Finite Group Databasebeta

← #11778822

Subgroups — #11778822

Order 1152.

443 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 443 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#5500C211yesmaximal, characteristic
2C3×#4986C211yesmaximal, characteristic
3#10591132C212yesmaximal
4#10589394C211yesmaximal, characteristic
5#10589153C212yesmaximal
6#71899—31nomaximal
7#69719—31nomaximal
8C2×C32×C4⋊C4C2211yescharacteristic
9C3×#926—21no—
10C2×C3×C4⋊Dic3C2211yescharacteristic
11C3×#924—21no—
12C3×#924C2212yes—
13C3×#890—22no—
14C3×#888—22no—
15#63657C2212yes—
16C3×C3⋊#95—21no—
17C3×C3⋊#95—21no—
18C3×C3⋊#95C2211yescharacteristic
19#63576—22no—
20#63565—22no—
21C3×#544—31no—
22#5500D311yescharacteristic
23C3×#400—31no—
24#5044—32no—
25#4986D311yescharacteristic
26#4970—32no—
27#4538—32no—
28#4528—31no—
29#4528—31no—
30#4528—61no—
31#4452—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3×Dic3—21no—
36C22×C3×Dic3—21no—
37C2×C3×Dic6—21no—
38C2×C3×Dic6D412yes—
39C32×C4⋊C4—22no—
40C2×C3⋊(C3⋊C8)—22no—
41C3×#217—22no—
42C3×C4⋊Dic3—21no—
43C3×C4⋊Dic3—21no—
44C3×C4⋊Dic3—21no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3D412yes—
47C3×Dic3⋊C4—22no—
48C3×Dic3⋊C4—22no—
49C3×C4×Dic3—22no—
50#1617—91noSylow
51C3×C4⋊Q8—62no—
52C3×#125—62no—
53C3×C22⋊Q8—32no—
54C3×C22⋊Q8—61no—
55C3×#117—61no—
56C2×C3×C4⋊C4—21no—
57C2×C3×C4⋊C4—31no—
58C2×C3×C4⋊C4C2×D311yescharacteristic
59C2×C3×C4⋊C4C2×D311yescharacteristic
60#926—21no—
61C2×C4⋊Dic3C2×D311yescharacteristic
62#924—21no—
63#924C2×D312yes—
64#890—22no—
65#888—22no—
66C3×#95—31no—
67C3×#95—61no—
68C3×#95—61no—
69#835—62no—
70C3⋊#95—21no—
71C3⋊#95—21no—
72C3⋊#95C2×D311yescharacteristic
73#830—32no—
74#830—32no—
75#830—62no—
76#810—62no—
77#807—62no—
78#807—62no—
79C23×C32C2×D411yescharacteristic
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4—41no—
84C2×C32×C4—41no—
85C2×C32×C4Q1612yes—
86C2×C32×C4C2×D412yes—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—41no—
93C2×C3×Dic3—41no—
94C3×Dic6—42no—
95C3×Dic6—81no—
96C3⋊(C3⋊C8)—42no—
97#544—31no—
98#484—92no—
99#400—31no—
100#328—92no—
101#324—91no—
102C2×C3×Q8—32no—
103C2×C3×Q8—61no—
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4—61no—
108C22×C3×C4—61no—
109C22×C3×C4#6711yescharacteristic
110C22×C3×C4#6711yescharacteristic
111C22×C3×C4#6711yescharacteristic
112C22×C3×C4#6711yescharacteristic
113C22×C3×C4C22×D311yescharacteristic
114C22×C3×C4C22×D311yescharacteristic
115C22×Dic3—21no—
116C22×Dic3—21no—
117C2×Dic6—21no—
118C2×Dic6#6712yes—
119C3×C4⋊C4—22no—
120C3×C4⋊C4—22no—
121C3×C4⋊C4—32no—
122C3×C4⋊C4—42no—
123C3×C4⋊C4—62no—
124C3×C4⋊C4—61no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—62no—
128C3×C4⋊C4—62no—
129C3×C22⋊C4—62no—
130C3×C42—62no—
131#217—22no—
132C4⋊Dic3—21no—
133C4⋊Dic3—21no—
134C4⋊Dic3—21no—
135C4⋊Dic3—22no—
136C4⋊Dic3#6712yes—
137Dic3⋊C4—22no—
138Dic3⋊C4—22no—
139C4×Dic3—22no—
140C2×C3⋊C8—62no—
141C2×C3⋊C8—62no—
142C2×C3⋊C8—122no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32#12011yescharacteristic
146C22×C32C2×Q1611yescharacteristic
147C22×C32#13711yescharacteristic
148C32×C4—22no—
149C32×C4—22no—
150C32×C4—41no—
151C3×Dic3—42no—
