Finite Group Databasebeta

← #37545380

Subgroups — #37545380

Order 23168.

482 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153848C211yesmaximal, characteristic, complemented
2C2×#19153846C211yesmaximal, characteristic, complemented
3#26041948C211yesmaximal, characteristic
4#26041942C211yesmaximal, characteristic, complemented
5#26041650C211yesmaximal, characteristic, complemented
6#26041527C211yesmaximal, characteristic, complemented
7#26041524C211yesmaximal, characteristic, complemented
8#26041487C211yesmaximal, characteristic, complemented
9#26041478C211yesmaximal, characteristic, complemented
10#26041444C211yesmaximal, characteristic, complemented
11#26041420C211yesmaximal, characteristic, complemented
12#26041416C211yesmaximal, characteristic, complemented
13#26041371C211yesmaximal, characteristic, complemented
14#26041354C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C22×Dic362C2211yescharacteristic
18C2×Q8×D181C2211yescharacteristic
19#19153848—24no—
20#19153846—24no—
21C2×#15668439C2211yescharacteristic
22C2×#15668439C2211yescharacteristic
23C2×#15668438C2211yescharacteristic
24C2×#15668438C2211yescharacteristic
25C2×#15668437C2211yescharacteristic
26C2×#15668437C2211yescharacteristic
27C2×#15668436C2211yescharacteristic
28C2×#15668433C2211yescharacteristic
29C2×#15668432C2211yescharacteristic
30#19153815—21no—
31#19153814C2211yescharacteristic
32#19153812—21no—
33#19153812C2211yescharacteristic
34#19153796C2211yescharacteristic
35#19153794—21no—
36#19153793—21no—
37#19153790—21no—
38#19153790C2211yescharacteristic
39#19153787—21no—
40#19153787C2211yescharacteristic
41Q8×Dic181C2211yescharacteristic
42#19153781C2211yescharacteristic
43C4×C22⋊D181—21no—
44C4×C22⋊D181C2211yescharacteristic
45#19153776—21no—
46#19153749C2211yescharacteristic
47#19153745C2211yescharacteristic
48#19153741C2211yescharacteristic
49#19153741C2211yescharacteristic
50#19153740C2211yescharacteristic
51#19153736C2211yescharacteristic
52#19153728C2211yescharacteristic
53C8×Dic181C2211yescharacteristic
54C2×#41×C181C2211yescharacteristic
55C2×Q16×C181C2211yescharacteristic
56C2×SD16×C181C2211yescharacteristic
57C22⋊Q8×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59#102×C181C2211yescharacteristic
60C22⋊C8×C181C2211yescharacteristic
61#15668450—22no—
62#15668450—41no—
63C2×Dic362—21no—
64C2×Dic362—22no—
65C2×Dic362—21no—
66C2×Dic362—41no—
67C2×Dic362C2311yescharacteristic
68C2×Dic362C2311yescharacteristic
69Q8×D181—22no—
70Q8×D181—41no—
71C2×D724—21no—
72C2×D724C2311yescharacteristic
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181—21no—
76C2×C22⋊D181—21no—
77C2×C22⋊D181D411yescharacteristic
78C22×Dic181—21no—
79C2×C4×D181—21no—
80C2×C4×D181—21no—
81C2×C4×D181C2311yescharacteristic
82#15668439—22no—
83#15668439D414yescomplemented
84#15668438—22no—
85#15668438—41no—
86#15668437—22no—
87#15668437—22no—
88#15668436—22no—
89#15668433—22no—
90#15668432—22no—
91C2×#13089678C2311yescharacteristic
92C2×#13089678C2311yescharacteristic
93C4⋊Dic181—21no—
94C4⋊Dic181—21no—
95C4⋊Dic181C2311yescharacteristic
96#15668428—21no—
97#15668428—21no—
98#15668428—21no—
99#15668428D411yescharacteristic
100C22⋊Dic181—21no—
101C22⋊Dic181D411yescharacteristic
102#15668426—21no—
103#15668426—21no—
104#15668426D411yescharacteristic
105C4×Dic181—21no—
