Finite Group Databasebeta

← #46821089

Subgroups — #46821089

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#31771211C211yesmaximal, characteristic, complemented
2#31771084C211yesmaximal, characteristic, complemented
3#31770925C211yesmaximal, characteristic, complemented
4#31770920C211yesmaximal, characteristic, complemented
5#31770909C211yesmaximal, characteristic, complemented
6#31770806C211yesmaximal, characteristic, complemented
7#31770800C211yesmaximal, characteristic, complemented
8#31770751C211yesmaximal, characteristic, complemented
9#31770751C211yesmaximal, characteristic, complemented
10#31770714C211yesmaximal, characteristic, complemented
11#31770704C211yesmaximal, characteristic, complemented
12#31770692C211yesmaximal, characteristic, complemented
13#31770685C211yesmaximal, characteristic, complemented
14#31770665C211yesmaximal, characteristic, complemented
15#478×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×#16864391C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21#22575450C2211yescharacteristic
22#22575438—21no—
23#22575438—21no—
24#22575428—21no—
25#22575428—21no—
26#22575428C2211yescharacteristic
27#22575428C2211yescharacteristic
28C4×Dic538C2211yescharacteristic
29#22575418C2211yescharacteristic
30D4×Dic269C2211yescharacteristic
31#22575415C2211yescharacteristic
32#22575415C2211yescharacteristic
33C4×C22⋊D269—21no—
34#22575413—21no—
35#22575410C2211yescharacteristic
36#22575409—21no—
37C2×#16864381—21no—
38C4⋊C4×D269C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575384C2211yescharacteristic
41C4⋊#14524130C2211yescharacteristic
42#22575376C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575373C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59#16864401—22no—
60#16864401—22no—
61C2×Dic538C2311yescharacteristic
62C2×D1076—21no—
63C2×D1076—21no—
64C2×D1076—21no—
65C2×D1076—21no—
66C2×D1076C2311yescharacteristic
67C2×D1076C2311yescharacteristic
68C2×C22⋊D269—21no—
69C22×Dic269—21no—
70C22×Dic269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269C2311yescharacteristic
75#16864391—22no—
76#16864391—22no—
77#16864387—22no—
78#16864387—22no—
79C2×#14524130C2311yescharacteristic
80C2×#14524130C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381D411yescharacteristic
86#16864381D411yescharacteristic
87C22⋊Dic269—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379D411yescharacteristic
93#16864379D411yescharacteristic
94C4×Dic269—21no—
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—21no—
110C22×D269C2×D411yescharacteristic
111Dic538—21no—
112Dic538#4112yes—
113D1076—21no—
114D1076—21no—
115D1076—21no—
116D1076—21no—
117D1076—81no—
118D1076—81no—
119D1076—81no—
120D1076—81no—
121C22⋊D269—24no—
122C2×Dic269—24no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—81no—
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C4×D269—21no—
130C4×D269—21no—
131C4×D269—81no—
132C4×D269—81no—
133C4×D269—81no—
134#14524130—21no—
135#14524130—21no—
136C23×C269—21no—
137D4×C269—21no—
138D4×C269#4112yes—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—81no—
143C2×C4×C269C2×D411yescharacteristic
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2411yescharacteristic
146C8×C269—21no—
147C8×C269—21no—
148C22×C269—22no—
149C22×C269—41no—
150C22×C269—41no—
151C22×C269C22×D411yescharacteristic
152C2×D269—21no—
153C2×D269—21no—
154C2×D269—21no—
155C2×D269—41no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C2×D269—41no—
160C2×D269—41no—
161C4×C269—21no—
162C4×C269—21no—
163C4×C269—41no—
164C4×C269—41no—
165C4×C269—41no—
166C4×C269C2×#4111yescharacteristic
167C4×C269C2×#4111yescharacteristic
168Dic269—21no—
169Dic269—22no—
170Dic269—21no—
171Dic269—21no—
172Dic269—41no—
173C2×C269—42no—
174C2×C269#52511yescharacteristic
175C2×C269#57611yescharacteristic
176C2×C269#57711yescharacteristic
177D269—41no—
178D269—81no—
