Finite Group Databasebeta

← #46821130

Subgroups — #46821130

Order 34432.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771211C211yesmaximal, characteristic, complemented
2#31771077C211yesmaximal, characteristic, complemented
3#31770932C211yesmaximal, characteristic, complemented
4#31770931C211yesmaximal, characteristic, complemented
5#31770902C211yesmaximal, characteristic, complemented
6#31770801C211yesmaximal, characteristic, complemented
7#31770800C211yesmaximal, characteristic, complemented
8#31770740C211yesmaximal, characteristic, complemented
9#31770740C211yesmaximal, characteristic, complemented
10#31770716C211yesmaximal, characteristic, complemented
11#31770714C211yesmaximal, characteristic, complemented
12#31770687C211yesmaximal, characteristic, complemented
13#31770685C211yesmaximal, characteristic, complemented
14#31770665C211yesmaximal, characteristic, complemented
15#478×C269C211yesmaximal, characteristic, complemented
16C2×D4×D269C2211yescharacteristic
17C2×D2152C2211yescharacteristic
18C2×D2152C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21#22575450C2211yescharacteristic, complemented
22#22575438—21no—
23#22575438—21no—
24#22575428—21no—
25#22575428—21no—
26#22575428C2211yescharacteristic
27#22575428C2211yescharacteristic
28C4×D1076C2211yescharacteristic
29D4×Dic269C2211yescharacteristic
30#22575415C2211yescharacteristic
31#22575415C2211yescharacteristic, complemented
32#22575415C2211yescharacteristic, complemented
33C4×C22⋊D269—21no—
34#22575413—21no—
35#22575411C2211yescharacteristic
36#22575410C2211yescharacteristic
37C2×#16864379—21no—
38C22⋊C4×D269—21no—
39#22575386C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41C4⋊#14524130C2211yescharacteristic, complemented
42#22575375C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic, complemented
44#22575373C2211yescharacteristic
45#22575373C2211yescharacteristic
46#22575373C2211yescharacteristic, complemented
47#22575373C2211yescharacteristic, complemented
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52#125×C269C2211yescharacteristic, complemented
53C4×D4×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56C4⋊C8×C269C2211yescharacteristic, complemented
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C23×D269—21no—
60C2×D1076—21no—
61C2×D1076—21no—
62C2×D1076—21no—
63C2×D1076—21no—
64C2×D1076C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68D4×D269—22no—
69D4×D269—22no—
70C22×Dic269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269C2311yescharacteristic
76D2152—22no—
77D2152—22no—
78#16864387—22no—
79#16864387—22no—
80C2×#14524130C2311yescharacteristic
81C2×#14524130C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381D411yescharacteristic
84#16864381D411yescharacteristic
85C22⋊Dic269—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
94#16864379D411yescharacteristic
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97C2×D4×C269C2311yescharacteristic
98C22×C4×C269—21no—
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C4⋊C4×C269—21no—
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269—24no—
110C22×D269—21no—
111C22×D269—21no—
112C22×D269—81no—
113C22×D269—81no—
114C22×D269C2×D411yescharacteristic
115D1076—21no—
116D1076—21no—
117D1076—21no—
118D1076—21no—
119D1076—21no—
120D1076—81no—
121D1076—81no—
122D1076—81no—
123D1076—81no—
124D1076#4112yes—
125C22⋊D269—24no—
126C2×Dic269—21no—
127C2×Dic269—81no—
128C2×Dic269C2×D411yescharacteristic
129C2×Dic269C2×D411yescharacteristic
130C2×Dic269C2×D411yescharacteristic
131C4×D269—21no—
132C4×D269—21no—
133C4×D269—81no—
134C4×D269—81no—
135C4×D269—81no—
136C4×D269—81no—
137#14524130—21no—
138#14524130—21no—
139C23×C269—21no—
140D4×C269—21no—
141D4×C269#4112yes—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—81no—
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2411yescharacteristic
149C8×C269—21no—
150C8×C269—21no—
151C22×C269—22no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269C22×D411yescharacteristic
155C2×D269—21no—
156C2×D269—22no—
157C2×D269—21no—
158C2×D269—21no—
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—41no—
162C2×D269—41no—
163C2×D269—41no—
164C2×D269—41no—
165C2×D269—41no—
166C2×D269—41no—
167C2×D269—84no—
168C4×C269—21no—
169C4×C269—21no—
170C4×C269—41no—
171C4×C269—41no—
172C4×C269—41no—
173C4×C269C2×#4111yescharacteristic
174C4×C269C2×#4111yescharacteristic
175Dic269—21no—
176Dic269—21no—
177Dic269—21no—
178Dic269—41no—
179C2×C269—42no—
180C2×C269#52511yescharacteristic
181C2×C269#57611yescharacteristic
182C2×C269#57611yescharacteristic
183D269—41no—
184D269—42no—
185D269—81no—
186D269—81no—
187C269#312211yescharacteristic, complemented, Sylow
188#3122—2691nomaximal, Sylow
189#540—2691no—
