Finite Group Databasebeta

← #49123855

Subgroups — #49123855

Order 36224.

672 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D283C211yesmaximal, characteristic
2#31826359C211yesmaximal, characteristic, complemented
3#31826358C211yesmaximal, characteristic, complemented
4#31826357C211yesmaximal, characteristic, complemented
5#31826356C211yesmaximal, characteristic, complemented
6#31826355C211yesmaximal, characteristic, complemented
7#31826354C211yesmaximal, characteristic, complemented
8#31826353C211yesmaximal, characteristic, complemented
9#31826324C211yesmaximal, characteristic, complemented
10#31826322C211yesmaximal, characteristic, complemented
11#31826320C211yesmaximal, characteristic
12#31826320C211yesmaximal, characteristic
13C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
14#31826312C211yesmaximal, characteristic, complemented
15#388×C283C211yesmaximal, characteristic, complemented
16C24×D283C2211yescharacteristic
17C22×C4×D283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19C2×C4⋊Dic283C2211yescharacteristic, complemented
20C2×Dic283⋊C4C2211yescharacteristic, complemented
21C2×Dic283⋊C4C2211yescharacteristic, complemented
22C2×C22⋊Dic283C2211yescharacteristic
23C2×C22⋊Dic283C2211yescharacteristic
24C2×C22⋊Dic283C2211yescharacteristic
25C2×(C2×D283)⋊C4C2211yescharacteristic
26C2×(C2×D283)⋊C4C2211yescharacteristic
27C2×(C2×D283)⋊C4C2211yescharacteristic
28C2×(C2×D283)⋊C4C2211yescharacteristic
29C2×(C2×D283)⋊C4C2211yescharacteristic
30C2×(C2×D283)⋊C4C2211yescharacteristic
31C2×(C2×D283)⋊C4C2211yescharacteristic
32C2×(C2×D283)⋊C4C2211yescharacteristic
33C2×(C2×D283)⋊C4C2211yescharacteristic
34C2×(C2×D283)⋊C4C2211yescharacteristic
35C22⋊C4×D283C418yescomplemented
36C2×C4×Dic283C2211yescharacteristic, complemented
37C2×C4×Dic283C2211yescharacteristic, complemented
38C2×C4×Dic283C2211yescharacteristic, complemented
39C283⋊#95C2211yescharacteristic, complemented
40C283⋊#95C2211yescharacteristic, complemented
41C283⋊#95C2211yescharacteristic, complemented
42C283⋊#95C2211yescharacteristic, complemented
43C283⋊#95C2211yescharacteristic, complemented
44C283⋊#95C2211yescharacteristic, complemented
45C2×C4⋊C4×C283C2211yescharacteristic, complemented
46C2×C22⋊C4×C283C2211yescharacteristic
47C2×C22⋊C4×C283C2211yescharacteristic
48C2×C22⋊C4×C283C2211yescharacteristic
49C2×C42×C283C2211yescharacteristic, complemented
50#95×C283C2211yescharacteristic, complemented
51#95×C283C2211yescharacteristic, complemented
52C23×D283—22no—
53C23×D283—22no—
54C23×D283—41no—
55C23×D283—41no—
56C23×D283—41no—
57C23×D283—41no—
58C23×D283C2×C414yes—
59C23×D283C2311yescharacteristic
60C23×D283C2311yescharacteristic
61C22×Dic283C2311yescharacteristic
62C22×Dic283C2311yescharacteristic
63C22×Dic283C2311yescharacteristic
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C22×Dic283C2311yescharacteristic
