Finite Group Databasebeta

← #37575866

Subgroups — #37575866

Order 24448.

908 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15690287C211yesmaximal, characteristic, complemented
2C2×#20259302C211yesmaximal, characteristic, complemented
3C2×#20259297C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D191C211yesmaximal, characteristic, complemented
5#27132579C212yesmaximal, complemented
6#27132572C212yesmaximal, complemented
7#27132568C211yesmaximal, characteristic, complemented
8#27132564C211yesmaximal, characteristic, complemented
9#27132541C212yesmaximal, complemented
10#27132537C212yesmaximal, complemented
11#380×C191C211yesmaximal, characteristic, complemented
12C2×#15690287—24no—
13C2×#15690287—24no—
14C2×#15690287—24no—
15C22×Dic382C2211yescharacteristic
16C22×D764C2212yes—
17C22×D764C2211yescharacteristic
18C22×C22⋊D191C2212yes—
19C22×C22⋊D191C2211yescharacteristic
20C22×C4×D191C2212yes—
21C22×C4×D191C2211yescharacteristic
22#20259302—24no—
23#20259297—24no—
24C4×C22⋊D191—24no—
25C2×C4⋊Dic191C2212yes—
26C2×Dic191⋊C4C2211yescharacteristic
27C2×C22⋊Dic191C2211yescharacteristic
28C2×(C2×D191)⋊C4C2212yes—
29C2×(C2×D191)⋊C4C2212yes—
30C2×(C2×D191)⋊C4C2211yescharacteristic
31C2×(C2×D191)⋊C4C2212yes—
32C2×(C2×D191)⋊C4C2212yes—
33C2×C4×Dic191C2211yescharacteristic
34C191⋊#95C2212yes—
35C191⋊#95C2212yes—
36C23×C4×C191C2211yescharacteristic
37C2×C4⋊C4×C191C2211yescharacteristic
38C2×C4⋊C4×C191C2211yescharacteristic
39C2×C22⋊C4×C191C2212yes—
40#95×C191C2212yes—
41C23×D191C2312yes—
42C23×D191C2311yescharacteristic
43#15690287—232no—
44C2×Dic382—22no—
45C2×Dic382—22no—
46C2×Dic382D414yescomplemented
47C2×D764—24no—
48C2×D764—24no—
49C2×D764—22no—
50C2×D764—22no—
51C2×D764—42no—
52C2×D764D414yescomplemented
53C2×C22⋊D191—24no—
54C2×C22⋊D191—22no—
55C2×C22⋊D191—24no—
56C2×C22⋊D191—22no—
57C2×C22⋊D191—24no—
58C2×C22⋊D191—22no—
59C22×Dic191C2311yescharacteristic
60C22×Dic191C2311yescharacteristic
61C22×Dic191C2312yes—
62C22×Dic191C2311yescharacteristic
63C2×C4×D191—24no—
64C2×C4×D191—24no—
65C2×C4×D191—24no—
66C2×C4×D191—22no—
67C2×C4×D191—22no—
68C2×C4×D191—22no—
69C4⋊Dic191—24no—
70Dic191⋊C4—22no—
71C22⋊Dic191—22no—
72(C2×D191)⋊C4—24no—
73(C2×D191)⋊C4—24no—
74(C2×D191)⋊C4—24no—
75(C2×D191)⋊C4—22no—
76(C2×D191)⋊C4—42no—
77C4×Dic191—22no—
78C24×C191C2311yescharacteristic
79C22×C4×C191—22no—
80C22×C4×C191—22no—
81C22×C4×C191D414yescomplemented
82C22×C4×C191C2312yes—
83C22×C4×C191C2312yes—
84C22×C4×C191C2311yescharacteristic
85C22×C4×C191C2311yescharacteristic
86C4⋊C4×C191—22no—
87C4⋊C4×C191—22no—
88C22⋊C4×C191—42no—
89C22×D191—21no—
90C22×D191—21no—
91C22×D191—22no—
92C22×D191—22no—
93C22×D191—21no—
94C22×D191—22no—
95C22×D191—21no—
96C22×D191—22no—
97C22×D191—22no—
98C22×D191—21no—
99C22×D191—22no—
100C22×D191—21no—
101C22×D191C2×D414yes—
102C22×D191#4112yescomplemented
103Dic382—28no—
104D764—28no—
105D764—48no—
106C22⋊D191—28no—
107C22⋊D191—216no—
108C2×Dic191—21no—
109C2×Dic191—22no—
110C2×Dic191—22no—
111C2×Dic191—21no—
112C2×Dic191—21no—
113C2×Dic191—21no—
