Finite Group Databasebeta

← #413×D283 #49129732

Subgroups — #413×D283 #49129732

Order 36224.

756 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D283C211yesmaximal, characteristic
2C2×M16×D283C212yesmaximal, complemented
3#31826449C211yesmaximal, characteristic, complemented
4#31826448C212yesmaximal, complemented
5#31826447C212yesmaximal, complemented
6#31826446C212yesmaximal, complemented
7#101×D283C212yesmaximal, complemented
8#100×D283C212yesmaximal, complemented
9#413×C283C211yesmaximal, characteristic, complemented
10C2×#17985393C2211yescharacteristic
11C2×#17985392C412yes—
12C2×#17985392C2211yescharacteristic
13C2×#17985391C412yes—
14C2×#17985391C2211yescharacteristic
15#41×D283—22no—
16#41×D283—22no—
17#41×D283—22no—
18#41×D283—22no—
19C2×Q8×D283C2211yescharacteristic
20C2×D4×D283C412yes—
21C2×D4×D283C2211yescharacteristic
22C22×C4×D283C412yes—
23C22×C4×D283C2211yescharacteristic
24C2×#17985376C2212yescomplemented
25C2×#17985375—22no—
26M16×D283—22no—
27M16×D283—22no—
28M16×D283C2214yes—
29M16×D283C2214yescomplemented
30C2×C8×D283—22no—
31#22583529C2212yescomplemented
32#22583528C2214yescomplemented
33#22583527C2212yescomplemented
34#22583526C2214yescomplemented
35C2×#41×C283C2211yescharacteristic
36C2×M16×C283C2212yescomplemented
37#101×C283C2212yescomplemented
38#100×C283C2212yescomplemented
39C23×D283C2×C412yes—
40C23×D283C2×C411yescharacteristic
41#17985393—22no—
42#17985393—22no—
43#17985392—24no—
44#17985392—24no—
45#17985392—22no—
46#17985392—22no—
47#17985391—24no—
48#17985391—24no—
49#17985391—22no—
50#17985391—22no—
51C2×Dic566C2×C412yes—
52C2×Dic566C2311yescharacteristic
53Q8×D283—22no—
54Q8×D283—22no—
55C2×D1132C2×C412yes—
56C2×D1132C2311yescharacteristic
57C2×C22⋊D283C2×C412yes—
58C2×C22⋊D283C2×C412yes—
59C2×C22⋊D283C2×C412yes—
60D4×D283—24no—
61D4×D283—24no—
62D4×D283—22no—
63D4×D283—22no—
64C22×Dic283C2×C412yes—
65C22×Dic283C2×C411yescharacteristic
66C2×C4×D283—22no—
67C2×C4×D283—22no—
68C2×C4×D283—22no—
69C2×C4×D283—22no—
70C2×C4×D283C2×C412yes—
71C2×C4×D283C2×C412yes—
72C2×C4×D283C2×C412yes—
73C2×C4×D283C2×C411yescharacteristic
74C2×C4×D283C2×C411yescharacteristic
75C2×C4×D283D412yes—
76C2×C4×D283D412yes—
77C2×C4×D283D412yes—
78C2×C4×D283D412yes—
79C2×C4×D283C2311yescharacteristic
80C2×C4×D283C2311yescharacteristic
81#17985376—22no—
82#17985376C2314yes—
83#17985375—24no—
84#17985375—24no—
85C2×C283⋊C8—22no—
86C8×D283—24no—
87C8×D283—24no—
88#41×C283—22no—
89#41×C283—22no—
90C2×Q8×C283C2311yescharacteristic
91C2×D4×C283C2×C412yes—
92C2×D4×C283C2311yescharacteristic
93C22×C4×C283C2×C412yes—
94C22×C4×C283C2311yescharacteristic
95M16×C283—22no—
96M16×C283C2314yes—
97C2×C8×C283—22no—
98C22×D283—22no—
99C22×D283—22no—
100C22×D283—42no—
101C22×D283—44no—
102C22×D283C22⋊C412yes—
103C22×D283C22⋊C412yes—
104C22×D283C22×C411yescharacteristic
105C22×D283C22×C412yes—
106C22×D283C22×C411yescharacteristic
107Dic566—22no—
108Dic566—24no—
109D1132—24no—
110D1132—22no—
111C22⋊D283—24no—
112C22⋊D283—24no—
113C22⋊D283—24no—
114C2×Dic283—22no—
115C2×Dic283—22no—
