Finite Group Databasebeta

← #46819333

Subgroups — #46819333

Order 34432.

774 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D269C211yesmaximal, characteristic
2C2×#22575461C211yesmaximal, characteristic, complemented
3C2×#22575459C211yesmaximal, characteristic, complemented
4#31770572C211yesmaximal, characteristic, complemented
5#31770570C212yesmaximal, complemented
6#31770570C212yesmaximal, complemented
7#31770568C211yesmaximal, characteristic, complemented
8#31770567C212yesmaximal, complemented
9C2×#22575365C211yesmaximal, characteristic, complemented
10C22⋊C8×D269C212yesmaximal, complemented
11#408×C269C211yesmaximal, characteristic, complemented
12C2×#16864403C411yescharacteristic
13C2×#16864402C2212yes—
14C2×#16864402C2211yescharacteristic
15C2×#16864401C411yescharacteristic
16C2×#16864401C412yes—
17#41×D269—24no—
18#41×D269—24no—
19C2×Q8×D269C411yescharacteristic
20C2×D4×D269C411yescharacteristic
21C2×D4×D269C412yes—
22C22×C4×D269C2212yes—
23C22×C4×D269C2211yescharacteristic
24#22575461—24no—
25#22575459—24no—
26C2×#16864386C2211yescharacteristic, complemented
27C2×#16864385C2212yescomplemented
28C2×#16864385C2212yescomplemented
29C22×#14524130C2211yescharacteristic, complemented
30C2×C8×D269C2212yescomplemented
31C2×C8×D269C2212yescomplemented
32C22⋊#14524130C2212yescomplemented
33C22⋊#14524130C2212yescomplemented
34#22575365C2211yescharacteristic
35#22575365C2212yes—
36#22575365C2211yescharacteristic
37#22575365C2211yescharacteristic, complemented
38#22575365C2211yescharacteristic, complemented
39#22575365C2212yescomplemented
40C2×#41×C269C2211yescharacteristic
41C2×M16×C269C2211yescharacteristic, complemented
42C22×C8×C269C2211yescharacteristic, complemented
43C22⋊C8×C269C2212yescomplemented
44C22⋊C8×C269C2212yescomplemented
45C23×D269C2×C412yes—
46C23×D269C2×C411yescharacteristic
47#16864403—24no—
48#16864402—24no—
49#16864402—24no—
50#16864402D414yes—
51#16864402D414yes—
52#16864401—24no—
53#16864401—28no—
54C2×Dic538C2×C412yes—
55C2×Dic538C2×C411yescharacteristic
56Q8×D269—24no—
57C2×D1076C2×C412yes—
58C2×D1076C2×C411yescharacteristic
59C2×C22⋊D269C2×C412yes—
60C2×C22⋊D269C2×C412yes—
61C2×C22⋊D269C2×C412yes—
62D4×D269—24no—
63D4×D269—28no—
64C22×Dic269C2×C412yes—
65C22×Dic269C2×C411yescharacteristic
66C2×C4×D269—24no—
67C2×C4×D269—24no—
68C2×C4×D269—22no—
69C2×C4×D269—22no—
70C2×C4×D269C2×C412yes—
71C2×C4×D269C2×C411yescharacteristic
72C2×C4×D269C2×C412yes—
73C2×C4×D269C2×C411yescharacteristic
74C2×C4×D269C2311yescharacteristic
75C2×C4×D269C2311yescharacteristic
76C2×C4×D269C2312yes—
77#16864386—22no—
78#16864385—24no—
79#16864385—24no—
80C2×#14524130—22no—
81C2×#14524130C2311yescharacteristic
82C2×#14524130C2312yes—
83C2×#14524130C2311yescharacteristic
84C8×D269—24no—
85C8×D269—24no—
86#41×C269—22no—
87#41×C269—22no—
88C2×Q8×C269C2×C411yescharacteristic
89C2×D4×C269C2×C412yes—
90C2×D4×C269C2×C411yescharacteristic
91C22×C4×C269C2312yes—
92C22×C4×C269C2311yescharacteristic
93M16×C269—22no—
94C2×C8×C269—22no—
95C2×C8×C269C2311yescharacteristic
96C2×C8×C269C2312yes—
97C2×C8×C269C2311yescharacteristic
98C22×D269—22no—
99C22×D269—24no—
100C22×D269—24no—
101C22×D269—22no—
102C22×D269—42no—
103C22×D269—41no—
