Finite Group Databasebeta

← #11786662

Subgroups — #11786662

Order 1152.

460 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 63 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#10594780C211yesmaximal, characteristic
2#10593808C211yesmaximal, characteristic
3#10593330C212yesmaximal, complemented
4#10591153C211yesmaximal, characteristic
5#10590050C212yesmaximal, complemented
6C2×#3828C2211yescharacteristic
7#64283C2212yes—
8C2×C3×#208—21no—
9C2×#3712C2211yescharacteristic
10#63818—21no—
11#63818C2212yes—
12#63817—24no—
13C2×#3710C2211yescharacteristic
14#63788C412yes—
15#63780C412yes—
16#63733—24no—
17C3×#830—21no—
18#63557—21no—
19#5745—61no—
20#4727—61no—
21C22×C32×C4D411yescharacteristic
22C2×#638C2×C411yescharacteristic
23C2×#638Q811yescharacteristic
24#3828—22no—
25#3828—22no—
26C2×C4⋊(C3⋊D3)Q811yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×#634C2×C411yescharacteristic
30#3792C2×C414yes—
31#3788—22no—
32#3787—22no—
33C3×#208—22no—
34C3×#208—22no—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8—21no—
37C2×C3×C3⋊C8—21no—
38#3712—22no—
39#3712—22no—
40#3712D414yes—
41#3710—22no—
42#3710—22no—
43#3710—22no—
44#1858—91nomaximal, Sylow
45C2×#235—61no—
46C2×#235—61no—
47C2×C3×M16—61no—
48C2×#208—21no—
49#907—64no—
50D3×M16—62no—
51D3×M16—62no—
52#901—64no—
53C2×ΓL(1,𝔽25)—61no—
54C2×D3×C8—61no—
55C3×C22⋊C8—61no—
56#830—21no—
57(C2×D3)⋊C8—61no—
58(C2×D3)⋊C8—61no—
59C23×C32C4⋊C411yescharacteristic
60C22×C3⋊D3C4⋊C411yescharacteristic
61C22×C3⋊D3C2×Q811yescharacteristic
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4C4⋊C411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66#638—22no—
67#638—22no—
68C2×C3⋊Dic3C4⋊C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C4⋊(C3⋊D3)—22no—
71C4×C3⋊D3—21no—
72C4×C3⋊D3—21no—
73C4×C3⋊D3C2×D412yes—
74C4×C3⋊D3#4112yes—
75#634—22no—
76#622—24no—
77C3×C3⋊C8—24no—
78C3×C3⋊C8—41no—
79C3×C3⋊C8—41no—
80#568—91no—
81#430—92no—
82#413—91no—
83#408—91no—
84#341—92no—
85C22×C3×C4—21no—
86C22×C3×C4—21no—
87C2×#67—61no—
88C2×#67—61no—
89C2×#67—61no—
90C2×#67—61no—
91#235—62no—
92#235—62no—
93#235—62no—
94#235—62no—
95#235—122no—
96#235—122no—
97C2×D12—61no—
98C2×D12—61no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×Dic6—61no—
104C2×Dic6—61no—
105C3×M16—62no—
106C3×M16—62no—
107C2×C3×C8—62no—
108C2×C3×C8—61no—
109C2×C3×C8—61no—
110#208—22no—
111#208—22no—
112C2×C3⋊C8—22no—
113C2×C3⋊C8—21no—
114C2×C3⋊C8—21no—
115ΓL(1,𝔽25)—64no—
116ΓL(1,𝔽25)—64no—
117ΓL(1,𝔽25)—122no—
118D3×C8—64no—
119D3×C8—64no—
120D3×C8—122no—
121C22×C32—21no—
122C22×C32—41no—
123C22×C32C2×C4⋊C411yescharacteristic
124C2×C3⋊D3—21no—
125C2×C3⋊D3—41no—
126C2×C3⋊D3—41no—
127C2×C3⋊D3C22⋊Q812yes—
128C32×C4—21no—
129C32×C4#12011yescharacteristic
130C32×C4#12311yescharacteristic
131C3⋊Dic3—21no—
132C3⋊Dic3C4×D412yes—
133C2×#41—91no—
134#131—184no—
135C2×M16—61no—
136C2×M16—91no—
137C2×M16—92no—
138C2×M16—92no—
