Finite Group Databasebeta

← #11785130

Subgroups — #11785130

Order 1152.

612 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 73 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×#3802C211yesmaximal, characteristic
2#10593729C211yesmaximal, characteristic, complemented
3C2×#63727C212yesmaximal
4#10590340C211yesmaximal, characteristic, complemented
5#10590052C212yesmaximal, complemented
6C2×#3802C2211yescharacteristic
7C2×C4×D32C412yes—
8C2×#3788C2212yes—
9C42×C3⋊D3C2211yescharacteristic
10C3×C4×D12—21no—
11#63921C412yes—
12#63902—21no—
13C4×#625—21no—
14#63900C2211yescharacteristic
15#63898—21no—
16C2×#3712C2212yes—
17#63779—21no—
18#63779—21no—
19#63727—24no—
20C3×C4⋊(C3⋊C8)—21no—
21#63572—21no—
22C4×D3×D4—61no—
23#4837—61no—
24C22×D32C2×C412yes—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×C3×D12—21no—
29C2×C3×C4×D3—22no—
30C2×#625—21no—
31C2×#624C2×C412yes—
32C2×D3×Dic3—22no—
33#3802—21no—
34#3802—21no—
35#3802D412yes—
36#3802Q812yes—
37C4×D32—44no—
38C2×#622—22no—
39#3788—22no—
40#3788—22no—
41C32×C42D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45C3×(C2×D3)⋊C4—22no—
46C3×C4⋊Dic3—21no—
47C2×C3×C3⋊C8—22no—
48#3724—21no—
49(C2×D3)⋊Dic3—22no—
50#3712—22no—
51#3712—22no—
52#1800—91nomaximal, Sylow
53C2×D3×D4—61no—
54C22×C4×D3—62no—
55C3×C4×D4—61no—
56D4×Dic3—61no—
57C4×#67—62no—
58C2×ΓL(1,𝔽25)—62no—
59#893—61no—
60D3×C4⋊C4—61no—
61#67⋊C4—62no—
62D3×C22⋊C4—62no—
63C4×D12—21no—
64C42×D3—61no—
65C42×D3—61no—
66C3×C4⋊C8—61no—
67Dic3⋊C8—62no—
68C4⋊(C3⋊C8)—21no—
69C22×C3⋊D3C22×C411yescharacteristic
70C22×C3×D3—22no—
71C2×D32—22no—
72C2×D32—42no—
73C2×D32—42no—
74C2×D32C4⋊C414yes—
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C2×D411yescharacteristic
81C4×C3⋊D3—22no—
82C4×C3⋊D3—41no—
83C4×C3⋊D3C2×D411yescharacteristic
84C4×C3⋊D3C2×Q811yescharacteristic
85C4×C3⋊D3#4111yescharacteristic
86C4×C3⋊D3#4111yescharacteristic
87C2×C3×Dic3—22no—
88C3×D12—22no—
89C3×D12—22no—
90C3×C4×D3—44no—
91#625—22no—
92#625—22no—
93#624—42no—
94D3×Dic3—44no—
95#622—42no—
96C3×C3⋊C8—42no—
97C2×C4×D4—91no—
98#423—91no—
99#423—91no—
100C2×#100—92no—
101#343—92no—
102C23×D3—62no—
103C2×C3×D4—61no—
104C22×C3×C4—62no—
105C2×#67—62no—
106C22×Dic3—62no—
107D3×D4—62no—
108D3×D4—62no—
109D3×D4—62no—
110D3×D4—62no—
111C2×D12—21no—
112C2×C4×D3—22no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—62no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—62no—
121C2×C4×D3—128no—
122C2×C3×C8—62no—
123C3×C4⋊C4—61no—
124C3×C22⋊C4—62no—
125C3×C42—21no—
126C3×C42—21no—
127#217—62no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—62no—
130C4⋊Dic3—21no—
131Dic3⋊C4—62no—
132C4×Dic3—61no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C2×C3⋊C8—22no—
139ΓL(1,𝔽25)—122no—
140ΓL(1,𝔽25)—122no—
141C22×C32C2×C22⋊C411yescharacteristic
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3C2×C4⋊C411yescharacteristic
145C2×C3⋊D3#11711yescharacteristic
146C2×C3×D3—24no—
147C2×C3×D3—42no—
148C2×C3×D3—42no—
149D32—44no—
150D32—44no—
151C32×C4—21no—
152C32×C4—21no—
153C32×C4#12111yescharacteristic
154C32×C4C22⋊Q811yescharacteristic
155C3⋊Dic3—21no—
156C3⋊Dic3#10012yescomplemented
157C3⋊Dic3#12111yescharacteristic
158C3⋊Dic3C22⋊Q811yescharacteristic
159C3×Dic3—42no—
160C22×D4—91no—
161C23×C4—92no—
162C2×M16—92no—
163C2×M16—92no—
164C4×D4—61no—
165C4×D4—181no—
