Finite Group Databasebeta

← #37536879

Subgroups — #37536879

Order 23168.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153788C211yesmaximal, characteristic
2#26041182C211yesmaximal, characteristic, complemented
3#26041179C211yesmaximal, characteristic, complemented
4#26041168C211yesmaximal, characteristic, complemented
5#26041167C211yesmaximal, characteristic, complemented
6#26041166C211yesmaximal, characteristic, complemented
7#26041161C211yesmaximal, characteristic, complemented
8#26041158C211yesmaximal, characteristic, complemented
9#26041155C211yesmaximal, characteristic, complemented
10#26041155C211yesmaximal, characteristic, complemented
11#26041153C211yesmaximal, characteristic, complemented
12#26041152C211yesmaximal, characteristic, complemented
13#26041140C211yesmaximal, characteristic, complemented
14#26041137C211yesmaximal, characteristic, complemented
15#386×C181C211yesmaximal, characteristic, complemented
16C22×C22⋊D181C2211yescharacteristic
17C22×C22⋊D181C2211yescharacteristic
18C23×Dic181C2211yescharacteristic
19C22×C4×D181C2211yescharacteristic
20#19153788C418yescomplemented
21C2×C4⋊Dic181C2211yescharacteristic
22C2×#15668428C2211yescharacteristic
23C2×#15668428C2211yescharacteristic
24C2×#15668428C2211yescharacteristic
25C2×#15668428C2211yescharacteristic
26C2×C22⋊Dic181C2211yescharacteristic
27C2×C22⋊Dic181C2211yescharacteristic
28C2×C22⋊Dic181C2211yescharacteristic
29C2×C22⋊Dic181C2211yescharacteristic
30C2×C22⋊Dic181C2211yescharacteristic
31C2×#15668426C2211yescharacteristic
32C2×#15668426C2211yescharacteristic
33C2×#15668426C2211yescharacteristic
34C2×#15668426C2211yescharacteristic
35C2×C4×Dic181C2211yescharacteristic
36C2×C4×Dic181C2211yescharacteristic
37#19153723C2211yescharacteristic
38#19153723C2211yescharacteristic
39#19153723C2211yescharacteristic
40#19153723C2211yescharacteristic
41#19153723C2211yescharacteristic
42#19153723C2211yescharacteristic
43#19153723C2211yescharacteristic
44#19153723C2211yescharacteristic
45C22×D4×C181C2211yescharacteristic
46C23×C4×C181C2211yescharacteristic
47C2×C22⋊C4×C181C2211yescharacteristic
48C2×C22⋊C4×C181C2211yescharacteristic
49C2×C22⋊C4×C181C2211yescharacteristic
50#95×C181C2211yescharacteristic
51#95×C181C2211yescharacteristic
52C23×D181C2311yescharacteristic
53C2×C22⋊D181—41no—
54C2×C22⋊D181—41no—
55C2×C22⋊D181—41no—
56C2×C22⋊D181—41no—
57C2×C22⋊D181C2×C414yes—
58C2×C22⋊D181C2×C414yescomplemented
59C22×Dic181—41no—
60C22×Dic181—41no—
61C22×Dic181C2×C414yescomplemented
62C22×Dic181C2311yescharacteristic
63C22×Dic181C2311yescharacteristic
64C22×Dic181C2311yescharacteristic
65C22×Dic181C2311yescharacteristic
66C22×Dic181C2311yescharacteristic
67C22×Dic181C2311yescharacteristic
68C22×Dic181C2311yescharacteristic
69C2×C4×D181—41no—
70C2×C4×D181—41no—
71C2×C4×D181—41no—
72C4⋊Dic181—41no—
73#15668428—41no—
74#15668428—41no—
75#15668428—41no—
76#15668428C2×C414yescomplemented
77C22⋊Dic181—41no—
78C22⋊Dic181—41no—
79C22⋊Dic181—41no—
80C22⋊Dic181—41no—
81C22⋊Dic181C2×C414yescomplemented
82#15668426—41no—
83#15668426—41no—
84#15668426—41no—
85#15668426C2×C414yescomplemented
86C4×Dic181—41no—
87C4×Dic181—41no—
88C24×C181C2311yescharacteristic
89C24×C181C2311yescharacteristic
90C2×D4×C181—41no—
91C2×D4×C181—41no—
92C2×D4×C181C2×C414yescomplemented
93C22×C4×C181—41no—
94C22×C4×C181—41no—
95C22×C4×C181—41no—
96C22×C4×C181C2311yescharacteristic
97C22×C4×C181C2311yescharacteristic
98C22×C4×C181C2311yescharacteristic
99C22×C4×C181C2311yescharacteristic
