Finite Group Databasebeta

← C2×#10592750 #11866774

Subgroups — C2×#10592750 #11866774

Order 1152.

1536 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
1C2×C32×C22⋊Q8C211yesmaximal, characteristic
2C22×#3756C211yesmaximal, characteristic, complemented
3C2×#64133C211yesmaximal, characteristic
4C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic
5C2×#63662C211yesmaximal, characteristic, complemented
6#10592750C218yesmaximal, direct product factor
7C2×#63637C211yesmaximal, characteristic, complemented
8C2×#63634C211yesmaximal, characteristic, complemented
9C2×#5051—34nomaximal
10C22×C32×Q8C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C32×C22⋊Q8—22no—
14C32×C22⋊Q8C2214yes—
15C2×C32×C4⋊C4—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C22⋊C4—21no—
18C2×#3757—21no—
19C2×#3756—24no—
20C2×#3756C2214yescomplemented
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22#64133—22no—
23#64133C2214yes—
24C2×#3750—21no—
25C22×C3⋊(C3⋊C8)—24no—
26C22×C3⋊(C3⋊C8)C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2214yes—
28C22×C3⋊(C3⋊C8)C2211yescharacteristic
29#63662C2214yescomplemented
30#63637C2214yescomplemented
31#63634C2214yescomplemented
32C2×C3×C22⋊Q8D314yes—
33C22×#216—34no—
34C2×#924—34no—
35C23×C3⋊C8—34no—
36C2×#835—34no—
37#5051—332no—
38C2×#810—34no—
39C2×#807—34no—
40C24×C32D411yescharacteristic
41C2×C32×Q8—21no—
42C2×C32×Q8—22no—
43C2×C32×Q8—22no—
44C2×C32×Q8C2312yes—
45C22×C32×C4—22no—
46C22×C32×C4—22no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4D411yescharacteristic
50C22×C32×C4D412yes—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—21no—
55C2×#634—22no—
56C2×#634—22no—
57C2×#634—21no—
58C2×#634C2312yes—
59C32×C4⋊C4—24no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62C32×C22⋊C4—24no—
63#3757—24no—
64#3756—28no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67#3750—24no—
68C2×C3⋊(C3⋊C8)—22no—
69C2×C3⋊(C3⋊C8)—28no—
70C2×C3⋊(C3⋊C8)D414yes—
71C2×C3⋊(C3⋊C8)C2312yes—
72C2×C3⋊(C3⋊C8)C2312yes—
73C2×#467—91noSylow
74C22×C3×Q8C2×D314yes—
75C23×C3×C4C2×D314yes—
76C22×Dic6—34no—
77C3×C22⋊Q8—28no—
78C3×C22⋊Q8C2×D3116yes—
79C2×C3×C4⋊C4—24no—
80C2×C3×C4⋊C4C2×D314yes—
81C2×C3×C22⋊C4—24no—
82C2×#217—64no—
83C2×#216—316no—
84C2×#216—616no—
85C2×C4⋊Dic3—34no—
86#924—316no—
87#924—68no—
88C2×Dic3⋊C4—64no—
89C22×C3⋊C8—34no—
90C22×C3⋊C8—34no—
91C22×C3⋊C8—316no—
92C22×C3⋊C8—616no—
93#835—316no—
94#810—316no—
95#807—316no—
96C23×C32—22no—
97C23×C32—22no—
98C23×C32Q1614yescomplemented
99C23×C32C2×D412yes—
100C23×C32C2×D411yescharacteristic
101C32×Q8—22no—
102C32×Q8—22no—
103C32×Q8—42no—
104C2×C32×C4—22no—
105C2×C32×C4—24no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—42no—