166C4×D4—181no—
167C4×D4—181no—
168C2×C4⋊C4—91no—
169C2×C22⋊C4—92no—
170C2×C42—91no—
171C4⋊C8—61no—
172C4⋊C8—181no—
173C4⋊C8—181no—
174C4⋊C8—181no—
175#100—184no—
176C23×C3—62no—
177C22×D3—22no—
178C22×D3—64no—
179C22×D3—61no—
180C22×D3—61no—
181C22×D3—64no—
182C22×D3—124no—
183C22×D3—124no—
184C3×D4—62no—
185C3×D4—62no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—62no—
193C2×C3×C4—124no—
194#67—64no—
195#67—64no—
196C2×Dic3—22no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—124no—
204D12—22no—
205D12—22no—
206C4×D3—44no—
207C4×D3—61no—
208C4×D3—61no—
209C4×D3—61no—
210C4×D3—61no—
211C4×D3—61no—
212C4×D3—61no—
213C4×D3—61no—
214C4×D3—61no—
215C4×D3—64no—
216C4×D3—122no—
217C4×D3—124no—
218C4×D3—124no—
219C4×D3—122no—
220C4×D3—122no—
221C3×C8—122no—
222C3⋊C8—42no—
223C2×C32#38011yescharacteristic
224C2×C32C2×#10011yescharacteristic
225C2×C32#41311yescharacteristic
226C3⋊D3—21no—
227C3⋊D3—21no—
228C3×D3—44no—
229C24—92no—
230C2×D4—61no—
231C2×D4—92no—
232C2×D4—92no—
233C2×D4—181no—
234C2×D4—181no—
235C2×D4—181no—
236C22×C4—62no—
237C22×C4—92no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—182no—
242C22×C4—364no—
243M16—182no—
244M16—182no—
245M16—182no—
246M16—182no—
247C2×C8—62no—
248C2×C8—182no—
249C4⋊C4—61no—
250C4⋊C4—181no—
251C22⋊C4—62no—
252C22⋊C4—182no—
253C42—91no—
254C42—91no—
255C42—91no—
256C42GO+(4,𝔽2)11yescharacteristic
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—64no—
260C22×C3—122no—
261C22×C3—122no—
262C2×D3—24no—
263C2×D3—42no—
264C2×D3—42no—
265C2×D3—61no—
266C2×D3—61no—
267C2×D3—61no—
268C2×D3—61no—
269C2×D3—62no—
270C2×D3—62no—
271C2×D3—121no—
272C2×D3—121no—
273C2×D3—128no—
274C2×D3—128no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—122no—
284Dic3—42no—
285Dic3—62no—
286Dic3—61no—
287Dic3—61no—
288Dic3—61no—
289Dic3—61no—
290Dic3—62no—
291Dic3—121no—
292Dic3—121no—
293C32#180011yescharacteristic, complemented, Sylow
294C23—62no—
295C23—94no—
296C23—91no—
297C23—182no—
298C23—362no—
299C23—362no—
300D4—62no—
301D4—62no—
302D4—182no—
303D4—182no—
304C2×C4—62no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—91no—
311C2×C4—91no—
312C2×C4—124no—
313C2×C4—182no—
314C2×C4—361no—
315C2×C4—364no—
316C2×C4—362no—
317C2×C4D32⋊C411yescharacteristic
318C2×C4D32⋊C411yescharacteristic
319C2×C4C2×GO+(4,𝔽2)11yescharacteristic
320C8—122no—
321C8—362no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—124no—
329D3—44no—
330D3—62no—
331D3—62no—
332D3—121no—
333D3—121no—
334C22—64no—
335C22—91no—
336C22—91no—
337C22—122no—
338C22—122no—
339C22—181no—
340C22—181no—
341C22—364no—
342C22—364no—
343C22C2×D32⋊C411yescharacteristic
344C4—21no—
345C4—21no—
346C4—92no—
347C4—91no—
348C4—91no—
349C4—122no—
350C4—181no—
351C4D32⋊Q811yescharacteristic
352C4#6423011yescharacteristic
353C3—21no—
354C3—21no—
355C2—124no—
356C2—181no—
357C2—181no—
358C2#1059331111yescharacteristic
359C2#1059331211yescharacteristic
360C2#1059340311yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C22
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1800
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593729C2semidirect
4. #10590340C2semidirect
5. #10590052C2semidirect
156. C3⋊Dic3#100semidirect
293. C32#1800semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105937292
C2×#637272
#105903402
#105900522
#18009