Finite Group Databasebeta

← C2×#10591633 #11865650

Subgroups — C2×#10591633 #11865650

Order 1152.

1109 conjugacy classes of subgroups; only the 252 normal subgroups are shown.

normal subgroups only

This group has 1109 conjugacy classes of subgroups — too many to draw. Only its 252 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×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C22×C3×#216C212yesmaximal
3C2×#63873C211yesmaximal, characteristic
4#10591633C218yesmaximal, direct product factor
5C2×#63572C211yesmaximal, characteristic
6C2×#63566C212yesmaximal
7C2×#5182—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10Q8×C3⋊Dic3—22no—
11Q8×C3⋊Dic3C2214yes—
12C2×C4⋊(C3⋊Dic3)—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×#216—28no—
17C2×C3×#216C2218yes—
18C22×C3×C3⋊C8C2212yes—
19C2×#3724—21no—
20C2×#3724—21no—
21#63873—22no—
22#63873C2214yes—
23#63572C2214yes—
24#63566C2218yes—
25C22×C3×Q16—32no—
26C2×Q8×Dic3—32no—
27C2×Q8×Dic3—61no—
28C2×#944—32no—
29C22×#216D312yes—
30C2×#835—32no—
31#5182—316no—
32C2×#816—32no—
33C2×Dic3⋊C8—32no—
34C2×C32×Q8—21no—
35C2×C32×Q8—22no—
36C2×C32×Q8D414yes—
37C2×C32×Q8C2312yes—
38C22×C32×C4—21no—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43C22×C3×Dic3—22no—
44C2×C3×Dic6—24no—
45C2×C3×Dic6—24no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6C2314yes—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—24no—
50C4⋊(C3⋊Dic3)C2312yes—
51C4×C3⋊Dic3—24no—
52C4×C3⋊Dic3D412yes—
53C4×C3⋊Dic3C2312yes—
54C3×#216—216no—
55C2×C3×C3⋊C8—24no—
56C2×C3×C3⋊C8C2314yes—
57#3724—24no—
58#3724—24no—
59C2×#462—91noSylow
60C22×C3×Q8—21no—
61C22×C3×Q8—32no—
62C22×C3×Q8C2×D312yes—
63C22×Dic6C2×D312yes—
64C2×C3×Q16—38no—
65C2×C3×Q16—68no—
66C22×C3×C8—32no—
67Q8×Dic3—38no—
68Q8×Dic3—64no—
69Q8×Dic3—64no—
70Q8×Dic3—64no—
71#944—38no—
72#944—64no—
73C2×#216—28no—
74C2×#216C2×D318yes—
75C2×C4⋊Dic3—32no—
76C2×C4⋊Dic3—61no—
77C2×C4⋊Dic3—62no—
78C2×C4⋊Dic3—62no—
79C2×Dic3⋊C4—62no—
80C2×Dic3⋊C4—62no—
81C2×C4×Dic3—32no—
82C2×C4×Dic3—61no—
83C2×C4×Dic3—62no—
84C2×C4×Dic3—62no—
85C22×C3⋊C8C2×D312yes—
86#835—38no—
87#816—38no—
88Dic3⋊C8—38no—
89C23×C32C2×D411yescharacteristic
90C32×Q8—24no—
91C32×Q8—22no—
92C32×Q8C2×D414yes—
93C2×C32×C4—24no—
94C2×C32×C4—22no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D412yes—
97C2×C32×C4#4112yes—
98C2×C32×C4C2411yescharacteristic
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3Q1614yescomplemented
103C2×C3⋊Dic3C2×D412yes—
104C2×C3⋊Dic3C2×D412yes—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—44no—
107C3×Dic6—24no—
108C3×Dic6—24no—
109C3×Dic6—44no—
110C3×C3⋊C8—24no—
111C22×Q16—32no—
112C2×C4⋊Q8—91no—
113C2×C4×Q8—91no—
114#462—98no—
115C2×C4⋊C8—91no—
116C2×#103—92no—
117C2×C3×Q8—22no—
118C2×C3×Q8—24no—
119C2×C3×Q8—22no—
120C2×C3×Q8—24no—
121C2×C3×Q8—24no—
122C2×C3×Q8—22no—
123C2×C3×Q8—34no—
124C2×C3×Q8—62no—
125C2×C3×Q8—64no—
126C2×C3×Q8—64no—
127C2×C3×Q8#6718yes—
128C2×C3×Q8C22×D314yes—
129C22×C3×C4—22no—
130C22×C3×C4—22no—
131C22×C3×C4—21no—
132C22×C3×C4—62no—
133C22×C3×C4C22×D312yes—
134C22×Dic3—22no—
135C22×Dic3—32no—
136C22×Dic3—32no—
137C22×Dic3—61no—
138C22×Dic3—61no—
139C22×Dic3—62no—
140C22×Dic3—62no—
141C2×Dic6—24no—
142C2×Dic6—24no—
143C2×Dic6—22no—
144C2×Dic6C22×D314yes—
145C3×Q16—616no—
146C2×C3×C8—34no—
147C2×C3×C8—64no—
148#216—216no—
149C4⋊Dic3—34no—
150C4⋊Dic3—62no—
151C4⋊Dic3—68no—
152C4⋊Dic3—68no—
153C4⋊Dic3—62no—
154C4⋊Dic3—62no—
155Dic3⋊C4—68no—
156Dic3⋊C4—68no—
157C4×Dic3—34no—
158C4×Dic3—34no—
159C4×Dic3—62no—
160C4×Dic3—62no—
161C4×Dic3—68no—
162C4×Dic3—68no—
163C2×C3⋊C8—24no—
164C2×C3⋊C8C22×D314yes—
165C22×C32#12112yes—
166C22×C32C2×Q1612yes—
167C22×C32#13712yes—
168C22×C32C22×D411yescharacteristic
169C32×C4—24no—
170C32×C4#12112yes—
