Finite Group Databasebeta

← #11778714

Subgroups — #11778714

Order 1152.

565 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 565 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#10594981C211yesmaximal, characteristic
2#10592376C211yesmaximal, characteristic
3#10591103C212yesmaximal, complemented
4C3×#4452C212yesmaximal, complemented
5#10589146C211yesmaximal, characteristic
6#68322—32nomaximal
7C2×#3752—21no—
8C2×#3752C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)—21no—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C3×#924C2212yes—
12#63982—21no—
13#63974—21no—
14#63895—22no—
15#63888—22no—
16C32×#95C2211yescharacteristic
17C3×#830C2212yes—
18#63575—22no—
19#63566—22no—
20#5634—32no—
21#5044—32no—
22#4722—32no—
23#4677—32no—
24#4677—61no—
25C3×#328—32no—
26#4468—32no—
27#4452D312yescomplemented
28C23×C3⋊D3D411yescharacteristic
29C22×C32×C4—21no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3D411yescharacteristic
33C2×C3×Dic6D412yes—
34C2×#627—21no—
35C2×#624—21no—
36C2×#624—21no—
37#3752—22no—
38#3752—42no—
39C4⋊(C3⋊Dic3)—22no—
40C4⋊(C3⋊Dic3)—42no—
41C3×#217—22no—
42C3×C4⋊Dic3D412yes—
43C3×Dic3⋊C4—22no—
44C2×C3×C3⋊C8—22no—
45#3724—21no—
46Dic3⋊Dic3—22no—
47#3722—22no—
48#1614—91noSylow
49C3×C22⋊Q8—32no—
50#946—62no—
51C2×(C2×D3)⋊C4—32no—
52C2×(C2×D3)⋊C4—61no—
53C2×(C2×D3)⋊C4—62no—
54C2×(C2×D3)⋊C4—62no—
55C2×C4⋊Dic3—32no—
56C2×C4⋊Dic3—61no—
57C2×C4⋊Dic3—62no—
58C2×C4⋊Dic3—62no—
59#924C2×D312yes—
60#897—62no—
61#896—62no—
62#896—62no—
63D3×C22⋊C4—62no—
64#878—62no—
65C3×C22⋊C8—32no—
66C3×#95—21no—
67C3×#95C2×D312yes—
68#835—62no—
69#830C2×D312yes—
70#818—62no—
71#816—62no—
72#807—62no—
73C23×C32C2×D411yescharacteristic
74C22×C3⋊D3—21no—
75C22×C3⋊D3—21no—
76C22×C3⋊D3—41no—
77C22×C3⋊D3—41no—
78C22×C3⋊D3Q1612yes—
79C2×C32×C4—22no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C32×C4C2×D412yes—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C3×Dic6—42no—
92#627—81no—
93#624—81no—
94#624—81no—
95C3×C3⋊C8—42no—
96#543—91no—
97#484—92no—
98#399—91no—
99#328—32no—
100#323—91no—
101C23×D3—32no—
102C23×D3—61no—
103C2×C3×Q8—32no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—21no—
107C22×C3×C4C22×D312yes—
108C22×Dic3—32no—
109C22×Dic3—61no—
110C22×Dic3—62no—
111C22×Dic3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×Dic6—62no—
115C2×Dic6D1212yes—
116C2×C3×C8—62no—
117C3×C4⋊C4—32no—
118C3×C4⋊C4—62no—
119C3×C22⋊C4—62no—
120#217—22no—
121(C2×D3)⋊C4—62no—
122(C2×D3)⋊C4—62no—
123(C2×D3)⋊C4—62no—
124(C2×D3)⋊C4—62no—
125(C2×D3)⋊C4—122no—
126(C2×D3)⋊C4—124no—
127(C2×D3)⋊C4—124no—
128C4⋊Dic3—62no—
129C4⋊Dic3—62no—
130C4⋊Dic3—62no—
131C4⋊Dic3—122no—
132C4⋊Dic3—124no—
133C4⋊Dic3—124no—
134C4⋊Dic3D1212yes—
135Dic3⋊C4—22no—
136Dic3⋊C4—62no—
137Dic3⋊C4—62no—
138C2×C3⋊C8—22no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32#12011yescharacteristic
142C22×C32C2×Q1611yescharacteristic
143C22×C32#13711yescharacteristic
144C2×C3⋊D3—22no—
145C2×C3⋊D3—42no—
146C2×C3⋊D3—41no—
147C2×C3⋊D3—41no—
148C2×C3⋊D3—81no—
149C32×C4—22no—
150C32×C4—42no—
151C3⋊Dic3—41no—
152C3⋊Dic3—81no—
153C3×Dic3—42no—
154C3×Dic3—42no—
155C22⋊Q8—32no—
156C22⋊Q8—181no—
157C22⋊Q8—182no—
158C22⋊Q8—182no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—181no—
161C2×C22⋊C4—91no—
162C2×C22⋊C4—181no—
163C2×C22⋊C4—181no—