100C22×C4×C181C2311yescharacteristic
101C22⋊C4×C181—41no—
102C22⋊C4×C181—41no—
103C22⋊C4×C181—41no—
104C22×D181—21no—
105C22×D181—21no—
106C22×D181—21no—
107C22×D181—21no—
108C22×D181—21no—
109C22×D181—21no—
110C22×D181C22×C412yes—
111C22⋊D181—44no—
112C22⋊D181—44no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—21no—
130C2×Dic181—21no—
131C2×Dic181—44no—
132C2×Dic181C22×C412yes—
133C2×Dic181C22×C412yes—
134C2×Dic181C22×C412yes—
135C4×D181—44no—
136C23×C181—21no—
137C23×C181—21no—
138C23×C181—21no—
139C23×C181—21no—
140C23×C181—21no—
141C23×C181—21no—
142C23×C181—21no—
143C23×C181—21no—
144C23×C181—21no—
145C23×C181—21no—
146C23×C181—21no—
147C23×C181—21no—
148C23×C181C22×C412yes—
149C23×C181C22×C412yes—
150C23×C181C2411yescharacteristic
151D4×C181—44no—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—21no—
157C2×C4×C181—21no—
158C2×C4×C181—21no—
159C2×C4×C181—21no—
160C2×C4×C181—21no—
161C2×C4×C181—21no—
162C2×C4×C181—21no—
163C2×C4×C181—21no—
164C2×C4×C181—21no—
165C2×C4×C181—21no—
166C2×C4×C181—44no—
167C2×C4×C181C22×C412yes—
168C22×C181—22no—
169C22×C181—22no—
170C22×C181—22no—
171C22×C181—22no—
172C22×C181—22no—
173C22×C181—22no—
174C22×C181—41no—
175C22×C181—41no—
176C22×C181—41no—
177C22×C181—41no—
178C22×C181—41no—
179C22×C181—41no—
180C22×C181—41no—
181C22×C181—41no—
182C22×C181C23×C411yescharacteristic
183C22×C181H(5,𝔽2)11yescharacteristic
184C22×C181H(5,𝔽2)11yescharacteristic
185C22×C181H(5,𝔽2)11yescharacteristic
186C22×C181H(5,𝔽2)11yescharacteristic
187C22×C181H(5,𝔽2)11yescharacteristic
188C22×C1812−1+411yescharacteristic
189C2×D181—22no—
190C2×D181—22no—
191C2×D181—22no—
192C2×D181—41no—
193C2×D181—41no—
194C2×D181—41no—
195C2×D181—41no—
196C4×C181—22no—
197C4×C181—41no—
198C4×C181—41no—
199C4×C181—41no—
200C4×C181—41no—
201Dic181—22no—
202Dic181—22no—
203Dic181—22no—
204Dic181—41no—
205Dic181—41no—
206Dic181—41no—
207Dic181—41no—
208C2×C181—42no—
209C2×C181—42no—
210C2×C181#51811yescharacteristic
211C2×C181#51811yescharacteristic
212C2×C181#52011yescharacteristic
213C2×C181#56011yescharacteristic
214C2×C181#56011yescharacteristic
215C2×C181#56211yescharacteristic
216C2×C181#56211yescharacteristic
217D181—42no—
218C181#237711yescharacteristic, complemented, Sylow
219#2377—1811nomaximal, Sylow
220C2×#121—1811no—
221#390—1811no—
222#390—1811no—
223#388—1811no—
224#388—1811no—
225#387—1811no—
226#387—1811no—
227#386—1811no—
228#386—1811no—
229#386—1811no—
230#386D18111yescharacteristic, complemented
231#385—1811no—
232#385—1811no—
233#381—1811no—
234#380—1811no—
235C22×D4—1811no—
236C22×D4—1811no—
237C22×D4C2×D18111yescharacteristic
238C23×C4—1811no—
239C23×C4—1811no—
240C23×C4C2×D18111yescharacteristic
241#121—1818no—
242C2×C4⋊C4—1811no—
243C2×C4⋊C4—1811no—
244C2×C4⋊C4—1811no—
245C2×C4⋊C4—1811no—
246C2×C4⋊C4—1811no—
247C2×C22⋊C4—1811no—
248C2×C22⋊C4—1811no—
249C2×C22⋊C4—1811no—
250C2×C22⋊C4—1811no—
251C2×C22⋊C4—1811no—
252C2×C22⋊C4—1811no—
253C2×C22⋊C4—1811no—
254C2×C22⋊C4—1811no—
255C2×C22⋊C4—1811no—
256C2×C22⋊C4C2×D18111yescharacteristic
257C2×C22⋊C4C2×D18111yescharacteristic
258C2×C22⋊C4C2×D18111yescharacteristic
259C2×C42—1811no—
260C2×C42—1811no—
261#95—1811no—
262#95—1811no—
263#95—1811no—
264#95—1811no—
265#95—1811no—
266#95—1811no—
267#95—1811no—
268#95—1811no—
269#95C2×D18111yescharacteristic
270#95C2×D18111yescharacteristic
271C24—1811no—
272C24C22×D18111yescharacteristic
273C24C22×D18111yescharacteristic
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—1814no—
277C2×D4—1814no—
278C2×D4—7241no—
