Finite Group Databasebeta

← #11785358

Subgroups — #11785358

Order 1152.

570 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×D32×C8C211yesmaximal, characteristic
2C2×#63768C211yesmaximal, characteristic, complemented
3#10593403C212yesmaximal
4#10590685C211yesmaximal, characteristic, complemented
5#10590049C212yesmaximal, complemented
6C2×C4×D32C2211yescharacteristic
7C2×C4⋊#157C2212yes—
8C2×D32⋊C4—22no—
9C2×C8×C3⋊D3C2211yescharacteristic
10C2×C3×D3×C8—21no—
11#63900C2212yes—
12C2×#3710C2211yescharacteristic
13C2×D3×C3⋊C8—21no—
14D32×C8—22no—
15D32×C8C414yescomplemented
16#63768—22no—
17#63737—22no—
18C3×#817—21no—
19#63574—21no—
20C22×D3×C8—61no—
21D3×#106—61no—
22C22×D32D411yescharacteristic
23C22×#157—22no—
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×C3×C4×D3—21no—
26C2×#624—22no—
27C2×#624D411yescharacteristic
28C2×D3×Dic3—21no—
29C4×D32—21no—
30C4×D32—21no—
31C4×D32C2×C412yes—
32C4×D32Q812yes—
33C4⋊#157—22no—
34C4⋊#157—22no—
35D32⋊C4—44no—
36C2×C32×C8D411yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C8×C3⋊D3C2×C412yes—
39C8×C3⋊D3D412yes—
40C3×C4⋊Dic3—22no—
41C2×C3×C3⋊C8—21no—
42C3×D3×C8—24no—
43#3724—22no—
44#3710—21no—
45#3710C2×C412yes—
46D3×C3⋊C8—24no—
47#1807—91nomaximal, Sylow
48C22×C4×D3—61no—
49C22×C3×C8—61no—
50C22×C3⋊C8—61no—
51C2×D3×C8—21no—
52C2×D3×C8—64no—
53C2×D3×C8—61no—
54C2×D3×C8—61no—
55C2×D3×C8—61no—
56C2×D3×C8—64no—
57C2×D3×C8—61no—
58D3×C4⋊C4—62no—
59C3×#106—61no—
60#817—21no—
61#808—62no—
62C22×C3⋊D3C2×D411yescharacteristic
63C22×C3×D3—21no—
64C2×D32—21no—
65C2×D32—22no—
66C2×D32C4⋊C412yes—
67C2×D32SD1614yes—
68C2×#157—42no—
69C2×#157—42no—
70C2×#157—42no—
71C2×C32×C4C2×D411yescharacteristic
72C2×C3⋊Dic3#4111yescharacteristic
73C4×C3⋊D3C22×C411yescharacteristic
74C4×C3⋊D3C2×D411yescharacteristic
75C4×C3⋊D3C2×Q811yescharacteristic
76C4×C3⋊D3#4111yescharacteristic
77C2×C3×Dic3—21no—
78C2×C3×Dic3—42no—
79C3×C4×D3—22no—
80C3×C4×D3—22no—
81#624—21no—
82#624—42no—
83#624—42no—
84#624C4⋊C412yes—
85D3×Dic3—22no—
86D3×Dic3—22no—
87C32×C8C22⋊C412yescomplemented
88C3⋊(C3⋊C8)C22⋊C412yescomplemented
89C3×C3⋊C8—22no—
90C23×C8—91no—
91C2×#106—91no—
92C2×#106—91no—
93#380—92no—
94#340—92no—
95C23×D3—61no—
96C22×C3×C4—61no—
97C22×Dic3—61no—
98C2×C4×D3—21no—
99C2×C4×D3—62no—
100C2×C4×D3—62no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—61no—
107C2×C4×D3—122no—
108C2×C3×C8—21no—
109C2×C3×C8—21no—
110C2×C3×C8—64no—
111C2×C3×C8—61no—
112C3×C4⋊C4—62no—
113C4⋊Dic3—22no—
114Dic3⋊C4—122no—
115C2×C3⋊C8—21no—
116C2×C3⋊C8—61no—
117C2×C3⋊C8—61no—
118C2×C3⋊C8—64no—
119D3×C8—24no—
120D3×C8—62no—
121D3×C8—62no—
122D3×C8—62no—
123D3×C8—62no—
124D3×C8—62no—
125D3×C8—62no—
126D3×C8—64no—
127C22×C32#12111yescharacteristic
128C2×C3⋊D3C2×C4⋊C411yescharacteristic
129C2×C3⋊D3#12111yescharacteristic
130C2×C3⋊D3C2×SD1612yes—
131C2×C3⋊D3#13512yes—
132C2×C3×D3—22no—
133C2×C3×D3—24no—
134D32—22no—
135D32—24no—
136D32#10614yescomplemented
137#157—82no—
138C32×C4C2×C22⋊C411yescharacteristic
139C32×C4C22⋊Q811yescharacteristic
140C3⋊Dic3#11711yescharacteristic
141C3⋊Dic3C22⋊Q811yescharacteristic
142C3×Dic3—22no—
143C3×Dic3—82no—
144C23×C4—91no—
145C22×C8—61no—
146C22×C8—91no—
147C22×C8—94no—
148C22×C8—91no—
149C22×C8—182no—
150C22×C8—181no—
151C2×C4⋊C4—92no—
152C2×C4⋊C4—92no—
153C2×C22⋊C4—182no—
154#106—61no—
