Finite Group Databasebeta

← #11783610

Subgroups — #11783610

Order 1152.

538 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 98 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×#64286C211yesmaximal, characteristic
2#10593800C211yesmaximal, characteristic
3C2×#63767C211yesmaximal, characteristic, complemented
4C2×C8×#157C211yesmaximal, characteristic, complemented
5C3⋊D3×C22⋊C8C211yesmaximal, characteristic
6#10590181C211yesmaximal, characteristic, complemented
7#10590181C211yesmaximal, characteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157C412yes—
10#64286—22no—
11#64286—22no—
12C2×C4⋊#157C412yes—
13C2×C4×#157C2211yescharacteristic
14C2×C4×#157C2211yescharacteristic
15C2×#3787C2211yescharacteristic
16C2×#3787C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18C2×C8×C3⋊D3C2211yescharacteristic
19C22⋊#622C412yescomplemented
20#63778C412yescomplemented
21#63767—22no—
22C8×#157—22no—
23C32×C22⋊C8C411yescharacteristic, complemented
24#63657C411yescharacteristic, complemented
25#63647C411yescharacteristic, complemented
26#63647C411yescharacteristic, complemented
27D3×C22⋊C8—62no—
28C23×C3⋊D3C2×C411yescharacteristic
29C22×#157C2×C412yes—
30C22×#157C2×C412yes—
31C22×C32×C4C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3C2311yescharacteristic
41C22⋊#157—24no—
42C2×#622C2×C412yes—
43C2×#622C2×C412yes—
44C4⋊#157—24no—
45C4×#157—21no—
46C4×#157—21no—
47C4×#157D412yes—
48C4×#157D412yes—
49#3787—21no—
50#3787—21no—
51#3787—21no—
52#3787—21no—
53C2×C32×C8C2×C411yescharacteristic
54C2×C32×C8C2×C411yescharacteristic
55C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
56C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
57C8×C3⋊D3—21no—
58C8×C3⋊D3—21no—
59C8×C3⋊D3—21no—
60C8×C3⋊D3—21no—
61#1750—91nomaximal, Sylow
62C22×C4×D3—62no—
63C2×D3×C8—62no—
64C2×D3×C8—62no—
65C3×C22⋊C8—22no—
66#830—62no—
67(C2×D3)⋊C8—62no—
68(C2×D3)⋊C8—62no—
69C23×C32C4211yescharacteristic
70C22×C3⋊D3—22no—
71C22×C3⋊D3—21no—
72C22×C3⋊D3—21no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3C4211yescharacteristic
75C22×C3⋊D3C22×C411yescharacteristic
76C2×#157—22no—
77C2×#157—22no—
78C2×#157—22no—
79C2×#157—22no—
80C2×#157—22no—
81C2×#157C22⋊C414yes—
82C2×C32×C4—21no—
83C2×C32×C4—21no—
84C2×C32×C4C4211yescharacteristic
85C2×C32×C4C22×C411yescharacteristic
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3C4211yescharacteristic
89C2×C3⋊Dic3C22×C411yescharacteristic
90C4×C3⋊D3—21no—
91C4×C3⋊D3—21no—
92C4×C3⋊D3—21no—
93C4×C3⋊D3—21no—
94C4×C3⋊D3—21no—
95C4×C3⋊D3—21no—
96C4×C3⋊D3C2×D411yescharacteristic
97C4×C3⋊D3C2×D411yescharacteristic
98C4×C3⋊D3#4111yescharacteristic
99C4×C3⋊D3#4111yescharacteristic
100#622—22no—
101#622—22no—
102C32×C8—21no—
103C32×C8—21no—
104C3⋊(C3⋊C8)—21no—
105C3⋊(C3⋊C8)—21no—
106C2×#117—91no—
107C2×C22⋊C8—91no—
108C2×C22⋊C8—91no—
109C2×#97—91no—
110C2×C4×C8—91no—
111#336—91no—
112#336—91no—
113C23×D3—62no—
114C22×C3×C4—22no—
115C22×Dic3—62no—
116C2×C4×D3—62no—
117C2×C4×D3—62no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3—122no—
121C2×C4×D3—122no—
122C2×C4×D3—122no—
123C2×C4×D3—122no—
124C2×C3×C8—22no—
125C2×C3×C8—22no—
126C2×C3⋊C8—62no—
127C2×C3⋊C8—62no—
128D3×C8—122no—
129D3×C8—122no—
130D3×C8—122no—
131D3×C8—122no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32C2×C4211yescharacteristic
136C2×C3⋊D3—21no—
137C2×C3⋊D3—21no—
138C2×C3⋊D3—21no—
139C2×C3⋊D3—42no—
140C2×C3⋊D3—42no—
141C2×C3⋊D3C2×C22⋊C411yescharacteristic
142C2×C3⋊D3#11711yescharacteristic
143C2×C3⋊D3#13112yes—
144C2×C3⋊D3#13112yes—
145#157—24no—
146#157—42no—
147C32×C4—21no—
148C32×C4C4×D411yescharacteristic
149C32×C4C4×D411yescharacteristic
150C3⋊Dic3—21no—
151C3⋊Dic3C4×D411yescharacteristic
