Finite Group Databasebeta

← #15683658

Subgroups — #15683658

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#13093036C211yesmaximal, characteristic, complemented
2#13092899C211yesmaximal, characteristic, complemented
3#13092751C211yesmaximal, characteristic, complemented
4#13092729C211yesmaximal, characteristic, complemented
5#13092712C211yesmaximal, characteristic, complemented
6#13092698C211yesmaximal, characteristic, complemented
7#13092629C211yesmaximal, characteristic, complemented
8#13092578C211yesmaximal, characteristic, complemented
9#13092561C211yesmaximal, characteristic
10#13092520C211yesmaximal, characteristic, complemented
11#13092518C211yesmaximal, characteristic, complemented
12Q16×Dic23C211yesmaximal, characteristic, complemented
13#13092497C211yesmaximal, characteristic, complemented
14#13092477C211yesmaximal, characteristic, complemented
15C23×#464C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×Q16×C23C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C23×#124C2211yescharacteristic
20C4×Q8×C23C2211yescharacteristic
21#10625117C2211yescharacteristic
22Q8×Dic23C2211yescharacteristic
23Q8×Dic23C2211yescharacteristic
24C2×#67274C2211yescharacteristic
25#10625109C2211yescharacteristic
26D4×Dic23C2211yescharacteristic
27C2×#67272C2211yescharacteristic
28#10625064—21no—
29#10625064C2211yescharacteristic
30C4⋊C4×D23—21no—
31C4⋊C4×D23C2211yescharacteristic
32#10625057—21no—
33#10625056—21no—
34#10625050—21no—
35#10625049—21no—
36C4×D92—21no—
37C4×D92C2211yescharacteristic
38#10625043—21no—
39#10625043C2211yescharacteristic
40#10625040C2211yescharacteristic
41C23×C4⋊C8C2211yescharacteristic
42C23×#103C2211yescharacteristic
43C23×#102C2211yescharacteristic
44#10625017C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51(C2×D23)⋊C8C2211yescharacteristic
52#10625000C2211yescharacteristic
53#10625000C2211yescharacteristic
54#10624997C2211yescharacteristic
55C8×Dic23C2211yescharacteristic
56#10624989C2211yescharacteristic
57#10624989C2211yescharacteristic
58C4⋊(C23⋊C8)C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23C2311yescharacteristic
62C2×C22⋊D23—21no—
63C22×Dic23—21no—
64#67292—22no—
65#67292—22no—
66C2×D92—21no—
67C2×D92C2311yescharacteristic
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23C2311yescharacteristic
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⋊C4×C23—21no—
82C42×C23—21no—
83C42×C23C2311yescharacteristic
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86#67274—22no—
87#67272—22no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4D411yescharacteristic
92(C2×D23)⋊C4D411yescharacteristic
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4D411yescharacteristic
102Dic23⋊C4D411yescharacteristic
103C4×Dic23—21no—
104C4×Dic23—21no—
105C4×Dic23C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C22×D23—21no—
110C22×D23C2×D411yescharacteristic
111Q8×C23—21no—
112Q8×C23—21no—
113Q8×C23—21no—
114Q8×C23#4112yes—
115D4×C23—21no—
116D4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2×D411yescharacteristic
122C2×C4×C23C2411yescharacteristic
123C22⋊D23—81no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23—21no—
127C2×Dic23—81no—
128C2×Dic23C2×D411yescharacteristic
129C2×Dic23C2×D411yescharacteristic
130C2×Dic23C2×D411yescharacteristic
131D92—24no—
132D92—21no—
133D92#4112yes—
134C4×D23—24no—
135C4×D23—21no—
136C4×D23—21no—
137C4×D23—81no—
138C4×D23—81no—
139C4×D23—81no—
140Dic46—81no—
141C8×C23—21no—
142C8×C23—21no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3124—231nomaximal, Sylow
146C22×C23—41no—
147C22×C23—41no—
148C22×C23—41no—
149C22×C23C22×D411yescharacteristic