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#478D26911yescharacteristic, complemented
188#460—2691no—
189#459—2691no—
190#449—2691no—
191#449—2691no—
192#442—2691no—
193#440—2691no—
194C4×SD16—2691no—
195C4×D8—2691no—
196#433—2691no—
197C2×#41—2691no—
198C2×SD16—2691no—
199C2×SD16—2691no—
200C2×D8—2691no—
201C2×D8—2691no—
202#127—2691no—
203#125C2×D26911yescharacteristic
204#123—5381no—
205#123—5381no—
206#121—2691no—
207#121—2691no—
208#121—5381no—
209#121—5381no—
210C4×Q8—2691no—
211C4×Q8—2691no—
212C4×D4—2691no—
213C4×D4—2691no—
214C4×D4—2691no—
215C4×D4—5381no—
216C4×D4—5381no—
217C4×D4C2×D26911yescharacteristic
218#117—2691no—
219#117—5381no—
220C2×C4⋊C4—2691no—
221C2×C4⋊C4—5381no—
222#107—2691no—
223#107C2×D26911yescharacteristic
224#106—2691no—
225#106C2×D26911yescharacteristic
226C4⋊C8—2691no—
227C4⋊C8C2×D26911yescharacteristic
228#103—2691no—
229#103—2691no—
230#102—2691no—
231#102—2691no—
232#102—2691no—
233#102—2691no—
234#102C2×D26911yescharacteristic
235#102C2×D26911yescharacteristic
236C22⋊C8—2691no—
237C22⋊C8—2691no—
238#97—2691no—
239C4×C8—2691no—
240#41—5382no—
241#41—5382no—
242C2×Q8—2691no—
243C2×D4—2691no—
244C2×D4—2691no—
245C2×D4—5381no—
246C2×D4—5381no—
247C2×D4—5381no—
248C2×D4—5381no—
249C2×D4—5381no—
250C2×D4C22×D26911yescharacteristic
251C22×C4—21no—
252C22×C4—2691no—
253C22×C4—5381no—
254C22×C4—5381no—
255C22×C4—5381no—
256C22×C4—5381no—
257C22×C4—5381no—
258SD16—5382no—
259SD16—5382no—
260D8—5382no—
261D8—5382no—
262C2×C8—2691no—
263C2×C8—2691no—
264C2×C8C22×D26911yescharacteristic
265C2×C8C22×D26911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—2691no—
269C4⋊C4—2691no—
270C4⋊C4—2691no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4C22×D26911yescharacteristic
275C4⋊C4C22×D26911yescharacteristic
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—5381no—
287C42—5381no—
288C42C22×D26911yescharacteristic
289C23—21no—
290C23—2691no—
291C23—5381no—
292C23—5381no—
293Q8—2692no—
294Q8—5381no—
295D4—21no—
296D4—5384no—
297D4—5381no—
298D4—5381no—
299D4—5381no—
300D4—5381no—
301D4—21521no—
302D4—21521no—
303D4—21521no—
304D4—21521no—
305D4#1686440312yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—2691no—
311C2×C4—2691no—
312C2×C4—2691no—
313C2×C4—5384no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—21521no—
319C2×C4—21521no—
320C2×C4—21521no—
321C2×C4—21521no—
322C2×C4D4×D26911yescharacteristic
323C2×C4D4×D26911yescharacteristic
324C2×C4C23×D26911yescharacteristic
325C8—21no—
326C8—21no—
327C8—5381no—
328C8—5381no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—5381no—
333C22—5381no—
334C22—5381no—
335C22—10761no—
336C22—10761no—
337C22—10761no—
338C22—10761no—
339C22—10761no—
340C22—10761no—
341C22C2×D4×D26911yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—5381no—
348C4—5381no—
349C4—5381no—
350C4—5382no—
351C4—10761no—
352C4#41×D26911yescharacteristic
353C4C2×#1686440311yescharacteristic
354C2—42no—
355C2—10761no—
356C2—21521no—
357C2—21521no—
358C2#3177111811yescharacteristic
359C2#3177140911yescharacteristic
360C2#3177141211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#478×C269C2
socleC22×C269C22×D4
hypercenter#478D269
hypocenterC269#3119
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. #31771084C2semidirect
3. #31770925C2semidirect
4. #31770920C2semidirect
5. #31770909C2semidirect
6. #31770806C2semidirect
7. #31770800C2semidirect
8. #31770751C2semidirect
9. #31770751C2semidirect
10. #31770714C2semidirect
11. #31770704C2semidirect
12. #31770692C2semidirect
13. #31770685C2semidirect
14. #31770665C2semidirect
15. #478×C269C2semidirect
180. C269#3119semidirect
187. #478D269semidirect

Maximal subgroups

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

subgroupindex
#317712112
#317710842
#317709252
#317709202
#317709092
#317708062
#317708002
#317707512
#317707142
#317707042
#317706922
#317706852
#317706652
#478×C2692
#3119269