Finite Group Databasebeta

← #15685299

Subgroups — #15685299

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#13093113C211yesmaximal, characteristic, complemented
2#13092771C211yesmaximal, characteristic, complemented
3#13092755C211yesmaximal, characteristic, complemented
4#13092733C211yesmaximal, characteristic, complemented
5#13092724C211yesmaximal, characteristic, complemented
6#13092651C211yesmaximal, characteristic, complemented
7#13092648C211yesmaximal, characteristic, complemented
8#13092629C211yesmaximal, characteristic, complemented
9#13092562C211yesmaximal, characteristic, complemented
10#13092556C211yesmaximal, characteristic, complemented
11C4×#67274C211yesmaximal, characteristic, complemented
12D4×C23⋊C8C211yesmaximal, characteristic, complemented
13#13092413C211yesmaximal, characteristic, complemented
14C2×#10625017C211yesmaximal, characteristic, complemented
15C23×#548C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C22×Q8×C23C2211yescharacteristic
18C23×#124—21no—
19C23×#124C2211yescharacteristic
20C23×C22⋊Q8—21no—
21C23×C22⋊Q8C2211yescharacteristic
22C23×#121—21no—
23C23×#121C2211yescharacteristic
24C4×Q8×C23C2211yescharacteristic
25C4×D4×C23—21no—
26C4×D4×C23C2211yescharacteristic
27C2×#67274C2211yescharacteristic
28C2×#67274C2211yescharacteristic
29#10625110—21no—
30C2×#67272C2211yescharacteristic
31#10625101C2211yescharacteristic
32#10625101C2211yescharacteristic
33#10625097C2211yescharacteristic
34C2×C4⋊Dic23C2211yescharacteristic
35C22×C23⋊C8C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic
37#10625069—21no—
38#10625054—21no—
39(C22⋊D23)⋊C4—21no—
40C4×D92C2211yescharacteristic
41#10625041C2211yescharacteristic
42#10625017C2211yescharacteristic
43#10625017C2211yescharacteristic
44#10625017C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625017C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic
50#10625014C2211yescharacteristic
51C22⋊(C23⋊C8)C2211yescharacteristic
52C22⋊(C23⋊C8)C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624990C2211yescharacteristic
55#10624990C2211yescharacteristic
56#10624989C2211yescharacteristic
57C4⋊(C23⋊C8)C2211yescharacteristic
58C4×C23⋊C8C2211yescharacteristic
59#41×C23—22no—
60#41×C23—41no—
61C2×Q8×C23—21no—
62C2×Q8×C23—22no—
63C2×Q8×C23—41no—
64C2×Q8×C23C2311yescharacteristic
65C2×Q8×C23C2311yescharacteristic
66C2×D4×C23—21no—
67C2×D4×C23—21no—
68C2×D4×C23D411yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C22×C4×C23—21no—
71C22×C4×C23—21no—
72C22×C4×C23C2311yescharacteristic
73C22×C4×C23C2311yescharacteristic
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76C22×Dic23—21no—
77C2×D92C2311yescharacteristic
78C2×C4×D23—21no—
79C4⋊C4×C23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23D411yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C22⋊C4×C23—21no—
84C22⋊C4×C23—21no—
85C22⋊C4×C23—21no—
86C22⋊C4×C23—21no—
87C22⋊C4×C23D411yescharacteristic
88C22⋊C4×C23D411yescharacteristic
89C42×C23—21no—
90C42×C23C2311yescharacteristic
91C22⋊Dic23—21no—
92#67274—22no—
93#67274—41no—
94#67272—41no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98C4⋊Dic23—21no—
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104C4×Dic23—21no—
105C2×C23⋊C8—41no—
106C2×C23⋊C8—41no—
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C2×C23⋊C8C2311yescharacteristic
111C23×C23—21no—
112C23×C23C2×D411yescharacteristic
113C23×C23C2×D411yescharacteristic
114C22×D23—21no—
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23—21no—
118Q8×C23—42no—
119Q8×C23#4112yes—
120D4×C23—22no—
121D4×C23—21no—
122D4×C23—21no—
123D4×C23—42no—
124D4×C23—42no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—42no—
133C2×C4×C23—42no—
134C2×C4×C23C2×D411yescharacteristic
135C2×C4×C23C2×D411yescharacteristic
136C2×C4×C23C2×D411yescharacteristic
137C2×C4×C23C2×D411yescharacteristic
138C2×C4×C23C2411yescharacteristic
139C22⋊D23—42no—
140C22⋊D23—81no—
141C2×Dic23—21no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—81no—
145D92—21no—
146D92—21no—
147C4×D23—81no—
148C23⋊C8—21no—
149C23⋊C8—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3301—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—21no—
