Finite Group Databasebeta

← #11873365

Subgroups — #11873365

Order 1152.

1137 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 1137 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#10594008C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic, complemented
3C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×#4694C212yesmaximal, complemented
5#10590940C214yesmaximal, complemented
6#10590885C214yesmaximal, complemented
7#10590277C212yesmaximal, complemented
8D3×#486—32nomaximal
9C2×#3802—21no—
10C2×#3802—21no—
11C2×#3802C2212yes—
12C2×#3797—21no—
13C2×C8×C3⋊D3C2212yes—
14C42×C3⋊D3C2211yescharacteristic
15C3×#874C2212yes—
16C3×#869C2212yescomplemented
17#63919—21no—
18#63919C2212yescomplemented
19#63914—21no—
20#63914—21no—
21#63914C2212yes—
22#63900—21no—
23#63900C2212yes—
24#63873—21no—
25C32×C4×C8C2211yescharacteristic, complemented
26C8×C3⋊Dic3C2212yescomplemented
27C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C3×#821C2218yescomplemented
29#63562C2218yescomplemented
30D3×C4⋊Q8—32no—
31D3×#127—32no—
32C3×#486—32no—
33#5088—32no—
34#5070—32no—
35D3×#102—38no—
36#4760—38no—
37#4694D312yescomplemented
38C4×D3×C8—32no—
39C4×D3×C8—61no—
40C22×D32—22no—
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C3×D12—22no—
45C2×C3×D12—22no—
46C2×C3×D12C2314yes—
47C2×C3×Dic6—22no—
48C2×#627—22no—
49C2×#625—22no—
50C2×#625—22no—
51C2×#625—22no—
52C2×#624—22no—
53#3802—28no—
54#3802—44no—
55#3802—44no—
56#3797—44no—
57C2×C32×C8C2312yes—
58C32×C42C2311yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3C2311yescharacteristic
62C2×C3⋊(C3⋊C8)C2312yes—
63C8×C3⋊D3—24no—
64C3×C4⋊Dic3—22no—
65C3×C4⋊Dic3C2314yes—
66#3724—22no—
67#3724—22no—
68C2×#486—91noSylow
69C2×D3×Q8—62no—
70C2×D3×D4—34no—
71C2×D3×D4—62no—
72C2×D3×D4—62no—
73C3×C4⋊Q8—32no—
74C3×#127—32no—
75#944—62no—
76#940—34no—
77#940—62no—
78#940—62no—
79C2×D3×C8—34no—
80C2×D3×C8—62no—
81D3×C4⋊C4—34no—
82D3×C4⋊C4—62no—
83#888—34no—
84#888—62no—
85#874C2×D312yes—
86C42×D3—32no—
87C42×D3—61no—
88#869C2×D312yescomplemented
89C3×#102—38no—
90C3×C4×C8—21no—
91C3×C4×C8C2×D312yescomplemented
92#832—38no—
93#821C2×D318yescomplemented
94C8×Dic3—34no—
95C8×Dic3—62no—
96#809—38no—
97C4×C3⋊C8—32no—
98C4×C3⋊C8—61no—
99C22×C3⋊D3C2×D411yescharacteristic
100C22×C3×D3—24no—
101C2×D32—44no—
102C2×D32—44no—
103C2×D32—44no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2411yescharacteristic
107C2×C3⋊Dic3C2×D411yescharacteristic
108C2×C3⋊Dic3C2×D411yescharacteristic
109C2×C3⋊Dic3C2×D411yescharacteristic
110C4×C3⋊D3D814yes—
111C4×C3⋊D3SD1614yes—
112C4×C3⋊D3#4114yes—
113C2×C3×Dic3—24no—
114C3×D12—28no—
115C3×D12—44no—
116C3×D12—44no—
