Finite Group Databasebeta

← #15685293

Subgroups — #15685293

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#13093076C211yesmaximal, characteristic, complemented
2#13092774C211yesmaximal, characteristic, complemented
3#13092758C211yesmaximal, characteristic, complemented
4#13092735C211yesmaximal, characteristic, complemented
5#13092721C211yesmaximal, characteristic, complemented
6#13092651C211yesmaximal, characteristic, complemented
7#13092644C211yesmaximal, characteristic, complemented
8#13092632C211yesmaximal, characteristic, complemented
9#13092560C211yesmaximal, characteristic, complemented
10#13092555C211yesmaximal, characteristic, complemented
11C4×#67273C211yesmaximal, characteristic, complemented
12D4×C23⋊C8C211yesmaximal, characteristic, complemented
13#13092411C211yesmaximal, characteristic, complemented
14C2×#10624992C211yesmaximal, characteristic, complemented
15C23×#553C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C22×Dic46C2211yescharacteristic
18C23×#126—21no—
19C23×#125C2211yescharacteristic
20C23×#123—21no—
21C23×#121—21no—
22C23×#121C2211yescharacteristic
23C23×#121C2211yescharacteristic
24C4×D4×C23—21no—
25C4×D4×C23C2211yescharacteristic
26C4×D4×C23C2211yescharacteristic
27C23×#117C2211yescharacteristic
28C2×C4⋊C4×C23C2211yescharacteristic
29#10625110—21no—
30C2×#67273C2211yescharacteristic
31C2×#67273C2211yescharacteristic
32C2×#67272C2211yescharacteristic
33#10625101C2211yescharacteristic
34#10625095C2211yescharacteristic
35C22×C23⋊C8C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic
37#10625067—21no—
38#10625056—21no—
39(C22⋊D23)⋊C4—21no—
40#10625046C2211yescharacteristic
41C4×Dic46C2211yescharacteristic
42#10625014C2211yescharacteristic
43C22⋊(C23⋊C8)C2211yescharacteristic
44C22⋊(C23⋊C8)C2211yescharacteristic
45#10624992C2211yescharacteristic
46#10624992C2211yescharacteristic
47#10624992C2211yescharacteristic
48#10624992C2211yescharacteristic
49#10624992C2211yescharacteristic
50#10624992C2211yescharacteristic
51#10624991C2211yescharacteristic
52#10624991C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624990C2211yescharacteristic
55#10624990C2211yescharacteristic
56#10624989C2211yescharacteristic
57C4⋊(C23⋊C8)C2211yescharacteristic
58C4×C23⋊C8C2211yescharacteristic
59C2×D4×C23—21no—
60C2×D4×C23—21no—
61C2×D4×C23D411yescharacteristic
62C2×D4×C23C2311yescharacteristic
63C22×C4×C23—21no—
64C22×C4×C23—21no—
65C22×C4×C23C2311yescharacteristic
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C22×Dic23—21no—
70#67288—22no—
71#67288—41no—
72C2×D92C2311yescharacteristic
73C2×C4×D23—21no—
74C2×Dic46—22no—
75C2×Dic46—21no—
76C2×Dic46—41no—
77C2×Dic46C2311yescharacteristic
78C2×Dic46C2311yescharacteristic
79C4⋊C4×C23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23—21no—
82C4⋊C4×C23D411yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C4⋊C4×C23C2311yescharacteristic
86C22⋊C4×C23—21no—
87C22⋊C4×C23—21no—
88C22⋊C4×C23—21no—
89C22⋊C4×C23—21no—
90C22⋊C4×C23D411yescharacteristic
91C22⋊C4×C23D411yescharacteristic
92C42×C23—21no—
93C42×C23C2311yescharacteristic
94C22⋊Dic23—21no—
95#67273—22no—
96#67273—41no—
97#67272—41no—
98(C2×D23)⋊C4—21no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4—21no—
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—
115D4×C23—22no—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—42no—
119D4×C23—81no—
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—21no—
127C2×C4×C23—81no—
128C2×C4×C23—81no—
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2×D411yescharacteristic
131C2×C4×C23C2×D411yescharacteristic
132C2×C4×C23C2×D411yescharacteristic
133C2×C4×C23C2411yescharacteristic
134C22⋊D23—42no—
135C22⋊D23—42no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138C2×Dic23—21no—
139C2×Dic23—42no—
140D92—21no—
141D92—21no—
142C4×D23—42no—
143Dic46—21no—
144Dic46—21no—
145Dic46—21no—
146Dic46—42no—
147Dic46#4112yes—
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—21no—
169C4×C23—21no—
170C4×C23—41no—
171C4×C23—41no—
172C4×C23—41no—
173C4×C23C2×#4111yescharacteristic
174C4×C23H(5,𝔽2)11yescharacteristic
175Dic23—22no—
176Dic23—41no—
177Dic23—41no—
178#553D2311yescharacteristic, complemented
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×#103—231no—
193C2×C23—22no—
194C2×C23—41no—
195C2×C23—81no—
196C2×C23#54611yescharacteristic
197C2×C23C2×#13511yescharacteristic
198C2×C23#57711yescharacteristic
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—21no—
208#125C2×D2311yescharacteristic
209#124—231no—
210#124—461no—
211#123—21no—
212C22⋊Q8—231no—
213C22⋊Q8—461no—
214#121—21no—
215#121—231no—
216#121—461no—
217#121C2×D2311yescharacteristic
218#121C2×D2311yescharacteristic
219C4×Q8—231no—
220C4×D4—21no—
221C4×D4—461no—
222C4×D4C2×D2311yescharacteristic
223C4×D4C2×D2311yescharacteristic
224#117C2×D2311yescharacteristic
225C2×C4⋊C4C2×D2311yescharacteristic
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—462no—
245#41—921no—
246C2×Q8—231no—
247C2×Q8—231no—
248C2×Q8—462no—
249C2×Q8—461no—
250C2×Q8—921no—
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—21no—
276C4⋊C4—231no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4C22⋊D2311yescharacteristic
280C4⋊C4C22×D2311yescharacteristic
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—232no—
301Q8—461no—
302Q8—461no—
303Q8—461no—
304Q8—922no—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—461no—
311D4—461no—
312D4—922no—
313D4—922no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—922no—
327C2×C4—922no—
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—41no—
355C4—41no—
356C4—41no—
357C4—462no—
358C4—921no—
359C4—921no—
360C4#41×D2311yescharacteristic
361C4#1062516011yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—1841no—
366C2#1309305511yescharacteristic
367C2C2×#1062512111yescharacteristic
368C2#1309322811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#553C2
socleC22×C23C22×D4
hypercenter#553D23
hypocenterC23#3301
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #13093076C2semidirect
2. #13092774C2semidirect
3. #13092758C2semidirect
4. #13092735C2semidirect
5. #13092721C2semidirect
6. #13092651C2semidirect
7. #13092644C2semidirect
8. #13092632C2semidirect
9. #13092560C2semidirect
10. #13092555C2semidirect
11. C4×#67273C2semidirect
12. D4×C23⋊C8C2semidirect
13. #13092411C2semidirect
14. C2×#10624992C2semidirect
15. C23×#553C2semidirect
178. #553D23semidirect
243. C23#3301semidirect

Maximal subgroups

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

subgroupindex
#130930762
#130927742
#130927582
#130927352
#130927212
#130926512
#130926442
#130926322
#130925602
#130925552
C4×#672732
D4×C23⋊C82
#130924112
C2×#106249922
C23×#5532
#330123