Finite Group Databasebeta

← #11787788

Subgroups — #11787788

Order 1152.

819 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 819 conjugacy classes of subgroups — too many to draw. Only its 124 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#10595948C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic, complemented
3#10591232C211yesmaximal, characteristic, complemented
4#10591113C212yesmaximal, complemented
5C3×#4523C212yesmaximal, complemented
6#68777—32nomaximal
7C2×#3828C2211yescharacteristic
8C2×#3828C2211yescharacteristic
9C2×C32×C42C2211yescharacteristic
10#64139—22no—
11#64084C411yescharacteristic, complemented
12#64084C411yescharacteristic, complemented
13#64083C411yescharacteristic, complemented
14C4×C4⋊(C3⋊D3)—22no—
15#64078C411yescharacteristic, complemented
16C3×#926C2212yes—
17C2×C3×#208C2212yes—
18#63818—22no—
19#63817—24no—
20#63581—22no—
21#63570—24no—
22#5745—32no—
23#5477—32no—
24#5477—61no—
25#5139—32no—
26#5006—32no—
27#5005—32no—
28C3×#339—32no—
29#4523D312yescomplemented
30C22×C32×C4—21no—
31C22×C32×C4C2311yescharacteristic
32C2×#638—21no—
33C2×#638D412yes—
34#3828—22no—
35#3828—22no—
36#3828—22no—
37#3828—22no—
38C2×C4⋊(C3⋊D3)—22no—
39C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
40C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3D412yes—
43C2×#634C2×C411yescharacteristic
44C2×#634C2×C411yescharacteristic
45C32×C42—21no—
46C32×C42C2×C411yescharacteristic
47C32×C42C2×C411yescharacteristic
48#3752—22no—
49#3752—22no—
50C4⋊(C3⋊Dic3)—22no—
51C3×#217—22no—
52C3×C4⋊Dic3—22no—
53C3×C4×Dic3—22no—
54C3×#208—22no—
55C3×#208D414yescomplemented
56C2×C3×C3⋊C8—22no—
57#3712—24no—
58#3710—24no—
59#1884—91noSylow
60C2×#235—32no—
61C2×#235—32no—
62C2×#235—61no—
63C2×#235—61no—
64C2×C3×M16—32no—
65C3×#117—32no—
66C2×C3×C42—21no—
67C2×C3×C42C2×D312yes—
68#930—64no—
69#930—64no—
70#926C2×D312yes—
71C2×#208C2×D312yes—
72#907—64no—
73D3×M16—64no—
74#901—64no—
75#875—32no—
76#875—32no—
77#875—61no—
78#875—61no—
79#874—32no—
80#874—61no—
81C4×D12—64no—
82C4×D12—64no—
83#869—32no—
84#869—61no—
85#825—64no—
86#806—64no—
87#805—64no—
88C23×C32C2×D411yescharacteristic
89C22×C3⋊D3—21no—
90C22×C3⋊D3C22⋊C412yes—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—42no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D412yes—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4112yes—
98#638—24no—
99#638—42no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3C22⋊C412yes—
102C4⋊(C3⋊D3)—22no—
103C4⋊(C3⋊D3)—22no—
104C4⋊(C3⋊D3)—44no—
105C4×C3⋊D3—22no—
106C4×C3⋊D3—22no—
107C4×C3⋊D3—41no—
108C4×C3⋊D3—41no—
109#634—22no—
110#634—22no—
111C2×C3×Dic3—42no—
112C3×C3⋊C8—24no—
113#568—91no—
114#532—91no—
115#421—92no—
116#410—91no—
117#339—32no—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—21no—
121C22×C3×C4C22×D312yes—
122C2×#67—34no—
123C2×#67—62no—
124C2×#67—62no—
125C2×#67—62no—
126#235—62no—
127#235—62no—
128#235—62no—
129#235—62no—
130#235—62no—
131#235—62no—
132#235—62no—
133#235—62no—
134#235—122no—
135#235—122no—
136#235—122no—
137#235—122no—
138C2×D12—32no—
139C2×D12—32no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—64no—
143C2×D12—64no—
144C2×C4×D3—34no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×Dic6—32no—
149C2×Dic6—32no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C3×M16—34no—
153C3×M16—62no—
154C2×C3×C8—62no—
155C3×C4⋊C4—62no—
156C3×C22⋊C4—62no—
157C3×C42—22no—
158C3×C42—22no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42—62no—
162C3×C42C4×D312yes—
163C3×C42C4×D312yes—
164#217—22no—
165(C2×D3)⋊C4—64no—
166(C2×D3)⋊C4—64no—
167(C2×D3)⋊C4—64no—
168(C2×D3)⋊C4—64no—
169C4⋊Dic3—22no—
170C4⋊Dic3—64no—
171C4⋊Dic3—64no—
172C4×Dic3—22no—
173#208—22no—
174#208D1214yescomplemented
175C2×C3⋊C8—22no—
176ΓL(1,𝔽25)—68no—
177D3×C8—68no—
178C22×C32—41no—
179C22×C32C2×C22⋊C411yescharacteristic
180C22×C32#12112yes—
181C2×C3⋊D3—22no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—41no—
185C32×C4—22no—
186C32×C4—41no—
187C32×C4C4×D412yes—
