Finite Group Databasebeta

← #11895491

Subgroups — #11895491

Order 1152.

723 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5570C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic
3Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic
4#10590384C213yesmaximal
5C4×#3718C213yesmaximal
6#10590310C213yesmaximal
7#10590290C213yesmaximal
8#83707—31nomaximal
9#83696—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×Q8×Dic3—21no—
12C3×Q8×Dic3—21no—
13C3×#890—23no—
14C3×#888—23no—
15C3×#869C2213yes—
16C3×#869C2213yes—
17C3×C4×Dic6C2213yes—
18C3×C4×Dic6C2213yes—
19C2×#3718C2213yes—
20C4⋊(C3⋊(C3⋊C8))C2213yes—
21C4×C3⋊(C3⋊C8)C2213yes—
22#63576C2213yes—
23#63565C2213yes—
24#63565C2216yes—
25#63565C2211yescharacteristic
26C3×Q82—31no—
27C3×#557—31no—
28#5570D311yescharacteristic
29Q8×Dic6D311yescharacteristic
30#5093—33no—
31#5091—33no—
32#5090—33no—
33#5079—33no—
34#5031—33no—
35C4×#216—33no—
36C4×#216—33no—
37Q8×C3⋊C8—31no—
38Q8×C3⋊C8—31no—
39Q8×C3⋊C8—61no—
40#5021—33no—
41C2×C32×Q8D411yescharacteristic
42C2×C3×Dic6—23no—
43C2×C3×Dic6C2313yes—
44C2×C3×Dic6C2311yescharacteristic
45C32×C4⋊C4D413yes—
46C32×C42C2313yes—
47C2×C3⋊(C3⋊C8)C2311yescharacteristic
48C2×C3⋊(C3⋊C8)C2313yes—
49C3×C4⋊Dic3—23no—
50C3×C4⋊Dic3—23no—
51C3×C4⋊Dic3—23no—
52C3×C4⋊Dic3C2313yes—
53C3×C4⋊Dic3C2311yescharacteristic
54C3×Dic3⋊C4—23no—
55C3×Dic3⋊C4—23no—
56C3×C4×Dic3—23no—
57C3×C4×Dic3—23no—
58#3718—26no—
59#3363—91noSylow
60C3×C4⋊Q8—33no—
61C3×C4⋊Q8—33no—
62C3×C4⋊Q8—63no—
63C3×#125—63no—
64C3×C4×Q8—21no—
65C3×C4×Q8—33no—
66C3×C4×Q8—33no—
67C3×C4×Q8—61no—
68C3×C4×Q8—61no—
69C3×C4×Q8C2×D311yescharacteristic
70C3×C4×Q8C2×D311yescharacteristic
71Q8×Dic3—21no—
72Q8×Dic3—21no—
73C2×#216—33no—
74C2×#216—33no—
75#890—23no—
76#888—23no—
77#869C2×D313yes—
78#869C2×D313yes—
79C4×Dic6C2×D313yes—
80C4×Dic6C2×D313yes—
81#835—36no—
82#835—31no—
83#835—33no—
84#810—31no—
85#810—33no—
86#810—36no—
87#807—33no—
88#807—33no—
89C4⋊(C3⋊C8)—33no—
90C4⋊(C3⋊C8)—33no—
91C4⋊(C3⋊C8)—63no—
92C4×C3⋊C8—33no—
93C4×C3⋊C8—33no—
94C4×C3⋊C8—63no—
95C32×Q8Q1614yescomplemented
96C2×C32×C4C2×D413yes—
97C2×C32×C4C2×D413yes—
98C2×C32×C4C2411yescharacteristic
99C2×C3×Dic3—21no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—23no—
102C2×C3×Dic3—23no—
103C3×Dic6—21no—
104C3×Dic6—23no—
105C3×Dic6—23no—
106C3×Dic6—83no—
107C3×Dic6#4112yes—
108C3⋊(C3⋊C8)—21no—
109C3⋊(C3⋊C8)—23no—
110Q82—31no—
111#557—31no—
112#487—93no—
113#477—93no—
114#462—93no—
115C8×Q8—91no—
116C4×Q16—93no—
117C2×C3×Q8—21no—
118C2×C3×Q8—31no—
119C2×C3×Q8—33no—
120C2×C3×Q8—63no—
121C2×C3×Q8#6711yescharacteristic
122C2×C3×Q8#6711yescharacteristic
123C2×Dic6—23no—
124C2×Dic6C22×D313yes—
125C2×Dic6C22×D311yescharacteristic
126C3×C4⋊C4—23no—
127C3×C4⋊C4—31no—
128C3×C4⋊C4—33no—
129C3×C4⋊C4—63no—
130C3×C4⋊C4—63no—
131C3×C4⋊C4—63no—
132C3×C4⋊C4—63no—
133C3×C4⋊C4—63no—
134C3×C4⋊C4#6713yes—
135C3×C4⋊C4#6713yes—
136C3×C42—23no—
137C3×C42—63no—
138C3×C42—63no—
139C3×C42C22×D313yes—
140C3×C42C22×D313yes—
141#216—66no—
142#216—66no—
143C4⋊Dic3—23no—
144C4⋊Dic3—23no—
145C4⋊Dic3—23no—
146C4⋊Dic3C22×D311yescharacteristic
147C4⋊Dic3C22×D313yes—
148Dic3⋊C4—23no—
149Dic3⋊C4—23no—
150C4×Dic3—23no—
151C4×Dic3—23no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—33no—
155C2×C3⋊C8—33no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—63no—
158C22×C32C22×D411yescharacteristic
159C32×C4—23no—
