Finite Group Databasebeta

← #46821169

Subgroups — #46821169

Order 34432.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771229C211yesmaximal, characteristic, complemented
2#31771087C211yesmaximal, characteristic, complemented
3#31770937C211yesmaximal, characteristic, complemented
4#31770925C211yesmaximal, characteristic, complemented
5#31770892C211yesmaximal, characteristic, complemented
6#31770827C211yesmaximal, characteristic, complemented
7#31770821C211yesmaximal, characteristic, complemented
8#31770770C211yesmaximal, characteristic, complemented
9#31770753C211yesmaximal, characteristic
10#31770716C211yesmaximal, characteristic, complemented
11#31770709C211yesmaximal, characteristic, complemented
12#31770692C211yesmaximal, characteristic, complemented
13#31770690C211yesmaximal, characteristic, complemented
14#31770665C211yesmaximal, characteristic, complemented
15#475×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864392C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×#16864389C2211yescharacteristic
20C2×D2152C2211yescharacteristic
21#22575448—21no—
22#22575442—21no—
23#22575441C2211yescharacteristic
24#22575438—21no—
25#22575433C2211yescharacteristic
26#22575429—21no—
27#22575428C2211yescharacteristic
28Q8×Dic269C2211yescharacteristic
29#22575418C2211yescharacteristic
30C4×D1076—21no—
31C4×D1076C2211yescharacteristic
32#22575415—21no—
33#22575415C2211yescharacteristic
34#22575415C2211yescharacteristic
35#22575410—21no—
36#22575410C2211yescharacteristic
37C4⋊C4×D269—21no—
38C4⋊C4×D269C2211yescharacteristic
39#22575384C2211yescharacteristic
40#22575384C2211yescharacteristic
41C4⋊#14524130C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575373C2211yescharacteristic
46#22575373C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C4⋊Q8×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54#106×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59#16864403—22no—
60#16864403—22no—
61C2×Dic538C2311yescharacteristic
62C2×D1076—21no—
63C2×D1076—21no—
64C2×D1076C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×C4×D269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269C2311yescharacteristic
72#16864392—22no—
73#16864391—22no—
74#16864389—22no—
75D2152—22no—
76C2×#14524130C2311yescharacteristic
77C2×#14524130C2311yescharacteristic
78C4⋊Dic269—21no—
79C4⋊Dic269—21no—
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84#16864381D411yescharacteristic
85#16864379—21no—
86#16864379—21no—
87#16864379—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×Q8×C269—21no—
98C2×Q8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
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×D269—21no—
110C22×D269C2×D411yescharacteristic
111Dic538—21no—
112Dic538—21no—
113D1076—24no—
114D1076—21no—
115D1076—21no—
116D1076—21no—
117D1076—81no—
118D1076#4112yes—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C4×D269—24no—
125C4×D269—21no—
126C4×D269—21no—
127C4×D269—81no—
128C4×D269—81no—
129C4×D269—81no—
130C4×D269—81no—
131#14524130—21no—
132#14524130—21no—
133Q8×C269—21no—
134Q8×C269—81no—
135Q8×C269#4112yes—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2×D411yescharacteristic
142C2×C4×C269C2411yescharacteristic
143C8×C269—21no—
144C8×C269—21no—
145C22×C269C22×D411yescharacteristic
146C2×D269—21no—
147C2×D269—22no—
148C2×D269—21no—
149C2×D269—21no—
150C2×D269—41no—
151C2×D269—41no—
152C2×D269—41no—
153C2×D269—41no—
154C2×D269—41no—
155C4×C269—22no—
156C4×C269—21no—
157C4×C269—21no—
158C4×C269—41no—
159C4×C269—41no—
160C4×C269—41no—
161C4×C269C2×#4111yescharacteristic
162C4×C269C2×#4111yescharacteristic
163Dic269—21no—
164Dic269—21no—
165Dic269—21no—
166Dic269—41no—
167Dic269—41no—
168C2×C269#52511yescharacteristic
169C2×C269#57711yescharacteristic
170C2×C269#57711yescharacteristic
171D269—41no—
172D269—42no—
173D269—81no—
174C269#312511yescharacteristic, complemented, Sylow
175#3125—2691nomaximal, Sylow
176#542—2691no—
177#520—2691no—
178#483—2691no—
179#481—2691no—
