Finite Group Databasebeta

← #11776297

Subgroups — #11776297

Order 1152.

625 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 625 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10590340C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4547C212yesmaximal, complemented
5#10589094C212yesmaximal, complemented
6#68420—32nomaximal
7C2×Q8×C3⋊D3—21no—
8C32×C4⋊Q8C2211yescharacteristic
9#64153—21no—
10C4⋊C4×C3⋊D3—21no—
11C4⋊C4×C3⋊D3C412yes—
12#64097—21no—
13#64097C412yes—
14C42×C3⋊D3C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×#3712—21no—
17C3×C4⋊(C3⋊C8)C2212yes—
18C3×C4⋊(C3⋊C8)C2212yes—
19#63572—21no—
20#63557—21no—
21#63553—21no—
22D3×C4⋊Q8—32no—
23D3×C4⋊Q8—61no—
24#4837—32no—
25#4833—32no—
26C3×#332—32no—
27#4547D312yescomplemented
28#4486—32no—
29#4482—32no—
30C2×C32×Q8—21no—
31Q8×C3⋊D3—42no—
32Q8×C3⋊D3—42no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×#634—21no—
38C2×#634—22no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4C2×C412yes—
41C32×C42C2311yescharacteristic
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)C2×C412yes—
44#3750—22no—
45#3750—22no—
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51#3712—42no—
52#1546—91noSylow
53C2×D3×Q8—62no—
54C2×D3×Q8—62no—
55C3×C4⋊Q8—21no—
56C3×C4⋊Q8C2×D312yes—
57#944—62no—
58#944—62no—
59C2×ΓL(1,𝔽25)—62no—
60D3×C4⋊C4—34no—
61D3×C4⋊C4—62no—
62D3×C4⋊C4—62no—
63D3×C4⋊C4—62no—
64#888—34no—
65#888—62no—
66#888—62no—
67#888—62no—
68C42×D3—32no—
69C42×D3—61no—
70#869—32no—
71#869—61no—
72C3×C4⋊C8—32no—
73C3×C4⋊C8—32no—
74(C2×D3)⋊C8—62no—
75Dic3⋊C8—62no—
76C8×Dic3—62no—
77C4⋊(C3⋊C8)C2×D312yes—
78C4⋊(C3⋊C8)C2×D312yes—
79C22×C3⋊D3C22⋊C411yescharacteristic
80C32×Q8—41no—
81C32×Q8—41no—
82C2×C32×C4—22no—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C22⋊C411yescharacteristic
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C4×C3⋊D3—22no—
91C4×C3⋊D3—22no—
92C4×C3⋊D3—44no—
93C4×C3⋊D3D812yes—
94C4×C3⋊D3SD1612yes—
95#634—41no—
96#634—41no—
97#634—44no—
98C3×C3⋊C8—42no—
99C3×C3⋊C8—42no—
100C2×C4⋊Q8—91no—
101#431—91no—
102#423—91no—
103#332—32no—
104#332—92no—
105C2×C3×Q8—22no—
106C2×C3×Q8—22no—
107D3×Q8—124no—
108D3×Q8—124no—
109D3×Q8—124no—
110D3×Q8—124no—
111C2×C4×D3—32no—
112C2×C4×D3—32no—
113C2×C4×D3—32no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C2×Dic6—64no—
120C2×Dic6—62no—
121C2×Dic6—64no—
122C2×Dic6—62no—
123C2×C3×C8—62no—
124C2×C3×C8—62no—
125C3×C4⋊C4—22no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4C4×D314yes—
129C3×C42—21no—
130C3×C42C22×D312yes—
131C4⋊Dic3—34no—
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—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C2×C3⋊C8—22no—
146C2×C3⋊C8—22no—
147ΓL(1,𝔽25)—124no—
148C22×C32C2×C22⋊C411yescharacteristic
149C2×C3⋊D3—21no—
150C2×C3⋊D3—21no—
151C2×C3⋊D3#10212yes—
152C32×C4—21no—
153C32×C4—42no—
154C32×C4C2×D811yescharacteristic
155C32×C4C2×SD1611yescharacteristic
156C32×C4#13712yes—
157C3⋊Dic3—21no—
158C3⋊Dic3—42no—
159C3⋊Dic3#10112yes—
160C3⋊Dic3#10212yes—
161C22×Q8—181no—
162C2×M16—181no—
163C4⋊Q8—92no—
164C4⋊Q8—91no—
165C4⋊Q8—181no—
