Finite Group Databasebeta

← #11800106

Subgroups — #11800106

Order 1152.

319 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 319 conjugacy classes of subgroups — too many to draw. Only its 74 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#10592577C211yesmaximal, characteristic, complemented
2#10590869C211yesmaximal, characteristic
3C3×#4492C211yesmaximal, characteristic, complemented
4C3×#4491C211yesmaximal, characteristic
5#10589118C211yesmaximal, characteristic, complemented
6#10589115C211yesmaximal, characteristic
7#10589102C211yesmaximal, characteristic, complemented
8#69216—31nomaximal
9#69184—31nomaximal
10#64099—21no—
11C2×C3×Dic12C2211yescharacteristic
12C2×C3×D24C2211yescharacteristic
13#63863—21no—
14C2×#3715—21no—
15C32×#107C2211yescharacteristic
16#63645C2211yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18#63635—21no—
19C2×C3×C3⋊C16C2211yescharacteristic
20C2×C3×C3⋊C16C2211yescharacteristic
21#5191—31no—
22#5155—31no—
23#4878—31no—
24#4878—31no—
25#4878—61no—
26C3×#358—31no—
27C3×#357—31no—
28#4564—31no—
29#4562—31no—
30#4509—31no—
31#4503—31no—
32Dic3×C16—31no—
33Dic3×C16—31no—
34#4492D311yescharacteristic, complemented
35#4491D311yescharacteristic
36C2×C3×D12—21no—
37C2×C3×Dic6—21no—
38C2×C32×C8C2311yescharacteristic
39C32×C4⋊C4—21no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—41no—
42#3750—41no—
43C4×C3⋊Dic3D411yescharacteristic
44C2×C3⋊(C3⋊C8)D411yescharacteristic
45C3×Dic12—21no—
46C3×Dic12—21no—
47C3×D24—21no—
48C3×D24—21no—
49(C2×D3)⋊Dic3—41no—
50(C2×D3)⋊Dic3—41no—
51#3715—42no—
52C3×C3⋊C16—21no—
53C3×C3⋊C16—21no—
54#2242—91noSylow
55C2×C3×Q16—31no—
56C2×C3×D8—31no—
57#947—61no—
58C2×#215—61no—
59#936—61no—
60C2×#214—61no—
61C2×Dic12C2×D311yescharacteristic
62C2×D24C2×D311yescharacteristic
63#890—61no—
64#890—61no—
65#890—62no—
66C2×C3×C16—31no—
67C2×C3×C16—31no—
68C3×#107—21no—
69C3×#107C2×D311yescharacteristic
70C3×#107C2×D311yescharacteristic
71#818—31no—
72#818—31no—
73#818—61no—
74C8×Dic3—31no—
75C8×Dic3—31no—
76C8×Dic3—61no—
77C2×C3⋊C16C2×D311yescharacteristic
78C2×C3⋊C16C2×D311yescharacteristic
79#808—61no—
80#808—61no—
81#808—62no—
82C22×C3×D3—41no—
83C2×C32×C4—41no—
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3D811yescharacteristic
87C2×C3⋊Dic3D811yescharacteristic
88C2×C3×Dic3—41no—
89C3×D12—41no—
90C3×D12—41no—
91C3×Dic6—41no—
92C3×Dic6—41no—
93C32×C8#4111yescharacteristic
94C32×C8#4111yescharacteristic
95C3⋊(C3⋊C8)SD1612yes—
96#499—91no—
97#495—91no—
98#358—31no—
99#358—91no—
100#357—31no—
101#357—91no—
102C4×C16—91no—
103C2×C3×Q8—61no—
104C2×C3×D4—61no—
105C2×D12—21no—
106C2×Dic6—21no—
107C3×Q16—61no—
108C3×Q16—61no—
109C3×D8—61no—
110C3×D8—61no—
111C2×C3×C8—21no—
112C2×C3×C8C22×D311yescharacteristic
113C2×C3×C8C22×D311yescharacteristic
114C3×C4⋊C4—22no—
115C3×C4⋊C4—21no—
116C3×C4⋊C4—21no—
117#217—121no—
118#217—121no—
119#215—122no—
120#214—122no—
121(C2×D3)⋊C4—121no—
122(C2×D3)⋊C4—121no—
123C4⋊Dic3—62no—
124C4⋊Dic3—61no—
125C4⋊Dic3—61no—
126C4⋊Dic3—121no—
127C4⋊Dic3—121no—
128C4⋊Dic3—122no—
129Dic3⋊C4—121no—
130Dic3⋊C4—121no—
131Dic3⋊C4—122no—
132C4×Dic3—31no—
133C4×Dic3—31no—
134C4×Dic3—61no—
135C2×C3⋊C8—31no—
136C2×C3⋊C8—31no—
137C2×C3⋊C8—61no—
138Dic12—21no—
139Dic12—21no—
140D24—21no—
141D24—21no—
142C3×C16—61no—
143C3×C16—61no—
144C3⋊C16—21no—
145C3⋊C16—21no—
146C22×C32C2×D811yescharacteristic
147C2×C3×D3—81no—
148C2×C3×D3—81no—
149C2×C3×D3—81no—
150C32×C4—81no—
151C32×C4#12411yescharacteristic
