Finite Group Databasebeta

← #37545970

Subgroups — #37545970

Order 23168.

392 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#26041973C211yesmaximal, characteristic, complemented
2#26041940C211yesmaximal, characteristic, complemented
3#26041635C211yesmaximal, characteristic, complemented
4#26041608C211yesmaximal, characteristic, complemented
5#26041603C211yesmaximal, characteristic, complemented
6#26041584C211yesmaximal, characteristic, complemented
7#26041532C211yesmaximal, characteristic, complemented
8#26041528C211yesmaximal, characteristic, complemented
9#26041497C211yesmaximal, characteristic, complemented
10#26041427C211yesmaximal, characteristic, complemented
11#26041418C211yesmaximal, characteristic, complemented
12#26041364C211yesmaximal, characteristic, complemented
13#26041355C211yesmaximal, characteristic, complemented
14#26041279C211yesmaximal, characteristic, complemented
15#419×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×D1448C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21#19153810—21no—
22#19153807C2211yescharacteristic
23#19153805—21no—
24#19153805C2211yescharacteristic
25#19153798—21no—
26#19153792—21no—
27#19153792C2211yescharacteristic
28#19153791C2211yescharacteristic
29#19153790—21no—
30#19153790C2211yescharacteristic
31#19153790C2211yescharacteristic
32#19153789—21no—
33Q8×Dic181C2211yescharacteristic
34C4×D724—21no—
35#19153778C2211yescharacteristic
36C4×C22⋊D181—21no—
37C4×C22⋊D181C2211yescharacteristic
38C4⋊C4×D181C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C22×Q8×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic
54#117×C181C2211yescharacteristic
55#103×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—41no—
61C2×D724—21no—
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181D411yescharacteristic
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181—21no—
71C2×C4×D181C2311yescharacteristic
72#15668436—22no—
73#15668436—41no—
74D1448—41no—
75#15668432—41no—
76C2×#13089678C2311yescharacteristic
77C2×#13089678C2311yescharacteristic
78C4⋊Dic181—21no—
79C4⋊Dic181—21no—
80C4⋊Dic181C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428D411yescharacteristic
86C22⋊Dic181D411yescharacteristic
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C2×Q8×C181—21no—
98C2×Q8×C181—22no—
99C2×Q8×C181—41no—
100C2×Q8×C181C2311yescharacteristic
101C2×Q8×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181C2311yescharacteristic
104M16×C181—41no—
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C22⋊C4×C181—21no—
110C42×C181—21no—
111C22×D181—21no—
112C22×D181—21no—
113C22×D181C2×D411yescharacteristic
114D724—21no—
115D724—21no—
116D724—21no—
117D724—21no—
118D724—42no—
119D724—42no—
120C22⋊D181—41no—
121C22⋊D181—42no—
122C22⋊D181—81no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C4×D181—21no—
129C4×D181—21no—
130C4×D181—42no—
131C4×D181—81no—
132C4×D181—81no—
133#13089678—21no—
134#13089678—21no—
135C23×C181C2×D411yescharacteristic
136Q8×C181—21no—
137Q8×C181—21no—
138Q8×C181—21no—
139Q8×C181—42no—
140Q8×C181#4112yes—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—42no—
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181—21no—
152C22×C181—21no—
153C22×C181—21no—
154C22×C181—21no—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—21no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C4×C181—21no—
166C4×C181—22no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181—41no—
170C4×C181C2×#4111yescharacteristic
171C4×C181H(5,𝔽2)11yescharacteristic
172Dic181—21no—
173Dic181—21no—
174Dic181—21no—
175Dic181—41no—
176Dic181—41no—
177C2×C181—41no—
178C2×C181#54611yescharacteristic
179C2×C181#57511yescharacteristic
180C2×C181#57711yescharacteristic
181D181—41no—
182D181—81no—
183D181—81no—
184C181#332611yescharacteristic, complemented, Sylow
185#3326—1811nomaximal, Sylow
186#553—1811no—