104C22×D269C22×C411yescharacteristic
105C22×D269C22×C412yes—
106C22×D269C22×C411yescharacteristic
107Dic538—24no—
108Dic538C22⋊C414yes—
109D1076—24no—
110D1076C22⋊C414yes—
111C22⋊D269—24no—
112C22⋊D269—24no—
113C22⋊D269C22⋊C418yes—
114C2×Dic269—22no—
115C2×Dic269—24no—
116C2×Dic269C22×C411yescharacteristic
117C2×Dic269C22×C411yescharacteristic
118C2×Dic269C22×C412yes—
119C4×D269—24no—
120C4×D269—22no—
121C4×D269—22no—
122C4×D269—21no—
123C4×D269—21no—
124C4×D269—21no—
125C4×D269—21no—
126C4×D269—24no—
127C4×D269C2×D414yes—
128C4×D269C2×D414yes—
129#14524130—21no—
130#14524130—22no—
131#14524130—21no—
132C23×C269C22×C412yes—
133C23×C269C22×C411yescharacteristic
134Q8×C269—22no—
135D4×C269—24no—
136D4×C269—22no—
137C2×C4×C269—22no—
138C2×C4×C269—22no—
139C2×C4×C269C22×C412yes—
140C2×C4×C269C22×C411yescharacteristic
141C2×C4×C269C2×D412yes—
142C2×C4×C269C2×D412yes—
143C2×C4×C269C2411yescharacteristic
144C8×C269—21no—
145C8×C269—21no—
146C8×C269—22no—
147C22×C269—21no—
148C22×C269—21no—
149C22×C269—22no—
150C22×C269—22no—
151C22×C269—22no—
152C22×C269C2×C22⋊C412yes—
153C22×C269C23×C411yescharacteristic
154C2×D269—21no—
155C2×D269—22no—
156C2×D269—21no—
157C2×D269—22no—
158C2×D269—21no—
159C2×D269—21no—
160C2×D269—21no—
161C2×D269—48no—
162C2×D269—44no—
163C2×D269C2×C22⋊C414yes—
164C2×D269#13112yescomplemented
165C4×C269—22no—
166C4×C269C2×C22⋊C412yes—
167C4×C269C22×D411yescharacteristic
168C4×C269C22×D411yescharacteristic
169Dic269—21no—
170Dic269—21no—
171Dic269C2×C22⋊C414yes—
172C2×C269—22no—
173C2×C269—42no—
174C2×C269C22×C22⋊C411yescharacteristic
175C2×C269C2×#13111yescharacteristic
176C2×C269#56811yescharacteristic
177D269—22no—
178D269—24no—
179D269—41no—
180C269#288011yescharacteristic, complemented, Sylow
181#2880—2691nomaximal, Sylow
182C22×#41—2691no—
183C2×#131—2691no—
184C2×#131—2691no—
185#408—2691no—
186#408—2692no—
187#408—2692no—
188#408D26911yescharacteristic, complemented
189#407—2691no—
190#407—2692no—
191C2×C22⋊C8—2691no—
192C2×C22⋊C8—2692no—
193C2×#41—2691no—
194C2×#41—2692no—
195C2×#41—2691no—
196C2×#41—2691no—
197C2×#41—2692no—
198C2×#41—5384no—
199C2×#41—5384no—
200C2×#41C2×D26911yescharacteristic
201C22×Q8—2691no—
202C22×D4—2692no—
203C22×D4—2691no—
204C23×C4—2692no—
205C23×C4—2691no—
206#131—5384no—
207#131—5384no—
208C2×M16—2691no—
209C2×M16—2692no—
210C2×M16—2692no—
211C2×M16C2×D26911yescharacteristic, complemented
212C22×C8—2691no—
213C22×C8—2692no—
214C22×C8—2692no—
215C22×C8C2×D26911yescharacteristic, complemented
216C22⋊C8—2692no—
217C22⋊C8—2692no—
218C22⋊C8—2691no—
219C22⋊C8—2692no—
220C22⋊C8—2691no—
221C22⋊C8—2691no—
222C22⋊C8—2691no—
223C22⋊C8—2692no—
224C22⋊C8C2×D26912yescomplemented
225C22⋊C8C2×D26912yescomplemented
226C24—2692no—
227C24—2691no—
228#41—22no—
229#41—22no—
230#41—2694no—
231#41—2694no—
232#41—5384no—
233#41—5384no—
234#41—5388no—
235#41—5384no—
236#41—5384no—
237C2×Q8—2691no—
238C2×Q8—2692no—
239C2×Q8—5384no—
240C2×Q8C4×D26911yescharacteristic
241C2×D4—2692no—
242C2×D4—2692no—
243C2×D4—2692no—
244C2×D4—2691no—
245C2×D4—2692no—
246C2×D4—5388no—
247C2×D4—5384no—
248C2×D4C4×D26912yes—
249C2×D4C4×D26911yescharacteristic
250C22×C4—2692no—
251C22×C4—2692no—
252C22×C4—2691no—
253C22×C4—2692no—
254C22×C4—2691no—
