Finite Group Databasebeta

← #37544572

Subgroups — #37544572

Order 23168.

422 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
1#26041857C211yesmaximal, characteristic, complemented
2#26041845C211yesmaximal, characteristic, complemented
3#26041618C211yesmaximal, characteristic, complemented
4#26041602C211yesmaximal, characteristic, complemented
5#26041598C211yesmaximal, characteristic, complemented
6#26041590C211yesmaximal, characteristic, complemented
7#26041529C211yesmaximal, characteristic, complemented
8#26041528C211yesmaximal, characteristic, complemented
9#26041514C211yesmaximal, characteristic, complemented
10#26041505C211yesmaximal, characteristic, complemented
11#26041428C211yesmaximal, characteristic, complemented
12#26041424C211yesmaximal, characteristic, complemented
13#26041411C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668432C2211yescharacteristic, complemented
21C2×C8×D181C2211yescharacteristic, complemented
22#19153812—21no—
23#19153802—21no—
24#19153795—21no—
25#19153792C2211yescharacteristic
26#19153792C2211yescharacteristic, complemented
27#19153791C2211yescharacteristic
28#19153790—21no—
29#19153790C2211yescharacteristic
30#19153788—21no—
31#19153788—21no—
32#19153787C2211yescharacteristic
33#19153787C2211yescharacteristic
34#19153787C2211yescharacteristic, complemented
35#19153786—21no—
36#19153784—21no—
37#19153774C2211yescharacteristic
38C2×C4⋊Dic181C2211yescharacteristic, complemented
39#19153749C2211yescharacteristic, complemented
40#19153749C2211yescharacteristic, complemented
41#19153748C2211yescharacteristic, complemented
42#19153748C2211yescharacteristic, complemented
43#19153740C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic, complemented
53C2×SD16×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668449—41no—
61#15668449—41no—
62C2×Dic362D411yescharacteristic
63C2×D724—21no—
64C2×D724D411yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181D411yescharacteristic
72C2×C22⋊D181D411yescharacteristic
73D4×D181—41no—
74D4×D181—41no—
75C22×Dic181—21no—
76C2×C4×D181C2311yescharacteristic
77C2×C4×D181C2311yescharacteristic
78#15668436—41no—
79#15668434—41no—
80#15668432—41no—
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C8×D181—41no—
84C4⋊Dic181—21no—
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87C4⋊Dic181C2311yescharacteristic
88#15668428—21no—
89#15668428—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98C4×Dic181—21no—
99#41×C181—41no—
100#41×C181—41no—
101C2×Q8×C181C2311yescharacteristic
102C2×D4×C181—21no—
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C2×D4×C181C2311yescharacteristic
106C22×C4×C181—21no—
107C22×C4×C181C2311yescharacteristic
108SD16×C181—41no—
109D8×C181—41no—
110C2×C8×C181C2311yescharacteristic
111C2×C8×C181C2311yescharacteristic
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—21no—
115C22×D181—42no—
116C22×D181—81no—
117C22×D181—81no—
118C22×D181C2×D411yescharacteristic
119C22×D181C2×D411yescharacteristic
120Dic362—41no—
121D724—21no—
122D724—21no—
123D724—41no—
124D724—81no—
125C22⋊D181—41no—
126C22⋊D181—41no—
127C22⋊D181—42no—
128C22⋊D181—81no—
129C22⋊D181—81no—
130C22⋊D181—81no—
