Finite Group Databasebeta

← C2×#10592921 #11808134

Subgroups — C2×#10592921 #11808134

Order 1152.

3756 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×D4C211yesmaximal, characteristic
2C22×#3757C212yesmaximal, complemented
3C22×#3757C212yesmaximal, complemented
4C22×#3750C211yesmaximal, characteristic, complemented
5#10592921C218yesmaximal, direct product factor
6C2×#63658C211yesmaximal, characteristic, complemented
7C2×#5222—34nomaximal
8C25×C32C2212yes—
9C22×C32×D4—24no—
10C22×C32×D4—28no—
11C22×C32×D4C2214yes—
12C23×C32×C4C2211yescharacteristic
13C23×C3⋊Dic3C2212yes—
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C2×#3757—28no—
17C2×#3757—28no—
18C2×#3757C2218yescomplemented
19C2×#3757C2218yescomplemented
20C2×#3750—24no—
21C2×#3750C2214yescomplemented
22#63658C2214yescomplemented
23C23×C3×D4D314yes—
24C22×#217—38no—
25C22×#217—38no—
26C22×Dic3⋊C4—34no—
27#5222—332no—
28C2×C3⋊#95—34no—
29C24×C32—24no—
30C24×C32—24no—
31C24×C32—24no—
32C24×C32—24no—
33C24×C32—24no—
34C24×C32—24no—
35C24×C32D418yes—
36C24×C32C2314yes—
37C24×C32C2311yescharacteristic
38C2×C32×D4—232no—
39C2×C32×D4—216no—
40C2×C32×D4—28no—
41C22×C32×C4—24no—
42C22×C32×C4D414yes—
43C22×C32×C4C2312yes—
44C22×C3⋊Dic3—22no—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3—22no—
47C22×C3⋊Dic3—24no—
48C22×C3⋊Dic3—24no—
49C22×C3⋊Dic3—24no—
50C22×C3⋊Dic3—24no—
51C22×C3⋊Dic3D414yescomplemented
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2314yes—
54C22×C3⋊Dic3C2312yes—
55#3757—216no—
56#3757—216no—
57#3750—28no—
58C2×#394—91noSylow
59C25×C3C2×D318yes—
60C22×C3×D4—232no—
61C22×C3×D4—216no—
62C22×C3×D4C2×D3116yes—
63C23×C3×C4C2×D314yes—
64C23×Dic3—34no—
65C23×Dic3—38no—
66C23×Dic3—34no—
67C2×#217—332no—
68C2×#217—332no—
69C2×#217—632no—
70C2×#217—632no—
71C2×Dic3⋊C4—316no—
72C2×Dic3⋊C4—616no—
73C3⋊#95—316no—
74C23×C32—216no—
75C23×C32—216no—
76C23×C32—216no—
77C23×C32—24no—
78C23×C32—24no—
79C23×C32—24no—
80C23×C32—24no—
81C23×C32—24no—
82C23×C32—24no—
83C23×C32—48no—
84C23×C32—48no—
85C23×C32—48no—
86C23×C32—48no—
87C23×C32C2×D412yes—
88C23×C32C2×D418yes—
89C23×C32C2×D414yes—
90C23×C32C2×D412yes—
91C23×C32#4112yes—
92C23×C32#4114yes—
93C23×C32C2411yescharacteristic
94C32×D4—232no—
95C2×C32×C4—28no—
96C2×C32×C4—24no—
97C2×C32×C4C2×D414yes—
98C2×C3⋊Dic3—28no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3—24no—
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3—44no—
107C2×C3⋊Dic3—48no—
108C2×C3⋊Dic3C2×D414yescomplemented
109C23×D4C3⋊D311yescharacteristic
110C22×C4⋊C4—91no—
111C22×C22⋊C4—92no—
112C22×C22⋊C4—92no—
113#394—98no—
114C2×#95—91no—
115C24×C3—216no—
