Finite Group Databasebeta

← #11798988

Subgroups — #11798988

Order 1152.

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

normal subgroups only

This group has 405 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, complemented
2C2×C3×#828C211yesmaximal, characteristic, complemented
3#10590777C211yesmaximal, characteristic, complemented
4C2×#63546C211yesmaximal, characteristic
5C3×#4564C211yesmaximal, characteristic, complemented
6#10589133C211yesmaximal, characteristic, complemented
7#10589116C211yesmaximal, characteristic, complemented
8#71477—31nomaximal
9#69235—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11#64156—21no—
12C2×#3755—21no—
13C2×#3745C2211yescharacteristic
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#63546—22no—
23C2×C3×SD32—31no—
24#5191—31no—
25#5191—31no—
26#5191—61no—
27C2×#828D311yescharacteristic, complemented
28Dic3×D8—31no—
29C2×#826—31no—
30C2×D48—31no—
31#4872—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×D12—21no—
41C2×D3×Dic3—41no—
42C32×Q16—21no—
43C32×Q16—21no—
44C2×C32×C8C2311yescharacteristic
45#3755—42no—
46#3752—41no—
47#3752—41no—
48C4×C3⋊Dic3D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50#3745—21no—
51#3745—21no—
52C3×C4⋊Dic3—21no—
53C3×D24—21no—
54C3×D24D412yes—
55(C2×D3)⋊Dic3—41no—
56C3×C3⋊C16—21no—
57C3×C3⋊C16—21no—
58#2210—91noSylow
59C2×C3×Q16—21no—
60C2×C3×Q16C2×D311yescharacteristic
61C2×C3×Q16C2×D311yescharacteristic
62C2×C3×D8—31no—
63#947—61no—
64#947—61no—
65#947—62no—
66C2×#215—61no—
67C2×#215—61no—
68C2×#215—62no—
69D4×Dic3—61no—
70C2×D24—31no—
71C2×D24—31no—
72C2×D24—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#826—62no—
82#818C2×D311yescharacteristic
83C8×Dic3—31no—
84C8×Dic3—31no—
85C8×Dic3—61no—
86C2×C3⋊C16C2×D311yescharacteristic
87C2×C3⋊C16C2×D311yescharacteristic
88#809—61no—
89D48—62no—
90C22×C3⋊D3—41no—
91C22×C3×D3—41no—
92C32×Q8—41no—
93C32×Q8—41no—
94C2×C32×C4—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C3⋊Dic3D811yescharacteristic
97C2×C3⋊Dic3D811yescharacteristic
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—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×D16—91no—
109#495—91no—
110C4×D8—91no—
111C4⋊C16—91no—
112#358—31no—
113#357—91no—
114C2×C3×Q8—22no—
115C2×C3×Q8—21no—
116C2×C3×Q8—21no—
117C2×C3×D4—61no—
118C22×Dic3—121no—
119C2×D12—21no—
120C2×D12—62no—
121C2×D12—61no—
122C2×D12—61no—
123C2×C4×D3—121no—
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#215—124no—
138#215—122no—
139#215—122no—
140(C2×D3)⋊C4—121no—
141(C2×D3)⋊C4—121no—
142(C2×D3)⋊C4—121no—
143(C2×D3)⋊C4—121no—
144(C2×D3)⋊C4—121no—
145(C2×D3)⋊C4—122no—
146(C2×D3)⋊C4—122no—
147C4⋊Dic3—21no—
148C4×Dic3—31no—
149C4×Dic3—31no—
150C4×Dic3—61no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—61no—
154D24—21no—
155D24—61no—
156D24—61no—
157D24—61no—
158D24—61no—
159D24—121no—
160D24—121no—
161D24#6712yes—
162C3×C16—61no—
163C3×C16—61no—
164C3⋊C16—21no—
165C3⋊C16—21no—
166C22×C32C2×D811yescharacteristic
167C2×C3⋊D3—81no—
168C2×C3⋊D3—81no—
169C2×C3⋊D3—81no—
170C2×C3×D3—42no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C32×C4—81no—
174C32×C4#12111yescharacteristic
175C32×C4AGL(1,ℤ/8)11yescharacteristic
176C3⋊Dic3—21no—
177C3⋊Dic3—21no—
178C3×Dic3—81no—
179C2×Q16D3211yescharacteristic
180C2×SD16—181no—
181C2×D8—31no—
182C2×D8—91no—
183#124—181no—
184C4×D4—181no—
185SD32—62no—
186D16—182no—
187C2×C16—31no—
188C2×C16—31no—
189#107—31no—
190#102—181no—
191C4×C8—91no—
192C23×C3—121no—
193C22×D3—41no—
194C22×D3—122no—
195C22×D3—121no—
196C22×D3—121no—
197C3×Q8—42no—
