Finite Group Databasebeta

← #15683655

Subgroups — #15683655

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#13093032C211yesmaximal, characteristic, complemented
2#13092896C211yesmaximal, characteristic, complemented
3#13092754C211yesmaximal, characteristic, complemented
4#13092729C211yesmaximal, characteristic, complemented
5#13092711C211yesmaximal, characteristic, complemented
6#13092695C211yesmaximal, characteristic, complemented
7#13092638C211yesmaximal, characteristic, complemented
8#13092630C211yesmaximal, characteristic, complemented
9#13092580C211yesmaximal, characteristic, complemented
10#13092559C211yesmaximal, characteristic
11#13092517C211yesmaximal, characteristic, complemented
12#13092517C211yesmaximal, characteristic, complemented
13C4×Dic92C211yesmaximal, characteristic, complemented
14#13092476C211yesmaximal, characteristic, complemented
15C4×D8×C23C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic
17C2×D8×C23C2211yescharacteristic
18C4×D4×C23C2211yescharacteristic
19C4×D4×C23C2211yescharacteristic
20#10625109C2211yescharacteristic
21#10625107C2211yescharacteristic
22D4×Dic23C2211yescharacteristic
23C2×#67273C2211yescharacteristic
24C2×#67273C2211yescharacteristic
25#10625100—21no—
26C4×C22⋊D23—21no—
27#10625095—21no—
28C2×Dic23⋊C4—21no—
29C2×Dic92C2211yescharacteristic
30#10625068C2211yescharacteristic
31C4⋊C4×D23C2211yescharacteristic
32#10625059C2211yescharacteristic
33#10625058C2211yescharacteristic
34#10625056—21no—
35(C22⋊D23)⋊C4—21no—
36#10625050—21no—
37#10625048—21no—
38#10625043C2211yescharacteristic
39C4×Dic46C2211yescharacteristic
40C4×Dic46C2211yescharacteristic
41C23×#107C2211yescharacteristic
42C23×#102C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C4×C8×C23C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47(C2×D23)⋊C8C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49#10625000C2211yescharacteristic
50#10624998C2211yescharacteristic
51#10624998C2211yescharacteristic
52Dic23⋊C8C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624989C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×D4×C23C2311yescharacteristic
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C22×C4×C23—21no—
63C2×C22⋊D23—21no—
64C2×C22⋊D23—21no—
65C22×Dic23—21no—
66C22×Dic23—21no—
67#67290—22no—
68#67290—22no—
69C2×C4×D23—21no—
70C2×C4×D23C2311yescharacteristic
71C2×Dic46—21no—
72C2×Dic46C2311yescharacteristic
73C2×Dic46C2311yescharacteristic
74D8×C23—22no—
75C2×C8×C23C2311yescharacteristic
76C2×C8×C23C2311yescharacteristic
77C4⋊C4×C23C2311yescharacteristic
78C4⋊C4×C23C2311yescharacteristic
79C22⋊C4×C23—21no—
80C22⋊C4×C23—21no—
81C42×C23C2311yescharacteristic
82C22⋊Dic23—21no—
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86#67273—22no—
87#67273—22no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4D411yescharacteristic
90(C2×D23)⋊C4D411yescharacteristic
91C4⋊Dic23—21no—
92C4⋊Dic23C2311yescharacteristic
93C4⋊Dic23C2311yescharacteristic
94Dic23⋊C4—21no—
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4D411yescharacteristic
100Dic23⋊C4D411yescharacteristic
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107Dic92—22no—
108C23×C23—21no—
109C23×C23—21no—
110C22×D23C2×D411yescharacteristic
111D4×C23—21no—
112D4×C23—21no—
113D4×C23—21no—
114D4×C23#4112yes—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—81no—
118C2×C4×C23—81no—
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2411yescharacteristic
122C22⋊D23—24no—
123C22⋊D23—81no—
124C2×Dic23—24no—
125C2×Dic23—21no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—81no—
130C2×Dic23C2×D411yescharacteristic
131C2×Dic23C2×D411yescharacteristic
132C2×Dic23C2×D411yescharacteristic
133C4×D23—21no—
134C4×D23—21no—
135C4×D23—81no—
136Dic46—21no—
137Dic46—21no—
138Dic46—21no—
139Dic46—81no—
140Dic46#4112yes—
141C8×C23—21no—
142C8×C23—21no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3124—231nomaximal, Sylow
146C22×C23—22no—
147C22×C23—41no—
148C22×C23—41no—
149C22×C23—41no—
150C22×C23—41no—
151C22×C23—41no—
152C22×C23C22×D411yescharacteristic
153C2×D23—21no—
154C2×D23—21no—
155C2×D23—21no—
