Finite Group Databasebeta

← #11798986

Subgroups — #11798986

Order 1152.

407 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 407 conjugacy classes of subgroups — too many to draw. Only its 80 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
1D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#827C211yesmaximal, characteristic, complemented
3C2×C3×#826C211yesmaximal, characteristic
4#10590869C211yesmaximal, characteristic, complemented
5#10589133C211yesmaximal, characteristic, complemented
6#10589118C211yesmaximal, characteristic, complemented
7#10589115C211yesmaximal, characteristic, complemented
8#71477—31nomaximal
9#71463—31nomaximal
10C2×C32×D8C2211yescharacteristic
11D4×C3⋊Dic3—21no—
12C2×C3×Dic12C2211yescharacteristic
13C2×C3×D24C2211yescharacteristic
14#63863—21no—
15C2×#3715—21no—
16#63659—21no—
17#63645C2211yescharacteristic
18C8×C3⋊Dic3C2211yescharacteristic
19C3×#827—22no—
20C3×#826—22no—
21C2×C3×C3⋊C16C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23C2×C3×SD32—31no—
24C2×C3×D16—31no—
25#5191—31no—
26#5155—31no—
27Dic3×D8—31no—
28Dic3×D8—31no—
29Dic3×D8—61no—
30C2×#827D311yescharacteristic, complemented
31C2×#826D311yescharacteristic
32#4564—31no—
33#4562—31no—
34#4509—31no—
35#4503—31no—
36Dic3⋊C16—31no—
37Dic3⋊C16—31no—
38C2×C32×D4—21no—
39C22×C3⋊Dic3—41no—
40C2×C3×D12—21no—
41C2×C3×Dic6—21no—
42C32×D8—21no—
43C32×D8D412yes—
44C2×C32×C8C2311yescharacteristic
45#3757—41no—
46C4⋊(C3⋊Dic3)—21no—
47C4×C3⋊Dic3D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C3×Dic12—21no—
50C3×Dic12—21no—
51C3×D24—21no—
52C3×D24—21no—
53(C2×D3)⋊Dic3—41no—
54(C2×D3)⋊Dic3—41no—
55#3715—42no—
56C3×C3⋊C16—21no—
57C3×C3⋊C16—21no—
58#2210—91noSylow
59C2×C3×Q16—31no—
60C2×C3×D8—21no—
61C2×C3×D8—31no—
62C2×C3×D8C2×D311yescharacteristic
63C2×C3×D8C2×D311yescharacteristic
64#947—61no—
65C2×#215—61no—
66#936—61no—
67D4×Dic3—61no—
68D4×Dic3—61no—
69D4×Dic3—62no—
70C2×#214—61no—
71C2×Dic12C2×D311yescharacteristic
72C2×D24C2×D311yescharacteristic
73C3×SD32—62no—
74C3×D16—62no—
75C2×C3×C16—31no—
76C2×C3×C16—31no—
77#832—61no—
78#832—61no—
79#832—62no—
80#827—22no—
81#826—22no—
82#818—31no—
83#818—31no—
84#818—61no—
85C8×Dic3—31no—
86C8×Dic3—31no—
87C8×Dic3—61no—
88C2×C3⋊C16C2×D311yescharacteristic
89C2×C3⋊C16C2×D311yescharacteristic
90C23×C32—41no—
91C22×C3×D3—41no—
92C32×D4—22no—
93C32×D4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—82no—
97C2×C3⋊Dic3D811yescharacteristic
98C2×C3⋊Dic3D811yescharacteristic
99C2×C3×Dic3—41no—
100C3×D12—41no—
101C3×D12—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C32×C8C2×D411yescharacteristic
105C32×C8#4111yescharacteristic
106C3⋊(C3⋊C8)—21no—
107C2×SD32—31no—
108C2×D16—31no—
109#495—91no—
110C4×D8—91no—
111C4⋊C16—91no—
112#358—91no—
113#357—91no—
114C2×C3×Q8—61no—
115C2×C3×D4—22no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—61no—
119C22×Dic3—121no—
120C22×Dic3—121no—
121C22×Dic3—122no—
122C2×D12—21no—
123C2×Dic6—21no—
124C3×Q16—61no—
125C3×Q16—61no—
126C3×D8—22no—
127C3×D8—21no—
128C3×D8—21no—
129C3×D8—22no—
130C3×D8—61no—
131C3×D8—61no—
132C3×D8#6712yes—
133C3×D8#6712yes—
134C2×C3×C8—21no—
135C2×C3×C8C22×D311yescharacteristic
136C2×C3×C8C22×D311yescharacteristic
137#217—121no—
138#217—121no—
139#217—121no—
140#217—121no—
141#217—122no—
142#215—122no—
143#214—122no—
144(C2×D3)⋊C4—121no—
145(C2×D3)⋊C4—121no—
146C4⋊Dic3—62no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4×Dic3—31no—
150C4×Dic3—31no—
151C4×Dic3—61no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—61no—
155Dic12—21no—
156Dic12—21no—
157D24—21no—
158D24—21no—
159C3×C16—61no—
160C3×C16—61no—
161C3⋊C16—21no—
162C3⋊C16—21no—
163C22×C32—42no—
164C22×C32—81no—
165C22×C32—81no—
166C22×C32C2×D811yescharacteristic
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C32×C4#12111yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C3⋊Dic3—21no—
173C3⋊Dic3—21no—
174C3⋊Dic3—81no—