155#106—181no—
156#106—182no—
157#95—182no—
158C23×C3—61no—
159C22×D3—21no—
160C22×D3—62no—
161C22×D3—64no—
162C22×D3—61no—
163C22×D3—61no—
164C22×D3—62no—
165C22×D3—64no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—62no—
169C2×C3×C4—62no—
170C2×C3×C4—61no—
171C2×C3×C4—122no—
172C2×Dic3—21no—
173C2×Dic3—42no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C4×D3—22no—
179C4×D3—22no—
180C4×D3—62no—
181C4×D3—61no—
182C4×D3—61no—
183C4×D3—61no—
184C4×D3—61no—
185C4×D3—61no—
186C4×D3—61no—
187C4×D3—61no—
188C4×D3—61no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—242no—
193C4×D3—242no—
194C3×C8—22no—
195C3×C8—22no—
196C3×C8—62no—
197C3⋊C8—22no—
198C3⋊C8—62no—
199C3⋊C8—62no—
200C2×C32#38011yescharacteristic
201C2×C32#46512yes—
202C3⋊D3C2×#10611yescharacteristic
203C3⋊D3#42711yescharacteristic
204C3⋊D3#46512yes—
205C3×D3—24no—
206C24—91no—
207C22×C4—61no—
208C22×C4—91no—
209C22×C4—92no—
210C22×C4—92no—
211C22×C4—91no—
212C22×C4—181no—
213C22×C4—181no—
214C22×C4—181no—
215C22×C4—182no—
216C22×C4—182no—
217C2×C8—61no—
218C2×C8—64no—
219C2×C8—92no—
220C2×C8—91no—
221C2×C8—92no—
222C2×C8—92no—
223C2×C8—181no—
224C2×C8—184no—
225C2×C8GO+(4,𝔽2)11yescharacteristic
226C4⋊C4—62no—
227C4⋊C4—182no—
228C4⋊C4—182no—
229C4⋊C4—182no—
230C22⋊C4—364no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—62no—
234C22×C3—64no—
235C2×D3—22no—
236C2×D3—24no—
237C2×D3—64no—
238C2×D3—61no—
239C2×D3—61no—
240C2×D3—61no—
241C2×D3—61no—
242C2×D3—62no—
243C2×D3—62no—
244C2×D3—62no—
245C2×D3—62no—
246C2×D3—64no—
247C2×D3—68no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—62no—
253C3×C4—242no—
254Dic3—22no—
255Dic3—61no—
256Dic3—61no—
257Dic3—61no—
258Dic3—61no—
259Dic3—82no—
260C32#180711yescharacteristic, complemented, Sylow
261C23—61no—
262C23—94no—
263C23—92no—
264C23—91no—
265C23—181no—
266C23—182no—
267C2×C4—61no—
268C2×C4—62no—
269C2×C4—62no—
270C2×C4—92no—
271C2×C4—91no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—122no—
277C2×C4—181no—
278C2×C4—182no—
279C2×C4—182no—
280C2×C4—362no—
281C2×C4—362no—
282C2×C4—362no—
283C2×C4—362no—
284C2×C4—362no—
285C2×C4C2×GO+(4,𝔽2)11yescharacteristic
286C8—62no—
287C8—92no—
288C8D32⋊C412yescomplemented
289C2×C3—22no—
290C2×C3—22no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—64no—
294D3—24no—
295D3—61no—
296D3—61no—
297D3—62no—
298D3—61no—
299D3—61no—
300D3—62no—
301C22—64no—
302C22—62no—
303C22—94no—
304C22—92no—
305C22—92no—
306C22—91no—
307C22—91no—
308C22—184no—
309C22—182no—
310C22#6423011yescharacteristic
311C4—62no—
312C4—91no—
313C4—91no—
314C4—242no—
315C4—722no—
316C4D32⋊Q811yescharacteristic
317C4C2×D32⋊C411yescharacteristic
318C3—21no—
319C3—21no—
320C2—64no—
321C2—92no—
322C2—91no—
323C2—91no—
324C2#1059328412yes—
325C2#1059340311yescharacteristic
subgroupG/H
centerC22#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×D32D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1807
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63768C2semidirect
4. #10590685C2semidirect
5. #10590049C2semidirect
15. D32×C8C4semidirect
87. C32×C8C22⋊C4semidirect
88. C3⋊(C3⋊C8)C22⋊C4semidirect
136. D32#106semidirect
260. C32#1807semidirect
288. C8D32⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×D32×C82
C2×#637682
#105934032
#105906852
#105900492
#18079