Finite Group Databasebeta

← #11791882

Subgroups — #11791882

Order 1152.

665 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 665 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C2×#64097C211yesmaximal, characteristic
2#10591120C211yesmaximal, characteristic
3#10591060C211yesmaximal, characteristic
4C3×#4530C212yesmaximal
5#10589168C212yesmaximal
6#68974—32nomaximal
7C22×#634C412yes—
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×#3750C412yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64097—21no—
13#64097—21no—
14#64097—21no—
15#64097—21no—
16C2×C3×#208C2212yes—
17C2×C3×#208C2212yes—
18#63572—21no—
19#63572—21no—
20#63555—21no—
21#63553—21no—
22C2×#888—32no—
23C2×#888—61no—
24#5118—32no—
25Dic3×M16—32no—
26C3×#343—32no—
27#4554—32no—
28#4554—32no—
29#4530D312yes—
30C22×C32×C4C2×C412yes—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C412yes—
35C2×#634—22no—
36C2×#634—22no—
37C2×#634—44no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—21no—
42#3750—22no—
43#3750—22no—
44C4×C3⋊Dic3D411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C3×#208—22no—
49C3×#208—22no—
50C3×#208—22no—
51C3×#208Q814yescomplemented
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8—22no—
54#1997—91noSylow
55C22×Dic6—34no—
56C22×Dic6—62no—
57C2×C3×M16—32no—
58C2×C3×M16—32no—
59C2×C3×C4⋊C4—21no—
60C2×C3×C4⋊C4C2×D312yes—
61C2×C4⋊Dic3—32no—
62C2×C4⋊Dic3—61no—
63C2×Dic3⋊C4—34no—
64C2×Dic3⋊C4—62no—
65C2×C4×Dic3—32no—
66C2×C4×Dic3—61no—
67C2×#208C2×D312yes—
68C2×#208C2×D312yes—
69#888—62no—
70#888—62no—
71#888—62no—
72#888—62no—
73#888—62no—
74#888—62no—
75#888—62no—
76#888—62no—
77#815—62no—
78Dic3⋊C8—62no—
79Dic3⋊C8—62no—
80C8×Dic3—62no—
81C23×C32C22×C411yescharacteristic
82C2×C32×C4—22no—
83C2×C32×C4—42no—
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×Q812yes—
87C2×C32×C4#4112yes—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—42no—
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C22⋊C411yescharacteristic
94C2×C3⋊Dic3C22⋊C411yescharacteristic
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96#634—44no—
97#634—44no—
98C3×C3⋊C8—24no—
99C3×C3⋊C8—42no—
100C2×C4⋊Q8—91no—
101#423—91no—
102C4×M16—91no—
103#343—32no—
104#343—92no—
105C22×C3×C4—22no—
106C22×C3×C4—21no—
107C22×C3×C4C4×D314yes—
108C22×C3×C4C22×D312yes—
109C22×Dic3—32no—
110C22×Dic3—32no—
111C22×Dic3—34no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—62no—
115C2×Dic6—64no—
116C2×Dic6—64no—
117C2×Dic6—64no—
118C2×Dic6—64no—
119C2×Dic6—128no—
120C2×Dic6—128no—
121C3×M16—34no—
122C3×M16—62no—
123C3×M16—62no—
124C3×M16—62no—
125C2×C3×C8—62no—
126C2×C3×C8—62no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—22no—
131C4⋊Dic3—62no—
132C4⋊Dic3—62no—
133C4⋊Dic3—62no—
134C4⋊Dic3—62no—
135Dic3⋊C4—64no—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138Dic3⋊C4—64no—
139C4×Dic3—32no—
140C4×Dic3—32no—
141C4×Dic3—32no—
142C4×Dic3—32no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147#208—22no—
148#208—22no—
149#208—22no—
150#208Dic614yescomplemented
151C2×C3⋊C8—22no—
152C2×C3⋊C8—22no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32C2×C22⋊C411yescharacteristic
