Finite Group Databasebeta

← #11774819

Subgroups — #11774819

Order 1152.

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

normal subgroups only

This group has 428 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
2#10593804C211yesmaximal, characteristic, complemented
3C2×#63553C211yesmaximal, characteristic, complemented
4#10590031C212yesmaximal, complemented
5#10590030C212yesmaximal, complemented
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#929—21no—
8C22×C3×C3⋊C8—21no—
9#63982C411yescharacteristic
10#63980C411yescharacteristic
11#67⋊Dic3—21no—
12#63915C411yescharacteristic
13#63902C2211yescharacteristic
14#63878—21no—
15#63870C411yescharacteristic
16#63862—21no—
17#63838C2211yescharacteristic
18C22⋊#622—21no—
19#63779C2212yes—
20#63777—21no—
21#63553—21no—
22#63553C2212yes—
23#5649—61no—
24C2×C8×Dic3—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—
33C4×C3⋊Dic3C2×C411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×#217—21no—
38C3×(C2×D3)⋊C4—21no—
39C3×(C2×D3)⋊C4—21no—
40C3×Dic3⋊C4—21no—
41C3×Dic3⋊C4—21no—
42C2×C3×C3⋊C8—24no—
43C2×C3×C3⋊C8—22no—
44#3724C2×C411yescharacteristic
45#3724C2×C411yescharacteristic
46Dic3⋊Dic3—21no—
47Dic3⋊Dic3—21no—
48(C2×D3)⋊Dic3—21no—
49(C2×D3)⋊Dic3—21no—
50Dic32—21no—
51#1494—91nomaximal, Sylow
52C22×C3×C8—61no—
53C3×#123—61no—
54#939—61no—
55D4×Dic3—61no—
56#929—21no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—61no—
59C22×C3⋊C8—21no—
60#898—61no—
61#892—61no—
62#889—61no—
63#887—61no—
64#885—61no—
65#67⋊C4—61no—
66#67⋊C4—61no—
67#879—61no—
68#878—61no—
69#877—61no—
70C8×Dic3—62no—
71C8×Dic3—62no—
72C23×C32C22⋊C411yescharacteristic
73C22×C3×D3—21no—
74C2×C32×C4—22no—
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22×C411yescharacteristic
82C2×C3⋊Dic3C2×D411yescharacteristic
83C3×#67—42no—
84C2×C3×Dic3—21no—
85C2×C3×Dic3—21no—
86C2×C3×Dic3—21no—
87#627—22no—
88#625—22no—
89D3×Dic3—42no—
90#622—42no—
91C3×C3⋊C8—24no—
92#529—91no—
93#432—91no—
94C2×C4×C8—91no—
95Q8⋊C8—92no—
96D4⋊C8—92no—
97C2×C3×D4—61no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C2×#67—21no—
101C2×#67—61no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C2×C4×D3—61no—
108C2×Dic6—61no—
109C2×C3×C8—62no—
110C2×C3×C8—64no—
111C3×C4⋊C4—61no—
112C3×C4⋊C4—61no—
113C3×C22⋊C4—61no—
114C3×C22⋊C4—61no—
115C3×C22⋊C4—61no—
116#217—21no—
117#217—61no—
118#217—61no—
119(C2×D3)⋊C4—21no—
120(C2×D3)⋊C4—21no—
121(C2×D3)⋊C4—61no—
122(C2×D3)⋊C4—61no—
123C4⋊Dic3—61no—
124C4⋊Dic3—61no—
125Dic3⋊C4—21no—
126Dic3⋊C4—21no—
127Dic3⋊C4—61no—
128Dic3⋊C4—61no—
129Dic3⋊C4—61no—
130Dic3⋊C4—61no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C2×C3⋊C8—22no—
142C2×C3⋊C8—24no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32#10412yes—
146C22×C32C2×C22⋊C411yescharacteristic
147C2×C3×D3—41no—
148C2×C3×D3—41no—
149C2×C3×D3—41no—
150C32×C4—21no—
151C32×C4—21no—
152C3⋊Dic3—21no—
153C3⋊Dic3—21no—
154C3⋊Dic3#13112yes—
155C3⋊Dic3#13512yes—
156C3×Dic3—41no—
157C3×Dic3—41no—
