Finite Group Databasebeta

← #49124105

Subgroups — #49124105

Order 36224.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583567C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D283C211yesmaximal, characteristic
3C2×C22⋊C4×D283C211yesmaximal, characteristic
4#31826359C211yesmaximal, characteristic, complemented
5#31826358C211yesmaximal, characteristic, complemented
6#31826353C211yesmaximal, characteristic, complemented
7#31826339C211yesmaximal, characteristic, complemented
8#31826336C211yesmaximal, characteristic, complemented
9#31826327C211yesmaximal, characteristic, complemented
10#31826322C211yesmaximal, characteristic, complemented
11#31826320C211yesmaximal, characteristic
12C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
13#31826312C211yesmaximal, characteristic, complemented
14#31826312C211yesmaximal, characteristic, complemented
15#388×C283C211yesmaximal, characteristic, complemented
16C24×D283C2211yescharacteristic
17C22×C4×D283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19C22×C4×D283C2211yescharacteristic
20C22×C4×D283C2211yescharacteristic
21#22583567—24no—
22C2×C4⋊Dic283C2211yescharacteristic, complemented
23C2×Dic283⋊C4C2211yescharacteristic, complemented
24C2×Dic283⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic283C2211yescharacteristic
26C2×C22⋊Dic283C2211yescharacteristic
27C2×C22⋊Dic283C2211yescharacteristic
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
35C2×(C2×D283)⋊C4C2211yescharacteristic
36C22⋊C4×D283—24no—
37C22⋊C4×D283C418yescomplemented
38C2×C4×Dic283C2211yescharacteristic, complemented
39C2×C4×Dic283C2211yescharacteristic, complemented
40C2×C4×Dic283C2211yescharacteristic, complemented
41C283⋊#95C2211yescharacteristic, complemented
42C283⋊#95C2211yescharacteristic, complemented
43C283⋊#95C2211yescharacteristic, complemented
44C283⋊#95C2211yescharacteristic, complemented
45C283⋊#95C2211yescharacteristic, complemented
46C283⋊#95C2211yescharacteristic, complemented
47C2×C4⋊C4×C283C2211yescharacteristic, complemented
48C2×C22⋊C4×C283C2211yescharacteristic
49C2×C22⋊C4×C283C2211yescharacteristic
50C2×C22⋊C4×C283C2211yescharacteristic
51C2×C42×C283C2211yescharacteristic, complemented
52#95×C283C2211yescharacteristic, complemented
53#95×C283C2211yescharacteristic, complemented
54C23×D283—22no—
55C23×D283—22no—
56C23×D283—22no—
57C23×D283—22no—
58C23×D283—41no—
59C23×D283—41no—
60C23×D283C2×C414yes—
61C23×D283C2311yescharacteristic
62C23×D283C2311yescharacteristic
63C22×Dic283C2311yescharacteristic
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C22×Dic283C2311yescharacteristic
67C22×Dic283C2311yescharacteristic
68C22×Dic283C2311yescharacteristic
69C2×C4×D283—22no—
70C2×C4×D283—22no—
71C2×C4×D283—22no—
72C2×C4×D283—22no—
73C2×C4×D283—22no—
74C2×C4×D283—22no—
75C2×C4×D283—41no—
76C2×C4×D283—41no—
77C2×C4×D283—41no—
78C2×C4×D283—41no—
79C2×C4×D283C2×C414yescomplemented