116C24×C3—216no—
117C24×C3—216no—
118C24×C3—216no—
119C24×C3—216no—
120C24×C3—216no—
121C24×C3#67132yes—
122C24×C3C22×D3116yes—
123C24×C3C22×D314yes—
124C2×C3×D4—2128no—
125C2×C3×D4—264no—
126C2×C3×D4—232no—
127C22×C3×C4—216no—
128C22×C3×C4#67116yes—
129C22×C3×C4C22×D318yes—
130C22×Dic3—316no—
131C22×Dic3—38no—
132C22×Dic3—316no—
133C22×Dic3—38no—
134C22×Dic3—68no—
135C22×Dic3—68no—
136C22×Dic3—616no—
137C22×Dic3—616no—
138C22×Dic3—68no—
139C22×Dic3—616no—
140C22×Dic3—616no—
141#217—664no—
142#217—664no—
143Dic3⋊C4—632no—
144C22×C32—28no—
145C22×C32—28no—
146C22×C32—28no—
147C22×C32—44no—
148C22×C32—44no—
149C22×C32—44no—
150C22×C32—44no—
151C22×C32—432no—
152C22×C32#12014yes—
153C22×C32#12114yes—
154C22×C32#12118yes—
155C22×C32#12318yes—
156C22×C32#12414yes—
157C22×C32C22×D411yescharacteristic
158C22×C32C22×D412yes—
159C22×C32C22×D411yescharacteristic
160C22×C32C2×#4111yescharacteristic
161C22×C32C2×#4112yes—
162C32×C4—24no—
163C3⋊Dic3—24no—
164C3⋊Dic3—42no—
165C3⋊Dic3—44no—
166C25C2×C3⋊D312yes—
167C22×D4—28no—
168C22×D4—24no—
169C22×D4C2×C3⋊D314yes—
170C23×C4—91no—
171C23×C4—91no—
172C23×C4—92no—
173C23×C4C2×C3⋊D311yescharacteristic
174C2×C4⋊C4—94no—
175C2×C4⋊C4—184no—
176C2×C22⋊C4—98no—
177C2×C22⋊C4—98no—
178C2×C22⋊C4—188no—
179C2×C22⋊C4—188no—
180#95—94no—
181C23×C3—264no—
182C23×C3—264no—
183C23×C3—264no—
184C23×C3—216no—
185C23×C3—216no—
186C23×C3—216no—
187C23×C3—216no—
188C23×C3—216no—
189C23×C3—216no—
190C23×C3—432no—
191C23×C3—432no—
192C23×C3—432no—
193C23×C3—432no—
194C23×C3D3×D418yes—
195C23×C3#23718yes—
196C23×C3#237116yes—
197C23×C3C2×#67132yes—
198C23×C3C2×#67116yes—
199C23×C3C2×#6718yes—
200C23×C3C23×D314yes—
201C3×D4—2128no—
202C2×C3×C4—232no—
203C2×C3×C4—216no—
204C2×C3×C4C2×#67116yes—
205C2×Dic3—316no—
206C2×Dic3—632no—
207C2×Dic3—68no—
208C2×Dic3—68no—
209C2×Dic3—616no—
210C2×Dic3—616no—
211C2×Dic3—68no—
212C2×Dic3—616no—
213C2×Dic3—616no—
214C2×Dic3—1232no—
215C2×Dic3—1216no—
216C2×C32—48no—
217C2×C32#39418yescomplemented
218C2×C32C2×#12011yescharacteristic
219C2×C32C2×#12111yescharacteristic
220C2×C32C2×#12112yes—
221C2×C32C2×#12312yes—
222C2×C32C2×#12411yescharacteristic
223C24—24no—
224C24—24no—
225C24—24no—
226C24—24no—
227C24—24no—
228C24—24no—
229C24#63818yes—
230C24C22×C3⋊D314yes—
231C24C22×C3⋊D311yescharacteristic
232C2×D4—232no—
233C2×D4—216no—
234C2×D4—28no—
235C22×C4—24no—
236C22×C4—92no—
237C22×C4—94no—
238C22×C4—94no—
239C22×C4—92no—
240C22×C4—182no—
241C22×C4—182no—
242C22×C4—184no—
243C22×C4—184no—
244C22×C4—184no—
245C22×C4—184no—
246C22×C4—182no—
247C22×C4#63814yes—
248C22×C4C22×C3⋊D312yes—
249C4⋊C4—188no—
250C22⋊C4—1816no—