158C3×Dic3—41no—
159C22×C8—61no—
160#126—181no—
161#125—91no—
162#124—91no—
163#123—61no—
164C22⋊Q8—91no—
165#121—91no—
166C4×Q8—91no—
167C4×D4—91no—
168C4×D4—181no—
169#117—181no—
170C2×C42—91no—
171C4⋊C8—92no—
172C22⋊C8—181no—
173#97—181no—
174C4×C8—92no—
175C4×C8—181no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—61no—
179C22×D3—21no—
180C3×D4—122no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—42no—
188C2×C3×C4—61no—
189C2×C3×C4—61no—
190C2×C3×C4—61no—
191#67—42no—
192#67—122no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—122no—
207C2×Dic3—122no—
208C2×Dic3—122no—
209C4×D3—122no—
210Dic6—122no—
211C3×C8—64no—
212C3⋊C8—24no—
213C2×C32—22no—
214C2×C32#40811yescharacteristic
215C2×C32#41611yescharacteristic
216C2×C32C2×#10411yescharacteristic
217C3×D3—81no—
218C2×Q8—91no—
219C2×D4—61no—
220C2×D4—91no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—181no—
224C22×C4GO+(4,𝔽2)11yescharacteristic
225C2×C8—64no—
226C2×C8—62no—
227C2×C8—182no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4—91no—
231C4⋊C4—91no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C22⋊C4—61no—
235C22⋊C4—61no—
236C22⋊C4—61no—
237C22⋊C4—181no—
238C22⋊C4—181no—
239C42—91no—
240C42—91no—
241C42—91no—
242C42—91no—
243C42—181no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3—121no—
253C22×C3—121no—
254C22×C3—121no—
255C2×D3—41no—
256C2×D3—41no—
257C2×D3—41no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—22no—
261C3×C4—41no—
262C3×C4—41no—
263C3×C4—121no—
264C3×C4—121no—
265C3×C4—121no—
266Dic3—41no—
267Dic3—41no—
268Dic3—41no—
269Dic3—62no—
270Dic3—62no—
271Dic3—62no—
272Dic3—62no—
273Dic3—62no—
274Dic3—62no—
275Dic3—121no—
276Dic3—121no—
277C32#149411yescharacteristic, complemented, Sylow
278C23—61no—
279C23D32⋊C411yescharacteristic
280Q8—182no—
281D4—122no—
282D4—182no—
283C2×C4—22no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—91no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—91no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—362no—
294C2×C4D32⋊C411yescharacteristic
295C2×C4C2×GO+(4,𝔽2)11yescharacteristic
296C8—64no—
297C8—362no—
298C2×C3—24no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—42no—
306C2×C3—241no—
307D3—81no—
308C22—21no—
309C22—21no—
310C22—121no—
311C22—121no—
312C22—121no—
313C22#6374112yes—
314C22C2×D32⋊C411yescharacteristic
315C4—21no—
316C4—21no—
317C4—92no—
318C4—92no—
319C4—121no—
320C4—121no—
321C4—121no—
322C4—181no—
323C4—181no—
324C3—21no—
325C3—21no—
326C2—22no—
327C2—241no—
328C2#1059330811yescharacteristic
329C2#1059331711yescharacteristic
330C2C2×#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#1494
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. #10593804C2semidirect
3. C2×#63553C2semidirect
4. #10590031C2semidirect
5. #10590030C2semidirect
277. C32#1494semidirect

Maximal subgroups

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

subgroupindex
#105949632
#105938042
C2×#635532
#105900312
#105900302
#14949