198C3×Q8—42no—
199C3×Q8—41no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—41no—
203C3×D4—62no—
204C3×D4—121no—
205C2×C3×C4—21no—
206C2×C3×C4—42no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—121no—
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×Dic3—31no—
213C2×Dic3—31no—
214C2×Dic3—31no—
215C2×Dic3—31no—
216C2×Dic3—41no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—242no—
220D12—22no—
221D12—41no—
222D12—122no—
223D12—122no—
224D12—121no—
225D12—121no—
226D12—121no—
227D12—121no—
228C4×D3—242no—
229C3×C8—21no—
230C3×C8—21no—
231C3×C8#23511yescharacteristic
232C3×C8D3×D411yescharacteristic
233C3×C8#23711yescharacteristic
234C3×C8C2×#6711yescharacteristic
235C3⋊C8—62no—
236C3⋊C8—61no—
237C3⋊C8—61no—
238C2×C32#45911yescharacteristic
239C2×C32#50811yescharacteristic
240C2×C32#50911yescharacteristic
241C3⋊D3—161no—
242C3×D3—82no—
243C2×Q8—21no—
244C2×D4—61no—
245C2×D4—181no—
246C22×C4—361no—
247Q16—21no—
248Q16—21no—
249SD16—362no—
250D8—32no—
251D8—61no—
252D8—181no—
253D8—181no—
254C2×C8—91no—
255C2×C8C2×D3211yescharacteristic
256C4⋊C4—61no—
257C22⋊C4—361no—
258C22⋊C4—361no—
259C22⋊C4—361no—
260C42—91no—
261C16—61no—
262C16—61no—
263C22×C3—21no—
264C22×C3—122no—
265C22×C3—241no—
266C22×C3—241no—
267C22×C3D3×D811yescharacteristic
268C22×C3D3×D811yescharacteristic
269C2×D3—42no—
270C2×D3—81no—
271C2×D3—81no—
272C2×D3—242no—
273C2×D3—242no—
274C2×D3—242no—
275C2×D3—241no—
276C2×D3—241no—
277C2×D3—241no—
278C2×D3—241no—
279C2×D3—241no—
280C2×D3—241no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—82no—
284C3×C4—81no—
285C3×C4—81no—
286C3×C4—241no—
287C3×C4#88411yescharacteristic
288C3×C4#91111yescharacteristic
289C3×C4#91411yescharacteristic
290C3×C4#93911yescharacteristic
291Dic3—61no—
292Dic3—61no—
293Dic3—61no—
294Dic3—61no—
295Dic3—81no—
296Dic3—121no—
297Dic3—121no—
298C32#221011yescharacteristic, complemented, Sylow
299C23—121no—
300C23—361no—
301Q8—41no—
302Q8—41no—
303D4—62no—
304D4—121no—
305D4—361no—
306D4—361no—
307C2×C4—41no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—121no—
311C2×C4—722no—
312C2×C4#381111yescharacteristic
313C8—181no—
314C8#380411yescharacteristic
315C8D3×#6711yescharacteristic
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—242no—
320C2×C3#478611yescharacteristic
321C2×C3#491411yescharacteristic
322C2×C3#491411yescharacteristic
323C2×C3#491611yescharacteristic
324C2×C3#491911yescharacteristic
325C2×C3#515011yescharacteristic
326D3—82no—
327D3—482no—
328D3—481no—
329D3—481no—
330C22—122no—
331C22—241no—
332C22—241no—
333C22—721no—
334C22—721no—
335C22—721no—
336C22#6392611yescharacteristic
337C4—81no—
338C4—181no—
339C4—181no—
340C4—241no—
341C4#6393711yescharacteristic
342C4#6397111yescharacteristic
343C3—21no—
344C3#6923511yescharacteristic, complemented
345C3#7147711yescharacteristic, complemented
346C2—242no—
347C2—1441no—
348C2#1059104011yescharacteristic
349C2#1059104911yescharacteristic
350C2#1059143311yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC2×#63546C2
hypercenterC2×Q16D32
hypocenterC32#2210
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. #10592890C2semidirect
2. C2×C3×#828C2semidirect
3. #10590777C2semidirect
5. C3×#4564C2semidirect
6. #10589133C2semidirect
7. #10589116C2semidirect
27. C2×#828D3semidirect
33. #4564D3semidirect
298. C32#2210semidirect
344. C3#69235semidirect
345. C3#71477semidirect

Maximal subgroups

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

subgroupindex
#105928902
C2×C3×#8282
#105907772
C2×#635462
C3×#45642
#105891332
#105891162
#714773
#692353