Finite Group Databasebeta

← #11785227

Subgroups — #11785227

Order 1152.

526 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 89 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#10593735C211yesmaximal, characteristic
3C2×#63730C212yesmaximal
4#10590331C211yesmaximal, characteristic
5#10590049C212yesmaximal
6C2×#3797C2211yescharacteristic
7C2×C4⋊#157—21no—
8C2×C4⋊#157—21no—
9C2×C4⋊#157C2212yes—
10C42×C3⋊D3C2211yescharacteristic
11C3×C4×Dic6—21no—
12C4×#627C412yescomplemented
13#63900C2211yescharacteristic
14#63883—21no—
15C4×#624—21no—
16#63843—21no—
17#63838C412yescomplemented
18C2×#3710C2212yes—
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—
38C4⋊#157—42no—
39C4⋊#157—42no—
40C32×C42D411yescharacteristic
41C4×C3⋊Dic3C2×C411yescharacteristic
42C4×C3⋊Dic3C2×C411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C3×C4⋊Dic3—21no—
45C3×Dic3⋊C4—22no—
46C3×C4×Dic3—22no—
47C2×C3×C3⋊C8—22no—
48#3724C2×C412yes—
49Dic3⋊Dic3—22no—
50Dic32—22no—
51#3710—22no—
52#3710—22no—
53#1803—91nomaximal, Sylow
54C2×D3×Q8—61no—
55C3×C4×Q8—61no—
56Q8×Dic3—61no—
57C2×D3×C8—62no—
58D3×C4⋊C4—61no—
59D3×C4⋊C4—62no—
60#887—62no—
61#887—61no—
62C42×D3—61no—
63C42×D3—61no—
64C42×D3—62no—
65C4×Dic6—21no—
66C4×Dic6—62no—
67C3×C4⋊C8—61no—
68Dic3⋊C8—62no—
69C4⋊(C3⋊C8)—21no—
70C22×C3⋊D3C2×D411yescharacteristic
71C2×#157—42no—
72C2×#157—42no—
73C2×#157—42no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C22×C411yescharacteristic
80C4×C3⋊D3—21no—
81C4×C3⋊D3—21no—
82C4×C3⋊D3SD1612yes—
83C4×C3⋊D3Q1612yes—
84C4×C3⋊D3C2×D411yescharacteristic
85C4×C3⋊D3C2×Q811yescharacteristic
86C4×C3⋊D3#4111yescharacteristic
87C4×C3⋊D3#4111yescharacteristic
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90C3×Dic6—22no—
91C3×Dic6—22no—
92#627—22no—
93#627C4⋊C414yescomplemented
94#624—22no—
95#624—22no—
96#624—41no—
97#624—41no—
98C3×C3⋊C8—42no—
99C2×C4×Q8—91no—
100C2×C4⋊C8—91no—
101C2×#103—92no—
102#384—91no—
103#340—92no—
104C2×C3×Q8—61no—
105D3×Q8—62no—
106D3×Q8—62no—
107D3×Q8—62no—
108D3×Q8—62no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×Dic6—21no—
118C2×Dic6—62no—
119C2×C3×C8—62no—
120C3×C4⋊C4—62no—
121C3×C4⋊C4—61no—
122C3×C42—21no—
123C3×C42—21no—
124C3×C42—62no—
125C4⋊Dic3—21no—
126C4⋊Dic3—62no—
127Dic3⋊C4—22no—
128Dic3⋊C4—62no—
129Dic3⋊C4—62no—
130C4×Dic3—22no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C4×Dic3—62no—
138C4×Dic3—62no—
139C2×C3⋊C8—22no—
140D3×C8—122no—
141D3×C8—122no—
142C22×C32C2×C22⋊C411yescharacteristic
143C2×C3⋊D3#12111yescharacteristic
144C2×C3⋊D3C22⋊Q811yescharacteristic
145C2×C3⋊D3C2×SD1611yescharacteristic
146C2×C3⋊D3C2×Q1611yescharacteristic
147C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
148C2×C3⋊D3#13711yescharacteristic
149#157—82no—
150C32×C4—21no—
151C32×C4#10312yescomplemented
152C32×C4#12111yescharacteristic
153C32×C4C22⋊Q811yescharacteristic
154C3⋊Dic3—21no—
155C3⋊Dic3#10312yescomplemented
156C3⋊Dic3C2×C4⋊C411yescharacteristic
157C3⋊Dic3#11711yescharacteristic
158C3×Dic3—24no—
159C3×Dic3—42no—
160C22×Q8—91no—
161C22×C8—92no—
162C4×Q8—61no—
163C4×Q8—92no—
164C4×Q8—92no—
165C4×Q8—181no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—92no—
168C2×C4⋊C4—181no—
169C2×C4⋊C4—181no—
170C2×C4⋊C4—181no—
171C2×C42—91no—
172C2×C42—181no—
173C4⋊C8—61no—
174C4⋊C8—181no—