80C2×C4×D283C2×C414yescomplemented
81C4⋊Dic283—41no—
82Dic283⋊C4—22no—
83Dic283⋊C4—22no—
84C22⋊Dic283—22no—
85C22⋊Dic283—41no—
86C22⋊Dic283C2×C414yescomplemented
87(C2×D283)⋊C4—22no—
88(C2×D283)⋊C4—22no—
89(C2×D283)⋊C4—22no—
90(C2×D283)⋊C4—22no—
91(C2×D283)⋊C4—22no—
92(C2×D283)⋊C4C2×C414yes—
93(C2×D283)⋊C4C2×C414yes—
94(C2×D283)⋊C4D414yes—
95C4×Dic283—22no—
96C4×Dic283—41no—
97C4×Dic283—41no—
98C24×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C22×C4×C283C2311yescharacteristic
101C22×C4×C283C2311yescharacteristic
102C22×C4×C283C2311yescharacteristic
103C22×C4×C283C2311yescharacteristic
104C22×C4×C283C2311yescharacteristic
105C4⋊C4×C283—41no—
106C22⋊C4×C283—22no—
107C22⋊C4×C283—41no—
108C22⋊C4×C283C2×C414yescomplemented
109C42×C283—22no—
110C22×D283—21no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—21no—
116C22×D283—21no—
117C22×D283—21no—
118C22×D283—28no—
119C22×D283—28no—
120C22×D283—44no—
121C22×D283—44no—
122C22×D283—44no—
123C22×D283—44no—
124C22×D283—44no—
125C22×D283C22×C412yes—
126C22×D283C22×C412yes—
127C22×D283C2×D412yes—
128C22×D283#4112yes—
129C22×D283#4112yes—
130C22×D283#4112yes—
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×Dic283—21no—
142C2×Dic283—21no—
143C2×Dic283—21no—
144C2×Dic283—21no—
145C2×Dic283—21no—
146C2×Dic283C22×C412yes—
147C2×Dic283C22×C412yes—
148C2×Dic283C2×D412yes—
149C4×D283—28no—
150C4×D283—44no—
151C4×D283—44no—
152C4×D283—44no—
153C23×C283—21no—
154C23×C283—21no—
155C23×C283—21no—
156C23×C283—21no—
157C23×C283—21no—
158C23×C283—21no—
159C23×C283C22×C412yes—
160C23×C283C2411yescharacteristic
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×C283—21no—
170C2×C4×C283—21no—
171C2×C4×C283—21no—
172C2×C4×C283—21no—
173C2×C4×C283—21no—
174C2×C4×C283—21no—
175C2×C4×C283—21no—
176C2×C4×C283C22×C412yes—
177C2×C4×C283C22×C412yes—
178C2×C4×C283C2×D412yes—
179C22×C283—22no—
180C22×C283—22no—
181C22×C283—22no—
182C22×C283—41no—
183C22×C283—41no—
184C22×C283—41no—
185C22×C283—41no—
186C22×C283C23×C411yescharacteristic
187C22×C283C22×D411yescharacteristic
188C22×C283C2×#4111yescharacteristic
189C22×C283C2×#4111yescharacteristic
190C22×C283C2×#4111yescharacteristic
191C22×C283H(5,𝔽2)11yescharacteristic
192C22×C283H(5,𝔽2)11yescharacteristic
193C2×D283—22no—
194C2×D283—22no—
195C2×D283—22no—
196C2×D283—22no—
197C2×D283—22no—
198C2×D283—22no—
199C2×D283—22no—
200C2×D283—22no—
201C2×D283—22no—
202C2×D283—22no—
203C2×D283—22no—
204C2×D283—22no—
205C2×D283—416no—
206C2×D283#11714yescomplemented
207C2×D283C4×D414yes—
208C4×C283—22no—
209C4×C283—22no—
210C4×C283—22no—
211C4×C283—41no—
212C4×C283—41no—
213C4×C283—41no—
214Dic283—22no—
215Dic283—22no—
216Dic283—22no—
217Dic283—41no—
218Dic283—41no—
219Dic283—41no—
220C2×C283—42no—
221C2×C283C2×#11711yescharacteristic
222C2×C283C2×C4×D411yescharacteristic
223C2×C283#51811yescharacteristic
224C2×C283#54611yescharacteristic
225C2×C283#54611yescharacteristic
