Finite Group Databasebeta

← #49123949

Subgroups — #49123949

Order 36224.

668 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583583C211yesmaximal, characteristic
2C2×(C22⋊D283)⋊C4C211yesmaximal, characteristic, complemented
3C2×#22583568C211yesmaximal, characteristic, complemented
4#31826367C211yesmaximal, characteristic, complemented
5#31826365C211yesmaximal, characteristic, complemented
6#31826365C211yesmaximal, characteristic, complemented
7#31826362C211yesmaximal, characteristic, complemented
8#31826355C211yesmaximal, characteristic, complemented
9#31826343C211yesmaximal, characteristic, complemented
10#31826342C211yesmaximal, characteristic, complemented
11#31826340C211yesmaximal, characteristic, complemented
12#31826339C211yesmaximal, characteristic, complemented
13#31826324C211yesmaximal, characteristic, complemented
14C4×Dic283⋊C4C211yesmaximal, characteristic, complemented
15#388×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C22×C22⋊D283C2211yescharacteristic
18C22×C22⋊D283C2211yescharacteristic
19C23×Dic283C2211yescharacteristic
20C22×C4×D283C2211yescharacteristic
21C22×C4×D283C2211yescharacteristic
22#22583583C418yescomplemented
23(C22⋊D283)⋊C4—24no—
24#22583568—24no—
25C2×C4⋊Dic283C2211yescharacteristic
26C2×C4⋊Dic283C2211yescharacteristic
27C2×Dic283⋊C4C2211yescharacteristic
28C2×Dic283⋊C4C2211yescharacteristic
29C2×Dic283⋊C4C2211yescharacteristic
30C2×Dic283⋊C4C2211yescharacteristic
31C2×C22⋊Dic283C2211yescharacteristic
32C2×(C2×D283)⋊C4C2211yescharacteristic
33C2×(C2×D283)⋊C4C2211yescharacteristic
34C2×(C2×D283)⋊C4C2211yescharacteristic
35C2×(C2×D283)⋊C4C2211yescharacteristic
36C2×(C2×D283)⋊C4C2211yescharacteristic
37C2×(C2×D283)⋊C4C2211yescharacteristic
38C2×(C2×D283)⋊C4C2211yescharacteristic
39C2×(C2×D283)⋊C4C2211yescharacteristic
40C2×C4×Dic283C2211yescharacteristic
41C2×C4×Dic283C2211yescharacteristic
42C2×C4×Dic283C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C283⋊#95C2211yescharacteristic
46C283⋊#95C2211yescharacteristic
47C2×C4⋊C4×C283C2211yescharacteristic
48C2×C22⋊C4×C283C2211yescharacteristic
49C2×C22⋊C4×C283C2211yescharacteristic
50C2×C22⋊C4×C283C2211yescharacteristic
51C2×C42×C283C2211yescharacteristic
52#95×C283C2211yescharacteristic
53#95×C283C2211yescharacteristic
54C23×D283C2311yescharacteristic
55C23×D283C2311yescharacteristic
56C2×D1132—41no—
57C2×D1132—41no—
58C2×D1132C2×C414yescomplemented
59C2×C22⋊D283—22no—
60C2×C22⋊D283—22no—
61C2×C22⋊D283—41no—
62C2×C22⋊D283—41no—
63C2×C22⋊D283C2×C414yes—
64C2×C22⋊D283C2×C414yescomplemented
65C22×Dic283—22no—
66C22×Dic283—41no—
67C22×Dic283—41no—
68C22×Dic283C2311yescharacteristic
69C22×Dic283C2311yescharacteristic
70C22×Dic283C2311yescharacteristic
71C22×Dic283C2311yescharacteristic
72C22×Dic283C2311yescharacteristic
73C22×Dic283C2311yescharacteristic
74C2×C4×D283—22no—
75C2×C4×D283—22no—
76C2×C4×D283—22no—
77C2×C4×D283—41no—
78C2×C4×D283—41no—
79C2×C4×D283C2×C414yescomplemented
80C4⋊Dic283—22no—
81C4⋊Dic283—41no—
82Dic283⋊C4—22no—
83Dic283⋊C4—22no—
84Dic283⋊C4—41no—
85Dic283⋊C4C2×C414yescomplemented
86C22⋊Dic283—41no—
87(C2×D283)⋊C4—22no—
88(C2×D283)⋊C4—22no—
89(C2×D283)⋊C4—22no—
90(C2×D283)⋊C4—41no—
91(C2×D283)⋊C4—41no—
92(C2×D283)⋊C4—41no—
93(C2×D283)⋊C4—41no—
94(C2×D283)⋊C4C2×C414yescomplemented
95C4×Dic283—22no—
96C4×Dic283—41no—
97C4×Dic283D414yescomplemented
98C24×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C22×C4×C283C2311yescharacteristic
101C22×C4×C283C2311yescharacteristic
102C22×C4×C283C2311yescharacteristic
103C22×C4×C283C2311yescharacteristic
104C22×C4×C283C2311yescharacteristic
