Finite Group Databasebeta

← #15685304

Subgroups — #15685304

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#13093117C211yesmaximal, characteristic, complemented
2#13093079C211yesmaximal, characteristic, complemented
3#13092772C211yesmaximal, characteristic, complemented
4#13092761C211yesmaximal, characteristic, complemented
5#13092737C211yesmaximal, characteristic, complemented
6#13092724C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092645C211yesmaximal, characteristic, complemented
9#13092632C211yesmaximal, characteristic, complemented
10#13092561C211yesmaximal, characteristic, complemented
11#13092554C211yesmaximal, characteristic, complemented
12C8×D92C211yesmaximal, characteristic, complemented
13#13092412C211yesmaximal, characteristic, complemented
14#103×D23C211yesmaximal, characteristic, complemented
15C4×SD16×C23C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×Q8×D23C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C4×Q8×C23C2211yescharacteristic
20C4×D4×C23C2211yescharacteristic
21#10625109C2211yescharacteristic
22#10625109C2211yescharacteristic
23C2×#67273C2211yescharacteristic
24C2×#67272C2211yescharacteristic
25#10625100—21no—
26C4×C22⋊D23—21no—
27C2×C8×D23C2211yescharacteristic
28C2×C8×D23C2211yescharacteristic
29#10625068—21no—
30#10625068C2211yescharacteristic
31#10625066—21no—
32#10625066C2211yescharacteristic
33#10625063C2211yescharacteristic
34C4⋊C4×D23C2211yescharacteristic
35#10625055—21no—
36#10625050—21no—
37#10625046—21no—
38#10625046C2211yescharacteristic
39C4×D92—21no—
40C4×D92C2211yescharacteristic
41#10625041C2211yescharacteristic
42C23×#106C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C23×#102C2211yescharacteristic
45C4×C8×C23C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625017C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51(C2×D23)⋊C8C2211yescharacteristic
52#10624998C2211yescharacteristic
53#10624998C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58C4⋊(C23⋊C8)C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C2×C22⋊D23—21no—
63C2×C22⋊D23—21no—
64#67292—22no—
65#67292—41no—
66Q8×D23—22no—
67Q8×D23—41no—
68C2×D92—21no—
69C2×D92—21no—
70C2×D92D411yescharacteristic
71C2×D92C2311yescharacteristic
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23C2311yescharacteristic
76C2×C4×D23C2311yescharacteristic
77C2×Dic46—21no—
78C2×Dic46C2311yescharacteristic
79SD16×C23—22no—
80C2×C8×C23C2311yescharacteristic
81C2×C8×C23C2311yescharacteristic
82C4⋊C4×C23—21no—
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊C4×C23—21no—
86C42×C23—21no—
87C42×C23C2311yescharacteristic
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90#67273—41no—
91#67272—41no—
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—
97(C2×D23)⋊C4D411yescharacteristic
98(C2×D23)⋊C4D411yescharacteristic
99C4⋊Dic23—21no—
100C4⋊Dic23D411yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102C4⋊Dic23C2311yescharacteristic
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105Dic23⋊C4—21no—
106C4×Dic23—21no—
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C8×D23—41no—
110C8×D23—41no—
111C23×C23—21no—
112C22×D23—21no—
113C22×D23C2×D411yescharacteristic
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23#4112yes—
117D4×C23—21no—
118D4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—81no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C22⋊D23—42no—
127C22⋊D23—81no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23C2×D411yescharacteristic
132C2×Dic23C2×D411yescharacteristic
133D92—22no—
134D92—21no—
135D92—21no—
136D92—42no—
137D92—42no—
138C4×D23—21no—
139C4×D23—21no—
140C4×D23—21no—
141C4×D23—21no—
142C4×D23—42no—
143C4×D23—42no—
144C4×D23—81no—
145Dic46—21no—
146Dic46—21no—
147Dic46—42no—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3301—231nomaximal, Sylow
153C22×C23—41no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23C22×D411yescharacteristic
