Finite Group Databasebeta

← #11774751

Subgroups — #11774751

Order 1152.

494 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 69 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#10593972C211yesmaximal, characteristic
2C4×#3787C211yesmaximal, characteristic, complemented
3#10590340C211yesmaximal, characteristic, complemented
4#10590029C214yesmaximal, complemented
5C2×#3798—21no—
6C2×#3787—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×D12—21no—
9#63919C411yescharacteristic
10#63916—21no—
11#63915—21no—
12#63914C411yescharacteristic
13#63912C412yes—
14C4×#625C2212yes—
15C2×#3712—21no—
16C4×#622—21no—
17C4×#622C2212yes—
18C3×C4⋊(C3⋊C8)—21no—
19#63572C2212yes—
20#5548—61no—
21#4837—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×D12—21no—
26C2×C3×C4×D3—22no—
27C2×#627—21no—
28C2×#626—22no—
29C2×#625—21no—
30C2×#625C2×C412yes—
31#3798—42no—
32#3798—42no—
33C2×#622—22no—
34#3787—24no—
35C32×C42D411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C3×(C2×D3)⋊C4—22no—
40C3×C4⋊Dic3—21no—
41C2×C3×C3⋊C8—22no—
42#3724C2×C412yes—
43(C2×D3)⋊Dic3—22no—
44#3712—42no—
45#1492—91nomaximal, Sylow
46C2×#235—62no—
47C3×C4×D4—61no—
48#940—61no—
49#938—61no—
50C4×#67—62no—
51C2×ΓL(1,𝔽25)—62no—
52#895—61no—
53#888—61no—
54#885—62no—
55#884—62no—
56C4×D12—21no—
57C42×D3—61no—
58C42×D3—61no—
59C3×C4⋊C8—61no—
60Dic3⋊C8—62no—
61C4⋊(C3⋊C8)—21no—
62C22×C3⋊D3C22⋊C411yescharacteristic
63C22×C3×D3—22no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22×C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C4×C3⋊D3—22no—
71C4×C3⋊D3—22no—
72C4×C3⋊D3D812yes—
73C4×C3⋊D3SD1612yes—
74C2×C3×Dic3—22no—
75C3×D12—42no—
76C3×C4×D3—42no—
77C3×C4×D3—42no—
78#627—42no—
79#626—44no—
80#625—24no—
81#625—42no—
82#622—24no—
83C3×C3⋊C8—42no—
84#532—91no—
85#423—91no—
86C2×C4×C8—91no—
87D4⋊C8—94no—
88C2×C3×D4—61no—
89C22×C3×C4—62no—
90C2×#67—62no—
91C2×#67—62no—
92C2×#67—62no—
93#235—124no—
94#235—124no—
95C2×D12—21no—
96C2×D12—62no—
97C2×C4×D3—22no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×Dic6—62no—
105C2×C3×C8—62no—
106C3×C4⋊C4—61no—
107C3×C22⋊C4—62no—
108C3×C42—21no—
109C3×C42—21no—
110#217—62no—
111(C2×D3)⋊C4—22no—
112(C2×D3)⋊C4—62no—
113C4⋊Dic3—21no—
114Dic3⋊C4—62no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C2×C3⋊C8—22no—
122ΓL(1,𝔽25)—124no—
123C22×C32C2×C22⋊C411yescharacteristic
124C2×C3⋊D3—21no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3#10212yes—
127C2×C3×D3—42no—
128C2×C3×D3—42no—
129C2×C3×D3—42no—
130C32×C4—21no—
131C32×C4#10412yes—
132C32×C4C2×D811yescharacteristic
133C32×C4C2×SD1611yescharacteristic
134C3⋊Dic3—21no—
135C3⋊Dic3#10212yes—
136C3⋊Dic3#13112yes—
137C3×Dic3—42no—
138C2×#41—181no—
139C2×M16—181no—
140C22×C8—181no—
141C4⋊Q8—91no—
142#127—91no—
143#124—181no—
144#121—92no—
145#121—181no—
146C4×D4—61no—
147C4×D4—92no—
148C2×C42—91no—
149C4⋊C8—61no—
150C4⋊C8—92no—
151C4×C8—92no—
152C4×C8—181no—
153C23×C3—62no—
154C22×D3—22no—
155C22×D3—61no—
156C22×D3—61no—
157C3×D4—122no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—62no—
165C2×C3×C4—122no—
166C2×C3×C4—122no—
167#67—124no—
168#67—124no—
169#67—124no—
170C2×Dic3—22no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177D12—42no—
178D12—124no—
179C4×D3—42no—
180C4×D3—42no—
181C4×D3—62no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—122no—
186C4×D3—122no—
187C4×D3—122no—
188C4×D3—122no—
189Dic6—124no—
190C3×C8—122no—
191C3⋊C8—42no—
192C2×C32#40811yescharacteristic
193C2×C32C2×#10211yescharacteristic
194C2×C32C2×#10411yescharacteristic
195C3⋊D3—22no—
196C3×D3—82no—
197#41—362no—
198#41—362no—
199C2×Q8—181no—
200C2×D4—61no—
201C2×D4—92no—
202C2×D4—182no—
203C2×D4—181no—
204C22×C4—62no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208M16—362no—
209C2×C8—62no—
210C2×C8—182no—
211C2×C8—184no—
212C4⋊C4—61no—
213C4⋊C4—92no—
214C22⋊C4—62no—
215C22⋊C4—182no—
216C42—91no—
217C42—91no—
218C42—91no—
219C42GO+(4,𝔽2)11yescharacteristic
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—122no—
223C22×C3—122no—
224C22×C3—122no—
225C2×D3—42no—
226C2×D3—42no—
227C2×D3—42no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—121no—
231C2×D3—121no—
232C2×D3—121no—
233C2×D3—121no—
234C3×C4—21no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—41no—
241C3×C4—41no—
242C3×C4—122no—
243Dic3—42no—
244Dic3—62no—
245Dic3—62no—
246Dic3—62no—
247Dic3—62no—
248Dic3—121no—
249Dic3—121no—
250C32#149211yescharacteristic, complemented, Sylow
251C23—62no—
252C23—91no—
253Q8—362no—
254D4—122no—
255D4—184no—
256D4—362no—
257D4—364no—
258C2×C4—62no—
259C2×C4—91no—
260C2×C4—91no—
261C2×C4—92no—
262C2×C4—92no—
263C2×C4—91no—
264C2×C4—122no—
265C2×C4—122no—
266C2×C4—182no—
267C2×C4—182no—
268C2×C4D32⋊C411yescharacteristic
269C2×C4D32⋊C411yescharacteristic
270C2×C4C2×GO+(4,𝔽2)11yescharacteristic
271C8—122no—
272C8—184no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—242no—
280D3—82no—
281D3—122no—
282D3—122no—
283C22—92no—
284C22—122no—
285C22—122no—
286C22—122no—
287C22—181no—
288C22—181no—
289C22C2×D32⋊C411yescharacteristic
290C4—21no—
291C4—92no—
292C4—92no—
293C4—122no—
294C4—181no—
295C4#6373112yes—
296C4#6422511yescharacteristic
297C4#6422711yescharacteristic
298C3—21no—
299C3—21no—
300C2—182no—
301C2—242no—
302C2#1059330911yescharacteristic
303C2C2×#6373111yescharacteristic
304C2#1059336511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1492
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×#3787C2semidirect
3. #10590340C2semidirect
4. #10590029C2semidirect
250. C32#1492semidirect

Maximal subgroups

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

subgroupindex
#105939722
C4×#37872
#105903402
#105900292
#14929