Finite Group Databasebeta

← #15683603

Subgroups — #15683603

Order 2944.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093023C211yesmaximal, characteristic, complemented
2#13092899C211yesmaximal, characteristic, complemented
3#13092737C211yesmaximal, characteristic, complemented
4#13092732C211yesmaximal, characteristic, complemented
5#13092714C211yesmaximal, characteristic, complemented
6#13092617C211yesmaximal, characteristic, complemented
7#13092613C211yesmaximal, characteristic, complemented
8#13092565C211yesmaximal, characteristic, complemented
9#13092565C211yesmaximal, characteristic, complemented
10#13092528C211yesmaximal, characteristic, complemented
11#13092520C211yesmaximal, characteristic, complemented
12#13092502C211yesmaximal, characteristic, complemented
13#13092499C211yesmaximal, characteristic, complemented
14#13092477C211yesmaximal, characteristic, complemented
15C23×#479C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C23×#125C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19Q8×Dic23C2211yescharacteristic
20C2×#67274C2211yescharacteristic
21C2×#67274C2211yescharacteristic
22C2×D184C2211yescharacteristic
23C2×D184C2211yescharacteristic
24#10625066—21no—
25#10625066—21no—
26#10625066C2211yescharacteristic
27#10625066C2211yescharacteristic
28#10625065—21no—
29#10625065—21no—
30#10625064—21no—
31#10625064C2211yescharacteristic
32#10625064C2211yescharacteristic
33#10625064C2211yescharacteristic
34C4⋊C4×D23—21no—
35C4⋊C4×D23C2211yescharacteristic
36#10625045C2211yescharacteristic
37C4×D92—21no—
38C4×D92C2211yescharacteristic
39#10625043—21no—
40#10625043C2211yescharacteristic
41C23×#107C2211yescharacteristic
42C23×#106C2211yescharacteristic
43C23×C4⋊C8C2211yescharacteristic
44C23×#103C2211yescharacteristic
45C23×#103C2211yescharacteristic
46#10625003C2211yescharacteristic
47#10625003C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50#10624997C2211yescharacteristic
51C8×Dic23C2211yescharacteristic
52#10624991C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58C4⋊(C23⋊C8)C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60#67292—22no—
61#67292—22no—
62C2×D92—21no—
63C2×D92—21no—
64C2×D92—21no—
65C2×D92—21no—
66C2×D92—21no—
67C2×D92C2311yescharacteristic
68C2×D92C2311yescharacteristic
69C2×D92C2311yescharacteristic
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×C4×D23C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C4⋊C4×C23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23—21no—
82C4⋊C4×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C42×C23—21no—
86C42×C23C2311yescharacteristic
87#67274—22no—
88#67274—22no—
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)⋊C4D411yescharacteristic
96(C2×D23)⋊C4D411yescharacteristic
97C4⋊Dic23—21no—
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4D411yescharacteristic
101Dic23⋊C4D411yescharacteristic
102C4×Dic23—21no—
103C4×Dic23C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106D184—22no—
107D184—22no—
108C22×D23—21no—
109C22×D23—21no—
110C22×D23—21no—
111C22×D23C2×D411yescharacteristic
112Q8×C23—21no—
113Q8×C23#4112yes—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23C2×D411yescharacteristic
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2411yescharacteristic
121C2×Dic23—21no—
122C2×Dic23C2×D411yescharacteristic
123C2×Dic23C2×D411yescharacteristic
124C2×Dic23C2×D411yescharacteristic
125D92—24no—
126D92—21no—
127D92—21no—
128D92—21no—
129D92—21no—
130D92—21no—
131D92—81no—
132D92—81no—
133D92—81no—
134D92—81no—
135D92#4112yes—
136C4×D23—24no—
137C4×D23—21no—
138C4×D23—21no—
139C4×D23—81no—
140C4×D23—81no—
141C4×D23—81no—
142C4×D23—81no—
143C4×D23—81no—
144C8×C23—21no—
145C8×C23—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3119—231nomaximal, Sylow
149C22×C23C22×D411yescharacteristic
150C2×D23—21no—
151C2×D23—22no—
152C2×D23—21no—
153C2×D23—21no—
154C2×D23—41no—
155C2×D23—41no—
156C2×D23—41no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C4×C23—22no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—41no—
166C4×C23—41no—
167C4×C23—41no—
168C4×C23C2×#4111yescharacteristic
