Finite Group Databasebeta

← #46822740

Subgroups — #46822740

Order 34432.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771305C211yesmaximal, characteristic, complemented
2#31771250C211yesmaximal, characteristic, complemented
3#31770960C211yesmaximal, characteristic, complemented
4#31770942C211yesmaximal, characteristic, complemented
5#31770932C211yesmaximal, characteristic, complemented
6#31770905C211yesmaximal, characteristic, complemented
7#31770840C211yesmaximal, characteristic, complemented
8#31770833C211yesmaximal, characteristic, complemented
9#31770820C211yesmaximal, characteristic, complemented
10#31770747C211yesmaximal, characteristic, complemented
11#31770737C211yesmaximal, characteristic, complemented
12C8×D1076C211yesmaximal, characteristic, complemented
13#31770598C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15C4×D8×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×D4×D269C2211yescharacteristic
18C2×#16864390C2211yescharacteristic, complemented
19C2×#16864387C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21C2×C8×D269C2211yescharacteristic, complemented
22#22575446—21no—
23#22575445C2211yescharacteristic, complemented
24#22575441C2211yescharacteristic
25#22575437—21no—
26#22575436—21no—
27#22575433C2211yescharacteristic
28#22575428C2211yescharacteristic
29#22575427—21no—
30#22575426—21no—
31#22575424C2211yescharacteristic
32#22575424C2211yescharacteristic, complemented
33#22575423—21no—
34C4×D1076C2211yescharacteristic
35C4×C22⋊D269—21no—
36#22575411C2211yescharacteristic, complemented
37C4⋊C4×D269C2211yescharacteristic
38C2×#16864379—21no—
39#22575386C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41C4⋊#14524130C2211yescharacteristic, complemented
42#22575378C2211yescharacteristic, complemented
43#22575378C2211yescharacteristic, complemented
44#22575376C2211yescharacteristic, complemented
45#22575375C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575373C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575365C2211yescharacteristic, complemented
52C2×D8×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic, complemented
55#107×C269C2211yescharacteristic, complemented
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic, complemented
58C4×C8×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60#16864401—22no—
61#16864401—41no—
62C2×Dic538C2311yescharacteristic
63C2×D1076—21no—
64C2×D1076D411yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70D4×D269—22no—
71D4×D269—41no—
72C22×Dic269—21no—
73C2×C4×D269—21no—
74C2×C4×D269C2311yescharacteristic
75C2×C4×D269C2311yescharacteristic
76#16864390—41no—
77#16864387—41no—
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C8×D269—41no—
81C8×D269—41no—
82C4⋊Dic269—21no—
83C4⋊Dic269D411yescharacteristic
84C4⋊Dic269C2311yescharacteristic
85C4⋊Dic269C2311yescharacteristic
86#16864381—21no—
87#16864381—21no—
88#16864381—21no—
89C22⋊Dic269—21no—
90C22⋊Dic269—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379D411yescharacteristic
97#16864379D411yescharacteristic
98C4×Dic269—21no—
99C2×D4×C269C2311yescharacteristic
100C2×D4×C269C2311yescharacteristic
101C22×C4×C269—21no—
102C22×C4×C269—21no—
103D8×C269—22no—
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C22⋊C4×C269—21no—
109C22⋊C4×C269—21no—
