Finite Group Databasebeta

← #11789758

Subgroups — #11789758

Order 1152.

418 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 72 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#10593837C211yesmaximal, characteristic
2C2×#63784C211yesmaximal, characteristic
3C2×C8×#157C211yesmaximal, characteristic
4#10593759C211yesmaximal, characteristic
5C3⋊D3×#103C211yesmaximal, characteristic
6#10590182C211yesmaximal, characteristic
7#10590163C211yesmaximal, characteristic
8C2×Q8×C3⋊D3C2211yescharacteristic
9C2×C4⋊#157—21no—
10C2×C4⋊#157C2211yescharacteristic
11C2×C4⋊#157C2211yescharacteristic
12C2×C4×#157C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15C4⋊C4×C3⋊D3C2211yescharacteristic
16#63784—22no—
17#63781—21no—
18#63781—21no—
19#63781—21no—
20C8×#157—22no—
21C32×#103C411yescharacteristic, complemented
22#63662C411yescharacteristic, complemented
23#63643C411yescharacteristic, complemented
24#63637C411yescharacteristic, complemented
25D3×#103—62no—
26C22×#157—21no—
27C22×#157—21no—
28C22×#157D411yescharacteristic
29C22×#157D411yescharacteristic
30C2×C32×Q8C2×C411yescharacteristic
31Q8×C3⋊D3—21no—
32Q8×C3⋊D3—21no—
33Q8×C3⋊D3—21no—
34Q8×C3⋊D3—21no—
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3C2311yescharacteristic
38C2×#634—21no—
39C2×#634C2×C411yescharacteristic
40C2×#622—21no—
41C4⋊#157—21no—
42C4⋊#157—21no—
43C4⋊#157—21no—
44C4⋊#157—21no—
45C4⋊#157—42no—
46C4×#157—21no—
47C4×#157—21no—
48#3787—21no—
49#3787D412yes—
50C2×C32×C8C2×C411yescharacteristic
51C32×C4⋊C4C2×C411yescharacteristic
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53#3750—21no—
54C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
55C8×C3⋊D3—21no—
56C8×C3⋊D3—21no—
57#1933—91nomaximal, Sylow
58C2×D3×Q8—62no—
59C2×D3×C8—62no—
60D3×C4⋊C4—62no—
61C3×#103—22no—
62#835—62no—
63#816—62no—
64#810—62no—
65C22×C3⋊D3C2×D411yescharacteristic
66C2×#157—21no—
67C2×#157—21no—
68C2×#157—21no—
69C2×#157—21no—
70C2×#157—41no—
71C2×#157—41no—
72C2×#157—41no—
73C2×#157—41no—
74C2×#157—41no—
75C2×#157—41no—
76C2×#157SD1612yes—
77C2×#157Q1612yes—
78C32×Q8—21no—
79C32×Q8—21no—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4C22×C411yescharacteristic
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3#4111yescharacteristic
86C4×C3⋊D3—41no—
87C4×C3⋊D3—41no—
88C4×C3⋊D3—41no—
89C4×C3⋊D3—41no—
90C4×C3⋊D3C2×D411yescharacteristic
91C4×C3⋊D3#4111yescharacteristic
92C4×C3⋊D3#4111yescharacteristic
93C4×C3⋊D3#4111yescharacteristic
94#634—21no—
95#634—21no—
96#634—41no—
97#634—41no—
98#622—22no—
99C32×C8—21no—
100C3⋊(C3⋊C8)—21no—
101C2×#103—91no—
102C2×#103—91no—
103C2×C4×C8—91no—
104#391—91no—
105#389—91no—
106#340—91no—
107#340—91no—
108C2×C3×Q8—22no—
109D3×Q8—64no—
110D3×Q8—64no—
111D3×Q8—122no—
112D3×Q8—122no—
113C2×C4×D3—62no—
114C2×C4×D3—122no—
115C2×C4×D3—122no—
116C2×Dic6—62no—
117C2×Dic6—122no—
118C2×C3×C8—22no—
119C3×C4⋊C4—22no—
120C4⋊Dic3—62no—
121Dic3⋊C4—122no—
122C2×C3⋊C8—62no—
123D3×C8—122no—
124D3×C8—122no—
125C22×C32C4×D411yescharacteristic
126C2×C3⋊D3#12111yescharacteristic
127C2×C3⋊D3#12411yescharacteristic
128C2×C3⋊D3C2×SD1611yescharacteristic
129C2×C3⋊D3C2×Q1611yescharacteristic
130C2×C3⋊D3#13511yescharacteristic
131C2×C3⋊D3#13511yescharacteristic
132#157—22no—
133#157—22no—
134#157—81no—
135#157—81no—
136C32×C4—41no—
137C32×C4—41no—
138C32×C4#11711yescharacteristic
139C32×C4C4×D411yescharacteristic
140C3⋊Dic3—41no—
141C3⋊Dic3—41no—
142C3⋊Dic3#12311yescharacteristic
