Finite Group Databasebeta

← C2×#10591188 #11866800

Subgroups — C2×#10591188 #11866800

Order 1152.

1193 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C2×C3×#924C212yesmaximal
3C22×#3718C211yesmaximal, characteristic, complemented
4#10591188C218yesmaximal, direct product factor
5C2×#63576C211yesmaximal, characteristic, complemented
6C2×#63565C212yesmaximal, complemented
7C2×#5051—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C22×C3⋊(C3⋊C8)—24no—
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2214yes—
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#217—22no—
15C2×C3×C4⋊Dic3C2212yes—
16C3×#924—24no—
17C3×#924C2218yes—
18C2×C3×Dic3⋊C4—22no—
19C2×#3718—24no—
20C2×#3718C2214yescomplemented
21#63576C2214yescomplemented
22#63565C2218yescomplemented
23C2×C3×C22⋊Q8—32no—
24C22×#216—32no—
25C2×#924D312yes—
26C23×C3⋊C8—32no—
27C23×C3⋊C8—61no—
28C2×#835—32no—
29#5051—316no—
30C2×#810—32no—
31C2×#807—32no—
32C24×C32D411yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D412yes—
37C22×C32×C4C2312yes—
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3—22no—
40C22×C3×Dic3—22no—
41C2×C3×Dic6—24no—
42C2×C3×Dic6—24no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6C2314yes—
45C2×C3⋊(C3⋊C8)—22no—
46C2×C3⋊(C3⋊C8)—28no—
47C2×C3⋊(C3⋊C8)D414yes—
48C2×C3⋊(C3⋊C8)C2312yes—
49C2×C3⋊(C3⋊C8)C2312yes—
50C3×#217—28no—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3C2314yes—
53C3×Dic3⋊C4—28no—
54#3718—28no—
55C2×#467—91noSylow
56C22×C3×Q8—32no—
57C23×C3×C4—21no—
58C23×C3×C4C2×D312yes—
59C22×Dic6C2×D312yes—
60C3×C22⋊Q8—38no—
61C3×C22⋊Q8—64no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4—62no—
64C2×C3×C22⋊C4—62no—
65C2×#217—22no—
66C2×#216—38no—
67C2×#216—68no—
68C2×C4⋊Dic3C2×D312yes—
69#924—24no—
70#924C2×D318yes—
71C2×Dic3⋊C4—22no—
72C22×C3⋊C8—32no—
73C22×C3⋊C8—32no—
74C22×C3⋊C8—38no—
75C22×C3⋊C8—61no—
76C22×C3⋊C8—61no—
77C22×C3⋊C8—64no—
78C22×C3⋊C8—68no—
79C22×C3⋊C8—68no—
80#835—38no—
81#810—38no—
82#807—38no—
83C23×C32—22no—
84C23×C32—22no—
85C23×C32Q1614yescomplemented
86C23×C32C2×D412yes—
87C23×C32C2×D411yescharacteristic
88C2×C32×C4—22no—
89C2×C32×C4—24no—
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2×D412yes—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4112yes—
96C2×C32×C4C2411yescharacteristic
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—
104C3⋊(C3⋊C8)—22no—
105C3⋊(C3⋊C8)C2×D414yes—
106C22×Q16—91no—
107C23×C8—91no—
108C2×C22⋊Q8—32no—
109#467—98no—
110C2×#107—91no—
111C2×#103—92no—
112C24×C3—21no—
113C24×C3#6712yes—
114C2×C3×Q8—34no—
115C2×C3×Q8—62no—
116C2×C3×Q8—64no—
117C2×C3×Q8—64no—
118C22×C3×C4—24no—
119C22×C3×C4—24no—
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C22×C3×C4—22no—
123C22×C3×C4—21no—
124C22×C3×C4—22no—
125C22×C3×C4—21no—
126C22×C3×C4—62no—
127C22×C3×C4—62no—
128C22×C3×C4#6712yes—
129C22×C3×C4#6714yes—
130C22×C3×C4C22×D314yes—
131C22×C3×C4C22×D312yes—
132C22×Dic3—22no—
133C22×Dic3—22no—
134C2×Dic6—24no—
135C2×Dic6—24no—
136C2×Dic6—22no—
137C2×Dic6C22×D314yes—
138C3×C4⋊C4—34no—
139C3×C4⋊C4—68no—
140C3×C4⋊C4—62no—
141C3×C22⋊C4—68no—
142#217—28no—
143#216—616no—
144C4⋊Dic3—22no—
145C4⋊Dic3C22×D314yes—
146Dic3⋊C4—28no—
147C2×C3⋊C8—38no—
148C2×C3⋊C8—34no—
149C2×C3⋊C8—34no—
150C2×C3⋊C8—64no—
151C2×C3⋊C8—62no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—616no—
154C2×C3⋊C8—616no—
155C2×C3⋊C8—64no—
156C2×C3⋊C8—64no—
157C22×C32—22no—
158C22×C32—22no—
159C22×C32—28no—
160C22×C32#12112yes—
161C22×C32C2×Q1612yes—
162C22×C32C2×Q1614yescomplemented
163C22×C32#13512yes—
164C22×C32C22×D411yescharacteristic
165C32×C4—22no—
166C32×C4#12112yes—
167C32×C4C22×D411yescharacteristic
168C32×C4C2×#4111yescharacteristic
169C3×Dic3—44no—
170C3×Dic3—44no—
171C22×Q8—32no—
172C23×C4D3211yescharacteristic
173C2×Q16—94no—
174C2×Q16—184no—
175C22×C8—91no—
176C22×C8—91no—
177C22×C8—94no—
178C22×C8—184no—
179C22⋊Q8—38no—
