Finite Group Databasebeta

← #49132771

Subgroups — #49132771

Order 36224.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583639C211yesmaximal, characteristic, complemented
2Q8×C22⋊D283C211yesmaximal, characteristic, complemented
3#31827109C211yesmaximal, characteristic
4#31826856C211yesmaximal, characteristic, complemented
5#31826708C211yesmaximal, characteristic, complemented
6#31826706C211yesmaximal, characteristic, complemented
7#31826685C211yesmaximal, characteristic, complemented
8#31826668C211yesmaximal, characteristic, complemented
9#31826624C211yesmaximal, characteristic, complemented
10#31826621C211yesmaximal, characteristic, complemented
11#31826616C211yesmaximal, characteristic, complemented
12#31826602C211yesmaximal, characteristic, complemented
13#31826566C211yesmaximal, characteristic, complemented
14#31826536C211yesmaximal, characteristic, complemented
15C22×SD16×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic, complemented
18#22583639—24no—
19C2×Dic1132C2211yescharacteristic, complemented
20C2×#17985382C2211yescharacteristic, complemented
21C2×#17985382C2211yescharacteristic, complemented
22C2×#17985380C2211yescharacteristic
23C2×#17985380C2211yescharacteristic
24C2×#17985375C2211yescharacteristic, complemented
25#22583608—21no—
26#22583608C2211yescharacteristic, complemented
27#22583597C2211yescharacteristic
28#22583591—21no—
29#22583589—21no—
30#22583589C2211yescharacteristic
31#22583589C2211yescharacteristic
32#22583586—21no—
33#22583586C2211yescharacteristic, complemented
34#22583582—21no—
35#22583581C2211yescharacteristic
36#22583579—21no—
37Q8×Dic283C2211yescharacteristic, complemented
38D4×Dic283C2211yescharacteristic
39C4×C22⋊D283—21no—
40C4×C22⋊D283C2211yescharacteristic
41C2×C22⋊Dic283—21no—
42#22583544C2211yescharacteristic, complemented
43Dic283⋊C8C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583535C2211yescharacteristic, complemented
46#22583534C2211yescharacteristic, complemented
47#22583534C2211yescharacteristic, complemented
48#22583531C2211yescharacteristic
49#22583531C2211yescharacteristic
50C22⋊(C283⋊C8)C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic, complemented
52#22583520C2211yescharacteristic, complemented
53C22×Q8×C283C2211yescharacteristic
54C22×D4×C283C2211yescharacteristic
55C2×SD16×C283—24no—
56C2×SD16×C283C2211yescharacteristic
57C2×SD16×C283C2211yescharacteristic
58C2×SD16×C283C2211yescharacteristic
59C2×SD16×C283C2211yescharacteristic
60C22×C8×C283C2211yescharacteristic
61#17985391—22no—
62#17985391—41no—
63C2×Dic566—21no—
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66Q8×D283—22no—
67Q8×D283—41no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283D411yescharacteristic
71C22×Dic283—21no—
72C22×Dic283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75Dic1132—22no—
76#17985382—22no—
77#17985382—41no—
78#17985380—22no—
79#17985380—41no—
80#17985375—22no—
81C2×C283⋊C8C2311yescharacteristic
82C2×C283⋊C8C2311yescharacteristic
83C4⋊Dic283—21no—
84C4⋊Dic283C2311yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91Dic283⋊C4D411yescharacteristic
92C22⋊Dic283—21no—
93C22⋊Dic283—21no—
94C22⋊Dic283—21no—
95C22⋊Dic283—21no—
96C22⋊Dic283—21no—
97C22⋊Dic283—21no—
98C22⋊Dic283D411yescharacteristic
99(C2×D283)⋊C4—21no—
100(C2×D283)⋊C4D411yescharacteristic
101C4×Dic283—21no—
102C4×Dic283C2311yescharacteristic
103C24×C283—21no—
104C2×Q8×C283—21no—
105C2×Q8×C283—22no—
106C2×Q8×C283—41no—
107C2×Q8×C283C2311yescharacteristic
108C2×Q8×C283C2311yescharacteristic
109C2×D4×C283—22no—
110C2×D4×C283—21no—
