Finite Group Databasebeta

← #34110337

Subgroups — #34110337

Order 20096.

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#23757878C211yesmaximal, characteristic, complemented
2#23757753C211yesmaximal, characteristic, complemented
3#23757592C211yesmaximal, characteristic, complemented
4#23757587C211yesmaximal, characteristic, complemented
5#23757581C211yesmaximal, characteristic, complemented
6#23757574C211yesmaximal, characteristic, complemented
7#23757474C211yesmaximal, characteristic, complemented
8#23757469C211yesmaximal, characteristic, complemented
9#23757420C211yesmaximal, characteristic, complemented
10#23757420C211yesmaximal, characteristic, complemented
11#23757386C211yesmaximal, characteristic, complemented
12#23757375C211yesmaximal, characteristic, complemented
13C4×#14578943C211yesmaximal, characteristic, complemented
14C4×D1256C211yesmaximal, characteristic, complemented
15#433×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578943C2211yescharacteristic
18C2×#14578943C2211yescharacteristic
19C2×D1256C2211yescharacteristic
20C2×D1256C2211yescharacteristic
21#19097768C2211yescharacteristic
22#19097763C2211yescharacteristic
23#19097756—21no—
24#19097756—21no—
25#19097745C2211yescharacteristic
26#19097745C2211yescharacteristic
27#19097744—21no—
28#19097744—21no—
29C4×Dic314C2211yescharacteristic
30C4×Dic314C2211yescharacteristic
31C4×D628C2211yescharacteristic
32C4×D628C2211yescharacteristic
33C4×D628C2211yescharacteristic
34C4×D628C2211yescharacteristic
35#19097731—21no—
36#19097731—21no—
37#19097729—21no—
38C2×C4⋊Dic157C2211yescharacteristic
39C4⋊C4×D157—21no—
40#19097705C2211yescharacteristic
41#19097705C2211yescharacteristic
42#19097703C2211yescharacteristic
43#19097703C2211yescharacteristic
44#19097696C2211yescharacteristic
45#19097696C2211yescharacteristic
46#19097693C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097693C2211yescharacteristic
49#19097693C2211yescharacteristic
50#19097693C2211yescharacteristic
51#19097693C2211yescharacteristic
52#117×C157C2211yescharacteristic
53C4⋊C8×C157C2211yescharacteristic
54C4⋊C8×C157C2211yescharacteristic
55C22⋊C8×C157C2211yescharacteristic
56C22⋊C8×C157C2211yescharacteristic
57#97×C157C2211yescharacteristic
58C4×C8×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—22no—
61C2×Dic314C2311yescharacteristic
62C2×D628—21no—
63C2×D628—21no—
64C2×D628C2311yescharacteristic
65C2×D628C2311yescharacteristic
66C2×D628C2311yescharacteristic
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C22×Dic157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157—21no—
76#14578943—22no—
77#14578943—22no—
78D1256—22no—
79D1256—22no—
80C4⋊Dic157—21no—
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83C4⋊Dic157C2311yescharacteristic
84C4⋊Dic157C2311yescharacteristic
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88#14578933—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95C4×Dic157—21no—
96C4×Dic157—21no—
97C22×C4×C157C2311yescharacteristic
98C2×C8×C157C2311yescharacteristic