166C4⋊Q8—181no—
167C4⋊Q8D3211yescharacteristic
168C2×C4⋊C4—92no—
169C2×C4⋊C4—181no—
170C2×C42—91no—
171C4⋊C8—32no—
172C4⋊C8—32no—
173C4⋊C8—181no—
174C22⋊C8—181no—
175C4×C8—181no—
176C22×D3—32no—
177C22×D3—61no—
178C3×Q8—42no—
179C3×Q8—42no—
180C3×Q8—42no—
181C3×Q8—42no—
182C2×C3×C4—24no—
183C2×C3×C4—24no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4C2×C4×D312yes—
188C2×C3×C4D3×D412yes—
189C2×C3×C4D3×D412yes—
190C2×Dic3—32no—
191C2×Dic3—32no—
192C2×Dic3—32no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C4×D3—34no—
199C4×D3—34no—
200C4×D3—62no—
201C4×D3—62no—
202C4×D3—64no—
203C4×D3—64no—
204C4×D3—64no—
205C4×D3—62no—
206C4×D3—62no—
207C4×D3—128no—
208C4×D3—128no—
209Dic6—128no—
210Dic6—128no—
211Dic6—122no—
212Dic6—122no—
213Dic6—122no—
214Dic6—122no—
215C3×C8—122no—
216C3×C8—122no—
217C3⋊C8—42no—
218C3⋊C8—42no—
219C2×C32C2×#10111yescharacteristic
220C2×C32C2×#10211yescharacteristic
221C2×C32#41911yescharacteristic
222C3⋊D3—22no—
223C2×Q8—21no—
224C2×Q8—182no—
225C2×Q8—181no—
226C2×Q8—362no—
227C2×Q8—362no—
228C22×C4—91no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—182no—
232M16—362no—
233C2×C8—62no—
234C2×C8—62no—
235C4⋊C4—21no—
236C4⋊C4—92no—
237C4⋊C4—182no—
238C4⋊C4—182no—
239C4⋊C4—181no—
240C4⋊C4#62412yes—
241C42—91no—
242C42—91no—
243C42—91no—
244C42C2×D3211yescharacteristic
245C22×C3—21no—
246C22×C3D3×C22⋊C412yes—
247C2×D3—34no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—62no—
251C2×D3—62no—
252C2×D3—62no—
253C3×C4—22no—
254C3×C4—22no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—22no—
258C3×C4—44no—
259C3×C4—44no—
260C3×C4D3×D812yes—
261C3×C4D3×SD1612yes—
262C3×C4#91512yes—
263C3×C4#91812yes—
264Dic3—34no—
265Dic3—34no—
266Dic3—62no—
267Dic3—62no—
268Dic3—62no—
269Dic3—62no—
270Dic3—124no—
271Dic3—124no—
272C32#154611yescharacteristic, complemented, Sylow
273C23—91no—
274Q8—41no—
275Q8—41no—
276Q8—364no—
277Q8—361no—
278Q8—361no—
279C2×C4—22no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—92no—
283C2×C4—92no—
284C2×C4—91no—
285C2×C4—182no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4—364no—
289C2×C4C2×#62411yescharacteristic
290C2×C4#381111yescharacteristic
291C2×C4#381111yescharacteristic
292C8—122no—
293C8—122no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3D3×#10112yes—
298C2×C3D3×#10212yes—
299C2×C3#480212yes—
300D3—64no—
301D3—64no—
302C22—92no—
303C22—181no—
304C22—181no—
305C22#6397411yescharacteristic
306C4—21no—
307C4—42no—
308C4—92no—
309C4—92no—
310C4—181no—
311C4—362no—
312C4#6392611yescharacteristic
313C4#6393011yescharacteristic
314C4#6395112yes—
315C3—21no—
316C3#6842012yescomplemented
317C2—182no—
318C2#1059141611yescharacteristic
319C2#1059156211yescharacteristic
320C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊Q8D32
hypocenterC32#1546
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C3×#4547C2semidirect
5. #10589094C2semidirect
27. #4547D3semidirect
272. C32#1546semidirect
316. C3#68420semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105903402
#105902562
C3×#45472
#105890942
#684203