175C3×Dic3—81no—
176C2×Q16—31no—
177C2×SD16—181no—
178C2×D8—31no—
179C2×D8D3211yescharacteristic
180#124—181no—
181C4×D4—181no—
182SD32—62no—
183D16—62no—
184C2×C16—31no—
185C2×C16—31no—
186#107—91no—
187#102—181no—
188C4×C8—91no—
189C23×C3—42no—
190C23×C3—41no—
191C23×C3—41no—
192C23×C3—121no—
193C22×D3—41no—
194C3×Q8—121no—
195C3×Q8—121no—
196C3×D4—24no—
197C3×D4—22no—
198C3×D4—22no—
199C3×D4—42no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—121no—
203C3×D4—121no—
204C2×C3×C4—21no—
205C2×C3×C4—121no—
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×Dic3—31no—
209C2×Dic3—31no—
210C2×Dic3—31no—
211C2×Dic3—31no—
212C2×Dic3—41no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—122no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218C2×Dic3—244no—
219C2×Dic3—242no—
220C2×Dic3—242no—
221D12—41no—
222D12—41no—
223Dic6—41no—
224Dic6—41no—
225C3×C8—21no—
226C3×C8—21no—
227C3×C8#23711yescharacteristic
228C3×C8#23711yescharacteristic
229C3×C8C2×#6711yescharacteristic
230C3×C8C2×#6711yescharacteristic
231C3⋊C8—61no—
232C3⋊C8—61no—
233C3⋊C8—121no—
234C2×C32—82no—
235C2×C32#45911yescharacteristic
236C2×C32#50811yescharacteristic
237C2×C32#50911yescharacteristic
238C3×D3—161no—
239C2×Q8—61no—
240C2×D4—21no—
241C2×D4—61no—
242C22×C4—361no—
243Q16—61no—
244Q16—61no—
245SD16—362no—
246D8—21no—
247D8—61no—
248D8—61no—
249D8#62512yes—
250C2×C8—91no—
251C2×C8C2×D3211yescharacteristic
252C4⋊C4—181no—
253C22⋊C4—361no—
254C22⋊C4—361no—
255C22⋊C4—361no—
256C42—91no—
257C16—61no—
258C16—61no—
259C22×C3—21no—
260C22×C3—44no—
261C22×C3—42no—
262C22×C3—42no—
263C22×C3—82no—
264C22×C3—82no—
265C22×C3—81no—
266C22×C3—81no—
267C22×C3—81no—
268C22×C3—81no—
269C22×C3—241no—
270C22×C3—241no—
271C22×C3—241no—
272C22×C3D3×D811yescharacteristic
273C22×C3D3×D811yescharacteristic
274C2×D3—81no—
275C2×D3—81no—
276C2×D3—81no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—241no—
280C3×C4#91111yescharacteristic
281C3×C4#91111yescharacteristic
282C3×C4#93911yescharacteristic
283C3×C4#93911yescharacteristic
284Dic3—62no—
285Dic3—61no—
286Dic3—61no—
287Dic3—61no—
288Dic3—61no—
289Dic3—81no—
290Dic3—121no—
291Dic3—242no—
292Dic3—241no—
293Dic3—241no—
294C32#221011yescharacteristic, complemented, Sylow
295C23—41no—
296C23—121no—
297Q8—121no—
298Q8—121no—
299D4—22no—
300D4—41no—
301D4—121no—
302D4—121no—
303C2×C4—91no—
304C2×C4—91no—
305C2×C4—121no—
306C2×C4—361no—
307C2×C4—722no—
308C2×C4#381111yescharacteristic
309C8—181no—
310C8#380511yescharacteristic
311C8C2×#62511yescharacteristic
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—84no—
316C2×C3—82no—
317C2×C3—82no—
318C2×C3—481no—
319C2×C3#491111yescharacteristic
320C2×C3#491211yescharacteristic
321C2×C3#491411yescharacteristic
322C2×C3#491611yescharacteristic
323C2×C3#515011yescharacteristic
324C2×C3#515011yescharacteristic
325D3—161no—
326C22—42no—
327C22—81no—
328C22—81no—
329C22—241no—
330C22—241no—
331C22—241no—
332C22#6392611yescharacteristic
333C4—181no—
334C4—181no—
335C4—241no—
336C4—721no—
337C4#6392711yescharacteristic
338C4#6398011yescharacteristic
339C3—21no—
340C3#7146311yescharacteristic, complemented
341C3#7147711yescharacteristic, complemented
342C2—82no—
343C2—481no—
344C2#1059103511yescharacteristic
345C2#1059103611yescharacteristic
346C2#1059148611yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC22×C32C2×D8
prime radicalC2×C3×#826C2
hypercenterC2×D8D32
hypocenterC32#2210
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. D8×C3⋊Dic3C2semidirect
2. C2×C3×#827C2semidirect
4. #10590869C2semidirect
5. #10589133C2semidirect
6. #10589118C2semidirect
7. #10589115C2semidirect
30. C2×#827D3semidirect
294. C32#2210semidirect
340. C3#71463semidirect
341. C3#71477semidirect

Maximal subgroups

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

subgroupindex
D8×C3⋊Dic32
C2×C3×#8272
C2×C3×#8262
#105908692
#105891332
#105891182
#105891152
#714773
#714633