Finite Group Databasebeta

← #46821085

Subgroups — #46821085

Order 34432.

396 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
1#31771208C211yesmaximal, characteristic, complemented
2#31771088C211yesmaximal, characteristic, complemented
3#31770924C211yesmaximal, characteristic, complemented
4#31770916C211yesmaximal, characteristic, complemented
5#31770910C211yesmaximal, characteristic, complemented
6#31770907C211yesmaximal, characteristic, complemented
7#31770803C211yesmaximal, characteristic, complemented
8#31770798C211yesmaximal, characteristic, complemented
9#31770750C211yesmaximal, characteristic, complemented
10#31770717C211yesmaximal, characteristic, complemented
11#31770708C211yesmaximal, characteristic, complemented
12SD16×Dic269C211yesmaximal, characteristic, complemented
13#31770685C211yesmaximal, characteristic, complemented
14#31770663C211yesmaximal, characteristic, complemented
15#449×C269C211yesmaximal, characteristic, complemented
16C2×#16864389C2211yescharacteristic
17C2×#16864387C2211yescharacteristic
18#22575449C2211yescharacteristic
19#22575444C2211yescharacteristic
20#22575437—21no—
21#22575435—21no—
22#22575427C2211yescharacteristic
23#22575425—21no—
24#22575424—21no—
25Q8×Dic269C2211yescharacteristic
26Q8×Dic269C2211yescharacteristic
27D4×Dic269—21no—
28D4×Dic269—21no—
29D4×Dic269C2211yescharacteristic
30D4×Dic269C2211yescharacteristic
31D4×Dic269C2211yescharacteristic
32#22575415C2211yescharacteristic
33#22575412—21no—
34#22575412C2211yescharacteristic
35C2×C4⋊Dic269—21no—
36C2×C4⋊Dic269C2211yescharacteristic
37#22575386C2211yescharacteristic
38#22575386C2211yescharacteristic
39#22575385C2211yescharacteristic
40#22575385C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×#41×C269C2211yescharacteristic
53C2×SD16×C269C2211yescharacteristic
54C2×D8×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59C2×D1076C2311yescharacteristic
60C2×C22⋊D269—21no—
61C2×C22⋊D269—21no—
62C2×C22⋊D269—21no—
63C22×Dic269—21no—
64C22×Dic269—21no—
65C22×Dic269—21no—
66C22×Dic269—21no—
67C2×C4×D269—21no—
68#16864389—22no—
69#16864387—22no—
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C4⋊Dic269—21no—
73C4⋊Dic269—21no—
74C4⋊Dic269—21no—
75C4⋊Dic269—21no—
76C4⋊Dic269D411yescharacteristic
77C4⋊Dic269D411yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82C22⋊Dic269—21no—
83C22⋊Dic269—21no—
84C22⋊Dic269—21no—
85C22⋊Dic269D411yescharacteristic
86C22⋊Dic269D411yescharacteristic
87#16864379—21no—
88#16864379—21no—
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269C2311yescharacteristic
92C4×Dic269C2311yescharacteristic
93#41×C269—22no—
94#41×C269—22no—
95C2×Q8×C269C2311yescharacteristic
96C2×D4×C269—21no—
97C2×D4×C269—21no—
98C2×D4×C269C2311yescharacteristic
99C2×D4×C269C2311yescharacteristic
100C22×C4×C269—21no—
101C22×C4×C269C2311yescharacteristic
102SD16×C269—22no—
103D8×C269—22no—
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C22⋊C4×C269—21no—
108C22×D269—21no—
109D1076—21no—
110D1076—21no—
111C22⋊D269—81no—
112C22⋊D269—81no—
113C22⋊D269—81no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—81no—
118C2×Dic269—81no—
119C2×Dic269—81no—
120C2×Dic269—81no—
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C4×D269—81no—
126#14524130—21no—
127#14524130—21no—
128C23×C269—21no—
129C23×C269—21no—
130C23×C269C2×D411yescharacteristic
131Q8×C269—21no—
132Q8×C269#4112yes—
133D4×C269—24no—
134D4×C269—21no—
135D4×C269—21no—
136D4×C269—21no—
137D4×C269—81no—
138D4×C269#4112yes—
139C2×C4×C269—24no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2411yescharacteristic
146C8×C269—21no—
147C8×C269—21no—
148C22×C269—21no—
149C22×C269—22no—
150C22×C269—21no—
151C22×C269—21no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269C22×D411yescharacteristic
158C2×D269—41no—
159C2×D269—41no—
160C2×D269—41no—
161C4×C269—21no—
162C4×C269—22no—
163C4×C269—41no—
164C4×C269C2×#4111yescharacteristic
165C4×C269C2×#4111yescharacteristic
166Dic269—21no—
167Dic269—21no—
168Dic269—21no—
169Dic269—21no—
170Dic269—41no—
171Dic269—41no—
172Dic269—41no—
173C2×C269—41no—
174C2×C269—42no—
175C2×C269—81no—
176C2×C269#52511yescharacteristic
177C2×C269#57611yescharacteristic