152C3⋊Dic3C4×D411yescharacteristic
153C23×C4—91no—
154C22×C8—91no—
155C22×C8—91no—
156C22×C8—91no—
157C22×C8—91no—
158#117—182no—
159#117—182no—
160C2×C4⋊C4—92no—
161C2×C22⋊C4—92no—
162C2×C42—91no—
163C2×C42—91no—
164C22⋊C8—92no—
165C22⋊C8—92no—
166C22⋊C8—91no—
167C22⋊C8—91no—
168C22⋊C8—91no—
169C22⋊C8#15711yescharacteristic, complemented
170#97—182no—
171C4×C8—182no—
172C23×C3—22no—
173C22×D3—62no—
174C22×D3—62no—
175C22×D3—68no—
176C22×D3—122no—
177C22×D3—122no—
178C22×D3—124no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—42no—
182C2×C3×C4—42no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C4×D3—62no—
188C4×D3—62no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—122no—
192C4×D3—122no—
193C4×D3—122no—
194C4×D3—122no—
195C4×D3—122no—
196C4×D3—122no—
197C3×C8—42no—
198C3×C8—42no—
199C3⋊C8—122no—
200C3⋊C8—122no—
201C2×C32—41no—
202C2×C32C4×C22⋊C411yescharacteristic
203C2×C32#40511yescharacteristic
204C2×C32#40511yescharacteristic
205C3⋊D3—41no—
206C3⋊D3#40812yes—
207C3⋊D3#43312yes—
208C24—91no—
209C22×C4—91no—
210C22×C4—92no—
211C22×C4—91no—
212C22×C4—91no—
213C22×C4—91no—
214C22×C4—91no—
215C22×C4—92no—
216C22×C4—181no—
217C22×C4—181no—
218C22×C4—181no—
219C22×C4—181no—
220C22×C4C2×#15711yescharacteristic
221C2×C8—92no—
222C2×C8—92no—
223C2×C8—91no—
224C2×C8—91no—
225C2×C8—181no—
226C2×C8—181no—
227C2×C8—181no—
228C2×C8—181no—
229C2×C8—181no—
230C2×C8—181no—
231C2×C8—181no—
232C2×C8—181no—
233C2×C8C2×#15711yescharacteristic
234C2×C8C2×#15711yescharacteristic
235C4⋊C4—184no—
236C22⋊C4—184no—
237C42—92no—
238C42—92no—
239C42—181no—
240C42—181no—
241C22×C3—24no—
242C22×C3—22no—
243C22×C3—42no—
244C22×C3—42no—
245C2×D3—62no—
246C2×D3—62no—
247C2×D3—64no—
248C2×D3—64no—
249C2×D3—64no—
250C2×D3—122no—
251C2×D3—122no—
252C2×D3—128no—
253C2×D3—128no—
254C3×C4—22no—
255C3×C4—22no—
256C3×C4—42no—
257Dic3—62no—
258Dic3—62no—
259Dic3—122no—
260C32#175011yescharacteristic, complemented, Sylow
261C23—91no—
262C23—91no—
263C23—181no—
264C23—181no—
265C23—182no—
266C23—182no—
267C23C4×#15711yescharacteristic
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—91no—
271C2×C4—91no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—94no—
276C2×C4—91no—
277C2×C4—181no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4—181no—
286C2×C4—181no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4C4×#15711yescharacteristic
291C2×C4C22×#15711yescharacteristic
292C8—21no—
293C8—21no—
294C8—182no—
295C8—182no—
296C8—181no—
297C8—181no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—22no—
301C2×C3—44no—
302D3—64no—
303D3—64no—
304D3—124no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—91no—
309C22—91no—
310C22—92no—
311C22—92no—
312C22—181no—
313C22—181no—
314C22—181no—
315C22—362no—
316C22—362no—
317C22C2×C4×#15711yescharacteristic
318C4—21no—
319C4—91no—
320C4—91no—
321C4—184no—
322C4—181no—
323C4—362no—
324C4D4×#15711yescharacteristic
325C4D4×#15711yescharacteristic
326C3—22no—
327C2—41no—
328C2—92no—
329C2—92no—
330C2—361no—
331C2C22⋊C4×#15711yescharacteristic
332C2#1059376511yescharacteristic
333C2#1059377511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C2×C42
FittingC32×C22⋊C8C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22⋊C8#157
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#63767C2semidirect
4. C2×C8×#157C2semidirect
6. #10590181C2semidirect
7. #10590181C2semidirect
19. C22⋊#622C4semidirect
20. #63778C4semidirect
23. C32×C22⋊C8C4semidirect
24. #63657C4semidirect
25. #63647C4semidirect
26. #63647C4semidirect
169. C22⋊C8#157semidirect
260. C32#1750semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
#105938002
C2×#637672
C2×C8×#1572
C3⋊D3×C22⋊C82
#105901812
#17509