Finite Group Databasebeta

← #11783293

Subgroups — #11783293

Order 1152.

822 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#3792C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic
3C2×#63957C211yesmaximal, characteristic
4#10590075C214yesmaximal, complemented
5C23×C3⋊Dic3C2211yescharacteristic
6C23×C3×Dic3—21no—
7C2×#3792—22no—
8C2×#3792—22no—
9C2×#3792C414yescomplemented
10C22×#622C2212yes—
11C2×C3×#217—21no—
12C2×#3724—21no—
13C2×#3724—22no—
14C2×#3724C414yescomplemented
15C2×#3724C2212yes—
16C2×#3724C2212yes—
17#63957—22no—
18#63957C414yescomplemented
19C2×Dic32—21no—
20C22×Dic3⋊C4—61no—
21C2×#877—61no—
22C24×C32D411yescharacteristic
23C22×C3⋊Dic3C2×C412yes—
24C22×C3⋊Dic3C2×C412yes—
25C22×C3⋊Dic3C2×C412yes—
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3D412yes—
28C22×C3⋊Dic3D412yes—
29C22×C3⋊Dic3Q812yes—
30C22×C3⋊Dic3C2311yescharacteristic
31C22×C3×Dic3—24no—
32C22×C3×Dic3—22no—
33C22×C3×Dic3—22no—
34C22×C3×Dic3—44no—
35#3792—28no—
36C2×#622—22no—
37C2×#622—22no—
38C2×#622C2×C414yescomplemented
39C3×#217—24no—
40#3724—24no—
41#3724—22no—
42#3724—22no—
43#3724C2×C414yes—
44#3724C2×C414yescomplemented
45Dic32—24no—
46#1736—91nomaximal, Sylow
47C23×C3×C4—61no—
48C23×Dic3—21no—
49C23×Dic3—61no—
50C23×Dic3—61no—
51C2×C3×C22⋊C4—61no—
52C2×#217—21no—
53C2×Dic3⋊C4—62no—
54C2×Dic3⋊C4—64no—
55C2×Dic3⋊C4—62no—
56C2×Dic3⋊C4—62no—
57C2×Dic3⋊C4—64no—
58C2×C4×Dic3—62no—
59#877—64no—
60#877—64no—
61C23×C32—22no—
62C23×C32—22no—
63C23×C32C22⋊C412yes—
64C23×C32C22⋊C412yes—
65C23×C32C4⋊C412yes—
66C23×C32C2×D411yescharacteristic
67C2×C3⋊Dic3C4214yes—
68C2×C3⋊Dic3C22⋊C412yes—
69C2×C3⋊Dic3C22⋊C412yes—
70C2×C3⋊Dic3C22⋊C414yes—
71C2×C3⋊Dic3C4⋊C412yes—
72C2×C3⋊Dic3C4⋊C414yes—
73C2×C3⋊Dic3C4⋊C414yes—
74C2×C3⋊Dic3C22×C411yescharacteristic
75C2×C3⋊Dic3C22×C411yescharacteristic
76C2×C3⋊Dic3C22×C411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C2×C3⋊Dic3C2×Q811yescharacteristic
80C2×C3×Dic3—24no—
81C2×C3×Dic3—24no—
82C2×C3×Dic3—48no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—44no—
85C2×C3×Dic3—42no—
86#622—24no—
87C22×M16—91no—
88C2×#117—91no—
89C22×C4⋊C4—91no—
90#340—94no—
91C24×C3—21no—
92C24×C3—21no—
93C22×C3×C4—62no—
94C22×C3×C4—62no—
95C22×C3×C4—64no—
96C22×C3×C4—124no—
97C22×Dic3—22no—
98C22×Dic3—22no—
99C22×Dic3—24no—
100C22×Dic3—44no—
101C22×Dic3—62no—
102C22×Dic3—62no—
103C22×Dic3—61no—
104C22×Dic3—62no—
105C22×Dic3—61no—
106C22×Dic3—62no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C22×Dic3—62no—
110C22×Dic3—62no—
111C22×Dic3—62no—
112C22×Dic3—62no—
113C22×Dic3—62no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C22×Dic3—62no—
117C3×C22⋊C4—64no—
118#217—24no—
119Dic3⋊C4—64no—
120Dic3⋊C4—64no—
121Dic3⋊C4—64no—
122Dic3⋊C4—68no—
123Dic3⋊C4—64no—
124C4×Dic3—68no—
125C22×C32—24no—
126C22×C32—22no—
127C22×C32—22no—
128C22×C32—24no—
129C22×C32#9514yes—
130C22×C32C2×C22⋊C411yescharacteristic
131C22×C32C2×C22⋊C411yescharacteristic
132C22×C32C2×C4⋊C411yescharacteristic
133C22×C32AGL(1,ℤ/8)12yes—
134C22×C32#13712yes—
135C3⋊Dic3#9514yes—
136C3⋊Dic3C2×C4211yescharacteristic
137C3⋊Dic3C2×C22⋊C411yescharacteristic
138C3⋊Dic3C2×C4⋊C411yescharacteristic
139C3⋊Dic3C2×C4⋊C411yescharacteristic
140C3×Dic3—44no—
141C3×Dic3—44no—
142C23×C4—61no—
143C23×C4—91no—
144C2×M16—94no—
145C2×M16—182no—
