Finite Group Databasebeta

← #11774481

Subgroups — #11774481

Order 1152.

420 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 59 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#10593980C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic, complemented
3#10590331C211yesmaximal, characteristic, complemented
4#10590032C212yesmaximal, complemented
5#10590029C212yesmaximal, complemented
6C2×#3788—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×#872—21no—
9C4×#627C2211yescharacteristic
10#63915C411yescharacteristic
11#63912C411yescharacteristic
12C4×#626—21no—
13C4×#625C2211yescharacteristic
14#63870C411yescharacteristic
15#63865C411yescharacteristic
16#63862—21no—
17#63853—21no—
18C2×#3710—21no—
19#63777—21no—
20C4×#622C2212yes—
21C3×C4⋊(C3⋊C8)—21no—
22#63572C2212yes—
23#5528—61no—
24D3×C4⋊C8—61no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C3×C4×D3—21no—
29C2×#627C2×C411yescharacteristic
30C2×#626—21no—
31C2×#625C2×C411yescharacteristic
32C2×#622—22no—
33#3788—24no—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C3×(C2×D3)⋊C4—21no—
39C3×(C2×D3)⋊C4—21no—
40C3×Dic3⋊C4—21no—
41C3×Dic3⋊C4—21no—
42C3×C4×Dic3—21no—
43C2×C3×C3⋊C8—22no—
44#3724C2×C411yescharacteristic
45#3724C2×C411yescharacteristic
46Dic3⋊Dic3—21no—
47Dic3⋊Dic3—21no—
48#3722—21no—
49(C2×D3)⋊Dic3—21no—
50(C2×D3)⋊Dic3—21no—
51#3710—42no—
52#1483—91nomaximal, Sylow
53C3×#117—61no—
54C4×#67—61no—
55C4×#67—61no—
56C2×D3×C8—62no—
57#898—61no—
58#896—61no—
59#894—61no—
60#889—61no—
61#885—61no—
62#884—61no—
63#883—61no—
64#879—61no—
65C4×D12—61no—
66#872—21no—
67C42×D3—61no—
68C42×D3—61no—
69C4×Dic6—61no—
70C3×C4⋊C8—61no—
71Dic3⋊C8—62no—
72C4⋊(C3⋊C8)—21no—
73C22×C3⋊D3C22⋊C411yescharacteristic
74C22×C3×D3—21no—
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—21no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3—22no—
84C4×C3⋊D3—22no—
85C2×C3×Dic3—21no—
86C2×C3×Dic3—21no—
87C2×C3×Dic3—21no—
88C3×C4×D3—41no—
89C3×C4×D3—41no—
90#627—22no—
91#626—42no—
92#625—22no—
93#622—24no—
94C3×C3⋊C8—42no—
95#529—91no—
96C2×C4⋊C8—91no—
97C4×M16—91no—
98Q8⋊C8—92no—
99D4⋊C8—92no—
100C22×C3×C4—61no—
101C2×#67—61no—
102C2×#67—61no—
103C2×D12—61no—
104C2×C4×D3—21no—
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×Dic6—61no—
112C2×C3×C8—62no—
113C3×C4⋊C4—61no—
114C3×C4⋊C4—61no—
115C3×C22⋊C4—61no—
116C3×C22⋊C4—61no—
117C3×C42—21no—
118C3×C42—21no—
119C3×C42—61no—
120#217—61no—
121#217—61no—
122(C2×D3)⋊C4—21no—
123(C2×D3)⋊C4—21no—
124(C2×D3)⋊C4—61no—
125(C2×D3)⋊C4—61no—
126(C2×D3)⋊C4—61no—
127(C2×D3)⋊C4—61no—
128C4⋊Dic3—61no—
129C4⋊Dic3—61no—
130Dic3⋊C4—21no—
131Dic3⋊C4—21no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136C4×Dic3—21no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C2×C3⋊C8—22no—
144D3×C8—124no—
145C22×C32C2×C22⋊C411yescharacteristic
146C2×C3⋊D3—21no—
147C2×C3⋊D3—21no—
148C2×C3⋊D3#10412yes—
149C2×C3×D3—41no—
150C2×C3×D3—41no—
151C2×C3×D3—41no—
152C32×C4—21no—
153C32×C4—21no—
154C32×C4AGL(1,ℤ/8)11yescharacteristic
155C32×C4#13711yescharacteristic
156C3⋊Dic3—21no—
157C3⋊Dic3—21no—
158C3⋊Dic3#13112yes—
159C3×Dic3—41no—
160C3×Dic3—41no—
161C3×Dic3—41no—
162C2×M16—181no—
163C22×C8—181no—
164#126—181no—
