Finite Group Databasebeta

← #11873401

Subgroups — #11873401

Order 1152.

929 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 929 conjugacy classes of subgroups — too many to draw. Only its 192 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#10593909C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic
3C4×C8×C3⋊D3C211yesmaximal, characteristic
4C3×#4681C212yesmaximal, complemented
5#10590901C214yesmaximal, complemented
6#10590672C214yesmaximal
7#10590290C212yesmaximal, complemented
8D3×#487—32nomaximal
9C2×#3797—21no—
10C2×#3797C2212yes—
11C2×C8×C3⋊D3C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13C3×#869C2212yes—
14C3×#869C2212yes—
15#63919—21no—
16#63919—21no—
17#63919—21no—
18#63919C2212yes—
19#63900—21no—
20#63900—21no—
21#63900—21no—
22#63900C2212yes—
23#63873—21no—
24#63873C2212yes—
25C32×C4×C8C2211yescharacteristic
26C8×C3⋊Dic3C2212yes—
27C4×C3⋊(C3⋊C8)C2211yescharacteristic
28C3×#816C2218yes—
29#63565C2218yes—
30D3×C4⋊Q8—32no—
31D3×C4⋊Q8—32no—
32C3×#487—32no—
33#5093—32no—
34#5079—32no—
35D3×#103—38no—
36#4792—38no—
37C4×D3×C8—32no—
38C4×D3×C8—61no—
39#4681D312yescomplemented
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3C2311yescharacteristic
43C2×C3×Dic6—22no—
44C2×C3×Dic6C2314yes—
45C2×#627—22no—
46C2×#627—22no—
47C2×#624—22no—
48C2×#624—22no—
49#3797—28no—
50#3797—44no—
51C2×C32×C8C2312yes—
52C32×C42C2311yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3C2311yescharacteristic
56C2×C3⋊(C3⋊C8)C2312yes—
57C8×C3⋊D3—24no—
58C3×C4⋊Dic3—22no—
59C3×C4⋊Dic3—22no—
60C3×C4⋊Dic3—22no—
61C3×C4⋊Dic3C2314yes—
62#3724—22no—
63#3724—22no—
64#3724—22no—
65#3724—22no—
66C2×#487—91noSylow
67C2×D3×Q8—34no—
68C2×D3×Q8—62no—
69C3×C4⋊Q8—32no—
70C3×C4⋊Q8—32no—
71#944—34no—
72#944—62no—
73C2×D3×C8—34no—
74C2×D3×C8—62no—
75D3×C4⋊C4—34no—
76D3×C4⋊C4—62no—
77D3×C4⋊C4—62no—
78D3×C4⋊C4—62no—
79#888—34no—
80#888—62no—
81#888—62no—
82#888—62no—
83C42×D3—32no—
84C42×D3—61no—
85#869C2×D312yes—
86#869C2×D312yes—
87C3×#103—38no—
88C3×C4×C8—21no—
89C3×C4×C8C2×D312yes—
90#835—38no—
91#816C2×D318yes—
92C8×Dic3—34no—
93C8×Dic3—62no—
94#810—38no—
95C4×C3⋊C8—32no—
96C4×C3⋊C8—61no—
97C22×C3⋊D3C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2411yescharacteristic
101C2×C3⋊Dic3C2×D411yescharacteristic
102C2×C3⋊Dic3C2×D411yescharacteristic
103C2×C3⋊Dic3C2×D411yescharacteristic
104C4×C3⋊D3SD1614yes—
105C4×C3⋊D3Q1614yes—
106C4×C3⋊D3#4114yes—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C3×Dic6—28no—
110C3×Dic6—44no—
111#627—44no—
112#627—44no—
113#624—44no—
114#624—44no—
115C32×C8—22no—
116C3⋊(C3⋊C8)—22no—
117C2×C4⋊Q8—91no—
118C2×C4⋊Q8—91no—
119#487—32no—
120#487—94no—
121#487—92no—
122C2×#103—94no—
123C2×C4×C8—91no—
124C2×C3×Q8—34no—
125C2×C3×Q8—62no—
126D3×Q8—616no—
127D3×Q8—128no—
128C2×C4×D3—32no—
129C2×C4×D3—32no—
130C2×C4×D3—32no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—64no—
135C2×C4×D3—64no—
136C2×Dic6—22no—
137C2×Dic6—64no—
138C2×Dic6—64no—
139C2×Dic6C22×D314yes—
140C2×C3×C8—22no—
141C2×C3×C8C22×D314yes—
142C3×C4⋊C4—34no—
143C3×C4⋊C4—62no—
144C3×C4⋊C4—62no—
145C3×C4⋊C4—62no—
146C3×C42—21no—
147C3×C42C22×D312yes—
148C4⋊Dic3—22no—
149C4⋊Dic3—22no—
150C4⋊Dic3—22no—
151C4⋊Dic3C22×D314yes—
152Dic3⋊C4—64no—
153Dic3⋊C4—64no—
154Dic3⋊C4—64no—
155Dic3⋊C4—64no—
156C4×Dic3—32no—
157C4×Dic3—32no—
158C4×Dic3—32no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C2×C3⋊C8—34no—
163C2×C3⋊C8—62no—
164D3×C8—68no—
165D3×C8—68no—