116C2×Dic283C22⋊C412yes—
117C2×Dic283C22⋊C412yes—
118C2×Dic283C22×C412yes—
119C2×Dic283C22×C411yescharacteristic
120C2×Dic283C22×C411yescharacteristic
121C4×D283—22no—
122C4×D283—22no—
123C4×D283—22no—
124C4×D283—22no—
125C4×D283—22no—
126C4×D283—22no—
127C4×D283C22⋊C411yescharacteristic
128C4×D283C22⋊C411yescharacteristic
129C4×D283C22⋊C411yescharacteristic
130C4×D283C22⋊C411yescharacteristic
131C4×D283C22⋊C412yes—
132C4×D283C22⋊C412yes—
133C4×D283C2×D412yes—
134C4×D283C2×D412yes—
135C4×D283C2×D412yes—
136C4×D283C2×D412yes—
137C283⋊C8—24no—
138C23×C283C22×C412yes—
139C23×C283C22×C411yescharacteristic
140Q8×C283—22no—
141D4×C283—24no—
142D4×C283—22no—
143C2×C4×C283—22no—
144C2×C4×C283—22no—
145C2×C4×C283C22×C412yes—
146C2×C4×C283C22×C411yescharacteristic
147C2×C4×C283C2×D412yes—
148C2×C4×C283C2×D412yes—
149C2×C4×C283C2411yescharacteristic
150C8×C283—24no—
151C22×C283—22no—
152C22×C283—41no—
153C22×C283—42no—
154C22×C283C2×C22⋊C412yes—
155C22×C283C23×C411yescharacteristic
156C2×D283—22no—
157C2×D283—24no—
158C2×D283—22no—
159C2×D283—42no—
160C2×D283—41no—
161C2×D283—44no—
162C2×D283—44no—
163C2×D283—42no—
164C2×D283C2×C22⋊C411yescharacteristic
165C2×D283C2×C22⋊C412yes—
166C2×D283C2×C22⋊C411yescharacteristic
167C4×C283—22no—
168C4×C283C2×C22⋊C411yescharacteristic
169C4×C283C2×C22⋊C411yescharacteristic
170C4×C283C22×D412yes—
171Dic283—22no—
172Dic283C2×C22⋊C411yescharacteristic
173Dic283C2×C22⋊C411yescharacteristic
174Dic283C2×C22⋊C412yes—
175C2×C283—21no—
176C2×C283—22no—
177C2×C283—42no—
178C2×C283C22×C22⋊C411yescharacteristic
179D283—21no—
180D283—22no—
181D283—42no—
182D283#41312yesdirect product factor
183C283C2×#41311yescharacteristic, complemented, Sylow
184C2×#413—2831nomaximal, Sylow
185C22×#41—2831no—
186C22×M16—2832no—
187#413—2831no—
188#413—2832no—
189#413—2832no—
190#413—2832no—
191#413D28311yescharacteristic, direct product factor
192C2×#101—2832no—
193C2×#100—2832no—
194C2×#41—2831no—
195C2×#41—2832no—
196C2×#41—2831no—
197C2×#41—2832no—
198C2×#41—2831no—
199C2×#41—5662no—
200C2×#41—5662no—
201C2×#41—5662no—
202C2×#41—5662no—
203C2×#41C2×D28311yescharacteristic
204C22×Q8—2831no—
205C22×D4—2832no—
206C22×D4—2831no—
207C23×C4—2831no—
208C23×C4—2832no—
209C2×M16—2832no—
210C2×M16—2834no—
211C2×M16—2834no—
212C2×M16—5662no—
213C2×M16—5662no—
214C2×M16—5662no—
215C2×M16C2×D28312yescomplemented
216C22×C8—5662no—
217#101—2832no—
218#101—2834no—
219#101C2×D28312yescomplemented
220#100—2832no—
221#100—2834no—
222#100C2×D28312yescomplemented
223C24—2831no—
224C24—2832no—
225#41—22no—
226#41—22no—
227#41—5664no—
228#41—5664no—
229#41—5664no—
230#41—5664no—
231#41—5662no—
232#41—5662no—
233#41—5662no—
234#41—5662no—
235#41—5662no—
236#41—5662no—
237C2×Q8—2832no—
238C2×Q8—2831no—
239C2×Q8—5662no—
240C2×Q8—5662no—
241C2×Q8C22×D28311yescharacteristic
242C2×D4—2832no—
243C2×D4—2832no—
244C2×D4—2832no—
245C2×D4—2832no—
246C2×D4—2831no—
247C2×D4—5662no—
248C2×D4—5662no—
249C2×D4—5664no—
250C2×D4—5664no—
251C2×D4C4×D28312yes—
252C2×D4C22×D28311yescharacteristic
253C22×C4—2831no—
254C22×C4—2831no—
