Finite Group Databasebeta

← #11858596

Subgroups — #11858596

Order 1152.

1099 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic
2C3×#5827C211yesmaximal, characteristic
3C2×C3×#948C211yesmaximal, characteristic
4#10591131C213yesmaximal, complemented
5#10591130C213yesmaximal, complemented
6C2×#63575C213yesmaximal, complemented
7#10591122C213yesmaximal, complemented
8#83785—31nomaximal
9#82562—31nomaximal
10C2×C32×#41C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12D4×C3⋊Dic3—23no—
13#64135C2213yes—
14C2×C4⋊(C3⋊Dic3)C2213yes—
15C3×#948C418yescomplemented
16C3×Q8×Dic3—21no—
17C3×D4×Dic3—23no—
18C3×#926C2213yes—
19C2×C3×C4⋊Dic3C2213yes—
20C2×C3×#208C2213yes—
21C22×C3×C3⋊C8C2213yes—
22#63575C2211yescharacteristic
23#63575C2213yes—
24#63575C2216yes—
25#63573C2213yes—
26#63573C2213yes—
27C2×C3×#131—31no—
28C3×#520—31no—
29#5827—31no—
30#5827—31no—
31#5827—61no—
32#5827D311yescharacteristic
33C2×#948D311yescharacteristic
34#5121—33no—
35#5121—33no—
36#5106—33no—
37C2×#818—33no—
38#4998—33no—
39#4995—33no—
40#4964—33no—
41C2×#807—33no—
42C32×#41C2×C414yes—
43C32×#41Q814yes—
44C2×C32×Q8D411yescharacteristic
45C2×C32×D4D413yes—
46C22×C32×C4C2313yes—
47C22×C3⋊Dic3—23no—
48C22×C3×Dic3—23no—
49#3757—23no—
50C4⋊(C3⋊Dic3)—23no—
51C4⋊(C3⋊Dic3)C2311yescharacteristic
52C4⋊(C3⋊Dic3)C2313yes—
53C4×C3⋊Dic3—23no—
54C3×#217—23no—
55C3×C4⋊Dic3—23no—
56C3×C4⋊Dic3C2313yes—
57C3×C4⋊Dic3C2311yescharacteristic
58C3×C4×Dic3—23no—
59C3×#208C2×C4112yescomplemented
60C2×C3×C3⋊C8C2×C4112yescomplemented
61C2×C3×C3⋊C8C2311yescharacteristic
62C2×C3×C3⋊C8C2313yes—
63#2913—91noSylow
64C2×C3×#41—21no—
65C2×C3×#41C2×D311yescharacteristic
66C2×C3×#41C2×D311yescharacteristic
67C3×#131—38no—
68C2×C3×M16—33no—
69C22×C3×C8—33no—
70C3×C4×Q8—61no—
71C3×C4×D4—63no—
72C3×#117—33no—
73C2×C3×C4⋊C4—33no—
74#948Dic318yescomplemented
75Q8×Dic3—21no—
76Q8×Dic3—62no—
77Q8×Dic3—61no—
78Q8×Dic3—61no—
79D4×Dic3—23no—
80D4×Dic3—66no—
81D4×Dic3—63no—
82D4×Dic3—63no—
83#926—33no—
84#926—33no—
85#926—63no—
86#926C2×D313yes—
87C2×C4⋊Dic3—33no—
88C2×C4⋊Dic3—33no—
89C2×C4⋊Dic3—63no—
90C2×C4⋊Dic3C2×D313yes—
91C2×#208C2×D313yes—
92C22×C3⋊C8C2×D313yes—
93#818—36no—
94#818—33no—
95#818—31no—
96#817—33no—
97#817—33no—
98#808—33no—
99#808—33no—
100#807—33no—
101#807—36no—
102#807—31no—
103C23×C32C2×D413yes—
104C32×Q8C4⋊C414yes—
105C32×D4C4⋊C4112yes—
106C2×C32×C4C22×C416yes—
107C2×C32×C4C2×D413yes—
108C2×C32×C4C2×Q816yes—
109C2×C32×C4C2411yescharacteristic
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—23no—
112C2×C3⋊Dic3—83no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—23no—
115C2×C3×Dic3—83no—
116C3×C3⋊C8C22×C412yes—
117C3×C3⋊C8C22×C416yes—
118C2×#131—31no—
119#520—31no—