105C4⋊C4×C283—22no—
106C22⋊C4×C283—22no—
107C22⋊C4×C283—41no—
108C22⋊C4×C283C2×C414yescomplemented
109C42×C283—41no—
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—21no—
119C22×D283—21no—
120C22×D283—21no—
121C22×D283—21no—
122C22×D283C22×C412yes—
123C22×D283C22×C412yes—
124D1132—44no—
125C22⋊D283—28no—
126C22⋊D283—44no—
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—44no—
141C2×Dic283C22×C412yes—
142C2×Dic283C22×C412yes—
143C2×Dic283C2×D412yes—
144C2×Dic283C2×D412yes—
145C2×Dic283#4112yes—
146C4×D283—28no—
147C4×D283—44no—
148C23×C283—21no—
149C23×C283—21no—
150C23×C283—21no—
151C23×C283—21no—
152C23×C283—21no—
153C23×C283—21no—
154C23×C283C22×C412yes—
155C23×C283C2411yescharacteristic
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×C283—21no—
170C2×C4×C283—21no—
171C2×C4×C283C22×C412yes—
172C2×C4×C283C22×C412yes—
173C2×C4×C283C2×D412yes—
174C22×C283—22no—
175C22×C283—22no—
176C22×C283—22no—
177C22×C283—41no—
178C22×C283—41no—
179C22×C283—41no—
180C22×C283—41no—
181C22×C283C23×C411yescharacteristic
182C22×C283C22×D411yescharacteristic
183C22×C283C2×#4111yescharacteristic
184C22×C283H(5,𝔽2)11yescharacteristic
185C22×C283H(5,𝔽2)11yescharacteristic
186C22×C283H(5,𝔽2)11yescharacteristic
187C22×C2832−1+411yescharacteristic
188C2×D283—22no—
189C2×D283—22no—
190C2×D283—22no—
191C2×D283—22no—
192C2×D283—22no—
193C2×D283—22no—
194C2×D283—41no—
195C2×D283—41no—
196C2×D283—41no—
197C2×D283—41no—
198C2×D283—41no—
199C2×D283—41no—
200C2×D283—41no—
201C2×D283—41no—
202C4×C283—22no—
203C4×C283—22no—
204C4×C283—22no—
205C4×C283—41no—
206C4×C283—41no—
207C4×C283—41no—
208Dic283—22no—
209Dic283—22no—
210Dic283—41no—
211Dic283—41no—
212Dic283—41no—
213Dic283C4×D414yes—
214C2×C283—42no—
215C2×C283C2×C4×D411yescharacteristic
216C2×C283#51811yescharacteristic
217C2×C283#52011yescharacteristic
218C2×C283#53511yescharacteristic
219C2×C283#53711yescharacteristic
220C2×C283#54011yescharacteristic
221C2×C283#54211yescharacteristic
222D283—42no—
223D283—42no—
224C283#232411yescharacteristic, complemented, Sylow
225#2324—2831nomaximal, Sylow
226C2×#121—2831no—
227C2×C4×D4—2831no—
228C2×#117—2831no—
229#390—2831no—
230#390—2831no—
231#390—2831no—
232#389—2831no—
233#388—2831no—
234#388D28311yescharacteristic, complemented
235#386—2831no—
236#386—2831no—
237#385—2831no—
238#385—2831no—
239#380—2831no—
240C4×C4⋊C4—2831no—
241C22×D4—2831no—
242C22×D4—2831no—
243C22×D4—2831no—
244C23×C4—2831no—
245C23×C4—2831no—
246C23×C4—2831no—
247#121—2838no—
248C4×D4—5664no—
249#117—5664no—
250C2×C4⋊C4—2831no—
251C2×C4⋊C4—2831no—
252C2×C4⋊C4—2831no—
253C2×C4⋊C4—2831no—
254C2×C4⋊C4—2831no—
255C2×C4⋊C4—2831no—
256C2×C4⋊C4C2×D28311yescharacteristic
257C2×C22⋊C4—2831no—
258C2×C22⋊C4—2831no—
259C2×C22⋊C4—2831no—
260C2×C22⋊C4—2831no—
261C2×C22⋊C4—2831no—
262C2×C22⋊C4—2831no—
263C2×C22⋊C4—2831no—
264C2×C22⋊C4—2831no—
265C2×C22⋊C4—2831no—
266C2×C22⋊C4C2×D28311yescharacteristic
267C2×C22⋊C4C2×D28311yescharacteristic
268C2×C22⋊C4C2×D28311yescharacteristic
269C2×C42—2831no—
270C2×C42—2831no—
271C2×C42—2831no—
272C2×C42C2×D28311yescharacteristic
273#95—2831no—
274#95—2831no—
275#95—2831no—
276#95—2831no—
277#95C2×D28311yescharacteristic
278#95C2×D28311yescharacteristic
279C24—2831no—
280C24—2831no—
281C24C22×D28311yescharacteristic
282C2×D4—2834no—
283C2×D4—2834no—
284C2×D4—2834no—
285C2×D4—5662no—
286C2×D4—5662no—
287C2×D4—11321no—
288C2×D4—11321no—
289C2×D4—11321no—
290C2×D4—11321no—
291C22×C4—2831no—
292C22×C4—2831no—
293C22×C4—2831no—
294C22×C4—2834no—
295C22×C4—2831no—
296C22×C4—2831no—
297C22×C4—2831no—