106C4×Dic181—21no—
107C4×Dic181C2311yescharacteristic
108#41×C181—22no—
109#41×C181—41no—
110C2×Q8×C181C2311yescharacteristic
111C2×Q8×C181C2311yescharacteristic
112C2×D4×C181—21no—
113C2×D4×C181C2311yescharacteristic
114C22×C4×C181—21no—
115C22×C4×C181C2311yescharacteristic
116Q16×C181—22no—
117SD16×C181—41no—
118C2×C8×C181C2311yescharacteristic
119C2×C8×C181C2311yescharacteristic
120C4⋊C4×C181—21no—
121C4⋊C4×C181C2311yescharacteristic
122C22⋊C4×C181—21no—
123C22×D181—21no—
124C22×D181C2×D411yescharacteristic
125Dic362—21no—
126Dic362—21no—
127Dic362—21no—
128Dic362—42no—
129Dic362—42no—
130Dic362C2×D412yes—
131D724—21no—
132D724—21no—
133D724—42no—
134C22⋊D181—22no—
135C22⋊D181—42no—
136C22⋊D181—81no—
137C22⋊D181—81no—
138C22⋊D181—81no—
139C2×Dic181—21no—
140C2×Dic181—21no—
141C2×Dic181—21no—
142C2×Dic181—42no—
143C2×Dic181C2×D411yescharacteristic
144C2×Dic181C2×D411yescharacteristic
145C2×Dic181C2×D411yescharacteristic
146C4×D181—21no—
147C4×D181—21no—
148C4×D181—42no—
149C4×D181—42no—
150#13089678—21no—
151#13089678C2×D412yes—
152C23×C181—21no—
153C23×C181C2×D411yescharacteristic
154Q8×C181—21no—
155Q8×C181—21no—
156Q8×C181—21no—
157Q8×C181C2×D412yes—
158D4×C181—21no—
159D4×C181—21no—
160D4×C181—42no—
161C2×C4×C181—21no—
162C2×C4×C181—21no—
163C2×C4×C181—21no—
164C2×C4×C181—21no—
165C2×C4×C181—21no—
166C2×C4×C181—42no—
167C2×C4×C181C2×D411yescharacteristic
168C2×C4×C181C2411yescharacteristic
169C8×C181—21no—
170C8×C181—21no—
171C22×C181—21no—
172C22×C181—21no—
173C22×C181—21no—
174C22×C181—41no—
175C22×C181—41no—
176C22×C181—41no—
177C22×C181C22×D411yescharacteristic
178C2×D181—21no—
179C2×D181—21no—
180C2×D181—21no—
181C2×D181—41no—
182C2×D181—41no—
183C2×D181—41no—
184C4×C181—21no—
185C4×C181—22no—
186C4×C181—41no—
187C4×C181—41no—
188C4×C181C22×D411yescharacteristic
189C4×C181H(5,𝔽2)11yescharacteristic
190Dic181—21no—
191Dic181—22no—
192Dic181—21no—
193Dic181—41no—
194Dic181—41no—
195Dic181#13712yescomplemented
196C2×C181—41no—
197C2×C181—81no—
198C2×C181D4211yescharacteristic
199C2×C181C2×#13711yescharacteristic
200C2×C181#57711yescharacteristic
201D181—41no—
202D181—81no—
203C181#327811yescharacteristic, complemented, Sylow
204#3278—1811nomaximal, Sylow
205C2×#137—1811no—
206C2×#137—1811no—
207#550—1811no—
208D4×Q8—1811no—
209#492—1811no—
210#468—1811no—
211#468—1811no—
212#462—1811no—
213#460—1811no—
214#452—1811no—
215#452D18111yescharacteristic, complemented
216#448—1811no—
217#448—1811no—
218C4×Q16—1811no—
219#436—1811no—
220C2×#41—1811no—
221C2×#41C2×D18111yescharacteristic
222C22×Q8—1811no—
223C22×Q8—1811no—
224#137—3624no—
225#137—3624no—
226C2×Q16—1811no—
227C2×Q16—1811no—
228C2×Q16C2×D18111yescharacteristic
229C2×SD16—1811no—
230C2×SD16—1811no—
231C2×SD16—1811no—
232C2×SD16—1811no—
233C2×SD16—1811no—
234C2×SD16C2×D18111yescharacteristic
235C2×M16—1811no—
236C2×M16—1811no—
237C4⋊Q8—3621no—
238C4⋊Q8—1811no—
239#127—3621no—
240#127—1811no—
241C22⋊Q8—3621no—
242C22⋊Q8—3621no—
243C22⋊Q8—1811no—
244C22⋊Q8C2×D18111yescharacteristic
245#121—3621no—
246#121—3621no—
247#121—1811no—
248#121—1811no—
249C4×Q8—1811no—
250C4×Q8—1811no—
251C4×D4—3621no—
252C4×D4—3621no—
253C4×D4—1811no—
254#107—1811no—
255C4⋊C8—1811no—
256#103—1811no—
257#103—1811no—
258#103—1811no—
259#103C2×D18111yescharacteristic
260#102—1811no—
261#102C2×D18111yescharacteristic