67C2×C4×D283—41no—
68C2×C4×D283—41no—
69C2×C4×D283—41no—
70C2×C4×D283—41no—
71C2×C4×D283C2×C414yes—
72C2×C4×D283C2×C414yes—
73C4⋊Dic283—41no—
74Dic283⋊C4—41no—
75Dic283⋊C4—41no—
76C22⋊Dic283—41no—
77C22⋊Dic283—41no—
78C22⋊Dic283C2×C414yes—
79(C2×D283)⋊C4—22no—
80(C2×D283)⋊C4—22no—
81(C2×D283)⋊C4—22no—
82(C2×D283)⋊C4—22no—
83(C2×D283)⋊C4—41no—
84(C2×D283)⋊C4—41no—
85(C2×D283)⋊C4—41no—
86(C2×D283)⋊C4—41no—
87(C2×D283)⋊C4C2×C414yes—
88(C2×D283)⋊C4C2×C414yes—
89C4×Dic283—41no—
90C4×Dic283—41no—
91C4×Dic283—41no—
92C24×C283C2311yescharacteristic
93C22×C4×C283C2311yescharacteristic
94C22×C4×C283C2311yescharacteristic
95C22×C4×C283C2311yescharacteristic
96C22×C4×C283C2311yescharacteristic
97C22×C4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C4⋊C4×C283—41no—
100C22⋊C4×C283—41no—
101C22⋊C4×C283—41no—
102C22⋊C4×C283C2×C414yes—
103C42×C283—41no—
104C22×D283—21no—
105C22×D283—21no—
106C22×D283—21no—
107C22×D283—21no—
108C22×D283—21no—
109C22×D283—21no—
110C22×D283—21no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—28no—
115C22×D283—44no—
116C22×D283—44no—
117C22×D283—44no—
118C22×D283—44no—
119C22×D283—44no—
120C22×D283—44no—
121C22×D283C22×C412yes—
122C22×D283C22×C412yes—
123C22×D283#4112yes—
124C22×D283#4112yes—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—21no—
131C2×Dic283—21no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283—21no—
137C2×Dic283—21no—
138C2×Dic283—21no—
139C2×Dic283—21no—
140C2×Dic283—21no—
141C2×Dic283C22×C412yes—
142C2×Dic283C22×C412yes—
143C4×D283—44no—
144C4×D283—44no—
145C23×C283—21no—
146C23×C283—21no—
147C23×C283—21no—
148C23×C283—21no—
149C23×C283—21no—
150C23×C283—21no—
151C23×C283C22×C412yes—
152C23×C283C2411yescharacteristic
153C2×C4×C283—21no—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283—21no—
164C2×C4×C283—21no—
165C2×C4×C283—21no—
166C2×C4×C283—21no—
167C2×C4×C283—21no—
168C2×C4×C283—21no—
169C2×C4×C283C22×C412yes—
170C2×C4×C283C22×C412yes—
171C22×C283—22no—
172C22×C283—22no—
173C22×C283—22no—
174C22×C283—41no—
175C22×C283—41no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283C23×C411yescharacteristic
179C22×C283C2×#4111yescharacteristic
180C22×C283C2×#4111yescharacteristic
181C22×C283H(5,𝔽2)11yescharacteristic
182C22×C283H(5,𝔽2)11yescharacteristic
183C22×C283H(5,𝔽2)11yescharacteristic
184C22×C283H(5,𝔽2)11yescharacteristic
185C2×D283—22no—
186C2×D283—22no—
187C2×D283—22no—
188C2×D283—22no—
189C2×D283—22no—
190C2×D283—22no—
191C2×D283—22no—
192C2×D283—22no—
193C2×D283—22no—
194C2×D283—416no—
195C2×D283—41no—
196C2×D283—41no—
197C2×D283—41no—
198C2×D283—41no—
199C2×D283#11714yes—
200C4×C283—22no—
201C4×C283—22no—
202C4×C283—41no—
203C4×C283—41no—
204C4×C283—41no—
205C4×C283—41no—
206Dic283—22no—
207Dic283—22no—
208Dic283—41no—
209Dic283—41no—
210Dic283—41no—
211Dic283—41no—
212C2×C283—42no—
