Finite Group Databasebeta

← #37544713

Subgroups — #37544713

Order 23168.

434 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041825C211yesmaximal, characteristic, complemented
2#26041824C211yesmaximal, characteristic, complemented
3#26041667C211yesmaximal, characteristic, complemented
4#26041665C211yesmaximal, characteristic, complemented
5#26041640C211yesmaximal, characteristic, complemented
6#26041637C211yesmaximal, characteristic, complemented
7#26041483C211yesmaximal, characteristic, complemented
8#26041482C211yesmaximal, characteristic, complemented
9#26041473C211yesmaximal, characteristic, complemented
10#26041472C211yesmaximal, characteristic, complemented
11#26041426C211yesmaximal, characteristic, complemented
12#26041424C211yesmaximal, characteristic, complemented
13#26041422C211yesmaximal, characteristic, complemented
14#26041333C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668448—21no—
18C2×#15668438C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×#15668436C2211yescharacteristic
21C2×D1448C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23C2×#15668434C2211yescharacteristic
24#19153815C2211yescharacteristic
25#19153814C2211yescharacteristic
26#19153812C2211yescharacteristic
27#19153812C2211yescharacteristic
28#19153805C2211yescharacteristic
29#19153803C2211yescharacteristic
30#19153802—21no—
31#19153790C2211yescharacteristic
32#19153788—21no—
33#19153788—21no—
34#19153788—21no—
35D4×Dic181C2211yescharacteristic
36#19153778C2211yescharacteristic
37C4×C22⋊D181—21no—
38C4×C22⋊D181—21no—
39#19153776—21no—
40C2×C4×Dic181C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51#19153726C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668449—41no—
60#15668449—41no—
61#15668448—44no—
62C2×Dic362—21no—
63C2×Dic362C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C22×Dic181—21no—
73C22×Dic181D411yescharacteristic
74C22×Dic181D411yescharacteristic
75C2×C4×D181—21no—
76C2×C4×D181—21no—
77#15668438—41no—
78#15668437—41no—
79#15668436—41no—
80D1448—41no—
81#15668434—41no—
82#15668434—41no—
83C2×#13089678C2311yescharacteristic
84C2×#13089678C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96C4×Dic181D411yescharacteristic
97C4×Dic181D411yescharacteristic
98C4×Dic181C2311yescharacteristic
99C4×Dic181C2311yescharacteristic
100#41×C181—41no—
101#41×C181—41no—
102C2×Q8×C181C2311yescharacteristic
103C2×D4×C181—21no—
104C2×D4×C181—21no—
105C2×D4×C181C2311yescharacteristic
106C2×D4×C181C2311yescharacteristic
107C22×C4×C181—21no—
108C22×C4×C181C2311yescharacteristic
109SD16×C181—41no—
110D8×C181—41no—
111C2×C8×C181C2311yescharacteristic
112C2×C8×C181C2311yescharacteristic
113C4⋊C4×C181C2311yescharacteristic
114C22⋊C4×C181—21no—
115C22×D181—21no—
116C22×D181—21no—
117Dic362—21no—
118Dic362—21no—
119Dic362—42no—
120D724—21no—
121D724—21no—
122D724—21no—
123D724—21no—
124C22⋊D181—42no—
125C22⋊D181—42no—
126C22⋊D181—42no—
127C22⋊D181—42no—
128C22⋊D181—42no—
129C22⋊D181—42no—
130C2×Dic181—22no—
131C2×Dic181—21no—
132C2×Dic181—21no—
133C2×Dic181—41no—
134C2×Dic181—42no—
135C2×Dic181C2×D411yescharacteristic
136C2×Dic181C2×D411yescharacteristic
137C2×Dic181C2×D411yescharacteristic
138C2×Dic181C2×D411yescharacteristic
139C4×D181—42no—
140C4×D181—42no—
141#13089678—21no—
142#13089678—21no—
143C23×C181—21no—
144C23×C181—21no—
145C23×C181C2×D411yescharacteristic
146Q8×C181—21no—
147Q8×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—21no—
151D4×C181—21no—
152D4×C181—42no—
153D4×C181—42no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—21no—
157C2×C4×C181—21no—
158C2×C4×C181—42no—
159C2×C4×C181C2×D411yescharacteristic
160C2×C4×C181C2411yescharacteristic
161C8×C181—21no—
162C8×C181—21no—
163C22×C181—21no—
164C22×C181—21no—
165C22×C181—21no—
166C22×C181—41no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181C22×D411yescharacteristic
173C2×D181—41no—
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—41no—
177C2×D181—41no—
178C2×D181—41no—
179C4×C181—21no—
180C4×C181—41no—
181C4×C181—41no—
182C4×C181H(5,𝔽2)11yescharacteristic
183C4×C181H(5,𝔽2)11yescharacteristic
184Dic181—21no—
185Dic181—21no—
186Dic181—21no—
187Dic181—41no—
188Dic181—41no—
189Dic181AGL(1,ℤ/8)12yes—
190C2×C181—41no—
191C2×C181—81no—
192C2×C181—81no—
