Finite Group Databasebeta

← #37583111

Subgroups — #37583111

Order 24448.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133210C211yesmaximal, characteristic, complemented
2#27133200C211yesmaximal, characteristic, complemented
3#27133070C211yesmaximal, characteristic, complemented
4#27133049C211yesmaximal, characteristic, complemented
5#27133026C211yesmaximal, characteristic, complemented
6#27133024C211yesmaximal, characteristic, complemented
7#27132917C211yesmaximal, characteristic, complemented
8#27132915C211yesmaximal, characteristic, complemented
9#27132912C211yesmaximal, characteristic, complemented
10#27132906C211yesmaximal, characteristic, complemented
11C4×#15690274C211yesmaximal, characteristic, complemented
12C4×D1528C211yesmaximal, characteristic, complemented
13C4×#15690272C211yesmaximal, characteristic, complemented
14C4×#15690270C211yesmaximal, characteristic, complemented
15C4×SD16×C191C211yesmaximal, characteristic, complemented
16C2×#15690287—21no—
17C2×#15690274C2211yescharacteristic
18C2×D1528C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20C2×#15690270C2211yescharacteristic
21C2×#15690270C2211yescharacteristic
22#20259321C2211yescharacteristic
23#20259318C2211yescharacteristic
24#20259317—21no—
25#20259313C2211yescharacteristic
26#20259311C2211yescharacteristic
27#20259308—21no—
28#20259307—21no—
29#20259298C2211yescharacteristic
30#20259297C2211yescharacteristic
31#20259297C2211yescharacteristic
32#20259295—21no—
33#20259293C2211yescharacteristic
34C4×D764—21no—
35C4×D764C2211yescharacteristic
36C4×D764C2211yescharacteristic
37C4×C22⋊D191—21no—
38#20259279—21no—
39C42×D191C2211yescharacteristic
40#20259256C2211yescharacteristic
41#20259255C2211yescharacteristic
42#20259253C2211yescharacteristic
43#20259246C2211yescharacteristic
44#20259244C2211yescharacteristic
45#20259244C2211yescharacteristic
46#20259243C2211yescharacteristic
47#20259242C2211yescharacteristic
48#20259242C2211yescharacteristic
49#20259232C2211yescharacteristic
50#20259232C2211yescharacteristic
51C4×C191⋊C8C2211yescharacteristic
52C2×SD16×C191C2211yescharacteristic
53C4×Q8×C191C2211yescharacteristic
54C4×D4×C191C2211yescharacteristic
55#106×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C4×C8×C191C2211yescharacteristic
59#15690287—44no—
60C2×Dic382—21no—
61C2×D764—21no—
62C2×D764—21no—
63C2×D764C2311yescharacteristic
64C2×D764C2311yescharacteristic
65C2×C22⋊D191—21no—
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191D411yescharacteristic
71C2×C4×D191D411yescharacteristic
72C2×C4×D191C2311yescharacteristic
73#15690274—22no—
74D1528—22no—
75#15690272—22no—
76#15690270—22no—
77#15690270—22no—
78C2×C191⋊C8C2311yescharacteristic
79C2×C191⋊C8C2311yescharacteristic
80C4⋊Dic191—21no—
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86C22⋊Dic191—21no—
87(C2×D191)⋊C4—21no—
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94C4×Dic191D411yescharacteristic
95C4×Dic191D411yescharacteristic
96C4×Dic191C2311yescharacteristic
97C2×Q8×C191C2311yescharacteristic
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191—21no—