255C22×C4—2831no—
256C22×C4—2832no—
257C22×C4—2832no—
258C22×C4—2832no—
259C22×C4—2832no—
260C22×C4—2831no—
261C22×C4—2831no—
262C22×C4—2832no—
263C22×C4—2832no—
264C22×C4—2832no—
265C22×C4—2832no—
266C22×C4—5662no—
267C22×C4—5662no—
268C22×C4—5662no—
269C22×C4—5662no—
270C22×C4C4×D28312yes—
271C22×C4C22×D28311yescharacteristic
272M16—22no—
273M16—2834no—
274M16—5664no—
275M16—5664no—
276M16—5662no—
277M16C22×D28314yes—
278C2×C8—22no—
279C2×C8—5664no—
280C2×C8—5664no—
281C2×C8—5662no—
282C23—2832no—
283C23—2831no—
284C23—2832no—
285C23—2831no—
286C23—2832no—
287C23—5662no—
288C23—5662no—
289C23—11322no—
290C23—11324no—
291C23C2×C4×D28312yes—
292C23C2×C4×D28311yescharacteristic
293Q8—22no—
294Q8—5664no—
295Q8—5662no—
296D4—24no—
297D4—22no—
298D4—5664no—
299D4—5664no—
300D4—5664no—
301D4—5664no—
302D4—5662no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—2832no—
306C2×C4—2832no—
307C2×C4—2831no—
308C2×C4—2831no—
309C2×C4—2831no—
310C2×C4—2831no—
311C2×C4—2832no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—2832no—
315C2×C4—2832no—
316C2×C4—2832no—
317C2×C4—2832no—
318C2×C4—2832no—
319C2×C4—2832no—
320C2×C4—5662no—
321C2×C4—5662no—
322C2×C4—5662no—
323C2×C4—5662no—
324C2×C4—5662no—
325C2×C4—5662no—
326C2×C4—5662no—
327C2×C4—5662no—
328C2×C4C2×C4×D28312yes—
329C2×C4C2×C4×D28311yescharacteristic
330C2×C4D4×D28312yes—
331C2×C4D4×D28312yes—
332C2×C4C23×D28311yescharacteristic
333C8—24no—
334C8—5664no—
335C22—22no—
336C22—41no—
337C22—42no—
338C22—2831no—
339C22—2831no—
340C22—2832no—
341C22—5662no—
342C22—5664no—
343C22—5662no—
344C22—11321no—
345C22—11322no—
346C22—11322no—
347C22—11324no—
348C22—11324no—
349C22C22⋊C4×D28312yes—
350C22C22×C4×D28311yescharacteristic
351C4—22no—
352C4—2831no—
353C4—2831no—
354C4—2832no—
355C4—5662no—
356C4C22⋊C4×D28311yescharacteristic
357C4C22⋊C4×D28311yescharacteristic
358C4C2×D4×D28312yes—
359C2—21no—
360C2—22no—
361C2—42no—
362C2—2832no—
363C2—5661no—
364C2—5662no—
365C2—11322no—
366C2C2×C22⋊C4×D28311yescharacteristic
subgroupG/H
centerC4C22⋊C4×D283
commutatorC22×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#413×C283C2
socleC2×C283C22×C22⋊C4
prime radicalC2×#41×D283C2
cosocleC2×C4×C283C24
hypercenter#413D283
hypocenterC283C2×#413
LCSG ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. C2×M16×D283C2semidirect
3. #31826449C2semidirect
4. #31826448C2semidirect
5. #31826447C2semidirect
6. #31826446C2semidirect
7. #101×D283C2semidirect
8. #100×D283C2semidirect
9. #413×C283C2semidirect
24. C2×#17985376C22semidirect
29. M16×D283C22semidirect
31. #22583529C22semidirect
32. #22583528C22semidirect
33. #22583527C22semidirect
34. #22583526C22semidirect
36. C2×M16×C283C22semidirect
37. #101×C283C22semidirect
38. #100×C283C22semidirect
182. D283#413direct (N × H)
183. C283C2×#413semidirect
191. #413D283direct (N × H)
215. C2×M16C2×D283semidirect
219. #101C2×D283semidirect
222. #100C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2832
C2×M16×D2832
#318264492
#318264482
#318264472
#318264462
#101×D2832
#100×D2832
#413×C2832
C2×#413283