156C22×C23—21no—
157C22×C23—21no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23#13512yes—
162C22×C23C22×D411yescharacteristic
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—41no—
166C4×C23—21no—
167C4×C23—21no—
168C4×C23—22no—
169C4×C23—21no—
170C4×C23—21no—
171C4×C23—41no—
172C4×C23—41no—
173C4×C23C2×#4111yescharacteristic
174C4×C23H(5,𝔽2)11yescharacteristic
175Dic23—41no—
176Dic23—41no—
177Dic23—41no—
178#553—231no—
179#548D2311yescharacteristic, complemented
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×#103—231no—
193C2×C23—22no—
194C2×C23—41no—
195C2×C23—81no—
196C2×C23#54611yescharacteristic
197C2×C23C2×#13511yescharacteristic
198C2×C23#57711yescharacteristic
199D23—81no—
200C2×#41C2×D2311yescharacteristic
201C22×Q8C2×D2311yescharacteristic
202C2×SD16—231no—
203C2×SD16—231no—
204C2×D8—231no—
205C22×C8—231no—
206C22×C8—231no—
207#126—461no—
208#125—231no—
209#124—21no—
210#124C2×D2311yescharacteristic
211#123—461no—
212C22⋊Q8—21no—
213C22⋊Q8C2×D2311yescharacteristic
214#121—21no—
215#121—231no—
216#121—231no—
217#121—461no—
218#121C2×D2311yescharacteristic
219C4×Q8C2×D2311yescharacteristic
220C4×D4—21no—
221C4×D4—231no—
222C4×D4—461no—
223C4×D4C2×D2311yescharacteristic
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#103—231no—
235#103—231no—
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—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D2311yescharacteristic
250C2×Q8C22×D2311yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—231no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4C22⋊D2311yescharacteristic
257C2×D4C22×D2311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4C22×D2311yescharacteristic
263C22×C4C22×D2311yescharacteristic
264SD16—462no—
265SD16—921no—
266D8—921no—
267C2×C8—231no—
268C2×C8—231no—
269C2×C8—231no—
270C2×C8—231no—
271C2×C8—921no—
272C2×C8—921no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—231no—
276C4⋊C4—231no—
277C4⋊C4—231no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4C22⋊D2311yescharacteristic
282C4⋊C4C22×D2311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4C22⋊D2311yescharacteristic
292C22⋊C4C22⋊D2311yescharacteristic
293C42—21no—
294C42—461no—
295C42C22×D2311yescharacteristic
296C23—21no—
297C23—461no—
298C23C2×C22⋊D2311yescharacteristic
299C23C2×C22⋊D2311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#6729012yes—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—42no—
310D4—461no—
311D4—461no—
312D4—922no—
313D4—1841no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—1841no—
327C2×C4—1841no—
328C2×C4C2×C22⋊D2311yescharacteristic
329C2×C4C2×C22⋊D2311yescharacteristic
330C2×C4C2×C22⋊D2311yescharacteristic
331C2×C4C2×C22⋊D2311yescharacteristic
332C2×C4C23×D2311yescharacteristic
333C8—461no—
334C8—461no—
335C8—461no—
336C8—461no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—921no—
346C22—921no—
347C22—921no—
348C22#1062512112yes—
349C22C22×C22⋊D2311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—921no—
358C4—921no—
359C4—921no—
360C4C2×#6729011yescharacteristic
361C4#1062515511yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—1841no—
366C2#1309306111yescharacteristic
367C2C2×#1062512111yescharacteristic
368C2#1309322511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#548C2
socleC22×C23C22×D4
hypercenter#548D23
hypocenterC23#3301
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #13093113C2semidirect
2. #13092771C2semidirect
3. #13092755C2semidirect
4. #13092733C2semidirect
5. #13092724C2semidirect
6. #13092651C2semidirect
7. #13092648C2semidirect
8. #13092629C2semidirect
9. #13092562C2semidirect
10. #13092556C2semidirect
11. C4×#67274C2semidirect
12. D4×C23⋊C8C2semidirect
13. #13092413C2semidirect
14. C2×#10625017C2semidirect
15. C23×#548C2semidirect
179. #548D23semidirect
243. C23#3301semidirect

Maximal subgroups

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

subgroupindex
#130931132
#130927712
#130927552
#130927332
#130927242
#130926512
#130926482
#130926292
#130925622
#130925562
C4×#672742
D4×C23⋊C82
#130924132
C2×#106250172
C23×#5482
#330123