Finite Group Databasebeta

← #11799033

Subgroups — #11799033

Order 1152.

381 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 381 conjugacy classes of subgroups — too many to draw. Only its 76 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#10592890C211yesmaximal, characteristic
2C2×C3×#829C211yesmaximal, characteristic, complemented
3#10590818C211yesmaximal, characteristic, complemented
4C2×#63549C211yesmaximal, characteristic
5C3×#4564C211yesmaximal, characteristic, complemented
6#10589133C211yesmaximal, characteristic, complemented
7#10589116C211yesmaximal, characteristic
8#71498—31nomaximal
9#69237—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11#64156—21no—
12C2×#3755—21no—
13C2×#3745C2211yescharacteristic
14C2×C3×Dic12C2211yescharacteristic
15#63843—21no—
16C8×C3⋊Dic3C2211yescharacteristic
17C3×#829—22no—
18C3×#818C2211yescharacteristic
19C2×C3×C3⋊C16C2211yescharacteristic
20C2×C3×C3⋊C16C2211yescharacteristic
21#63565—21no—
22#63549—22no—
23C2×C3×Q32—31no—
24#5191—31no—
25#5191—31no—
26#5191—61no—
27Dic3×Q16—31no—
28C2×#829D311yescharacteristic, complemented
29C2×#828—31no—
30C2×#800—31no—
31#4873—31no—
32C3×#358—31no—
33#4564D311yescharacteristic, complemented
34#4509—31no—
35Dic3⋊C16—31no—
36Dic3⋊C16—31no—
37#4491—31no—
38C2×C32×Q8—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C3×Dic6—21no—
41C32×Q16—21no—
42C32×Q16—21no—
43C2×C32×C8C2311yescharacteristic
44#3755—42no—
45#3752—41no—
46#3752—41no—
47C4×C3⋊Dic3D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49#3745—21no—
50#3745—21no—
51C3×C4⋊Dic3—21no—
52C3×Dic12—21no—
53C3×Dic12D412yes—
54Dic3⋊Dic3—41no—
55Dic32—41no—
56C3×C3⋊C16—21no—
57C3×C3⋊C16—21no—
58#2211—91noSylow
59C2×C3×Q16—21no—
60C2×C3×Q16—31no—
61C2×C3×Q16C2×D311yescharacteristic
62C2×C3×Q16C2×D311yescharacteristic
63#947—61no—
64#947—61no—
65#947—62no—
66Q8×Dic3—61no—
67C2×#215—61no—
68C2×#215—61no—
69C2×#215—62no—
70C2×Dic12C2×D311yescharacteristic
71C2×D24—31no—
72C2×D24—31no—
73C2×D24—61no—
74#887—61no—
75C3×Q32—62no—
76C2×C3×C16—31no—
77C2×C3×C16—31no—
78C3×#107—31no—
79#835—61no—
80#829—22no—
81#828—62no—
82#818C2×D311yescharacteristic
83C8×Dic3—31no—
84C8×Dic3—31no—
85C8×Dic3—61no—
86C2×C3⋊C16C2×D311yescharacteristic
87C2×C3⋊C16C2×D311yescharacteristic
88#810—61no—
89#800—62no—
90C22×C3⋊D3—41no—
91C32×Q8—41no—
92C32×Q8—41no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C3⋊Dic3D811yescharacteristic
96C2×C3⋊Dic3D811yescharacteristic
97C4⋊(C3⋊D3)—41no—
98C4⋊(C3⋊D3)—41no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C3×Dic6—22no—
102C3×Dic6—41no—
103C32×C8C2×D411yescharacteristic
104C32×C8#4111yescharacteristic
105C3⋊(C3⋊C8)—21no—
106C2×Q32—31no—
107C2×SD32—91no—
108#495—91no—
109C4×Q16—91no—
110C4⋊C16—91no—
111#358—31no—
112#357—91no—
113C2×C3×Q8—22no—
114C2×C3×Q8—21no—
115C2×C3×Q8—21no—
116C2×C3×Q8—61no—
117C2×D12—62no—
118C2×D12—61no—
119C2×D12—61no—
120C2×Dic6—21no—
121C3×Q16—21no—
122C3×Q16—21no—
123C3×Q16—21no—
124C3×Q16—21no—
125C3×Q16—32no—
126C3×Q16—41no—
127C3×Q16—41no—
128C3×Q16—61no—
129C2×C3×C8—21no—
130C2×C3×C8C22×D311yescharacteristic
131C2×C3×C8C22×D311yescharacteristic
132C3×C4⋊C4—61no—
133#215—124no—
134#215—122no—
135#215—122no—
136(C2×D3)⋊C4—121no—
137(C2×D3)⋊C4—121no—
138(C2×D3)⋊C4—121no—
139(C2×D3)⋊C4—121no—
140(C2×D3)⋊C4—122no—
141(C2×D3)⋊C4—122no—
142C4⋊Dic3—21no—
143C4⋊Dic3—121no—
144Dic3⋊C4—121no—
145C4×Dic3—31no—
146C4×Dic3—31no—
147C4×Dic3—61no—
148C4×Dic3—121no—
149C4×Dic3—121no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—61no—
153Dic12—21no—
154Dic12#6712yes—
155D24—61no—
156D24—61no—
157D24—61no—
158D24—61no—
159D24—121no—
160D24—121no—
161C3×C16—61no—
162C3×C16—61no—
163C3⋊C16—21no—
164C3⋊C16—21no—
165C22×C32C2×D811yescharacteristic