110C42×C269C2311yescharacteristic
111C22×D269—21no—
112C22×D269—42no—
113C22×D269—42no—
114C22×D269—81no—
115C22×D269C2×D411yescharacteristic
116C22×D269C2×D411yescharacteristic
117Dic538—21no—
118Dic538—21no—
119D1076—22no—
120D1076—21no—
121D1076—21no—
122D1076—81no—
123C22⋊D269—42no—
124C22⋊D269—42no—
125C22⋊D269—42no—
126C22⋊D269—81no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—42no—
131C2×Dic269C2×D411yescharacteristic
132C2×Dic269C2×D411yescharacteristic
133C4×D269—21no—
134C4×D269—21no—
135C4×D269—21no—
136C4×D269—21no—
137C4×D269—81no—
138#14524130—21no—
139#14524130—21no—
140C23×C269—21no—
141C23×C269—21no—
142D4×C269—21no—
143D4×C269—21no—
144D4×C269—21no—
145D4×C269#4112yes—
146C2×C4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269—81no—
149C2×C4×C269—81no—
150C2×C4×C269C2×D411yescharacteristic
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2411yescharacteristic
153C8×C269—21no—
154C8×C269—21no—
155C22×C269—22no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269C22×D411yescharacteristic
162C2×D269—21no—
163C2×D269—21no—
164C2×D269—21no—
165C2×D269—21no—
166C2×D269—21no—
167C2×D269—41no—
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—84no—
171C2×D269#13512yes—
172C4×C269—21no—
173C4×C269—21no—
174C4×C269—41no—
175C4×C269—41no—
176C4×C269C2×#4111yescharacteristic
177C4×C269H(5,𝔽2)11yescharacteristic
178Dic269—21no—
179Dic269—21no—
180Dic269—41no—
181Dic269—41no—
182Dic269—41no—
183C2×C269—42no—
184C2×C269—81no—
185C2×C269#54611yescharacteristic
186C2×C269C2×#13511yescharacteristic
187C2×C269#57611yescharacteristic
188D269—22no—
189D269—41no—
190D269—81no—
191C269#329711yescharacteristic, complemented, Sylow
192#3297—2691nomaximal, Sylow
193#553—2691no—
194#546—2691no—
195#488—2691no—
196#484—2691no—
197#482—2691no—
198#478—2691no—
199#466—2691no—
200#465—2691no—
201#463—2691no—
202#449—2691no—
203#447—2691no—
204C4×D8D26911yescharacteristic, complemented
205C8×D4—2691no—
206#416—2691no—
207C2×#102—2691no—
208C2×#41—2691no—
209C22×D4—2691no—
210C2×SD16—2691no—
211C2×D8—2691no—
212C2×D8C2×D26911yescharacteristic
213C22×C8—2691no—
214C22×C8—2691no—
215#126—5381no—
216#125—2691no—
217#124—2691no—
218#123—5381no—
219#123—5381no—
220C22⋊Q8—2691no—
221#121—2691no—
222#121—2691no—
223#121—2691no—
224#121—5381no—
225#121—5381no—
226#120—5381no—
227C4×D4—2691no—
228C4×D4—5381no—
229C4×D4C2×D26911yescharacteristic
230C4×D4C2×D26911yescharacteristic, complemented
231#117—2691no—
232C2×C4⋊C4—2691no—
233C2×C22⋊C4—5381no—
234#107—2691no—
235#107C2×D26911yescharacteristic, complemented
236#106—2691no—
237C4⋊C8—2691no—
238#103—2691no—
239#103—2691no—
240#103—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244#102—2691no—
245#102—2691no—
246#102C2×D26911yescharacteristic
247#102C2×D26911yescharacteristic, complemented
248C22⋊C8—2691no—
249C22⋊C8—2691no—
250C4×C8C2×D26911yescharacteristic, complemented
251C24—5381no—
252#41—5382no—
253#41—10761no—
254C2×Q8—2691no—
255C2×D4—2691no—
256C2×D4—2691no—
257C2×D4—5381no—
258C2×D4—5381no—
259C2×D4—5382no—
260C2×D4—5381no—
261C2×D4—5381no—
262C2×D4—5381no—
263C2×D4—10761no—
264C2×D4C22×D26911yescharacteristic
265C2×D4C22×D26911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2691no—
269C22×C4—2691no—
270C22×C4—5381no—
