Finite Group Databasebeta

← #11773394

Subgroups — #11773394

Order 1152.

850 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 130 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×C4⋊#157C211yesmaximal, characteristic
2C2×#63781C211yesmaximal, characteristic
3C2×#63781C212yesmaximal
4C2×#63781C212yesmaximal
5C3⋊D3×#95C211yesmaximal, characteristic
6C23×#157C2211yescharacteristic
7C23×#157C2212yes—
8C23×#157C2211yescharacteristic
9C22×C4×C3⋊D3C2212yes—
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C4⋊#157—22no—
12C2×C4⋊#157—24no—
13#63781—22no—
14#63781—24no—
15#63781—24no—
16C32×#95C411yescharacteristic, complemented
17#63658C411yescharacteristic, complemented
18#63658C412yescomplemented
19D3×#95—62no—
20C23×C3⋊D3C2311yescharacteristic
21C22×#157—22no—
22C22×#157—22no—
23C22×#157—22no—
24C22×#157—21no—
25C22×#157—22no—
26C22×#157—21no—
27C22×#157—22no—
28C22×#157—21no—
29C22×#157—22no—
30C22×#157—21no—
31C22×#157—22no—
32C22×#157—22no—
33C22×#157—22no—
34C22×#157—22no—
35C22×#157D414yes—
36C22×#157D412yes—
37C22×#157Q812yes—
38C22×C32×C4C2×C412yes—
39C22×C32×C4C2×C411yescharacteristic
40C22×C3⋊Dic3C2×C412yes—
41C22×C3⋊Dic3C2×C411yescharacteristic
42C2×C4×C3⋊D3—22no—
43C2×C4×C3⋊D3—22no—
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3—22no—
46C2×C4×C3⋊D3—22no—
47C2×C4×C3⋊D3—22no—
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3—22no—
50C2×C4×C3⋊D3D412yes—
51C2×C4×C3⋊D3Q812yes—
52C4⋊#157—28no—
53#1442—91nomaximal, Sylow
54C22×C4×D3—62no—
55C22×C4×D3—64no—
56C3×#95—22no—
57C3⋊#95—64no—
58C3⋊#95—62no—
59C23×C32C22×C411yescharacteristic
60C22×C3⋊D3C2×D412yes—
61C22×C3⋊D3C2×D411yescharacteristic
62C22×C3⋊D3C2×D411yescharacteristic
63C22×C3⋊D3C2×Q811yescharacteristic
64C22×C3⋊D3C2×Q811yescharacteristic
65C22×C3⋊D3#4111yescharacteristic
66C22×C3⋊D3#4112yes—
67C22×C3⋊D3#4112yes—
68C22×C3⋊D3#4112yes—
69C22×C3⋊D3#4111yescharacteristic
70C2×#157—24no—
71C2×#157—24no—
72C2×#157—22no—
73C2×#157—24no—
74C2×#157—22no—
75C2×#157—24no—
76C2×#157—24no—
77C2×#157—41no—
78C2×#157—42no—
79C2×#157—42no—
80C2×#157—42no—
81C2×#157—41no—
82C2×#157—41no—
83C2×#157—42no—
84C2×#157—42no—
85C2×#157—41no—
86C2×#157—42no—
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4C4⋊C412yes—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3C4⋊C412yes—
97C4×C3⋊D3—22no—
98C4×C3⋊D3—24no—
99C4×C3⋊D3—22no—
100C4×C3⋊D3—42no—
101C4×C3⋊D3—42no—
102C4×C3⋊D3—42no—
103C4×C3⋊D3—42no—
104C22×C4⋊C4—91no—
105C2×#95—91no—
106C2×#95—91no—
107C2×#95—92no—
108C2×#95—92no—
109C23×D3—62no—
110C22×C3×C4—24no—
111C22×C3×C4—22no—
112C22×Dic3—62no—
113C22×Dic3—64no—
114C2×C4×D3—64no—
115C2×C4×D3—64no—
116C2×C4×D3—68no—
117C2×C4×D3—68no—
118C2×C4×D3—124no—
119C2×C4×D3—124no—
120C2×C4×D3—124no—
121C2×C4×D3—124no—
122C2×C4×D3—124no—
123C2×C4×D3—124no—
124C22×C32C2×C4⋊C411yescharacteristic
125C22×C32#11712yes—
126C22×C32C4×D412yes—
127C22×C32C4×D411yescharacteristic
128C22×C32C4×Q811yescharacteristic
129C2×C3⋊D3#12011yescharacteristic
130C2×C3⋊D3#12111yescharacteristic
131C2×C3⋊D3#12112yes—
132C2×C3⋊D3C22⋊Q812yes—
133C2×C3⋊D3C22⋊Q811yescharacteristic
134C2×C3⋊D3C22⋊Q812yes—
135C2×C3⋊D3#12312yes—
136C2×C3⋊D3#12312yes—
137C2×C3⋊D3#12311yescharacteristic
138C2×C3⋊D3#12411yescharacteristic
139C2×C3⋊D3#12412yes—
140C2×C3⋊D3#12411yescharacteristic
141C2×C3⋊D3#12512yes—
142C2×C3⋊D3#12512yes—
143C2×C3⋊D3#12511yescharacteristic
144C2×C3⋊D3#12612yes—
145C2×C3⋊D3#12612yes—
146C2×C3⋊D3C4⋊Q811yescharacteristic
147#157—42no—
148#157—44no—
149#157—42no—
150C32×C4—22no—
151C32×C4—42no—
152C3⋊Dic3—22no—
153C3⋊Dic3—42no—
154C23×C4—91no—
155C23×C4—92no—
156C23×C4—91no—
157C23×C4—91no—
158C23×C4—92no—
159C2×C4⋊C4—182no—
160C2×C4⋊C4—184no—
161#95—92no—
162#95—91no—
163#95—182no—
164#95—184no—
165#95—184no—