117C3×Dic6—44no—
118#627—44no—
119#625—44no—
120#625—44no—
121#625—44no—
122#624—44no—
123C32×C8—22no—
124C3⋊(C3⋊C8)—22no—
125C2×C4⋊Q8—91no—
126C2×#127—91no—
127#486—32no—
128#486—94no—
129#486—92no—
130C2×#102—94no—
131C2×C4×C8—91no—
132C23×D3—64no—
133C2×C3×Q8—62no—
134C2×C3×D4—34no—
135C2×C3×D4—62no—
136C2×C3×D4—62no—
137C2×#67—64no—
138C2×#67—64no—
139C2×#67—64no—
140D3×Q8—128no—
141D3×D4—616no—
142D3×D4—128no—
143D3×D4—128no—
144C2×D12—22no—
145C2×D12—22no—
146C2×D12C22×D314yes—
147C2×C4×D3—32no—
148C2×C4×D3—32no—
149C2×C4×D3—32no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—64no—
154C2×Dic6—22no—
155C2×Dic6—64no—
156C2×C3×C8—22no—
157C2×C3×C8C22×D314yes—
158C3×C4⋊C4—34no—
159C3×C4⋊C4—62no—
160C3×C42—21no—
161C3×C42C22×D312yes—
162C4⋊Dic3—22no—
163C4⋊Dic3C22×D314yes—
164Dic3⋊C4—64no—
165Dic3⋊C4—64no—
166C4×Dic3—32no—
167C4×Dic3—32no—
168C4×Dic3—32no—
169C4×Dic3—61no—
170C4×Dic3—61no—
171C4×Dic3—61no—
172C2×C3⋊C8—34no—
173C2×C3⋊C8—62no—
174D3×C8—68no—
175D3×C8—68no—
176C22×C32C22×D411yescharacteristic
177C2×C3⋊D3#12412yes—
178C2×C3⋊D3C2×D812yes—
179C2×C3⋊D3C2×SD1612yes—
180C2×C3×D3—44no—
181C2×C3×D3—44no—
182C2×C3×D3—44no—
183D32—88no—
184C32×C4C2×D812yes—
185C32×C4C2×SD1612yes—
186C32×C4C2×#4112yes—
187C3⋊Dic3#12412yes—
188C3⋊Dic3C2×D812yes—
189C3⋊Dic3C2×SD1612yes—
190C3×Dic3—44no—
191C22×Q8—181no—
192C22×D4—92no—
193C22×D4—181no—
194C22×D4—181no—
195C22×C8—92no—
196C4⋊Q8—32no—
197C4⋊Q8—92no—
198C4⋊Q8—181no—
199C4⋊Q8—181no—
200#127—32no—
201#127—92no—
202#127—181no—
203#127—181no—
204C2×C4⋊C4—92no—
205C2×C4⋊C4—181no—
206C2×C42—91no—
207#102—38no—
208#102—98no—
209C4×C8—92no—
210C4×C8—91no—
211C4×C8D3211yescharacteristic, complemented
212C23×C3—64no—
213C22×D3—24no—
214C22×D3—32no—
215C22×D3—61no—
216C22×D3—128no—
217C22×D3—128no—
218C22×D3—128no—
219C3×Q8—124no—
220C3×D4—68no—
221C3×D4—124no—
222C3×D4—124no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—64no—
227C2×C3×C4D3×D412yes—
228C2×C3×C4D3×D412yes—
229C2×C3×C4C23×D312yes—
230#67—128no—
231#67—128no—
232#67—128no—
233C2×Dic3—24no—
234C2×Dic3—32no—
235C2×Dic3—32no—
236C2×Dic3—32no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240D12—28no—
241D12—44no—
242D12—44no—
243C4×D3—38no—
244C4×D3—38no—
245C4×D3—38no—
246C4×D3—64no—
247C4×D3—64no—
248C4×D3—64no—
249C4×D3—128no—
250Dic6—44no—
251Dic6—128no—
252C3×C8—24no—
253C3×C8—24no—
254C3⋊C8—64no—
255C3⋊C8—64no—
256C2×C32C2×#12411yescharacteristic
257C2×C32C22×D811yescharacteristic
258C2×C32C22×SD1611yescharacteristic
259C3⋊D3#48614yescomplemented
260C3×D3—84no—
261C24—182no—
262C2×Q8—62no—
263C2×Q8—182no—
264C2×Q8—364no—
265C2×D4—34no—
266C2×D4—62no—
267C2×D4—62no—
268C2×D4—188no—
