Finite Group Databasebeta

← #11775615

Subgroups — #11775615

Order 1152.

566 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#10594925C211yesmaximal, characteristic
2#10593800C211yesmaximal, characteristic
3#10591325C211yesmaximal, characteristic
4#10590072C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3797C411yescharacteristic, complemented
7C2×#3787—21no—
8C2×C3×C4⋊Dic3—21no—
9C3×#924—21no—
10#63982C2212yes—
11#63974—21no—
12C2×#3722—21no—
13#63900C411yescharacteristic, complemented
14#63883—21no—
15#63871—21no—
16#63865C412yescomplemented
17C22⋊#622C2212yes—
18#63778—21no—
19#63579C2212yes—
20D3×C22⋊Q8—61no—
21#4987—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C4×C3⋊D3—42no—
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C22×C3×Dic3—22no—
31C2×C3×Dic6—21no—
32C2×#627C2×C412yes—
33C2×#624—21no—
34C2×#624—21no—
35#3797—42no—
36C2×#622—22no—
37#3787—42no—
38C3×#217—22no—
39C3×C4⋊Dic3—21no—
40C3×C4⋊Dic3—42no—
41C3×Dic3⋊C4—22no—
42#3724C2×C412yes—
43Dic3⋊Dic3—22no—
44#3722—22no—
45#3722—42no—
46#1520—91nomaximal, Sylow
47C2×D3×Q8—61no—
48C22×C4×D3—61no—
49C22×C4×D3—61no—
50C3×C22⋊Q8—61no—
51C2×C3×C4⋊C4—61no—
52#946—61no—
53C2×(C2×D3)⋊C4—62no—
54C2×C4⋊Dic3—21no—
55#924—21no—
56#897—61no—
57#896—62no—
58D3×C4⋊C4—61no—
59D3×C4⋊C4—62no—
60D3×C22⋊C4—62no—
61#878—62no—
62C3⋊#95—62no—
63C23×C32C2×D411yescharacteristic
64C22×C3⋊D3—41no—
65C22×C3⋊D3—41no—
66C22×C3⋊D3C22⋊C411yescharacteristic
67C22×C3⋊D3C22⋊C411yescharacteristic
68C22×C3⋊D3SD1612yes—
69C22×C3⋊D3Q1612yes—
70C2×C32×C4—22no—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3C22×C411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4×C3⋊D3—22no—
77C4×C3⋊D3—22no—
78C4×C3⋊D3—41no—
79C4×C3⋊D3—41no—
80C2×C3×Dic3—22no—
81C2×C3×Dic3—22no—
82C2×C3×Dic3—42no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—42no—
85C3×Dic6—42no—
86#627—42no—
87#624—42no—
88#624—42no—
89#622—42no—
90C2×C22⋊Q8—91no—
91C2×C22⋊C8—91no—
92#380—91no—
93#328—94no—
94C23×D3—61no—
95C23×D3—61no—
96C2×C3×Q8—61no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—62no—
100C22×Dic3—22no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103D3×Q8—124no—
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—61no—
111C2×C4×D3—61no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—124no—
115C2×C4×D3—122no—
116C2×C4×D3—122no—
117C2×Dic6—21no—
118C2×Dic6—62no—
119C3×C4⋊C4—62no—
120C3×C4⋊C4—61no—
121C3×C4⋊C4—122no—
122C3×C22⋊C4—62no—
123#217—22no—
124(C2×D3)⋊C4—62no—
125(C2×D3)⋊C4—62no—
126(C2×D3)⋊C4—124no—
127C4⋊Dic3—21no—
128C4⋊Dic3—42no—
129C4⋊Dic3—62no—
130Dic3⋊C4—22no—
131Dic3⋊C4—62no—
132Dic3⋊C4—62no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32C2×C22⋊C411yescharacteristic
136C22×C32C2×SD1611yescharacteristic
137C22×C32C2×Q1611yescharacteristic
138C2×C3⋊D3—21no—
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—42no—
143C2×C3⋊D3—42no—
144C2×C3⋊D3#10312yes—
145C2×C3⋊D3#10312yes—
146C32×C4—21no—
147C32×C4#9912yes—
148C3⋊Dic3—21no—
149C3⋊Dic3—21no—
150C3×Dic3—42no—
151C3×Dic3—42no—
152C3×Dic3—82no—
153C22×Q8—91no—
154C23×C4—91no—
155C22×C8—181no—
156C22⋊Q8—61no—
157C22⋊Q8—92no—
158C22⋊Q8—92no—
159C22⋊Q8—181no—
160C2×C4⋊C4—61no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—181no—
163C2×C22⋊C4—181no—
164C2×C22⋊C4—181no—
165C22⋊C8—92no—
166C22⋊C8—181no—
167#95—92no—
168C23×C3—21no—
169C23×C3—21no—
170C22×D3—61no—
171C22×D3—61no—
172C22×D3—61no—
