Finite Group Databasebeta

← #15683660

Subgroups — #15683660

Order 2944.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093040C211yesmaximal, characteristic, complemented
2#13092900C211yesmaximal, characteristic, complemented
3#13092750C211yesmaximal, characteristic, complemented
4#13092731C211yesmaximal, characteristic, complemented
5#13092710C211yesmaximal, characteristic, complemented
6#13092695C211yesmaximal, characteristic, complemented
7#13092641C211yesmaximal, characteristic, complemented
8#13092634C211yesmaximal, characteristic, complemented
9#13092562C211yesmaximal, characteristic
10#13092520C211yesmaximal, characteristic, complemented
11#13092518C211yesmaximal, characteristic, complemented
12Q16×Dic23C211yesmaximal, characteristic, complemented
13#13092497C211yesmaximal, characteristic, complemented
14#13092475C211yesmaximal, characteristic, complemented
15C23×#452C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×Q16×C23C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C23×C22⋊Q8C2211yescharacteristic
20#10625118C2211yescharacteristic
21Q8×Dic23C2211yescharacteristic
22Q8×Dic23C2211yescharacteristic
23Q8×Dic23C2211yescharacteristic
24C2×#67274C2211yescharacteristic
25D4×Dic23—21no—
26D4×Dic23—21no—
27D4×Dic23C2211yescharacteristic
28D4×Dic23C2211yescharacteristic
29C2×#67272C2211yescharacteristic
30#10625101C2211yescharacteristic
31#10625097—21no—
32#10625097C2211yescharacteristic
33C2×C4⋊Dic23—21no—
34C2×C4⋊Dic23C2211yescharacteristic
35#10625069—21no—
36#10625068—21no—
37#10625064C2211yescharacteristic
38#10625059C2211yescharacteristic
39#10625056—21no—
40#10625054—21no—
41C23×#103C2211yescharacteristic
42C23×#102C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic
44#10625017C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625014C2211yescharacteristic
48C22⋊(C23⋊C8)C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625000C2211yescharacteristic
52#10625000C2211yescharacteristic
53#10624997C2211yescharacteristic
54Dic23⋊C8C2211yescharacteristic
55Dic23⋊C8C2211yescharacteristic
56C8×Dic23C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624989C2211yescharacteristic
59#41×C23—22no—
60#41×C23—22no—
61C2×Q8×C23C2311yescharacteristic
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—21no—
68C22×Dic23—21no—
69C22×Dic23—21no—
70C22×Dic23—21no—
71C2×D92C2311yescharacteristic
72C2×C4×D23—21no—
73C2×Dic46—21no—
74Q16×C23—22no—
75SD16×C23—22no—
76C2×C8×C23C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C4⋊C4×C23—21no—
79C4⋊C4×C23C2311yescharacteristic
80C22⋊C4×C23—21no—
81C22⋊Dic23—21no—
82C22⋊Dic23—21no—
83C22⋊Dic23D411yescharacteristic
84C22⋊Dic23D411yescharacteristic
85#67274—22no—
86#67272—22no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91C4⋊Dic23—21no—
92C4⋊Dic23—21no—
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23D411yescharacteristic
96C4⋊Dic23D411yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100Dic23⋊C4—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C4×Dic23C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C23×C23C2×D411yescharacteristic
110C22×D23—21no—
111Q8×C23—21no—
112Q8×C23—21no—
113Q8×C23—21no—
114Q8×C23#4112yes—
115D4×C23—24no—
116D4×C23—21no—
117D4×C23#4112yes—
118C2×C4×C23—24no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C22⋊D23—81no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—81no—
131C2×Dic23—81no—
132C2×Dic23—81no—
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135C2×Dic23C2×D411yescharacteristic
136C2×Dic23C2×D411yescharacteristic
137D92—21no—
138D92—21no—
139C4×D23—81no—
140Dic46—81no—
141C8×C23—21no—
142C8×C23—21no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3124—231nomaximal, Sylow
146C22×C23—21no—
147C22×C23—22no—
148C22×C23—21no—
149C22×C23—21no—
150C22×C23—41no—
151C22×C23—41no—
152C22×C23C22×D411yescharacteristic
153C2×D23—41no—
154C2×D23—41no—
155C2×D23—41no—
156C4×C23—21no—
157C4×C23—22no—
158C4×C23—41no—
159C4×C23—41no—
160C4×C23C2×#4111yescharacteristic
161C4×C23C2×#4111yescharacteristic
162Dic23—21no—
163Dic23—21no—
164Dic23—21no—
