Finite Group Databasebeta

← #11873412

Subgroups — #11873412

Order 1152.

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

normal subgroups only

This group has 993 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic
3C3×#5079C212yesmaximal, complemented
4#10591552C214yesmaximal
5#10591538C214yesmaximal, complemented
6C4×#3710C211yesmaximal, characteristic
7#10590288C212yesmaximal, complemented
8D3×#487—32nomaximal
9C2×Q8×C3⋊D3C2212yes—
10C2×#3797—21no—
11C32×C4⋊Q8C2211yescharacteristic
12#64153C2212yes—
13C4⋊C4×C3⋊D3—21no—
14C4⋊C4×C3⋊D3—21no—
15#64097—21no—
16#64097—21no—
17C42×C3⋊D3C2211yescharacteristic
18#64078C2211yescharacteristic
19C3×#869C2212yes—
20#63919—21no—
21#63919C2212yes—
22#63900—21no—
23#63900C2212yes—
24#63873—21no—
25C2×#3710C2212yes—
26C3×#835C2218yes—
27C3×C4×C3⋊C8C2212yes—
28#63567C2218yes—
29#63553C2212yes—
30D3×C4⋊Q8—32no—
31D3×C4⋊Q8—32no—
32D3×C4⋊Q8—61no—
33C3×#487—32no—
34#5093—32no—
35#5079D312yescomplemented
36D3×#103—38no—
37#4792—38no—
38C4×D3×C8—32no—
39#4681—32no—
40C2×C32×Q8C2312yes—
41Q8×C3⋊D3—28no—
42C2×C4×C3⋊D3—22no—
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×#634—22no—
47C2×#634C2312yes—
48C2×C3×Dic6—22no—
49C2×#627—22no—
50C2×#624—22no—
51#3797—44no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57#3750—22no—
58#3750—22no—
59C4×C3⋊Dic3D411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3C2311yescharacteristic
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3C2314yes—
64C2×C3×C3⋊C8C2314yes—
65#3724—22no—
66#3724—22no—
67#3710—24no—
68C2×#487—91noSylow
69C2×D3×Q8—34no—
70C2×D3×Q8—62no—
71C2×D3×Q8—62no—
72C3×C4⋊Q8—21no—
73C3×C4⋊Q8—32no—
74C3×C4⋊Q8C2×D312yes—
75#944—34no—
76#944—62no—
77#944—62no—
78C2×D3×C8—34no—
79D3×C4⋊C4—34no—
80D3×C4⋊C4—62no—
81D3×C4⋊C4—62no—
82D3×C4⋊C4—62no—
83D3×C4⋊C4—62no—
84D3×C4⋊C4—62no—
85#888—34no—
86#888—62no—
87#888—62no—
88#888—62no—
89#888—62no—
90#888—62no—
91C42×D3—32no—
92C42×D3—61no—
93#869—32no—
94#869—61no—
95#869C2×D312yes—
96C3×#103—38no—
97C3×C4×C8—32no—
98#835C2×D318yes—
99#816—38no—
100C8×Dic3—34no—
101#810—38no—
102C4×C3⋊C8C2×D312yes—
103C22×C3⋊D3C2×D411yescharacteristic
104C32×Q8—24no—
105C2×C32×C4—22no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2411yescharacteristic
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3C2×D411yescharacteristic
111C2×C3⋊Dic3C2×D411yescharacteristic
112C2×C3⋊Dic3C2×D411yescharacteristic
113C4×C3⋊D3—44no—
114C4×C3⋊D3SD1614yes—
115C4×C3⋊D3Q1614yes—
116C4×C3⋊D3#4114yes—
117#634—24no—
118#634—44no—
119C2×C3×Dic3—24no—
120C3×Dic6—44no—
121#627—44no—
122#624—44no—
123C3×C3⋊C8—24no—
124C2×C4⋊Q8—91no—
125C2×C4⋊Q8—91no—
126#487—32no—
127#487—92no—
128#487—94no—
129C2×#103—94no—
130C2×C4×C8—91no—
131C2×C3×Q8—22no—
132C2×C3×Q8—62no—
133C2×C3×Q8C22×D314yes—
134D3×Q8—616no—
135D3×Q8—128no—
136D3×Q8—128no—
137C2×C4×D3—32no—
138C2×C4×D3—32no—
139C2×C4×D3—32no—
140C2×C4×D3—61no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×C4×D3—64no—
144C2×C4×D3—64no—
145C2×C4×D3—64no—
146C2×Dic6—22no—
147C2×Dic6—34no—
148C2×Dic6—62no—
149C2×Dic6—64no—
150C2×Dic6—64no—
151C2×Dic6—64no—
152C2×C3×C8—34no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—34no—
158C3×C4⋊C4—62no—
159C3×C42—21no—
160C3×C42C22×D312yes—
161C4⋊Dic3—22no—
162C4⋊Dic3—62no—
163C4⋊Dic3—62no—
164C4⋊Dic3—62no—
165C4⋊Dic3—62no—
166C4⋊Dic3C22×D314yes—
167Dic3⋊C4—64no—
168Dic3⋊C4—64no—
169Dic3⋊C4—64no—
170Dic3⋊C4—64no—
171Dic3⋊C4—64no—
172Dic3⋊C4—64no—
173C4×Dic3—32no—
174C4×Dic3—32no—
175C4×Dic3—32no—
176C4×Dic3—61no—
177C4×Dic3—61no—
178C4×Dic3—61no—
179C2×C3⋊C8C22×D314yes—
180D3×C8—68no—
