Finite Group Databasebeta

← #15683659

Subgroups — #15683659

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#13093038C211yesmaximal, characteristic, complemented
2#13092752C211yesmaximal, characteristic, complemented
3#13092730C211yesmaximal, characteristic, complemented
4#13092712C211yesmaximal, characteristic, complemented
5#13092697C211yesmaximal, characteristic, complemented
6#13092639C211yesmaximal, characteristic, complemented
7#13092632C211yesmaximal, characteristic, complemented
8#13092579C211yesmaximal, characteristic, complemented
9#13092562C211yesmaximal, characteristic
10#13092517C211yesmaximal, characteristic, complemented
11#13092515C211yesmaximal, characteristic, complemented
12C4×#67275C211yesmaximal, characteristic, complemented
13C4×#67272C211yesmaximal, characteristic, complemented
14#13092478C211yesmaximal, characteristic, complemented
15C23×#520C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C4×Q8×C23C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19C4×D4×C23—21no—
20C4×D4×C23—21no—
21C4×D4×C23C2211yescharacteristic
22C4×D4×C23C2211yescharacteristic
23C23×#117—21no—
24C23×#117C2211yescharacteristic
25C2×C4⋊C4×C23—21no—
26C2×C4⋊C4×C23C2211yescharacteristic
27C2×#67275C2211yescharacteristic
28C2×#67274C2211yescharacteristic
29C2×#67273C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625101C2211yescharacteristic
32#10625095C2211yescharacteristic
33#10625069—21no—
34#10625067—21no—
35#10625056—21no—
36#10625054—21no—
37#10625046C2211yescharacteristic
38C4×D92C2211yescharacteristic
39#10625040C2211yescharacteristic
40C4×Dic46C2211yescharacteristic
41#10625017C2211yescharacteristic
42#10625017C2211yescharacteristic
43#10625014C2211yescharacteristic
44#10625014C2211yescharacteristic
45C22⋊(C23⋊C8)C2211yescharacteristic
46C22⋊(C23⋊C8)C2211yescharacteristic
47#10624992C2211yescharacteristic
48#10624992C2211yescharacteristic
49#10624991C2211yescharacteristic
50#10624991C2211yescharacteristic
51#10624989C2211yescharacteristic
52#10624989C2211yescharacteristic
53#10624989C2211yescharacteristic
54#10624989C2211yescharacteristic
55C4⋊(C23⋊C8)C2211yescharacteristic
56C4⋊(C23⋊C8)C2211yescharacteristic
57#10624985C2211yescharacteristic
58C4×C23⋊C8C2211yescharacteristic
59#41×C23—22no—
60#41×C23—22no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C22×C4×C23—21no—
66C22×C4×C23—21no—
67C22×C4×C23—21no—
68C22×C4×C23C2311yescharacteristic
69C2×C22⋊D23—21no—
70C2×D92C2311yescharacteristic
71C2×C4×D23—21no—
72C2×Dic46—21no—
73C2×Dic46C2311yescharacteristic
74C4⋊C4×C23—21no—
75C4⋊C4×C23—21no—
76C4⋊C4×C23—21no—
77C4⋊C4×C23D411yescharacteristic
78C4⋊C4×C23D411yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C4⋊C4×C23C2311yescharacteristic
81C22⋊C4×C23—21no—
82C22⋊C4×C23—21no—
83C22⋊C4×C23D411yescharacteristic
84C22⋊C4×C23D411yescharacteristic
85C42×C23—21no—
86C42×C23—21no—
87C42×C23C2311yescharacteristic
88C42×C23C2311yescharacteristic
89C22⋊Dic23—21no—
90#67275—22no—
91#67274—22no—
92#67273—22no—
93#67272—22no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98C4⋊Dic23—21no—
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103C4×Dic23—21no—
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C23×C23C2×D411yescharacteristic
110C22×D23—21no—
111Q8×C23—21no—
112Q8×C23#4112yes—
113D4×C23—24no—
114D4×C23—21no—
115D4×C23#4112yes—
116C2×C4×C23—24no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—81no—
123C2×C4×C23—81no—
124C2×C4×C23—81no—
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C22⋊D23—81no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135D92—21no—
136D92—21no—
137C4×D23—81no—
138Dic46—21no—
139Dic46—21no—
140Dic46—81no—
141C23⋊C8—21no—
142C23⋊C8—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—21no—
159C4×C23—21no—