213C2×C283C2×#11711yescharacteristic
214C2×C283#51811yescharacteristic
215C2×C283#51811yescharacteristic
216C2×C283#53811yescharacteristic
217C2×C283#53811yescharacteristic
218C2×C283#53811yescharacteristic
219C2×C283#53811yescharacteristic
220D283—24no—
221D283—42no—
222C283#231211yescharacteristic, complemented, Sylow
223#2312—2831nomaximal, Sylow
224C22×C22⋊C4—2831no—
225#388—2831no—
226#388—2831no—
227#388—2831no—
228#388—2831no—
229#388—2831no—
230#388—2831no—
231#388—2831no—
232#388D28311yescharacteristic, complemented
233#380—2831no—
234#380—2831no—
235#379—2831no—
236#379—2831no—
237C4×C22⋊C4—2831no—
238C4×C22⋊C4—2831no—
239C25—2831no—
240C23×C4—2831no—
241C23×C4—2831no—
242C2×C4⋊C4—2831no—
243C2×C4⋊C4—2831no—
244C2×C4⋊C4—2831no—
245C2×C4⋊C4C2×D28311yescharacteristic, complemented
246C2×C22⋊C4—2831no—
247C2×C22⋊C4—2831no—
248C2×C22⋊C4—2831no—
249C2×C22⋊C4—2838no—
250C2×C22⋊C4—2831no—
251C2×C22⋊C4—2831no—
252C2×C22⋊C4—2831no—
253C2×C22⋊C4—2831no—
254C2×C22⋊C4—2831no—
255C2×C22⋊C4—2831no—
256C2×C22⋊C4—2831no—
257C2×C22⋊C4—2831no—
258C2×C22⋊C4—2831no—
259C2×C22⋊C4—2831no—
260C2×C22⋊C4C2×D28311yescharacteristic
261C2×C22⋊C4C2×D28311yescharacteristic
262C2×C22⋊C4C2×D28311yescharacteristic
263C2×C42—2831no—
264C2×C42—2831no—
265C2×C42—2831no—
266C2×C42C2×D28311yescharacteristic, complemented
267#95—2831no—
268#95—2831no—
269#95—2831no—
270#95—2831no—
271#95—2831no—
272#95—2831no—
273#95C2×D28311yescharacteristic, complemented
274#95C2×D28311yescharacteristic, complemented
275C24—2831no—
276C24—2831no—
277C24—2834no—
278C24—5662no—
279C24—5662no—
280C24—11321no—
281C24—11321no—
282C24—11321no—
283C24—11321no—
284C24C22×D28311yescharacteristic
285C22×C4—2831no—
286C22×C4—2831no—
287C22×C4—2834no—
288C22×C4—2834no—
289C22×C4—2831no—
290C22×C4—2831no—
291C22×C4—2831no—
292C22×C4—2831no—
293C22×C4—11321no—
294C22×C4—11321no—
295C22×C4—11321no—
296C22×C4—11321no—
297C22×C4C22×D28311yescharacteristic
298C22×C4C22×D28311yescharacteristic
299C22×C4C22×D28311yescharacteristic
300C22×C4C22×D28311yescharacteristic
301C22×C4C22×D28311yescharacteristic
302C22×C4C22×D28311yescharacteristic
303C4⋊C4—41no—
304C4⋊C4—11321no—
305C4⋊C4—11321no—
306C4⋊C4—11321no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—2834no—
310C22⋊C4—2834no—
311C22⋊C4—2834no—
312C22⋊C4—5662no—
313C22⋊C4—5662no—
314C22⋊C4—5662no—
315C22⋊C4—5662no—
316C22⋊C4—11321no—
317C22⋊C4—11321no—
318C22⋊C4—11321no—
319C22⋊C4—11321no—
320C22⋊C4—11321no—
321C22⋊C4—11321no—
322C22⋊C4C4×D28314yes—
323C42—41no—
324C42—11321no—
325C42—11321no—
326C42—11321no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—2832no—
334C23—2832no—
335C23—2832no—
336C23—2832no—
337C23—5668no—
338C23—5661no—
339C23—5661no—
340C23—5661no—
341C23—5661no—
342C23—5661no—
343C23—5661no—
344C23—5661no—
345C23—5661no—
346C23—5661no—
347C23—5661no—
348C23—11324no—
349C23—11324no—