111C2×C32×C4—42no—
112C2×C32×C4C2×D412yes—
113C2×C32×C4C2×D412yes—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4#4112yes—
116C2×C32×C4C2411yescharacteristic
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—42no—
120C2×C3⋊Dic3—42no—
121#634—22no—
122#634—22no—
123#634—42no—
124C3⋊(C3⋊C8)—22no—
125C3⋊(C3⋊C8)C2×D414yes—
126C22×Q16—91no—
127C23×C8—91no—
128C2×C22⋊Q8—91no—
129C2×C22⋊Q8C3⋊D311yescharacteristic
130#467—98no—
131C2×#107—91no—
132C2×#103—91no—
133C2×#103—91no—
134C24×C3#6714yes—
135C2×C3×Q8—24no—
136C2×C3×Q8—28no—
137C2×C3×Q8—28no—
138C2×C3×Q8C22×D318yes—
139C22×C3×C4—28no—
140C22×C3×C4—28no—
141C22×C3×C4—24no—
142C22×C3×C4—24no—
143C22×C3×C4#6714yes—
144C22×C3×C4#6718yes—
145C22×C3×C4C22×D318yes—
146C22×C3×C4C22×D314yes—
147C22×Dic3—64no—
148C22×Dic3—64no—
149C2×Dic6—38no—
150C2×Dic6—68no—
151C2×Dic6—68no—
152C2×Dic6—64no—
153C3×C4⋊C4—216no—
154C3×C4⋊C4—24no—
155C3×C4⋊C4C22×D318yes—
156C3×C22⋊C4—216no—
157#217—616no—
158#216—632no—
159C4⋊Dic3—38no—
160C4⋊Dic3—64no—
161Dic3⋊C4—616no—
162C2×C3⋊C8—316no—
163C2×C3⋊C8—38no—
164C2×C3⋊C8—38no—
165C2×C3⋊C8—632no—
166C2×C3⋊C8—68no—
167C22×C32—22no—
168C22×C32—22no—
169C22×C32—28no—
170C22×C32#12112yes—
171C22×C32C2×Q1612yes—
172C22×C32C2×Q1614yescomplemented
173C22×C32#13512yes—
174C22×C32C22×D411yescharacteristic
175C32×C4—22no—
176C32×C4—42no—
177C32×C4—42no—
178C32×C4#12112yes—
179C32×C4C22×D411yescharacteristic
180C32×C4C2×#4111yescharacteristic
181C3⋊Dic3—42no—
182C3⋊Dic3—42no—
183C22×Q8—91no—
184C22×Q8C2×C3⋊D311yescharacteristic
185C23×C4C2×C3⋊D311yescharacteristic
186C2×Q16—94no—
187C2×Q16—184no—
188C22×C8—91no—
189C22×C8—91no—
190C22×C8—94no—
191C22×C8—184no—
192C22⋊Q8—22no—
193C22⋊Q8—94no—
194C22⋊Q8—182no—
195C22⋊Q8C2×C3⋊D314yes—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—91no—
198C2×C4⋊C4—181no—
199C2×C4⋊C4C2×C3⋊D311yescharacteristic
200C2×C22⋊C4—21no—
201C2×C22⋊C4—181no—
202#107—94no—
203#103—94no—
204#103—94no—
205C23×C3—28no—
206C23×C3—28no—
207C23×C3#216116yescomplemented
208C23×C3C2×#6718yes—
209C23×C3C2×#6714yes—
210C3×Q8—28no—
211C3×Q8—28no—
212C3×Q8—48no—
213C2×C3×C4—28no—
214C2×C3×C4—216no—
215C2×C3×C4—28no—
216C2×C3×C4—28no—
217C2×C3×C4—28no—
218C2×C3×C4—28no—
219C2×C3×C4—48no—
220C2×C3×C4—48no—
221C2×C3×C4D3×D418yes—
222C2×C3×C4#23718yes—
223C2×C3×C4C2×#6718yes—
224C2×C3×C4C2×#6714yes—
225C2×C3×C4C23×D314yes—
226C2×Dic3—68no—
227C2×Dic3—68no—
228C2×Dic3—128no—
229C2×Dic3—128no—
230Dic6—68no—
231Dic6—68no—
232Dic6—128no—
233C3⋊C8—316no—
234C3⋊C8—68no—
235C2×C32—24no—
236C2×C32#46714yescomplemented
237C2×C32C2×#12111yescharacteristic
238C2×C32C22×Q1611yescharacteristic
239C2×C32C2×#13511yescharacteristic
240C24#63811yescharacteristic