131C22⋊D181—81no—
132C2×Dic181—21no—
133C2×Dic181—21no—
134C2×Dic181—21no—
135C2×Dic181—81no—
136C2×Dic181C2×D411yescharacteristic
137C2×Dic181C2×D411yescharacteristic
138C4×D181—21no—
139C4×D181—21no—
140C4×D181—21no—
141C4×D181—21no—
142#13089678—21no—
143#13089678—21no—
144C23×C181—21no—
145C23×C181—21no—
146C23×C181C2×D411yescharacteristic
147Q8×C181—21no—
148Q8×C181—21no—
149D4×C181—21no—
150D4×C181—21no—
151D4×C181—21no—
152D4×C181—21no—
153D4×C181—42no—
154D4×C181—81no—
155C2×C4×C181—21no—
156C2×C4×C181—21no—
157C2×C4×C181—21no—
158C2×C4×C181—21no—
159C2×C4×C181—42no—
160C2×C4×C181C2×D411yescharacteristic
161C2×C4×C181C2411yescharacteristic
162C8×C181—21no—
163C8×C181—21no—
164C22×C181—21no—
165C22×C181—21no—
166C22×C181—21no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181—41no—
173C22×C181C22×D411yescharacteristic
174C2×D181—21no—
175C2×D181—21no—
176C2×D181—21no—
177C2×D181—21no—
178C2×D181—21no—
179C2×D181—21no—
180C2×D181—41no—
181C2×D181—41no—
182C2×D181—41no—
183C2×D181—84no—
184C4×C181—21no—
185C4×C181—41no—
186C4×C181—41no—
187C4×C181H(5,𝔽2)11yescharacteristic
188C4×C181H(5,𝔽2)11yescharacteristic
189Dic181—21no—
190Dic181—21no—
191Dic181—41no—
192Dic181—41no—
193Dic181—41no—
194C2×C181—41no—
195C2×C181—81no—
196C2×C181—81no—
197C2×C181#53411yescharacteristic
198C2×C181#57611yescharacteristic
199C2×C181#57711yescharacteristic
200D181—41no—
201D181—41no—
202D181—81no—
203C181#319811yescharacteristic, complemented, Sylow
204#3198—1811nomaximal, Sylow
205#537—1811no—
206#535—1811no—
207#485—1811no—
208#482—1811no—
209#481—1811no—
210#480—1811no—
211#469—1811no—
212#468—1811no—
213#466—1811no—
214#465—1811no—
215#450—1811no—
216#449—1811no—
217#449D18111yescharacteristic, complemented
218#447—1811no—
219#408—1811no—
220C2×#41—1811no—
221C2×#41C2×D18111yescharacteristic, complemented
222C22×D4—1811no—
223C2×SD16—1811no—
224C2×SD16C2×D18111yescharacteristic
225C2×D8—1811no—
226C2×D8C2×D18111yescharacteristic
227C2×M16—1811no—
228C22×C8—1811no—
229#127—3621no—
230#124—3621no—
231C22⋊Q8—3621no—
232C22⋊Q8—1811no—
233C22⋊Q8—1811no—
234#121—3621no—
235#121—3621no—
236#121—3621no—
237#121—1811no—
238#121—1811no—
239#121—1811no—
240#121—1811no—
241#121—1811no—
242#121C2×D18111yescharacteristic
243#120—3621no—
244#120—3621no—
245#117—1811no—
246C2×C4⋊C4—1811no—
247#107—1811no—
248#107—1811no—
249#106—1811no—
250#106—1811no—
251#103—1811no—
252#103C2×D18111yescharacteristic, complemented
253#102—1811no—
254#102—1811no—
255#102—1811no—
256#102—1811no—
257#102—1811no—
258#102C2×D18111yescharacteristic, complemented
259C22⋊C8—1811no—
260C22⋊C8—1811no—
261C22⋊C8—1811no—
262C22⋊C8C2×D18111yescharacteristic, complemented
263C24—3621no—
264#41—41no—
265#41—41no—
266#41—7241no—
267#41—7241no—
268C2×Q8—1811no—
269C2×Q8C22×D18111yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—3621no—
273C2×D4—3621no—
274C2×D4—3621no—
275C2×D4—3621no—
276C2×D4—3621no—
277C2×D4—3621no—
278C2×D4—1811no—
279C2×D4—1811no—
280C2×D4—1811no—
281C2×D4—1811no—
282C2×D4—7241no—
283C2×D4—7241no—
284C2×D4C22×D18111yescharacteristic
285C2×D4C22×D18111yescharacteristic
286C22×C4—21no—
287C22×C4—3621no—
288C22×C4—1811no—
