Finite Group Databasebeta

← #49124104

Subgroups — #49124104

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
2C22×(C2×D283)⋊C4C211yesmaximal, characteristic
3C2×C22⋊C4×D283C211yesmaximal, characteristic
4#31826356C211yesmaximal, characteristic, complemented
5#31826356C211yesmaximal, characteristic, complemented
6#31826354C211yesmaximal, characteristic, complemented
7#31826354C211yesmaximal, characteristic, complemented
8#31826338C211yesmaximal, characteristic, complemented
9#31826337C211yesmaximal, characteristic, complemented
10#31826327C211yesmaximal, characteristic, complemented
11#31826324C211yesmaximal, characteristic, complemented
12#31826320C211yesmaximal, characteristic
13C22⋊C4×Dic283C211yesmaximal, characteristic, complemented
14C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C283C211yesmaximal, characteristic, complemented
16C24×D283C2211yescharacteristic
17C23×Dic283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19C22×C4×D283C2211yescharacteristic
20#22583567—24no—
21C2×Dic283⋊C4C2211yescharacteristic, complemented
22C2×Dic283⋊C4C2211yescharacteristic, complemented
23C2×Dic283⋊C4C2211yescharacteristic, complemented
24C2×Dic283⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic283C2211yescharacteristic
26C2×C22⋊Dic283C2211yescharacteristic
27C2×(C2×D283)⋊C4—24no—
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
36C2×(C2×D283)⋊C4C2211yescharacteristic
37C2×(C2×D283)⋊C4C2211yescharacteristic
38C22⋊C4×D283C418yescomplemented
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
47C23×C4×C283C2211yescharacteristic
48C2×C22⋊C4×C283C2211yescharacteristic
49C2×C22⋊C4×C283C2211yescharacteristic
50C2×C42×C283C2211yescharacteristic, complemented
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×Dic283—22no—
64C22×Dic283—22no—
65C22×Dic283—41no—
66C22×Dic283C2311yescharacteristic
67C22×Dic283C2311yescharacteristic
68C22×Dic283C2311yescharacteristic
69C22×Dic283C2311yescharacteristic
70C22×Dic283C2311yescharacteristic
71C22×Dic283C2311yescharacteristic
72C2×C4×D283—22no—
73C2×C4×D283—22no—
74C2×C4×D283—41no—
75C2×C4×D283—41no—
76C2×C4×D283C2×C414yescomplemented
77C2×C4×D283C2×C414yescomplemented
78Dic283⋊C4—22no—
79Dic283⋊C4—22no—
80Dic283⋊C4—41no—
81Dic283⋊C4—41no—
82C22⋊Dic283—22no—
83C22⋊Dic283C2×C414yes—
84(C2×D283)⋊C4—22no—
85(C2×D283)⋊C4—22no—
86(C2×D283)⋊C4—22no—
87(C2×D283)⋊C4—22no—
88(C2×D283)⋊C4—22no—
89(C2×D283)⋊C4—41no—
90(C2×D283)⋊C4—41no—
91(C2×D283)⋊C4C2×C414yescomplemented
92(C2×D283)⋊C4C2×C414yescomplemented
93(C2×D283)⋊C4D414yes—
94C4×Dic283—22no—
95C4×Dic283—41no—
96C24×C283C2311yescharacteristic
97C22×C4×C283—22no—
98C22×C4×C283—22no—
99C22×C4×C283—41no—
100C22×C4×C283C2311yescharacteristic
101C22×C4×C283C2311yescharacteristic
102C22×C4×C283C2311yescharacteristic
103C22×C4×C283C2311yescharacteristic
104C22×C4×C283C2311yescharacteristic
105C22×C4×C283C2311yescharacteristic
106C22⋊C4×C283—22no—
107C22⋊C4×C283C2×C414yes—
108C42×C283—22no—
109C42×C283—41no—
110C22×D283—21no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—28no—
115C22×D283—21no—
116C22×D283—21no—
117C22×D283—21no—
118C22×D283—21no—
119C22×D283—21no—
120C22×D283—21no—
121C22×D283—28no—
122C22×D283—44no—
123C22×D283—44no—
124C22×D283—44no—
125C22×D283—44no—
126C22×D283—44no—
127C22×D283C22×C412yes—
128C22×D283C22×C412yes—
129C22×D283C2×D412yes—
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×Dic283—44no—
147C2×Dic283C22×C412yes—
148C2×Dic283C22×C412yes—
149C2×Dic283C2×D412yes—
150C4×D283—28no—
151C4×D283—44no—
152C23×C283—21no—
153C23×C283—21no—
154C23×C283—21no—
155C23×C283—21no—
156C23×C283C22×C412yes—
157C23×C283#4112yes—
158C23×C283#4112yes—
159C23×C283C2411yescharacteristic
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×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—44no—
176C2×C4×C283C22×C412yes—
177C2×C4×C283C22×C412yes—
178C2×C4×C283C2×D412yes—
179C22×C283—22no—
180C22×C283—22no—
181C22×C283—22no—
182C22×C283—22no—
183C22×C283—22no—
184C22×C283—22no—
185C22×C283#11714yescomplemented
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—416no—
203C2×D283—41no—
204C2×D283—41no—
205C2×D283—41no—
206C2×D283—41no—
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—24no—
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—42no—
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#388—2831no—