262C22⋊C8—1811no—
263C22⋊C8C2×D18111yescharacteristic
264C4×C8—1811no—
265#41—22no—
266#41—41no—
267#41—3622no—
268#41—7241no—
269C2×Q8—3621no—
270C2×Q8—3622no—
271C2×Q8—3621no—
272C2×Q8—3622no—
273C2×Q8—1811no—
274C2×Q8—1811no—
275C2×Q8—7241no—
276C2×Q8—7241no—
277C2×Q8C22×D18111yescharacteristic
278C2×Q8C22×D18111yescharacteristic
279C2×D4—21no—
280C2×D4—3621no—
281C2×D4—3621no—
282C2×D4—3621no—
283C2×D4—3621no—
284C2×D4—3621no—
285C2×D4—1811no—
286C2×D4—1811no—
287C2×D4C22×D18111yescharacteristic
288C22×C4—21no—
289C22×C4—3621no—
290C22×C4—3621no—
291C22×C4—3621no—
292C22×C4—1811no—
293C22×C4C22×D18111yescharacteristic
294Q16—22no—
295Q16—3622no—
296Q16—1814no—
297SD16—41no—
298SD16—3622no—
299SD16—3622no—
300SD16—3622no—
301SD16—3622no—
302SD16—7241no—
303M16—3622no—
304M16—3622no—
305C2×C8—1811no—
306C2×C8—1811no—
307C2×C8C22×D18111yescharacteristic
308C2×C8C22×D18111yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—3621no—
311C4⋊C4—3621no—
312C4⋊C4—3621no—
313C4⋊C4—3621no—
314C4⋊C4—3621no—
315C4⋊C4—1811no—
316C4⋊C4—1811no—
317C4⋊C4C22×D18111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—3621no—
320C22⋊C4—3621no—
321C22⋊C4—3621no—
322C22⋊C4—1811no—
323C22⋊C4—1811no—
324C42—3621no—
325C42—3621no—
326C42—1811no—
327C23—21no—
328C23—3621no—
329C23—1811no—
330C23D4×D18111yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—3621no—
335Q8—3621no—
336Q8—3621no—
337Q8—1812no—
338Q8—7242no—
339Q8—7242no—
340Q8D4×D18112yes—
341D4—21no—
342D4—21no—
343D4—42no—
344D4—3622no—
345D4—3621no—
346D4—3621no—
347D4—14481no—
348D4—14481no—
349D4—14481no—
350D4—7242no—
351D4—7242no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—3621no—
359C2×C4—3621no—
360C2×C4—3621no—
361C2×C4—3621no—
362C2×C4—3621no—
363C2×C4—1811no—
364C2×C4—1811no—
365C2×C4—1811no—
366C2×C4—7242no—
367C2×C4—7242no—
368C2×C4—7242no—
369C2×C4D4×D18111yescharacteristic
370C2×C4C23×D18111yescharacteristic
371C8—21no—
372C8—21no—
373C8—3621no—
374C8—1812no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—3621no—
382C22—3621no—
383C22—3621no—
384C22—7241no—
385C22—7241no—
386C22—7241no—
387C22C2×D4×D18111yescharacteristic
388C4—21no—
389C4—22no—
390C4—41no—
391C4—41no—
392C4—3621no—
393C4—3622no—
394C4—3621no—
395C4—1812no—
396C4—7241no—
397C4—7241no—
398C4C2×D4×D18111yescharacteristic
399C4#1915386111yescharacteristic
400C2—41no—
401C2—81no—
402C2—14481no—
403C2—7241no—
404C2#2604191111yescharacteristic
405C2#137×D18111yescharacteristic
406C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
prime radical#26041948C2
hypercenter#452D181
hypocenterC181#3278
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#19153848C2semidirect
2. C2×#19153846C2semidirect
4. #26041942C2semidirect
5. #26041650C2semidirect
6. #26041527C2semidirect
7. #26041524C2semidirect
8. #26041487C2semidirect
9. #26041478C2semidirect
10. #26041444C2semidirect
11. #26041420C2semidirect
12. #26041416C2semidirect
13. #26041371C2semidirect
14. #26041354C2semidirect
15. #452×C181C2semidirect
83. #15668439D4semidirect
195. Dic181#137semidirect
203. C181#3278semidirect
215. #452D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538482
C2×#191538462
#260419482
#260419422
#260416502
#260415272
#260415242
#260414872
#260414782
#260414442
#260414202
#260414162
#260413712
#260413542
#452×C1812
#3278181