111C2×D4×C283—41no—
112C2×D4×C283C2311yescharacteristic
113C2×D4×C283C2311yescharacteristic
114C22×C4×C283—21no—
115C22×C4×C283C2311yescharacteristic
116SD16×C283—22no—
117SD16×C283—22no—
118SD16×C283—22no—
119SD16×C283D414yescomplemented
120C2×C8×C283—22no—
121C2×C8×C283C2311yescharacteristic
122C2×C8×C283C2311yescharacteristic
123C22×D283C2×D411yescharacteristic
124Dic566—21no—
125Dic566—21no—
126Dic566—21no—
127Dic566—21no—
128Dic566—42no—
129C22⋊D283—22no—
130C22⋊D283—42no—
131C22⋊D283—81no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283—42no—
137C2×Dic283—81no—
138C2×Dic283C2×D411yescharacteristic
139C2×Dic283C2×D411yescharacteristic
140C2×Dic283C2×D411yescharacteristic
141C4×D283—21no—
142C4×D283—21no—
143C4×D283—42no—
144C283⋊C8—21no—
145C283⋊C8—21no—
146C23×C283—21no—
147C23×C283—21no—
148C23×C283—42no—
149C23×C283—42no—
150C23×C283—81no—
151C23×C283C2×D411yescharacteristic
152Q8×C283—21no—
153Q8×C283—21no—
154Q8×C283—21no—
155Q8×C283—42no—
156Q8×C283C2×D412yes—
157D4×C283—21no—
158D4×C283—21no—
159D4×C283—21no—
160D4×C283—42no—
161D4×C283C2×D412yes—
162C2×C4×C283—21no—
163C2×C4×C283—21no—
164C2×C4×C283—21no—
165C2×C4×C283—21no—
166C2×C4×C283—42no—
167C2×C4×C283C2×D411yescharacteristic
168C2×C4×C283C2411yescharacteristic
169C8×C283—21no—
170C8×C283C2×D412yes—
171C22×C283—21no—
172C22×C283—21no—
173C22×C283—22no—
174C22×C283—41no—
175C22×C283—41no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283—41no—
179C22×C283—84no—
180C22×C283#13712yescomplemented
181C22×C283C22×D411yescharacteristic
182C2×D283—21no—
183C2×D283—21no—
184C2×D283—21no—
185C4×C283—21no—
186C4×C283—22no—
187C4×C283—41no—
188C4×C283C22×D411yescharacteristic
189C4×C283H(5,𝔽2)11yescharacteristic
190Dic283—21no—
191Dic283—21no—
192Dic283—21no—
193Dic283—41no—
194Dic283—41no—
195Dic283—41no—
196Dic283—41no—
197C2×C283—22no—
198C2×C283—42no—
199C2×C283—81no—
200C2×C283D4211yescharacteristic
201C2×C283C2×#13711yescharacteristic
202C2×C283#57711yescharacteristic
203D283—41no—
204C283#326611yescharacteristic, complemented, Sylow
205#3266—2831nomaximal, Sylow
206C2×#137—2831no—
207C22×SD16D28311yescharacteristic, complemented
208D4×Q8—2831no—
209#546—2831no—
210#497—2831no—
211#468—2831no—
212#467—2831no—
213#464—2831no—
214#461—2831no—
215#452—2831no—
216#451—2831no—
217#450—2831no—
218#448—2831no—
219#440—2831no—
220#435—2831no—
221C2×#41—2831no—
222C22×Q8—2831no—
223C22×Q8C2×D28311yescharacteristic
224C22×D4C2×D28311yescharacteristic
225#137—5664no—
226C2×Q16—2831no—
227C2×Q16—2831no—
228C2×Q16—2831no—
229C2×SD16—24no—
230C2×SD16—2831no—
231C2×SD16—2831no—
232C2×SD16C2×D28311yescharacteristic
233C2×SD16C2×D28311yescharacteristic
234C2×SD16C2×D28311yescharacteristic
235C2×SD16C2×D28311yescharacteristic
236C2×M16—2831no—
237C22×C8C2×D28311yescharacteristic
238C4⋊Q8—2831no—
239C4⋊Q8—5661no—
240#124—2831no—
241#123—5661no—
242C22⋊Q8—2831no—
243C22⋊Q8—2831no—
244C22⋊Q8—2831no—
245C22⋊Q8—5661no—
246C22⋊Q8—5661no—
247#121—2831no—
248#121—5661no—
249#120—5661no—
250C4×Q8—2831no—
251C4×D4—2831no—
252C4×D4—2831no—
253C4×D4—5661no—
254C2×C22⋊C4—5661no—
255#107—2831no—
256C4⋊C8—2831no—
257#103—2831no—
258#103—2831no—
259#103—2831no—
260#103—2831no—
261#102—2831no—
262#102—2831no—
263C22⋊C8—2831no—
264C22⋊C8—2831no—
265#97—2831no—
266C24—21no—
267#41—5662no—
268#41—11321no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—2831no—
273C2×Q8—2831no—
274C2×Q8—5661no—
275C2×Q8—5662no—
276C2×Q8—11321no—
277C2×Q8C22×D28311yescharacteristic
278C2×Q8C22×D28311yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—2831no—