187#548—1811no—
188#488—1811no—
189#483—1811no—
190#482—1811no—
191#479—1811no—
192#469—1811no—
193#468—1811no—
194#463—1811no—
195#449—1811no—
196#448—1811no—
197C4×SD16—1811no—
198#436—1811no—
199#419D18111yescharacteristic, complemented
200#417—1811no—
201C2×#41—1811no—
202C22×Q8C2×D18111yescharacteristic
203C2×SD16—1811no—
204C2×SD16—1811no—
205C2×D8—1811no—
206C2×M16—1811no—
207C2×M16C2×D18111yescharacteristic
208#126—3621no—
209#125—1811no—
210#124—3621no—
211#124—1811no—
212#123—3621no—
213C22⋊Q8—3621no—
214C22⋊Q8—1811no—
215#121—3621no—
216#121—3621no—
217#121—1811no—
218#121—1811no—
219#121—1811no—
220C4×Q8—1811no—
221C4×D4—3621no—
222C4×D4—3621no—
223C4×D4—1811no—
224C4×D4—1811no—
225#117C2×D18111yescharacteristic
226C2×C4⋊C4—1811no—
227#107—1811no—
228#106—1811no—
229#106—1811no—
230C4⋊C8—1811no—
231#103—1811no—
232#103—1811no—
233#103C2×D18111yescharacteristic
234#103C2×D18111yescharacteristic
235#103C2×D18111yescharacteristic
236#103C2×D18111yescharacteristic
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102—1811no—
241C22⋊C8—1811no—
242C22⋊C8—1811no—
243C4×C8—1811no—
244#41—3622no—
245#41—7241no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D18111yescharacteristic
250C2×Q8C22×D18111yescharacteristic
251C2×D4—3621no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—1811no—
256C2×D4—1811no—
257C2×D4—1811no—
258C22×C4—21no—
259C22×C4—3621no—
260C22×C4—3621no—
261C22×C4—3621no—
262C22×C4—1811no—
263C22×C4C22×D18111yescharacteristic
264SD16—3622no—
265SD16—7241no—
266D8—7241no—
267M16—41no—
268M16—7241no—
269C2×C8—1811no—
270C2×C8—1811no—
271C2×C8C22×D18111yescharacteristic
272C2×C8C22×D18111yescharacteristic
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—1811no—
279C4⋊C4—1811no—
280C4⋊C4—1811no—
281C4⋊C4C22×D18111yescharacteristic
282C4⋊C4C22×D18111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—1811no—
292C22⋊C4—1811no—
293C42—21no—
294C42—3621no—
295C42—1811no—
296C23—3621no—
297C23—3621no—
298C23—1811no—
299C23D4×D18111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1566844912yes—
305D4—3621no—
306D4—3621no—
307D4—3621no—
308D4—3621no—
309D4—14481no—
310D4—7242no—
311D4—7242no—
312D4—7241no—
313D4—7242no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—14481no—
326C2×C4—14481no—
327C2×C4—1811no—
328C2×C4—1811no—
329C2×C4—1811no—
330C2×C4—7242no—
331C2×C4D4×D18111yescharacteristic
332C2×C4C23×D18111yescharacteristic
333C8—21no—
334C8—21no—
335C8—3621no—
336C8—3621no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—3621no—
341C22—3621no—
342C22—3621no—
343C22—7241no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22—7241no—
348C22—7241no—
349C22C2×D4×D18111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3621no—
356C4—3621no—
357C4—3621no—
358C4—7241no—
359C4—7241no—
360C4C2×#1566844911yescharacteristic
361C4#1915386111yescharacteristic
362C2—41no—
363C2—14481no—
364C2—14481no—
365C2—7241no—
366C2#2604191911yescharacteristic
367C2#2604207811yescharacteristic
368C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#419×C181C2
socleC22×C181C22×D4
hypercenter#419D181
hypocenterC181#3326
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #26041973C2semidirect
2. #26041940C2semidirect
3. #26041635C2semidirect
4. #26041608C2semidirect
5. #26041603C2semidirect
6. #26041584C2semidirect
7. #26041532C2semidirect
8. #26041528C2semidirect
9. #26041497C2semidirect
10. #26041427C2semidirect
11. #26041418C2semidirect
12. #26041364C2semidirect
13. #26041355C2semidirect
14. #26041279C2semidirect
15. #419×C181C2semidirect
184. C181#3326semidirect
199. #419D181semidirect

Maximal subgroups

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

subgroupindex
#260419732
#260419402
#260416352
#260416082
#260416032
#260415842
#260415322
#260415282
#260414972
#260414272
#260414182
#260413642
#260413552
#260412792
#419×C1812
#3326181