190#518—2691no—
191#482—2691no—
192#482—2691no—
193#478—2691no—
194#478D26911yescharacteristic, complemented
195#459—2691no—
196#459—2691no—
197#447—2691no—
198#447—2691no—
199#442—2691no—
200#442—2691no—
201C4×D8—2691no—
202C4×D8—2691no—
203#433—2691no—
204C22×D4—2691no—
205C2×D8—2691no—
206C2×D8—2691no—
207C2×D8—2691no—
208C2×D8—2691no—
209#127—2691no—
210#125C2×D26911yescharacteristic, complemented
211#123—5381no—
212#123—5381no—
213#121—2691no—
214#121—2691no—
215#121—5381no—
216#121—5381no—
217C4×D4—2691no—
218C4×D4—2691no—
219C4×D4—2691no—
220C4×D4—2691no—
221C4×D4—2691no—
222C4×D4—5381no—
223C4×D4—5381no—
224C4×D4C2×D26911yescharacteristic
225#117—2691no—
226#117—2691no—
227C2×C22⋊C4—5381no—
228C2×C22⋊C4—5381no—
229#107—2691no—
230#107C2×D26911yescharacteristic, complemented
231#106—2691no—
232#106C2×D26911yescharacteristic, complemented
233C4⋊C8—2691no—
234C4⋊C8C2×D26911yescharacteristic, complemented
235#102—2691no—
236#102—2691no—
237#102—2691no—
238#102—2691no—
239#102—2691no—
240#102—2691no—
241#102C2×D26911yescharacteristic
242#102C2×D26911yescharacteristic
243C22⋊C8—2691no—
244C22⋊C8—2691no—
245#97—2691no—
246C4×C8—2691no—
247C24—5381no—
248C2×D4—2691no—
249C2×D4—2691no—
250C2×D4—2691no—
251C2×D4—5381no—
252C2×D4—5381no—
253C2×D4—5381no—
254C2×D4—5382no—
255C2×D4—5382no—
256C2×D4—5381no—
257C2×D4—5381no—
258C2×D4C22×D26911yescharacteristic
259C22×C4—21no—
260C22×C4—2691no—
261C22×C4—5381no—
262C22×C4—5381no—
263C22×C4—5381no—
264C22×C4—5381no—
265C22×C4—5381no—
266D8—5382no—
267D8—5382no—
268D8—5382no—
269D8—5382no—
270C2×C8—2691no—
271C2×C8—2691no—
272C2×C8C22×D26911yescharacteristic
273C2×C8C22×D26911yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—2691no—
277C4⋊C4—2691no—
278C4⋊C4—2691no—
279C4⋊C4C22×D26911yescharacteristic
280C4⋊C4C22×D26911yescharacteristic
281C4⋊C4C22×D26911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—2691no—
284C22⋊C4—2691no—
285C22⋊C4—5381no—
286C22⋊C4—5381no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4—5381no—
292C22⋊C4—5381no—
293C42—2691no—
294C42—5381no—
295C42C22×D26911yescharacteristic
296C23—21no—
297C23—2691no—
298C23—5384no—
299C23—5381no—
300C23—5381no—
301C23—5381no—
302C23—21521no—
303C23—21521no—
304D4—21no—
305D4—2692no—
306D4—5384no—
307D4—5381no—
308D4—5381no—
309D4—5381no—
310D4—5381no—
311D4—5381no—
312D4—21521no—
313D4—21521no—
314D4—21521no—
315D4—21521no—
316D4#1686440312yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—2691no—
322C2×C4—2691no—
323C2×C4—2691no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—21521no—
328C2×C4—21521no—
329C2×C4—21521no—
330C2×C4—21521no—
331C2×C4—21521no—
332C2×C4D4×D26911yescharacteristic
333C2×C4D4×D26911yescharacteristic
334C2×C4C23×D26911yescharacteristic
335C8—21no—
336C8—21no—
337C8—5381no—
338C8—5381no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—5381no—
343C22—5381no—
344C22—5381no—
345C22—5382no—
346C22—10761no—
347C22—10761no—
348C22—10761no—
349C22—10761no—
350C22—10761no—
351C22—10761no—
352C22—10761no—
353C22—10761no—
354C22—21524no—
355C22C2×D4×D26911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—5381no—
362C4—5381no—
363C4—5381no—
364C4—10761no—
365C4#41×D26911yescharacteristic
366C4C2×#1686440311yescharacteristic
367C2—42no—
368C2—10761no—
369C2—10762no—
370C2—21521no—
371C2—21521no—
372C2#3177111811yescharacteristic
373C2#3177140711yescharacteristic
374C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#478×C269C2
socleC22×C269C22×D4
hypercenter#478D269
hypocenterC269#3122
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #31771211C2semidirect
2. #31771077C2semidirect
3. #31770932C2semidirect
4. #31770931C2semidirect
5. #31770902C2semidirect
6. #31770801C2semidirect
7. #31770800C2semidirect
8. #31770740C2semidirect
9. #31770740C2semidirect
10. #31770716C2semidirect
11. #31770714C2semidirect
12. #31770687C2semidirect
13. #31770685C2semidirect
14. #31770665C2semidirect
15. #478×C269C2semidirect
21. #22575450C22semidirect
31. #22575415C22semidirect
32. #22575415C22semidirect
39. #22575386C22semidirect
40. #22575384C22semidirect
41. C4⋊#14524130C22semidirect
42. #22575375C22semidirect
43. #22575375C22semidirect
46. #22575373C22semidirect
47. #22575373C22semidirect
50. #22575363C22semidirect
51. C8×Dic269C22semidirect
52. #125×C269C22semidirect
54. #107×C269C22semidirect
55. #106×C269C22semidirect
56. C4⋊C8×C269C22semidirect
187. C269#3122semidirect
194. #478D269semidirect
210. #125C2×D269semidirect
230. #107C2×D269semidirect
232. #106C2×D269semidirect
234. C4⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712112
#317710772
#317709322
#317709312
#317709022
#317708012
#317708002
#317707402
#317707162
#317707142
#317706872
#317706852
#317706652
#478×C2692
#3122269