160C4×C23—21no—
161C4×C23—21no—
162C4×C23—41no—
163C4×C23—41no—
164C4×C23C2×#4111yescharacteristic
165C4×C23C2×#4111yescharacteristic
166Dic23—41no—
167Dic23—41no—
168Dic23—41no—
169#542—231no—
170#520D2311yescharacteristic, complemented
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×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×Q16—231no—
192C2×SD16—231no—
193C2×SD16—231no—
194C2×D8—231no—
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×Q8C2×D2311yescharacteristic
205C4×Q8C2×D2311yescharacteristic
206C4×D4—21no—
207C4×D4—21no—
208C4×D4—231no—
209C4×D4C2×D2311yescharacteristic
210C4×D4C2×D2311yescharacteristic
211#117—21no—
212#117C2×D2311yescharacteristic
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×D2311yescharacteristic
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#103—231no—
225#102—231no—
226#102—231no—
227#102—231no—
228#102—231no—
229C22⋊C8—231no—
230C22⋊C8—231no—
231#97—231no—
232C4×C8—231no—
233C23#312411yescharacteristic, complemented, Sylow
234#41—22no—
235#41—22no—
236C2×Q8—231no—
237C2×Q8—461no—
238C2×Q8C22×D2311yescharacteristic
239C2×D4—21no—
240C2×D4—231no—
241C2×D4—461no—
242C2×D4C22×D2311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—461no—
248C22×C4C22×D2311yescharacteristic
249Q16—462no—
250SD16—462no—
251SD16—462no—
252D8—462no—
253C2×C8—231no—
254C2×C8—231no—
255C2×C8—231no—
256C2×C8—231no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—231no—
261C4⋊C4—231no—
262C4⋊C4—461no—
263C4⋊C4—461no—
264C4⋊C4—461no—
265C4⋊C4C22⋊D2311yescharacteristic
266C4⋊C4C22⋊D2311yescharacteristic
267C4⋊C4C22×D2311yescharacteristic
268C4⋊C4C22×D2311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—461no—
272C22⋊C4—461no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4C22⋊D2311yescharacteristic
277C22⋊C4C22⋊D2311yescharacteristic
278C42—21no—
279C42—21no—
280C42—461no—
281C42C22×D2311yescharacteristic
282C42C22×D2311yescharacteristic
283C23—21no—
284C23—461no—
285C23C2×C22⋊D2311yescharacteristic
286Q8—21no—
287Q8—461no—
288Q8—461no—
289Q8—1841no—
290Q8#6728812yes—
291D4—24no—
292D4—21no—
293D4—461no—
294D4—461no—
295D4—1841no—
296D4#6728812yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—461no—
307C2×C4—461no—
308C2×C4—461no—
309C2×C4—1841no—
310C2×C4C2×C22⋊D2311yescharacteristic
311C2×C4C2×C22⋊D2311yescharacteristic
312C2×C4C2×C22⋊D2311yescharacteristic
313C2×C4C2×C22⋊D2311yescharacteristic
314C2×C4C2×C22⋊D2311yescharacteristic
315C2×C4C23×D2311yescharacteristic
316C8—461no—
317C8—461no—
318C8—461no—
319C8—461no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—921no—
327C22—921no—
328C22—921no—
329C22C22×C22⋊D2311yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—921no—
339C4—921no—
340C4—921no—
341C4C2×#6728811yescharacteristic
342C4C2×#6728811yescharacteristic
343C2—41no—
344C2—42no—
345C2—1841no—
346C2#1309292811yescharacteristic
347C2#1309322011yescharacteristic
348C2#1309323211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#520C2
socleC22×C23C22×D4
prime radical#13092562C2
hypercenter#520D23
hypocenterC23#3124
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #13093038C2semidirect
2. #13092752C2semidirect
3. #13092730C2semidirect
4. #13092712C2semidirect
5. #13092697C2semidirect
6. #13092639C2semidirect
7. #13092632C2semidirect
8. #13092579C2semidirect
10. #13092517C2semidirect
11. #13092515C2semidirect
12. C4×#67275C2semidirect
13. C4×#67272C2semidirect
14. #13092478C2semidirect
15. C23×#520C2semidirect
170. #520D23semidirect
233. C23#3124semidirect

Maximal subgroups

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

subgroupindex
#130930382
#130927522
#130927302
#130927122
#130926972
#130926392
#130926322
#130925792
#130925622
#130925172
#130925152
C4×#672752
C4×#672722
#130924782
C23×#5202
#312423