Finite Group Databasebeta

← #15686481

Subgroups — #15686481

Order 2944.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093152C211yesmaximal, characteristic, complemented
2#13092807C211yesmaximal, characteristic, complemented
3#13092804C211yesmaximal, characteristic, complemented
4#13092799C211yesmaximal, characteristic, complemented
5#13092639C211yesmaximal, characteristic, complemented
6#13092636C211yesmaximal, characteristic, complemented
7#13092632C211yesmaximal, characteristic, complemented
8#13092629C211yesmaximal, characteristic, complemented
9#13092612C211yesmaximal, characteristic, complemented
10#13092609C211yesmaximal, characteristic, complemented
11#13092548C211yesmaximal, characteristic, complemented
12#13092517C211yesmaximal, characteristic, complemented
13#13092515C211yesmaximal, characteristic, complemented
14C4×#67272C211yesmaximal, characteristic, complemented
15C23×#559C211yesmaximal, characteristic, complemented
16C23×#127C2211yescharacteristic
17C23×#124—21no—
18C23×#124C2211yescharacteristic
19C23×#124C2211yescharacteristic
20C23×#123—21no—
21C23×#123—21no—
22C4×Q8×C23C2211yescharacteristic
23C4×Q8×C23C2211yescharacteristic
24C4×D4×C23—21no—
25C4×D4×C23C2211yescharacteristic
26C4×D4×C23C2211yescharacteristic
27#10625118—21no—
28C2×#67275C2211yescharacteristic
29C2×#67274C2211yescharacteristic
30C2×#67274C2211yescharacteristic
31C2×#67273C2211yescharacteristic
32C2×#67273C2211yescharacteristic
33C2×#67272C2211yescharacteristic
34C2×#67272C2211yescharacteristic
35C2×#67272C2211yescharacteristic
36C2×#67272C2211yescharacteristic
37#10625065—21no—
38#10625065—21no—
39#10625064—21no—
40#10625046C2211yescharacteristic
41#10625046C2211yescharacteristic
42#10625045C2211yescharacteristic
43C4×D92C2211yescharacteristic
44C4×D92C2211yescharacteristic
45C4×Dic46C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10624992C2211yescharacteristic
50#10624991C2211yescharacteristic
51#10624991C2211yescharacteristic
52#10624989C2211yescharacteristic
53C4⋊(C23⋊C8)C2211yescharacteristic
54C4⋊(C23⋊C8)C2211yescharacteristic
55C4⋊(C23⋊C8)C2211yescharacteristic
56#10624985C2211yescharacteristic
57#10624985C2211yescharacteristic
58C4×C23⋊C8C2211yescharacteristic
59C2×Q8×C23D411yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23—21no—
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23—21no—
67C2×D92—21no—
68C2×D92—21no—
69C2×D92C2311yescharacteristic
70C2×D92C2311yescharacteristic
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×Dic46C2311yescharacteristic
74C4⋊C4×C23—21no—
75C4⋊C4×C23D411yescharacteristic
76C4⋊C4×C23D411yescharacteristic
77C4⋊C4×C23D411yescharacteristic
78C4⋊C4×C23C2311yescharacteristic
79C22⋊C4×C23—21no—
80C22⋊C4×C23—21no—
81C22⋊C4×C23—21no—
82C22⋊C4×C23—21no—
83C22⋊C4×C23—21no—
84C22⋊C4×C23—21no—
85C42×C23—21no—
86C42×C23C2311yescharacteristic
87C42×C23C2311yescharacteristic
88C42×C23C2311yescharacteristic
89#67275—41no—
90#67274—22no—
91#67274—41no—
92#67273—22no—
93#67273—41no—
94#67272—22no—
95#67272—41no—
96#67272—41no—
97#67272—41no—
98(C2×D23)⋊C4—21no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4—21no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—21no—
104C4⋊Dic23C2311yescharacteristic
105Dic23⋊C4—21no—
106C4×Dic23—21no—
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C2×C23⋊C8C2311yescharacteristic
111C23×C23—21no—
112C23×C23—21no—
113C22×D23—21no—
114C22×D23—21no—
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23—41no—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23—42no—
123D4×C23—81no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—81no—
127C2×C4×C23—81no—
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2×D411yescharacteristic
131C2×C4×C23C2×D411yescharacteristic
132C2×C4×C23C2×D411yescharacteristic
133C2×C4×C23C2×D411yescharacteristic
134C2×C4×C23C2411yescharacteristic
135C2×Dic23—21no—
136C2×Dic23—21no—
137D92—21no—
138D92—21no—
139D92—21no—
140D92—21no—
141D92—42no—
142D92—81no—
143C4×D23—81no—
144C4×D23—81no—
145Dic46—21no—
146Dic46—21no—
147C23⋊C8—21no—
148C23⋊C8—21no—
149C23⋊C8—21no—
150C23⋊C8#4112yes—
151#3403—231nomaximal, Sylow
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23C22×D411yescharacteristic
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—21no—
168C4×C23—21no—
169C4×C23—21no—