143C3⋊Dic3#12611yescharacteristic
144C22×Q8—91no—
145C22×C8—91no—
146C22×C8—91no—
147C2×C4⋊C4—91no—
148C2×C4⋊C4—91no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—181no—
151C2×C42—91no—
152#103—91no—
153#103—91no—
154#103—91no—
155#103—182no—
156#103#15711yescharacteristic, complemented
157C4×C8—182no—
158#95—181no—
159#95—181no—
160#95—181no—
161C22×D3—62no—
162C3×Q8—24no—
163C3×Q8—42no—
164C2×C3×C4—22no—
165C2×C3×C4—42no—
166C2×C3×C4—42no—
167C2×Dic3—62no—
168C2×Dic3—122no—
169C2×Dic3—122no—
170C4×D3—62no—
171C4×D3—62no—
172C4×D3—62no—
173C4×D3—62no—
174C4×D3—124no—
175C4×D3—124no—
176C4×D3—242no—
177C4×D3—242no—
178Dic6—64no—
179Dic6—122no—
180Dic6—124no—
181Dic6—124no—
182C3×C8—42no—
183C3⋊C8—122no—
184C2×C32#38811yescharacteristic
185C2×C32C4×SD1611yescharacteristic
186C2×C32C4×Q1611yescharacteristic
187C3⋊D3#46511yescharacteristic
188C3⋊D3#46711yescharacteristic
189C3⋊D3#48711yescharacteristic
190C3⋊D3#48811yescharacteristic
191C2×Q8—91no—
192C2×Q8—181no—
193C2×Q8—181no—
194C2×Q8—181no—
195C2×Q8—181no—
196C2×Q8—181no—
197C2×Q8C2×#15711yescharacteristic
198C22×C4—91no—
199C22×C4—91no—
200C22×C4—91no—
201C22×C4—181no—
202C22×C4—181no—
203C22×C4—181no—
204C22×C4—181no—
205C2×C8—92no—
206C2×C8—91no—
207C2×C8—181no—
208C2×C8—181no—
209C2×C8—181no—
210C2×C8—181no—
211C2×C8C2×#15711yescharacteristic
212C4⋊C4—91no—
213C4⋊C4—181no—
214C4⋊C4—181no—
215C4⋊C4—181no—
216C4⋊C4—181no—
217C4⋊C4—181no—
218C4⋊C4—362no—
219C4⋊C4C2×#15711yescharacteristic
220C42—181no—
221C42—181no—
222C22×C3—22no—
223C2×D3—62no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—62no—
227C2×D3—62no—
228C2×D3—62no—
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—44no—
232C3×C4—82no—
233Dic3—62no—
234Dic3—62no—
235Dic3—124no—
236Dic3—242no—
237C32#193311yescharacteristic, complemented, Sylow
238C23—91no—
239Q8—21no—
240Q8—21no—
241Q8—181no—
242Q8—181no—
243Q8—361no—
244Q8—361no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—91no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—181no—
255C2×C4—181no—
256C2×C4—181no—
257C2×C4—181no—
258C2×C4—181no—
259C2×C4—181no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4—361no—
264C2×C4—361no—
265C2×C4—361no—
266C2×C4—361no—
267C2×C4—361no—
268C2×C4—361no—
269C2×C4—361no—
270C2×C4C22×#15711yescharacteristic
271C8—21no—
272C8—182no—
273C8—181no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—22no—
277D3—62no—
278D3—62no—
279D3—62no—
280D3—62no—
281C22—91no—
282C22—91no—
283C22—91no—
284C22—91no—
285C22—91no—
286C22—91no—
287C22D4×#15711yescharacteristic
288C4—41no—
289C4—41no—
290C4—91no—
291C4—91no—
292C4—182no—
293C4—182no—
294C4—361no—
295C4—361no—
296C4—721no—
297C4—721no—
298C4#6428611yescharacteristic
299C4D4×#15711yescharacteristic
300C3—22no—
301C2—91no—
302C2—91no—
303C2—91no—
304C2—91no—
305C2#1059374711yescharacteristic
306C2SD16×#15711yescharacteristic
307C2Q16×#15711yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#103C4
socleC22×C32C4×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenter#103#157
hypocenterC32#1933
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
21. C32×#103C4semidirect
22. #63662C4semidirect
23. #63643C4semidirect
24. #63637C4semidirect
156. #103#157semidirect
237. C32#1933semidirect

Maximal subgroups

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

subgroupindex
#105938372
C2×#637842
C2×C8×#1572
#105937592
C3⋊D3×#1032
#105901822
#105901632
#19339