99C2×C8×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C4⋊C4×C157D411yescharacteristic
103C4⋊C4×C157D411yescharacteristic
104C22⋊C4×C157D411yescharacteristic
105C22⋊C4×C157D411yescharacteristic
106C42×C157C2311yescharacteristic
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—21no—
110C22×D157—21no—
111Dic314—21no—
112Dic314#4112yes—
113D628—21no—
114D628—21no—
115D628—21no—
116D628—21no—
117D628—21no—
118D628—81no—
119D628—81no—
120D628#4112yes—
121C22⋊D157—24no—
122C22⋊D157—81no—
123C22⋊D157—81no—
124C2×Dic157—21no—
125C2×Dic157—21no—
126C2×Dic157—21no—
127C2×Dic157—21no—
128C2×Dic157—21no—
129C2×Dic157—81no—
130C4×D157—24no—
131C4×D157—81no—
132C4×D157—81no—
133C4×D157—81no—
134C4×D157—81no—
135C23×C157C2×D411yescharacteristic
136C2×C4×C157—21no—
137C2×C4×C157—21no—
138C2×C4×C157C2×D411yescharacteristic
139C2×C4×C157C2×D411yescharacteristic
140C2×C4×C157C2×D411yescharacteristic
141C2×C4×C157C2×D411yescharacteristic
142C2×C4×C157C2×D411yescharacteristic
143C2×C4×C157C2411yescharacteristic
144C8×C157—21no—
145C8×C157—21no—
146C8×C157—21no—
147C8×C157—21no—
148C22×C157—21no—
149C22×C157—21no—
150C22×C157—21no—
151C22×C157C22×D411yescharacteristic
152C2×D157—22no—
153C2×D157—41no—
154C2×D157—41no—
155C2×D157—41no—
156C2×D157—41no—
157C2×D157—41no—
158C2×D157—41no—
159C2×D157—41no—
160C2×D157—41no—
161C4×C157—21no—
162C4×C157—21no—
163C4×C157—21no—
164C4×C157—21no—
165C4×C157—21no—
166C4×C157C2×#4111yescharacteristic
167C4×C157C2×#4111yescharacteristic
168Dic157—22no—
169Dic157—41no—
170Dic157—41no—
171Dic157—41no—
172Dic157—41no—
173C2×C157—41no—
174C2×C157#52511yescharacteristic
175C2×C157#57611yescharacteristic
176C2×C157#57711yescharacteristic
177D157—42no—
178D157—81no—
179D157—81no—
180C157#311911yescharacteristic, complemented, Sylow
181#3119—1571nomaximal, Sylow
182#540—1571no—
183#520—1571no—
184#481—1571no—
185#480—1571no—
186#479—1571no—
187#478—1571no—
188#460—1571no—
189#459—1571no—
190#449—1571no—
191#449—1571no—
192#442—1571no—
193#440—1571no—
194C4×SD16—1571no—
195C4×D8—1571no—
196#433D15711yescharacteristic, complemented
197C2×#41—1571no—
198C2×SD16—1571no—
199C2×SD16—1571no—
200C2×D8—1571no—
201C2×D8—1571no—
202#127—1571no—
203#125—1571no—
204#123—3141no—
205#123—3141no—
206#121—3141no—
207#121—3141no—
208#121—1571no—
209#121—1571no—
210C4×Q8—1571no—
211C4×Q8—1571no—
212C4×D4—3141no—
213C4×D4—3141no—
214C4×D4—1571no—
215C4×D4—1571no—
216C4×D4—1571no—
217C4×D4—1571no—
218#117—3141no—
219#117C2×D15711yescharacteristic
220C2×C4⋊C4—3141no—
221C2×C4⋊C4—1571no—
222#107—1571no—
223#107—1571no—
224#106—1571no—
225#106—1571no—
226C4⋊C8C2×D15711yescharacteristic
227C4⋊C8C2×D15711yescharacteristic
228#103—1571no—
229#103—1571no—
230#102—1571no—
231#102—1571no—
232#102—1571no—
233#102—1571no—
234#102—1571no—
235#102—1571no—
236C22⋊C8C2×D15711yescharacteristic
237C22⋊C8C2×D15711yescharacteristic
238#97C2×D15711yescharacteristic
239C4×C8C2×D15711yescharacteristic
240#41—3142no—
241#41—3142no—
242C2×Q8—1571no—
243C2×D4—3141no—
244C2×D4—3141no—
245C2×D4—3141no—