120#520—91no—
121#428—93no—
122#428—93no—
123#427—93no—
124C2×#107—93no—
125C3×#41—24no—
126C3×#41—24no—
127C3×#41Dic614yes—
128C3×#41Dic614yes—
129C3×#41C4×D314yes—
130C3×#41C2×Dic314yes—
131C2×C3×Q8—21no—
132C2×C3×Q8D1211yescharacteristic
133C2×C3×Q8#6711yescharacteristic
134C2×C3×D4—23no—
135C2×C3×D4D1213yes—
136C2×C3×D4#6713yes—
137C22×C3×C4—23no—
138C22×C3×C4—63no—
139C22×C3×C4C22×D313yes—
140C22×C3×C4C22×D313yes—
141C22×Dic3—23no—
142C22×Dic3—66no—
143C22×Dic3—63no—
144C22×Dic3—63no—
145C3×M16—312no—
146C2×C3×C8—312no—
147C2×C3×C8—33no—
148C2×C3×C8—31no—
149C3×C4⋊C4—33no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—63no—
152C3×C22⋊C4—63no—
153C3×C42—63no—
154#217—23no—
155#217—66no—
156#217—63no—
157#217—63no—
158C4⋊Dic3—23no—
159C4⋊Dic3—33no—
160C4⋊Dic3—31no—
161C4⋊Dic3—31no—
162C4⋊Dic3—33no—
163C4⋊Dic3—63no—
164C4⋊Dic3—61no—
165C4⋊Dic3—66no—
166C4⋊Dic3—63no—
167C4⋊Dic3—63no—
168C4⋊Dic3C22×D311yescharacteristic
169C4⋊Dic3C22×D313yes—
170C4×Dic3—23no—
171C4×Dic3—66no—
172C4×Dic3—63no—
173C4×Dic3—63no—
174#208C2×Dic3112yescomplemented
175C2×C3⋊C8C2×Dic3112yescomplemented
176C2×C3⋊C8C22×D311yescharacteristic
177C2×C3⋊C8C22×D313yes—
178C22×C32—23no—
179C22×C32—23no—
180C22×C32C2×C4⋊C416yes—
181C22×C32C22×D411yescharacteristic
182C32×C4C2×C4⋊C416yes—
183C32×C4C23×C411yescharacteristic
184C32×C4C22×Q811yescharacteristic
185C3⋊Dic3—43no—
186C3⋊Dic3—41no—
187C3×Dic3—43no—
188C3×Dic3—41no—
189C2×#41D3211yescharacteristic
190#131—38no—
191C2×M16—33no—
192C22×C8—33no—
193C4×Q8—61no—
194C4×Q8—181no—
195C4×D4—63no—
196C4×D4—183no—
197#117—33no—
198#117—93no—
199C2×C4⋊C4—33no—
200C2×C4⋊C4—93no—
201#107—93no—
202#107—96no—
203#107—91no—
204#106—93no—
205#106—93no—
206C23×C3—23no—
207C23×C3C2×D1213yes—
208C23×C3C2×#6713yes—
209C3×Q8—24no—
210C3×Q8Dic3⋊C414yes—
211C3×Q8C4⋊Dic314yes—
212C3×D4—212no—
213C3×D4Dic3⋊C4112yes—
214C3×D4C4⋊Dic3112yes—
215C2×C3×C4—21no—
216C2×C3×C4—26no—
217C2×C3×C4—23no—
218C2×C3×C4—26no—
219C2×C3×C4—61no—
220C2×C3×C4—63no—
221C2×C3×C4—243no—
222C2×C3×C4C2×Dic616yes—
223C2×C3×C4C2×Dic616yes—
224C2×C3×C4C2×C4×D316yes—
225C2×C3×C4C2×D1213yes—
226C2×C3×C4C22×Dic316yes—
227C2×C3×C4C2×#6713yes—
228C2×C3×C4C23×D311yescharacteristic
229C2×C3×C4C23×D311yescharacteristic
230C2×Dic3—21no—
231C2×Dic3—23no—
232C2×Dic3—62no—
233C2×Dic3—66no—
234C2×Dic3—61no—
235C2×Dic3—63no—
236C2×Dic3—61no—
237C2×Dic3—63no—
238C2×Dic3—83no—
239C2×Dic3—243no—
240C2×Dic3—243no—
241C2×Dic3—246no—
242C3×C8—32no—
243C3×C8—36no—
244C3⋊C8C22×Dic312yes—
245C3⋊C8C22×Dic316yes—
246C2×C32—26no—
247C2×C32C22×C4⋊C411yescharacteristic
248C2×C32#57611yescharacteristic
249C2×C32#57811yescharacteristic
250#41D3×Dic314yes—
251#41#62714yes—
252C2×Q8#62611yescharacteristic
