Finite Group Databasebeta

← #11798911

Subgroups — #11798911

Order 1152.

393 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 393 conjugacy classes of subgroups — too many to draw. Only its 78 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#10592882C211yesmaximal, characteristic, complemented
2C2×C3×#828C211yesmaximal, characteristic
3#10590777C211yesmaximal, characteristic
4C2×#63548C211yesmaximal, characteristic
5C3×#4564C211yesmaximal, characteristic, complemented
6#10589133C211yesmaximal, characteristic, complemented
7#10589119C211yesmaximal, characteristic, complemented
8#71476—31nomaximal
9#69234—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11#64153—21no—
12C2×#3756—21no—
13C2×#3746C2211yescharacteristic
14C2×C3×D24C2211yescharacteristic
15#63898—21no—
16C8×C3⋊Dic3C2211yescharacteristic
17C3×#828—22no—
18C3×#818C2211yescharacteristic
19C2×C3×C3⋊C16C2211yescharacteristic
20C2×C3×C3⋊C16C2211yescharacteristic
21#63562—21no—
22#63548—22no—
23C2×C3×SD32—31no—
24#5183—31no—
25#5183—31no—
26#5183—61no—
27C2×#828D311yescharacteristic
28Dic3×D8—31no—
29C2×#827—31no—
30C2×#800—31no—
31#4872—31no—
32C3×#358—31no—
33#4564D311yescharacteristic, complemented
34#4503—31no—
35Dic3⋊C16—31no—
36Dic3⋊C16—31no—
37#4492—31no—
38C2×C32×Q8—21no—
39C2×#634—21no—
40C2×C3×D12—21no—
41C2×D3×Dic3—41no—
42C32×Q16—21no—
43C32×Q16—21no—
44C2×C32×C8C2311yescharacteristic
45#3756—42no—
46#3750—41no—
47#3750—41no—
48C4×C3⋊Dic3D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50#3746—21no—
51#3746—21no—
52C3×C4⋊Dic3—21no—
53C3×D24—21no—
54C3×D24D412yes—
55(C2×D3)⋊Dic3—41no—
56C3×C3⋊C16—21no—
57C3×C3⋊C16—21no—
58#2208—91noSylow
59C2×C3×Q16—21no—
60C2×C3×Q16C2×D311yescharacteristic
61C2×C3×Q16C2×D311yescharacteristic
62C2×C3×D8—31no—
63#944—61no—
64#944—61no—
65#944—62no—
66C2×#216—61no—
67C2×#216—61no—
68C2×#216—62no—
69D4×Dic3—61no—
70C2×Dic12—31no—
71C2×Dic12—31no—
72C2×Dic12—61no—
73C2×D24C2×D311yescharacteristic
74#893—61no—
75C3×SD32—62no—
76C2×C3×C16—31no—
77C2×C3×C16—31no—
78C3×#107—31no—
79#832—61no—
80#828—22no—
81#827—62no—
82#818C2×D311yescharacteristic
83C8×Dic3—31no—
84C8×Dic3—31no—
85C8×Dic3—61no—
86C2×C3⋊C16C2×D311yescharacteristic
87C2×C3⋊C16C2×D311yescharacteristic
88#809—61no—
89#800—62no—
90C22×C3×D3—41no—
91C32×Q8—41no—
92C32×Q8—41no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3D811yescharacteristic
97C2×C3⋊Dic3D811yescharacteristic
98#634—41no—
99#634—41no—
100C2×C3×Dic3—41no—
101C3×D12—22no—
102C3×D12—41no—
103D3×Dic3—82no—
104C32×C8C2×D411yescharacteristic
105C32×C8#4111yescharacteristic
106C3⋊(C3⋊C8)—21no—
107C2×SD32—31no—
108C2×SD32—91no—
109#494—91no—
110C4×D8—91no—
111C4⋊C16—91no—
112#358—31no—
113#358—91no—
114C2×C3×Q8—22no—
115C2×C3×Q8—21no—
116C2×C3×Q8—21no—
117C2×C3×D4—61no—
118C22×Dic3—121no—
119C2×D12—21no—
120C2×C4×D3—121no—
121C2×Dic6—62no—
122C2×Dic6—61no—
123C2×Dic6—61no—
124C3×Q16—21no—
125C3×Q16—21no—
126C3×Q16—21no—
127C3×Q16—21no—
128C3×Q16—41no—
129C3×Q16—41no—
130C3×D8—32no—
131C3×D8—61no—
132C2×C3×C8—21no—
133C2×C3×C8C22×D311yescharacteristic
134C2×C3×C8C22×D311yescharacteristic
135C3×C4⋊C4—61no—
136#217—121no—
137#216—124no—
138#216—122no—
139#216—122no—
140(C2×D3)⋊C4—121no—
141C4⋊Dic3—21no—
142Dic3⋊C4—121no—
143Dic3⋊C4—121no—
144Dic3⋊C4—121no—
145Dic3⋊C4—121no—
146Dic3⋊C4—122no—
147Dic3⋊C4—122no—
148C4×Dic3—31no—
149C4×Dic3—31no—
150C4×Dic3—61no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—61no—
154Dic12—61no—
155Dic12—61no—
156Dic12—61no—
157Dic12—61no—
158Dic12—121no—
159Dic12—121no—
160D24—21no—
161D24#6712yes—
162C3×C16—61no—
163C3×C16—61no—
164C3⋊C16—21no—
165C3⋊C16—21no—
166C22×C32C2×D811yescharacteristic
167C2×C3×D3—42no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C32×C4—81no—