152C3×Dic3—42no—
153C3×Dic3—81no—
154C3×Dic3—81no—
155C4⋊Q8—62no—
156#125—62no—
157C22⋊Q8—32no—
158C22⋊Q8—61no—
159#117—61no—
160C2×C4⋊C4—31no—
161C2×C4⋊C4D3211yescharacteristic
162#107—182no—
163#103—182no—
164C22⋊C8—92no—
165#95—31no—
166#95—61no—
167#95—61no—
168C23×C3—21no—
169C23×C3C2×#6711yescharacteristic
170C23×C3C2×#6711yescharacteristic
171C3×Q8—122no—
172C3×Q8—241no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—62no—
189C2×C3×C4—62no—
190C2×C3×C4—81no—
191C2×C3×C4—81no—
192C2×C3×C4—121no—
193C2×C3×C4—121no—
194C2×C3×C4—122no—
195C2×C3×C4—121no—
196C2×C3×C4—121no—
197C2×C3×C4#21612yes—
198C2×C3×C4#21612yes—
199C2×C3×C4D3×D412yes—
200C2×C3×C4C2×#6712yes—
201C2×Dic3—22no—
202C2×Dic3—22no—
203C2×Dic3—41no—
204C2×Dic3—41no—
205C2×Dic3—42no—
206C2×Dic3—41no—
207C2×Dic3—41no—
208Dic6—42no—
209Dic6—81no—
210C3⋊C8—122no—
211C3⋊C8—122no—
212C3⋊C8—242no—
213C2×C32—21no—
214C2×C32—21no—
215C2×C32#45111yescharacteristic
216C2×C32#45411yescharacteristic
217C2×C32#45811yescharacteristic
218C2×Q8—32no—
219C2×Q8—61no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4#62511yescharacteristic
223C22×C4#62511yescharacteristic
224C22×C4C2×D3211yescharacteristic
225C2×C8—182no—
226C4⋊C4—22no—
227C4⋊C4—32no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C4⋊C4—62no—
232C4⋊C4—62no—
233C4⋊C4—62no—
234C22⋊C4—62no—
235C42—62no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—41no—
244C22×C3—41no—
245C22×C3#93711yescharacteristic
246C22×C3#94211yescharacteristic
247C22×C3C2×#21611yescharacteristic
248C22×C3C2×#21611yescharacteristic
249C22×C3#95111yescharacteristic
250C22×C3#95311yescharacteristic
251C3×C4—22no—
252C3×C4—22no—
253C3×C4—22no—
254C3×C4—22no—
255C3×C4—42no—
256C3×C4—42no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4—81no—
260C3×C4—122no—
261C3×C4—122no—
262C3×C4—241no—
263C3×C4—241no—
264Dic3—42no—
265Dic3—42no—
266Dic3—81no—
267Dic3—81no—
268C32#161711yescharacteristic, complemented, Sylow
269C23C2×#62511yescharacteristic
270Q8—122no—
271Q8—241no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—62no—
278C2×C4—62no—
279C2×C4—121no—
280C2×C4—121no—
281C2×C4—122no—
282C2×C4—121no—
283C2×C4—121no—
284C2×C4#371812yes—
285C2×C4D3×#6712yes—
286C8—362no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—41no—
295C2×C3—41no—
296C2×C3#505011yescharacteristic
297C2×C3#505311yescharacteristic
298C2×C3#506211yescharacteristic
299C2×C3#522811yescharacteristic
300C2×C3#524311yescharacteristic
301C2×C3#524511yescharacteristic
302C22—21no—
303C22—21no—
304C22#6382711yescharacteristic
305C22C2×#371811yescharacteristic
306C22#6397611yescharacteristic
307C4—22no—
308C4—22no—
309C4—41no—
310C4—122no—
311C4—122no—
312C4—241no—
313C4—241no—
314C3—21no—
315C3#6971911yescharacteristic, complemented
316C3#7189911yescharacteristic, complemented
317C2—21no—
318C2—21no—
319C2#1059118511yescharacteristic
320C2#1059153311yescharacteristic
321C2#1059164511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
268. C32#1617semidirect
315. C3#69719semidirect
316. C3#71899semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
C3×#49862
#105911322
#105893942
#105891532
#718993
#697193