188C32×C4#12011yescharacteristic
189C32×C4#12311yescharacteristic
190C3⋊Dic3—22no—
191C3⋊Dic3—41no—
192C3×Dic3—82no—
193C2×#41—91no—
194C2×#41—91no—
195#131—184no—
196C2×M16—32no—
197C2×M16—182no—
198C4⋊Q8—91no—
199#127—91no—
200#124—91no—
201#124—91no—
202#121—182no—
203C4×D4—182no—
204#117—32no—
205C2×C42D3211yescharacteristic
206#104—184no—
207#99—182no—
208C23×C3—21no—
209C23×C3D3×D412yes—
210C22×D3—34no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—62no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4—122no—
225C2×C3×C4C2×C4×D312yes—
226C2×C3×C4C2×D1212yes—
227C2×C3×C4#23512yes—
228C2×C3×C4D3×D412yes—
229C2×C3×C4D3×D412yes—
230C2×C3×C4#23912yes—
231#67—64no—
232#67—64no—
233#67—124no—
234#67—124no—
235#67—122no—
236#67—122no—
237C2×Dic3—34no—
238C2×Dic3—42no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242D12—62no—
243D12—62no—
244D12—62no—
245D12—62no—
246D12—122no—
247D12—122no—
248D12—128no—
249D12—128no—
250C4×D3—64no—
251C4×D3—64no—
252C4×D3—122no—
253C4×D3—122no—
254C4×D3—122no—
255C4×D3—122no—
256C4×D3—122no—
257C4×D3—122no—
258Dic6—62no—
259Dic6—62no—
260Dic6—62no—
261Dic6—62no—
262Dic6—122no—
263Dic6—122no—
264C3×C8—64no—
265C3⋊C8—24no—
266C2×C32—21no—
267C2×C32—22no—
268C2×C32#38611yescharacteristic
269C3⋊D3—42no—
270C3⋊D3—81no—
271#41—182no—
272#41—182no—
273#41—182no—
274#41—182no—
275C2×Q8—91no—
276C2×Q8—91no—
277C2×D4—92no—
278C2×D4—91no—
279C2×D4—91no—
280C2×D4—182no—
281C2×D4—181no—
282C22×C4—21no—
283C22×C4—92no—
284C22×C4—181no—
285C22×C4C2×D3211yescharacteristic
286M16—34no—
287M16—62no—
288M16—184no—
289C2×C8—62no—
290C2×C8—184no—
291C4⋊C4—62no—
292C4⋊C4—182no—
293C22⋊C4—62no—
294C22⋊C4—182no—
295C22⋊C4—182no—
296C42—21no—
297C42—62no—
298C42#62411yescharacteristic
299C42#62411yescharacteristic
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—42no—
303C22×C3—42no—
304C22×C3D3×C22⋊C412yes—
305C22×C3#88412yes—
306C22×C3#89512yes—
307C2×D3—64no—
308C2×D3—122no—
309C2×D3—124no—
310C2×D3—122no—
311C2×D3—124no—
312C2×D3—124no—
313C2×D3—124no—
314C2×D3—122no—
315C3×C4—24no—
316C3×C4—24no—
317C3×C4—22no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—42no—
321C3×C4—42no—
322C3×C4—242no—
323C3×C4C4×D1212yes—
324C3×C4#88212yes—
325C3×C4#89312yes—
326C3×C4#89412yes—
327Dic3—64no—
328Dic3—82no—
329Dic3—122no—
330Dic3—122no—
331Dic3—122no—
332C32#188411yescharacteristic, complemented, Sylow
333C23—92no—
334C23—181no—
335C23#381111yescharacteristic
336Q8—182no—
337Q8—182no—
338D4—184no—
339D4—182no—
340D4—182no—
341D4—364no—
342D4—362no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—92no—
347C2×C4—122no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—181no—
351C2×C4—361no—
352C2×C4—361no—
353C2×C4#379912yes—
354C2×C4D3×D1212yes—
355C2×C4C2×#62411yescharacteristic
356C2×C4#381111yescharacteristic
357C8—64no—
358C2×C3—22no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—22no—
362C2×C3—21no—
363C2×C3—42no—
364C2×C3#466512yes—
365D3—124no—
366D3—242no—
367D3—242no—
368D3—242no—
369C22—41no—
370C22—182no—
371C22—362no—
372C22—362no—
373C22—361no—
374C22#6391012yes—
375C22#6397411yescharacteristic
376C4—22no—
377C4—41no—
378C4—182no—
379C4—242no—
380C4—361no—
381C4#6389412yes—
382C4#6389711yescharacteristic
383C4#6392311yescharacteristic
384C3—21no—
385C3#6877712yescomplemented
386C2—21no—
387C2—22no—
388C2—362no—
389C2—721no—
390C2#1059138011yescharacteristic
subgroupG/H
centerC4#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC2×C32#386
prime radical#10595948C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10594780C2semidirect
3. #10591232C2semidirect
4. #10591113C2semidirect
5. C3×#4523C2semidirect
11. #64084C4semidirect
12. #64084C4semidirect
13. #64083C4semidirect
15. #64078C4semidirect
29. #4523D3semidirect
55. C3×#208D4semidirect
174. #208D12semidirect
332. C32#1884semidirect
385. C3#68777semidirect

Maximal subgroups

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

subgroupindex
#105959482
#105947802
#105912322
#105911132
C3×#45232
#687773