289C22×C4—1811no—
290C22×C4C22×D18111yescharacteristic
291SD16—41no—
292SD16—7241no—
293D8—41no—
294D8—7241no—
295M16—7241no—
296C2×C8—1811no—
297C2×C8—1811no—
298C2×C8—7241no—
299C2×C8C22×D18111yescharacteristic
300C2×C8C22×D18111yescharacteristic
301C4⋊C4—3621no—
302C4⋊C4—3621no—
303C4⋊C4—3621no—
304C4⋊C4—1811no—
305C4⋊C4—1811no—
306C4⋊C4—1811no—
307C4⋊C4C22×D18111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—3621no—
310C22⋊C4—3621no—
311C22⋊C4—3621no—
312C22⋊C4—3621no—
313C22⋊C4—3621no—
314C22⋊C4—3621no—
315C22⋊C4—3621no—
316C22⋊C4—3621no—
317C42—3621no—
318C23—21no—
319C23—21no—
320C23—3621no—
321C23—14481no—
322C23—14481no—
323C23—1811no—
324C23—1811no—
325C23—7242no—
326C23D4×D18111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—7241no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—3621no—
337D4—3621no—
338D4—14481no—
339D4—14481no—
340D4—14481no—
341D4—14481no—
342D4—14481no—
343D4—7241no—
344D4—7241no—
345D4—7241no—
346D4—7242no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—3621no—
353C2×C4—3621no—
354C2×C4—3621no—
355C2×C4—3621no—
356C2×C4—3621no—
357C2×C4—3621no—
358C2×C4—3621no—
359C2×C4—14481no—
360C2×C4—1811no—
361C2×C4—1811no—
362C2×C4D4×D18111yescharacteristic
363C2×C4C23×D18111yescharacteristic
364C8—21no—
365C8—21no—
366C8—3621no—
367C8—3621no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—3621no—
378C22—3621no—
379C22—3621no—
380C22—3621no—
381C22—3621no—
382C22—3621no—
383C22—14484no—
384C22—7241no—
385C22—7241no—
386C22—7241no—
387C22C2×D4×D18111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—3621no—
392C4—3621no—
393C4—7241no—
394C4—7241no—
395C4—7241no—
396C4#1915386111yescharacteristic
397C4#1915386111yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—14481no—
402C2—7241no—
403C2—7241no—
404C2#2604183911yescharacteristic
405C2#2604208311yescharacteristic
406C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3198
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. #26041857C2semidirect
2. #26041845C2semidirect
3. #26041618C2semidirect
4. #26041602C2semidirect
5. #26041598C2semidirect
6. #26041590C2semidirect
7. #26041529C2semidirect
8. #26041528C2semidirect
9. #26041514C2semidirect
10. #26041505C2semidirect
11. #26041428C2semidirect
12. #26041424C2semidirect
13. #26041411C2semidirect
14. #26041244C2semidirect
15. #449×C181C2semidirect
20. C2×#15668432C22semidirect
21. C2×C8×D181C22semidirect
26. #19153792C22semidirect
34. #19153787C22semidirect
38. C2×C4⋊Dic181C22semidirect
39. #19153749C22semidirect
40. #19153749C22semidirect
41. #19153748C22semidirect
42. #19153748C22semidirect
43. #19153740C22semidirect
48. #19153737C22semidirect
49. C22⋊#13089678C22semidirect
52. C2×#41×C181C22semidirect
56. #103×C181C22semidirect
57. #102×C181C22semidirect
58. C22⋊C8×C181C22semidirect
203. C181#3198semidirect
217. #449D181semidirect
221. C2×#41C2×D181semidirect
252. #103C2×D181semidirect
258. #102C2×D181semidirect
262. C22⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418572
#260418452
#260416182
#260416022
#260415982
#260415902
#260415292
#260415282
#260415142
#260415052
#260414282
#260414242
#260414112
#260412442
#449×C1812
#3198181