180#476—2691no—
181#475D26911yescharacteristic, complemented
182#464—2691no—
183#463—2691no—
184#452—2691no—
185#449—2691no—
186#442—2691no—
187#441—2691no—
188C4×SD16—2691no—
189C4×SD16—2691no—
190#433—2691no—
191C2×#41—2691no—
192C2×Q16—2691no—
193C2×SD16—2691no—
194C2×SD16—2691no—
195C2×D8—2691no—
196C4⋊Q8C2×D26911yescharacteristic
197#126—5381no—
198#124—2691no—
199#124—5381no—
200#123—5381no—
201C22⋊Q8—2691no—
202C22⋊Q8—5381no—
203#121—2691no—
204C4×Q8—2691no—
205C4×Q8—2691no—
206C4×Q8C2×D26911yescharacteristic
207C4×D4—2691no—
208C4×D4—2691no—
209C4×D4—2691no—
210C4×D4—5381no—
211C4×D4—5381no—
212#117—2691no—
213#117—5381no—
214C2×C4⋊C4—2691no—
215C2×C4⋊C4—5381no—
216#106—2691no—
217#106—2691no—
218#106C2×D26911yescharacteristic
219#106C2×D26911yescharacteristic
220C4⋊C8—2691no—
221C4⋊C8C2×D26911yescharacteristic
222#103—2691no—
223#103—2691no—
224#103C2×D26911yescharacteristic
225#103C2×D26911yescharacteristic
226#102—2691no—
227#102—2691no—
228#102—2691no—
229#102—2691no—
230C22⋊C8—2691no—
231C22⋊C8—2691no—
232#97—2691no—
233C4×C8—2691no—
234#41—5382no—
235#41—5382no—
236C2×Q8—21no—
237C2×Q8—2691no—
238C2×Q8C22×D26911yescharacteristic
239C2×D4—2691no—
240C2×D4—2691no—
241C2×D4—5381no—
242C2×D4—5381no—
243C22×C4—2691no—
244C22×C4—5381no—
245C22×C4—5381no—
246C22×C4—5381no—
247C22×C4—5381no—
248C22×C4—5381no—
249Q16—5382no—
250SD16—5382no—
251SD16—5382no—
252D8—5382no—
253C2×C8—2691no—
254C2×C8—2691no—
255C2×C8C22×D26911yescharacteristic
256C2×C8C22×D26911yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—2691no—
260C4⋊C4—2691no—
261C4⋊C4—2691no—
262C4⋊C4—5381no—
263C4⋊C4—5381no—
264C4⋊C4—5381no—
265C4⋊C4—5381no—
266C4⋊C4C22×D26911yescharacteristic
267C4⋊C4C22×D26911yescharacteristic
268C4⋊C4C22×D26911yescharacteristic
269C22⋊C4—2691no—
270C22⋊C4—2691no—
271C22⋊C4—5381no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C22⋊C4—5381no—
277C22⋊C4—5381no—
278C42—21no—
279C42—2691no—
280C42—5381no—
281C42—5381no—
282C42C22×D26911yescharacteristic
283C23—2691no—
284C23—5381no—
285C23—5381no—
286Q8—21no—
287Q8—81no—
288Q8—5381no—
289Q8—5381no—
290Q8#1686440312yes—
291D4—2692no—
292D4—5384no—
293D4—5381no—
294D4—5381no—
295D4—5381no—
296D4—21521no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2691no—
302C2×C4—2691no—
303C2×C4—2691no—
304C2×C4—5384no—
305C2×C4—5381no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4—5381no—
309C2×C4—21521no—
310C2×C4—21521no—
311C2×C4—21521no—
312C2×C4—21521no—
313C2×C4D4×D26911yescharacteristic
314C2×C4D4×D26911yescharacteristic
315C2×C4C23×D26911yescharacteristic
316C8—21no—
317C8—21no—
318C8—5381no—
319C8—5381no—
320C22—5381no—
321C22—5381no—
322C22—5382no—
323C22—5381no—
324C22—10761no—
325C22—10761no—
326C22—10761no—
327C22—10761no—
328C22—10761no—
329C22C2×D4×D26911yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—5381no—
337C4—5381no—
338C4—5381no—
339C4—10761no—
340C4—10761no—
341C4#41×D26911yescharacteristic
342C4C2×#1686440311yescharacteristic
343C2—10761no—
344C2—10762no—
345C2—21521no—
346C2#3177111811yescharacteristic
347C2#3177141111yescharacteristic
348C2#3177141411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#475×C269C2
socleC22×C269C22×D4
prime radical#31770753C2
hypercenter#475D269
hypocenterC269#3125
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #31771229C2semidirect
2. #31771087C2semidirect
3. #31770937C2semidirect
4. #31770925C2semidirect
5. #31770892C2semidirect
6. #31770827C2semidirect
7. #31770821C2semidirect
8. #31770770C2semidirect
10. #31770716C2semidirect
11. #31770709C2semidirect
12. #31770692C2semidirect
13. #31770690C2semidirect
14. #31770665C2semidirect
15. #475×C269C2semidirect
174. C269#3125semidirect
181. #475D269semidirect

Maximal subgroups

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

subgroupindex
#317712292
#317710872
#317709372
#317709252
#317708922
#317708272
#317708212
#317707702
#317707532
#317707162
#317707092
#317706922
#317706902
#317706652
#475×C2692
#3125269