Finite Group Databasebeta

← C2×#10590855 #11866805

Subgroups — C2×#10590855 #11866805

Order 1152.

1193 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 1193 conjugacy classes of subgroups — too many to draw. Only its 228 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×C8×C3⋊D3C211yesmaximal, characteristic
2C2×#63871C212yesmaximal
3C22×#3718C211yesmaximal, characteristic, complemented
4C2×C3×#816C212yesmaximal, complemented
5C2×#63576C211yesmaximal, characteristic, complemented
6#10590855C218yesmaximal, direct product factor
7C2×#4813—32nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C22×C32×C8C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×C8×C3⋊D3—24no—
13C2×C8×C3⋊D3C2214yes—
14C2×C3×C4⋊Dic3C2212yes—
15C2×Dic3⋊Dic3—22no—
16C2×#3722—22no—
17#63871—24no—
18#63871C2218yes—
19C2×#3718—24no—
20C2×#3718C2214yescomplemented
21C3×#816C2218yescomplemented
22#63576C2214yescomplemented
23C2×#946—32no—
24C22×#216—32no—
25C22×D3×C8—32no—
26C22×D3×C8—61no—
27C2×#897—32no—
28C2×C3×#103—32no—
29C2×#816D312yescomplemented
30C2×#807—32no—
31#4813—316no—
32C23×C3⋊D3D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3—22no—
37C2×C4×C3⋊D3D412yes—
38C2×C4×C3⋊D3C2312yes—
39C22×C3×Dic3—22no—
40C22×C3×Dic3—22no—
41C2×C3×Dic6—24no—
42C2×C3×Dic6—24no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6C2314yes—
45C2×C32×C8—22no—
46C2×C32×C8C2312yes—
47C2×C3⋊(C3⋊C8)D414yes—
48C2×C3⋊(C3⋊C8)C2312yes—
49C8×C3⋊D3—28no—
50C3×C4⋊Dic3—22no—
51C3×C4⋊Dic3C2314yes—
52Dic3⋊Dic3—28no—
53#3722—28no—
54#3718—28no—
55C2×#467—91noSylow
56C22×C3×Q8—32no—
57C22×C4×D3—32no—
58C22×C4×D3—61no—
59C22×Dic6C2×D312yes—
60C22×C3×C8—21no—
61C22×C3×C8C2×D312yes—
62C2×C3×C4⋊C4—32no—
63#946—38no—
64#946—64no—
65C2×#216—38no—
66C2×#216—68no—
67C2×(C2×D3)⋊C4—62no—
68C2×(C2×D3)⋊C4—62no—
69C2×C4⋊Dic3—62no—
70C2×C4⋊Dic3C2×D312yes—
71C2×Dic3⋊C4—62no—
72C22×C3⋊C8—32no—
73C22×C3⋊C8—61no—
74C2×D3×C8—38no—
75C2×D3×C8—64no—
76C2×D3×C8—68no—
77C2×D3×C8—68no—
78#897—38no—
79#897—64no—
80C3×#103—38no—
81#816C2×D318yescomplemented
82#807—38no—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—22no—
85C22×C3⋊D3—22no—
86C22×C3⋊D3Q1614yescomplemented
87C22×C3⋊D3C2×D412yes—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D412yes—
90C2×C32×C4#4112yes—
91C2×C32×C4C2411yescharacteristic
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3C2×D412yes—
94C4×C3⋊D3—24no—
95C4×C3⋊D3—22no—
96C4×C3⋊D3—22no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—44no—
100C2×C3×Dic3—44no—
101C3×Dic6—24no—
102C3×Dic6—24no—
103C3×Dic6—44no—
104C32×C8—22no—
105C3⋊(C3⋊C8)C2×D414yes—
106C22×Q16—91no—
107C23×C8—91no—
108C2×C22⋊Q8—92no—
109#467—98no—
110C2×#107—91no—
111C2×#103—32no—
112C23×D3—32no—
113C23×D3—61no—
114C2×C3×Q8—34no—
115C2×C3×Q8—62no—
116C2×C3×Q8—64no—
117C2×C3×Q8—64no—
118C22×C3×C4—21no—
119C22×C3×C4—62no—
120C22×C3×C4—62no—
121C22×C3×C4C22×D312yes—
122C22×Dic3—22no—
123C22×Dic3—22no—
124C22×Dic3—32no—
125C22×Dic3—61no—
126C2×C4×D3—34no—
127C2×C4×D3—34no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—64no—
131C2×C4×D3—64no—
132C2×C4×D3—64no—
133C2×C4×D3—64no—
134C2×Dic6—24no—
135C2×Dic6—24no—
136C2×Dic6—22no—
137C2×Dic6C22×D314yes—
138C2×C3×C8—24no—
139C2×C3×C8—24no—
140C2×C3×C8—22no—
141C2×C3×C8C22×D314yes—
142C3×C4⋊C4—34no—
143C3×C4⋊C4—62no—
144#216—616no—
145(C2×D3)⋊C4—68no—
146(C2×D3)⋊C4—68no—
147C4⋊Dic3—22no—
148C4⋊Dic3—68no—
149C4⋊Dic3C22×D314yes—
150Dic3⋊C4—68no—
151C2×C3⋊C8—38no—
152C2×C3⋊C8—34no—
153C2×C3⋊C8—64no—
154C2×C3⋊C8—62no—
155D3×C8—616no—
156D3×C8—616no—
157C22×C32#12112yes—
158C22×C32C2×Q1612yes—
159C22×C32#13512yes—
160C22×C32C22×D411yescharacteristic
161C2×C3⋊D3—22no—
162C2×C3⋊D3—22no—
163C2×C3⋊D3—28no—
164C2×C3⋊D3C2×Q1614yescomplemented
165C32×C4#12112yes—
166C32×C4C22×D411yescharacteristic
167C32×C4C2×#4111yescharacteristic
168C3⋊Dic3—22no—
169C3×Dic3—44no—