165Dic23—21no—
166Dic23—41no—
167Dic23—41no—
168Dic23—41no—
169#542—231no—
170#520—231no—
171#484—231no—
172#480—231no—
173#477—231no—
174#474—231no—
175#464—231no—
176#463—231no—
177#452D2311yescharacteristic, complemented
178#449—231no—
179#440—231no—
180#440—231no—
181C4×Q16—231no—
182C4×D8—231no—
183#433—231no—
184C2×C23—41no—
185C2×C23—42no—
186C2×C23#52511yescharacteristic
187C2×C23#57611yescharacteristic
188C2×C23#57811yescharacteristic
189D23—81no—
190C2×#41C2×D2311yescharacteristic
191C2×Q16C2×D2311yescharacteristic
192C2×SD16—231no—
193C2×SD16C2×D2311yescharacteristic
194C2×D8—231no—
195C4⋊Q8—231no—
196#126—461no—
197#124—231no—
198#124—461no—
199#123—461no—
200C22⋊Q8—461no—
201C22⋊Q8C2×D2311yescharacteristic
202#121—231no—
203C4×Q8—231no—
204C4×Q8—231no—
205C4×Q8—231no—
206C4×D4—231no—
207C4×D4—231no—
208C4×D4—231no—
209C4×D4—461no—
210C4×D4—461no—
211#117—231no—
212#117—461no—
213C2×C4⋊C4—231no—
214C2×C4⋊C4—461no—
215#107—231no—
216#107—231no—
217#107—231no—
218#107—231no—
219C4⋊C8—231no—
220C4⋊C8—231no—
221#103—231no—
222#103—231no—
223#103—231no—
224#103C2×D2311yescharacteristic
225#102—231no—
226#102—231no—
227#102—231no—
228#102C2×D2311yescharacteristic
229C22⋊C8—231no—
230C22⋊C8C2×D2311yescharacteristic
231#97—231no—
232C4×C8—231no—
233C23#312411yescharacteristic, complemented, Sylow
234#41—22no—
235#41—22no—
236C2×Q8—461no—
237C2×Q8C22×D2311yescharacteristic
238C2×Q8C22×D2311yescharacteristic
239C2×D4—21no—
240C2×D4—231no—
241C2×D4—461no—
242C2×D4C22×D2311yescharacteristic
243C22×C4—21no—
244C22×C4—461no—
245C22×C4—461no—
246C22×C4—461no—
247C22×C4—461no—
248C22×C4C22×D2311yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—462no—
252D8—462no—
253C2×C8—231no—
254C2×C8—231no—
255C2×C8C22×D2311yescharacteristic
256C2×C8C22×D2311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—231no—
259C4⋊C4—231no—
260C4⋊C4—231no—
261C4⋊C4—231no—
262C4⋊C4—231no—
263C4⋊C4—461no—
264C4⋊C4—461no—
265C4⋊C4—461no—
266C4⋊C4—461no—
267C4⋊C4—461no—
268C4⋊C4C22×D2311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—231no—
271C22⋊C4—231no—
272C22⋊C4—461no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4—461no—
277C22⋊C4—461no—
278C42—231no—
279C42—231no—
280C42—461no—
281C42—461no—
282C42—461no—
283C23—21no—
284C23—461no—
285C23D4×D2311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—1841no—
290Q8#6729012yes—
291D4—24no—
292D4—21no—
293D4—461no—
294D4—461no—
295D4—1841no—
296D4#6729012yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—231no—
304C2×C4—231no—
305C2×C4—231no—
306C2×C4—231no—
307C2×C4—461no—
308C2×C4—461no—
309C2×C4—461no—
310C2×C4—1841no—
311C2×C4—1841no—
312C2×C4—1841no—
313C2×C4—1841no—
314C2×C4D4×D2311yescharacteristic
315C2×C4C23×D2311yescharacteristic
316C8—21no—
317C8—21no—
318C8—461no—
319C8—461no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—921no—
327C22—921no—
328C22—921no—
329C22C2×D4×D2311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—461no—
335C4—461no—
336C4—461no—
337C4—461no—
338C4—921no—
339C4—921no—
340C4—921no—
341C4C2×#6729011yescharacteristic
342C4C2×#6729011yescharacteristic
343C2—41no—
344C2—42no—
345C2—1841no—
346C2#1309292311yescharacteristic
347C2#1309321911yescharacteristic
348C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#452C2
socleC22×C23C22×D4
prime radical#13092562C2
hypercenter#452D23
hypocenterC23#3124
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #13093040C2semidirect
2. #13092900C2semidirect
3. #13092750C2semidirect
4. #13092731C2semidirect
5. #13092710C2semidirect
6. #13092695C2semidirect
7. #13092641C2semidirect
8. #13092634C2semidirect
10. #13092520C2semidirect
11. #13092518C2semidirect
12. Q16×Dic23C2semidirect
13. #13092497C2semidirect
14. #13092475C2semidirect
15. C23×#452C2semidirect
177. #452D23semidirect
233. C23#3124semidirect

Maximal subgroups

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

subgroupindex
#130930402
#130929002
#130927502
#130927312
#130927102
#130926952
#130926412
#130926342
#130925622
#130925202
#130925182
Q16×Dic232
#130924972
#130924752
C23×#4522
#312423