Finite Group Databasebeta

← #11785296

Subgroups — #11785296

Order 1152.

510 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C4×#3797C211yesmaximal, characteristic
2#10593736C211yesmaximal, characteristic
3C2×#63730C212yesmaximal
4#10590331C211yesmaximal, characteristic
5#10590049C212yesmaximal
6C2×#3797C2211yescharacteristic
7C2×C4⋊#157C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×Dic6—21no—
10C4×#627C412yescomplemented
11#63900C2211yescharacteristic
12#63883—21no—
13C4×#624—21no—
14#63843—21no—
15#63838C412yescomplemented
16C2×#3710C2212yes—
17#63781—21no—
18#63781—21no—
19#63730—24no—
20C3×C4⋊(C3⋊C8)—21no—
21#63572—21no—
22C4×D3×Q8—61no—
23D3×C4⋊C8—61no—
24C22×#157—22no—
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×C3×Dic6—21no—
29C2×#627C2×C412yes—
30C2×#624—21no—
31C2×#624—21no—
32#3797—21no—
33#3797—21no—
34#3797D412yes—
35#3797Q812yes—
36C4⋊#157—22no—
37C4⋊#157—22no—
38C32×C42D411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C3×C4⋊Dic3—21no—
43C3×Dic3⋊C4—22no—
44C3×C4×Dic3—22no—
45C2×C3×C3⋊C8—22no—
46#3724C2×C412yes—
47Dic3⋊Dic3—22no—
48Dic32—22no—
49#3710—22no—
50#3710—22no—
51#1805—91nomaximal, Sylow
52C2×D3×Q8—61no—
53C3×C4×Q8—61no—
54Q8×Dic3—61no—
55C2×D3×C8—62no—
56D3×C4⋊C4—61no—
57D3×C4⋊C4—62no—
58#887—62no—
59#887—61no—
60C42×D3—61no—
61C42×D3—61no—
62C42×D3—62no—
63C4×Dic6—21no—
64C4×Dic6—62no—
65C3×C4⋊C8—61no—
66Dic3⋊C8—62no—
67C4⋊(C3⋊C8)—21no—
68C22×C3⋊D3C2×D411yescharacteristic
69C2×#157—42no—
70C2×#157—42no—
71C2×#157—42no—
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C22⋊C411yescharacteristic
74C2×C32×C4C2×D411yescharacteristic
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C2×C3⋊Dic3C22×C411yescharacteristic
78C4×C3⋊D3—22no—
79C4×C3⋊D3—22no—
80C4×C3⋊D3C2×D411yescharacteristic
81C4×C3⋊D3C2×Q811yescharacteristic
82C4×C3⋊D3#4111yescharacteristic
83C4×C3⋊D3#4111yescharacteristic
84C2×C3×Dic3—22no—
85C2×C3×Dic3—22no—
86C3×Dic6—22no—
87C3×Dic6—22no—
88#627—22no—
89#627C4⋊C414yes—
90#624—22no—
91#624—22no—
92#624—42no—
93C3×C3⋊C8—42no—
94C2×C4×Q8—91no—
95C2×C4⋊C8—91no—
96C2×#103—92no—
97#382—91no—
98#340—92no—
99C2×C3×Q8—61no—
100D3×Q8—62no—
101D3×Q8—62no—
102D3×Q8—62no—
103D3×Q8—62no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×Dic6—21no—
113C2×Dic6—62no—
114C2×C3×C8—62no—
115C3×C4⋊C4—62no—
116C3×C4⋊C4—61no—
117C3×C42—21no—
118C3×C42—21no—
119C3×C42—62no—
120C4⋊Dic3—21no—
121C4⋊Dic3—62no—
122Dic3⋊C4—22no—
123Dic3⋊C4—62no—
124Dic3⋊C4—62no—
125C4×Dic3—22no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C2×C3⋊C8—22no—
135D3×C8—122no—
136D3×C8—122no—
137C22×C32C2×C22⋊C411yescharacteristic
138C2×C3⋊D3#12111yescharacteristic
139C2×C3⋊D3C22⋊Q811yescharacteristic
140C2×C3⋊D3#13512yes—
141C2×C3⋊D3#13712yes—
142#157—82no—
143C32×C4—21no—
144C32×C4—21no—
145C32×C4#12111yescharacteristic
146C32×C4C22⋊Q811yescharacteristic
147C3⋊Dic3—21no—
148C3⋊Dic3—21no—
149C3⋊Dic3C2×C4⋊C411yescharacteristic
150C3⋊Dic3#11711yescharacteristic