100SD16×C191—22no—
101C2×C8×C191C2311yescharacteristic
102C2×C8×C191C2311yescharacteristic
103C4⋊C4×C191—21no—
104C4⋊C4×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C22⋊C4×C191—21no—
107C42×C191—21no—
108C42×C191C2311yescharacteristic
109C22×D191—21no—
110C22×D191—21no—
111C22×D191C2×D411yescharacteristic
112Dic382—42no—
113D764—21no—
114D764—21no—
115D764—21no—
116D764—21no—
117D764—42no—
118D764—42no—
119C22⋊D191—42no—
120C22⋊D191—42no—
121C22⋊D191—42no—
122C2×Dic191—21no—
123C2×Dic191—21no—
124C2×Dic191C2×D411yescharacteristic
125C2×Dic191C2×D411yescharacteristic
126C2×Dic191C2×D411yescharacteristic
127C4×D191—22no—
128C4×D191—21no—
129C4×D191—21no—
130C4×D191—41no—
131C4×D191—42no—
132C4×D191—42no—
133C191⋊C8—21no—
134C191⋊C8#4112yescomplemented
135C23×C191—21no—
136Q8×C191—21no—
137Q8×C191—21no—
138D4×C191—21no—
139D4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—21no—
143C2×C4×C191—42no—
144C2×C4×C191C2×D411yescharacteristic
145C2×C4×C191C2×D411yescharacteristic
146C2×C4×C191C2411yescharacteristic
147C8×C191—21no—
148C8×C191#4112yescomplemented
149C22×C191—41no—
150C22×C191—41no—
151C22×C191—41no—
152C22×C191C22×D411yescharacteristic
153C2×D191—21no—
154C2×D191—21no—
155C2×D191—21no—
156C2×D191—41no—
157C2×D191—41no—
158C2×D191—41no—
159C2×D191—41no—
160C2×D191—41no—
161C2×D191—41no—
162C4×C191—21no—
163C4×C191—41no—
164C4×C191—41no—
165C4×C191—41no—
166C4×C191AGL(1,ℤ/8)12yes—
167C4×C191C2×#4111yescharacteristic
168C4×C191C2×#4111yescharacteristic
169Dic191—21no—
170Dic191—21no—
171Dic191—21no—
172Dic191—41no—
173Dic191—41no—
174C2×C191—81no—
175C2×C191#53211yescharacteristic
176C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C191#57511yescharacteristic
178D191—41no—
179D191—81no—
180D191—81no—
181C191#317111yescharacteristic, complemented, Sylow
182#3171—1911nomaximal, Sylow
183#532—1911no—
184#529—1911no—
185#501—1911no—
186#496—1911no—
187#490—1911no—
188#489—1911no—
189#469—1911no—
190#469—1911no—
191#468—1911no—
192#468—1911no—
193C4×SD16—1911no—
194C4×SD16D19111yescharacteristic, complemented
195C4×D8—1911no—
196C4×D8—1911no—
197C4×M16—1911no—
198C2×#41—3821no—
199C2×SD16—1911no—
200C2×SD16C2×D19111yescharacteristic
201C2×D8—1911no—
202C2×D8—1911no—
203C2×M16—1911no—
204C2×M16—1911no—
205C4⋊Q8—1911no—
206#127—1911no—
207#126—3821no—
208#125—1911no—
209#124—3821no—
210#124—1911no—
211#123—3821no—
212C22⋊Q8—1911no—
213#121—3821no—
214#121—1911no—
215#121—1911no—
216#121—1911no—
217C4×Q8C2×D19111yescharacteristic
218C4×D4—3821no—
219C4×D4—3821no—
220C4×D4—1911no—
221C4×D4—1911no—
222C4×D4C2×D19111yescharacteristic
223#117—3821no—
224C2×C42—1911no—
225#107—1911no—
226#107—1911no—
227#106—1911no—
228#106C2×D19111yescharacteristic
229#103—1911no—
230#103C2×D19111yescharacteristic
231#102—1911no—
232#102—1911no—
233#102—1911no—
234#102—1911no—
235#102—1911no—
236#102C2×D19111yescharacteristic
237#97—1911no—
238#97—1911no—
239C4×C8—1911no—
240C4×C8C2×D19111yescharacteristic
241#41—7644no—
242C2×Q8—3821no—
243C2×Q8C22×D19111yescharacteristic
244C2×D4—3821no—
245C2×D4—3821no—
246C2×D4—3821no—
247C2×D4—3821no—
