Finite Group Databasebeta

← #11787764

Subgroups — #11787764

Order 1152.

996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 179 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#10596216C211yesmaximal, characteristic, complemented
2#10595948C211yesmaximal, characteristic
3#10592838C211yesmaximal, characteristic, complemented
4#10592705C211yesmaximal, characteristic, complemented
5#10592704C211yesmaximal, characteristic, complemented
6C32×#339C211yesmaximal, characteristic, complemented
7#10589389C211yesmaximal, characteristic, complemented
8#68777—34nomaximal
9C2×#3828C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14#64139—22no—
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17#64116—22no—
18M16×C3⋊D3—22no—
19#64110—22no—
20#64084C411yescharacteristic, complemented
21#64084C411yescharacteristic, complemented
22#64083C411yescharacteristic, complemented
23C4×C4⋊(C3⋊D3)—22no—
24#64078C411yescharacteristic, complemented
25#63652—22no—
26#63633—22no—
27#63632—22no—
28#5745—34no—
29#5477—34no—
30#5139—34no—
31#5006—34no—
32#5005—34no—
33C3×#339D314yescomplemented
34#4523—34no—
35C22×C32×C4—21no—
36C22×C32×C4C2311yescharacteristic
37C2×#638—21no—
38C2×#638D412yes—
39#3828—21no—
40#3828—21no—
41#3828—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47C2×C4⋊(C3⋊D3)—22no—
48C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3D412yes—
52C2×#634C2×C411yescharacteristic
53C2×#634C2×C411yescharacteristic
54C32×M16—21no—
55C32×M16D412yescomplemented
56C2×C32×C8—21no—
57C32×C4⋊C4—21no—
58C32×C22⋊C4—21no—
59C32×C42—21no—
60C32×C42—21no—
61C32×C42C2×C411yescharacteristic
62C32×C42C2×C411yescharacteristic
63#3757—21no—
64#3752—22no—
65#3752—22no—
66C4⋊(C3⋊Dic3)—22no—
67C4⋊(C3⋊Dic3)—21no—
68C4×C3⋊Dic3—21no—
69#3748—21no—
70#3748D412yescomplemented
71C2×C3⋊(C3⋊C8)—21no—
72#3743—24no—
73C8×C3⋊D3—24no—
74#1884—91noSylow
75C2×#235—34no—
76C2×#235—34no—
77C2×C3×M16C2×D314yes—
78C3×#117C2×D314yes—
79C2×C3×C42C2×D314yes—
80#930—68no—
81#926—34no—
82C2×#208—34no—
83#907—68no—
84D3×M16—68no—
85#901—68no—
86#875—34no—
87#875—34no—
88#874—34no—
89C4×D12—68no—
90#869—34no—
91#825—68no—
92#806—68no—
93#805—68no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3⋊D3C22⋊C412yes—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—42no—
100C2×C32×C4—41no—
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C32×C4#4111yescharacteristic
107#638—22no—
108#638—22no—
109#638—41no—
110#638—41no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3C22⋊C412yes—
114C4⋊(C3⋊D3)—21no—
115C4⋊(C3⋊D3)—21no—
116C4⋊(C3⋊D3)—21no—
117C4⋊(C3⋊D3)—21no—
118C4⋊(C3⋊D3)—44no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—41no—
122C4×C3⋊D3—41no—
123#634—21no—
124#634—21no—
125#634—21no—
126#634—21no—
127C32×C8—22no—
128C3⋊(C3⋊C8)—22no—
129#568—91no—
130#532—91no—
131#421—91no—
132#421—91no—
133#410—91no—
134#339—91no—
135#339C3⋊D311yescharacteristic, complemented
136C22×C3×C4—24no—
137C22×C3×C4C22×D314yes—
138C2×#67—38no—
139C2×#67—64no—
140#235—64no—
141#235—64no—
142#235—64no—
143#235—64no—
144#235—64no—
145#235—64no—
146#235—64no—
147#235—64no—
148C2×D12—34no—
149C2×D12—34no—
150C2×D12—68no—
151C2×C4×D3—38no—
152C2×C4×D3—64no—
153C2×Dic6—34no—
154C2×Dic6—34no—
155C3×M16—24no—
156C3×M16D1218yescomplemented
157C2×C3×C8—24no—
158C3×C4⋊C4—24no—
159C3×C22⋊C4—24no—
160C3×C42—24no—
161C3×C42—24no—
162C3×C42C4×D314yes—
163C3×C42C4×D314yes—
164#217—64no—
165(C2×D3)⋊C4—68no—
166(C2×D3)⋊C4—68no—
167C4⋊Dic3—68no—
168C4⋊Dic3—64no—
169C4×Dic3—64no—
170#208—38no—
171#208—64no—
172C2×C3⋊C8—64no—
173ΓL(1,𝔽25)—616no—
174D3×C8—616no—
175C22×C32—41no—
176C22×C32C2×C22⋊C411yescharacteristic
177C22×C32#12111yescharacteristic
178C22×C32#12111yescharacteristic
179C2×C3⋊D3—22no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—41no—
183C32×C4—22no—
184C32×C4—41no—
185C32×C4—81no—
186C32×C4C4×D411yescharacteristic
187C32×C4C4×D411yescharacteristic
188C32×C4#12011yescharacteristic
189C32×C4#12311yescharacteristic
190C3⋊Dic3—22no—
191C3⋊Dic3—41no—
192C3⋊Dic3—81no—
193C2×#41—91no—
194C2×#41—91no—
195#131—182no—