152C32×C4C2×SD1611yescharacteristic
153C3⋊Dic3—21no—
154C3⋊Dic3—21no—
155C3⋊Dic3—81no—
156C3×Dic3—81no—
157C2×Q16—31no—
158C2×SD16—181no—
159C2×D8—31no—
160#125—181no—
161#124—181no—
162C2×C16—31no—
163C2×C16—31no—
164#107—91no—
165#107D3211yescharacteristic
166#106—181no—
167C4×C8—91no—
168C23×C3—121no—
169C22×D3—41no—
170C3×Q8—121no—
171C3×Q8—121no—
172C3×D4—121no—
173C3×D4—121no—
174C2×C3×C4—21no—
175C2×C3×C4—42no—
176C2×C3×C4—41no—
177C2×C3×C4—41no—
178C2×C3×C4—121no—
179C2×C3×C4D3×D411yescharacteristic
180C2×C3×C4D3×D411yescharacteristic
181C2×Dic3—31no—
182C2×Dic3—31no—
183C2×Dic3—31no—
184C2×Dic3—31no—
185C2×Dic3—41no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—122no—
189C2×Dic3—121no—
190C2×Dic3—121no—
191D12—41no—
192D12—41no—
193Dic6—41no—
194Dic6—41no—
195C3×C8—21no—
196C3×C8—21no—
197C3×C8#23511yescharacteristic
198C3×C8#23511yescharacteristic
199C3×C8#23711yescharacteristic
200C3×C8#23711yescharacteristic
201C3⋊C8—32no—
202C3⋊C8—32no—
203C3⋊C8—62no—
204C2×C32#48611yescharacteristic
205C2×C32#50811yescharacteristic
206C2×C32#50811yescharacteristic
207C3×D3—161no—
208C2×Q8—61no—
209C2×D4—61no—
210Q16—61no—
211Q16—61no—
212SD16—362no—
213D8—61no—
214D8—61no—
215C2×C8—91no—
216C2×C8C2×D3211yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—181no—
219C4⋊C4—361no—
220C4⋊C4—361no—
221C22⋊C4—361no—
222C22⋊C4—361no—
223C42—91no—
224C16—61no—
225C16—61no—
226C22×C3—21no—
227C22×C3—241no—
228C22×C3—241no—
229C22×C3—241no—
230C22×C3D3×D811yescharacteristic
231C22×C3D3×D811yescharacteristic
232C2×D3—81no—
233C2×D3—81no—
234C2×D3—81no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—82no—
238C3×C4—81no—
239C3×C4—81no—
240C3×C4—241no—
241C3×C4#88511yescharacteristic
242C3×C4#88511yescharacteristic
243C3×C4D3×SD1611yescharacteristic
244C3×C4D3×SD1611yescharacteristic
245Dic3—61no—
246Dic3—61no—
247Dic3—61no—
248Dic3—61no—
249Dic3—81no—
250Dic3—121no—
251Dic3—121no—
252Dic3—242no—
253Dic3—241no—
254Dic3—241no—
255C32#224211yescharacteristic, complemented, Sylow
256C23—121no—
257Q8—121no—
258Q8—121no—
259D4—121no—
260D4—121no—
261C2×C4—41no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—121no—
265C2×C4—361no—
266C2×C4#381111yescharacteristic
267C8—92no—
268C8#379511yescharacteristic
269C8#379511yescharacteristic
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—481no—
274C2×C3#476011yescharacteristic
275C2×C3#476011yescharacteristic
276C2×C3#491211yescharacteristic
277C2×C3#491611yescharacteristic
278C2×C3#491611yescharacteristic
279C2×C3#491911yescharacteristic
280D3—161no—
281C22—241no—
282C22—241no—
283C22—241no—
284C22#6392611yescharacteristic
285C4—81no—
286C4—181no—
287C4—181no—
288C4—241no—
289C4—721no—
290C4#6391311yescharacteristic
291C4#6394011yescharacteristic
292C3—21no—
293C3#6918411yescharacteristic, complemented
294C3#6921611yescharacteristic, complemented
295C2—481no—
296C2#1059055211yescharacteristic
297C2#1059103511yescharacteristic
298C2#1059104911yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC2×C3×D24C22
hypercenter#107D32
hypocenterC32#2242
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10592577C2semidirect
3. C3×#4492C2semidirect
5. #10589118C2semidirect
7. #10589102C2semidirect
34. #4492D3semidirect
255. C32#2242semidirect
293. C3#69184semidirect
294. C3#69216semidirect

Maximal subgroups

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

subgroupindex
#105925772
#105908692
C3×#44922
C3×#44912
#105891182
#105891152
#105891022
#692163
#691843