251C22⋊C4—1816no—
252C22×C3—232no—
253C22×C3—232no—
254C22×C3—232no—
255C22×C3—4128no—
256C22×C3—416no—
257C22×C3—416no—
258C22×C3—416no—
259C22×C3—416no—
260C22×C3#935132yes—
261C22×C3#936116yes—
262C22×C3#938116yes—
263C22×C3#939132yes—
264C22×C3#953116yes—
265C22×C3C2×D3×D414yes—
266C22×C3C2×#23714yes—
267C22×C3C2×#23718yes—
268C22×C3C22×#6718yes—
269C22×C3C22×#6714yes—
270C3×C4—216no—
271Dic3—616no—
272Dic3—1216no—
273Dic3—128no—
274C32C2×#39411yescharacteristic, complemented, Sylow
275C23—24no—
276C23—24no—
277C23—24no—
278C23—24no—
279C23—24no—
280C23—24no—
281C23—216no—
282C23—216no—
283C23—216no—
284C23—48no—
285C23—48no—
286C23—48no—
287C23—48no—
288C23D4×C3⋊D312yes—
289C23#383012yes—
290C23#383014yes—
291C23C2×#63818yes—
292C23C2×#63814yes—
293C23C2×#63812yes—
294C23C23×C3⋊D311yescharacteristic
295D4—232no—
296C2×C4—24no—
297C2×C4—28no—
298C2×C4—94no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—188no—
302C2×C4—184no—
303C2×C4—184no—
304C2×C4—184no—
305C2×C4—184no—
306C2×C4—182no—
307C2×C4—368no—
308C2×C4—364no—
309C2×C4C2×#63814yes—
310C2×C3—432no—
311C2×C3#5222132yescomplemented
312C2×C3C2×#93518yes—
313C2×C3C2×#93614yes—
314C2×C3C2×#93814yes—
315C2×C3C2×#93918yes—
316C2×C3C2×#95314yes—
317C22—28no—
318C22—28no—
319C22—28no—
320C22—432no—
321C22—44no—
322C22—44no—
323C22—44no—
324C22—44no—
325C22#6414418yes—
326C22#6414514yes—
327C22#6414714yes—
328C22#6414818yes—
329C22#6416214yes—
330C22C2×D4×C3⋊D311yescharacteristic
331C22C2×#383011yescharacteristic
332C22C2×#383012yes—
333C22C22×#63812yes—
334C22C22×#63811yescharacteristic
335C4—24no—
336C4—184no—
337C4—364no—
338C4—362no—
339C3C2×#522214yescomplemented
340C2—48no—
341C2#1059292118yesdirect product factor
342C2C2×#6414412yes—
343C2C2×#6414511yescharacteristic
344C2C2×#6414711yescharacteristic
345C2C2×#6414812yes—
346C2C2×#6416211yescharacteristic
subgroupG/H
centerC24C22×C3⋊D3
commutator, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
Fitting, prime radicalC23×C32×D4C2
socleC24×C32C23
hypercenterC23×D4C3⋊D3
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
2. C22×#3757C2semidirect
3. C22×#3757C2semidirect
4. C22×#3750C2semidirect
5. #10592921C2direct (N × H)
6. C2×#63658C2semidirect
18. C2×#3757C22semidirect
19. C2×#3757C22semidirect
21. C2×#3750C22semidirect
22. #63658C22semidirect
51. C22×C3⋊Dic3D4semidirect
108. C2×C3⋊Dic3C2×D4semidirect
217. C2×C32#394semidirect
274. C32C2×#394semidirect
311. C2×C3#5222semidirect
339. C3C2×#5222semidirect
341. C2#10592921direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×D42
C22×#37572
C22×#37502
#105929212
C2×#636582
C2×#52223