Finite Group Databasebeta

← #15683653

Subgroups — #15683653

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#13092897C211yesmaximal, characteristic, complemented
2#13092750C211yesmaximal, characteristic, complemented
3#13092728C211yesmaximal, characteristic, complemented
4#13092709C211yesmaximal, characteristic, complemented
5#13092694C211yesmaximal, characteristic, complemented
6#13092636C211yesmaximal, characteristic, complemented
7#13092629C211yesmaximal, characteristic, complemented
8#13092577C211yesmaximal, characteristic, complemented
9#13092560C211yesmaximal, characteristic
10#13092517C211yesmaximal, characteristic, complemented
11#13092515C211yesmaximal, characteristic, complemented
12C4×#67275C211yesmaximal, characteristic, complemented
13C4×#67272C211yesmaximal, characteristic, complemented
14#13092478C211yesmaximal, characteristic, complemented
15C23×#542C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C23×C4⋊Q8C2211yescharacteristic
18C23×#126—21no—
19C23×#124—21no—
20C23×#124C2211yescharacteristic
21C23×#123—21no—
22C23×C22⋊Q8—21no—
23C23×C22⋊Q8C2211yescharacteristic
24C23×#121C2211yescharacteristic
25C4×Q8×C23C2211yescharacteristic
26C4×D4×C23C2211yescharacteristic
27C23×#117C2211yescharacteristic
28C2×#67275C2211yescharacteristic
29C2×#67274C2211yescharacteristic
30C2×#67273C2211yescharacteristic
31C2×#67272C2211yescharacteristic
32C2×C4⋊Dic23C2211yescharacteristic
33#10625063—21no—
34C4⋊C4×D23—21no—
35(C22⋊D23)⋊C4—21no—
36(C22⋊D23)⋊C4—21no—
37C4×D92C2211yescharacteristic
38C4×D92C2211yescharacteristic
39C4×Dic46C2211yescharacteristic
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
59C2×Q8×C23—21no—
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23—21no—
62C2×D4×C23C2311yescharacteristic
63C22×C4×C23—21no—
64C22×C4×C23C2311yescharacteristic
65C2×C22⋊D23—21no—
66C22×Dic23—21no—
67#67288—22no—
68#67288—22no—
69C2×D92C2311yescharacteristic
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23—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×C23—21no—
84C22⋊C4×C23—21no—
85C22⋊C4×C23—21no—
86C22⋊C4×C23D411yescharacteristic
87C22⋊C4×C23D411yescharacteristic
88C42×C23—21no—
89C42×C23C2311yescharacteristic
90C42×C23C2311yescharacteristic
91#67275—22no—
92#67274—22no—
93#67273—22no—
94#67272—22no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97C4⋊Dic23—21no—
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102C4×Dic23—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—21no—
113Q8×C23—81no—
114D4×C23—21no—
115D4×C23—21no—
116D4×C23—81no—
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×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2411yescharacteristic
129C22⋊D23—24no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—81no—
134D92—21no—
135D92#4112yes—
136C4×D23—24no—
137C4×D23—81no—
138C4×D23—81no—
139Dic46—21no—
140Dic46#4112yes—
141C23⋊C8—21no—
142C23⋊C8—21no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3124—231nomaximal, Sylow
146C22×C23—21no—
147C22×C23—21no—
148C22×C23—21no—
149C22×C23—41no—
150C22×C23—41no—
151C22×C23—41no—
152C22×C23C22×D411yescharacteristic
153C2×D23—22no—
154C2×D23—41no—
155C2×D23—41no—
156C4×C23—21no—
157C4×C23—21no—
158C4×C23—21no—
159C4×C23—21no—
160C4×C23—21no—
161C4×C23—41no—
162C4×C23—41no—
163C4×C23—41no—
164C4×C23C2×#4111yescharacteristic
165C4×C23C2×#4111yescharacteristic
166Dic23—22no—
167Dic23—41no—
168Dic23—41no—
169#542D2311yescharacteristic, complemented
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×D8—231no—
183#433—231no—
184C2×C23—41no—
185C2×C23—81no—
186C2×C23#52511yescharacteristic
187C2×C23#57611yescharacteristic
188C2×C23#57811yescharacteristic
189D23—42no—
190C2×#41—231no—
191C2×Q16—231no—
192C2×SD16—231no—
193C2×SD16—231no—
194C2×D8—231no—
195C4⋊Q8C2×D2311yescharacteristic
196#126—21no—
197#124—21no—
198#124C2×D2311yescharacteristic
199#123—21no—
200C22⋊Q8—21no—
201C22⋊Q8C2×D2311yescharacteristic
202#121C2×D2311yescharacteristic
203C4×Q8—231no—
204C4×Q8—231no—
205C4×Q8C2×D2311yescharacteristic
206C4×D4—231no—
207C4×D4—231no—
208C4×D4—461no—
209C4×D4—461no—
210C4×D4C2×D2311yescharacteristic
211#117—461no—
212#117C2×D2311yescharacteristic
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#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—462no—
235#41—462no—
236C2×Q8—21no—
237C2×Q8—231no—
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—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—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4C22⋊D2311yescharacteristic
277C22⋊C4C22⋊D2311yescharacteristic
278C42—21no—
279C42—461no—
280C42—461no—
281C42C22×D2311yescharacteristic
282C42C22×D2311yescharacteristic
283C23—21no—
284C23—461no—
285C23C2×C22⋊D2311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—232no—
290Q8—461no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—232no—
295D4—464no—
296D4—461no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—464no—
304C2×C4—461no—
305C2×C4—461no—
306C2×C4—461no—
307C2×C4—1841no—
308C2×C4—1841no—
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—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—462no—
327C22—921no—
328C22—921no—
329C22C22×C22⋊D2311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—462no—
339C4—921no—
340C4—921no—
341C4#41×D2311yescharacteristic
342C4#41×D2311yescharacteristic
343C2—41no—
344C2—81no—
345C2—922no—
346C2#1309292411yescharacteristic
347C2#1309322011yescharacteristic
348C2#1309323211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#542C2
socleC22×C23C22×D4
prime radical#13092560C2
hypercenter#542D23
hypocenterC23#3124
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #13092897C2semidirect
2. #13092750C2semidirect
3. #13092728C2semidirect
4. #13092709C2semidirect
5. #13092694C2semidirect
6. #13092636C2semidirect
7. #13092629C2semidirect
8. #13092577C2semidirect
10. #13092517C2semidirect
11. #13092515C2semidirect
12. C4×#67275C2semidirect
13. C4×#67272C2semidirect
14. #13092478C2semidirect
15. C23×#542C2semidirect
169. #542D23semidirect
233. C23#3124semidirect

Maximal subgroups

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

subgroupindex
#130928972
#130927502
#130927282
#130927092
#130926942
#130926362
#130926292
#130925772
#130925602
#130925172
#130925152
C4×#672752
C4×#672722
#130924782
C23×#5422
#312423