175#103—184no—
176C22×D3—61no—
177C22×D3—61no—
178C3×Q8—62no—
179C3×Q8—62no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—62no—
187C2×C3×C4—62no—
188C2×Dic3—22no—
189C2×Dic3—22no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—62no—
199C4×D3—62no—
200C4×D3—61no—
201C4×D3—61no—
202C4×D3—61no—
203C4×D3—61no—
204C4×D3—61no—
205C4×D3—61no—
206C4×D3—61no—
207C4×D3—61no—
208C4×D3—64no—
209C4×D3—64no—
210C4×D3—121no—
211C4×D3—121no—
212C4×D3—121no—
213C4×D3—121no—
214C4×D3—122no—
215C4×D3—122no—
216Dic6—22no—
217Dic6—22no—
218Dic6—64no—
219Dic6—64no—
220C3×C8—122no—
221C3⋊C8—42no—
222C2×C32#38011yescharacteristic
223C2×C32C2×#10311yescharacteristic
224C2×C32#41711yescharacteristic
225C3⋊D3#46011yescharacteristic
226C3⋊D3#46211yescharacteristic
227C3⋊D3#47511yescharacteristic
228C3⋊D3#47711yescharacteristic
229C2×Q8—61no—
230C2×Q8—92no—
231C2×Q8—92no—
232C2×Q8—92no—
233C2×Q8—181no—
234C2×Q8—181no—
235C22×C4—91no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4—181no—
239C22×C4—181no—
240C22×C4—182no—
241C2×C8—62no—
242C2×C8—182no—
243C2×C8—182no—
244C4⋊C4—61no—
245C4⋊C4—62no—
246C4⋊C4—92no—
247C4⋊C4—182no—
248C4⋊C4—182no—
249C4⋊C4—182no—
250C4⋊C4—362no—
251C4⋊C4—362no—
252C42—62no—
253C42—91no—
254C42—91no—
255C42—91no—
256C42—182no—
257C42GO+(4,𝔽2)11yescharacteristic
258C22×C3—21no—
259C22×C3—21no—
260C2×D3—61no—
261C2×D3—61no—
262C2×D3—61no—
263C2×D3—61no—
264C2×D3—61no—
265C2×D3—61no—
266C2×D3—61no—
267C2×D3—61no—
268C2×D3—61no—
269C2×D3—61no—
270C2×D3—61no—
271C2×D3—61no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—64no—
281C3×C4—122no—
282Dic3—24no—
283Dic3—42no—
284Dic3—61no—
285Dic3—61no—
286Dic3—62no—
287Dic3—62no—
288Dic3—61no—
289Dic3—61no—
290Dic3—121no—
291Dic3—121no—
292C32#180311yescharacteristic, complemented, Sylow
293C23—91no—
294Q8—62no—
295Q8—62no—
296Q8—94no—
297Q8—182no—
298C2×C4—62no—
299C2×C4—62no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—91no—
303C2×C4—91no—
304C2×C4—91no—
305C2×C4—91no—
306C2×C4—92no—
307C2×C4—92no—
308C2×C4—91no—
309C2×C4—181no—
310C2×C4—181no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4—361no—
314C2×C4—361no—
315C2×C4—362no—
316C2×C4—362no—
317C2×C4—362no—
318C2×C4D32⋊C411yescharacteristic
319C2×C4D32⋊C411yescharacteristic
320C2×C4C2×GO+(4,𝔽2)11yescharacteristic
321C8—122no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328D3—61no—
329D3—61no—
330D3—61no—
331D3—61no—
332D3—61no—
333D3—61no—
334D3—61no—
335D3—61no—
336C22—91no—
337C22—91no—
338C22—91no—
339C22—91no—
340C22—91no—
341C22—91no—
342C22C2×D32⋊C411yescharacteristic
343C4—21no—
344C4—64no—
345C4—92no—
346C4—91no—
347C4—91no—
348C4—122no—
349C4—181no—
350C4—722no—
351C4#6373012yescomplemented
352C4D32⋊Q811yescharacteristic
353C4#6423011yescharacteristic
354C3—21no—
355C3—21no—
356C2—91no—
357C2—91no—
358C2—91no—
359C2—91no—
360C2#1059331911yescharacteristic
361C2C2×#6373011yescharacteristic
362C2#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#1803
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
12. C4×#627C4semidirect
17. #63838C4semidirect
93. #627C4⋊C4semidirect
151. C32×C4#103semidirect
155. C3⋊Dic3#103semidirect
292. C32#1803semidirect
351. C4#63730semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
#105937352
C2×#637302
#105903312
#105900492
#18039