Finite Group Databasebeta

← #11785446

Subgroups — #11785446

Order 1152.

514 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 73 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
2#10593771C211yesmaximal, characteristic, complemented
3#10593307C212yesmaximal
4#10590913C211yesmaximal, characteristic, complemented
5#10590050C212yesmaximal, complemented
6C2×C4×D32C2211yescharacteristic
7#64283C2212yes—
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×D3×C8—21no—
10#63818C2212yes—
11C2×#3710C2211yescharacteristic
12C2×D3×C3⋊C8—21no—
13D32×C8—21no—
14D32×C8—21no—
15D32×C8C412yes—
16D32×C8C412yes—
17#63771—21no—
18#63770—21no—
19D32⋊C8—24no—
20C3×#819—21no—
21#63578—21no—
22C22×D3×C8—61no—
23D3×#108—61no—
24C22×D32Q811yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×C4×D3—21no—
27C2×#624Q811yescharacteristic
28C2×D3×Dic3—21no—
29C4×D32—21no—
30C4×D32—21no—
31C4×D32C2×C412yes—
32C4×D32D412yes—
33#3792—22no—
34#3788—22no—
35#3787—22no—
36C2×C32×C8D411yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C8×C3⋊D3C2×C411yescharacteristic
39C8×C3⋊D3C2×C411yescharacteristic
40C8×C3⋊D3D411yescharacteristic
41C8×C3⋊D3D411yescharacteristic
42C3×#208—22no—
43C2×C3×C3⋊C8—21no—
44C3×D3×C8—22no—
45C3×D3×C8—22no—
46#3712—22no—
47#3710—21no—
48#3710—22no—
49#3710C2×C412yes—
50D3×C3⋊C8—22no—
51D3×C3⋊C8—22no—
52#1810—91nomaximal, Sylow
53C22×C4×D3—61no—
54C22×C3×C8—61no—
55C22×C3⋊C8—61no—
56D3×M16—62no—
57C2×D3×C8—21no—
58C2×D3×C8—62no—
59C2×D3×C8—62no—
60C2×D3×C8—61no—
61C2×D3×C8—61no—
62C2×D3×C8—61no—
63C2×D3×C8—62no—
64C2×D3×C8—62no—
65C2×D3×C8—61no—
66C3×#108—61no—
67#822—62no—
68#819—21no—
69C22×C3⋊D3C2×Q811yescharacteristic
70C22×C3×D3—21no—
71C2×D32—21no—
72C2×D32—24no—
73C2×D32C4⋊C412yes—
74C2×C32×C4C2×D411yescharacteristic
75C2×C3⋊Dic3#4111yescharacteristic
76C4×C3⋊D3C22×C411yescharacteristic
77C4×C3⋊D3C2×D411yescharacteristic
78C4×C3⋊D3C2×D411yescharacteristic
79C4×C3⋊D3#4111yescharacteristic
80C2×C3×Dic3—21no—
81C3×C4×D3—22no—
82C3×C4×D3—22no—
83#624—21no—
84#624C4⋊C412yes—
85D3×Dic3—22no—
86D3×Dic3—22no—
87#622—42no—
88C32×C8C22⋊C411yescharacteristic
89C32×C8C22⋊C411yescharacteristic
90C3⋊(C3⋊C8)C22⋊C411yescharacteristic
91C3⋊(C3⋊C8)C22⋊C411yescharacteristic
92C3×C3⋊C8—22no—
93C3×C3⋊C8—42no—
94C23×C8—91no—
95C2×#108—91no—
96C2×#108—91no—
97#407—92no—
98#341—92no—
99C23×D3—61no—
100C22×C3×C4—61no—
101C22×Dic3—61no—
102C2×C4×D3—21no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—61no—
111C3×M16—62no—
112C2×C3×C8—21no—
113C2×C3×C8—21no—
114C2×C3×C8—62no—
115C2×C3×C8—62no—
116C2×C3×C8—61no—
117#208—22no—
118C2×C3⋊C8—21no—
119C2×C3⋊C8—61no—
120C2×C3⋊C8—61no—
121C2×C3⋊C8—62no—
122C2×C3⋊C8—62no—
123ΓL(1,𝔽25)—122no—
124D3×C8—22no—
125D3×C8—22no—
126D3×C8—62no—
127D3×C8—61no—
128D3×C8—61no—
129D3×C8—61no—
130D3×C8—61no—
131D3×C8—61no—
132D3×C8—61no—
133D3×C8—61no—
134D3×C8—61no—
135D3×C8—62no—
136D3×C8—62no—
137D3×C8—62no—
138D3×C8—122no—
139C22×C32C22⋊Q811yescharacteristic
140C2×C3⋊D3—22no—
141C2×C3⋊D3C2×C4⋊C411yescharacteristic
142C2×C3⋊D3C22⋊Q811yescharacteristic
143C2×C3×D3—24no—
144C2×C3×D3—22no—
145D32—24no—
146D32—22no—
147D32#10814yescomplemented
148C32×C4C2×C22⋊C411yescharacteristic
149C32×C4#12111yescharacteristic
150C3⋊Dic3#11711yescharacteristic
151C3⋊Dic3#12111yescharacteristic