350C23—11324no—
351C23—11324no—
352C23—11324no—
353C23—11324no—
354C23C2×C4×D28312yes—
355C23C23×D28311yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—2832no—
373C2×C4—2832no—
374C2×C4—5661no—
375C2×C4—5661no—
376C2×C4—5661no—
377C2×C4—5661no—
378C2×C4—5661no—
379C2×C4—5661no—
380C2×C4—5661no—
381C2×C4—5661no—
382C2×C4—5661no—
383C2×C4—5661no—
384C2×C4—5661no—
385C2×C4—5661no—
386C2×C4—5661no—
387C2×C4—5661no—
388C2×C4—5661no—
389C2×C4—5661no—
390C2×C4—11324no—
391C2×C4—11324no—
392C2×C4C2×C4×D28312yes—
393C2×C4C2×C4×D28312yes—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—2834no—
402C22—5662no—
403C22—5662no—
404C22—5662no—
405C22—5662no—
406C22—5662no—
407C22—5662no—
408C22—5662no—
409C22—5662no—
410C22—5662no—
411C22—113216no—
412C22—11321no—
413C22—11321no—
414C22—11321no—
415C22—11321no—
416C22C22×C4×D28311yescharacteristic
417C22#41×D28311yescharacteristic
418C22#41×D28311yescharacteristic
419C22#2258365511yescharacteristic
420C22#2258365511yescharacteristic
421C22#2258365611yescharacteristic
422C22#2258365611yescharacteristic
423C4—22no—
424C4—22no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—5662no—
430C4—5662no—
431C4—11321no—
432C4—11321no—
433C4—11321no—
434C4—11321no—
435C2—42no—
436C2—5664no—
437C2—11322no—
438C2#117×D28311yescharacteristic
439C2#3182693711yescharacteristic
440C2#3182693711yescharacteristic
441C2#3182704711yescharacteristic
442C2#3182704911yescharacteristic
443C2#3182705111yescharacteristic
444C2#3182705411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#388×C283C2
socle, cosocleC23×C283C24
prime radicalC24×D283C22
hypercenter#388D283
hypocenterC283#2312
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #31826359C2semidirect
3. #31826358C2semidirect
4. #31826357C2semidirect
5. #31826356C2semidirect
6. #31826355C2semidirect
7. #31826354C2semidirect
8. #31826353C2semidirect
9. #31826324C2semidirect
10. #31826322C2semidirect
13. C4×(C2×D283)⋊C4C2semidirect
14. #31826312C2semidirect
15. #388×C283C2semidirect
19. C2×C4⋊Dic283C22semidirect
20. C2×Dic283⋊C4C22semidirect
21. C2×Dic283⋊C4C22semidirect
35. C22⋊C4×D283C4semidirect
36. C2×C4×Dic283C22semidirect
37. C2×C4×Dic283C22semidirect
38. C2×C4×Dic283C22semidirect
39. C283⋊#95C22semidirect
40. C283⋊#95C22semidirect
41. C283⋊#95C22semidirect
42. C283⋊#95C22semidirect
43. C283⋊#95C22semidirect
44. C283⋊#95C22semidirect
45. C2×C4⋊C4×C283C22semidirect
49. C2×C42×C283C22semidirect
50. #95×C283C22semidirect
51. #95×C283C22semidirect
222. C283#2312semidirect
232. #388D283semidirect
245. C2×C4⋊C4C2×D283semidirect
266. C2×C42C2×D283semidirect
273. #95C2×D283semidirect
274. #95C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D2832
#318263592
#318263582
#318263572
#318263562
#318263552
#318263542
#318263532
#318263242
#318263222
#318263202
C4×(C2×D283)⋊C42
#318263122
#388×C2832
#2312283