Finite Group Databasebeta

← #11784743

Subgroups — #11784743

Order 1152.

1118 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3797C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3C2×#63730C214yesmaximal, complemented
4#10591152C211yesmaximal, characteristic
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×C3×Dic6—21no—
7C22×#627C412yescomplemented
8C22×#624—21no—
9C2×#3797—21no—
10C2×#3797—21no—
11C2×#3797—28no—
12C2×#3797C412yescomplemented
13C2×#3797C2212yes—
14C2×C22⋊#157—21no—
15C2×C4⋊#157C2212yes—
16C2×#3710C2212yes—
17#63781—21no—
18#63730—28no—
19C3×#830—21no—
20#63557—21no—
21C22×D3×Q8—61no—
22D3×C22⋊C8—61no—
23C23×C3⋊D3D411yescharacteristic
24C22×#157—22no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C22×C3×Dic3—22no—
33C2×C3×Dic6—28no—
34C2×C3×Dic6—22no—
35C2×C3×Dic6—22no—
36C2×#627—22no—
37C2×#627—28no—
38C2×#627C2×C414yes—
39C2×#624—28no—
40C2×#624—22no—
41C2×#624—22no—
42#3797—28no—
43#3797—28no—
44#3797—24no—
45#3797—28no—
46#3797D418yes—
47C22⋊#157—42no—
48C4⋊#157—24no—
49C2×C3×C3⋊C8—22no—
50#3710—24no—
51#1787—91nomaximal, Sylow
52C22×C3×Q8—61no—
53C2×D3×Q8—62no—
54C2×D3×Q8—62no—
55C2×D3×Q8—62no—
56C2×D3×Q8—62no—
57C2×D3×Q8—616no—
58C22×C4×D3—61no—
59C22×C4×D3—61no—
60C22×C4×D3—62no—
61C22×Dic6—21no—
62C22×Dic6—62no—
63C2×D3×C8—62no—
64C3×C22⋊C8—61no—
65#830—21no—
66(C2×D3)⋊C8—62no—
67C23×C32C22⋊C411yescharacteristic
68C22×C3⋊D3—22no—
69C22×C3⋊D3—22no—
70C22×C3⋊D3C22⋊C411yescharacteristic
71C22×C3⋊D3SD1612yes—
72C22×C3⋊D3Q1612yes—
73C22×C3⋊D3C2×D411yescharacteristic
74C2×#157—42no—
75C2×#157—42no—
76C2×#157—42no—
77C2×C32×C4—22no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22×C411yescharacteristic
83C4×C3⋊D3—22no—
84C4×C3⋊D3—22no—
85C4×C3⋊D3—22no—
86C4×C3⋊D3C2×D414yes—
87C2×C3×Dic3—28no—
88C2×C3×Dic3—24no—
89C3×Dic6—28no—
90C3×Dic6—28no—
91#627—28no—
92#627—24no—
93#627C22⋊C418yescomplemented
94#624—28no—
95#624—28no—
96C3×C3⋊C8—42no—
97C23×Q8—91no—
98C2×#103—94no—
99C2×C22⋊C8—91no—
100#380—91no—
101C23×D3—61no—
102C23×D3—61no—
103C2×C3×Q8—68no—
104C2×C3×Q8—62no—
105C2×C3×Q8—62no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—62no—
109C22×Dic3—22no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112D3×Q8—68no—
113D3×Q8—68no—
114D3×Q8—616no—
115D3×Q8—616no—
116D3×Q8—616no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—64no—
126C2×C4×D3—64no—
127C2×C4×D3—616no—
128C2×C4×D3—68no—
129C2×C4×D3—124no—
130C2×Dic6—28no—
131C2×Dic6—22no—
132C2×Dic6—22no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C2×Dic6—616no—
136C2×C3×C8—62no—
137C2×C3⋊C8—22no—
138D3×C8—124no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32#10312yescomplemented
142C22×C32C2×C22⋊C411yescharacteristic
143C2×C3⋊D3—21no—
144C2×C3⋊D3—21no—
145C2×C3⋊D3—24no—
146C2×C3⋊D3—24no—
147C2×C3⋊D3#10312yescomplemented
148C2×C3⋊D3#12012yes—
149C2×C3⋊D3C2×SD1611yescharacteristic
150C2×C3⋊D3C2×Q1611yescharacteristic
151C2×C3⋊D3#13712yes—
152#157—82no—
153C32×C4—21no—
154C32×C4#12012yes—
155C3⋊Dic3—21no—
156C3⋊Dic3C2×C22⋊C412yes—
157C3×Dic3—28no—
158C22×Q8—61no—
159C22×Q8—92no—
160C22×Q8—92no—
161C22×Q8—92no—
162C22×Q8—181no—
163C22×Q8—181no—
164C22×Q8—188no—
165C23×C4—91no—
166C23×C4—181no—
167C22×C8—92no—
168C2×C4⋊C4—92no—
169C2×C22⋊C4—181no—
170#103—188no—
171C22⋊C8—61no—
172C22⋊C8—181no—
173#95—181no—
174C23×C3—21no—
175C23×C3—21no—