165#125—91no—
166#124—91no—
167#123—181no—
168C22⋊Q8—91no—
169#121—91no—
170C4×Q8—91no—
171C4×D4—91no—
172C4×D4—181no—
173#117—61no—
174C2×C42—91no—
175C4⋊C8—61no—
176C4⋊C8—92no—
177#97—181no—
178C4×C8—92no—
179C23×C3—61no—
180C22×D3—21no—
181C22×D3—61no—
182C22×D3—61no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—61no—
190C2×C3×C4—61no—
191C2×C3×C4—61no—
192C2×C3×C4—121no—
193C2×C3×C4—121no—
194#67—122no—
195#67—122no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205D12—122no—
206C4×D3—41no—
207C4×D3—41no—
208C4×D3—62no—
209C4×D3—64no—
210C4×D3—62no—
211C4×D3—122no—
212C4×D3—121no—
213C4×D3—121no—
214C4×D3—122no—
215C4×D3—122no—
216Dic6—122no—
217C3×C8—122no—
218C3⋊C8—42no—
219C2×C32#40811yescharacteristic
220C2×C32#41711yescharacteristic
221C2×C32C2×#10411yescharacteristic
222C3⋊D3—22no—
223C3×D3—81no—
224C2×Q8—91no—
225C2×D4—91no—
226C2×D4—181no—
227C22×C4—61no—
228C22×C4—91no—
229C22×C4—91no—
230C22×C4—91no—
231M16—184no—
232C2×C8—62no—
233C2×C8—182no—
234C2×C8—362no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—91no—
238C4⋊C4—91no—
239C4⋊C4—181no—
240C4⋊C4—181no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C22⋊C4—181no—
244C22⋊C4—181no—
245C22⋊C4—181no—
246C42—61no—
247C42—91no—
248C42—91no—
249C42—91no—
250C42GO+(4,𝔽2)11yescharacteristic
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—121no—
254C22×C3—121no—
255C22×C3—121no—
256C2×D3—41no—
257C2×D3—41no—
258C2×D3—41no—
259C2×D3—62no—
260C2×D3—62no—
261C2×D3—62no—
262C2×D3—62no—
263C2×D3—121no—
264C2×D3—121no—
265C3×C4—22no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4—121no—
274C3×C4—121no—
275C3×C4—121no—
276Dic3—41no—
277Dic3—41no—
278Dic3—41no—
279Dic3—62no—
280Dic3—62no—
281Dic3—62no—
282Dic3—121no—
283Dic3—121no—
284Dic3—121no—
285C32#148311yescharacteristic, complemented, Sylow
286C23—61no—
287C23—91no—
288Q8—182no—
289D4—182no—
290D4—362no—
291C2×C4—61no—
292C2×C4—61no—
293C2×C4—61no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—121no—
298C2×C4—121no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—181no—
302C2×C4—181no—
303C2×C4D32⋊C411yescharacteristic
304C2×C4D32⋊C411yescharacteristic
305C2×C4C2×GO+(4,𝔽2)11yescharacteristic
306C8—122no—
307C8—184no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—241no—
315D3—64no—
316D3—81no—
317D3—122no—
318C22—92no—
319C22—121no—
320C22—121no—
321C22—121no—
322C22—181no—
323C22—181no—
324C22C2×D32⋊C411yescharacteristic
325C4—21no—
326C4—21no—
327C4—92no—
328C4—121no—
329C4—121no—
330C4—121no—
331C4—181no—
332C4—181no—
333C4#6422411yescharacteristic
334C4#6422611yescharacteristic
335C3—21no—
336C3—21no—
337C2—182no—
338C2—241no—
339C2#1059330811yescharacteristic
340C2#1059332511yescharacteristic
341C2#1059336011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#63912C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1483
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#3788C2semidirect
3. #10590331C2semidirect
4. #10590032C2semidirect
5. #10590029C2semidirect
285. C32#1483semidirect

Maximal subgroups

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

subgroupindex
#105939802
C4×#37882
#105903312
#105900322
#105900292
#14839