114C2×Dic191—21no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C2×Dic191—21no—
118C2×Dic191C2×D414yes—
119C2×Dic191#4112yescomplemented
120C4×D191—216no—
121C4×D191—44no—
122C23×C191—21no—
123C23×C191—21no—
124C23×C191—21no—
125C23×C191—21no—
126C23×C191—21no—
127C23×C191—21no—
128C23×C191C2×D412yes—
129C23×C191C2411yescharacteristic
130C2×C4×C191—21no—
131C2×C4×C191—21no—
132C2×C4×C191—28no—
133C2×C4×C191—22no—
134C2×C4×C191—22no—
135C2×C4×C191—22no—
136C2×C4×C191—22no—
137C2×C4×C191—22no—
138C2×C4×C191—22no—
139C2×C4×C191C2×D412yes—
140C2×C4×C191C2×D412yes—
141C2×C4×C191C2×D412yes—
142C2×C4×C191C2×D412yes—
143C22×C191—22no—
144C22×C191—22no—
145C22×C191—22no—
146C22×C191—41no—
147C22×C191—41no—
148C22×C191—41no—
149C22×C191—41no—
150C22×C191C22×D411yescharacteristic
151C22×C191C22×D411yescharacteristic
152C22×C191C22×D411yescharacteristic
153C22×C191C2×#4111yescharacteristic
154C22×C191C2×#4111yescharacteristic
155C22×C191H(5,𝔽2)11yescharacteristic
156C22×C1912−1+411yescharacteristic
157C2×D191—24no—
158C2×D191—22no—
159C2×D191—22no—
160C2×D191—24no—
161C2×D191—24no—
162C2×D191—22no—
163C2×D191—41no—
164C2×D191—42no—
165C2×D191—41no—
166C2×D191—42no—
167C2×D191—41no—
168C2×D191—42no—
169C2×D191—41no—
170C2×D191—42no—
171C4×C191—22no—
172C4×C191—42no—
173C4×C191—42no—
174C4×C191#12014yes—
175Dic191—24no—
176Dic191—22no—
177Dic191—41no—
178Dic191—41no—
179C2×C191—42no—
180C2×C191C2×#12011yescharacteristic
181C2×C191#52511yescharacteristic
182C2×C191#53711yescharacteristic
183C2×C191#54611yescharacteristic
184C2×C191#54711yescharacteristic
185C2×C191#54811yescharacteristic
186C2×C191#55011yescharacteristic
187D191—44no—
188D191—42no—
189C191#240711yescharacteristic, complemented, Sylow
190#2407—1911nomaximal, Sylow
191C22×#41—1911no—
192C2×C22⋊Q8—1911no—
193C2×#121—1911no—
194C2×C4×D4—1911no—
195#394—1912no—
196#392—1912no—
197#391—1911no—
198#390—1911no—
199#386—1912no—
200#385—1912no—
201#380D19111yescharacteristic, complemented
202C2×#41—3824no—
203C2×#41—3824no—
204C2×#41—3824no—
205C22×Q8—1911no—
206C22×D4—1911no—
207C22×D4—1912no—
208C22×D4—1911no—
209C22×D4—1912no—
210C23×C4—1911no—
211C23×C4—1912no—
212C23×C4C2×D19111yescharacteristic
213C22⋊Q8—3824no—
214#121—3824no—
215C4×D4—3824no—
216C2×C4⋊C4—1911no—
217C2×C4⋊C4—1912no—
218C2×C4⋊C4C2×D19111yescharacteristic
219C2×C4⋊C4C2×D19111yescharacteristic
220C2×C22⋊C4—1911no—
221C2×C22⋊C4—1911no—
222C2×C22⋊C4—1912no—
223C2×C22⋊C4—1912no—
224C2×C22⋊C4—1912no—
225C2×C22⋊C4—1912no—
226C2×C22⋊C4C2×D19112yes—
227C2×C42—1911no—
228#95—1912no—
229#95—1912no—
230#95C2×D19112yes—
231C24—1911no—
232C24—1912no—
233C24C22×D19111yescharacteristic
234#41—38232no—
235C2×Q8—3822no—
236C2×Q8—3822no—
237C2×Q8—1914no—
238C2×D4—3824no—
239C2×D4—3824no—
240C2×D4—3822no—
241C2×D4—3824no—
242C2×D4—3822no—
243C2×D4—3824no—
244C2×D4—3822no—
245C2×D4—3824no—
246C2×D4—3822no—
247C2×D4—3822no—
248C2×D4—1914no—
249C2×D4—7642no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—3824no—
253C22×C4—3824no—
254C22×C4—3824no—
255C22×C4—3822no—
256C22×C4—3822no—
