Finite Group Databasebeta

← #37543921

Subgroups — #37543921

Order 23168.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041882C211yesmaximal, characteristic, complemented
2#26041762C211yesmaximal, characteristic, complemented
3#26041598C211yesmaximal, characteristic, complemented
4#26041590C211yesmaximal, characteristic, complemented
5#26041584C211yesmaximal, characteristic, complemented
6#26041581C211yesmaximal, characteristic, complemented
7#26041477C211yesmaximal, characteristic, complemented
8#26041472C211yesmaximal, characteristic, complemented
9#26041424C211yesmaximal, characteristic, complemented
10#26041391C211yesmaximal, characteristic, complemented
11#26041382C211yesmaximal, characteristic, complemented
12SD16×Dic181C211yesmaximal, characteristic, complemented
13#26041359C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C2×#15668436C2211yescharacteristic
17C2×#15668434C2211yescharacteristic
18#19153812C2211yescharacteristic
19#19153807C2211yescharacteristic
20#19153800—21no—
21#19153798—21no—
22#19153790C2211yescharacteristic
23#19153788—21no—
24#19153787—21no—
25Q8×Dic181C2211yescharacteristic
26Q8×Dic181C2211yescharacteristic
27D4×Dic181—21no—
28D4×Dic181—21no—
29D4×Dic181C2211yescharacteristic
30D4×Dic181C2211yescharacteristic
31D4×Dic181C2211yescharacteristic
32#19153778C2211yescharacteristic
33#19153775—21no—
34#19153775C2211yescharacteristic
35C2×C4⋊Dic181—21no—
36C2×C4⋊Dic181C2211yescharacteristic
37#19153749C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×D724C2311yescharacteristic
60C2×C22⋊D181—21no—
61C2×C22⋊D181—21no—
62C2×C22⋊D181—21no—
63C22×Dic181—21no—
64C22×Dic181—21no—
65C22×Dic181—21no—
66C22×Dic181—21no—
67C2×C4×D181—21no—
68#15668436—22no—
69#15668434—22no—
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C4⋊Dic181—21no—
73C4⋊Dic181—21no—
74C4⋊Dic181—21no—
75C4⋊Dic181—21no—
76C4⋊Dic181D411yescharacteristic
77C4⋊Dic181D411yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82C22⋊Dic181—21no—
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181D411yescharacteristic
86C22⋊Dic181D411yescharacteristic
87#15668426—21no—
88#15668426—21no—
89C4×Dic181—21no—
90C4×Dic181—21no—
91C4×Dic181C2311yescharacteristic
92C4×Dic181C2311yescharacteristic
93#41×C181—22no—
94#41×C181—22no—
95C2×Q8×C181C2311yescharacteristic
96C2×D4×C181—21no—
97C2×D4×C181—21no—
98C2×D4×C181C2311yescharacteristic
99C2×D4×C181C2311yescharacteristic
100C22×C4×C181—21no—
101C22×C4×C181C2311yescharacteristic
102SD16×C181—22no—
103D8×C181—22no—
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C22⋊C4×C181—21no—
108C22×D181—21no—
109D724—21no—
110D724—21no—
111C22⋊D181—81no—
112C22⋊D181—81no—
113C22⋊D181—81no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—81no—
118C2×Dic181—81no—
119C2×Dic181—81no—
120C2×Dic181—81no—
121C2×Dic181C2×D411yescharacteristic
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C4×D181—81no—
126#13089678—21no—
127#13089678—21no—
128C23×C181—21no—
129C23×C181—21no—
130C23×C181C2×D411yescharacteristic
131Q8×C181—21no—
132Q8×C181#4112yes—
133D4×C181—24no—
134D4×C181—21no—
135D4×C181—21no—
136D4×C181—21no—
137D4×C181—81no—
138D4×C181#4112yes—
139C2×C4×C181—24no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2411yescharacteristic
146C8×C181—21no—
147C8×C181—21no—
148C22×C181—21no—
149C22×C181—22no—
150C22×C181—21no—
151C22×C181—21no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181C22×D411yescharacteristic
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C4×C181—21no—
162C4×C181—22no—
163C4×C181—41no—
164C4×C181C2×#4111yescharacteristic
165C4×C181C2×#4111yescharacteristic
166Dic181—21no—
167Dic181—21no—
168Dic181—21no—
169Dic181—21no—
170Dic181—41no—
171Dic181—41no—
172Dic181—41no—
173C2×C181—41no—
174C2×C181—42no—
175C2×C181—81no—
176C2×C181#52511yescharacteristic
177C2×C181#57611yescharacteristic