226C2×C283#55111yescharacteristic
227C2×C283#55111yescharacteristic
228D283—24no—
229D283—24no—
230C283#234211yescharacteristic, complemented, Sylow
231#2342—2831nomaximal, Sylow
232C2×#117—2831no—
233C22×C22⋊C4—2831no—
234C22×C22⋊C4—2831no—
235#388—2831no—
236#388—2831no—
237#388—2831no—
238#388D28311yescharacteristic, complemented
239#385—2831no—
240#385—2831no—
241#381—2831no—
242#380—2831no—
243#379—2831no—
244C4×C22⋊C4—2831no—
245C4×C22⋊C4—2831no—
246C4×C22⋊C4—2831no—
247C25—2831no—
248C23×C4—2831no—
249C23×C4—2831no—
250C23×C4—2831no—
251C23×C4—2831no—
252#117—5664no—
253C2×C4⋊C4—2831no—
254C2×C4⋊C4—2831no—
255C2×C4⋊C4—2831no—
256C2×C4⋊C4C2×D28311yescharacteristic, complemented
257C2×C22⋊C4—2831no—
258C2×C22⋊C4—2831no—
259C2×C22⋊C4—2831no—
260C2×C22⋊C4—2831no—
261C2×C22⋊C4—2838no—
262C2×C22⋊C4—2831no—
263C2×C22⋊C4—2831no—
264C2×C22⋊C4—2831no—
265C2×C22⋊C4—2831no—
266C2×C22⋊C4—2831no—
267C2×C22⋊C4—2831no—
268C2×C22⋊C4—2831no—
269C2×C22⋊C4—5664no—
270C2×C22⋊C4C2×D28311yescharacteristic
271C2×C22⋊C4C2×D28311yescharacteristic
272C2×C22⋊C4C2×D28311yescharacteristic
273C2×C42—2831no—
274C2×C42—2831no—
275C2×C42—2831no—
276C2×C42C2×D28311yescharacteristic, complemented
277#95—2831no—
278#95—2831no—
279#95—2831no—
280#95—2831no—
281#95—2831no—
282#95—2831no—
283#95C2×D28311yescharacteristic, complemented
284#95C2×D28311yescharacteristic, complemented
285C24—2831no—
286C24—2831no—
287C24—2834no—
288C24—5662no—
289C24—5662no—
290C24—5662no—
291C24—5662no—
292C24—11321no—
293C24—11321no—
294C24C22×D28311yescharacteristic
295C22×C4—2831no—
296C22×C4—2831no—
297C22×C4—2831no—
298C22×C4—2834no—
299C22×C4—2834no—
300C22×C4—2831no—
301C22×C4—2831no—
302C22×C4—2831no—
303C22×C4—5662no—
304C22×C4—5662no—
305C22×C4—5662no—
306C22×C4—5662no—
307C22×C4—5662no—
308C22×C4—5662no—
309C22×C4—11321no—
310C22×C4—11321no—
311C22×C4—11321no—
312C22×C4—11321no—
313C22×C4C22×D28311yescharacteristic
314C22×C4C22×D28311yescharacteristic
315C22×C4C22×D28311yescharacteristic
316C22×C4C22×D28311yescharacteristic
317C22×C4C22×D28311yescharacteristic
318C22×C4C22×D28311yescharacteristic
319C4⋊C4—41no—
320C4⋊C4—5662no—
321C4⋊C4—5662no—
322C4⋊C4—11321no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—2834no—
326C22⋊C4—2834no—
327C22⋊C4—2834no—
328C22⋊C4—2834no—
329C22⋊C4—5662no—
330C22⋊C4—5662no—
331C22⋊C4—5662no—
332C22⋊C4—5662no—
333C22⋊C4—5662no—
334C22⋊C4—5662no—
335C22⋊C4—11321no—
336C22⋊C4C4×D28314yescomplemented
337C42—22no—
338C42—5662no—
339C42—11321no—
340C42—11321no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—2832no—
348C23—2832no—
349C23—2832no—
350C23—2832no—
351C23—2832no—
352C23—2832no—
353C23—5668no—
354C23—5668no—
355C23—5661no—
356C23—5661no—
357C23—5661no—
358C23—5661no—
359C23—5661no—
360C23—5661no—
361C23—5661no—
362C23—5661no—
363C23—11324no—
364C23—11324no—
365C23—11324no—
366C23—11324no—
367C23—11324no—
368C23C2×C4×D28312yes—