257C22×C4—3822no—
258C22×C4—1911no—
259C22×C4—1911no—
260C22×C4—1911no—
261C22×C4—1912no—
262C22×C4D76414yescomplemented
263C22×C4C22×D19112yes—
264C22×C4C22×D19112yes—
265C22×C4C22×D19111yescharacteristic
266C22×C4C22×D19111yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—3824no—
270C4⋊C4—3822no—
271C22⋊C4—42no—
272C22⋊C4—3824no—
273C22⋊C4—3824no—
274C22⋊C4—3824no—
275C22⋊C4—3822no—
276C22⋊C4—3822no—
277C22⋊C4—7642no—
278C42—3822no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—3821no—
286C23—3821no—
287C23—3822no—
288C23—3821no—
289C23—3822no—
290C23—3822no—
291C23—3822no—
292C23—3821no—
293C23—3822no—
294C23—3821no—
295C23—3822no—
296C23—3821no—
297C23—1914no—
298C23—1912no—
299C23C2×D76412yes—
300C23C23×D19111yescharacteristic
301Q8—3828no—
302D4—38216no—
303D4—3828no—
304D4—3828no—
305D4—7648no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—28no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—38216no—
316C2×C4—3822no—
317C2×C4—3821no—
318C2×C4—3822no—
319C2×C4—3821no—
320C2×C4—3821no—
321C2×C4—3821no—
322C2×C4—3821no—
323C2×C4—3821no—
324C2×C4—3821no—
325C2×C4—3821no—
326C2×C4—1914no—
327C2×C4—1912no—
328C2×C4—7644no—
329C2×C4D4×D19112yes—
330C2×C4D4×D19112yes—
331C2×C4C2×D76412yes—
332C2×C4C2×D76412yes—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—3822no—
341C22—3824no—
342C22—3824no—
343C22—3822no—
344C22—3824no—
345C22—3822no—
346C22—7641no—
347C22—7642no—
348C22—7641no—
349C22—7642no—
350C22—7641no—
351C22—7642no—
352C22—7641no—
353C22—7642no—
354C22C2×D4×D19111yescharacteristic
355C22C2×D4×D19111yescharacteristic
356C22C22×D76411yescharacteristic
357C22#41×D19111yescharacteristic
358C22#41×D19111yescharacteristic
359C22#2025936711yescharacteristic
360C22#2025937011yescharacteristic
361C4—22no—
362C4—42no—
363C4—42no—
364C4—3824no—
365C4—3822no—
366C4—7641no—
367C4—7641no—
368C4#2025929214yes—
369C2—42no—
370C2—7642no—
371C2—7644no—
372C2C2×#2025929211yescharacteristic
373C2#2713317511yescharacteristic
374C2#2713324411yescharacteristic
375C2#2713331011yescharacteristic
376C2#2713331511yescharacteristic
377C2#2713332311yescharacteristic
378C2#2713333111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#380×C191C2
hypercenter#380D191
hypocenterC191#2407
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C22×#15690287C2semidirect
2. C2×#20259302C2semidirect
3. C2×#20259297C2semidirect
4. C2×C4×C22⋊D191C2semidirect
5. #27132579C2semidirect
6. #27132572C2semidirect
7. #27132568C2semidirect
8. #27132564C2semidirect
9. #27132541C2semidirect
10. #27132537C2semidirect
11. #380×C191C2semidirect
46. C2×Dic382D4semidirect
52. C2×D764D4semidirect
81. C22×C4×C191D4semidirect
102. C22×D191#41semidirect
119. C2×Dic191#41semidirect
189. C191#2407semidirect
201. #380D191semidirect
262. C22×C4D764semidirect

Maximal subgroups

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

subgroupindex
C22×#156902872
C2×#202593022
C2×#202592972
C2×C4×C22⋊D1912
#271325792
#271325722
#271325682
#271325642
#271325412
#271325372
#380×C1912
#2407191