Finite Group Databasebeta

← #46821061

Subgroups — #46821061

Order 34432.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771140C211yesmaximal, characteristic
2C4×Q8×D269C211yesmaximal, characteristic, complemented
3#31770942C211yesmaximal, characteristic, complemented
4#31770925C211yesmaximal, characteristic
5#31770909C211yesmaximal, characteristic, complemented
6#31770828C211yesmaximal, characteristic, complemented
7#31770827C211yesmaximal, characteristic, complemented
8#31770762C211yesmaximal, characteristic, complemented
9#31770745C211yesmaximal, characteristic
10#31770711C211yesmaximal, characteristic, complemented
11#31770709C211yesmaximal, characteristic, complemented
12#31770708C211yesmaximal, characteristic, complemented
13#31770704C211yesmaximal, characteristic, complemented
14#31770661C211yesmaximal, characteristic, complemented
15#479×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269C2211yescharacteristic
17C2×Dic1076C2211yescharacteristic
18C2×#16864392C2211yescharacteristic
19C2×#16864391C2211yescharacteristic
20C2×#16864389C2211yescharacteristic
21#22575448—21no—
22#22575441C2211yescharacteristic
23#22575438—21no—
24#22575433C2211yescharacteristic
25#22575428C2211yescharacteristic
26Q8×Dic269C2211yescharacteristic
27C4×Dic538—21no—
28C4×Dic538C2211yescharacteristic
29#22575418—21no—
30#22575418C2211yescharacteristic
31#22575418C2211yescharacteristic
32#22575415—21no—
33#22575415C2211yescharacteristic
34#22575411—21no—
35C4⋊C4×D269—21no—
36C4⋊C4×D269C2211yescharacteristic
37C42×D269—21no—
38C42×D269C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575384C2211yescharacteristic
41C4⋊#14524130C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575376C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic
51#22575363C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61C2×Dic538C2311yescharacteristic
62Q8×D269—22no—
63Q8×D269—22no—
64C2×D1076—21no—
65C2×D1076C2311yescharacteristic
66C2×C4×D269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269D411yescharacteristic
70C2×C4×D269D411yescharacteristic
71C2×C4×D269C2311yescharacteristic
72Dic1076—22no—
73#16864392—22no—
74#16864391—22no—
75#16864389—22no—
76C2×#14524130C2311yescharacteristic
77C2×#14524130C2311yescharacteristic
78C4⋊Dic269—21no—
79C4⋊Dic269—21no—
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864379—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90C4×Dic269—21no—
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269D411yescharacteristic
95C4×Dic269D411yescharacteristic
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C4⋊C4×C269—21no—
101C4⋊C4×C269—21no—
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C42×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269C2×D411yescharacteristic
110Dic538—24no—
111Dic538—21no—
112Dic538—21no—
113Dic538—21no—
114Dic538#4112yes—
115D1076—21no—
116D1076—21no—
117D1076—42no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C4×D269—24no—
125C4×D269—22no—
126C4×D269—21no—
127C4×D269—21no—
128C4×D269—41no—
129C4×D269—42no—
130C4×D269—42no—
131#14524130—21no—
132#14524130—21no—
133Q8×C269—21no—
134Q8×C269#4112yes—
135C2×C4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2411yescharacteristic
142C8×C269—21no—
143C8×C269—21no—
144C22×C269C22×D411yescharacteristic
145C2×D269—21no—
146C2×D269—21no—
147C2×D269—41no—
148C2×D269—41no—
149C2×D269—41no—
150C2×D269#13712yes—
151C4×C269—22no—
152C4×C269—21no—
153C4×C269—21no—
154C4×C269—41no—
155C4×C269—41no—
156C4×C269—41no—
157C4×C269C2×#4111yescharacteristic
158C4×C269C2×#4111yescharacteristic
159Dic269—22no—
160Dic269—21no—
161Dic269—21no—
162Dic269—21no—
163Dic269—41no—
164Dic269—41no—
165C2×C269#52511yescharacteristic
166C2×C269C2×#13711yescharacteristic
167C2×C269#57511yescharacteristic
168D269—22no—
169D269—81no—
170C269#311711yescharacteristic, complemented, Sylow
171#3117—2691nomaximal, Sylow