369C23C23×D28311yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—2832no—
386C2×C4—2832no—
387C2×C4—2832no—
388C2×C4—5668no—
389C2×C4—5661no—
390C2×C4—5661no—
391C2×C4—5661no—
392C2×C4—5661no—
393C2×C4—5661no—
394C2×C4—5661no—
395C2×C4—5661no—
396C2×C4—5661no—
397C2×C4—5661no—
398C2×C4—5661no—
399C2×C4—5661no—
400C2×C4—5661no—
401C2×C4—5661no—
402C2×C4—5661no—
403C2×C4—5661no—
404C2×C4—11324no—
405C2×C4—11324no—
406C2×C4—11324no—
407C2×C4C2×C4×D28312yes—
408C2×C4C2×C4×D28312yes—
409C2×C4D4×D28312yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—2834no—
418C22—2834no—
419C22—5662no—
420C22—5662no—
421C22—5662no—
422C22—5662no—
423C22—5662no—
424C22—5662no—
425C22—5662no—
426C22—5662no—
427C22—5662no—
428C22—5662no—
429C22—5662no—
430C22—5662no—
431C22—113216no—
432C22C22×C4×D28311yescharacteristic
433C22C2×D4×D28311yescharacteristic
434C22#41×D28311yescharacteristic
435C22#41×D28311yescharacteristic
436C22#41×D28311yescharacteristic
437C22#2258365511yescharacteristic
438C22#2258365611yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—5662no—
446C4—5662no—
447C4—5662no—
448C4—11321no—
449C4—11321no—
450C4—11321no—
451C2—42no—
452C2—5664no—
453C2—5664no—
454C2#117×D28311yescharacteristic
455C2C4×D4×D28311yescharacteristic
456C2#3182693711yescharacteristic
457C2#3182710711yescharacteristic
458C2#3182711211yescharacteristic
459C2#3182714011yescharacteristic
460C2#3182714511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#388×C283C2
socle, cosocleC23×C283C24
prime radicalC24×D283C22
hypercenter#388D283
hypocenterC283#2342
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#22583567C2semidirect
4. #31826359C2semidirect
5. #31826358C2semidirect
6. #31826353C2semidirect
7. #31826339C2semidirect
8. #31826336C2semidirect
9. #31826327C2semidirect
10. #31826322C2semidirect
12. C4×(C2×D283)⋊C4C2semidirect
13. #31826312C2semidirect
14. #31826312C2semidirect
15. #388×C283C2semidirect
22. C2×C4⋊Dic283C22semidirect
23. C2×Dic283⋊C4C22semidirect
24. C2×Dic283⋊C4C22semidirect
37. C22⋊C4×D283C4semidirect
38. C2×C4×Dic283C22semidirect
39. C2×C4×Dic283C22semidirect
40. C2×C4×Dic283C22semidirect
41. C283⋊#95C22semidirect
42. C283⋊#95C22semidirect
43. C283⋊#95C22semidirect
44. C283⋊#95C22semidirect
45. C283⋊#95C22semidirect
46. C283⋊#95C22semidirect
47. C2×C4⋊C4×C283C22semidirect
51. C2×C42×C283C22semidirect
52. #95×C283C22semidirect
53. #95×C283C22semidirect
79. C2×C4×D283C2×C4semidirect
80. C2×C4×D283C2×C4semidirect
86. C22⋊Dic283C2×C4semidirect
108. C22⋊C4×C283C2×C4semidirect
206. C2×D283#117semidirect
230. C283#2342semidirect
238. #388D283semidirect
256. C2×C4⋊C4C2×D283semidirect
276. C2×C42C2×D283semidirect
283. #95C2×D283semidirect
284. #95C2×D283semidirect
336. C22⋊C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835672
C2×C22⋊C4×D2832
#318263592
#318263582
#318263532
#318263392
#318263362
#318263272
#318263222
#318263202
C4×(C2×D283)⋊C42
#318263122
#388×C2832
#2342283