Finite Group Databasebeta

← #15685303

Subgroups — #15685303

Order 2944.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093119C211yesmaximal, characteristic, complemented
2#13093078C211yesmaximal, characteristic, complemented
3#13092773C211yesmaximal, characteristic, complemented
4#13092756C211yesmaximal, characteristic, complemented
5#13092736C211yesmaximal, characteristic, complemented
6#13092722C211yesmaximal, characteristic, complemented
7#13092651C211yesmaximal, characteristic, complemented
8#13092643C211yesmaximal, characteristic, complemented
9#13092634C211yesmaximal, characteristic, complemented
10#13092561C211yesmaximal, characteristic, complemented
11SD16×Dic23C211yesmaximal, characteristic, complemented
12(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
13#13092412C211yesmaximal, characteristic, complemented
14C2×#10625017C211yesmaximal, characteristic, complemented
15C23×#448C211yesmaximal, characteristic, complemented
16C22×Q8×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C2×SD16×C23C2211yescharacteristic
20C23×#121C2211yescharacteristic
21#10625118—21no—
22#10625118C2211yescharacteristic
23#10625117—21no—
24#10625117C2211yescharacteristic
25Q8×Dic23C2211yescharacteristic
26#10625110—21no—
27#10625109C2211yescharacteristic
28D4×Dic23—21no—
29D4×Dic23C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625101—21no—
32#10625101C2211yescharacteristic
33C4×C22⋊D23—21no—
34C4×C22⋊D23C2211yescharacteristic
35C2×C4⋊Dic23C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic
37C2×C8×D23C2211yescharacteristic
38#10625063C2211yescharacteristic
39#10625061C2211yescharacteristic
40#10625057—21no—
41#10625050—21no—
42C23×#103C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625017C2211yescharacteristic
48#10625017C2211yescharacteristic
49#10625014C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic
52(C2×D23)⋊C8C2211yescharacteristic
53#10624999C2211yescharacteristic
54#10624999C2211yescharacteristic
55Dic23⋊C8C2211yescharacteristic
56C8×Dic23C2211yescharacteristic
57#10624991C2211yescharacteristic
58#10624989C2211yescharacteristic
59C2×Q8×C23—21no—
60C2×Q8×C23—22no—
61C2×Q8×C23—41no—
62C2×Q8×C23C2311yescharacteristic
63C2×Q8×C23C2311yescharacteristic
64C2×D4×C23—21no—
65C2×D4×C23C2311yescharacteristic
66C22×C4×C23—21no—
67C22×C4×C23C2311yescharacteristic
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23D411yescharacteristic
71C22×Dic23—21no—
72C22×Dic23—21no—
73#67292—22no—
74#67292—41no—
75C2×D92—21no—
76C2×D92C2311yescharacteristic
77C2×C4×D23—21no—
78C2×C4×D23C2311yescharacteristic
79SD16×C23—22no—
80SD16×C23—41no—
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C22⋊C4×C23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23D411yescharacteristic
88#67272—41no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4D411yescharacteristic
95C4⋊Dic23—21no—
96C4⋊Dic23—21no—
97C4⋊Dic23—21no—
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8—41no—
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C8×D23—41no—
111C23×C23—21no—
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23—21no—
118Q8×C23—42no—
119Q8×C23#4112yes—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23—42no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—42no—
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C22⋊D23—22no—
132C22⋊D23—42no—
133C22⋊D23—81no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—81no—
138C2×Dic23—81no—
139C2×Dic23C2×D411yescharacteristic
140C2×Dic23C2×D411yescharacteristic
141C2×Dic23C2×D411yescharacteristic
142D92—21no—
143D92—21no—
144D92—42no—
145C4×D23—21no—
146C4×D23—21no—
147C4×D23—42no—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3301—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23#13512yes—
159C22×C23C22×D411yescharacteristic
160C2×D23—21no—
161C2×D23—21no—
162C2×D23—21no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—41no—
166C4×C23—22no—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23C2×#4111yescharacteristic
171C4×C23H(5,𝔽2)11yescharacteristic
172Dic23—21no—
173Dic23—21no—
174Dic23—21no—
175Dic23—41no—
176Dic23—41no—
177Dic23—41no—
178#553—231no—
