Finite Group Databasebeta

← #15685288

Subgroups — #15685288

Order 2944.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093109C211yesmaximal, characteristic, complemented
2#13093078C211yesmaximal, characteristic
3#13092773C211yesmaximal, characteristic, complemented
4#13092757C211yesmaximal, characteristic, complemented
5#13092731C211yesmaximal, characteristic, complemented
6#13092726C211yesmaximal, characteristic, complemented
7#13092655C211yesmaximal, characteristic, complemented
8#13092648C211yesmaximal, characteristic, complemented
9#13092641C211yesmaximal, characteristic, complemented
10#13092578C211yesmaximal, characteristic, complemented
11Q16×Dic23C211yesmaximal, characteristic, complemented
12(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
13#13092412C211yesmaximal, characteristic, complemented
14C2×#10625017C211yesmaximal, characteristic, complemented
15C23×#451C211yesmaximal, characteristic, complemented
16C22×Q8×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C2×Q16×C23C2211yescharacteristic
19C2×Q16×C23C2211yescharacteristic
20C23×C22⋊Q8C2211yescharacteristic
21#10625118—21no—
22#10625118C2211yescharacteristic
23#10625117—21no—
24#10625117C2211yescharacteristic
25#10625117C2211yescharacteristic
26Q8×Dic23C2211yescharacteristic
27Q8×Dic23C2211yescharacteristic
28C2×#67274C2211yescharacteristic
29#10625101—21no—
30#10625101C2211yescharacteristic
31C4×C22⋊D23—21no—
32C4×C22⋊D23C2211yescharacteristic
33C2×C4⋊Dic23C2211yescharacteristic
34C22×C23⋊C8C2211yescharacteristic
35C2×C8×D23C2211yescharacteristic
36#10625069—21no—
37#10625063C2211yescharacteristic
38#10625061—21no—
39#10625061C2211yescharacteristic
40#10625057—21no—
41#10625048—21no—
42C23×#103C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625017C2211yescharacteristic
48#10625017C2211yescharacteristic
49#10625017C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic
52(C2×D23)⋊C8C2211yescharacteristic
53#10625000C2211yescharacteristic
54#10625000C2211yescharacteristic
55Dic23⋊C8C2211yescharacteristic
56C8×Dic23C2211yescharacteristic
57#10624991C2211yescharacteristic
58#10624990C2211yescharacteristic
59C2×Q8×C23—21no—
60C2×Q8×C23—22no—
61C2×Q8×C23—41no—
62C2×Q8×C23C2311yescharacteristic
63C2×Q8×C23C2311yescharacteristic
64C2×Q8×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—21no—
68C2×C22⋊D23D411yescharacteristic
69C22×Dic23—21no—
70#67292—22no—
71#67292—41no—
72C2×D92—21no—
73C2×D92C2311yescharacteristic
74C2×C4×D23—21no—
75C2×C4×D23C2311yescharacteristic
76Q16×C23—22no—
77Q16×C23—41no—
78C2×C8×C23C2311yescharacteristic
79C2×C8×C23C2311yescharacteristic
80C4⋊C4×C23—21no—
81C4⋊C4×C23C2311yescharacteristic
82C22⋊C4×C23—21no—
83C22⋊Dic23D411yescharacteristic
84#67274—41no—
85(C2×D23)⋊C4—21no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4D411yescharacteristic
92C4⋊Dic23—21no—
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4D411yescharacteristic
103C4×Dic23—21no—
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8—41no—
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C8×D23—41no—
111C23×C23C2×D411yescharacteristic
112C22×D23—21no—
113C22×D23C2×D411yescharacteristic
114Q8×C23—21no—
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23—21no—
118Q8×C23—21no—
119Q8×C23—42no—
120Q8×C23#4112yes—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—42no—
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2411yescharacteristic
130C22⋊D23—22no—
131C22⋊D23—42no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—42no—
136C2×Dic23C2×D411yescharacteristic
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139D92—21no—
140D92—21no—
141D92—42no—
142C4×D23—21no—
143C4×D23—21no—
144C4×D23—42no—
145C8×C23—21no—
146C8×C23—21no—
147C23⋊C8—21no—
148C23⋊C8—21no—
149#3300—231nomaximal, Sylow
150C22×C23—21no—
151C22×C23—21no—
152C22×C23#13512yes—
153C22×C23C22×D411yescharacteristic
154C2×D23—21no—
155C2×D23—21no—
156C2×D23—21no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C4×C23—22no—
161C4×C23—21no—
162C4×C23—41no—
163C4×C23—41no—