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⋊C4D28311yescharacteristic, complemented
247C25—2831no—
248C23×C4—2831no—
249C23×C4—2831no—
250C23×C4—2831no—
251C23×C4C2×D28311yescharacteristic
252#117—5664no—
253C2×C4⋊C4—2831no—
254C2×C4⋊C4—2831no—
255C2×C4⋊C4—2831no—
256C2×C4⋊C4—2831no—
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—2831no—
270C2×C22⋊C4—5664no—
271C2×C22⋊C4C2×D28311yescharacteristic
272C2×C22⋊C4C2×D28311yescharacteristic
273C2×C42—2831no—
274C2×C42—2831no—
275C2×C42C2×D28311yescharacteristic, complemented
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—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—2831no—
299C22×C4—2831no—
300C22×C4—2831no—
301C22×C4—2834no—
302C22×C4—2834no—
303C22×C4—2831no—
304C22×C4—2831no—
305C22×C4—2831no—
306C22×C4—5662no—
307C22×C4—5662no—
308C22×C4—5662no—
309C22×C4—5662no—
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—5662no—
320C4⋊C4—5662no—
321C4⋊C4—11321no—
322C4⋊C4—11321no—
323C22⋊C4—22no—
324C22⋊C4—2834no—
325C22⋊C4—2834no—
326C22⋊C4—2834no—
327C22⋊C4—2834no—
328C22⋊C4—5662no—
329C22⋊C4—5662no—
330C22⋊C4—5662no—
331C22⋊C4—5662no—
332C22⋊C4—5662no—
333C22⋊C4—5662no—
334C22⋊C4—11321no—
335C22⋊C4—11321no—
336C22⋊C4C4×D28314yes—
337C42—22no—
338C42—41no—
339C42—5662no—
340C42—11321no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—2832no—
346C23—2832no—
347C23—2832no—
348C23—2832no—
349C23—5668no—
350C23—5661no—
351C23—5661no—
352C23—5661no—
353C23—5661no—
354C23—5668no—
355C23—5661no—
356C23—5661no—
357C23—5661no—
358C23—5661no—
359C23—5661no—
360C23—5661no—
361C23—11324no—
362C23—11324no—
363C23—11324no—
364C23—11324no—
365C23—11324no—
366C23C2×C4×D28312yes—
367C23#1798539212yes—
368C23#1798539212yes—
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—44no—
386C2×C4—2832no—
387C2×C4—2832no—
388C2×C4—2832no—
389C2×C4—5668no—
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—5661no—
405C2×C4—11324no—
406C2×C4—11324no—
407C2×C4C2×C4×D28312yes—
408C2×C4C2×C4×D28312yes—
409C2×C4D4×D28312yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—2834no—
417C22—5662no—
418C22—5662no—
419C22—5662no—
420C22—5662no—
421C22—5662no—
422C22—5662no—
423C22—5662no—
424C22—5662no—
425C22—5662no—
426C22—113216no—
427C22—11321no—
428C22—11321no—
429C22—11321no—
430C22—11321no—
431C22#2258356714yescomplemented
432C22C22×C4×D28311yescharacteristic
433C22C2×D4×D28311yescharacteristic
434C22#41×D28311yescharacteristic
435C22C2×#1798539211yescharacteristic
436C22C2×#1798539211yescharacteristic
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—24no—
452C2—5664no—
453C2—11322no—
454C2C2×#2258356711yescharacteristic
455C2C4×D4×D28311yescharacteristic
456C2#3182693711yescharacteristic
457C2#3182710511yescharacteristic
458C2#3182711111yescharacteristic
459C2#3182713911yescharacteristic
460C2#3182714411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC4×C22⋊C4×C283C2
socle, cosocleC23×C283C24
prime radicalC24×D283C22
hypercenterC4×C22⋊C4D283
hypocenterC283#2342
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#22583567C2semidirect
4. #31826356C2semidirect
5. #31826356C2semidirect
6. #31826354C2semidirect
7. #31826354C2semidirect
8. #31826338C2semidirect
9. #31826337C2semidirect
10. #31826327C2semidirect
11. #31826324C2semidirect
13. C22⋊C4×Dic283C2semidirect
14. C4×(C2×D283)⋊C4C2semidirect
15. C4×C22⋊C4×C283C2semidirect
21. C2×Dic283⋊C4C22semidirect
22. C2×Dic283⋊C4C22semidirect
23. C2×Dic283⋊C4C22semidirect
24. C2×Dic283⋊C4C22semidirect
38. C22⋊C4×D283C4semidirect
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
50. C2×C42×C283C22semidirect
51. C2×C42×C283C22semidirect
52. #95×C283C22semidirect
53. #95×C283C22semidirect
76. C2×C4×D283C2×C4semidirect
77. C2×C4×D283C2×C4semidirect
91. (C2×D283)⋊C4C2×C4semidirect
92. (C2×D283)⋊C4C2×C4semidirect
185. C22×C283#117semidirect
230. C283#2342semidirect
246. C4×C22⋊C4D283semidirect
275. C2×C42C2×D283semidirect
276. C2×C42C2×D283semidirect
283. #95C2×D283semidirect
284. #95C2×D283semidirect
431. C22#22583567semidirect

Maximal subgroups

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

subgroupindex
C2×#225835672
C22×(C2×D283)⋊C42
C2×C22⋊C4×D2832
#318263562
#318263542
#318263382
#318263372
#318263272
#318263242
#318263202
C22⋊C4×Dic2832
C4×(C2×D283)⋊C42
C4×C22⋊C4×C2832
#2342283