248C2×D4—3821no—
249C2×D4—1911no—
250C2×D4—1911no—
251C2×D4C22×D19111yescharacteristic
252C22×C4—21no—
253C22×C4—3821no—
254C22×C4—3821no—
255C22×C4—1911no—
256C22×C4—1911no—
257C22×C4—1911no—
258SD16—22no—
259SD16—3822no—
260D8—3822no—
261D8—3822no—
262M16—3822no—
263M16—3822no—
264C2×C8—1911no—
265C2×C8—1911no—
266C2×C8C22×D19111yescharacteristic
267C2×C8C22×D19111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—3821no—
270C4⋊C4—3821no—
271C4⋊C4—3821no—
272C4⋊C4—3821no—
273C4⋊C4—1911no—
274C4⋊C4—1911no—
275C4⋊C4C22×D19111yescharacteristic
276C4⋊C4C22×D19111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3821no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C22⋊C4—3821no—
282C22⋊C4—3821no—
283C22⋊C4—3821no—
284C22⋊C4—3821no—
285C22⋊C4—3821no—
286C42—21no—
287C42—1911no—
288C42—1911no—
289C42—1911no—
290C42C22×D19111yescharacteristic
291C23—21no—
292C23—3821no—
293C23—3821no—
294C23—1911no—
295Q8—21no—
296Q8—21no—
297Q8—7642no—
298D4—21no—
299D4—21no—
300D4—3821no—
301D4—3821no—
302D4—3821no—
303D4—3821no—
304D4—7642no—
305D4—7642no—
306D4—7642no—
307D4—7642no—
308D4—7642no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—3822no—
314C2×C4—3821no—
315C2×C4—3821no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—1911no—
319C2×C4—1911no—
320C2×C4—1911no—
321C2×C4—7641no—
322C2×C4—7642no—
323C2×C4—7642no—
324C2×C4D4×D19111yescharacteristic
325C2×C4D4×D19111yescharacteristic
326C2×C4C23×D19111yescharacteristic
327C8—21no—
328C8—3821no—
329C8—1912no—
330C8#1569028712yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—3821no—
335C22—3821no—
336C22—3821no—
337C22—7641no—
338C22—7641no—
339C22—7641no—
340C22—7641no—
341C22—7641no—
342C22—7641no—
343C22C2×D4×D19111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3821no—
349C4—3821no—
350C4—3821no—
351C4—7641no—
352C4—7641no—
353C4#2025934912yes—
354C4#41×D19111yescharacteristic
355C4C2×#1569028711yescharacteristic
356C2—81no—
357C2—15281no—
358C2—15281no—
359C2—7641no—
360C2#2713321011yescharacteristic
361C2C2×#2025934911yescharacteristic
362C2#2713346011yescharacteristic
subgroupG/H
centerC2×C4D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC4×SD16×C191C2
socleC22×C191C22×D4
hypercenterC4×SD16D191
hypocenterC191#3171
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #27133210C2semidirect
2. #27133200C2semidirect
3. #27133070C2semidirect
4. #27133049C2semidirect
5. #27133026C2semidirect
6. #27133024C2semidirect
7. #27132917C2semidirect
8. #27132915C2semidirect
9. #27132912C2semidirect
10. #27132906C2semidirect
11. C4×#15690274C2semidirect
12. C4×D1528C2semidirect
13. C4×#15690272C2semidirect
14. C4×#15690270C2semidirect
15. C4×SD16×C191C2semidirect
134. C191⋊C8#41semidirect
148. C8×C191#41semidirect
181. C191#3171semidirect
194. C4×SD16D191semidirect
330. C8#15690287semidirect

Maximal subgroups

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

subgroupindex
#271332102
#271332002
#271330702
#271330492
#271330262
#271330242
#271329172
#271329152
#271329122
#271329062
C4×#156902742
C4×D15282
C4×#156902722
C4×#156902702
C4×SD16×C1912
#3171191