146C2×M16—182no—
147C22×C8—92no—
148#117—94no—
149#117—182no—
150C2×C4⋊C4—92no—
151C2×C4⋊C4—94no—
152C2×C4⋊C4—92no—
153C2×C4⋊C4—181no—
154C2×C4⋊C4—182no—
155C2×C22⋊C4—61no—
156C2×C42—181no—
157C23×C3—24no—
158C23×C3—24no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—22no—
162C23×C3—22no—
163C23×C3—22no—
164C23×C3—22no—
165C23×C3—22no—
166C23×C3—22no—
167C23×C3—42no—
168C23×C3—42no—
169C2×C3×C4—64no—
170C2×C3×C4—64no—
171C2×C3×C4—122no—
172C2×C3×C4—122no—
173C2×C3×C4—128no—
174C2×C3×C4—124no—
175C2×Dic3—24no—
176C2×Dic3—24no—
177C2×Dic3—42no—
178C2×Dic3—42no—
179C2×Dic3—48no—
180C2×Dic3—44no—
181C2×Dic3—64no—
182C2×Dic3—64no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—62no—
187C2×Dic3—64no—
188C2×Dic3—64no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×C32—24no—
208C2×C32C2×#9511yescharacteristic
209C2×C32#41712yes—
210C2×C32#41811yescharacteristic
211C2×C32#41911yescharacteristic
212C2×C32#42812yes—
213C24GO+(4,𝔽2)11yescharacteristic
214C22×C4—62no—
215C22×C4—62no—
216C22×C4—64no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—92no—
220C22×C4—92no—
221C22×C4—92no—
222C22×C4—92no—
223C22×C4—92no—
224C22×C4—92no—
225C22×C4—124no—
226M16—188no—
227C2×C8—94no—
228C2×C8—182no—
229C2×C8—182no—
230C4⋊C4—94no—
231C4⋊C4—94no—
232C4⋊C4—182no—
233C4⋊C4—184no—
234C4⋊C4—182no—
235C22⋊C4—64no—
236C42—184no—
237C22×C3—24no—
238C22×C3—28no—
239C22×C3—24no—
240C22×C3—28no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—24no—
252C22×C3—24no—
253C22×C3—42no—
254C22×C3—44no—
255C22×C3—42no—
256C22×C3—44no—
257C3×C4—124no—
258C3×C4—124no—
259Dic3—44no—
260Dic3—44no—
261Dic3—64no—
262Dic3—64no—
263Dic3—61no—
264Dic3—61no—
265Dic3—61no—
266Dic3—61no—
267Dic3—61no—
268Dic3—61no—
269Dic3—61no—
270Dic3—61no—
271C32#173611yescharacteristic, complemented, Sylow
272C23—22no—
273C23—22no—
274C23D32⋊C412yes—
275C23D32⋊C412yes—
276C23#377312yes—
277C23C2×GO+(4,𝔽2)11yescharacteristic
278C2×C4—64no—
279C2×C4—64no—
280C2×C4—92no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—92no—
286C2×C4—91no—
287C2×C4—92no—
288C2×C4—91no—
289C2×C4—94no—
290C2×C4—94no—
291C2×C4—94no—
292C2×C4—94no—
293C2×C4—128no—
294C2×C4—124no—
295C2×C4—122no—
296C2×C4—122no—
297C8—184no—
298C2×C3—28no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—22no—
304C2×C3—22no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—22no—
308C2×C3—22no—
309C2×C3—44no—
310C22—22no—
311C22—24no—
312C22—22no—
313C22—24no—
314C22#6373714yes—
315C22C2×D32⋊C411yescharacteristic
316C22C2×D32⋊C411yescharacteristic
317C22C2×#377311yescharacteristic
318C22#6423612yes—
319C22#6423912yes—
320C4—91no—
321C4—94no—
322C4—91no—
323C4—91no—
324C4—91no—
325C4—124no—
326C4—124no—
327C3—21no—
328C3—21no—
329C2—24no—
330C2C2×#6373711yescharacteristic
331C2#1059349311yescharacteristic
332C2#1059349612yes—
333C2#1059350311yescharacteristic
334C2#1059350712yes—
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1736
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
4. #10590075C2semidirect
9. C2×#3792C4semidirect
14. C2×#3724C4semidirect
18. #63957C4semidirect
38. C2×#622C2×C4semidirect
44. #3724C2×C4semidirect
271. C32#1736semidirect

Maximal subgroups

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

subgroupindex
C22×#37922
C22×#37242
C2×#639572
#105900752
#17369