Finite Group Databasebeta

← #37544607

Subgroups — #37544607

Order 23168.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041859C211yesmaximal, characteristic
2#26041853C211yesmaximal, characteristic, complemented
3#26041617C211yesmaximal, characteristic, complemented
4#26041613C211yesmaximal, characteristic, complemented
5#26041608C211yesmaximal, characteristic, complemented
6#26041604C211yesmaximal, characteristic, complemented
7#26041534C211yesmaximal, characteristic, complemented
8#26041528C211yesmaximal, characteristic, complemented
9#26041517C211yesmaximal, characteristic, complemented
10#26041511C211yesmaximal, characteristic, complemented
11#26041440C211yesmaximal, characteristic, complemented
12#26041440C211yesmaximal, characteristic, complemented
13#26041418C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic, complemented
15#451×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668449C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×#15668436C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21C2×C8×D181C2211yescharacteristic
22#19153814—21no—
23#19153805—21no—
24#19153799—21no—
25#19153799—21no—
26#19153794—21no—
27#19153792C2211yescharacteristic
28#19153792C2211yescharacteristic
29#19153792C2211yescharacteristic
30#19153792C2211yescharacteristic
31#19153792C2211yescharacteristic
32#19153791—21no—
33#19153791C2211yescharacteristic
34#19153790C2211yescharacteristic
35#19153789—21no—
36#19153789—21no—
37#19153775C2211yescharacteristic
38C4⋊C4×D181C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153738C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C22×Q8×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C2×Q16×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668450—41no—
60#15668450—41no—
61#15668449—41no—
62#15668449—41no—
63C2×Dic362D411yescharacteristic
64C2×D724—21no—
65C2×D724—21no—
66C2×D724D411yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181D411yescharacteristic
70C2×C22⋊D181D411yescharacteristic
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74C2×C4×D181C2311yescharacteristic
75#15668436—41no—
76#15668436—41no—
77#15668432—41no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C8×D181—41no—
81C4⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90C22⋊Dic181—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98C4×Dic181—21no—
99C2×Q8×C181—21no—
100C2×Q8×C181—41no—
101C2×Q8×C181—41no—
102C2×Q8×C181C2311yescharacteristic
103C2×Q8×C181C2311yescharacteristic
104C2×Q8×C181C2311yescharacteristic
105C22×C4×C181—21no—
106C22×C4×C181C2311yescharacteristic
107Q16×C181—41no—
108Q16×C181—41no—
109C2×C8×C181C2311yescharacteristic
110C2×C8×C181C2311yescharacteristic
111C4⋊C4×C181—21no—
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—21no—
115C22×D181C2×D411yescharacteristic
116C22×D181C2×D411yescharacteristic
117Dic362—41no—
118D724—21no—
119D724—21no—
120D724—41no—
121D724—42no—
122D724—81no—
123C22⋊D181—41no—
124C22⋊D181—41no—
125C22⋊D181—81no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C4×D181—21no—
132C4×D181—21no—
133C4×D181—21no—
134C4×D181—21no—
135C4×D181—42no—
136C4×D181—81no—
137#13089678—21no—
138#13089678—21no—
139C23×C181C2×D411yescharacteristic
140Q8×C181—21no—
141Q8×C181—21no—
142Q8×C181—21no—
143Q8×C181—21no—
144Q8×C181—21no—
145Q8×C181—21no—
146Q8×C181—42no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—42no—
154C2×C4×C181C2×D411yescharacteristic
155C2×C4×C181C2411yescharacteristic
156C8×C181—21no—
157C8×C181—21no—
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—21no—
161C22×C181C22×D411yescharacteristic
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—21no—
165C2×D181—21no—
166C2×D181—21no—
167C2×D181—21no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C4×C181—21no—
172C4×C181—41no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181—41no—
176C4×C181H(5,𝔽2)11yescharacteristic
177C4×C181H(5,𝔽2)11yescharacteristic
178Dic181—21no—
179Dic181—21no—
180Dic181—41no—
181Dic181—41no—
182Dic181—41no—
183C2×C181—41no—
184C2×C181#53411yescharacteristic
185C2×C181#57711yescharacteristic
186C2×C181#57811yescharacteristic
187D181—41no—
