Finite Group Databasebeta

← #37543922

Subgroups — #37543922

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#26041884C211yesmaximal, characteristic, complemented
2#26041759C211yesmaximal, characteristic, complemented
3#26041598C211yesmaximal, characteristic, complemented
4#26041593C211yesmaximal, characteristic, complemented
5#26041587C211yesmaximal, characteristic, complemented
6#26041580C211yesmaximal, characteristic, complemented
7#26041480C211yesmaximal, characteristic, complemented
8#26041475C211yesmaximal, characteristic, complemented
9#26041426C211yesmaximal, characteristic, complemented
10#26041426C211yesmaximal, characteristic, complemented
11#26041392C211yesmaximal, characteristic, complemented
12#26041381C211yesmaximal, characteristic, complemented
13C4×#15668438C211yesmaximal, characteristic, complemented
14C4×D1448C211yesmaximal, characteristic, complemented
15#433×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668438C2211yescharacteristic
18C2×#15668438C2211yescharacteristic
19C2×D1448C2211yescharacteristic
20C2×D1448C2211yescharacteristic
21#19153813C2211yescharacteristic
22#19153808C2211yescharacteristic
23#19153801—21no—
24#19153801—21no—
25#19153790C2211yescharacteristic
26#19153790C2211yescharacteristic
27#19153789—21no—
28#19153789—21no—
29C4×Dic362C2211yescharacteristic
30C4×Dic362C2211yescharacteristic
31C4×D724C2211yescharacteristic
32C4×D724C2211yescharacteristic
33C4×D724C2211yescharacteristic
34C4×D724C2211yescharacteristic
35#19153776—21no—
36#19153776—21no—
37#19153774—21no—
38C2×C4⋊Dic181C2211yescharacteristic
39C4⋊C4×D181—21no—
40#19153750C2211yescharacteristic
41#19153750C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153748C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153738C2211yescharacteristic
50#19153738C2211yescharacteristic
51#19153738C2211yescharacteristic
52#117×C181C2211yescharacteristic
53C4⋊C8×C181C2211yescharacteristic
54C4⋊C8×C181C2211yescharacteristic
55C22⋊C8×C181C2211yescharacteristic
56C22⋊C8×C181C2211yescharacteristic
57#97×C181C2211yescharacteristic
58C4×C8×C181C2211yescharacteristic
59#15668449—22no—
60#15668449—22no—
61C2×Dic362C2311yescharacteristic
62C2×D724—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C22×Dic181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76#15668438—22no—
77#15668438—22no—
78D1448—22no—
79D1448—22no—
80C4⋊Dic181—21no—
81C4⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95C4×Dic181—21no—
96C4×Dic181—21no—
97C22×C4×C181C2311yescharacteristic
98C2×C8×C181C2311yescharacteristic
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181D411yescharacteristic
103C4⋊C4×C181D411yescharacteristic
104C22⋊C4×C181D411yescharacteristic
105C22⋊C4×C181D411yescharacteristic
106C42×C181C2311yescharacteristic
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—21no—
110C22×D181—21no—
111Dic362—21no—
112Dic362#4112yes—
113D724—21no—
114D724—21no—
115D724—21no—
116D724—21no—
117D724—21no—
118D724—81no—
119D724—81no—
120D724#4112yes—
121C22⋊D181—24no—
122C22⋊D181—81no—
123C22⋊D181—81no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—81no—
130C4×D181—24no—
131C4×D181—81no—
132C4×D181—81no—
133C4×D181—81no—
134C4×D181—81no—
135C23×C181C2×D411yescharacteristic
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181C2×D411yescharacteristic
139C2×C4×C181C2×D411yescharacteristic
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2×D411yescharacteristic
143C2×C4×C181C2411yescharacteristic
144C8×C181—21no—
145C8×C181—21no—
146C8×C181—21no—
147C8×C181—21no—
148C22×C181—21no—
149C22×C181—21no—
150C22×C181—21no—
151C22×C181C22×D411yescharacteristic
152C2×D181—22no—
153C2×D181—41no—
154C2×D181—41no—
155C2×D181—41no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C4×C181—21no—
162C4×C181—21no—
163C4×C181—21no—
164C4×C181—21no—
165C4×C181—21no—
166C4×C181C2×#4111yescharacteristic
167C4×C181C2×#4111yescharacteristic