151C3×Dic3—24no—
152C3×Dic3—42no—
153C22×Q8—91no—
154C22×C8—92no—
155C4×Q8—61no—
156C4×Q8—92no—
157C4×Q8—92no—
158C4×Q8—181no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—92no—
161C2×C4⋊C4—181no—
162C2×C42—91no—
163C2×C42—181no—
164C4⋊C8—61no—
165C4⋊C8—181no—
166#103—184no—
167#95—181no—
168#95—181no—
169C22×D3—61no—
170C22×D3—61no—
171C3×Q8—62no—
172C3×Q8—62no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—62no—
180C2×C3×C4—62no—
181C2×Dic3—22no—
182C2×Dic3—22no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
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—64no—
198C4×D3—64no—
199C4×D3—64no—
200C4×D3—64no—
201C4×D3—122no—
202C4×D3—122no—
203C4×D3—124no—
204Dic6—22no—
205Dic6—22no—
206Dic6—64no—
207Dic6—64no—
208C3×C8—122no—
209C3⋊C8—42no—
210C2×C32#38011yescharacteristic
211C2×C32#41611yescharacteristic
212C2×C32#41911yescharacteristic
213C3⋊D3#46412yes—
214C3⋊D3#47912yes—
215C2×Q8—61no—
216C2×Q8—92no—
217C2×Q8—92no—
218C2×Q8—92no—
219C2×Q8—181no—
220C2×Q8—181no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—181no—
225C22×C4—181no—
226C22×C4—182no—
227C2×C8—62no—
228C2×C8—182no—
229C2×C8—182no—
230C4⋊C4—61no—
231C4⋊C4—62no—
232C4⋊C4—92no—
233C4⋊C4—182no—
234C4⋊C4—182no—
235C4⋊C4—182no—
236C42—62no—
237C42—91no—
238C42—91no—
239C42—91no—
240C42—182no—
241C42GO+(4,𝔽2)11yescharacteristic
242C22×C3—21no—
243C22×C3—21no—
244C2×D3—61no—
245C2×D3—61no—
246C2×D3—61no—
247C2×D3—61no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—62no—
251C2×D3—62no—
252C3×C4—22no—
253C3×C4—22no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4—64no—
261C3×C4—122no—
262Dic3—24no—
263Dic3—42no—
264Dic3—61no—
265Dic3—61no—
266Dic3—61no—
267Dic3—61no—
268Dic3—62no—
269Dic3—62no—
270Dic3—121no—
271Dic3—121no—
272C32#180511yescharacteristic, complemented, Sylow
273C23—91no—
274Q8—62no—
275Q8—62no—
276Q8—94no—
277Q8—182no—
278C2×C4—62no—
279C2×C4—62no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—182no—
291C2×C4—362no—
292C2×C4—362no—
293C2×C4—362no—
294C2×C4—362no—
295C2×C4D32⋊C411yescharacteristic
296C2×C4D32⋊C411yescharacteristic
297C2×C4C2×GO+(4,𝔽2)11yescharacteristic
298C8—122no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305D3—62no—
306D3—62no—
307D3—62no—
308D3—62no—
309C22—92no—
310C22—92no—
311C22—91no—
312C22—91no—
313C22C2×D32⋊C411yescharacteristic
314C4—21no—
315C4—21no—
316C4—64no—
317C4—91no—
318C4—91no—
319C4—122no—
320C4—181no—
321C4—181no—
322C4—722no—
323C4D32⋊Q811yescharacteristic
324C4#6423011yescharacteristic
325C3—21no—
326C3—21no—
327C2—92no—
328C2—92no—
329C2#1059331711yescharacteristic
330C2#1059332111yescharacteristic
331C2#1059340311yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1805
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
10. C4×#627C4semidirect
15. #63838C4semidirect
272. C32#1805semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
#105937362
C2×#637302
#105903312
#105900492
#18059