279C2×D4—7241no—
280C2×D4—7241no—
281C2×D4—7241no—
282C2×D4C4×D18114yescomplemented
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—1811no—
287C22×C4—1811no—
288C22×C4—1811no—
289C22×C4—1811no—
290C22×C4—1811no—
291C22×C4—1811no—
292C22×C4—1811no—
293C22×C4—1814no—
294C22×C4—7241no—
295C22×C4—7241no—
296C22×C4—7241no—
297C22×C4—7241no—
298C22×C4—7241no—
299C22×C4C22×D18111yescharacteristic
300C22×C4C22×D18111yescharacteristic
301C22×C4C22×D18111yescharacteristic
302C22×C4C22×D18111yescharacteristic
303C22×C4C22×D18111yescharacteristic
304C4⋊C4—1814no—
305C4⋊C4—7241no—
306C4⋊C4—7241no—
307C4⋊C4—7241no—
308C4⋊C4—7241no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—1814no—
313C22⋊C4—1814no—
314C22⋊C4—7241no—
315C22⋊C4—7241no—
316C22⋊C4—7241no—
317C22⋊C4—7241no—
318C22⋊C4—7241no—
319C22⋊C4—7241no—
320C22⋊C4—7241no—
321C42—7241no—
322C42—7241no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—3621no—
336C23—3621no—
337C23—3621no—
338C23—3621no—
339C23—3621no—
340C23—3621no—
341C23—1812no—
342C23C2×C4×D18112yes—
343C23C2×C4×D18112yes—
344C23C23×D18111yescharacteristic
345D4—44no—
346D4—7244no—
347D4—7244no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—44no—
363C2×C4—3621no—
364C2×C4—3621no—
365C2×C4—3621no—
366C2×C4—3621no—
367C2×C4—3621no—
368C2×C4—3621no—
369C2×C4—3621no—
370C2×C4—3621no—
371C2×C4—3621no—
372C2×C4—3621no—
373C2×C4—3621no—
374C2×C4—3621no—
375C2×C4—3621no—
376C2×C4—3621no—
377C2×C4—3621no—
378C2×C4—3621no—
379C2×C4—3621no—
380C2×C4—3621no—
381C2×C4—1812no—
382C2×C4—1812no—
383C2×C4—1812no—
384C2×C4—7244no—
385C2×C4—7244no—
386C2×C4C2×C4×D18112yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—3622no—
402C22—3622no—
403C22—3622no—
404C22—7241no—
405C22—7241no—
406C22—7241no—
407C22—7241no—
408C22C22×C4×D18111yescharacteristic
409C22#1915386111yescharacteristic
410C22#1915386111yescharacteristic
411C22#1915386111yescharacteristic
412C22#1915386111yescharacteristic
413C22#1915386211yescharacteristic
414C22#1915386311yescharacteristic
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—3622no—
421C4—3622no—
422C4—3622no—
423C4—7241no—
424C4—7241no—
425C4—7241no—
426C4—7241no—
427C2—42no—
428C2—42no—
429C2—7242no—
430C2#2604175111yescharacteristic
431C2#2604175211yescharacteristic
432C2#2604175811yescharacteristic
433C2#2604201711yescharacteristic
434C2#2604201811yescharacteristic
435C2#2604202411yescharacteristic
436C2#2604202611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutatorC22×C181C23×C4
Fitting#386×C181C2
socle, cosocleC23×C181C24
prime radicalC2×#19153788C2
hypercenter#386D181
hypocenterC181#2377
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. #26041182C2semidirect
3. #26041179C2semidirect
4. #26041168C2semidirect
5. #26041167C2semidirect
6. #26041166C2semidirect
7. #26041161C2semidirect
8. #26041158C2semidirect
9. #26041155C2semidirect
10. #26041155C2semidirect
11. #26041153C2semidirect
12. #26041152C2semidirect
13. #26041140C2semidirect
14. #26041137C2semidirect
15. #386×C181C2semidirect
20. #19153788C4semidirect
58. C2×C22⋊D181C2×C4semidirect
61. C22×Dic181C2×C4semidirect
76. #15668428C2×C4semidirect
81. C22⋊Dic181C2×C4semidirect
85. #15668426C2×C4semidirect
92. C2×D4×C181C2×C4semidirect
218. C181#2377semidirect
230. #386D181semidirect
282. C2×D4C4×D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191537882
#260411822
#260411792
#260411682
#260411672
#260411662
#260411612
#260411582
#260411552
#260411532
#260411522
#260411402
#260411372
#386×C1812
#2377181