160C32×C4C2×Q1616yes—
161C32×C4C2×#4111yescharacteristic
162C32×C42−1+411yescharacteristic
163C3×Dic3—22no—
164C3×Dic3—43no—
165C3×Dic3—43no—
166C3×Dic3—41no—
167C2×Q16—93no—
168C4⋊Q8—33no—
169C4⋊Q8—33no—
170C4⋊Q8—63no—
171#125—63no—
172C4×Q8—33no—
173C4×Q8—33no—
174C4×Q8—61no—
175C4×Q8—61no—
176C4×Q8D3211yescharacteristic
177#107—93no—
178C4⋊C8—93no—
179#103—91no—
180#103—93no—
181#103—96no—
182C4×C8—93no—
183C3×Q8—24no—
184C3×Q8—32no—
185C3×Q8—61no—
186C3×Q8—63no—
187C3×Q8—63no—
188C3×Q8—243no—
189C3×Q8#21614yescomplemented
190C3×Q8#21614yescomplemented
191C2×C3×C4—21no—
192C2×C3×C4—23no—
193C2×C3×C4—23no—
194C2×C3×C4—61no—
195C2×C3×C4—61no—
196C2×C3×C4—63no—
197C2×C3×C4—63no—
198C2×C3×C4C2×#6713yes—
199C2×C3×C4C2×#6713yes—
200C2×C3×C4C2×#6713yes—
201C2×C3×C4C2×#6713yes—
202C2×C3×C4C23×D311yescharacteristic
203C2×C3×C4C23×D311yescharacteristic
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—23no—
207C2×Dic3—23no—
208Dic6—21no—
209Dic6—23no—
210Dic6—23no—
211Dic6—83no—
212Dic6#23912yes—
213C3⋊C8—62no—
214C3⋊C8—63no—
215C3⋊C8—61no—
216C3⋊C8—63no—
217C3⋊C8—61no—
218C3⋊C8—123no—
219C2×C32#54811yescharacteristic
220C2×C32C22×Q1611yescharacteristic
221C2×C32#57711yescharacteristic
222C2×Q8—31no—
223C2×Q8—33no—
224C2×Q8—63no—
225C2×Q8#62511yescharacteristic
226Q16—186no—
227C2×C8—91no—
228C2×C8—93no—
229C4⋊C4—33no—
230C4⋊C4—31no—
231C4⋊C4—63no—
232C4⋊C4—63no—
233C4⋊C4—63no—
234C4⋊C4—63no—
235C4⋊C4—63no—
236C4⋊C4#62513yes—
237C42—63no—
238C42—63no—
239C42C2×D3213yes—
240C22×C3—21no—
241C22×C3C22×#6711yescharacteristic
242C22×C3C22×#6711yescharacteristic
243C3×C4—23no—
244C3×C4—23no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—26no—
248C3×C4—43no—
249C3×C4—62no—
250C3×C4—123no—
251C3×C4—121no—
252C3×C4—123no—
253C3×C4C2×#21616yes—
254C3×C4C2×#21616yes—
255C3×C4C2×#23911yescharacteristic
256C3×C4#100711yescharacteristic
257C3×C4D3×#4111yescharacteristic
258C3×C4#101011yescharacteristic
259Dic3—22no—
260Dic3—43no—
261Dic3—43no—
262Dic3—41no—
263C32#336311yescharacteristic, complemented, Sylow
264Q8—32no—
265Q8—61no—
266Q8—63no—
267Q8—63no—
268Q8—243no—
269Q8#371814yescomplemented
270C2×C4—61no—
271C2×C4—61no—
272C2×C4—63no—
273C2×C4—63no—
274C2×C4C2×#62513yes—
275C2×C4C2×#62513yes—
276C2×C4C22×D3211yescharacteristic
277C8—181no—
278C8—183no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3C22×#21611yescharacteristic
283C2×C3C22×#21611yescharacteristic
284C2×C3#581711yescharacteristic
285C2×C3#583111yescharacteristic
286C2×C3#583611yescharacteristic
287C2×C3#583711yescharacteristic
288C22C22×#62511yescharacteristic
289C4—23no—
290C4—62no—
291C4—123no—
292C4—123no—
293C4—121no—
294C4C2×#371816yes—
295C4#6431511yescharacteristic
296C4D3×#23911yescharacteristic
297C3—21no—
298C3#8369611yescharacteristic, complemented
299C3#8370711yescharacteristic, complemented
300C2C22×#371811yescharacteristic
301C2#1059540911yescharacteristic
302C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3363
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
95. C32×Q8Q16semidirect
189. C3×Q8#216semidirect
190. C3×Q8#216semidirect
263. C32#3363semidirect
269. Q8#3718semidirect
298. C3#83696semidirect
299. C3#83707semidirect

Maximal subgroups

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

subgroupindex
C3×#55702
C3×Q8×Dic62
Q8×C3⋊(C3⋊C8)2
#105903842
C4×#37182
#105903102
#105902902
#837073
#836963