253C2×D4#62613yes—
254C22×C4—63no—
255C22×C4—183no—
256C22×C4C2×D3213yes—
257M16—312no—
258C2×C8—33no—
259C2×C8—31no—
260C2×C8—312no—
261C4⋊C4—31no—
262C4⋊C4—33no—
263C4⋊C4—63no—
264C4⋊C4—91no—
265C4⋊C4—93no—
266C4⋊C4—183no—
267C22⋊C4—63no—
268C22⋊C4—183no—
269C42—63no—
270C42—183no—
271C22×C3—23no—
272C22×C3—23no—
273C22×C3—23no—
274C22×C3—23no—
275C22×C3—21no—
276C22×C3—26no—
277C22×C3—43no—
278C22×C3—43no—
279C22×C3C2×Dic3⋊C416yes—
280C22×C3C2×C4⋊Dic316yes—
281C22×C3C22×D1211yescharacteristic
282C22×C3C22×#6711yescharacteristic
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—26no—
286C3×C4—123no—
287C3×C4—121no—
288C3×C4C2×Dic3⋊C416yes—
289C3×C4C2×C4⋊Dic316yes—
290C3×C4C22×Dic611yescharacteristic
291C3×C4C22×Dic611yescharacteristic
292C3×C4C22×C4×D311yescharacteristic
293C3×C4C23×Dic311yescharacteristic
294Dic3—43no—
295Dic3—41no—
296Dic3—126no—
297Dic3—122no—
298Dic3—123no—
299Dic3—121no—
300Dic3—123no—
301Dic3—121no—
302C32#291311yescharacteristic, complemented, Sylow
303C23C2×#62613yes—
304Q8Dic3⋊Dic314yes—
305D4Dic3⋊Dic3112yes—
306C2×C4—61no—
307C2×C4—63no—
308C2×C4—181no—
309C2×C4—183no—
310C2×C4—243no—
311C2×C4—723no—
312C2×C4C2×D3×Dic316yes—
313C2×C4C2×#62613yes—
314C2×C4C2×#62716yes—
315C2×C4C22×D3211yescharacteristic
316C8—32no—
317C8—36no—
318C2×C3—26no—
319C2×C3—26no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—46no—
324C2×C3#575211yescharacteristic
325C2×C3#575311yescharacteristic
326C2×C3C22×Dic3⋊C411yescharacteristic
327C2×C3C22×C4⋊Dic311yescharacteristic
328C2×C3#583511yescharacteristic
329C2×C3#583811yescharacteristic
330C22—23no—
331C22—23no—
332C22C2×Dic3⋊Dic316yes—
333C22C22×#62611yescharacteristic
334C4—123no—
335C4—121no—
336C4—363no—
337C4—361no—
338C4C2×Dic3⋊Dic316yes—
339C4C22×D3×Dic311yescharacteristic
340C4C22×#62711yescharacteristic
341C3—21no—
342C3#8256211yescharacteristic, complemented
343C3#8378511yescharacteristic, complemented
344C2—26no—
345C2#1059544911yescharacteristic
346C2#1059545011yescharacteristic
347C2C22×Dic3⋊Dic311yescharacteristic
subgroupG/H
centerC22C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2913
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591131C2semidirect
5. #10591130C2semidirect
6. C2×#63575C2semidirect
7. #10591122C2semidirect
15. C3×#948C4semidirect
59. C3×#208C2×C4semidirect
60. C2×C3×C3⋊C8C2×C4semidirect
74. #948Dic3semidirect
174. #208C2×Dic3semidirect
175. C2×C3⋊C8C2×Dic3semidirect
302. C32#2913semidirect
342. C3#82562semidirect
343. C3#83785semidirect

Maximal subgroups

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

subgroupindex
#105962982
C3×#58272
C2×C3×#9482
#105911312
#105911302
C2×#635752
#105911222
#837853
#825623