Finite Group Databasebeta

← #15686995

Subgroups — #15686995

Order 2944.

1112 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093150C213yesmaximal, complemented
2#13093143C211yesmaximal, characteristic, complemented
3#13093135C213yesmaximal, complemented
4#13093117C213yesmaximal, complemented
5#13093111C213yesmaximal, complemented
6#13093086C211yesmaximal, characteristic, complemented
7#13093079C211yesmaximal, characteristic, complemented
8#13093074C211yesmaximal, characteristic, complemented
9#13092964C213yesmaximal, complemented
10#13092951C213yesmaximal, complemented
11#13092949C213yesmaximal, complemented
12C4×#67292C211yesmaximal, characteristic, complemented
13C4×#67288C213yesmaximal, complemented
14C4×Q8×D23C211yesmaximal, characteristic, complemented
15C4×#41×C23C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C2×Q8×D23C2211yescharacteristic
19C2×#67288C2213yes—
20C4×Q8×C23C2211yescharacteristic
21C4×Q8×C23C2211yescharacteristic
22C4×D4×C23C2213yes—
23C4×D4×C23C2213yes—
24C23×#117C2213yes—
25C2×C42×C23C2213yes—
26Q8×Dic23C2211yescharacteristic
27Q8×Dic23C2211yescharacteristic
28#10625111C2213yes—
29#10625109C2213yes—
30#10625109C2213yes—
31#10625107C2213yes—
32#10625101C2213yes—
33#10625100C2216yes—
34C4×C22⋊D23C2213yes—
35C4×C22⋊D23C2213yes—
36C4×C22⋊D23C2213yes—
37C4×C22⋊D23C2213yes—
38C4×C22⋊D23C2216yes—
39#10625097C2213yes—
40#10625095C2213yes—
41#10625068C2213yes—
42#10625066C2213yes—
43#10625064C2213yes—
44#10625063C2213yes—
45C4⋊C4×D23C2213yes—
46#10625061C2213yes—
47#10625059C2213yes—
48#10625058C2213yes—
49#10625056C2216yes—
50#10625055C2216yes—
51#10625054C2216yes—
52#10625050C2216yes—
53#10625047C2216yes—
54#10625046C2213yes—
55C4×D92C2213yes—
56C4×D92C2213yes—
57C4×D92C2213yes—
58#10625043C2211yescharacteristic
59#10625043C2213yes—
60C42×D23C2213yes—
61C42×D23C2213yes—
62#10625041C2213yes—
63C4×Dic46C2213yes—
64C4×Dic46C2213yes—
65C4×Dic46C2213yes—
66#41×C23—24no—
67C2×Q8×C23C2311yescharacteristic
68C2×D4×C23C2313yes—
69C22×C4×C23C2313yes—
70C22×C4×C23C2313yes—
71C22×C4×C23C2313yes—
72C2×C22⋊D23C2313yes—
73C2×C22⋊D23C2313yes—
74C2×C22⋊D23C2316yes—
75#67292—24no—
76Q8×D23—24no—
77#67288—212no—
78C2×D92C2313yes—
79C2×D92C2313yes—
80C2×C4×D23C2313yes—
81C2×C4×D23C2313yes—
82C2×C4×D23C2313yes—
83C2×C4×D23C2313yes—
84C2×C4×D23C2313yes—
85C2×C4×D23C2311yescharacteristic
86C2×Dic46C2313yes—
87C2×Dic46C2313yes—
88C4⋊C4×C23C2313yes—
89C4⋊C4×C23C2313yes—
90C22⋊C4×C23C2316yes—
91C42×C23C2313yes—
92C42×C23C2313yes—
93C42×C23C2313yes—
94C42×C23C2311yescharacteristic
95C22⋊Dic23C2313yes—
96C22⋊Dic23C2316yes—
97C22⋊Dic23C2313yes—
98(C2×D23)⋊C4C2311yescharacteristic
99(C2×D23)⋊C4C2311yescharacteristic
100(C2×D23)⋊C4C2313yes—
101(C2×D23)⋊C4C2313yes—
102(C2×D23)⋊C4C2316yes—
103(C2×D23)⋊C4C2316yes—
104C4⋊Dic23C2313yes—
105C4⋊Dic23C2313yes—
106C4⋊Dic23C2313yes—
107C4⋊Dic23C2313yes—