166#95#15711yescharacteristic, complemented
167C23×C3—22no—
168C22×D3—62no—
169C22×D3—64no—
170C22×D3—62no—
171C22×D3—62no—
172C22×D3—62no—
173C22×D3—64no—
174C22×D3—64no—
175C22×D3—64no—
176C22×D3—62no—
177C22×D3—62no—
178C2×C3×C4—28no—
179C2×C3×C4—24no—
180C2×C3×C4—44no—
181C2×C3×C4—44no—
182C2×C3×C4—44no—
183C2×Dic3—64no—
184C2×Dic3—68no—
185C2×Dic3—124no—
186C2×Dic3—124no—
187C2×Dic3—124no—
188C4×D3—124no—
189C4×D3—128no—
190C4×D3—124no—
191C4×D3—128no—
192C4×D3—128no—
193C4×D3—128no—
194C4×D3—128no—
195C2×C32#38211yescharacteristic
196C2×C32#38511yescharacteristic
197C2×C32#38712yes—
198C2×C32#38812yes—
199C2×C32#38911yescharacteristic
200C3⋊D3#39311yescharacteristic
201C3⋊D3#39411yescharacteristic
202C3⋊D3#39711yescharacteristic
203C3⋊D3#39812yes—
204C3⋊D3#40011yescharacteristic
205C3⋊D3#40012yes—
206C24—91no—
207C22×C4—91no—
208C22×C4—92no—
209C22×C4—92no—
210C22×C4—92no—
211C22×C4—94no—
212C22×C4—92no—
213C22×C4—92no—
214C22×C4—182no—
215C22×C4—182no—
216C22×C4—182no—
217C22×C4—182no—
218C22×C4—182no—
219C22×C4—182no—
220C22×C4—182no—
221C22×C4—182no—
222C22×C4—181no—
223C22×C4—181no—
224C22×C4—182no—
225C22×C4—182no—
226C22×C4—182no—
227C22×C4—182no—
228C22×C4—182no—
229C22×C4—182no—
230C22×C4—182no—
231C22×C4—182no—
232C22×C4—182no—
233C22×C4—181no—
234C22×C4—182no—
235C22×C4—181no—
236C22×C4C2×#15712yes—
237C22×C4C2×#15711yescharacteristic
238C4⋊C4—188no—
239C22×C3—22no—
240C22×C3—24no—
241C22×C3—24no—
242C22×C3—22no—
243C22×C3—22no—
244C2×D3—62no—
245C2×D3—64no—
246C2×D3—64no—
247C2×D3—62no—
248C2×D3—64no—
249C2×D3—64no—
250C2×D3—64no—
251C2×D3—62no—
252C2×D3—64no—
253C2×D3—62no—
254C2×D3—64no—
255C2×D3—62no—
256C2×D3—62no—
257C2×D3—64no—
258C2×D3—64no—
259C2×D3—62no—
260C2×D3—64no—
261C2×D3—62no—
262C3×C4—44no—
263C3×C4—48no—
264Dic3—124no—
265Dic3—128no—
266C32#144211yescharacteristic, complemented, Sylow
267C23—91no—
268C23—91no—
269C23—92no—
270C23—92no—
271C23—92no—
272C23—91no—
273C23—92no—
274C23—91no—
275C23—91no—
276C23—91no—
277C23C22×#15711yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—92no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4—184no—
286C2×C4—182no—
287C2×C4—184no—
288C2×C4—184no—
289C2×C4—184no—
290C2×C4—184no—
291C2×C4—184no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—362no—
298C2×C4—362no—
299C2×C4—362no—
300C2×C4—362no—
301C2×C4—361no—
302C2×C4—361no—
303C2×C4—362no—
304C2×C4—361no—
305C2×C4—361no—
306C2×C4—362no—
307C2×C4—362no—
308C2×C4—362no—
309C2×C4—362no—
310C2×C4—362no—
311C2×C4C4⋊#15712yes—
312C2×C3—22no—
313C2×C3—22no—
314C2×C3—24no—
315C2×C3—24no—
316C2×C3—22no—
317D3—62no—
318D3—62no—
319D3—62no—
320D3—64no—
321D3—64no—
322D3—62no—
323C22—91no—
324C22—91no—
325C22—92no—
326C22—91no—
327C22—91no—
328C22—92no—
329C22—92no—
330C22—92no—
331C22—92no—
332C22—92no—
333C22—92no—
334C22—92no—
335C22—92no—
336C22—92no—
337C22—91no—
338C22—91no—
339C22—91no—
340C22—91no—
341C22C2×C4⋊#15711yescharacteristic
342C22#6428612yes—
343C22D4×#15712yes—
344C22D4×#15711yescharacteristic
345C22Q8×#15711yescharacteristic
346C4—22no—
347C4—42no—
348C4—182no—
349C4—364no—
350C4—362no—
351C4—362no—
352C4—362no—
353C3—22no—
354C2—91no—
355C2—91no—
356C2—91no—
357C2—91no—
358C2—92no—
359C2—92no—
360C2#1059373611yescharacteristic
361C2#1059374611yescharacteristic
362C2#1059374712yes—
363C2#1059375812yes—
364C2#1059375911yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socleC23×C32C22×C4
FittingC32×#95C4
prime radical, cosocleC23×C3⋊D3C23
hypercenter#95#157
hypocenterC32#1442
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
16. C32×#95C4semidirect
17. #63658C4semidirect
18. #63658C4semidirect
166. #95#157semidirect
266. C32#1442semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C2×#637812
C3⋊D3×#952
#14429