196#131—182no—
197C2×M16—91no—
198C2×M16—182no—
199C2×M16C2×C3⋊D311yescharacteristic
200C4⋊Q8—91no—
201#127—91no—
202#124—91no—
203#124—91no—
204#121—182no—
205C4×D4—182no—
206#117—91no—
207#117C2×C3⋊D311yescharacteristic
208C2×C42C2×C3⋊D311yescharacteristic
209#104—182no—
210#104—182no—
211#99—182no—
212C23×C3D3×D414yes—
213C22×D3—38no—
214C22×D3—64no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—48no—
218C2×C3×C4—44no—
219C2×C3×C4C2×C4×D314yes—
220C2×C3×C4C2×D1214yes—
221C2×C3×C4#23514yes—
222C2×C3×C4D3×D414yes—
223C2×C3×C4D3×D414yes—
224C2×C3×C4#23914yes—
225#67—68no—
226#67—68no—
227#67—124no—
228#67—124no—
229C2×Dic3—38no—
230C2×Dic3—64no—
231C2×Dic3—124no—
232D12—64no—
233D12—64no—
234D12—64no—
235D12—64no—
236D12—1216no—
237C4×D3—68no—
238C4×D3—68no—
239C4×D3—124no—
240C4×D3—124no—
241Dic6—64no—
242Dic6—64no—
243Dic6—64no—
244Dic6—64no—
245C3×C8—28no—
246C3⋊C8—68no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32—21no—
250C2×C32#38611yescharacteristic
251C3⋊D3—42no—
252C3⋊D3—81no—
253#41—181no—
254#41—181no—
255#41—181no—
256#41—181no—
257#41—181no—
258#41—181no—
259#41—181no—
260#41—181no—
261C2×Q8—91no—
262C2×Q8—91no—
263C2×D4—92no—
264C2×D4—91no—
265C2×D4—91no—
266C2×D4—182no—
267C2×D4—181no—
268C22×C4—21no—
269C22×C4—92no—
270C22×C4—181no—
271C22×C4C22×C3⋊D311yescharacteristic
272M16—21no—
273M16—92no—
274M16—184no—
275M16—181no—
276M16C4⋊(C3⋊D3)12yescomplemented
277C2×C8—21no—
278C2×C8—184no—
279C2×C8—181no—
280C4⋊C4—21no—
281C4⋊C4—182no—
282C4⋊C4—181no—
283C22⋊C4—21no—
284C22⋊C4—182no—
285C22⋊C4—182no—
286C22⋊C4—181no—
287C42—21no—
288C42—21no—
289C42—181no—
290C42C4×C3⋊D311yescharacteristic
291C42C4×C3⋊D311yescharacteristic
292C22×C3—44no—
293C22×C3D3×C22⋊C414yes—
294C22×C3#88414yes—
295C22×C3#89514yes—
296C2×D3—68no—
297C2×D3—128no—
298C2×D3—128no—
299C2×D3—124no—
300C3×C4—28no—
301C3×C4—44no—
302C3×C4—84no—
303C3×C4C4×D1214yes—
304C3×C4#88214yes—
305C3×C4#89314yes—
306C3×C4#89414yes—
307Dic3—68no—
308Dic3—124no—
309Dic3—244no—
310C32#188411yescharacteristic, complemented, Sylow
311C23—92no—
312C23—181no—
313C23D4×C3⋊D311yescharacteristic
314Q8—181no—
315Q8—181no—
316Q8—181no—
317Q8—181no—
318D4—182no—
319D4—182no—
320D4—181no—
321D4—181no—
322D4—181no—
323D4—181no—
324D4—364no—
325D4—361no—
326D4—361no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—92no—
332C2×C4—182no—
333C2×C4—182no—
334C2×C4—181no—
335C2×C4—361no—
336C2×C4—361no—
337C2×C4—361no—
338C2×C4C2×C4×C3⋊D311yescharacteristic
339C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
340C2×C4#382811yescharacteristic
341C2×C4D4×C3⋊D311yescharacteristic
342C2×C4D4×C3⋊D311yescharacteristic
343C2×C4#383211yescharacteristic
344C8—22no—
345C8—182no—
346C2×C3—24no—
347C2×C3—24no—
348C2×C3—24no—
349C2×C3#466514yes—
350D3—128no—
351D3—244no—
352C22—41no—
353C22—182no—
354C22—362no—
355C22—362no—
356C22—361no—
357C22C22⋊C4×C3⋊D311yescharacteristic
358C22#6409311yescharacteristic
359C22#6410411yescharacteristic
360C4—22no—
361C4—41no—
362C4—81no—
363C4—182no—
364C4—361no—
365C4—721no—
366C4C4×C4⋊(C3⋊D3)11yescharacteristic
367C4#6409111yescharacteristic
368C4#6410211yescharacteristic
369C4#6410311yescharacteristic
370C3#6877714yescomplemented
371C2—21no—
372C2—21no—
373C2—21no—
374C2—362no—
375C2—721no—
376C2#1059236411yescharacteristic
subgroupG/H
centerC4#64091
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC2×C32#386
prime radical#10595948C2
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #10596216C2semidirect
3. #10592838C2semidirect
4. #10592705C2semidirect
5. #10592704C2semidirect
6. C32×#339C2semidirect
7. #10589389C2semidirect
20. #64084C4semidirect
21. #64084C4semidirect
22. #64083C4semidirect
24. #64078C4semidirect
33. C3×#339D3semidirect
55. C32×M16D4semidirect
70. #3748D4semidirect
135. #339C3⋊D3semidirect
156. C3×M16D12semidirect
276. M16C4⋊(C3⋊D3)semidirect
310. C32#1884semidirect
370. C3#68777semidirect

Maximal subgroups

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

subgroupindex
#105962162
#105959482
#105928382
#105927052
#105927042
C32×#3392
#105893892
#687773