Finite Group Databasebeta

← #15685302

Subgroups — #15685302

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#13093111C211yesmaximal, characteristic, complemented
2#13093077C211yesmaximal, characteristic, complemented
3#13092773C211yesmaximal, characteristic, complemented
4#13092737C211yesmaximal, characteristic, complemented
5#13092723C211yesmaximal, characteristic, complemented
6#13092654C211yesmaximal, characteristic, complemented
7#13092648C211yesmaximal, characteristic, complemented
8#13092635C211yesmaximal, characteristic, complemented
9#13092564C211yesmaximal, characteristic, complemented
10#13092557C211yesmaximal, characteristic, complemented
11#13092504C211yesmaximal, characteristic, complemented
12(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
13#13092411C211yesmaximal, characteristic, complemented
14#103×D23C211yesmaximal, characteristic, complemented
15C23×#485C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C2×#67288C2211yescharacteristic
18C23×C22⋊Q8C2211yescharacteristic
19C23×#117C2211yescharacteristic
20#10625118C2211yescharacteristic
21C2×#67274C2211yescharacteristic
22#10625101C2211yescharacteristic
23C4×C22⋊D23C2211yescharacteristic
24C22×C23⋊C8C2211yescharacteristic
25C2×D184C2211yescharacteristic
26C2×#67263C2211yescharacteristic
27C2×C8×D23C2211yescharacteristic
28#10625067—21no—
29#10625066C2211yescharacteristic
30#10625066C2211yescharacteristic
31#10625064—21no—
32#10625064C2211yescharacteristic
33C4⋊C4×D23C2211yescharacteristic
34#10625061C2211yescharacteristic
35#10625058C2211yescharacteristic
36#10625056—21no—
37#10625055—21no—
38#10625055—21no—
39#10625054—21no—
40#10625047—21no—
41C4×D92—21no—
42C23×#107C2211yescharacteristic
43C23×#106C2211yescharacteristic
44C23×#103C2211yescharacteristic
45C23×#103C2211yescharacteristic
46C23×C22⋊C8C2211yescharacteristic
47#10625017C2211yescharacteristic
48#10625003C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50#10624998C2211yescharacteristic
51Dic23⋊C8C2211yescharacteristic
52C8×Dic23C2211yescharacteristic
53#10624992C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624991C2211yescharacteristic
58#10624990C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C22×C4×C23C2311yescharacteristic
61C2×C22⋊D23—21no—
62C2×C22⋊D23—21no—
63C2×C22⋊D23D411yescharacteristic
64Q8×D23—22no—
65Q8×D23—41no—
66#67288—22no—
67#67288—41no—
68C2×D92—21no—
69C2×D92—21no—
70C2×D92C2311yescharacteristic
71C2×D92C2311yescharacteristic
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×C4×D23C2311yescharacteristic
77C2×Dic46—21no—
78C2×Dic46C2311yescharacteristic
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C4⋊C4×C23—21no—
82C4⋊C4×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊C4×C23—21no—
86C22⋊C4×C23—21no—
87C42×C23—21no—
88C22⋊Dic23D411yescharacteristic
89#67274—41no—
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⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4D411yescharacteristic
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8—41no—
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108D184—41no—
109#67263—22no—
110C8×D23—41no—
111C23×C23C2×D411yescharacteristic
112C22×D23—21no—
113C22×D23—21no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2411yescharacteristic
125C22⋊D23—22no—
126C22⋊D23—42no—
127C22⋊D23—81no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23C2×D411yescharacteristic
131C2×Dic23C2×D411yescharacteristic
132C2×Dic23C2×D411yescharacteristic
133D92—21no—
134D92—21no—
135D92—21no—
136D92—21no—
137D92—42no—
138D92—42no—
139C4×D23—21no—
140C4×D23—21no—
141C4×D23—42no—
142C4×D23—42no—
143C4×D23—81no—
144C4×D23—81no—
145Dic46—21no—
146Dic46—42no—
147Dic46#4112yes—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3301—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—21no—
156C22×C23C22×D411yescharacteristic
157C2×D23—21no—
158C2×D23—21no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23#13512yes—
166C4×C23—21no—
167C4×C23—41no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23—41no—
171C4×C23C2×#4111yescharacteristic
172C4×C23H(5,𝔽2)11yescharacteristic
173Dic23—22no—
174Dic23—21no—
175Dic23—21no—
176Dic23—21no—
177Dic23—41no—
178#553—231no—
179#548—231no—
180#488—231no—
181#485D2311yescharacteristic, complemented
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×#103—231no—
193C2×C23—41no—
194C2×C23#54611yescharacteristic
195C2×C23C2×#13511yescharacteristic
196C2×C23#57711yescharacteristic
197D23—22no—
198D23—81no—
199D23—81no—
200C2×#41—231no—
201C22×Q8—231no—
202C2×SD16—231no—
203C2×SD16—231no—
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—461no—
213C22⋊Q8C2×D2311yescharacteristic
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#117C2×D2311yescharacteristic
225C2×C4⋊C4—231no—
226#107C2×D2311yescharacteristic
227#106—231no—
228#106C2×D2311yescharacteristic
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—231no—
247C2×Q8—461no—
248C2×Q8—462no—
249C2×Q8—921no—
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—231no—
259C22×C4—461no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4—461no—
263C22×C4C22×D2311yescharacteristic
264SD16—462no—
265SD16—921no—
266D8—921no—
267C2×C8—231no—
268C2×C8—231no—
269C2×C8—921no—
270C2×C8—921no—
271C2×C8C22×D2311yescharacteristic
272C2×C8C22×D2311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—461no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4C22×D2311yescharacteristic
281C4⋊C4C22×D2311yescharacteristic
282C4⋊C4C22×D2311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—231no—
286C22⋊C4—231no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C42—21no—
294C42—231no—
295C42—461no—
296C23—231no—
297C23—461no—
298C23—461no—
299C23D4×D2311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—232no—
303Q8—461no—
304Q8—922no—
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—231no—
321C2×C4—231no—
322C2×C4—231no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—922no—
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—21no—
340C22—232no—
341C22—461no—
342C22—461no—
343C22—921no—
344C22—921no—
345C22—921no—
346C22—921no—
347C22—921no—
348C22—921no—
349C22C2×D4×D2311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—461no—
356C4—461no—
357C4—461no—
358C4—462no—
359C4—921no—
360C4#41×D2311yescharacteristic
361C4#1062516011yescharacteristic
362C2—41no—
363C2—462no—
364C2—1841no—
365C2—1841no—
366C2#1309305911yescharacteristic
367C2#135×D2311yescharacteristic
368C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#485C2
socleC22×C23C22×D4
hypercenter#485D23
hypocenterC23#3301
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #13093111C2semidirect
2. #13093077C2semidirect
3. #13092773C2semidirect
4. #13092737C2semidirect
5. #13092723C2semidirect
6. #13092654C2semidirect
7. #13092648C2semidirect
8. #13092635C2semidirect
9. #13092564C2semidirect
10. #13092557C2semidirect
11. #13092504C2semidirect
12. (C22⋊D23)⋊C8C2semidirect
13. #13092411C2semidirect
14. #103×D23C2semidirect
15. C23×#485C2semidirect
181. #485D23semidirect
243. C23#3301semidirect

Maximal subgroups

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

subgroupindex
#130931112
#130930772
#130927732
#130927372
#130927232
#130926542
#130926482
#130926352
#130925642
#130925572
#130925042
(C22⋊D23)⋊C82
#130924112
#103×D232
C23×#4852
#330123