172#529—2691no—
173C2×C4×Q8—2691no—
174#484—2691no—
175#481—2691no—
176#479—2691no—
177#479D26911yescharacteristic, complemented
178#464—2691no—
179#464—2691no—
180#451—2691no—
181#448—2691no—
182#441—2691no—
183#441—2691no—
184#440—2691no—
185#440—2691no—
186#432—2691no—
187C22×Q8—2691no—
188C2×Q16—2691no—
189C2×Q16—2691no—
190C2×SD16—2691no—
191C2×SD16—2691no—
192#126—5381no—
193#125C2×D26911yescharacteristic
194#124—2691no—
195#123—5381no—
196C22⋊Q8—2691no—
197#121—2691no—
198C4×Q8—2691no—
199C4×Q8—2691no—
200C4×Q8—2691no—
201C4×Q8—2691no—
202C4×Q8—5381no—
203C4×Q8—5381no—
204C4×Q8C2×D26911yescharacteristic
205C4×D4—2691no—
206C4×D4—5381no—
207#117—5381no—
208C2×C4⋊C4—2691no—
209C2×C4⋊C4—5381no—
210C2×C42—2691no—
211C2×C42—5381no—
212#107—2691no—
213#107C2×D26911yescharacteristic
214#106—2691no—
215#106C2×D26911yescharacteristic
216C4⋊C8—2691no—
217C4⋊C8C2×D26911yescharacteristic
218#103—2691no—
219#103—2691no—
220#103—2691no—
221#103—2691no—
222#103C2×D26911yescharacteristic
223#103C2×D26911yescharacteristic
224#102—2691no—
225#102—2691no—
226C22⋊C8—2691no—
227C22⋊C8—2691no—
228#97—2691no—
229#97—2691no—
230C2×Q8—2691no—
231C2×Q8—2691no—
232C2×Q8—5381no—
233C2×Q8—5382no—
234C2×Q8—5382no—
235C2×Q8C22×D26911yescharacteristic
236C2×D4—2691no—
237C2×D4—5381no—
238C22×C4—2691no—
239C22×C4—2691no—
240C22×C4—2691no—
241C22×C4—5381no—
242C22×C4—5381no—
243C22×C4—5381no—
244Q16—5382no—
245Q16—5382no—
246SD16—5382no—
247SD16—5382no—
248C2×C8—2691no—
249C2×C8—2691no—
250C2×C8C22×D26911yescharacteristic
251C2×C8C22×D26911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—2691no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4—5381no—
261C4⋊C4—5381no—
262C4⋊C4C22×D26911yescharacteristic
263C4⋊C4C22×D26911yescharacteristic
264C4⋊C4C22×D26911yescharacteristic
265C22⋊C4—5381no—
266C22⋊C4—5381no—
267C22⋊C4—5381no—
268C22⋊C4—5381no—
269C22⋊C4—5381no—
270C42—21no—
271C42—2691no—
272C42—2691no—
273C42—2691no—
274C42—5381no—
275C42—5381no—
276C42—5381no—
277C42—5381no—
278C42C22×D26911yescharacteristic
279C23—2691no—
280C23—5381no—
281Q8—21no—
282Q8—2692no—
283Q8—5384no—
284Q8—5381no—
285Q8—5381no—
286Q8—5381no—
287Q8#1686440312yes—
288D4—5381no—
289D4—5381no—
290D4—10762no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—2691no—
296C2×C4—2691no—
297C2×C4—2691no—
298C2×C4—5382no—
299C2×C4—5384no—
300C2×C4—5381no—
301C2×C4—5381no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—10761no—
306C2×C4—10762no—
307C2×C4—10762no—
308C2×C4D4×D26911yescharacteristic
309C2×C4D4×D26911yescharacteristic
310C2×C4C23×D26911yescharacteristic
311C8—21no—
312C8—21no—
313C8—5381no—
314C8—5381no—
315C22—2692no—
316C22—5381no—
317C22—5381no—
318C22—10761no—
319C22—10761no—
320C22—10761no—
321C22C2×D4×D26911yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—5381no—
329C4—5381no—
330C4—5381no—
331C4—5382no—
332C4—10761no—
333C4—10761no—
334C4#41×D26911yescharacteristic
335C4C2×#1686440311yescharacteristic
336C2—5382no—
337C2—21521no—
338C2#3177111811yescharacteristic
339C2#137×D26911yescharacteristic
340C2#3177140211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#479×C269C2
socleC22×C269C22×D4
prime radical#22575428C22
hypercenter#479D269
hypocenterC269#3117
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D269C2semidirect
3. #31770942C2semidirect
5. #31770909C2semidirect
6. #31770828C2semidirect
7. #31770827C2semidirect
8. #31770762C2semidirect
10. #31770711C2semidirect
11. #31770709C2semidirect
12. #31770708C2semidirect
13. #31770704C2semidirect
14. #31770661C2semidirect
15. #479×C269C2semidirect
170. C269#3117semidirect
177. #479D269semidirect

Maximal subgroups

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

subgroupindex
#317711402
C4×Q8×D2692
#317709422
#317709252
#317709092
#317708282
#317708272
#317707622
#317707452
#317707112
#317707092
#317707082
#317707042
#317706612
#479×C2692
#3117269