108Dic23⋊C4C2311yescharacteristic
109Dic23⋊C4C2311yescharacteristic
110Dic23⋊C4C2313yes—
111Dic23⋊C4C2313yes—
112Dic23⋊C4C2316yes—
113Dic23⋊C4C2316yes—
114C4×Dic23C2313yes—
115C4×Dic23C2313yes—
116C4×Dic23C2313yes—
117C4×Dic23C2313yes—
118C4×Dic23C2313yes—
119C4×Dic23C2311yescharacteristic
120C23×C23C2413yes—
121C22×D23C2413yes—
122C22×D23C2411yescharacteristic
123Q8×C23#4114yescomplemented
124D4×C23—26no—
125C2×C4×C23—26no—
126C2×C4×C23—26no—
127C2×C4×C23—43no—
128C2×C4×C23C2413yes—
129C2×C4×C23C2411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C2×C4×C23C2413yes—
132C2×C4×C23C2413yes—
133C2×C4×C23C2411yescharacteristic
134C22⋊D23—26no—
135C22⋊D23—26no—
136C22⋊D23—46no—
137C2×Dic23C2411yescharacteristic
138C2×Dic23C2411yescharacteristic
139C2×Dic23C2413yes—
140C2×Dic23C2413yes—
141C2×Dic23C2413yes—
142C2×Dic23C2411yescharacteristic
143D92—26no—
144D92—26no—
145C4×D23—26no—
146C4×D23—26no—
147C4×D23—26no—
148C4×D23—43no—
149C4×D23—43no—
150C4×D23#4114yescomplemented
151Dic46—26no—
152Dic46—26no—
153#3480—231nomaximal, Sylow
154C22×C23—23no—
155C22×C23—23no—
156C22×C23—23no—
157C22×C23C2511yescharacteristic
158C2×D23—21no—
159C2×D23—21no—
160C2×D23—23no—
161C2×D23—23no—
162C2×D23—23no—
163C2×D23C2×#4112yes—
164C4×C23—23no—
165C4×C23—21no—
166C4×C23—23no—
167C4×C23—21no—
168C4×C23C2×#4116yes—
169C4×C23C2×#4112yes—
170Dic23—23no—
171Dic23—23no—
172Dic23—21no—
173Dic23—21no—
174Dic23—23no—
175Dic23C2×#4112yes—
176#559—233no—
177#557—231no—
178#556—233no—
179#553—233no—
180#553—233no—
181#550—231no—
182#548—231no—
183#548—231no—
184#532—233no—
185#529—233no—
186#529—233no—
187C4×#41—231no—
188C4×#41—233no—
189C4×#41D2311yescharacteristic, complemented
190C2×C4×Q8—231no—
191C2×C23—43no—
192C2×C23C22×#4111yescharacteristic
193C2×C23C22×#4111yescharacteristic
194C2×C23#58511yescharacteristic
195D23—22no—
196D23—43no—
197C2×#41—231no—
198C2×#41—233no—
199C2×#41C2×D2311yescharacteristic
200C22×Q8—231no—
201C4⋊Q8—233no—
202#127—233no—
203#126—236no—
204#126—236no—
205#125—233no—
206#125—233no—
207#124—233no—
208#124—236no—
209#124—233no—
210#123—236no—
211#123—236no—
212C22⋊Q8—233no—
213C22⋊Q8—233no—
214#121—233no—
215#121—233no—
216#121—233no—
217#121—233no—
218#121—236no—
219C4×Q8—231no—
220C4×Q8—231no—
221C4×Q8—233no—
222C4×Q8—233no—
223C4×Q8—233no—
224C4×Q8—233no—
225C4×Q8C2×D2311yescharacteristic
226C4×Q8C2×D2311yescharacteristic
227C4×D4—233no—
228C4×D4—233no—
229C4×D4—233no—
230C4×D4—233no—
231C4×D4—236no—
232C4×D4—233no—
233C4×D4—233no—
234C4×D4—233no—
235C4×D4—233no—
236C4×D4C2×D2313yes—
237C4×D4C2×D2313yes—
238#117—233no—
239#117—233no—
240#117—231no—
241#117—233no—
242#117C2×D2313yes—
243C2×C4⋊C4—233no—
244C2×C42—233no—
245C2×C42—233no—
246C2×C42C2×D2313yes—
247C23#348011yescharacteristic, complemented, Sylow
248#41—24no—
249#41—4612no—
250#41—464no—
251C2×Q8—233no—
252C2×Q8—233no—
253C2×Q8—464no—
254C2×Q8C22×D2311yescharacteristic