157C2×D23—21no—
158C2×D23—21no—
159C2×D23—21no—
160C2×D23—21no—
161C2×D23—21no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23#13512yes—
166C4×C23—22no—
167C4×C23—21no—
168C4×C23—21no—
169C4×C23—41no—
170C4×C23—41no—
171C4×C23C2×#4111yescharacteristic
172C4×C23H(5,𝔽2)11yescharacteristic
173Dic23—21no—
174Dic23—21no—
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×SD16D2311yescharacteristic, complemented
190C8×D4—231no—
191#416—231no—
192C2×#103—231no—
193C2×C23—81no—
194C2×C23#54611yescharacteristic
195C2×C23C2×#13511yescharacteristic
196C2×C23#57711yescharacteristic
197D23—22no—
198D23—41no—
199D23—81no—
200C2×#41—231no—
201C22×Q8—231no—
202C2×SD16—231no—
203C2×SD16C2×D2311yescharacteristic
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—231no—
213C22⋊Q8—461no—
214#121—231no—
215#121—231no—
216#121—231no—
217#121—461no—
218#121—461no—
219C4×Q8C2×D2311yescharacteristic
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#106C2×D2311yescharacteristic
229C4⋊C8—231no—
230#103—231no—
231#103—231no—
232#103—231no—
233#103—231no—
234#103—231no—
235#103C2×D2311yescharacteristic
236#102—231no—
237#102—231no—
238#102—231no—
239#102C2×D2311yescharacteristic
240C22⋊C8—231no—
241C22⋊C8—231no—
242C4×C8C2×D2311yescharacteristic
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—461no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4—461no—
257C2×D4C22×D2311yescharacteristic
258C22×C4—21no—
259C22×C4—231no—
260C22×C4—231no—
261C22×C4—461no—
262C22×C4—461no—
263C22×C4—461no—
264SD16—22no—
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—231no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4C22×D2311yescharacteristic
282C4⋊C4C22×D2311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—231no—
285C22⋊C4—231no—
286C22⋊C4—461no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C42—21no—
294C42—461no—
295C42C22×D2311yescharacteristic
296C23—21no—
297C23—231no—
298C23—231no—
299C23—461no—
300Q8—21no—
301Q8—461no—
302Q8—461no—
303Q8—922no—
304Q8#6728812yes—
305D4—21no—
306D4—21no—
307D4—462no—
308D4—461no—
309D4—461no—
310D4—922no—
311D4—922no—
312D4—922no—
313D4—1841no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—81no—
318C2×C4—231no—
319C2×C4—231no—
320C2×C4—461no—
321C2×C4—461no—
322C2×C4—461no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—922no—
328C2×C4—922no—
329C2×C4—1841no—
330C2×C4D4×D2311yescharacteristic
331C2×C4D4×D2311yescharacteristic
332C2×C4C23×D2311yescharacteristic
333C8—21no—
334C8—21no—
335C8—461no—
336C8—461no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—232no—
341C22—461no—
342C22—461no—
343C22—461no—
344C22—461no—
345C22—461no—
346C22—921no—
347C22—921no—
348C22—921no—
349C22C2×D4×D2311yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—461no—
356C4—461no—
357C4—921no—
358C4—921no—
359C4—921no—
360C4C2×#6728811yescharacteristic
361C4#1062516011yescharacteristic
362C2—81no—
363C2—462no—
364C2—921no—
365C2—1841no—
366C2#1309306311yescharacteristic
367C2#135×D2311yescharacteristic
368C2#1309322311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×SD16×C23C2
socleC22×C23C22×D4
hypercenterC4×SD16D23
hypocenterC23#3301
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #13093117C2semidirect
2. #13093079C2semidirect
3. #13092772C2semidirect
4. #13092761C2semidirect
5. #13092737C2semidirect
6. #13092724C2semidirect
7. #13092652C2semidirect
8. #13092645C2semidirect
9. #13092632C2semidirect
10. #13092561C2semidirect
11. #13092554C2semidirect
12. C8×D92C2semidirect
13. #13092412C2semidirect
14. #103×D23C2semidirect
15. C4×SD16×C23C2semidirect
189. C4×SD16D23semidirect
243. C23#3301semidirect

Maximal subgroups

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

subgroupindex
#130931172
#130930792
#130927722
#130927612
#130927372
#130927242
#130926522
#130926452
#130926322
#130925612
#130925542
C8×D922
#130924122
#103×D232
C4×SD16×C232
#330123