169C4×C23C2×#4111yescharacteristic
170Dic23—21no—
171Dic23—21no—
172Dic23—21no—
173Dic23—41no—
174#540—231no—
175#520—231no—
176#481—231no—
177#480—231no—
178#479D2311yescharacteristic, complemented
179#478—231no—
180#460—231no—
181#459—231no—
182#449—231no—
183#449—231no—
184#442—231no—
185#440—231no—
186C4×SD16—231no—
187C4×D8—231no—
188#433—231no—
189C2×C23#52511yescharacteristic
190C2×C23#57611yescharacteristic
191C2×C23#57711yescharacteristic
192D23—41no—
193D23—42no—
194D23—81no—
195D23—81no—
196C2×#41—231no—
197C2×SD16—231no—
198C2×SD16—231no—
199C2×D8—231no—
200C2×D8—231no—
201#127—231no—
202#125C2×D2311yescharacteristic
203#123—461no—
204#123—461no—
205#121—231no—
206#121—231no—
207#121—461no—
208#121—461no—
209C4×Q8—231no—
210C4×Q8C2×D2311yescharacteristic
211C4×D4—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—231no—
215C4×D4—461no—
216C4×D4—461no—
217#117—231no—
218#117—461no—
219C2×C4⋊C4—231no—
220C2×C4⋊C4—461no—
221#107—231no—
222#107C2×D2311yescharacteristic
223#106—231no—
224#106C2×D2311yescharacteristic
225C4⋊C8—231no—
226C4⋊C8C2×D2311yescharacteristic
227#103C2×D2311yescharacteristic
228#103C2×D2311yescharacteristic
229#102—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102—231no—
235C22⋊C8—231no—
236C22⋊C8—231no—
237#97—231no—
238C4×C8—231no—
239C23#311911yescharacteristic, complemented, Sylow
240#41—462no—
241#41—462no—
242C2×Q8C22×D2311yescharacteristic
243C2×D4—231no—
244C2×D4—231no—
245C2×D4—231no—
246C2×D4—461no—
247C2×D4—461no—
248C2×D4—461no—
249C2×D4—461no—
250C2×D4—461no—
251C22×C4—231no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4—461no—
258SD16—462no—
259SD16—462no—
260D8—462no—
261D8—462no—
262C2×C8—231no—
263C2×C8—231no—
264C2×C8C22×D2311yescharacteristic
265C2×C8C22×D2311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—231no—
270C4⋊C4—231no—
271C4⋊C4—231no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4C22×D2311yescharacteristic
275C4⋊C4C22×D2311yescharacteristic
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—231no—
278C22⋊C4—231no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C42—21no—
286C42—231no—
287C42—461no—
288C42C22×D2311yescharacteristic
289C23—231no—
290C23—461no—
291C23—461no—
292C23—461no—
293Q8—21no—
294Q8#6729212yes—
295D4—232no—
296D4—464no—
297D4—461no—
298D4—461no—
299D4—461no—
300D4—461no—
301D4—461no—
302D4—1841no—
303D4—1841no—
304D4—1841no—
305D4—1841no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—231no—
311C2×C4—231no—
312C2×C4—231no—
313C2×C4—464no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—1841no—
318C2×C4—1841no—
319C2×C4—1841no—
320C2×C4—1841no—
321C2×C4—1841no—
322C2×C4D4×D2311yescharacteristic
323C2×C4D4×D2311yescharacteristic
324C2×C4C23×D2311yescharacteristic
325C8—21no—
326C8—21no—
327C8—461no—
328C8—461no—
329C22—462no—
330C22—461no—
331C22—461no—
332C22—461no—
333C22—921no—
334C22—921no—
335C22—921no—
336C22—921no—
337C22—921no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22C2×D4×D2311yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—461no—
349C4—461no—
350C4—461no—
351C4—921no—
352C4C2×#6729211yescharacteristic
353C4#41×D2311yescharacteristic
354C2—921no—
355C2—922no—
356C2—1841no—
357C2—1841no—
358C2#1309293011yescharacteristic
359C2#1309321911yescharacteristic
360C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#479C2
socleC22×C23C22×D4
hypercenter#479D23
hypocenterC23#3119
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #13093023C2semidirect
2. #13092899C2semidirect
3. #13092737C2semidirect
4. #13092732C2semidirect
5. #13092714C2semidirect
6. #13092617C2semidirect
7. #13092613C2semidirect
8. #13092565C2semidirect
9. #13092565C2semidirect
10. #13092528C2semidirect
11. #13092520C2semidirect
12. #13092502C2semidirect
13. #13092499C2semidirect
14. #13092477C2semidirect
15. C23×#479C2semidirect
178. #479D23semidirect
239. C23#3119semidirect

Maximal subgroups

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

subgroupindex
#130930232
#130928992
#130927372
#130927322
#130927142
#130926172
#130926132
#130925652
#130925282
#130925202
#130925022
#130924992
#130924772
C23×#4792
#311923