Finite Group Databasebeta

← #11774482

Subgroups — #11774482

Order 1152.

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

normal subgroups only

This group has 422 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#10594963C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic, complemented
3#10591060C211yesmaximal, characteristic, complemented
4#10590031C212yesmaximal, complemented
5#10590030C212yesmaximal, complemented
6C22×#622—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#929—21no—
9C2×C3×#208—21no—
10#63982C411yescharacteristic
11#63980C411yescharacteristic
12#67⋊Dic3—21no—
13#63915C411yescharacteristic
14#63902C2211yescharacteristic
15#63878—21no—
16#63870C411yescharacteristic
17#63862—21no—
18#63838C2211yescharacteristic
19#63779—21no—
20#63779C2212yes—
21#63555—21no—
22#63553C2212yes—
23#5649—61no—
24Dic3×M16—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C3×#67—21no—
29C2×#627C2×C411yescharacteristic
30C2×#625C2×C411yescharacteristic
31C2×D3×Dic3—21no—
32C2×#622—22no—
33C2×#622—42no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C3×#217—21no—
39C3×(C2×D3)⋊C4—21no—
40C3×(C2×D3)⋊C4—21no—
41C3×Dic3⋊C4—21no—
42C3×Dic3⋊C4—21no—
43C3×#208—24no—
44C2×C3×C3⋊C8—22no—
45#3724C2×C411yescharacteristic
46#3724C2×C411yescharacteristic
47Dic3⋊Dic3—21no—
48Dic3⋊Dic3—21no—
49(C2×D3)⋊Dic3—21no—
50(C2×D3)⋊Dic3—21no—
51Dic32—21no—
52#1483—91nomaximal, Sylow
53C2×C3×M16—61no—
54C3×#123—61no—
55#939—61no—
56D4×Dic3—61no—
57#929—21no—
58C2×C4×Dic3—61no—
59C2×C4×Dic3—61no—
60C2×#208—21no—
61#898—61no—
62#892—61no—
63#889—61no—
64#887—61no—
65#885—61no—
66#67⋊C4—61no—
67#67⋊C4—61no—
68#879—61no—
69#878—61no—
70#877—61no—
71#815—62no—
72C8×Dic3—62no—
73C23×C32C22⋊C411yescharacteristic
74C22×C3×D3—21no—
75C2×C32×C4—22no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22×C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C3×#67—42no—
86C2×C3×Dic3—21no—
87C2×C3×Dic3—21no—
88C2×C3×Dic3—21no—
89#627—22no—
90#625—22no—
91D3×Dic3—41no—
92D3×Dic3—41no—
93#622—42no—
94C3×C3⋊C8—24no—
95#529—91no—
96C2×C4⋊C8—91no—
97C4×M16—91no—
98Q8⋊C8—92no—
99D4⋊C8—92no—
100C2×C3×D4—61no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C2×#67—21no—
104C2×#67—61no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C2×C4×D3—61no—
111C2×Dic6—61no—
112C3×M16—64no—
113C2×C3×C8—62no—
114C3×C4⋊C4—61no—
115C3×C4⋊C4—61no—
116C3×C22⋊C4—61no—
117C3×C22⋊C4—61no—
118C3×C22⋊C4—61no—
119#217—21no—
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—
126C4⋊Dic3—61no—
127C4⋊Dic3—61no—
128Dic3⋊C4—21no—
129Dic3⋊C4—21no—
130Dic3⋊C4—61no—
131Dic3⋊C4—61no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144#208—24no—
145C2×C3⋊C8—22no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32#10412yes—
149C22×C32C2×C22⋊C411yescharacteristic
150C2×C3×D3—41no—
151C2×C3×D3—41no—
152C2×C3×D3—41no—
153C32×C4—21no—
154C32×C4—21no—
155C3⋊Dic3—21no—
156C3⋊Dic3—21no—
157C3⋊Dic3#13112yes—
158C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
159C3⋊Dic3#13711yescharacteristic
160C3×Dic3—41no—
161C3×Dic3—41no—
162C3×Dic3—41no—
163C2×M16—61no—
164C22×C8—181no—
165#126—181no—
166#125—91no—
167#124—91no—
168#123—61no—
169C22⋊Q8—91no—
170#121—91no—
171C4×Q8—91no—
172C4×D4—91no—
173C4×D4—181no—
174#117—181no—
175C2×C42—91no—
176C4⋊C8—92no—
177C4⋊C8—181no—
178#97—181no—
179C4×C8—92no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—61no—
183C22×D3—21no—
184C3×D4—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—61no—
193C2×C3×C4—61no—
194C2×C3×C4—61no—
195#67—42no—
196#67—122no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—121no—
209C2×Dic3—121no—
210C2×Dic3—122no—
211C2×Dic3—121no—
212C2×Dic3—122no—
213C2×Dic3—121no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216C4×D3—121no—
217C4×D3—121no—
218Dic6—122no—
219C3×C8—64no—
220C3⋊C8—24no—
221C2×C32—22no—
222C2×C32#40811yescharacteristic
223C2×C32#41711yescharacteristic
224C2×C32C2×#10411yescharacteristic
225C3×D3—81no—
226C2×Q8—91no—
227C2×D4—61no—
228C2×D4—91no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—181no—
232C22×C4GO+(4,𝔽2)11yescharacteristic
233M16—64no—
234C2×C8—62no—
235C2×C8—182no—
236C2×C8—362no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—91no—
240C4⋊C4—91no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—181no—
247C22⋊C4—181no—
248C42—91no—
249C42—91no—
250C42—91no—
251C42—91no—
252C42—181no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—22no—
256C22×C3—22no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—121no—
262C22×C3—121no—
263C22×C3—121no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—22no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—121no—
273C3×C4—121no—
274C3×C4—121no—
275Dic3—41no—
276Dic3—41no—
277Dic3—41no—
278Dic3—62no—
279Dic3—61no—
280Dic3—61no—
281Dic3—62no—
282Dic3—61no—
283Dic3—61no—
284Dic3—121no—
285Dic3—121no—
286Dic3—121no—
287Dic3—121no—
288C32#148311yescharacteristic, complemented, Sylow
289C23—61no—
290C23D32⋊C411yescharacteristic
291Q8—182no—
292D4—122no—
293D4—182no—
294C2×C4—22no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—181no—
303C2×C4—182no—
304C2×C4—181no—
305C2×C4—361no—
306C2×C4—361no—
307C2×C4D32⋊C411yescharacteristic
308C2×C4C2×GO+(4,𝔽2)11yescharacteristic
309C8—64no—
310C8—362no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—42no—
318C2×C3—42no—
319C2×C3—241no—
320D3—81no—
321C22—21no—
322C22—21no—
323C22—121no—
324C22—121no—
325C22—121no—
326C22#6374112yes—
327C22C2×D32⋊C411yescharacteristic
328C4—21no—
329C4—21no—
330C4—92no—
331C4—91no—
332C4—91no—
333C4—121no—
334C4—121no—
335C4—121no—
336C4—181no—
337C4—181no—
338C3—21no—
339C3—21no—
340C2—22no—
341C2—241no—
342C2#1059330911yescharacteristic
343C2#1059331911yescharacteristic
344C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#63980C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1483
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
2. C2×#63779C2semidirect
3. #10591060C2semidirect
4. #10590031C2semidirect
5. #10590030C2semidirect
288. C32#1483semidirect

Maximal subgroups

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

subgroupindex
#105949632
C2×#637792
#105910602
#105900312
#105900302
#14839