Finite Group Databasebeta

← #11796960

Subgroups — #11796960

Order 1152.

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

normal subgroups only

This group has 406 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
1C2×#63809C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic, complemented
3#10590913C211yesmaximal, characteristic, complemented
4#10590066C212yesmaximal, complemented
5#10590065C212yesmaximal, complemented
6C2×#3796—21no—
7C2×C8×C3⋊D3C2211yescharacteristic
8C2×C3×#204—21no—
9C2×#3718C2211yescharacteristic
10C2×#3713C2211yescharacteristic
11#63818—21no—
12#63809—21no—
13#63809—21no—
14#63809C412yes—
15#63809C412yes—
16#63773C2212yes—
17#63765—21no—
18#63764—21no—
19C3×#819—21no—
20#63578C2212yes—
21C2×#916—61no—
22D3×#108—61no—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C3×D12—21no—
25C2×C3×Dic6—21no—
26C2×#626—41no—
27C2×D3×Dic3—41no—
28#3796—22no—
29#3796—22no—
30#3796—41no—
31#3796—41no—
32C2×C32×C8D411yescharacteristic
33C2×C3⋊(C3⋊C8)C2311yescharacteristic
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3C2×C411yescharacteristic
36C8×C3⋊D3D411yescharacteristic
37C8×C3⋊D3D411yescharacteristic
38C3×#208—22no—
39C3×#204—22no—
40C3×#204—22no—
41#3718—21no—
42#3718C2×C412yes—
43#3713—21no—
44#3713C2×C412yes—
45#3712—41no—
46#3710—41no—
47#3708—22no—
48#2148—91nomaximal, Sylow
49C2×#239—61no—
50C2×#237—61no—
51C2×C3×SD16—61no—
52C2×#216—61no—
53C2×#213—61no—
54#916—62no—
55#916—62no—
56#916—62no—
57#916—62no—
58D3×M16—62no—
59C2×#204—21no—
60C2×D3×C8—61no—
61C2×D3×C8—61no—
62C3×#108—61no—
63#822—62no—
64#819—21no—
65C22×C3⋊D3SD1611yescharacteristic
66C22×C3×D3—41no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3SD1611yescharacteristic
69C4×C3⋊D3C22⋊C411yescharacteristic
70C4×C3⋊D3C22⋊C411yescharacteristic
71C4×C3⋊D3D811yescharacteristic
72C4×C3⋊D3D811yescharacteristic
73C2×C3×Dic3—41no—
74C3×D12—22no—
75C3×D12—41no—
76C3×Dic6—22no—
77C3×Dic6—41no—
78#626—42no—
79#626—42no—
80D3×Dic3—42no—
81D3×Dic3—42no—
82C32×C8C22⋊C411yescharacteristic
83C32×C8C22⋊C411yescharacteristic
84C3⋊(C3⋊C8)C22×C411yescharacteristic
85C3⋊(C3⋊C8)C2×D411yescharacteristic
86C3×C3⋊C8—42no—
87C2×#135—91no—
88C2×M32—91no—
89C2×#108—91no—
90#362—92no—
91#361—92no—
92C2×C3×Q8—61no—
93C2×C3×D4—61no—
94C2×#67—121no—
95C22×Dic3—121no—
96#239—62no—
97#239—62no—
98#239—121no—
99#239—121no—
100#237—62no—
101#237—62no—
102#237—121no—
103#237—121no—
104C2×D12—21no—
105C2×D12—121no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—121no—
109C2×Dic6—21no—
110C3×SD16—62no—
111C3×SD16—62no—
112C3×M16—62no—
113C2×C3×C8—21no—
114C2×C3×C8—21no—
115#216—62no—
116#216—62no—
117#213—62no—
118#213—62no—
119#208—22no—
120C2×C3⋊C8—61no—
121C2×C3⋊C8—61no—
122#204—22no—
123#204—22no—
124ΓL(1,𝔽25)—122no—
125D3×C8—61no—
126D3×C8—61no—
127D3×C8—61no—
128D3×C8—61no—
129D3×C8—61no—
130D3×C8—61no—
131D3×C8—61no—
132D3×C8—61no—
133D3×C8—122no—
134C22×C32C2×SD1611yescharacteristic
135C2×C3⋊D3—41no—
136C2×C3⋊D3#10211yescharacteristic
137C2×C3⋊D3#10211yescharacteristic
138C2×C3×D3—42no—
139C2×C3×D3—82no—
140C32×C4C2×C22⋊C411yescharacteristic
141C32×C4C2×D811yescharacteristic
142C3⋊Dic3#10211yescharacteristic