269C2×D4—182no—
270C2×D4—182no—
271C2×D4—182no—
272C2×D4—364no—
273C2×D4—364no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—182no—
278C2×C8—92no—
279C2×C8—184no—
280C2×C8C2×D3212yes—
281C4⋊C4—34no—
282C4⋊C4—62no—
283C4⋊C4—182no—
284C4⋊C4—182no—
285C42—91no—
286C42—91no—
287C42—91no—
288C42C2×D3211yescharacteristic
289C22×C3—21no—
290C22×C3—124no—
291C22×C3—124no—
292C22×C3—124no—
293C22×C3C2×D3×D412yes—
294C2×D3—34no—
295C2×D3—34no—
296C2×D3—34no—
297C2×D3—44no—
298C2×D3—44no—
299C2×D3—44no—
300C2×D3—62no—
301C2×D3—62no—
302C2×D3—62no—
303C2×D3—2416no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—22no—
307C3×C4—124no—
308C3×C4D3×D814yes—
309C3×C4D3×SD1614yes—
310C3×C4D3×#4114yes—
311Dic3—34no—
312Dic3—34no—
313Dic3—34no—
314Dic3—44no—
315Dic3—62no—
316Dic3—62no—
317Dic3—62no—
318C32C2×#48611yescharacteristic, complemented, Sylow
319C23—64no—
320C23—91no—
321C23—364no—
322C23—364no—
323C23—364no—
324Q8—124no—
325Q8—364no—
326D4—68no—
327D4—124no—
328D4—124no—
329D4—364no—
330D4—364no—
331D4—364no—
332C2×C4—64no—
333C2×C4—91no—
334C2×C4—91no—
335C2×C4—91no—
336C2×C4—94no—
337C2×C4—94no—
338C2×C4—94no—
339C2×C4—364no—
340C2×C4#380211yescharacteristic
341C2×C4#380211yescharacteristic
342C2×C4C22×D3211yescharacteristic
343C8—22no—
344C8—182no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—244no—
349C2×C3D3×#12412yes—
350C2×C3C2×D3×D812yes—
351C2×C3C2×D3×SD1612yes—
352D3—38no—
353D3—64no—
354D3—84no—
355C22—92no—
356C22—92no—
357C22—92no—
358C22—124no—
359C22—124no—
360C22—124no—
361C22—728no—
362C22C2×#380211yescharacteristic
363C4—92no—
364C4—92no—
365C4—92no—
366C4—124no—
367C4#6379612yes—
368C4#6379712yes—
369C4#6430612yes—
370C3—21no—
371C3D3×#48612yescomplemented
372C2—94no—
373C2—244no—
374C2#1059400911yescharacteristic
375C2C2×#6379611yescharacteristic
376C2C2×#6379711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10594008C2
hypercenterC4×C8D32
hypocenterC32C2×#486
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
2. #10593909C2semidirect
3. C4×C8×C3⋊D3C2semidirect
4. C3×#4694C2semidirect
5. #10590940C2semidirect
6. #10590885C2semidirect
7. #10590277C2semidirect
16. C3×#869C22semidirect
18. #63919C22semidirect
25. C32×C4×C8C22semidirect
26. C8×C3⋊Dic3C22semidirect
27. C4×C3⋊(C3⋊C8)C22semidirect
28. C3×#821C22semidirect
29. #63562C22semidirect
37. #4694D3semidirect
88. #869C2×D3semidirect
91. C3×C4×C8C2×D3semidirect
93. #821C2×D3semidirect
211. C4×C8D32semidirect
259. C3⋊D3#486semidirect
318. C32C2×#486semidirect
371. C3D3×#486semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105939092
C4×C8×C3⋊D32
C3×#46942
#105909402
#105908852
#105902772
D3×#4863