150C2×D23—21no—
151C2×D23—22no—
152C2×D23—21no—
153C2×D23—21no—
154C2×D23—41no—
155C2×D23—41no—
156C4×C23—22no—
157C4×C23—21no—
158C4×C23—21no—
159C4×C23—41no—
160C4×C23—41no—
161C4×C23C2×#4111yescharacteristic
162C4×C23C2×#4111yescharacteristic
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#464D2311yescharacteristic, complemented
176#463—231no—
177#452—231no—
178#449—231no—
179#440—231no—
180#440—231no—
181C4×Q16—231no—
182C4×D8—231no—
183#433—231no—
184C2×C23—81no—
185C2×C23#52511yescharacteristic
186C2×C23#57611yescharacteristic
187C2×C23#57811yescharacteristic
188D23—41no—
189D23—42no—
190C2×#41—231no—
191C2×Q16C2×D2311yescharacteristic
192C2×SD16—231no—
193C2×SD16C2×D2311yescharacteristic
194C2×D8—231no—
195C4⋊Q8—231no—
196#126—461no—
197#124—461no—
198#124C2×D2311yescharacteristic
199#123—461no—
200C22⋊Q8—231no—
201C22⋊Q8—461no—
202#121—231no—
203C4×Q8—231no—
204C4×Q8—231no—
205C4×Q8C2×D2311yescharacteristic
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⋊C8C2×D2311yescharacteristic
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⋊C8—231no—
231#97—231no—
232C4×C8—231no—
233C23#312411yescharacteristic, complemented, Sylow
234#41—462no—
235#41—462no—
236C2×Q8—461no—
237C2×Q8C22×D2311yescharacteristic
238C2×Q8C22×D2311yescharacteristic
239C2×D4—231no—
240C2×D4—461no—
241C2×D4—461no—
242C2×D4C22×D2311yescharacteristic
243C22×C4—231no—
244C22×C4—461no—
245C22×C4—461no—
246C22×C4—461no—
247C22×C4—461no—
248C22×C4—461no—
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—21no—
271C22⋊C4—231no—
272C22⋊C4—231no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4—461no—
277C22⋊C4—461no—
278C42—21no—
279C42—231no—
280C42—461no—
281C42—461no—
282C42C22×D2311yescharacteristic
283C23—21no—
284C23—231no—
285C23—461no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—1841no—
290Q8#6729012yes—
291D4—21no—
292D4—21no—
293D4—232no—
294D4—464no—
295D4—461no—
296D4—1841no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—231no—
301C2×C4—231no—
302C2×C4—231no—
303C2×C4—464no—
304C2×C4—461no—
305C2×C4—461no—
306C2×C4—461no—
307C2×C4—461no—
308C2×C4—461no—
309C2×C4—1841no—
310C2×C4—1841no—
311C2×C4—1841no—
312C2×C4—1841no—
313C2×C4D4×D2311yescharacteristic
314C2×C4D4×D2311yescharacteristic
315C2×C4C23×D2311yescharacteristic
316C8—21no—
317C8—21no—
318C8—461no—
319C8—461no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—462no—
324C22—461no—
325C22—461no—
326C22—461no—
327C22—921no—
328C22—921no—
329C22C2×D4×D2311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—461no—
336C4—461no—
337C4—461no—
338C4—921no—
339C4—921no—
340C4—921no—
341C4C2×#6729011yescharacteristic
342C4#41×D2311yescharacteristic
343C2—81no—
344C2—921no—
345C2—922no—
346C2#1309292711yescharacteristic
347C2#1309321911yescharacteristic
348C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#464C2
socleC22×C23C22×D4
prime radical#13092561C2
hypercenter#464D23
hypocenterC23#3124
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #13093036C2semidirect
2. #13092899C2semidirect
3. #13092751C2semidirect
4. #13092729C2semidirect
5. #13092712C2semidirect
6. #13092698C2semidirect
7. #13092629C2semidirect
8. #13092578C2semidirect
10. #13092520C2semidirect
11. #13092518C2semidirect
12. Q16×Dic23C2semidirect
13. #13092497C2semidirect
14. #13092477C2semidirect
15. C23×#464C2semidirect
175. #464D23semidirect
233. C23#3124semidirect

Maximal subgroups

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

subgroupindex
#130930362
#130928992
#130927512
#130927292
#130927122
#130926982
#130926292
#130925782
#130925612
#130925202
#130925182
Q16×Dic232
#130924972
#130924772
C23×#4642
#312423