176C22×D3—61no—
177C22×D3—62no—
178C22×D3—62no—
179C22×D3—61no—
180C22×D3—61no—
181C22×D3—61no—
182C22×D3—62no—
183C22×D3—62no—
184C22×D3—64no—
185C22×D3—64no—
186C22×D3—122no—
187C22×D3—122no—
188C3×Q8—68no—
189C3×Q8—68no—
190C2×C3×C4—24no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—42no—
196C2×C3×C4—68no—
197C2×C3×C4—64no—
198C2×Dic3—28no—
199C2×Dic3—24no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—64no—
205C2×Dic3—122no—
206C4×D3—64no—
207C4×D3—64no—
208C4×D3—616no—
209C4×D3—616no—
210C4×D3—64no—
211C4×D3—64no—
212C4×D3—64no—
213C4×D3—122no—
214C4×D3—122no—
215C4×D3—122no—
216Dic6—28no—
217Dic6—28no—
218Dic6—68no—
219Dic6—68no—
220Dic6—616no—
221C3×C8—122no—
222C3⋊C8—42no—
223C2×C32—22no—
224C2×C32#37911yescharacteristic
225C2×C32C2×#10311yescharacteristic
226C2×C32#41911yescharacteristic
227C3⋊D3—22no—
228C3⋊D3#44812yes—
229C3⋊D3#45112yes—
230C24—91no—
231C2×Q8—68no—
232C2×Q8—62no—
233C2×Q8—62no—
234C2×Q8—94no—
235C2×Q8—98no—
236C2×Q8—182no—
237C2×Q8—188no—
238C2×Q8—184no—
239C2×Q8—188no—
240C2×Q8—188no—
241C2×Q8—188no—
242C22×C4—62no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—184no—
249C22×C4—182no—
250C22×C4—182no—
251C22×C4—188no—
252C22×C4—182no—
253C22×C4GO+(4,𝔽2)11yescharacteristic
254C2×C8—62no—
255C2×C8—184no—
256C4⋊C4—184no—
257C22⋊C4—362no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—41no—
265C22×C3—41no—
266C2×D3—62no—
267C2×D3—62no—
268C2×D3—62no—
269C2×D3—61no—
270C2×D3—61no—
271C2×D3—61no—
272C2×D3—61no—
273C2×D3—62no—
274C2×D3—62no—
275C2×D3—62no—
276C2×D3—62no—
277C2×D3—68no—
278C2×D3—68no—
279C2×D3—62no—
280C2×D3—124no—
281C2×D3—124no—
282C2×D3—121no—
283C2×D3—121no—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—41no—
288C3×C4—68no—
289Dic3—28no—
290Dic3—62no—
291Dic3—62no—
292Dic3—62no—
293Dic3—121no—
294C32#178711yescharacteristic, complemented, Sylow
295C23—91no—
296C23—91no—
297C23—92no—
298C23—92no—
299C23—182no—
300C23—182no—
301C23D32⋊C411yescharacteristic
302Q8—68no—
303Q8—68no—
304Q8—98no—
305Q8—184no—
306Q8—188no—
307C2×C4—22no—
308C2×C4—68no—
309C2×C4—64no—
310C2×C4—91no—
311C2×C4—94no—
312C2×C4—91no—
313C2×C4—182no—
314C2×C4—182no—
315C2×C4—188no—
316C2×C4—188no—
317C2×C4—182no—
318C2×C4—182no—
319C2×C4—362no—
320C2×C4—362no—
321C2×C4—362no—
322C2×C4D32⋊C411yescharacteristic
323C2×C4C2×GO+(4,𝔽2)11yescharacteristic
324C8—122no—
325C2×C3—24no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—42no—
333D3—62no—
334D3—62no—
335D3—62no—
336D3—62no—
337D3—64no—
338D3—122no—
339C22—21no—
340C22—21no—
341C22—91no—
342C22—91no—
343C22—92no—
344C22—92no—
345C22—92no—
346C22—184no—
347C22—184no—
348C22—181no—
349C22—181no—
350C22#6373012yescomplemented
351C22C2×D32⋊C411yescharacteristic
352C4—21no—
353C4—68no—
354C4—92no—
355C4—181no—
356C4—722no—
357C4#6424112yes—
358C3—21no—
359C3—21no—
360C2—22no—
361C2—92no—
362C2—92no—
363C2—182no—
364C2C2×#6373011yescharacteristic
365C2#1059332111yescharacteristic
366C2#1059351211yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1787
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63730C2semidirect
7. C22×#627C4semidirect
12. C2×#3797C4semidirect
93. #627C22⋊C4semidirect
141. C22×C32#103semidirect
147. C2×C3⋊D3#103semidirect
294. C32#1787semidirect
350. C22#63730semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
#105938122
C2×#637302
#105911522
#17879