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—92no—
245C2×Q8—181no—
246C2×Q8—182no—
247C2×Q8—182no—
248C2×Q8C22×C3⋊D312yes—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—181no—
254C22×C4—181no—
255C22×C4#63812yes—
256C22×C4#63811yescharacteristic
257C22×C4C22×C3⋊D312yes—
258C22×C4C22×C3⋊D311yescharacteristic
259Q16—188no—
260C2×C8—92no—
261C2×C8—94no—
262C2×C8—92no—
263C2×C8—188no—
264C2×C8—182no—
265C4⋊C4—24no—
266C4⋊C4—21no—
267C4⋊C4—92no—
268C4⋊C4—181no—
269C4⋊C4—184no—
270C4⋊C4C22×C3⋊D312yes—
271C22⋊C4—24no—
272C22⋊C4—184no—
273C22×C3—28no—
274C22×C3—232no—
275C22×C3—28no—
276C22×C3#93918yes—
277C22×C3C2×#21618yes—
278C22×C3C2×#216116yescomplemented
279C22×C3#95018yes—
280C22×C3C22×#6714yes—
281C3×C4—28no—
282C3×C4—48no—
283C3×C4—48no—
284C3×C4#93918yes—
285C3×C4C2×D3×D414yes—
286C3×C4C2×#23714yes—
287Dic3—128no—
288Dic3—128no—
289C32C2×#46711yescharacteristic, complemented, Sylow
290C23—22no—
291C23—22no—
292C23#375614yescomplemented
293C23C2×#63812yes—
294C23C2×#63811yescharacteristic
295Q8—22no—
296Q8—22no—
297Q8—42no—
298Q8—182no—
299Q8—182no—
300Q8—362no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—182no—
310C2×C4—182no—
311C2×C4—362no—
312C2×C4—362no—
313C2×C4D4×C3⋊D312yes—
314C2×C4#383012yes—
315C2×C4C2×#63812yes—
316C2×C4C2×#63811yescharacteristic
317C2×C4C23×C3⋊D311yescharacteristic
318C8—94no—
319C8—182no—
320C2×C3—216no—
321C2×C3#5051116yescomplemented
322C2×C3C2×#93914yes—
323C2×C3C22×#21614yes—
324C2×C3C2×#95014yes—
325C22—22no—
326C22—22no—
327C22—28no—
328C22#6414812yes—
329C22C2×#375612yes—
330C22C2×#375614yescomplemented
331C22#6415912yes—
332C22C22×#63811yescharacteristic
333C4—22no—
334C4—42no—
335C4—42no—
336C4—362no—
337C4—362no—
338C4#6414812yes—
339C4C2×D4×C3⋊D311yescharacteristic
340C4C2×#383011yescharacteristic
341C3C2×#505114yescomplemented
342C2—24no—
343C2#1059275014yesdirect product factor
344C2C2×#6414811yescharacteristic
345C2C22×#375611yescharacteristic
346C2C2×#6415911yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C22×#3756C2semidirect
5. C2×#63662C2semidirect
6. #10592750C2direct (N × H)
7. C2×#63637C2semidirect
8. C2×#63634C2semidirect
20. C2×#3756C22semidirect
29. #63662C22semidirect
30. #63637C22semidirect
31. #63634C22semidirect
98. C23×C32Q16semidirect
172. C22×C32C2×Q16semidirect
207. C23×C3#216semidirect
236. C2×C32#467semidirect
278. C22×C3C2×#216semidirect
289. C32C2×#467semidirect
292. C23#3756semidirect
321. C2×C3#5051semidirect
330. C22C2×#3756semidirect
341. C3C2×#5051semidirect
343. C2#10592750direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C22×#37562
C2×#641332
C23×C3⋊(C3⋊C8)2
C2×#636622
#105927502
C2×#636372
C2×#636342
C2×#50513