171C32×C4C22×D411yescharacteristic
172C32×C4C2×#4111yescharacteristic
173C3⋊Dic3—22no—
174C3⋊Dic3—42no—
175C3⋊Dic3C2×Q1614yescomplemented
176C3×Dic3—44no—
177C22×Q8—32no—
178C22×Q8D3211yescharacteristic
179C2×Q16—38no—
180C2×Q16—68no—
181C22×C8—32no—
182C4⋊Q8—94no—
183C4⋊Q8—182no—
184C4×Q8—94no—
185C4×Q8—182no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—181no—
188C2×C4⋊C4—181no—
189C2×C4⋊C4—181no—
190C2×C42—91no—
191C2×C42—181no—
192C4⋊C8—94no—
193#103—98no—
194C23×C3—21no—
195C23×C3D3×D412yes—
196C3×Q8—24no—
197C3×Q8—28no—
198C3×Q8—28no—
199C3×Q8—24no—
200C3×Q8—24no—
201C3×Q8—64no—
202C3×Q8—64no—
203C3×Q8—124no—
204C3×Q8C2×#6718yes—
205C2×C3×C4—24no—
206C2×C3×C4—28no—
207C2×C3×C4—28no—
208C2×C3×C4—24no—
209C2×C3×C4—21no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—21no—
213C2×C3×C4—64no—
214C2×C3×C4—124no—
215C2×C3×C4D3×D412yes—
216C2×C3×C4#23714yes—
217C2×C3×C4C2×#6714yes—
218C2×C3×C4C23×D312yes—
219C2×Dic3—24no—
220C2×Dic3—38no—
221C2×Dic3—34no—
222C2×Dic3—34no—
223C2×Dic3—44no—
224C2×Dic3—64no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—64no—
228C2×Dic3—64no—
229C2×Dic3—64no—
230C2×Dic3—122no—
231C2×Dic3—124no—
232C2×Dic3—124no—
233Dic6—24no—
234Dic6—24no—
235Dic6—44no—
236C3×C8—64no—
237C3⋊C8—24no—
238C2×C32#46214yescomplemented
239C2×C32C2×#12111yescharacteristic
240C2×C32C22×Q1611yescharacteristic
241C2×C32C2×#13711yescharacteristic
242C2×Q8—22no—
243C2×Q8—21no—
244C2×Q8—34no—
245C2×Q8—62no—
246C2×Q8—64no—
247C2×Q8—64no—
248C2×Q8#62514yes—
249C2×Q8C2×D3212yes—
250C22×C4—21no—
251C22×C4—62no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—181no—
255C22×C4C2×D3211yescharacteristic
256Q16—616no—
257C2×C8—34no—
258C2×C8—64no—
259C4⋊C4—92no—
260C4⋊C4—184no—
261C4⋊C4—184no—
262C4⋊C4—184no—
263C4⋊C4—181no—
264C42—92no—
265C42—92no—
266C42—184no—
267C22×C3—21no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3D3×Q1614yes—
272C22×C3#91814yes—
273C22×C3#93914yes—
274C22×C3C2×D3×D412yes—
275C3×C4—28no—
276C3×C4—28no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—22no—
280C3×C4—124no—
281C3×C4#93914yes—
282C3×C4C2×#23712yes—
283C3×C4C22×#6712yes—
284Dic3—38no—
285Dic3—44no—
286Dic3—64no—
287Dic3—64no—
288Dic3—122no—
289Dic3—124no—
290Dic3—124no—
291C32C2×#46211yescharacteristic, complemented, Sylow
292C23#381111yescharacteristic
293Q8—22no—
294Q8—24no—
295Q8—64no—
296Q8—64no—
297Q8—124no—
298Q8C2×#62514yes—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—64no—
302C2×C4—92no—
303C2×C4—94no—
304C2×C4—92no—
305C2×C4—124no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—362no—
309C2×C4#380512yes—
310C2×C4C2×#62512yes—
311C2×C4#381111yescharacteristic
312C2×C4C22×D3211yescharacteristic
313C8—64no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—24no—
317C2×C3—21no—
318C2×C3#518218yescomplemented
319C2×C3C2×D3×Q1612yes—
320C2×C3C2×#91812yes—
321C2×C3C2×#93912yes—
322C22#6394412yes—
323C22#6394512yes—
324C22#6398012yes—
325C22C2×#381111yescharacteristic
326C4—24no—
327C4—94no—
328C4—124no—
329C4—182no—
330C4—362no—
331C4#6398012yes—
332C4C2×#380511yescharacteristic
333C4C22×#62511yescharacteristic
334C3—21no—
335C3C2×#518212yescomplemented
336C2#1059163314yesdirect product factor
337C2C2×#6394411yescharacteristic
338C2C2×#6394511yescharacteristic
339C2C2×#6398011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32C2×#462
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10591633C2direct (N × H)
102. C2×C3⋊Dic3Q16semidirect
175. C3⋊Dic3C2×Q16semidirect
238. C2×C32#462semidirect
291. C32C2×#462semidirect
318. C2×C3#5182semidirect
335. C3C2×#5182semidirect
336. C2#10591633direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C22×C3×#2162
C2×#638732
#105916332
C2×#635722
C2×#635662
C2×#51823