255C22×C4—2692no—
256C22×C4—2691no—
257C22×C4—2691no—
258C22×C4—2691no—
259C22×C4—5384no—
260C22×C4—5384no—
261C22×C4—5382no—
262C22×C4—5382no—
263C22×C4C22×D26912yes—
264C22×C4C22×D26911yescharacteristic
265M16—22no—
266M16—5384no—
267M16—5384no—
268M16—5382no—
269C2×C8—22no—
270C2×C8—2691no—
271C2×C8—2692no—
272C2×C8—2691no—
273C2×C8—5384no—
274C2×C8—5384no—
275C2×C8—5382no—
276C2×C8C22×D26911yescharacteristic
277C2×C8C22×D26912yes—
278C2×C8C22×D26911yescharacteristic
279C23—2691no—
280C23—2692no—
281C23—2691no—
282C23—5384no—
283C23—5382no—
284C23—5384no—
285C23—5382no—
286C23—10761no—
287C23—10762no—
288C23C2×C4×D26912yes—
289C23C2×C4×D26911yescharacteristic
290Q8—22no—
291Q8—2694no—
292Q8—5384no—
293D4—24no—
294D4—22no—
295D4—2698no—
296D4—2694no—
297D4—5384no—
298D4—5384no—
299D4—5384no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—2692no—
303C2×C4—2694no—
304C2×C4—2694no—
305C2×C4—2691no—
306C2×C4—2691no—
307C2×C4—5384no—
308C2×C4—5384no—
309C2×C4—5384no—
310C2×C4—5382no—
311C2×C4—5382no—
312C2×C4—5382no—
313C2×C4—5381no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4C2×C4×D26912yes—
318C2×C4C2×C4×D26911yescharacteristic
319C2×C4D4×D26912yes—
320C2×C4D4×D26912yes—
321C2×C4C23×D26911yescharacteristic
322C8—21no—
323C8—21no—
324C8—22no—
325C8—5381no—
326C8—5382no—
327C8—5381no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—2694no—
334C22—2692no—
335C22—5381no—
336C22—5382no—
337C22—5381no—
338C22—5382no—
339C22—5381no—
340C22—5381no—
341C22—5381no—
342C22—10764no—
343C22—10768no—
344C22C22⋊C4×D26912yes—
345C22C22×C4×D26911yescharacteristic
346C4—22no—
347C4—2694no—
348C4—5381no—
349C4—5381no—
350C4C22⋊C4×D26912yes—
351C4C2×D4×D26911yescharacteristic
352C4C2×D4×D26911yescharacteristic
353C2—22no—
354C2—42no—
355C2—5382no—
356C2—5384no—
357C2—10761no—
358C2C2×C22⋊C4×D26911yescharacteristic
359C2#131×D26911yescharacteristic
360C2#3177137011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D269
commutator, socleC22×C269C23×C4
Fitting#408×C269C2
prime radicalC2×#41×D269C2
cosocleC2×C4×C269C24
hypercenter#408D269
hypocenterC269#2880
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#22575461C2semidirect
3. C2×#22575459C2semidirect
4. #31770572C2semidirect
5. #31770570C2semidirect
6. #31770570C2semidirect
7. #31770568C2semidirect
8. #31770567C2semidirect
9. C2×#22575365C2semidirect
10. C22⋊C8×D269C2semidirect
11. #408×C269C2semidirect
26. C2×#16864386C22semidirect
27. C2×#16864385C22semidirect
28. C2×#16864385C22semidirect
29. C22×#14524130C22semidirect
30. C2×C8×D269C22semidirect
31. C2×C8×D269C22semidirect
32. C22⋊#14524130C22semidirect
33. C22⋊#14524130C22semidirect
37. #22575365C22semidirect
38. #22575365C22semidirect
39. #22575365C22semidirect
41. C2×M16×C269C22semidirect
42. C22×C8×C269C22semidirect
43. C22⋊C8×C269C22semidirect
44. C22⋊C8×C269C22semidirect
164. C2×D269#131semidirect
180. C269#2880semidirect
188. #408D269semidirect
211. C2×M16C2×D269semidirect
215. C22×C8C2×D269semidirect
224. C22⋊C8C2×D269semidirect
225. C22⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2692
C2×#225754612
C2×#225754592
#317705722
#317705702
#317705682
#317705672
C2×#225753652
C22⋊C8×D2692
#408×C2692
#2880269