166C2×C3⋊D3—81no—
167C2×C3⋊D3—81no—
168C2×C3⋊D3—81no—
169C32×C4—81no—
170C32×C4#12111yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C3⋊Dic3—21no—
173C3⋊Dic3—21no—
174C3×Dic3—42no—
175C3×Dic3—81no—
176C2×Q16—31no—
177C2×Q16D3211yescharacteristic
178C2×SD16—181no—
179C2×D8—91no—
180#124—181no—
181C4×Q8—181no—
182Q32—62no—
183SD32—182no—
184C2×C16—31no—
185C2×C16—31no—
186#107—31no—
187#103—181no—
188C4×C8—91no—
189C22×D3—122no—
190C22×D3—121no—
191C22×D3—121no—
192C3×Q8—42no—
193C3×Q8—42no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—41no—
197C3×Q8—41no—
198C3×Q8—62no—
199C3×Q8—121no—
200C2×C3×C4—21no—
201C2×C3×C4—42no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4—121no—
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—41no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216D12—122no—
217D12—122no—
218D12—121no—
219D12—121no—
220D12—121no—
221D12—121no—
222Dic6—22no—
223Dic6—41no—
224C3×C8—21no—
225C3×C8—21no—
226C3×C8#23511yescharacteristic
227C3×C8D3×D411yescharacteristic
228C3×C8#23711yescharacteristic
229C3×C8C2×#6711yescharacteristic
230C3⋊C8—62no—
231C3⋊C8—61no—
232C3⋊C8—61no—
233C2×C32#45911yescharacteristic
234C2×C32#50811yescharacteristic
235C2×C32#51011yescharacteristic
236C3⋊D3—161no—
237C2×Q8—21no—
238C2×Q8—61no—
239C2×D4—181no—
240Q16—21no—
241Q16—21no—
242Q16—32no—
243Q16—61no—
244SD16—362no—
245D8—181no—
246D8—181no—
247C2×C8—91no—
248C2×C8C2×D3211yescharacteristic
249C4⋊C4—61no—
250C4⋊C4—361no—
251C22⋊C4—361no—
252C22⋊C4—361no—
253C42—91no—
254C42—361no—
255C16—61no—
256C16—61no—
257C22×C3—21no—
258C22×C3D3×D811yescharacteristic
259C22×C3D3×D811yescharacteristic
260C2×D3—242no—
261C2×D3—242no—
262C2×D3—242no—
263C2×D3—241no—
264C2×D3—241no—
265C2×D3—241no—
266C2×D3—241no—
267C2×D3—241no—
268C2×D3—241no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—82no—
272C3×C4—81no—
273C3×C4—81no—
274C3×C4—122no—
275C3×C4—241no—
276C3×C4#88411yescharacteristic
277C3×C4#91111yescharacteristic
278C3×C4#91411yescharacteristic
279C3×C4#93911yescharacteristic
280Dic3—42no—
281Dic3—61no—
282Dic3—61no—
283Dic3—61no—
284Dic3—61no—
285Dic3—81no—
286Dic3—121no—
287Dic3—121no—
288C32#221111yescharacteristic, complemented, Sylow
289C23—361no—
290Q8—41no—
291Q8—41no—
292Q8—62no—
293Q8—121no—
294D4—361no—
295D4—361no—
296C2×C4—41no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—121no—
300C2×C4—121no—
301C2×C4#381111yescharacteristic
302C8—181no—
303C8#380411yescharacteristic
304C8D3×#6711yescharacteristic
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3#478611yescharacteristic
309C2×C3#491611yescharacteristic
310C2×C3#491811yescharacteristic
311C2×C3#491811yescharacteristic
312C2×C3#491911yescharacteristic
313C2×C3#515011yescharacteristic
314D3—482no—
315D3—481no—
316D3—481no—
317C22—721no—
318C22—721no—
319C22—721no—
320C22#6392611yescharacteristic
321C4—81no—
322C4—122no—
323C4—181no—
324C4—181no—
325C4—241no—
326C4#6393711yescharacteristic
327C4#6397111yescharacteristic
328C3—21no—
329C3#6923711yescharacteristic, complemented
330C3#7149811yescharacteristic, complemented
331C2—1441no—
332C2#1059104411yescharacteristic
333C2#1059104911yescharacteristic
334C2#1059143311yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenterC2×Q16D32
hypocenterC32#2211
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
2. C2×C3×#829C2semidirect
3. #10590818C2semidirect
5. C3×#4564C2semidirect
6. #10589133C2semidirect
28. C2×#829D3semidirect
33. #4564D3semidirect
288. C32#2211semidirect
329. C3#69237semidirect
330. C3#71498semidirect

Maximal subgroups

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

subgroupindex
#105928902
C2×C3×#8292
#105908182
C2×#635492
C3×#45642
#105891332
#105891162
#714983
#692373