170C4×C23—21no—
171C4×C23—41no—
172C4×C23—41no—
173C4×C23C2×#4111yescharacteristic
174C4×C23H(5,𝔽2)11yescharacteristic
175Dic23—41no—
176Dic23—41no—
177#559—231no—
178#559D2311yescharacteristic, complemented
179#496—231no—
180#496—231no—
181#495—231no—
182#464—231no—
183#464—231no—
184#463—231no—
185#463—231no—
186#459—231no—
187#459—231no—
188#446—231no—
189#440—231no—
190#440—231no—
191C4×D8—231no—
192C2×C23—81no—
193C2×C23—81no—
194C2×C23#55011yescharacteristic
195C2×C23#57511yescharacteristic
196C2×C23#57611yescharacteristic
197D23—81no—
198D23—81no—
199C2×Q16—231no—
200C2×SD16—231no—
201C2×SD16—231no—
202C2×SD16—231no—
203C2×SD16—231no—
204C2×D8—231no—
205C2×D8—231no—
206C2×D8—231no—
207C2×D8—231no—
208#127—231no—
209#127C2×D2311yescharacteristic
210#124—21no—
211#124—231no—
212#124—231no—
213#124—461no—
214#124C2×D2311yescharacteristic
215#124C2×D2311yescharacteristic
216#123—21no—
217#123—21no—
218#123—461no—
219#123—461no—
220C4×Q8—231no—
221C4×Q8C2×D2311yescharacteristic
222C4×Q8C2×D2311yescharacteristic
223C4×D4—21no—
224C4×D4—231no—
225C4×D4—231no—
226C4×D4—461no—
227C4×D4C2×D2311yescharacteristic
228C4×D4C2×D2311yescharacteristic
229#107—231no—
230C4⋊C8—231no—
231C4⋊C8—231no—
232C4⋊C8—231no—
233#103—231no—
234#103—231no—
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#97—231no—
240#97—231no—
241C4×C8—231no—
242C23#340311yescharacteristic, complemented, Sylow
243C2×Q8—231no—
244C2×Q8C22⋊D2311yescharacteristic
245C2×Q8C22×D2311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—231no—
249C2×D4—231no—
250C2×D4—461no—
251C2×D4—461no—
252C2×D4C22×D2311yescharacteristic
253C2×D4C22×D2311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—461no—
257C22×C4—461no—
258Q16—921no—
259SD16—462no—
260SD16—462no—
261SD16—921no—
262SD16—921no—
263D8—462no—
264D8—921no—
265D8—921no—
266D8—921no—
267C2×C8—231no—
268C2×C8—231no—
269C2×C8—231no—
270C2×C8—231no—
271C4⋊C4—21no—
272C4⋊C4—231no—
273C4⋊C4—461no—
274C4⋊C4C22⋊D2311yescharacteristic
275C4⋊C4C22⋊D2311yescharacteristic
276C4⋊C4C22⋊D2311yescharacteristic
277C4⋊C4C22×D2311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—461no—
285C22⋊C4—461no—
286C22⋊C4—461no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C42—21no—
291C42—461no—
292C42C22×D2311yescharacteristic
293C42C22×D2311yescharacteristic
294C42C22×D2311yescharacteristic
295C23—21no—
296C23—21no—
297C23—461no—
298C23—461no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—461no—
303Q8—461no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—461no—
311D4—461no—
312D4—461no—
313D4—461no—
314D4—922no—
315D4—1841no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—461no—
321C2×C4—461no—
322C2×C4—1841no—
323C2×C4—1841no—
324C2×C4C2×C22⋊D2311yescharacteristic
325C2×C4C2×C22⋊D2311yescharacteristic
326C2×C4C2×C22⋊D2311yescharacteristic
327C2×C4C2×C22⋊D2311yescharacteristic
328C2×C4C2×C22⋊D2311yescharacteristic
329C2×C4C2×C22⋊D2311yescharacteristic
330C2×C4C23×D2311yescharacteristic
331C8—232no—
332C8—461no—
333C8—461no—
334C8—461no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—921no—
342C22—921no—
343C22—921no—
344C22—921no—
345C22—921no—
346C22—921no—
347C22C22×C22⋊D2311yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—921no—
357C4—921no—
358C4#41×D2311yescharacteristic
359C4#1062516011yescharacteristic
360C2—81no—
361C2—81no—
362C2—1841no—
363C2—1841no—
364C2#1309308611yescharacteristic
365C2#1309321511yescharacteristic
366C2#1309322011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#559C2
socleC22×C23C22×D4
hypercenter#559D23
hypocenterC23#3403
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #13093152C2semidirect
2. #13092807C2semidirect
3. #13092804C2semidirect
4. #13092799C2semidirect
5. #13092639C2semidirect
6. #13092636C2semidirect
7. #13092632C2semidirect
8. #13092629C2semidirect
9. #13092612C2semidirect
10. #13092609C2semidirect
11. #13092548C2semidirect
12. #13092517C2semidirect
13. #13092515C2semidirect
14. C4×#67272C2semidirect
15. C23×#559C2semidirect
178. #559D23semidirect
242. C23#3403semidirect

Maximal subgroups

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

subgroupindex
#130931522
#130928072
#130928042
#130927992
#130926392
#130926362
#130926322
#130926292
#130926122
#130926092
#130925482
#130925172
#130925152
C4×#672722
C23×#5592
#340323