255C2×D4—233no—
256C2×D4—233no—
257C2×D4—236no—
258C2×D4—233no—
259C2×D4—233no—
260C2×D4C22×D2313yes—
261C22×C4—231no—
262C22×C4—233no—
263C22×C4—233no—
264C22×C4—233no—
265C22×C4—233no—
266C22×C4—233no—
267C22×C4C22×D2313yes—
268C22×C4C22×D2313yes—
269C22×C4C22×D2313yes—
270C4⋊C4—233no—
271C4⋊C4—236no—
272C4⋊C4—231no—
273C4⋊C4—231no—
274C4⋊C4—233no—
275C4⋊C4—233no—
276C4⋊C4—233no—
277C4⋊C4—233no—
278C4⋊C4—233no—
279C4⋊C4—236no—
280C4⋊C4C22×D2313yes—
281C4⋊C4C22×D2313yes—
282C22⋊C4—233no—
283C22⋊C4—233no—
284C22⋊C4—236no—
285C22⋊C4—231no—
286C22⋊C4—231no—
287C22⋊C4—233no—
288C22⋊C4—236no—
289C22⋊C4—233no—
290C22⋊C4—236no—
291C22⋊C4C22×D2316yes—
292C42—233no—
293C42—233no—
294C42—233no—
295C42—233no—
296C42—231no—
297C42—233no—
298C42C22×D2313yes—
299C42C22×D2313yes—
300C42C22×D2313yes—
301C42C22×D2311yescharacteristic
302C23—231no—
303C23—233no—
304C23C23×D2313yes—
305Q8—466no—
306Q8—466no—
307Q8#6728814yescomplemented
308D4—26no—
309D4—466no—
310D4—466no—
311D4—466no—
312D4—466no—
313D4—926no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—231no—
318C2×C4—234no—
319C2×C4—231no—
320C2×C4—231no—
321C2×C4—233no—
322C2×C4—233no—
323C2×C4—233no—
324C2×C4—466no—
325C2×C4—466no—
326C2×C4—466no—
327C2×C4—923no—
328C2×C4—923no—
329C2×C4C23×D2313yes—
330C2×C4C23×D2311yescharacteristic
331C2×C4C23×D2311yescharacteristic
332C2×C4C23×D2313yes—
333C2×C4C23×D2313yes—
334C2×C4C23×D2311yescharacteristic
335C22—23no—
336C22—23no—
337C22—23no—
338C22—232no—
339C22—461no—
340C22—461no—
341C22—463no—
342C22—463no—
343C22—463no—
344C22C24×D2311yescharacteristic
345C4—23no—
346C4—21no—
347C4—21no—
348C4—23no—
349C4—232no—
350C4—463no—
351C4—461no—
352C4—463no—
353C4—461no—
354C4—463no—
355C4C2×#6728816yes—
356C4#41×D2312yes—
357C2—43no—
358C2—462no—
359C2—923no—
360C2C2×#41×D2311yescharacteristic
361C2C22×#6728811yescharacteristic
362C2#1309325311yescharacteristic
subgroupG/H
centerC2×C4C23×D23
commutator, socle, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC4×#41×C23C2
hypercenterC4×#41D23
hypocenterC23#3480
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #13093150C2semidirect
2. #13093143C2semidirect
3. #13093135C2semidirect
4. #13093117C2semidirect
5. #13093111C2semidirect
6. #13093086C2semidirect
7. #13093079C2semidirect
8. #13093074C2semidirect
9. #13092964C2semidirect
10. #13092951C2semidirect
11. #13092949C2semidirect
12. C4×#67292C2semidirect
13. C4×#67288C2semidirect
14. C4×Q8×D23C2semidirect
15. C4×#41×C23C2semidirect
123. Q8×C23#41semidirect
150. C4×D23#41semidirect
189. C4×#41D23semidirect
247. C23#3480semidirect
307. Q8#67288semidirect

Maximal subgroups

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

subgroupindex
#130931502
#130931432
#130931352
#130931172
#130931112
#130930862
#130930792
#130930742
#130929642
#130929512
#130929492
C4×#672922
C4×#672882
C4×Q8×D232
C4×#41×C232
#348023