168Dic181—22no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172Dic181—41no—
173C2×C181—41no—
174C2×C181#52511yescharacteristic
175C2×C181#57611yescharacteristic
176C2×C181#57711yescharacteristic
177D181—42no—
178D181—81no—
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#449—1811no—
192#442—1811no—
193#440—1811no—
194C4×SD16—1811no—
195C4×D8—1811no—
196#433D18111yescharacteristic, complemented
197C2×#41—1811no—
198C2×SD16—1811no—
199C2×SD16—1811no—
200C2×D8—1811no—
201C2×D8—1811no—
202#127—1811no—
203#125—1811no—
204#123—3621no—
205#123—3621no—
206#121—3621no—
207#121—3621no—
208#121—1811no—
209#121—1811no—
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#117C2×D18111yescharacteristic
220C2×C4⋊C4—3621no—
221C2×C4⋊C4—1811no—
222#107—1811no—
223#107—1811no—
224#106—1811no—
225#106—1811no—
226C4⋊C8C2×D18111yescharacteristic
227C4⋊C8C2×D18111yescharacteristic
228#103—1811no—
229#103—1811no—
230#102—1811no—
231#102—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102—1811no—
236C22⋊C8C2×D18111yescharacteristic
237C22⋊C8C2×D18111yescharacteristic
238#97C2×D18111yescharacteristic
239C4×C8C2×D18111yescharacteristic
240#41—3622no—
241#41—3622no—
242C2×Q8—1811no—
243C2×D4—3621no—
244C2×D4—3621no—
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—1811no—
249C2×D4—1811no—
250C2×D4—1811no—
251C22×C4—3621no—
252C22×C4—3621no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4C22×D18111yescharacteristic
258SD16—3622no—
259SD16—3622no—
260D8—3622no—
261D8—3622no—
262C2×C8C22×D18111yescharacteristic
263C2×C8C22×D18111yescharacteristic
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⋊C4D72411yescharacteristic
276C4⋊C4D72411yescharacteristic
277C22⋊C4—3621no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4D72411yescharacteristic
284C22⋊C4D72411yescharacteristic
285C42—3621no—
286C42—3621no—
287C42C22×D18111yescharacteristic
288C42C22×D18111yescharacteristic
289C23—3621no—
290C23—3621no—
291C23—3621no—
292C23C2×D72411yescharacteristic
293Q8—3621no—
294Q8—1812no—
295D4—3624no—
296D4—3621no—
297D4—3621no—
298D4—3621no—
299D4—3621no—
300D4—3621no—
301D4—14481no—
302D4—14481no—
303D4—14481no—
304D4—14481no—
305D4—1812no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—3624no—
309C2×C4—3621no—
310C2×C4—3621no—
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×C4C2×D72411yescharacteristic
320C2×C4C2×D72411yescharacteristic
321C2×C4C2×D72411yescharacteristic
322C2×C4C2×D72411yescharacteristic
323C2×C4C2×D72411yescharacteristic
324C2×C4C23×D18111yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—3622no—
333C22—7241no—
334C22—7241no—
335C22—7241no—
336C22—7241no—
337C22—7241no—
338C22—7241no—
339C22—7241no—
340C22—7241no—
341C22C22×D72411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—3622no—
348C4—7241no—
349C4—7241no—
350C4—7241no—
351C4—7241no—
352C4#41×D18111yescharacteristic
353C4#41×D18111yescharacteristic
354C2—41no—
355C2—14481no—
356C2—14481no—
357C2—7242no—
358C2#2604179111yescharacteristic
359C2#2604208411yescharacteristic
360C2#2604209111yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#433×C181C2
socleC22×C181C22×D4
hypercenter#433D181
hypocenterC181#3119
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #26041884C2semidirect
2. #26041759C2semidirect
3. #26041598C2semidirect
4. #26041593C2semidirect
5. #26041587C2semidirect
6. #26041580C2semidirect
7. #26041480C2semidirect
8. #26041475C2semidirect
9. #26041426C2semidirect
10. #26041426C2semidirect
11. #26041392C2semidirect
12. #26041381C2semidirect
13. C4×#15668438C2semidirect
14. C4×D1448C2semidirect
15. #433×C181C2semidirect
180. C181#3119semidirect
196. #433D181semidirect

Maximal subgroups

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

subgroupindex
#260418842
#260417592
#260415982
#260415932
#260415872
#260415802
#260414802
#260414752
#260414262
#260413922
#260413812
C4×#156684382
C4×D14482
#433×C1812
#3119181