139C2×M16—181no—
140C22×C8—91no—
141#108—184no—
142#101—92no—
143#100—92no—
144C22⋊C8—61no—
145C22⋊C8—181no—
146C23×C3—21no—
147C23×C3—21no—
148C22×D3—61no—
149C22×D3—61no—
150C22×D3—61no—
151C22×D3—61no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—41no—
161C2×C3×C4—41no—
162#67—62no—
163#67—62no—
164#67—62no—
165#67—62no—
166#67—122no—
167#67—122no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172D12—62no—
173D12—62no—
174D12—122no—
175C4×D3—62no—
176C4×D3—62no—
177C4×D3—62no—
178C4×D3—62no—
179C4×D3—62no—
180C4×D3—62no—
181C4×D3—121no—
182C4×D3—121no—
183Dic6—62no—
184Dic6—62no—
185Dic6—122no—
186C3×C8—64no—
187C3×C8—121no—
188C3×C8—121no—
189C3⋊C8—24no—
190C3⋊C8—41no—
191C3⋊C8—41no—
192C2×C32—21no—
193C2×C32—41no—
194C2×C32#38511yescharacteristic
195C3⋊D3—22no—
196C3⋊D3—41no—
197#41—182no—
198#41—182no—
199C2×Q8—91no—
200C2×D4—91no—
201C2×D4—91no—
202C2×D4—91no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4GO+(4,𝔽2)11yescharacteristic
206M16—62no—
207M16—62no—
208M16—94no—
209M16—94no—
210M16—182no—
211M16—182no—
212M16—182no—
213C2×C8—62no—
214C2×C8—61no—
215C2×C8—61no—
216C2×C8—182no—
217C2×C8—182no—
218C2×C8—182no—
219C2×C8—182no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—41no—
225C22×C3—42no—
226C22×C3—81no—
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—121no—
231C2×D3—122no—
232C2×D3—122no—
233C2×D3—241no—
234C2×D3—241no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—41no—
242Dic3—62no—
243Dic3—62no—
244Dic3—62no—
245Dic3—121no—
246C32#185811yescharacteristic, complemented, Sylow
247C23—91no—
248C23—91no—
249C23#377311yescharacteristic
250Q8—182no—
251D4—182no—
252D4—182no—
253D4—182no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—91no—
257C2×C4—92no—
258C2×C4—92no—
259C2×C4—91no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4#377311yescharacteristic
263C2×C4C2×GO+(4,𝔽2)11yescharacteristic
264C8—64no—
265C8—121no—
266C8—121no—
267C8—184no—
268C2×C3—22no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—41no—
272C2×C3—41no—
273C2×C3—41no—
274C2×C3—81no—
275D3—122no—
276D3—122no—
277D3—122no—
278D3—241no—
279C22—21no—
280C22—41no—
281C22—92no—
282C22—181no—
283C22—361no—
284C22—361no—
285C22C2×#377311yescharacteristic
286C4—21no—
287C4—92no—
288C4—181no—
289C4#6423311yescharacteristic
290C4#6424111yescharacteristic
291C3—21no—
292C3—21no—
293C2—21no—
294C2—41no—
295C2—182no—
296C2—361no—
297C2#1059348511yescharacteristic
subgroupG/H
centerC4#64241
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32#385
prime radicalC2×#3828C22
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1858
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10593330C2semidirect
5. #10590050C2semidirect
246. C32#1858semidirect

Maximal subgroups

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

subgroupindex
#105947802
#105938082
#105933302
#105911532
#105900502
#18589