Finite Group Databasebeta

← #15685295

Subgroups — #15685295

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#13093115C211yesmaximal, characteristic, complemented
2#13093078C211yesmaximal, characteristic, complemented
3#13092773C211yesmaximal, characteristic, complemented
4#13092757C211yesmaximal, characteristic, complemented
5#13092735C211yesmaximal, characteristic, complemented
6#13092726C211yesmaximal, characteristic, complemented
7#13092653C211yesmaximal, characteristic, complemented
8#13092649C211yesmaximal, characteristic, complemented
9#13092635C211yesmaximal, characteristic, complemented
10#13092565C211yesmaximal, characteristic, complemented
11#13092556C211yesmaximal, characteristic, complemented
12#13092502C211yesmaximal, characteristic, complemented
13C8×C22⋊D23C211yesmaximal, characteristic, complemented
14#13092412C211yesmaximal, characteristic, complemented
15C2×C23×#103C211yesmaximal, characteristic, complemented
16C22×Q8×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C22×C8×C23C2211yescharacteristic
19C2×C4⋊C4×C23C2211yescharacteristic
20#10625118—21no—
21#10625118C2211yescharacteristic
22#10625117—21no—
23#10625117C2211yescharacteristic
24Q8×Dic23C2211yescharacteristic
25C2×#67274C2211yescharacteristic
26C2×#67274C2211yescharacteristic
27#10625101—21no—
28#10625101—21no—
29#10625101C2211yescharacteristic
30#10625101C2211yescharacteristic
31C4×C22⋊D23—21no—
32C4×C22⋊D23—21no—
33C4×C22⋊D23C2211yescharacteristic
34C2×D184C2211yescharacteristic
35C2×C8×D23C2211yescharacteristic
36#10625069—21no—
37#10625066C2211yescharacteristic
38#10625065—21no—
39#10625064C2211yescharacteristic
40#10625063C2211yescharacteristic
41#10625061C2211yescharacteristic
42C23×#103C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C23×#103C2211yescharacteristic
45C23×#103C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625017C2211yescharacteristic
48C22⋊(C23⋊C8)C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51(C2×D23)⋊C8C2211yescharacteristic
52#10625000C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54C8×Dic23C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624990C2211yescharacteristic
59C2×Q8×C23—21no—
60C2×Q8×C23—22no—
61C2×Q8×C23—41no—
62C2×Q8×C23C2311yescharacteristic
63C2×Q8×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C22×C4×C23—21no—
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23D411yescharacteristic
70#67292—22no—
71#67292—41no—
72C2×D92—21no—
73C2×D92—21no—
74C2×D92C2311yescharacteristic
75C2×D92C2311yescharacteristic
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23C2311yescharacteristic
79C2×C8×C23—41no—
80C2×C8×C23C2311yescharacteristic
81C2×C8×C23C2311yescharacteristic
82C4⋊C4×C23—21no—
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊Dic23D411yescharacteristic
86#67274—22no—
87#67274—41no—
88(C2×D23)⋊C4—21no—
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)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4D411yescharacteristic
97C4⋊Dic23—21no—
98C4⋊Dic23—21no—
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109D184—41no—
110C8×D23—41no—
111C23×C23C2×D411yescharacteristic
112C22×D23—21no—
113C22×D23—21no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23—21no—
118Q8×C23—42no—
119Q8×C23#4112yes—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—42no—
127C2×C4×C23—81no—
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2411yescharacteristic
130C22⋊D23—22no—
131C22⋊D23—42no—
132C22⋊D23—42no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23C2×D411yescharacteristic
136C2×Dic23C2×D411yescharacteristic
137C2×Dic23C2×D411yescharacteristic
138D92—21no—
139D92—21no—
140D92—21no—
141D92—21no—
142D92—42no—
143D92—81no—
144C4×D23—21no—
145C4×D23—21no—
146C4×D23—42no—
147C4×D23—81no—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3301—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23#13512yes—
156C22×C23C22×D411yescharacteristic
157C2×D23—21no—
158C2×D23—21no—