180C22⋊Q8—64no—
181C2×C4⋊C4—32no—
182C2×C4⋊C4—62no—
183C2×C22⋊C4—62no—
184#107—94no—
185#103—98no—
186C23×C3—24no—
187C23×C3—24no—
188C23×C3—24no—
189C23×C3—24no—
190C23×C3—24no—
191C23×C3—22no—
192C23×C3—21no—
193C23×C3#21618yescomplemented
194C23×C3C2×#6714yes—
195C23×C3C2×#6712yes—
196C3×Q8—64no—
197C3×Q8—64no—
198C3×Q8—124no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—28no—
203C2×C3×C4—24no—
204C2×C3×C4—28no—
205C2×C3×C4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—21no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—22no—
212C2×C3×C4—64no—
213C2×C3×C4—64no—
214C2×C3×C4—124no—
215C2×C3×C4—124no—
216C2×C3×C4D3×D414yes—
217C2×C3×C4#23714yes—
218C2×C3×C4C2×#6714yes—
219C2×C3×C4C2×#6712yes—
220C2×C3×C4C23×D312yes—
221C2×Dic3—24no—
222C2×Dic3—24no—
223C2×Dic3—44no—
224C2×Dic3—44no—
225Dic6—24no—
226Dic6—24no—
227Dic6—44no—
228C3⋊C8—38no—
229C3⋊C8—64no—
230C3⋊C8—64no—
231C3⋊C8—64no—
232C2×C32—24no—
233C2×C32#46714yescomplemented
234C2×C32C2×#12111yescharacteristic
235C2×C32C22×Q1611yescharacteristic
236C2×C32C2×#13511yescharacteristic
237C24#62511yescharacteristic
238C2×Q8—34no—
239C2×Q8—62no—
240C2×Q8—64no—
241C2×Q8—64no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—62no—
245C22×C4—62no—
246C22×C4#62512yes—
247C22×C4#62511yescharacteristic
248C22×C4C2×D3212yes—
249C22×C4C2×D3211yescharacteristic
250Q16—188no—
251C2×C8—92no—
252C2×C8—94no—
253C2×C8—92no—
254C2×C8—188no—
255C2×C8—182no—
256C4⋊C4—34no—
257C4⋊C4—62no—
258C4⋊C4—68no—
259C22⋊C4—68no—
260C22×C3—24no—
261C22×C3—216no—
262C22×C3—24no—
263C22×C3—24no—
264C22×C3—216no—
265C22×C3—24no—
266C22×C3—21no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—24no—
270C22×C3—22no—
271C22×C3#93914yes—
272C22×C3C2×#21614yes—
273C22×C3C2×#21618yescomplemented
274C22×C3#95014yes—
275C22×C3C22×#6712yes—
276C3×C4—24no—
277C3×C4—24no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—22no—
281C3×C4—124no—
282C3×C4—124no—
283C3×C4#93914yes—
284C3×C4C2×D3×D412yes—
285C3×C4C2×#23712yes—
286Dic3—44no—
287Dic3—44no—
288C32C2×#46711yescharacteristic, complemented, Sylow
289C23—22no—
290C23—22no—
291C23#371814yescomplemented
292C23C2×#62512yes—
293C23C2×#62511yescharacteristic
294Q8—64no—
295Q8—64no—
296Q8—124no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—64no—
302C2×C4—64no—
303C2×C4—124no—
304C2×C4—124no—
305C2×C4#380512yes—
306C2×C4C2×#62512yes—
307C2×C4C2×#62511yescharacteristic
308C2×C4#381112yes—
309C2×C4C22×D3211yescharacteristic
310C8—94no—
311C8—182no—
312C2×C3—28no—
313C2×C3—28no—
314C2×C3—21no—
315C2×C3—24no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3#505118yescomplemented
319C2×C3C2×#93912yes—
320C2×C3C22×#21612yes—
321C2×C3C2×#95012yes—
322C22—22no—
323C22—28no—
324C22—22no—
325C22#6382212yes—
326C22C2×#371812yes—
327C22C2×#371814yescomplemented
328C22#6398012yes—
329C22C22×#62511yescharacteristic
330C4—22no—
331C4—124no—
332C4—124no—
333C4#6398012yes—
334C4C2×#380511yescharacteristic
335C4C2×#381111yescharacteristic
336C3—21no—
337C3C2×#505112yescomplemented
338C2—24no—
339C2#1059118814yesdirect product factor
340C2C2×#6382211yescharacteristic
341C2C22×#371811yescharacteristic
342C2C2×#6398011yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC23×C4D32
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C22×#3718C2semidirect
4. #10591188C2direct (N × H)
5. C2×#63576C2semidirect
6. C2×#63565C2semidirect
20. C2×#3718C22semidirect
21. #63576C22semidirect
22. #63565C22semidirect
85. C23×C32Q16semidirect
162. C22×C32C2×Q16semidirect
193. C23×C3#216semidirect
233. C2×C32#467semidirect
273. C22×C3C2×#216semidirect
288. C32C2×#467semidirect
291. C23#3718semidirect
318. C2×C3#5051semidirect
327. C22C2×#3718semidirect
337. C3C2×#5051semidirect
339. C2#10591188direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3⋊(C3⋊C8)2
C2×C3×#9242
C22×#37182
#105911882
C2×#635762
C2×#635652
C2×#50513