152C3×Dic3—22no—
153C23×C4—91no—
154C2×M16—92no—
155C2×M16—92no—
156C22×C8—61no—
157C22×C8—91no—
158C22×C8—92no—
159C22×C8—92no—
160C22×C8—91no—
161C22×C8—181no—
162C22×C8—181no—
163C22×C8—181no—
164#108—61no—
165#108—181no—
166#108—181no—
167#108—181no—
168C22⋊C8—184no—
169C23×C3—61no—
170C22×D3—21no—
171C22×D3—62no—
172C22×D3—61no—
173C22×D3—61no—
174C22×D3—62no—
175C22×D3—68no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—62no—
179C2×C3×C4—62no—
180C2×C3×C4—61no—
181C2×Dic3—21no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C4×D3—22no—
187C4×D3—22no—
188C4×D3—62no—
189C4×D3—61no—
190C4×D3—61no—
191C4×D3—61no—
192C4×D3—61no—
193C4×D3—61no—
194C4×D3—61no—
195C4×D3—61no—
196C4×D3—61no—
197C4×D3—62no—
198C4×D3—62no—
199C4×D3—62no—
200C3×C8—21no—
201C3×C8—21no—
202C3×C8—21no—
203C3×C8—21no—
204C3×C8—62no—
205C3×C8—122no—
206C3⋊C8—22no—
207C3⋊C8—42no—
208C3⋊C8—61no—
209C3⋊C8—61no—
210C3⋊C8—61no—
211C3⋊C8—61no—
212C2×C32—21no—
213C2×C32#38011yescharacteristic
214C3⋊D3—21no—
215C3⋊D3C2×#10812yes—
216C3×D3—24no—
217C24—91no—
218C22×C4—61no—
219C22×C4—92no—
220C22×C4—92no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—181no—
224C22×C4—181no—
225C22×C4—181no—
226M16—62no—
227M16—182no—
228M16—182no—
229M16—182no—
230C2×C8—61no—
231C2×C8—62no—
232C2×C8—62no—
233C2×C8—92no—
234C2×C8—91no—
235C2×C8—91no—
236C2×C8—91no—
237C2×C8—91no—
238C2×C8—91no—
239C2×C8—181no—
240C2×C8—182no—
241C2×C8—182no—
242C2×C8—182no—
243C2×C8—182no—
244C2×C8GO+(4,𝔽2)11yescharacteristic
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—62no—
248C22×C3—64no—
249C2×D3—22no—
250C2×D3—24no—
251C2×D3—64no—
252C2×D3—61no—
253C2×D3—61no—
254C2×D3—61no—
255C2×D3—61no—
256C2×D3—64no—
257C2×D3—68no—
258C2×D3—64no—
259C2×D3—122no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—62no—
265Dic3—22no—
266Dic3—61no—
267Dic3—61no—
268Dic3—61no—
269Dic3—61no—
270C32#181011yescharacteristic, complemented, Sylow
271C23—61no—
272C23—92no—
273C23—91no—
274C23—181no—
275C23—184no—
276C2×C4—61no—
277C2×C4—62no—
278C2×C4—62no—
279C2×C4—92no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—181no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4C2×GO+(4,𝔽2)11yescharacteristic
289C8—62no—
290C8—91no—
291C8—91no—
292C8—122no—
293C8—362no—
294C8D32⋊C411yescharacteristic
295C8D32⋊C411yescharacteristic
296C2×C3—22no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3—64no—
301D3—24no—
302D3—62no—
303D3—62no—
304D3—62no—
305D3—121no—
306C22—64no—
307C22—62no—
308C22—94no—
309C22—91no—
310C22—91no—
311C22—182no—
312C22—182no—
313C22—184no—
314C22D32⋊Q811yescharacteristic
315C4—62no—
316C4—91no—
317C4—91no—
318C4#6423011yescharacteristic
319C4C2×D32⋊C411yescharacteristic
320C3—21no—
321C3—21no—
322C2—21no—
323C2—64no—
324C2—92no—
325C2—181no—
326C2#1059340311yescharacteristic
subgroupG/H
centerC4#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#380
prime radicalC22×D32Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1810
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593771C2semidirect
4. #10590913C2semidirect
5. #10590050C2semidirect
147. D32#108semidirect
270. C32#1810semidirect

Maximal subgroups

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

subgroupindex
C2×D32×C82
#105937712
#105933072
#105909132
#105900502
#18109