Finite Group Databasebeta

← #15685301

Subgroups — #15685301

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#13093076C211yesmaximal, characteristic, complemented
3#13092772C211yesmaximal, characteristic, complemented
4#13092759C211yesmaximal, characteristic, complemented
5#13092736C211yesmaximal, characteristic, complemented
6#13092725C211yesmaximal, characteristic, complemented
7#13092653C211yesmaximal, characteristic, complemented
8#13092646C211yesmaximal, characteristic, complemented
9#13092633C211yesmaximal, characteristic, complemented
10#13092564C211yesmaximal, characteristic, complemented
11#13092558C211yesmaximal, characteristic, complemented
12C4×#67263C211yesmaximal, characteristic, complemented
13#13092414C211yesmaximal, characteristic, complemented
14C2×#10624998C211yesmaximal, characteristic, complemented
15C8×D4×C23C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C22×Dic46C2211yescharacteristic
18C22×C8×C23C2211yescharacteristic
19C22×C8×C23C2211yescharacteristic
20C4×D4×C23C2211yescharacteristic
21#10625110—21no—
22#10625110—21no—
23#10625101C2211yescharacteristic
24#10625101C2211yescharacteristic
25#10625101C2211yescharacteristic
26#10625097C2211yescharacteristic
27C2×C4⋊Dic23C2211yescharacteristic
28#10625095C2211yescharacteristic
29C2×D184C2211yescharacteristic
30C2×#67263C2211yescharacteristic
31C2×#67263C2211yescharacteristic
32#10625069—21no—
33#10625067—21no—
34#10625056—21no—
35#10625054—21no—
36(C22⋊D23)⋊C4—21no—
37(C22⋊D23)⋊C4—21no—
38#10625046C2211yescharacteristic
39C4×D92C2211yescharacteristic
40#10625041C2211yescharacteristic
41C4×Dic46C2211yescharacteristic
42C23×C4⋊C8C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic
45C4×C8×C23C2211yescharacteristic
46#10625003C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625000C2211yescharacteristic
51#10624999C2211yescharacteristic
52#10624999C2211yescharacteristic
53#10624998C2211yescharacteristic
54#10624998C2211yescharacteristic
55#10624998C2211yescharacteristic
56#10624998C2211yescharacteristic
57#10624998C2211yescharacteristic
58#10624998C2211yescharacteristic
59C2×D4×C23D411yescharacteristic
60C22×C4×C23C2311yescharacteristic
61C22×C4×C23C2311yescharacteristic
62C2×C22⋊D23—21no—
63C2×C22⋊D23—21no—
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C22×Dic23—21no—
67C22×Dic23—21no—
68#67288—22no—
69#67288—41no—
70C2×D92C2311yescharacteristic
71C2×D92C2311yescharacteristic
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×Dic46—22no—
75C2×Dic46—21no—
76C2×Dic46—41no—
77C2×Dic46C2311yescharacteristic
78C2×Dic46C2311yescharacteristic
79C2×C8×C23—41no—
80C2×C8×C23—41no—
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C2×C8×C23C2311yescharacteristic
84C2×C8×C23C2311yescharacteristic
85C4⋊C4×C23D411yescharacteristic
86C22⋊C4×C23D411yescharacteristic
87C22⋊C4×C23D411yescharacteristic
88C42×C23C2311yescharacteristic
89C22⋊Dic23—21no—
90C22⋊Dic23—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)⋊C4—21no—
97C4⋊Dic23—21no—
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105Dic23⋊C4—21no—
106C4×Dic23—21no—
107C4×Dic23—21no—
108D184—41no—
109#67263—22no—
110#67263—41no—
111C23×C23C2×D411yescharacteristic
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114C22×D23—21no—
115D4×C23—22no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2×D411yescharacteristic
122C2×C4×C23C2×D411yescharacteristic
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2411yescharacteristic
125C22⋊D23—42no—
126C22⋊D23—42no—
127C22⋊D23—42no—
128C22⋊D23—81no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—42no—
136C2×Dic23—81no—
137D92—21no—
138D92—21no—
139D92—21no—
140D92—21no—
141C4×D23—42no—
142C4×D23—81no—
143Dic46—21no—
144Dic46—21no—
145Dic46—21no—
146Dic46—42no—
147Dic46#4112yes—
148C8×C23—21no—
149C8×C23—21no—
150C8×C23—21no—
151C8×C23—21no—
152#3301—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—21no—
156C22×C23—21no—
157C22×C23—21no—
158C22×C23#13512yes—