188D181—41no—
189D181—81no—
190C181#320111yescharacteristic, complemented, Sylow
191#3201—1811nomaximal, Sylow
192#537—1811no—
193#536—1811no—
194#485—1811no—
195#484—1811no—
196#483—1811no—
197#482—1811no—
198#470—1811no—
199#468—1811no—
200#467—1811no—
201#465—1811no—
202#452—1811no—
203#452—1811no—
204#451D18111yescharacteristic, complemented
205#448—1811no—
206#408—1811no—
207C2×#41—1811no—
208C2×#41—1811no—
209C22×Q8C2×D18111yescharacteristic
210C2×Q16C2×D18111yescharacteristic
211C2×Q16C2×D18111yescharacteristic
212C2×SD16—1811no—
213C2×SD16—1811no—
214C2×M16—1811no—
215C22×C8—1811no—
216C4⋊Q8—3621no—
217#124—3621no—
218#123—3621no—
219#123—3621no—
220C22⋊Q8—3621no—
221C22⋊Q8—1811no—
222C22⋊Q8—1811no—
223C22⋊Q8—1811no—
224C22⋊Q8—1811no—
225C22⋊Q8—1811no—
226C22⋊Q8C2×D18111yescharacteristic
227#121—3621no—
228#121—3621no—
229#121—3621no—
230#121—1811no—
231#121—1811no—
232#117—1811no—
233C2×C4⋊C4—1811no—
234#107—1811no—
235#107—1811no—
236#106—1811no—
237#106—1811no—
238#103—1811no—
239#103—1811no—
240#103—1811no—
241#103—1811no—
242#103C2×D18111yescharacteristic
243#103C2×D18111yescharacteristic
244#102—1811no—
245#102—1811no—
246C22⋊C8—1811no—
247C22⋊C8—1811no—
248C22⋊C8—1811no—
249C22⋊C8C2×D18111yescharacteristic
250#41—7241no—
251#41—7241no—
252#41—7241no—
253#41—7241no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—1811no—
258C2×Q8C22×D18111yescharacteristic
259C2×Q8C22×D18111yescharacteristic
260C2×Q8C22×D18111yescharacteristic
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—3621no—
264C2×D4—1811no—
265C2×D4—1811no—
266C2×D4—1811no—
267C2×D4—1811no—
268C22×C4—21no—
269C22×C4—3621no—
270C22×C4—3621no—
271C22×C4—1811no—
272C22×C4—1811no—
273C22×C4C22×D18111yescharacteristic
274Q16—41no—
275Q16—41no—
276SD16—7241no—
277SD16—7241no—
278M16—7241no—
279C2×C8—1811no—
280C2×C8—1811no—
281C2×C8—7241no—
282C2×C8C22×D18111yescharacteristic
283C2×C8C22×D18111yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—3621no—
286C4⋊C4—3621no—
287C4⋊C4—3621no—
288C4⋊C4—3621no—
289C4⋊C4—3621no—
290C4⋊C4—3621no—
291C4⋊C4—1811no—
292C4⋊C4—1811no—
293C4⋊C4—1811no—
294C4⋊C4C22×D18111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4—3621no—
304C42—3621no—
305C23—3621no—
306C23—1811no—
307C23—1811no—
308C23D4×D18111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—42no—
316Q8—7241no—
317D4—3621no—
318D4—3621no—
319D4—14481no—
320D4—14481no—
321D4—7241no—
322D4—7242no—
323D4—7241no—
324D4—7241no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—3621no—
336C2×C4—3621no—
337C2×C4—3621no—
338C2×C4—3621no—
339C2×C4—14481no—
340C2×C4—1811no—
341C2×C4—1811no—
342C2×C4—7242no—
343C2×C4D4×D18111yescharacteristic
344C2×C4C23×D18111yescharacteristic
345C8—21no—
346C8—21no—
347C8—3621no—
348C8—3621no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—3621no—
353C22—3621no—
354C22—3621no—
355C22—3621no—
356C22—3621no—
357C22—3621no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22C2×D4×D18111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—3621no—
368C4—3621no—
369C4—7241no—
370C4—7241no—
371C4—7241no—
372C4#1915386111yescharacteristic
373C4#1915386111yescharacteristic
374C2—41no—
375C2—14481no—
376C2—7241no—
377C2—7241no—
378C2#2604183911yescharacteristic
379C2#2604208811yescharacteristic
380C2#2604209211yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#451×C181C2
socleC22×C181C22×D4
prime radical#26041859C2
hypercenter#451D181
hypocenterC181#3201
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #26041853C2semidirect
3. #26041617C2semidirect
4. #26041613C2semidirect
5. #26041608C2semidirect
6. #26041604C2semidirect
7. #26041534C2semidirect
8. #26041528C2semidirect
9. #26041517C2semidirect
10. #26041511C2semidirect
11. #26041440C2semidirect
12. #26041440C2semidirect
13. #26041418C2semidirect
14. #26041244C2semidirect
15. #451×C181C2semidirect
190. C181#3201semidirect
204. #451D181semidirect

Maximal subgroups

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

subgroupindex
#260418592
#260418532
#260416172
#260416132
#260416082
#260416042
#260415342
#260415282
#260415172
#260415112
#260414402
#260414182
#260412442
#451×C1812
#3201181