246C2×D4—3141no—
247C2×D4—3141no—
248C2×D4—1571no—
249C2×D4—1571no—
250C2×D4—1571no—
251C22×C4—3141no—
252C22×C4—3141no—
253C22×C4—3141no—
254C22×C4—3141no—
255C22×C4—3141no—
256C22×C4—3141no—
257C22×C4C22×D15711yescharacteristic
258SD16—3142no—
259SD16—3142no—
260D8—3142no—
261D8—3142no—
262C2×C8C22×D15711yescharacteristic
263C2×C8C22×D15711yescharacteristic
264C2×C8C22×D15711yescharacteristic
265C2×C8C22×D15711yescharacteristic
266C4⋊C4—3141no—
267C4⋊C4—3141no—
268C4⋊C4—3141no—
269C4⋊C4—3141no—
270C4⋊C4—3141no—
271C4⋊C4—1571no—
272C4⋊C4—1571no—
273C4⋊C4—1571no—
274C4⋊C4—1571no—
275C4⋊C4D62811yescharacteristic
276C4⋊C4D62811yescharacteristic
277C22⋊C4—3141no—
278C22⋊C4—3141no—
279C22⋊C4—3141no—
280C22⋊C4—3141no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C22⋊C4D62811yescharacteristic
284C22⋊C4D62811yescharacteristic
285C42—3141no—
286C42—3141no—
287C42C22×D15711yescharacteristic
288C42C22×D15711yescharacteristic
289C23—3141no—
290C23—3141no—
291C23—3141no—
292C23C2×D62811yescharacteristic
293Q8—3141no—
294Q8—1572no—
295D4—3144no—
296D4—3141no—
297D4—3141no—
298D4—3141no—
299D4—3141no—
300D4—3141no—
301D4—1572no—
302D4—12561no—
303D4—12561no—
304D4—12561no—
305D4—12561no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—3144no—
309C2×C4—3141no—
310C2×C4—3141no—
311C2×C4—3141no—
312C2×C4—3141no—
313C2×C4—3141no—
314C2×C4—12561no—
315C2×C4—12561no—
316C2×C4—12561no—
317C2×C4—12561no—
318C2×C4—12561no—
319C2×C4C2×D62811yescharacteristic
320C2×C4C2×D62811yescharacteristic
321C2×C4C2×D62811yescharacteristic
322C2×C4C2×D62811yescharacteristic
323C2×C4C2×D62811yescharacteristic
324C2×C4C23×D15711yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—3142no—
333C22—6281no—
334C22—6281no—
335C22—6281no—
336C22—6281no—
337C22—6281no—
338C22—6281no—
339C22—6281no—
340C22—6281no—
341C22C22×D62811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—3142no—
348C4—6281no—
349C4—6281no—
350C4—6281no—
351C4—6281no—
352C4#41×D15711yescharacteristic
353C4#41×D15711yescharacteristic
354C2—41no—
355C2—6282no—
356C2—12561no—
357C2—12561no—
358C2#2375778511yescharacteristic
359C2#2375807811yescharacteristic
360C2#2375808511yescharacteristic
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#433×C157C2
socleC22×C157C22×D4
hypercenter#433D157
hypocenterC157#3119
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23757878C2semidirect
2. #23757753C2semidirect
3. #23757592C2semidirect
4. #23757587C2semidirect
5. #23757581C2semidirect
6. #23757574C2semidirect
7. #23757474C2semidirect
8. #23757469C2semidirect
9. #23757420C2semidirect
10. #23757420C2semidirect
11. #23757386C2semidirect
12. #23757375C2semidirect
13. C4×#14578943C2semidirect
14. C4×D1256C2semidirect
15. #433×C157C2semidirect
180. C157#3119semidirect
196. #433D157semidirect

Maximal subgroups

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

subgroupindex
#237578782
#237577532
#237575922
#237575872
#237575812
#237575742
#237574742
#237574692
#237574202
#237573862
#237573752
C4×#145789432
C4×D12562
#433×C1572
#3119157