170C3×Dic3—44no—
171C22×Q8—32no—
172C23×C4—91no—
173C2×Q16—94no—
174C2×Q16—184no—
175C22×C8—91no—
176C22×C8—94no—
177C22×C8—184no—
178C22×C8D3211yescharacteristic
179C22⋊Q8—98no—
180C22⋊Q8—184no—
181C2×C4⋊C4—32no—
182C2×C4⋊C4—182no—
183C2×C22⋊C4—182no—
184#107—94no—
185#103—38no—
186C23×C3—21no—
187C23×C3D3×D412yes—
188C22×D3—38no—
189C22×D3—34no—
190C22×D3—64no—
191C22×D3—62no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—64no—
196C3×Q8—64no—
197C3×Q8—64no—
198C3×Q8—124no—
199C2×C3×C4—21no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—22no—
203C2×C3×C4—64no—
204C2×C3×C4—64no—
205C2×C3×C4—124no—
206C2×C3×C4—124no—
207C2×C3×C4#23514yes—
208C2×C3×C4D3×D412yes—
209C2×C3×C4D3×D414yes—
210C2×C3×C4C23×D312yes—
211C2×Dic3—24no—
212C2×Dic3—24no—
213C2×Dic3—34no—
214C2×Dic3—44no—
215C2×Dic3—44no—
216C2×Dic3—62no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C4×D3—64no—
220C4×D3—64no—
221C4×D3—68no—
222C4×D3—68no—
223C4×D3—64no—
224C4×D3—64no—
225Dic6—24no—
226Dic6—24no—
227Dic6—44no—
228C3×C8—24no—
229C3×C8—24no—
230C3⋊C8—38no—
231C3⋊C8—64no—
232C2×C32#46714yescomplemented
233C2×C32C2×#12111yescharacteristic
234C2×C32C22×Q1611yescharacteristic
235C2×C32C2×#13511yescharacteristic
236C3⋊D3—24no—
237C24—91no—
238C2×Q8—34no—
239C2×Q8—62no—
240C2×Q8—64no—
241C2×Q8—64no—
242C22×C4—62no—
243C22×C4—62no—
244C22×C4—91no—
245C22×C4—92no—
246C22×C4—92no—
247C22×C4—182no—
248C22×C4—182no—
249C22×C4C2×D3211yescharacteristic
250Q16—188no—
251C2×C8—22no—
252C2×C8—92no—
253C2×C8—94no—
254C2×C8—188no—
255C2×C8C2×D3212yes—
256C4⋊C4—34no—
257C4⋊C4—62no—
258C4⋊C4—188no—
259C22⋊C4—188no—
260C22×C3—21no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3#88414yes—
265C22×C3#91614yes—
266C22×C3D3×Q1614yes—
267C22×C3C2×D3×D412yes—
268C2×D3—38no—
269C2×D3—64no—
270C2×D3—64no—
271C2×D3—616no—
272C2×D3—64no—
273C2×D3—64no—
274C2×D3—64no—
275C2×D3—616no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—22no—
279C3×C4—124no—
280C3×C4—124no—
281C3×C4#88414yes—
282C3×C4C2×#23512yes—
283C3×C4C2×D3×D412yes—
284Dic3—44no—
285Dic3—44no—
286Dic3—64no—
287Dic3—64no—
288C32C2×#46711yescharacteristic, complemented, Sylow
289C23—92no—
290C23—94no—
291C23—182no—
292C23—182no—
293C23#380211yescharacteristic
294Q8—64no—
295Q8—64no—
296Q8—124no—
297C2×C4—64no—
298C2×C4—64no—
299C2×C4—92no—
300C2×C4—124no—
301C2×C4—124no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—184no—
306C2×C4#379812yes—
307C2×C4#380211yescharacteristic
308C2×C4#381112yes—
309C2×C4C22×D3211yescharacteristic
310C8—22no—
311C8—94no—
312C2×C3—21no—
313C2×C3—24no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3#481318yescomplemented
317C2×C3C2×#88412yes—
318C2×C3C2×#91612yes—
319C2×C3C2×D3×Q1612yes—
320D3—68no—
321D3—68no—
322C22—94no—
323C22—188no—
324C22—182no—
325C22—182no—
326C22#6380212yes—
327C22#6380912yes—
328C22#6391212yes—
329C22C2×#380211yescharacteristic
330C4—124no—
331C4—124no—
332C4—182no—
333C4#6391212yes—
334C4C2×#379811yescharacteristic
335C4C2×#381111yescharacteristic
336C3—21no—
337C3C2×#481312yescomplemented
338C2—184no—
339C2#1059085514yesdirect product factor
340C2C2×#6380211yescharacteristic
341C2C2×#6380911yescharacteristic
342C2C2×#6391211yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C8D32
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C22×#3718C2semidirect
4. C2×C3×#816C2semidirect
5. C2×#63576C2semidirect
6. #10590855C2direct (N × H)
20. C2×#3718C22semidirect
21. C3×#816C22semidirect
22. #63576C22semidirect
29. C2×#816D3semidirect
81. #816C2×D3semidirect
86. C22×C3⋊D3Q16semidirect
164. C2×C3⋊D3C2×Q16semidirect
232. C2×C32#467semidirect
288. C32C2×#467semidirect
316. C2×C3#4813semidirect
337. C3C2×#4813semidirect
339. C2#10590855direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
C2×#638712
C22×#37182
C2×C3×#8162
C2×#635762
#105908552
C2×#48133