283C2×D4—5661no—
284C2×D4—5661no—
285C2×D4C22×D28311yescharacteristic
286C2×D4C22×D28311yescharacteristic
287C22×C4—21no—
288C22×C4—2831no—
289C22×C4—5661no—
290C22×C4—5661no—
291C22×C4—5661no—
292C22×C4C22×D28311yescharacteristic
293Q16—5662no—
294Q16—5662no—
295Q16—11321no—
296SD16—22no—
297SD16—22no—
298SD16—22no—
299SD16—5662no—
300SD16—11321no—
301SD16C22⋊D28314yescomplemented
302M16—5662no—
303C2×C8—22no—
304C2×C8—2831no—
305C2×C8—2831no—
306C2×C8C22×D28311yescharacteristic
307C2×C8C22×D28311yescharacteristic
308C4⋊C4—2831no—
309C4⋊C4—2831no—
310C4⋊C4—2831no—
311C4⋊C4—5661no—
312C4⋊C4—5661no—
313C4⋊C4—5661no—
314C4⋊C4—5661no—
315C4⋊C4—5661no—
316C4⋊C4—5661no—
317C22⋊C4—2831no—
318C22⋊C4—2831no—
319C22⋊C4—5661no—
320C22⋊C4—5661no—
321C22⋊C4—5661no—
322C22⋊C4—5661no—
323C22⋊C4—5661no—
324C22⋊C4—5661no—
325C22⋊C4—5661no—
326C42—2831no—
327C42—5661no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—2831no—
334C23D4×D28311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—5661no—
340Q8—5661no—
341Q8—5661no—
342Q8—5661no—
343Q8—11322no—
344Q8C2×C22⋊D28312yes—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—5662no—
350D4—11322no—
351D4—22641no—
352D4C2×C22⋊D28312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—2831no—
359C2×C4—2831no—
360C2×C4—2831no—
361C2×C4—5661no—
362C2×C4—5661no—
363C2×C4—5661no—
364C2×C4—5661no—
365C2×C4—5661no—
366C2×C4—5661no—
367C2×C4—11322no—
368C2×C4—11322no—
369C2×C4—22641no—
370C2×C4D4×D28311yescharacteristic
371C2×C4C23×D28311yescharacteristic
372C8—21no—
373C8—5661no—
374C8—5661no—
375C8C2×C22⋊D28312yes—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—5661no—
386C22—5661no—
387C22—5661no—
388C22#2258363912yescomplemented
389C22C2×D4×D28311yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—5661no—
394C4—5661no—
395C4—5661no—
396C4—11321no—
397C4—11321no—
398C4—11321no—
399C4—11321no—
400C4C22×C22⋊D28311yescharacteristic
401C4#2258365511yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—11321no—
406C2D4×C22⋊D28311yescharacteristic
407C2C2×#2258363911yescharacteristic
408C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×SD16×C283C2
socleC22×C283C22×D4
prime radical#31827109C2
hypercenterC22×SD16D283
hypocenterC283#3266
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22583639C2semidirect
2. Q8×C22⋊D283C2semidirect
4. #31826856C2semidirect
5. #31826708C2semidirect
6. #31826706C2semidirect
7. #31826685C2semidirect
8. #31826668C2semidirect
9. #31826624C2semidirect
10. #31826621C2semidirect
11. #31826616C2semidirect
12. #31826602C2semidirect
13. #31826566C2semidirect
14. #31826536C2semidirect
15. C22×SD16×C283C2semidirect
17. C2×Q8×D283C22semidirect
19. C2×Dic1132C22semidirect
20. C2×#17985382C22semidirect
21. C2×#17985382C22semidirect
24. C2×#17985375C22semidirect
26. #22583608C22semidirect
33. #22583586C22semidirect
37. Q8×Dic283C22semidirect
42. #22583544C22semidirect
43. Dic283⋊C8C22semidirect
44. #22583535C22semidirect
45. #22583535C22semidirect
46. #22583534C22semidirect
47. #22583534C22semidirect
51. (C2×D283)⋊C8C22semidirect
52. #22583520C22semidirect
119. SD16×C283D4semidirect
180. C22×C283#137semidirect
204. C283#3266semidirect
207. C22×SD16D283semidirect
301. SD16C22⋊D283semidirect
388. C22#22583639semidirect

Maximal subgroups

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

subgroupindex
C2×#225836392
Q8×C22⋊D2832
#318271092
#318268562
#318267082
#318267062
#318266852
#318266682
#318266242
#318266212
#318266162
#318266022
#318265662
#318265362
C22×SD16×C2832
#3266283