4—64no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145C4×Dic3—24no—
146C4×Dic3—62no—
147C4×Dic3—62no—
148C4×Dic3—62no—
149C4×Dic3—62no—
150C4×Dic3—64no—
151C4×Dic3—64no—
152C22×C32C4×D412yes—
153C22×C32#13712yes—
154C22×C32#13712yes—
155C22×C32C22×D411yescharacteristic
156C32×C4—22no—
157C3⋊Dic3—22no—
158C3⋊Dic3C4×D412yes—
159C3⋊Dic3C23×C411yescharacteristic
160C3⋊Dic3C2×#4111yescharacteristic
161C3×Dic3—24no—
162C3×Dic3—24no—
163C3×Dic3—42no—
164C3×Dic3—42no—
165C22×Q8—91no—
166C22×Q8—91no—
167C2×Q16—94no—
168C2×Q16—98no—
169C22×C8—91no—
170C22×C8—91no—
171C4×Q8—94no—
172C4×Q8—94no—
173C4×Q8—182no—
174C4×Q8—182no—
175C2×C4⋊C4—61no—
176C2×C4⋊C4—91no—
177C2×C4⋊C4—91no—
178C2×C4⋊C4—181no—
179C2×C42—61no—
180C2×C42—91no—
181C2×C42—181no—
182#106—94no—
183#103—94no—
184#103—94no—
185#97—94no—
186C23×C3—21no—
187C23×C3—21no—
188C2×C3×C4—24no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—42no—
192C2×C3×C4—62no—
193C2×C3×C4—62no—
194C2×C3×C4—64no—
195C2×C3×C4—64no—
196C2×C3×C4—62no—
197C2×C3×C4—62no—
198C2×C3×C4—122no—
199C2×C3×C4—122no—
200C2×Dic3—22no—
201C2×Dic3—22no—
202C2×Dic3—24no—
203C2×Dic3—24no—
204C2×Dic3—22no—
205C2×Dic3—22no—
206C2×Dic3—42no—
207C2×Dic3—42no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—62no—
218C2×Dic3—64no—
219C2×Dic3—122no—
220Dic6—64no—
221Dic6—64no—
222Dic6—68no—
223Dic6—68no—
224Dic6—64no—
225Dic6—64no—
226C2×C32#44114yescomplemented
227C2×C32C2×C4×D411yescharacteristic
228C2×C32C2×#13711yescharacteristic
229C2×C32C2×#13711yescharacteristic
230C2×Q8—92no—
231C2×Q8—92no—
232C2×Q8—94no—
233C2×Q8—94no—
234C2×Q8—181no—
235C2×Q8—181no—
236C2×Q8—182no—
237C2×Q8—182no—
238C22×C4—61no—
239C22×C4—61no—
240C22×C4—61no—
241C22×C4—61no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4GO+(4,𝔽2)11yescharacteristic
245Q16—916no—
246C2×C8—92no—
247C2×C8—94no—
248C2×C8—92no—
249C2×C8—182no—
250C4⋊C4—64no—
251C4⋊C4—92no—
252C4⋊C4—92no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—184no—
256C42—64no—
257C42—92no—
258C42—92no—
259C42—184no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C3×C4—24no—
269C3×C4—42no—
270C3×C4—64no—
271C3×C4—64no—
272C3×C4—122no—
273C3×C4—122no—
274Dic3—24no—
275Dic3—24no—
276Dic3—42no—
277Dic3—42no—
278Dic3—62no—
279Dic3—62no—
280Dic3—61no—
281Dic3—61no—
282Dic3—61no—
283Dic3—61no—
284Dic3—64no—
285Dic3—122no—
286C32C2×#44111yescharacteristic, complemented, Sylow
287C23C2×GO+(4,𝔽2)11yescharacteristic
288Q8—94no—
289Q8—94no—
290Q8—182no—
291Q8—182no—
292Q8—184no—
293Q8—184no—
294C2×C4—22no—
295C2×C4—62no—
296C2×C4—62no—
297C2×C4—64no—
298C2×C4—64no—
299C2×C4—62no—
300C2×C4—62no—
301C2×C4—91no—
302C2×C4—91no—
303C2×C4—92no—
304C2×C4—92no—
305C2×C4—92no—
306C2×C4—122no—
307C2×C4—122no—
308C2×C4—182no—
309C2×C4C2×GO+(4,𝔽2)12yes—
310C8—94no—
311C8—182no—
312C2×C3—24no—
313C2×C3—24no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C22#6422612yes—
321C22C4×GO+(4,𝔽2)12yes—
322C22#6423912yes—
323C22C22×GO+(4,𝔽2)11yescharacteristic
324C4—22no—
325C4—64no—
326C4—64no—
327C4—91no—
328C4—91no—
329C4—92no—
330C4—122no—
331C4—122no—
332C4—182no—
333C3—21no—
334C3—21no—
335C2#1059336914yesdirect product factor
336C2C2×#6422611yescharacteristic
337C2C2×C4×GO+(4,𝔽2)11yescharacteristic
338C2C2×#6423911yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#441
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #10593369C2direct (N × H)
13. C2×#3776C4semidirect
51. #3776C2×C4semidirect
226. C2×C32#441semidirect
286. C32C2×#441semidirect
335. C2#10593369direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37762
C2×C4×#6272
C2×#638382
C2×#637772
C2×#637422
C2×#637402
#105933692
C2×#4419