171C32×C4#12111yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C3⋊Dic3—21no—
174C3⋊Dic3—81no—
175C3⋊Dic3SD3212yescomplemented
176C3×Dic3—81no—
177C2×Q16—91no—
178C2×Q16—181no—
179C2×Q16D3211yescharacteristic
180C2×D8—31no—
181C4⋊Q8—181no—
182C4×D4—181no—
183SD32—62no—
184SD32—182no—
185C2×C16—31no—
186C2×C16—31no—
187#107—31no—
188#102—181no—
189C4×C8—91no—
190C23×C3—121no—
191C22×D3—41no—
192C3×Q8—42no—
193C3×Q8—42no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—41no—
197C3×Q8—41no—
198C3×D4—62no—
199C3×D4—121no—
200C2×C3×C4—21no—
201C2×C3×C4—42no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4—121no—
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×Dic3—31no—
208C2×Dic3—31no—
209C2×Dic3—31no—
210C2×Dic3—31no—
211C2×Dic3—41no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—122no—
215C2×Dic3—121no—
216C2×Dic3—121no—
217C2×Dic3—242no—
218D12—22no—
219D12—41no—
220C4×D3—242no—
221Dic6—122no—
222Dic6—122no—
223Dic6—121no—
224Dic6—121no—
225Dic6—121no—
226Dic6—121no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8#23511yescharacteristic
230C3×C8D3×D411yescharacteristic
231C3×C8#23711yescharacteristic
232C3×C8C2×#6711yescharacteristic
233C3⋊C8—62no—
234C3⋊C8—61no—
235C3⋊C8—61no—
236C2×C32#45911yescharacteristic
237C2×C32C2×SD3211yescharacteristic
238C2×C32#51011yescharacteristic
239C3×D3—82no—
240C2×Q8—21no—
241C2×Q8—181no—
242C2×D4—61no—
243C22×C4—361no—
244Q16—21no—
245Q16—21no—
246Q16—181no—
247Q16—181no—
248Q16—362no—
249D8—32no—
250D8—61no—
251C2×C8—91no—
252C2×C8C2×D3211yescharacteristic
253C4⋊C4—61no—
254C4⋊C4—361no—
255C4⋊C4—361no—
256C22⋊C4—361no—
257C42—91no—
258C16—61no—
259C16—61no—
260C22×C3—21no—
261C22×C3—122no—
262C22×C3—241no—
263C22×C3—241no—
264C22×C3D3×D811yescharacteristic
265C22×C3D3×D811yescharacteristic
266C2×D3—42no—
267C2×D3—81no—
268C2×D3—81no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—82no—
272C3×C4—81no—
273C3×C4—81no—
274C3×C4—241no—
275C3×C4#88411yescharacteristic
276C3×C4#91111yescharacteristic
277C3×C4#91411yescharacteristic
278C3×C4#93911yescharacteristic
279Dic3—32no—
280Dic3—32no—
281Dic3—62no—
282Dic3—62no—
283Dic3—61no—
284Dic3—61no—
285Dic3—81no—
286Dic3—242no—
287Dic3—241no—
288Dic3—241no—
289C32#220811yescharacteristic, complemented, Sylow
290C23—121no—
291Q8—41no—
292Q8—41no—
293Q8—361no—
294Q8—361no—
295D4—62no—
296D4—121no—
297C2×C4—41no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—121no—
301C2×C4—361no—
302C2×C4—722no—
303C2×C4#381111yescharacteristic
304C8—181no—
305C8#380411yescharacteristic
306C8D3×#6711yescharacteristic
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—242no—
311C2×C3#478611yescharacteristic
312C2×C3D3×SD3211yescharacteristic
313C2×C3D3×SD3211yescharacteristic
314C2×C3#491511yescharacteristic
315C2×C3#491811yescharacteristic
316C2×C3#515011yescharacteristic
317D3—82no—
318C22—122no—
319C22—241no—
320C22—241no—
321C22#6392611yescharacteristic
322C4—81no—
323C4—92no—
324C4—181no—
325C4—241no—
326C4—721no—
327C4#6393711yescharacteristic
328C4#6397111yescharacteristic
329C3—21no—
330C3#6923411yescharacteristic, complemented
331C3#7147611yescharacteristic, complemented
332C2—242no—
333C2#1059103911yescharacteristic
334C2#1059105011yescharacteristic
335C2#1059143311yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC2×C3×D24C22
hypercenterC2×Q16D32
hypocenterC32#2208
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #10592882C2semidirect
5. C3×#4564C2semidirect
6. #10589133C2semidirect
7. #10589119C2semidirect
33. #4564D3semidirect
175. C3⋊Dic3SD32semidirect
289. C32#2208semidirect
330. C3#69234semidirect
331. C3#71476semidirect

Maximal subgroups

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

subgroupindex
#105928822
C2×C3×#8282
#105907772
C2×#635482
C3×#45642
#105891332
#105891192
#714763
#692343