298C22×C4—5662no—
299C22×C4—5662no—
300C22×C4—5662no—
301C22×C4—5662no—
302C22×C4—11321no—
303C22×C4—11321no—
304C22×C4—11321no—
305C22×C4—11321no—
306C22×C4C22×D28311yescharacteristic
307C22×C4C22×D28311yescharacteristic
308C22×C4C22×D28311yescharacteristic
309C22×C4C22×D28311yescharacteristic
310C22×C4C22×D28311yescharacteristic
311C22×C4C22×D28311yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—2834no—
314C4⋊C4—5662no—
315C4⋊C4—5662no—
316C4⋊C4—5662no—
317C4⋊C4—11321no—
318C4⋊C4—11321no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—2834no—
322C22⋊C4—5662no—
323C22⋊C4—5662no—
324C22⋊C4—5662no—
325C22⋊C4—11321no—
326C22⋊C4—11321no—
327C22⋊C4—11321no—
328C22⋊C4—11321no—
329C22⋊C4—11321no—
330C22⋊C4C4×D28314yescomplemented
331C42—41no—
332C42—2834no—
333C42—5662no—
334C42—11321no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—2832no—
342C23—2832no—
343C23—5661no—
344C23—5661no—
345C23—5661no—
346C23—5661no—
347C23—5661no—
348C23—5661no—
349C23—5661no—
350C23—5661no—
351C23—5661no—
352C23—5661no—
353C23—5661no—
354C23—5661no—
355C23C2×C4×D28312yes—
356C23C23×D28311yescharacteristic
357D4—5668no—
358D4—11324no—
359D4—11324no—
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—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—2832no—
376C2×C4—2832no—
377C2×C4—2832no—
378C2×C4—2832no—
379C2×C4—2832no—
380C2×C4—5668no—
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—5661no—
391C2×C4—5661no—
392C2×C4—5661no—
393C2×C4—5661no—
394C2×C4—11324no—
395C2×C4—11324no—
396C2×C4C2×C4×D28312yes—
397C2×C4C2×C4×D28312yes—
398C2×C4D4×D28312yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—5662no—
407C22—5662no—
408C22—5662no—
409C22—5662no—
410C22—5662no—
411C22—5662no—
412C22—11321no—
413C22—11321no—
414C22—11321no—
415C22—11321no—
416C22—11321no—
417C22—11321no—
418C22—11321no—
419C22—11321no—
420C22C22×C4×D28311yescharacteristic
421C22C2×D4×D28311yescharacteristic
422C22#41×D28311yescharacteristic
423C22#2258365511yescharacteristic
424C22#2258365611yescharacteristic
425C22#2258365611yescharacteristic
426C22#2258365711yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—2834no—
434C4—5662no—
435C4—5662no—
436C4—11321no—
437C4—11321no—
438C4—11321no—
439C2—42no—
440C2—11322no—
441C2—11322no—
442C2C4×D4×D28311yescharacteristic
443C2#3182693711yescharacteristic
444C2#3182694511yescharacteristic
445C2#3182703311yescharacteristic
446C2#3182704211yescharacteristic
447C2#3182706711yescharacteristic
448C2#3182708111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#388×C283C2
socle, cosocleC23×C283C24
prime radicalC2×#22583583C2
hypercenter#388D283
hypocenterC283#2324
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D283)⋊C4C2semidirect
3. C2×#22583568C2semidirect
4. #31826367C2semidirect
5. #31826365C2semidirect
6. #31826365C2semidirect
7. #31826362C2semidirect
8. #31826355C2semidirect
9. #31826343C2semidirect
10. #31826342C2semidirect
11. #31826340C2semidirect
12. #31826339C2semidirect
13. #31826324C2semidirect
14. C4×Dic283⋊C4C2semidirect
15. #388×C283C2semidirect
22. #22583583C4semidirect
58. C2×D1132C2×C4semidirect
64. C2×C22⋊D283C2×C4semidirect
79. C2×C4×D283C2×C4semidirect
85. Dic283⋊C4C2×C4semidirect
94. (C2×D283)⋊C4C2×C4semidirect
97. C4×Dic283D4semidirect
108. C22⋊C4×C283C2×C4semidirect
224. C283#2324semidirect
234. #388D283semidirect
330. C22⋊C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835832
C2×(C22⋊D283)⋊C42
C2×#225835682
#318263672
#318263652
#318263622
#318263552
#318263432
#318263422
#318263402
#318263392
#318263242
C4×Dic283⋊C42
#388×C2832
#2324283