164#107—182no—
165#103—182no—
166C22⋊C8—32no—
167#95D3211yescharacteristic
168C23×C3—21no—
169C23×C3D3×D412yes—
170C22×D3—34no—
171C22×D3—62no—
172C22×D3—62no—
173C22×D3—62no—
174C22×D3—121no—
175C22×D3—121no—
176C22×D3—122no—
177C22×D3—122no—
178C22×D3—122no—
179C22×D3—122no—
180C3×Q8—122no—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—22no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187C2×C3×C4—42no—
188C2×C3×C4—42no—
189C2×C3×C4—42no—
190C2×C3×C4—62no—
191C2×C3×C4—62no—
192C2×C3×C4C2×D1212yes—
193C2×C3×C4D3×D412yes—
194C2×Dic3—22no—
195C2×Dic3—22no—
196C2×Dic3—62no—
197C2×Dic3—121no—
198C2×Dic3—122no—
199C2×Dic3—122no—
200C2×Dic3—122no—
201C2×Dic3—122no—
202C2×Dic3—122no—
203C2×Dic3—122no—
204C2×Dic3—122no—
205C2×Dic3—122no—
206C4×D3—242no—
207C4×D3—242no—
208Dic6—42no—
209Dic6—242no—
210C3×C8—122no—
211C3⋊C8—42no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32#45111yescharacteristic
215C2×C32#45311yescharacteristic
216C2×C32#45811yescharacteristic
217C3⋊D3—42no—
218C24—91no—
219C2×Q8—32no—
220C2×Q8—181no—
221C22×C4—21no—
222C22×C4—91no—
223C22×C4—181no—
224C22×C4—181no—
225C22×C4—181no—
226C22×C4C2×D3211yescharacteristic
227C2×C8—62no—
228C4⋊C4—32no—
229C4⋊C4—62no—
230C4⋊C4—181no—
231C4⋊C4—182no—
232C4⋊C4—182no—
233C4⋊C4—362no—
234C22⋊C4—62no—
235C22⋊C4—182no—
236C22⋊C4—182no—
237C22⋊C4—362no—
238C22×C3—22no—
239C22×C3—22no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3#88212yes—
246C22×C3#91512yes—
247C22×C3D3×Q1612yes—
248C2×D3—64no—
249C2×D3—122no—
250C2×D3—122no—
251C2×D3—122no—
252C2×D3—124no—
253C2×D3—124no—
254C2×D3—241no—
255C2×D3—241no—
256C2×D3—242no—
257C2×D3—242no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—42no—
261C3×C4—44no—
262C3×C4—44no—
263C3×C4—122no—
264C3×C4—122no—
265Dic3—42no—
266Dic3—42no—
267Dic3—122no—
268Dic3—241no—
269Dic3—242no—
270Dic3—242no—
271C32#161411yescharacteristic, complemented, Sylow
272C23—92no—
273C23—181no—
274C23—181no—
275C23—361no—
276C23—361no—
277C23#381111yescharacteristic
278Q8—122no—
279Q8—721no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—62no—
285C2×C4—62no—
286C2×C4—181no—
287C2×C4—361no—
288C2×C4—361no—
289C2×C4—361no—
290C2×C4—361no—
291C2×C4—721no—
292C2×C4—721no—
293C2×C4D3×D1212yes—
294C8—122no—
295C2×C3—22no—
296C2×C3—22no—
297C2×C3—22no—
298C2×C3—22no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3#474212yes—
303C2×C3#480912yes—
304C2×C3#482212yes—
305D3—124no—
306D3—242no—
307C22—21no—
308C22—21no—
309C22—182no—
310C22—362no—
311C22—361no—
312C22—361no—
313C22—721no—
314C22#6392311yescharacteristic
315C22#6393111yescharacteristic
316C22#6394411yescharacteristic
317C4—22no—
318C4—42no—
319C4—122no—
320C4—122no—
321C4—361no—
322C4—721no—
323C3—21no—
324C3#6832212yescomplemented
325C2—21no—
326C2—21no—
327C2—362no—
328C2#1059039711yescharacteristic
329C2#1059040911yescharacteristic
330C2#1059060511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radicalC23×C3⋊D3D4
hypercenter#95D32
hypocenterC32#1614
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #10591103C2semidirect
4. C3×#4452C2semidirect
27. #4452D3semidirect
271. C32#1614semidirect
324. C3#68322semidirect

Maximal subgroups

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

subgroupindex
#105949812
#105923762
#105911032
C3×#44522
#105891462
#683223