159C2×D23—21no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—41no—
166C4×C23—22no—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23—41no—
171C4×C23C2×#4111yescharacteristic
172C4×C23H(5,𝔽2)11yescharacteristic
173Dic23—21no—
174Dic23—21no—
175Dic23—21no—
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#448—231no—
189C4×SD16—231no—
190C8×D4—231no—
191#416—231no—
192C2×#103D2311yescharacteristic, complemented
193C2×C23—22no—
194C2×C23#54611yescharacteristic
195C2×C23C2×#13511yescharacteristic
196C2×C23#57711yescharacteristic
197D23—41no—
198D23—81no—
199D23—81no—
200C2×#41—231no—
201C22×Q8C2×D2311yescharacteristic
202C2×SD16—231no—
203C2×SD16—231no—
204C2×D8—231no—
205C22×C8—231no—
206C22×C8C2×D2311yescharacteristic
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—231no—
217#121—461no—
218#121—461no—
219C4×Q8—231no—
220C4×D4—231no—
221C4×D4—231no—
222C4×D4—461no—
223C4×D4—461no—
224#117—231no—
225C2×C4⋊C4C2×D2311yescharacteristic
226#107—231no—
227#106—231no—
228#106—231no—
229C4⋊C8—231no—
230#103—231no—
231#103—231no—
232#103C2×D2311yescharacteristic
233#103C2×D2311yescharacteristic
234#103C2×D2311yescharacteristic
235#103C2×D2311yescharacteristic
236#102—231no—
237#102—231no—
238#102—231no—
239#102—231no—
240C22⋊C8—231no—
241C22⋊C8—231no—
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—231no—
252C2×D4—231no—
253C2×D4—231no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4—461no—
257C2×D4—461no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—231no—
261C22×C4—461no—
262C22×C4—461no—
263C22×C4C22×D2311yescharacteristic
264SD16—462no—
265SD16—921no—
266D8—921no—
267C2×C8—41no—
268C2×C8—231no—
269C2×C8—231no—
270C2×C8—921no—
271C2×C8C22×D2311yescharacteristic
272C2×C8C22×D2311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—231no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4C22×D2311yescharacteristic
282C4⋊C4C22×D2311yescharacteristic
283C22⋊C4—231no—
284C22⋊C4—231no—
285C22⋊C4—461no—
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—231no—
297C23—461no—
298C23—461no—
299C23D4×D2311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#6728812yes—
305D4—462no—
306D4—461no—
307D4—461no—
308D4—461no—
309D4—461no—
310D4—922no—
311D4—922no—
312D4—922no—
313D4—1841no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—231no—
323C2×C4—231no—
324C2×C4—231no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—461no—
328C2×C4—461no—
329C2×C4—922no—
330C2×C4—1841no—
331C2×C4D4×D2311yescharacteristic
332C2×C4C23×D2311yescharacteristic
333C8—21no—
334C8—21no—
335C8—461no—
336C8—461no—
337C22—21no—
338C22—21no—
339C22—461no—
340C22—461no—
341C22—461no—
342C22—921no—
343C22—921no—
344C22—921no—
345C22—921no—
346C22—921no—
347C22—921no—
348C22#1062509012yes—
349C22C2×D4×D2311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—461no—
356C4—461no—
357C4—461no—
358C4—921no—
359C4—921no—
360C4C2×#6728811yescharacteristic
361C4#1062515511yescharacteristic
362C2—22no—
363C2—921no—
364C2—1841no—
365C2—1841no—
366C2#1309305711yescharacteristic
367C2C2×#1062509011yescharacteristic
368C2#1309322311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#103C2
socleC22×C23C22×D4
hypercenterC2×#103D23
hypocenterC23#3301
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #13093115C2semidirect
2. #13093078C2semidirect
3. #13092773C2semidirect
4. #13092757C2semidirect
5. #13092735C2semidirect
6. #13092726C2semidirect
7. #13092653C2semidirect
8. #13092649C2semidirect
9. #13092635C2semidirect
10. #13092565C2semidirect
11. #13092556C2semidirect
12. #13092502C2semidirect
13. C8×C22⋊D23C2semidirect
14. #13092412C2semidirect
15. C2×C23×#103C2semidirect
192. C2×#103D23semidirect
243. C23#3301semidirect

Maximal subgroups

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

subgroupindex
#130931152
#130930782
#130927732
#130927572
#130927352
#130927262
#130926532
#130926492
#130926352
#130925652
#130925562
#130925022
C8×C22⋊D232
#130924122
C2×C23×#1032
#330123