159C22×C23C22×D411yescharacteristic
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—41no—
166C4×C23—21no—
167C4×C23—21no—
168C4×C23—21no—
169C4×C23—21no—
170C4×C23C2×#4111yescharacteristic
171C4×C23H(5,𝔽2)11yescharacteristic
172Dic23—22no—
173Dic23—41no—
174Dic23—41no—
175Dic23—41no—
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×D4D2311yescharacteristic, complemented
191#416—231no—
192C2×#103—231no—
193C2×C23—22no—
194C2×C23—41no—
195C2×C23#54611yescharacteristic
196C2×C23C2×#13511yescharacteristic
197C2×C23#57711yescharacteristic
198D23—81no—
199D23—81no—
200C2×#41—231no—
201C22×Q8—231no—
202C2×SD16—231no—
203C2×SD16—231no—
204C2×D8—231no—
205C22×C8C2×D2311yescharacteristic
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—461no—
222C4×D4—461no—
223C4×D4C2×D2311yescharacteristic
224#117—231no—
225C2×C4⋊C4—231no—
226#107—231no—
227#106—231no—
228#106—231no—
229C4⋊C8C2×D2311yescharacteristic
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⋊C8C2×D2311yescharacteristic
241C22⋊C8C2×D2311yescharacteristic
242C4×C8C2×D2311yescharacteristic
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—231no—
252C2×D4—231no—
253C2×D4—461no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4—461no—
257C2×D4D9211yescharacteristic
258C22×C4—461no—
259C22×C4—461no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4C22×D2311yescharacteristic
263C22×C4C22×D2311yescharacteristic
264SD16—462no—
265SD16—921no—
266D8—921no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D2311yescharacteristic
270C2×C8C22×D2311yescharacteristic
271C2×C8C22×D2311yescharacteristic
272C2×C8C22×D2311yescharacteristic
273C4⋊C4—231no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—231no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4—461no—
282C4⋊C4D9211yescharacteristic
283C22⋊C4—461no—
284C22⋊C4—461no—
285C22⋊C4—461no—
286C22⋊C4—461no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4D9211yescharacteristic
292C22⋊C4D9211yescharacteristic
293C42—461no—
294C42—461no—
295C42C22×D2311yescharacteristic
296C23—461no—
297C23—461no—
298C23C2×D9211yescharacteristic
299C23C2×D9211yescharacteristic
300Q8—232no—
301Q8—461no—
302Q8—461no—
303Q8—461no—
304Q8—922no—
305D4—22no—
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—461no—
319C2×C4—461no—
320C2×C4—461no—
321C2×C4—461no—
322C2×C4—461no—
323C2×C4—461no—
324C2×C4—922no—
325C2×C4—922no—
326C2×C4—1841no—
327C2×C4—1841no—
328C2×C4C2×D9211yescharacteristic
329C2×C4C2×D9211yescharacteristic
330C2×C4C2×D9211yescharacteristic
331C2×C4C2×D9211yescharacteristic
332C2×C4C23×D2311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—921no—
343C22—921no—
344C22—921no—
345C22—921no—
346C22—921no—
347C22—921no—
348C22#1062507512yes—
349C22C22×D9211yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—462no—
355C4—921no—
356C4—921no—
357C4—921no—
358C4—921no—
359C4—921no—
360C4#1062515511yescharacteristic
361C4#41×D2311yescharacteristic
362C2—22no—
363C2—41no—
364C2—1841no—
365C2—1841no—
366C2#1309306211yescharacteristic
367C2C2×#1062507511yescharacteristic
368C2#1309322911yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC8×D4×C23C2
socleC22×C23C22×D4
hypercenterC8×D4D23
hypocenterC23#3301
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #13093113C2semidirect
2. #13093076C2semidirect
3. #13092772C2semidirect
4. #13092759C2semidirect
5. #13092736C2semidirect
6. #13092725C2semidirect
7. #13092653C2semidirect
8. #13092646C2semidirect
9. #13092633C2semidirect
10. #13092564C2semidirect
11. #13092558C2semidirect
12. C4×#67263C2semidirect
13. #13092414C2semidirect
14. C2×#10624998C2semidirect
15. C8×D4×C23C2semidirect
190. C8×D4D23semidirect
243. C23#3301semidirect

Maximal subgroups

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

subgroupindex
#130931132
#130930762
#130927722
#130927592
#130927362
#130927252
#130926532
#130926462
#130926332
#130925642
#130925582
C4×#672632
#130924142
C2×#106249982
C8×D4×C232
#330123