173C22×D3—61no—
174C22×D3—62no—
175C22×D3—62no—
176C22×D3—62no—
177C22×D3—62no—
178C22×D3—122no—
179C22×D3—122no—
180C22×D3—121no—
181C22×D3—121no—
182C22×D3—121no—
183C22×D3—121no—
184C3×Q8—122no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—42no—
192C2×C3×C4—62no—
193C2×C3×C4—62no—
194C2×C3×C4—122no—
195C2×C3×C4—122no—
196C2×C3×C4—122no—
197C2×Dic3—22no—
198C2×Dic3—22no—
199C2×Dic3—42no—
200C2×Dic3—42no—
201C2×Dic3—42no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—122no—
207C2×Dic3—121no—
208C2×Dic3—121no—
209C4×D3—64no—
210C4×D3—122no—
211C4×D3—122no—
212C4×D3—122no—
213C4×D3—124no—
214C4×D3—124no—
215C4×D3—122no—
216C4×D3—122no—
217C4×D3—122no—
218C4×D3—122no—
219Dic6—42no—
220Dic6—124no—
221C2×C32—21no—
222C2×C32—21no—
223C2×C32C2×#9911yescharacteristic
224C2×C32C2×#10311yescharacteristic
225C2×C32#42111yescharacteristic
226C3⋊D3—22no—
227C3⋊D3—22no—
228C24—91no—
229C2×Q8—61no—
230C2×Q8—92no—
231C2×Q8—362no—
232C22×C4—62no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4—91no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4—181no—
239C22×C4—181no—
240C22×C4—362no—
241C22×C4GO+(4,𝔽2)11yescharacteristic
242C2×C8—182no—
243C2×C8—362no—
244C4⋊C4—61no—
245C4⋊C4—62no—
246C4⋊C4—92no—
247C4⋊C4—122no—
248C4⋊C4—182no—
249C22⋊C4—62no—
250C22⋊C4—182no—
251C22⋊C4—362no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—41no—
263C22×C3—41no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—62no—
267C2×D3—62no—
268C2×D3—62no—
269C2×D3—62no—
270C2×D3—121no—
271C2×D3—121no—
272C2×D3—121no—
273C2×D3—121no—
274C2×D3—121no—
275C2×D3—121no—
276C2×D3—124no—
277C2×D3—124no—
278C2×D3—122no—
279C2×D3—122no—
280C2×D3—122no—
281C2×D3—122no—
282C3×C4—22no—
283C3×C4—22no—
284C3×C4—22no—
285C3×C4—41no—
286C3×C4—122no—
287C3×C4—122no—
288C3×C4—242no—
289Dic3—42no—
290Dic3—42no—
291Dic3—62no—
292Dic3—82no—
293Dic3—121no—
294Dic3—121no—
295Dic3—121no—
296C32#152011yescharacteristic, complemented, Sylow
297C23—91no—
298C23—91no—
299C23—92no—
300C23—92no—
301C23—361no—
302C23—361no—
303C23C2×GO+(4,𝔽2)11yescharacteristic
304Q8—122no—
305Q8—362no—
306C2×C4—22no—
307C2×C4—62no—
308C2×C4—62no—
309C2×C4—91no—
310C2×C4—91no—
311C2×C4—122no—
312C2×C4—122no—
313C2×C4—122no—
314C2×C4—182no—
315C2×C4—182no—
316C2×C4—361no—
317C2×C4—361no—
318C2×C4—362no—
319C2×C4—362no—
320C2×C4—361no—
321C2×C4D32⋊C411yescharacteristic
322C2×C4D32⋊C411yescharacteristic
323C8—362no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—41no—
335C2×C3—41no—
336D3—64no—
337D3—122no—
338D3—122no—
339D3—122no—
340C22—21no—
341C22—21no—
342C22—92no—
343C22—92no—
344C22—181no—
345C22—181no—
346C22—181no—
347C22—181no—
348C22—362no—
349C22—362no—
350C22#6422711yescharacteristic
351C22#6422811yescharacteristic
352C22C2×D32⋊C411yescharacteristic
353C4—21no—
354C4—122no—
355C4—122no—
356C4—181no—
357C4—181no—
358C4—242no—
359C4#6373812yes—
360C3—21no—
361C3—21no—
362C2—21no—
363C2—21no—
364C2—182no—
365C2—182no—
366C2#1059337511yescharacteristic
367C2#1059338111yescharacteristic
368C2C2×#6373811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1520
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590072C2semidirect
6. C2×#3797C4semidirect
13. #63900C4semidirect
16. #63865C4semidirect
296. C32#1520semidirect

Maximal subgroups

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

subgroupindex
#105949252
#105938002
#105913252
#105900722
#15209