271C22×C4—5381no—
272SD16—10761no—
273D8—22no—
274D8—10761no—
275C2×C8—2691no—
276C2×C8—2691no—
277C2×C8—10761no—
278C2×C8—10761no—
279C2×C8C22×D26911yescharacteristic
280C2×C8C22×D26911yescharacteristic
281C4⋊C4—2691no—
282C4⋊C4—2691no—
283C4⋊C4—2691no—
284C4⋊C4—5381no—
285C4⋊C4—5381no—
286C4⋊C4—5381no—
287C4⋊C4—5381no—
288C4⋊C4C22×D26911yescharacteristic
289C4⋊C4C22×D26911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2691no—
293C22⋊C4—2691no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C22⋊C4—5381no—
299C22⋊C4—5381no—
300C22⋊C4—5381no—
301C42—5381no—
302C42C22×D26911yescharacteristic
303C23—21no—
304C23—21no—
305C23—2691no—
306C23—2691no—
307C23—5381no—
308C23—10762no—
309C23—10762no—
310C23—21521no—
311Q8—5381no—
312Q8—5381no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—5382no—
317D4—5381no—
318D4—5381no—
319D4—10762no—
320D4—10762no—
321D4—10762no—
322D4—21521no—
323D4—21521no—
324D4#1686440212yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—2691no—
330C2×C4—2691no—
331C2×C4—5381no—
332C2×C4—5381no—
333C2×C4—5381no—
334C2×C4—5381no—
335C2×C4—5381no—
336C2×C4—5381no—
337C2×C4—5381no—
338C2×C4—10762no—
339C2×C4—21521no—
340C2×C4D4×D26911yescharacteristic
341C2×C4D4×D26911yescharacteristic
342C2×C4C23×D26911yescharacteristic
343C8—21no—
344C8—21no—
345C8—5381no—
346C8—5381no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2692no—
354C22—5381no—
355C22—5381no—
356C22—5381no—
357C22—5381no—
358C22—5381no—
359C22—10761no—
360C22—10761no—
361C22—10761no—
362C22—21524no—
363C22C2×D4×D26911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—5381no—
369C4—5381no—
370C4—10761no—
371C4—10761no—
372C4—10761no—
373C4C2×#1686440211yescharacteristic
374C4#2257549911yescharacteristic
375C2—42no—
376C2—81no—
377C2—5382no—
378C2—10761no—
379C2—21521no—
380C2#3177125111yescharacteristic
381C2#135×D26911yescharacteristic
382C2#3177140611yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC4×D8×C269C2
socleC22×C269C22×D4
hypercenterC4×D8D269
hypocenterC269#3297
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31771305C2semidirect
2. #31771250C2semidirect
3. #31770960C2semidirect
4. #31770942C2semidirect
5. #31770932C2semidirect
6. #31770905C2semidirect
7. #31770840C2semidirect
8. #31770833C2semidirect
9. #31770820C2semidirect
10. #31770747C2semidirect
11. #31770737C2semidirect
12. C8×D1076C2semidirect
13. #31770598C2semidirect
14. #102×D269C2semidirect
15. C4×D8×C269C2semidirect
18. C2×#16864390C22semidirect
21. C2×C8×D269C22semidirect
23. #22575445C22semidirect
32. #22575424C22semidirect
36. #22575411C22semidirect
39. #22575386C22semidirect
40. #22575384C22semidirect
41. C4⋊#14524130C22semidirect
42. #22575378C22semidirect
43. #22575378C22semidirect
44. #22575376C22semidirect
51. #22575365C22semidirect
54. C4×D4×C269C22semidirect
55. #107×C269C22semidirect
57. #102×C269C22semidirect
58. C4×C8×C269C22semidirect
191. C269#3297semidirect
204. C4×D8D269semidirect
230. C4×D4C2×D269semidirect
235. #107C2×D269semidirect
247. #102C2×D269semidirect
250. C4×C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317713052
#317712502
#317709602
#317709422
#317709322
#317709052
#317708402
#317708332
#317708202
#317707472
#317707372
C8×D10762
#317705982
#102×D2692
C4×D8×C2692
#3297269