156C4×C23—21no—
157C4×C23—21no—
158C4×C23—41no—
159C4×C23—41no—
160C4×C23C2×#4111yescharacteristic
161C4×C23C2×#4111yescharacteristic
162Dic23—22no—
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#452—231no—
178#449—231no—
179#440—231no—
180#440—231no—
181C4×Q16—231no—
182C4×D8D2311yescharacteristic, complemented
183#433—231no—
184C2×C23—42no—
185C2×C23—81no—
186C2×C23#52511yescharacteristic
187C2×C23#57611yescharacteristic
188C2×C23#57811yescharacteristic
189D23—41no—
190C2×#41—231no—
191C2×Q16—231no—
192C2×SD16—231no—
193C2×SD16—231no—
194C2×D8C2×D2311yescharacteristic
195C4⋊Q8—231no—
196#126—461no—
197#124—231no—
198#124—461no—
199#123—461no—
200C22⋊Q8—231no—
201C22⋊Q8—461no—
202#121—231no—
203C4×Q8—231no—
204C4×Q8—231no—
205C4×Q8—231no—
206C4×D4—231no—
207C4×D4—461no—
208C4×D4—461no—
209C4×D4C2×D2311yescharacteristic
210C4×D4C2×D2311yescharacteristic
211#117—231no—
212#117—461no—
213C2×C4⋊C4—231no—
214C2×C4⋊C4—461no—
215#107—231no—
216#107—231no—
217#107—231no—
218#107C2×D2311yescharacteristic
219C4⋊C8—231no—
220C4⋊C8—231no—
221#103—231no—
222#103—231no—
223#103—231no—
224#103—231no—
225#102—231no—
226#102—231no—
227#102C2×D2311yescharacteristic
228#102C2×D2311yescharacteristic
229C22⋊C8—231no—
230C22⋊C8—231no—
231#97—231no—
232C4×C8C2×D2311yescharacteristic
233C23#312411yescharacteristic, complemented, Sylow
234#41—462no—
235#41—462no—
236C2×Q8—231no—
237C2×Q8—231no—
238C2×Q8—461no—
239C2×D4—461no—
240C2×D4—461no—
241C2×D4C22×D2311yescharacteristic
242C2×D4C22×D2311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—231no—
246C22×C4—461no—
247C22×C4—461no—
248C22×C4—461no—
249Q16—462no—
250SD16—462no—
251SD16—462no—
252D8—22no—
253C2×C8—231no—
254C2×C8—231no—
255C2×C8C22×D2311yescharacteristic
256C2×C8C22×D2311yescharacteristic
257C4⋊C4—231no—
258C4⋊C4—231no—
259C4⋊C4—231no—
260C4⋊C4—231no—
261C4⋊C4—461no—
262C4⋊C4—461no—
263C4⋊C4—461no—
264C4⋊C4—461no—
265C4⋊C4—461no—
266C4⋊C4—461no—
267C4⋊C4C22×D2311yescharacteristic
268C4⋊C4C22×D2311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—231no—
272C22⋊C4—231no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4—461no—
277C22⋊C4—461no—
278C42—231no—
279C42—461no—
280C42—461no—
281C42—461no—
282C42C22×D2311yescharacteristic
283C23—21no—
284C23—21no—
285C23—231no—
286Q8—232no—
287Q8—461no—
288Q8—461no—
289Q8—461no—
290Q8—1841no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—464no—
295D4—1841no—
296D4#6728812yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—231no—
302C2×C4—231no—
303C2×C4—231no—
304C2×C4—464no—
305C2×C4—461no—
306C2×C4—461no—
307C2×C4—461no—
308C2×C4—461no—
309C2×C4—461no—
310C2×C4—461no—
311C2×C4—1841no—
312C2×C4—1841no—
313C2×C4D4×D2311yescharacteristic
314C2×C4D4×D2311yescharacteristic
315C2×C4C23×D2311yescharacteristic
316C8—21no—
317C8—21no—
318C8—461no—
319C8—461no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—461no—
327C22—461no—
328C22—461no—
329C22C2×D4×D2311yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—461no—
335C4—462no—
336C4—461no—
337C4—461no—
338C4—921no—
339C4—921no—
340C4—921no—
341C4C2×#6728811yescharacteristic
342C4#41×D2311yescharacteristic
343C2—42no—
344C2—81no—
345C2—921no—
346C2#1309292611yescharacteristic
347C2#1309321811yescharacteristic
348C2#1309323111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×D8×C23C2
socleC22×C23C22×D4
prime radical#13092559C2
hypercenterC4×D8D23
hypocenterC23#3124
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #13093032C2semidirect
2. #13092896C2semidirect
3. #13092754C2semidirect
4. #13092729C2semidirect
5. #13092711C2semidirect
6. #13092695C2semidirect
7. #13092638C2semidirect
8. #13092630C2semidirect
9. #13092580C2semidirect
11. #13092517C2semidirect
12. #13092517C2semidirect
13. C4×Dic92C2semidirect
14. #13092476C2semidirect
15. C4×D8×C23C2semidirect
182. C4×D8D23semidirect
233. C23#3124semidirect

Maximal subgroups

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

subgroupindex
#130930322
#130928962
#130927542
#130927292
#130927112
#130926952
#130926382
#130926302
#130925802
#130925592
#130925172
C4×Dic922
#130924762
C4×D8×C232
#312423