166C22×C32C22×D411yescharacteristic
167C2×C3⋊D3#12412yes—
168C2×C3⋊D3C2×SD1612yes—
169C2×C3⋊D3C2×Q1612yes—
170C32×C4C2×SD1612yes—
171C32×C4C2×Q1612yes—
172C32×C4C2×#4112yes—
173C3⋊Dic3#12412yes—
174C3⋊Dic3C2×SD1612yes—
175C3⋊Dic3C2×Q1612yes—
176C3×Dic3—44no—
177C3×Dic3—44no—
178C22×Q8—92no—
179C22×Q8—181no—
180C22×C8—92no—
181C4⋊Q8—32no—
182C4⋊Q8—32no—
183C4⋊Q8—92no—
184C4⋊Q8—92no—
185C4⋊Q8—181no—
186C4⋊Q8—181no—
187C4⋊Q8—181no—
188C4⋊Q8—181no—
189C2×C4⋊C4—92no—
190C2×C4⋊C4—181no—
191C2×C4⋊C4—181no—
192C2×C4⋊C4—181no—
193C2×C42—91no—
194#103—38no—
195#103—98no—
196C4×C8—92no—
197C4×C8—91no—
198C4×C8D3211yescharacteristic
199C22×D3—32no—
200C22×D3—61no—
201C3×Q8—68no—
202C3×Q8—124no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—64no—
207C2×C3×C4—64no—
208C2×C3×C4D3×D412yes—
209C2×C3×C4D3×D412yes—
210C2×C3×C4C23×D312yes—
211C2×Dic3—24no—
212C2×Dic3—24no—
213C2×Dic3—32no—
214C2×Dic3—32no—
215C2×Dic3—32no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C4×D3—38no—
220C4×D3—38no—
221C4×D3—38no—
222C4×D3—64no—
223C4×D3—64no—
224C4×D3—64no—
225C4×D3—128no—
226C4×D3—128no—
227Dic6—28no—
228Dic6—44no—
229Dic6—128no—
230Dic6—128no—
231C3×C8—24no—
232C3×C8—24no—
233C3⋊C8—64no—
234C3⋊C8—64no—
235C2×C32C2×#12411yescharacteristic
236C2×C32C22×SD1611yescharacteristic
237C2×C32C22×Q1611yescharacteristic
238C3⋊D3#48714yescomplemented
239C2×Q8—34no—
240C2×Q8—62no—
241C2×Q8—182no—
242C2×Q8—182no—
243C2×Q8—188no—
244C2×Q8—364no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—182no—
249C22×C4—182no—
250C2×C8—92no—
251C2×C8—184no—
252C2×C8C2×D3212yes—
253C4⋊C4—34no—
254C4⋊C4—62no—
255C4⋊C4—62no—
256C4⋊C4—62no—
257C4⋊C4—182no—
258C4⋊C4—182no—
259C4⋊C4—182no—
260C4⋊C4—182no—
261C42—91no—
262C42—91no—
263C42—91no—
264C42C2×D3211yescharacteristic
265C22×C3—21no—
266C22×C3C2×D3×D412yes—
267C2×D3—34no—
268C2×D3—34no—
269C2×D3—34no—
270C2×D3—62no—
271C2×D3—62no—
272C2×D3—62no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—124no—
277C3×C4—124no—
278C3×C4D3×SD1614yes—
279C3×C4D3×Q1614yes—
280C3×C4D3×#4114yes—
281Dic3—34no—
282Dic3—34no—
283Dic3—34no—
284Dic3—44no—
285Dic3—44no—
286Dic3—62no—
287Dic3—62no—
288Dic3—62no—
289C32C2×#48711yescharacteristic, complemented, Sylow
290C23—91no—
291Q8—68no—
292Q8—124no—
293Q8—364no—
294Q8—364no—
295C2×C4—64no—
296C2×C4—64no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—94no—
301C2×C4—94no—
302C2×C4—94no—
303C2×C4—364no—
304C2×C4—364no—
305C2×C4#380211yescharacteristic
306C2×C4#380211yescharacteristic
307C2×C4C22×D3211yescharacteristic
308C8—22no—
309C8—182no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3D3×#12412yes—
314C2×C3C2×D3×SD1612yes—
315C2×C3C2×D3×Q1612yes—
316D3—38no—
317D3—64no—
318C22—92no—
319C22—92no—
320C22—92no—
321C22C2×#380211yescharacteristic
322C4—92no—
323C4—92no—
324C4—92no—
325C4—124no—
326C4—124no—
327C4#6379612yes—
328C4#6380212yes—
329C4#6430612yes—
330C3—21no—
331C3D3×#48712yescomplemented
332C2—94no—
333C2#1059400911yescharacteristic
334C2C2×#6379611yescharacteristic
335C2C2×#6380211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×C8D32
hypocenterC32C2×#487
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
4. C3×#4681C2semidirect
5. #10590901C2semidirect
7. #10590290C2semidirect
39. #4681D3semidirect
238. C3⋊D3#487semidirect
289. C32C2×#487semidirect
331. C3D3×#487semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×C8×C3⋊D32
C3×#46812
#105909012
#105906722
#105902902
D3×#4873