164C4×C23—41no—
165C4×C23C2×#4111yescharacteristic
166C4×C23H(5,𝔽2)11yescharacteristic
167Dic23—21no—
168Dic23—21no—
169Dic23—21no—
170Dic23—41no—
171Dic23—41no—
172Dic23—41no—
173#552—231no—
174#548—231no—
175#488—231no—
176#485—231no—
177#480—231no—
178#479—231no—
179#467—231no—
180#465—231no—
181#464—231no—
182#452—231no—
183#451D2311yescharacteristic, complemented
184C4×Q16—231no—
185C8×D4—231no—
186#416—231no—
187C2×#103—231no—
188C2×C23—22no—
189C2×C23#54611yescharacteristic
190C2×C23C2×#13511yescharacteristic
191C2×C23#57811yescharacteristic
192D23—41no—
193D23—81no—
194C2×#41—231no—
195C22×Q8C2×D2311yescharacteristic
196C2×Q16C2×D2311yescharacteristic
197C2×Q16C2×D2311yescharacteristic
198C2×SD16—231no—
199C22×C8—231no—
200C22×C8—231no—
201#126—461no—
202#125—231no—
203#125—461no—
204#124—231no—
205#124—461no—
206#123—461no—
207C22⋊Q8—231no—
208C22⋊Q8—231no—
209C22⋊Q8—461no—
210C22⋊Q8C2×D2311yescharacteristic
211#121—231no—
212#121—461no—
213C4×Q8—231no—
214C4×Q8—231no—
215C4×D4—231no—
216C4×D4—461no—
217#117—231no—
218#117—461no—
219C2×C4⋊C4—231no—
220#107—231no—
221#107—231no—
222#106—231no—
223C4⋊C8—231no—
224#103—231no—
225#103—231no—
226#103—231no—
227#103—231no—
228#103—231no—
229#103C2×D2311yescharacteristic
230#103C2×D2311yescharacteristic
231#102—231no—
232#102—231no—
233#102—231no—
234C22⋊C8—231no—
235C22⋊C8C2×D2311yescharacteristic
236C4×C8—231no—
237C23#330011yescharacteristic, complemented, Sylow
238#41—462no—
239#41—921no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8C22×D2311yescharacteristic
244C2×Q8C22×D2311yescharacteristic
245C2×Q8C22×D2311yescharacteristic
246C2×D4—231no—
247C2×D4—231no—
248C2×D4—461no—
249C2×D4—461no—
250C22×C4—21no—
251C22×C4—231no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4C22×D2311yescharacteristic
255Q16—22no—
256Q16—41no—
257SD16—921no—
258C2×C8—231no—
259C2×C8—231no—
260C2×C8—921no—
261C2×C8—921no—
262C2×C8C22×D2311yescharacteristic
263C2×C8C22×D2311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4—461no—
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—231no—
279C22⋊C4—231no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C22⋊C4—461no—
286C42—231no—
287C42—461no—
288C42—461no—
289C42—461no—
290C23—231no—
291C23—461no—
292C23D4×D2311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8#6729012yes—
300D4—462no—
301D4—461no—
302D4—461no—
303D4—922no—
304D4—922no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—231no—
313C2×C4—231no—
314C2×C4—231no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—461no—
319C2×C4—461no—
320C2×C4—922no—
321C2×C4—922no—
322C2×C4D4×D2311yescharacteristic
323C2×C4C23×D2311yescharacteristic
324C8—21no—
325C8—21no—
326C8—461no—
327C8—461no—
328C22—21no—
329C22—21no—
330C22—461no—
331C22—461no—
332C22—461no—
333C22—921no—
334C22—921no—
335C22—921no—
336C22#1062509012yes—
337C22C2×D4×D2311yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—461no—
344C4—461no—
345C4—461no—
346C4—921no—
347C4—921no—
348C4—921no—
349C4C2×#6729011yescharacteristic
350C4#1062515511yescharacteristic
351C2—22no—
352C2—921no—
353C2—1841no—
354C2#1309305411yescharacteristic
355C2C2×#1062509011yescharacteristic
356C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#451C2
socleC22×C23C22×D4
prime radical#13093078C2
hypercenter#451D23
hypocenterC23#3300
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #13093109C2semidirect
3. #13092773C2semidirect
4. #13092757C2semidirect
5. #13092731C2semidirect
6. #13092726C2semidirect
7. #13092655C2semidirect
8. #13092648C2semidirect
9. #13092641C2semidirect
10. #13092578C2semidirect
11. Q16×Dic23C2semidirect
12. (C22⋊D23)⋊C8C2semidirect
13. #13092412C2semidirect
14. C2×#10625017C2semidirect
15. C23×#451C2semidirect
183. #451D23semidirect
237. C23#3300semidirect

Maximal subgroups

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

subgroupindex
#130931092
#130930782
#130927732
#130927572
#130927312
#130927262
#130926552
#130926482
#130926412
#130925782
Q16×Dic232
(C22⋊D23)⋊C82
#130924122
C2×#106250172
C23×#4512
#330023