156C22×C32C4×Q812yes—
157C32×C4—42no—
158C32×C4C22⋊Q812yes—
159C32×C4#12411yescharacteristic
160C32×C4C4⋊Q811yescharacteristic
161C3⋊Dic3—21no—
162C3⋊Dic3—21no—
163C3⋊Dic3—42no—
164C3⋊Dic3#10012yes—
165C3⋊Dic3#10112yes—
166C22×Q8—92no—
167C2×M16—32no—
168C2×M16—32no—
169C4⋊Q8—181no—
170C4⋊Q8—181no—
171C4⋊Q8—181no—
172C4⋊Q8—181no—
173C2×C4⋊C4—92no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4D3211yescharacteristic
176C2×C42—91no—
177C4⋊C8—181no—
178C4⋊C8—181no—
179#97—181no—
180C4×C8—181no—
181C23×C3—21no—
182C23×C3C2×C4×D312yes—
183C2×C3×C4—24no—
184C2×C3×C4—24no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—44no—
190C2×C3×C4—44no—
191C2×C3×C4C2×Dic612yes—
192C2×C3×C4#23512yes—
193C2×C3×C4D3×D412yes—
194C2×C3×C4D3×D412yes—
195C2×C3×C4#23712yes—
196C2×C3×C4D3×Q812yes—
197C2×Dic3—32no—
198C2×Dic3—32no—
199C2×Dic3—32no—
200C2×Dic3—32no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—64no—
211C2×Dic3—124no—
212C2×Dic3—124no—
213Dic6—128no—
214Dic6—128no—
215Dic6—128no—
216Dic6—128no—
217C3×C8—64no—
218C3×C8—122no—
219C3⋊C8—24no—
220C3⋊C8—42no—
221C2×C32—22no—
222C2×C32#39111yescharacteristic
223C2×C32C2×#10011yescharacteristic
224C2×C32C2×#10111yescharacteristic
225C2×Q8—182no—
226C2×Q8—182no—
227C2×Q8—364no—
228C22×C4—91no—
229C22×C4—91no—
230C22×C4—92no—
231C22×C4#62412yes—
232C22×C4C2×D3211yescharacteristic
233M16—34no—
234M16—62no—
235M16—62no—
236M16—62no—
237C2×C8—62no—
238C2×C8—62no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—182no—
242C4⋊C4—182no—
243C4⋊C4—181no—
244C4⋊C4—181no—
245C42—91no—
246C42—91no—
247C42—91no—
248C42—91no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3—21no—
255C22×C3C4×Dic612yes—
256C22×C3D3×C22⋊C412yes—
257C22×C3#88712yes—
258C3×C4—21no—
259C3×C4—22no—
260C3×C4—21no—
261C3×C4—44no—
262C3×C4—44no—
263C3×C4#87812yes—
264C3×C4#88512yes—
265C3×C4#88812yes—
266C3×C4#89612yes—
267Dic3—34no—
268Dic3—34no—
269Dic3—62no—
270Dic3—62no—
271Dic3—62no—
272Dic3—62no—
273Dic3—62no—
274Dic3—62no—
275Dic3—124no—
276Dic3—124no—
277C32#199711yescharacteristic, complemented, Sylow
278C23C2×#62411yescharacteristic
279Q8—364no—
280Q8—364no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—362no—
291C2×C4D3×Dic612yes—
292C2×C4#379512yes—
293C2×C4#381111yescharacteristic
294C2×C4#381111yescharacteristic
295C8—64no—
296C8—122no—
297C2×C3—24no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3#464612yes—
304C2×C3D3×#10012yes—
305C2×C3D3×#10112yes—
306C22—21no—
307C22—21no—
308C22#6384412yes—
309C22#6397411yescharacteristic
310C4—42no—
311C4—92no—
312C4—92no—
313C4—181no—
314C4—181no—
315C4—362no—
316C4#6384011yescharacteristic
317C4#6389612yes—
318C4#6391311yescharacteristic
319C3—21no—
320C3#6897412yescomplemented
321C2—22no—
322C2#1059127311yescharacteristic
323C2#1059150311yescharacteristic
324C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1997
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
51. C3×#208Q8semidirect
150. #208Dic6semidirect
277. C32#1997semidirect
320. C3#68974semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
#105911202
#105910602
C3×#45302
#105891682
#689743