193C2×C181#53511yescharacteristic
194C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C181#57511yescharacteristic
196D181—81no—
197D181—81no—
198C181#321411yescharacteristic, complemented, Sylow
199#3214—1811nomaximal, Sylow
200#532—1811no—
201#532—1811no—
202#496—1811no—
203#496—1811no—
204#489—1811no—
205#489—1811no—
206#461—1811no—
207#461—1811no—
208#459—1811no—
209#459—1811no—
210#449—1811no—
211#449—1811no—
212#449—1811no—
213#449D18111yescharacteristic, complemented
214#432—1811no—
215C2×#41—3621no—
216C2×#41—1811no—
217C2×#41C2×D18111yescharacteristic
218C2×SD16—1811no—
219C2×SD16—1811no—
220C2×SD16—1811no—
221C2×SD16C2×D18111yescharacteristic
222C2×D8—1811no—
223C2×D8—1811no—
224C2×D8—1811no—
225C2×D8C2×D18111yescharacteristic
226C4⋊Q8—1811no—
227C4⋊Q8—1811no—
228#127—1811no—
229#127—1811no—
230#124—3621no—
231#124—1811no—
232#124—1811no—
233#121—3621no—
234#121—3621no—
235#121—3621no—
236#121—1811no—
237#121C2×D18111yescharacteristic
238C4×D4—3621no—
239C4×D4—3621no—
240C4×D4—3621no—
241C4×D4—1811no—
242C4×D4—1811no—
243C2×C42—1811no—
244C4⋊C8—1811no—
245C4⋊C8—1811no—
246#103—1811no—
247#103—1811no—
248#103—1811no—
249#103C2×D18111yescharacteristic
250#102—1811no—
251#102—1811no—
252#102—1811no—
253#102C2×D18111yescharacteristic
254C22⋊C8—1811no—
255C22⋊C8C2×D18111yescharacteristic
256#97—1811no—
257#97—1811no—
258#41—41no—
259#41—41no—
260#41—7241no—
261#41—7241no—
262#41—7244no—
263C2×Q8—3621no—
264C2×Q8—1811no—
265C2×Q8C22×D18111yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—3621no—
274C2×D4—1811no—
275C2×D4—1811no—
276C2×D4C22×D18111yescharacteristic
277C2×D4C22×D18111yescharacteristic
278C22×C4—21no—
279C22×C4—3621no—
280C22×C4—3621no—
281C22×C4—3621no—
282C22×C4—1811no—
283C22×C4—1811no—
284C22×C4C22×D18111yescharacteristic
285SD16—41no—
286SD16—7241no—
287SD16—7241no—
288SD16—7241no—
289D8—41no—
290D8—7241no—
291D8—7241no—
292D8—7241no—
293C2×C8—1811no—
294C2×C8—1811no—
295C2×C8C22×D18111yescharacteristic
296C2×C8C22×D18111yescharacteristic
297C4⋊C4—3621no—
298C4⋊C4—3621no—
299C4⋊C4—3621no—
300C4⋊C4—1811no—
301C4⋊C4C22×D18111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C42—1811no—
311C42—1811no—
312C42—1811no—
313C42—1811no—
314C23—21no—
315C23—21no—
316C23—3621no—
317C23—3621no—
318C23D4×D18111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—3621no—
322Q8—3621no—
323Q8—7242no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—3621no—
331D4—3621no—
332D4—3621no—
333D4—3621no—
334D4—7242no—
335D4—7242no—
336D4—7242no—
337D4—7242no—
338D4—7242no—
339D4—7242no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—3622no—
346C2×C4—3621no—
347C2×C4—3621no—
348C2×C4—1811no—
349C2×C4—1811no—
350C2×C4—1811no—
351C2×C4—1811no—
352C2×C4—7242no—
353C2×C4—7242no—
354C2×C4—7241no—
355C2×C4—7242no—
356C2×C4D4×D18111yescharacteristic
357C2×C4C23×D18111yescharacteristic
358C8—21no—
359C8—21no—
360C8—3621no—
361C8—3621no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—7241no—
372C22—7241no—
373C22—7241no—
374C22—7241no—
375C22—7241no—
376C22—7241no—
377C22C2×D4×D18111yescharacteristic
378C4—21no—
379C4—41no—
380C4—41no—
381C4—3621no—
382C4—3621no—
383C4—3621no—
384C4—1812no—
385C4—7241no—
386C4—7241no—
387C4#1915386111yescharacteristic
388C4#1915386111yescharacteristic
389C2—41no—
390C2—81no—
391C2—81no—
392C2—14481no—
393C2—14481no—
394C2#2604184411yescharacteristic
395C2AGL(1,ℤ/8)×D18111yescharacteristic
396C2#2604207611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3214
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. #26041825C2semidirect
2. #26041824C2semidirect
3. #26041667C2semidirect
4. #26041665C2semidirect
5. #26041640C2semidirect
6. #26041637C2semidirect
7. #26041483C2semidirect
8. #26041482C2semidirect
9. #26041473C2semidirect
10. #26041472C2semidirect
11. #26041426C2semidirect
12. #26041424C2semidirect
13. #26041422C2semidirect
14. #26041333C2semidirect
15. #449×C181C2semidirect
198. C181#3214semidirect
213. #449D181semidirect

Maximal subgroups

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

subgroupindex
#260418252
#260418242
#260416672
#260416652
#260416402
#260416372
#260414832
#260414822
#260414732
#260414722
#260414262
#260414242
#260414222
#260413332
#449×C1812
#3214181