181C22×C32C22×D411yescharacteristic
182C2×C3⋊D3#12412yes—
183C2×C3⋊D3C2×SD1612yes—
184C2×C3⋊D3C2×Q1612yes—
185C32×C4—42no—
186C32×C4C2×SD1612yes—
187C32×C4C2×Q1612yes—
188C32×C4C2×#4112yes—
189C3⋊Dic3—42no—
190C3⋊Dic3#12412yes—
191C3⋊Dic3C2×SD1612yes—
192C3⋊Dic3C2×Q1612yes—
193C3×Dic3—44no—
194C22×Q8—92no—
195C22×Q8—181no—
196C22×C8—92no—
197C4⋊Q8—32no—
198C4⋊Q8—92no—
199C4⋊Q8—92no—
200C4⋊Q8—91no—
201C4⋊Q8—181no—
202C4⋊Q8—181no—
203C4⋊Q8—181no—
204C4⋊Q8—181no—
205C4⋊Q8D3211yescharacteristic
206C2×C4⋊C4—92no—
207C2×C4⋊C4—181no—
208C2×C4⋊C4—181no—
209C2×C4⋊C4—181no—
210C2×C42—91no—
211#103—38no—
212#103—98no—
213C4×C8—32no—
214C4×C8—92no—
215C22×D3—32no—
216C22×D3—61no—
217C3×Q8—28no—
218C3×Q8—44no—
219C3×Q8—124no—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—64no—
226C2×C3×C4D3×D412yes—
227C2×C3×C4D3×D412yes—
228C2×C3×C4C23×D312yes—
229C2×Dic3—24no—
230C2×Dic3—32no—
231C2×Dic3—32no—
232C2×Dic3—32no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C4×D3—38no—
239C4×D3—38no—
240C4×D3—38no—
241C4×D3—64no—
242C4×D3—64no—
243C4×D3—64no—
244C4×D3—128no—
245C4×D3—128no—
246C4×D3—128no—
247Dic6—44no—
248Dic6—68no—
249Dic6—124no—
250Dic6—128no—
251Dic6—128no—
252Dic6—128no—
253C3×C8—64no—
254C3⋊C8—24no—
255C2×C32C2×#12411yescharacteristic
256C2×C32C22×SD1611yescharacteristic
257C2×C32C22×Q1611yescharacteristic
258C3⋊D3#48714yescomplemented
259C2×Q8—62no—
260C2×Q8—92no—
261C2×Q8—182no—
262C2×Q8—182no—
263C2×Q8—188no—
264C2×Q8—364no—
265C2×Q8C2×D3212yes—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—91no—
269C22×C4—182no—
270C22×C4—182no—
271C2×C8—34no—
272C2×C8—184no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—34no—
276C4⋊C4—62no—
277C4⋊C4—182no—
278C4⋊C4—182no—
279C4⋊C4—182no—
280C4⋊C4—182no—
281C4⋊C4—181no—
282C4⋊C4—181no—
283C42—91no—
284C42—91no—
285C42—91no—
286C42C2×D3211yescharacteristic
287C22×C3—21no—
288C22×C3C2×D3×D412yes—
289C2×D3—34no—
290C2×D3—34no—
291C2×D3—34no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—62no—
295C3×C4—22no—
296C3×C4—22no—
297C3×C4—22no—
298C3×C4—44no—
299C3×C4—44no—
300C3×C4—124no—
301C3×C4D3×SD1614yes—
302C3×C4D3×Q1614yes—
303C3×C4D3×#4114yes—
304Dic3—34no—
305Dic3—34no—
306Dic3—34no—
307Dic3—44no—
308Dic3—62no—
309Dic3—62no—
310Dic3—62no—
311Dic3—124no—
312Dic3—124no—
313C32C2×#48711yescharacteristic, complemented, Sylow
314C23—91no—
315Q8—24no—
316Q8—124no—
317Q8—184no—
318Q8—364no—
319Q8—364no—
320C2×C4—22no—
321C2×C4—64no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—94no—
326C2×C4—94no—
327C2×C4—94no—
328C2×C4—182no—
329C2×C4—364no—
330C2×C4—364no—
331C2×C4#381111yescharacteristic
332C2×C4#381111yescharacteristic
333C2×C4C22×D3211yescharacteristic
334C8—64no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3D3×#12412yes—
339C2×C3C2×D3×SD1612yes—
340C2×C3C2×D3×Q1612yes—
341D3—38no—
342D3—64no—
343C22—92no—
344C22—92no—
345C22—92no—
346C22C2×#381111yescharacteristic
347C4—42no—
348C4—92no—
349C4—92no—
350C4—92no—
351C4—124no—
352C4—362no—
353C4#6394012yes—
354C4#6394412yes—
355C4#6431212yes—
356C3—21no—
357C3D3×#48712yescomplemented
358C2—94no—
359C2#1059517011yescharacteristic
360C2C2×#6394011yescharacteristic
361C2C2×#6394411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32C2×#487
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5079C2semidirect
5. #10591538C2semidirect
7. #10590288C2semidirect
35. #5079D3semidirect
258. C3⋊D3#487semidirect
313. C32C2×#487semidirect
357. C3D3×#487semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105939092
C3×#50792
#105915522
#105915382
C4×#37102
#105902882
D3×#4873