143C3⋊Dic3#10211yescharacteristic
144C3×Dic3—42no—
145C2×#41—181no—
146#135—92no—
147#135—92no—
148#135—181no—
149#135—181no—
150C2×Q16—91no—
151C2×SD16—61no—
152C2×D8—91no—
153C2×M16—181no—
154C22×C8—91no—
155M32—92no—
156M32—181no—
157C2×C16—181no—
158#108—61no—
159#108—92no—
160C23×C3—121no—
161C22×D3—41no—
162C22×D3—61no—
163C22×D3—61no—
164C3×Q8—62no—
165C3×Q8—121no—
166C3×D4—62no—
167C3×D4—121no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—121no—
171#67—122no—
172#67—122no—
173C2×Dic3—41no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—122no—
177C2×Dic3—122no—
178D12—22no—
179D12—41no—
180D12—122no—
181D12—122no—
182C4×D3—61no—
183C4×D3—61no—
184C4×D3—61no—
185C4×D3—61no—
186C4×D3—61no—
187C4×D3—61no—
188C4×D3—61no—
189C4×D3—61no—
190C4×D3—122no—
191C4×D3—122no—
192Dic6—22no—
193Dic6—41no—
194C3×C8—21no—
195C3×C8—21no—
196C3×C8—21no—
197C3×C8—21no—
198C3×C8—122no—
199C3⋊C8—42no—
200C3⋊C8—61no—
201C3⋊C8—61no—
202C3⋊C8—61no—
203C3⋊C8—61no—
204C2×C32—21no—
205C2×C32C2×#10211yescharacteristic
206C3⋊D3—21no—
207C3⋊D3—21no—
208C3×D3—82no—
209#41—182no—
210#41—182no—
211#41—361no—
212#41—361no—
213C2×Q8—61no—
214C2×D4—61no—
215C2×D4—361no—
216C22×C4—91no—
217C22×C4—361no—
218Q16—92no—
219Q16—181no—
220SD16—62no—
221SD16—62no—
222D8—92no—
223D8—181no—
224M16—62no—
225M16—361no—
226C2×C8—91no—
227C2×C8—91no—
228C2×C8—91no—
229C2×C8—91no—
230C2×C8—91no—
231C2×C8—361no—
232C2×C8GO+(4,𝔽2)11yescharacteristic
233C16—182no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—122no—
237C22×C3—242no—
238C2×D3—42no—
239C2×D3—61no—
240C2×D3—61no—
241C2×D3—61no—
242C2×D3—61no—
243C2×D3—82no—
244C2×D3—122no—
245C2×D3—122no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—122no—
251Dic3—42no—
252Dic3—61no—
253Dic3—61no—
254Dic3—61no—
255Dic3—61no—
256C32#214811yescharacteristic, complemented, Sylow
257C23—91no—
258C23—121no—
259Q8—62no—
260Q8—121no—
261D4—62no—
262D4—121no—
263D4—362no—
264D4—362no—
265C2×C4—91no—
266C2×C4—91no—
267C2×C4—91no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—121no—
271C2×C4—362no—
272C2×C4—362no—
273C2×C4C2×GO+(4,𝔽2)11yescharacteristic
274C8—91no—
275C8—91no—
276C8—122no—
277C8D32⋊C411yescharacteristic
278C8D32⋊C411yescharacteristic
279C2×C3—22no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—41no—
283C2×C3—242no—
284D3—62no—
285D3—82no—
286D3—121no—
287D3—121no—
288D3—121no—
289C22—91no—
290C22—91no—
291C22—122no—
292C22—242no—
293C22—361no—
294C22#6422711yescharacteristic
295C4—91no—
296C4—91no—
297C4—122no—
298C4#6422511yescharacteristic
299C4C2×D32⋊C411yescharacteristic
300C3—21no—
301C3—21no—
302C2—21no—
303C2—181no—
304C2—181no—
305C2—242no—
306C2#1059336511yescharacteristic
subgroupG/H
centerC2#10593365
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radicalC2×#63809C2
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2148
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593762C2semidirect
3. #10590913C2semidirect
4. #10590066C2semidirect
5. #10590065C2semidirect
256. C32#2148semidirect

Maximal subgroups

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

subgroupindex
C2×#638092
#105937622
#105909132
#105900662
#105900652
#21489