178C2×C181#57711yescharacteristic
179D181—81no—
180C181#311911yescharacteristic, complemented, Sylow
181#3119—1811nomaximal, Sylow
182#540—1811no—
183#520—1811no—
184#481—1811no—
185#480—1811no—
186#479—1811no—
187#478—1811no—
188#460—1811no—
189#459—1811no—
190#449—1811no—
191#449D18111yescharacteristic, complemented
192#442—1811no—
193#440—1811no—
194C4×SD16—1811no—
195C4×D8—1811no—
196#433—1811no—
197C2×#41C2×D18111yescharacteristic
198C2×SD16—1811no—
199C2×SD16C2×D18111yescharacteristic
200C2×D8—1811no—
201C2×D8C2×D18111yescharacteristic
202#127—1811no—
203#125—1811no—
204#123—3621no—
205#123—3621no—
206#121—3621no—
207#121—3621no—
208#121—1811no—
209#121C2×D18111yescharacteristic
210C4×Q8—1811no—
211C4×Q8—1811no—
212C4×D4—3621no—
213C4×D4—3621no—
214C4×D4—1811no—
215C4×D4—1811no—
216C4×D4—1811no—
217C4×D4—1811no—
218#117—3621no—
219#117—1811no—
220C2×C4⋊C4—3621no—
221C2×C4⋊C4—1811no—
222#107—1811no—
223#107—1811no—
224#106—1811no—
225#106—1811no—
226C4⋊C8—1811no—
227C4⋊C8—1811no—
228#103—1811no—
229#103C2×D18111yescharacteristic
230#102—1811no—
231#102—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102C2×D18111yescharacteristic
236C22⋊C8—1811no—
237C22⋊C8C2×D18111yescharacteristic
238#97—1811no—
239C4×C8—1811no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D18111yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—1811no—
249C2×D4C22×D18111yescharacteristic
250C2×D4C22×D18111yescharacteristic
251C22×C4—21no—
252C22×C4—3621no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4C22×D18111yescharacteristic
258SD16—22no—
259SD16—3622no—
260D8—22no—
261D8—3622no—
262C2×C8—1811no—
263C2×C8—1811no—
264C2×C8C22×D18111yescharacteristic
265C2×C8C22×D18111yescharacteristic
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—1811no—
272C4⋊C4—1811no—
273C4⋊C4—1811no—
274C4⋊C4—1811no—
275C4⋊C4—1811no—
276C4⋊C4C22×D18111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—1811no—
284C22⋊C4—1811no—
285C42—3621no—
286C42—3621no—
287C42—1811no—
288C42—1811no—
289C23—21no—
290C23—21no—
291C23—3621no—
292C23D4×D18111yescharacteristic
293Q8—21no—
294Q8#1566844812yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—3621no—
301D4—3621no—
302D4—14481no—
303D4—14481no—
304D4—14481no—
305D4#1566844812yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—14481no—
315C2×C4—14481no—
316C2×C4—14481no—
317C2×C4—14481no—
318C2×C4—14481no—
319C2×C4—1811no—
320C2×C4—1811no—
321C2×C4—1811no—
322C2×C4—1811no—
323C2×C4D4×D18111yescharacteristic
324C2×C4C23×D18111yescharacteristic
325C8—21no—
326C8—21no—
327C8—3621no—
328C8—3621no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—7241no—
339C22—7241no—
340C22—7241no—
341C22C2×D4×D18111yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—3621no—
346C4—3621no—
347C4—3621no—
348C4—3621no—
349C4—7241no—
350C4—7241no—
351C4—7241no—
352C4C2×#1566844811yescharacteristic
353C4C2×#1566844811yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—14481no—
358C2#2604178511yescharacteristic
359C2#2604208311yescharacteristic
360C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3119
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #26041882C2semidirect
2. #26041762C2semidirect
3. #26041598C2semidirect
4. #26041590C2semidirect
5. #26041584C2semidirect
6. #26041581C2semidirect
7. #26041477C2semidirect
8. #26041472C2semidirect
9. #26041424C2semidirect
10. #26041391C2semidirect
11. #26041382C2semidirect
12. SD16×Dic181C2semidirect
13. #26041359C2semidirect
14. #26041337C2semidirect
15. #449×C181C2semidirect
180. C181#3119semidirect
191. #449D181semidirect

Maximal subgroups

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

subgroupindex
#260418822
#260417622
#260415982
#260415902
#260415842
#260415812
#260414772
#260414722
#260414242
#260413912
#260413822
SD16×Dic1812
#260413592
#260413372
#449×C1812
#3119181