178C2×C269#57711yescharacteristic
179D269—81no—
180C269#311911yescharacteristic, complemented, Sylow
181#3119—2691nomaximal, Sylow
182#540—2691no—
183#520—2691no—
184#481—2691no—
185#480—2691no—
186#479—2691no—
187#478—2691no—
188#460—2691no—
189#459—2691no—
190#449—2691no—
191#449D26911yescharacteristic, complemented
192#442—2691no—
193#440—2691no—
194C4×SD16—2691no—
195C4×D8—2691no—
196#433—2691no—
197C2×#41C2×D26911yescharacteristic
198C2×SD16—2691no—
199C2×SD16C2×D26911yescharacteristic
200C2×D8—2691no—
201C2×D8C2×D26911yescharacteristic
202#127—2691no—
203#125—2691no—
204#123—5381no—
205#123—5381no—
206#121—2691no—
207#121—5381no—
208#121—5381no—
209#121C2×D26911yescharacteristic
210C4×Q8—2691no—
211C4×Q8—2691no—
212C4×D4—2691no—
213C4×D4—2691no—
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—5381no—
217C4×D4—5381no—
218#117—2691no—
219#117—5381no—
220C2×C4⋊C4—2691no—
221C2×C4⋊C4—5381no—
222#107—2691no—
223#107—2691no—
224#106—2691no—
225#106—2691no—
226C4⋊C8—2691no—
227C4⋊C8—2691no—
228#103—2691no—
229#103C2×D26911yescharacteristic
230#102—2691no—
231#102—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235#102C2×D26911yescharacteristic
236C22⋊C8—2691no—
237C22⋊C8C2×D26911yescharacteristic
238#97—2691no—
239C4×C8—2691no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D26911yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—2691no—
246C2×D4—5381no—
247C2×D4—5381no—
248C2×D4—5381no—
249C2×D4C22×D26911yescharacteristic
250C2×D4C22×D26911yescharacteristic
251C22×C4—21no—
252C22×C4—5381no—
253C22×C4—5381no—
254C22×C4—5381no—
255C22×C4—5381no—
256C22×C4—5381no—
257C22×C4C22×D26911yescharacteristic
258SD16—22no—
259SD16—5382no—
260D8—22no—
261D8—5382no—
262C2×C8—2691no—
263C2×C8—2691no—
264C2×C8C22×D26911yescharacteristic
265C2×C8C22×D26911yescharacteristic
266C4⋊C4—2691no—
267C4⋊C4—2691no—
268C4⋊C4—2691no—
269C4⋊C4—2691no—
270C4⋊C4—2691no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4—5381no—
275C4⋊C4—5381no—
276C4⋊C4C22×D26911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2691no—
279C22⋊C4—2691no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C42—2691no—
286C42—2691no—
287C42—5381no—
288C42—5381no—
289C23—21no—
290C23—21no—
291C23—5381no—
292C23D4×D26911yescharacteristic
293Q8—21no—
294Q8#1686440112yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—5381no—
301D4—5381no—
302D4—21521no—
303D4—21521no—
304D4—21521no—
305D4#1686440112yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2691no—
312C2×C4—2691no—
313C2×C4—2691no—
314C2×C4—2691no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—21521no—
319C2×C4—21521no—
320C2×C4—21521no—
321C2×C4—21521no—
322C2×C4—21521no—
323C2×C4D4×D26911yescharacteristic
324C2×C4C23×D26911yescharacteristic
325C8—21no—
326C8—21no—
327C8—5381no—
328C8—5381no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—10761no—
339C22—10761no—
340C22—10761no—
341C22C2×D4×D26911yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—5381no—
346C4—5381no—
347C4—5381no—
348C4—5381no—
349C4—10761no—
350C4—10761no—
351C4—10761no—
352C4C2×#1686440111yescharacteristic
353C4C2×#1686440111yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—21521no—
358C2#3177111111yescharacteristic
359C2#3177140911yescharacteristic
360C2#3177141211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#449×C269C2
socleC22×C269C22×D4
hypercenter#449D269
hypocenterC269#3119
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #31771208C2semidirect
2. #31771088C2semidirect
3. #31770924C2semidirect
4. #31770916C2semidirect
5. #31770910C2semidirect
6. #31770907C2semidirect
7. #31770803C2semidirect
8. #31770798C2semidirect
9. #31770750C2semidirect
10. #31770717C2semidirect
11. #31770708C2semidirect
12. SD16×Dic269C2semidirect
13. #31770685C2semidirect
14. #31770663C2semidirect
15. #449×C269C2semidirect
180. C269#3119semidirect
191. #449D269semidirect

Maximal subgroups

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

subgroupindex
#317712082
#317710882
#317709242
#317709162
#317709102
#317709072
#317708032
#317707982
#317707502
#317707172
#317707082
SD16×Dic2692
#317706852
#317706632
#449×C2692
#3119269