179#548—231no—
180#488—231no—
181#485—231no—
182#481—231no—
183#479—231no—
184#466—231no—
185#465—231no—
186#463—231no—
187#449—231no—
188#448D2311yescharacteristic, complemented
189C4×SD16—231no—
190C8×D4—231no—
191#416—231no—
192C2×#103—231no—
193C2×C23—22no—
194C2×C23—81no—
195C2×C23#54611yescharacteristic
196C2×C23C2×#13511yescharacteristic
197C2×C23#57711yescharacteristic
198D23—41no—
199D23—81no—
200C2×#41—231no—
201C22×Q8C2×D2311yescharacteristic
202C2×SD16C2×D2311yescharacteristic
203C2×SD16C2×D2311yescharacteristic
204C2×D8—231no—
205C22×C8—231no—
206C22×C8—231no—
207#126—461no—
208#125—231no—
209#124—231no—
210#124—461no—
211#123—461no—
212C22⋊Q8—231no—
213C22⋊Q8—461no—
214#121—231no—
215#121—231no—
216#121—461no—
217#121—461no—
218#121C2×D2311yescharacteristic
219C4×Q8—231no—
220C4×D4—231no—
221C4×D4—231no—
222C4×D4—461no—
223C4×D4—461no—
224#117—231no—
225C2×C4⋊C4—231no—
226#107—231no—
227#106—231no—
228#106—231no—
229C4⋊C8—231no—
230#103—231no—
231#103—231no—
232#103—231no—
233#103—231no—
234#103C2×D2311yescharacteristic
235#103C2×D2311yescharacteristic
236#102—231no—
237#102—231no—
238#102—231no—
239#102—231no—
240C22⋊C8—231no—
241C22⋊C8C2×D2311yescharacteristic
242C4×C8—231no—
243C23#330111yescharacteristic, complemented, Sylow
244#41—462no—
245#41—921no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D2311yescharacteristic
250C2×Q8C22×D2311yescharacteristic
251C2×D4—21no—
252C2×D4—231no—
253C2×D4—231no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4—461no—
257C2×D4C22×D2311yescharacteristic
258C22×C4—21no—
259C22×C4—231no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4—461no—
263C22×C4C22×D2311yescharacteristic
264SD16—22no—
265SD16—41no—
266D8—921no—
267C2×C8—231no—
268C2×C8—231no—
269C2×C8—921no—
270C2×C8—921no—
271C2×C8C22×D2311yescharacteristic
272C2×C8C22×D2311yescharacteristic
273C4⋊C4—231no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—231no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4—461no—
282C4⋊C4C22×D2311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—231no—
285C22⋊C4—231no—
286C22⋊C4—461no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C42—231no—
294C42—461no—
295C42—461no—
296C23—21no—
297C23—231no—
298C23—461no—
299C23D4×D2311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#6729012yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—462no—
309D4—461no—
310D4—461no—
311D4—922no—
312D4—922no—
313D4—1841no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—231no—
321C2×C4—231no—
322C2×C4—231no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—461no—
328C2×C4—922no—
329C2×C4—1841no—
330C2×C4—1841no—
331C2×C4D4×D2311yescharacteristic
332C2×C4C23×D2311yescharacteristic
333C8—21no—
334C8—21no—
335C8—461no—
336C8—461no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—461no—
343C22—461no—
344C22—461no—
345C22—921no—
346C22—921no—
347C22—921no—
348C22#1062508712yes—
349C22C2×D4×D2311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—461no—
355C4—461no—
356C4—461no—
357C4—921no—
358C4—921no—
359C4—921no—
360C4C2×#6729011yescharacteristic
361C4#1062515511yescharacteristic
362C2—22no—
363C2—81no—
364C2—921no—
365C2—1841no—
366C2#1309305411yescharacteristic
367C2C2×#1062508711yescharacteristic
368C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#448C2
socleC22×C23C22×D4
hypercenter#448D23
hypocenterC23#3301
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #13093119C2semidirect
2. #13093078C2semidirect
3. #13092773C2semidirect
4. #13092756C2semidirect
5. #13092736C2semidirect
6. #13092722C2semidirect
7. #13092651C2semidirect
8. #13092643C2semidirect
9. #13092634C2semidirect
10. #13092561C2semidirect
11. SD16×Dic23C2semidirect
12. (C22⋊D23)⋊C8C2semidirect
13. #13092412C2semidirect
14. C2×#10625017C2semidirect
15. C23×#448C2semidirect
188. #448D23semidirect
243. C23#3301semidirect

Maximal subgroups

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

subgroupindex
#130931192
#130930782
#130927732
#130927562
#130927362
#130927222
#130926512
#130926432
#130926342
#130925612
SD16×Dic232
(C22⋊D23)⋊C82
#130924122
C2×#106250172
C23×#4482
#330123