Finite Group Databasebeta

← #34110335

Subgroups — #34110335

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#23757591C211yesmaximal, characteristic, complemented
3#23757586C211yesmaximal, characteristic, complemented
4#23757580C211yesmaximal, characteristic, complemented
5#23757573C211yesmaximal, characteristic, complemented
6#23757473C211yesmaximal, characteristic, complemented
7#23757468C211yesmaximal, characteristic, complemented
8#23757418C211yesmaximal, characteristic, complemented
9#23757418C211yesmaximal, characteristic, complemented
10#23757383C211yesmaximal, characteristic, complemented
11#23757371C211yesmaximal, characteristic, complemented
12C4×#14578941C211yesmaximal, characteristic, complemented
13C4×#14578939C211yesmaximal, characteristic, complemented
14#23757334C211yesmaximal, characteristic, complemented
15#520×C157C211yesmaximal, characteristic, complemented
16C2×#14578941C2211yescharacteristic
17C2×#14578941C2211yescharacteristic
18C2×#14578939C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20#19097768C2211yescharacteristic
21#19097763C2211yescharacteristic
22#19097756—21no—
23#19097756—21no—
24#19097745C2211yescharacteristic
25#19097745C2211yescharacteristic
26#19097744—21no—
27#19097744—21no—
28C4×D628C2211yescharacteristic
29C4×D628C2211yescharacteristic
30#19097704C2211yescharacteristic
31#19097704C2211yescharacteristic
32#19097702C2211yescharacteristic
33#19097702C2211yescharacteristic
34C4⋊#11929434C2211yescharacteristic
35C4⋊#11929434C2211yescharacteristic
36#19097695C2211yescharacteristic
37#19097695C2211yescharacteristic
38#19097692C2211yescharacteristic
39#19097692C2211yescharacteristic
40#19097691C2211yescharacteristic
41#19097691C2211yescharacteristic
42#19097691C2211yescharacteristic
43#19097691C2211yescharacteristic
44C22⋊#11929434C2211yescharacteristic
45C22⋊#11929434C2211yescharacteristic
46#19097682C2211yescharacteristic
47C4×#11929434C2211yescharacteristic
48C2×#41×C157C2211yescharacteristic
49C4×Q8×C157C2211yescharacteristic
50C4×Q8×C157C2211yescharacteristic
51C4×D4×C157—21no—
52C4×D4×C157—21no—
53C4×D4×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55#117×C157—21no—
56#117×C157C2211yescharacteristic
57C2×C4⋊C4×C157—21no—
58C2×C4⋊C4×C157C2211yescharacteristic
59C2×D628—21no—
60C2×D628—21no—
61C2×D628C2311yescharacteristic
62C2×D628C2311yescharacteristic
63C2×C22⋊D157—21no—
64C2×C22⋊D157—21no—
65C2×C4×D157—21no—
66C2×C4×D157—21no—
67#14578941—22no—
68#14578941—22no—
69#14578939—22no—
70#14578939—22no—
71C2×#11929434C2311yescharacteristic
72C2×#11929434C2311yescharacteristic
73C2×#11929434C2311yescharacteristic
74C2×#11929434C2311yescharacteristic
75C4⋊Dic157C2311yescharacteristic
76C4⋊Dic157C2311yescharacteristic
77#14578933—21no—
78#14578933—21no—
79#14578931—21no—
80#14578931—21no—
81#14578931—21no—
82#14578931—21no—
83#41×C157—22no—
84#41×C157—22no—
85C2×Q8×C157C2311yescharacteristic
86C2×D4×C157—21no—
87C2×D4×C157C2311yescharacteristic
88C22×C4×C157—21no—
89C22×C4×C157—21no—
90C22×C4×C157—21no—
91C22×C4×C157—21no—
92C22×C4×C157C2311yescharacteristic
93C4⋊C4×C157—21no—
94C4⋊C4×C157—21no—
95C4⋊C4×C157—21no—
96C4⋊C4×C157D411yescharacteristic
97C4⋊C4×C157D411yescharacteristic
98C4⋊C4×C157C2311yescharacteristic
99C4⋊C4×C157C2311yescharacteristic
100C22⋊C4×C157—21no—
101C22⋊C4×C157—21no—
102C22⋊C4×C157D411yescharacteristic
103C22⋊C4×C157D411yescharacteristic
104C42×C157—21no—
105C42×C157—21no—
106C42×C157C2311yescharacteristic
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—21no—
110D628—21no—
111D628—21no—
112D628—21no—
113D628—21no—
114D628—81no—
115D628—81no—
116C22⋊D157—81no—
117C22⋊D157—81no—
118C2×Dic157—21no—
119C2×Dic157—21no—
120C4×D157—81no—
121C4×D157—81no—
122#11929434—21no—
123#11929434—21no—
124#11929434—21no—
125#11929434—21no—
126C23×C157—21no—
127C23×C157C2×D411yescharacteristic
128Q8×C157—21no—
129Q8×C157#4112yes—
130D4×C157—24no—
131D4×C157—21no—
132D4×C157#4112yes—
133C2×C4×C157—24no—
134C2×C4×C157—21no—
135C2×C4×C157—21no—
136C2×C4×C157—21no—
137C2×C4×C157—21no—
138C2×C4×C157—21no—
139C2×C4×C157—81no—
140C2×C4×C157—81no—
141C2×C4×C157—81no—
142C2×C4×C157C2×D411yescharacteristic
143C2×C4×C157C2×D411yescharacteristic
144C2×C4×C157C2×D411yescharacteristic
145C2×C4×C157C2×D411yescharacteristic
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2411yescharacteristic
148C22×C157—21no—
149C22×C157—22no—
150C22×C157—21no—
151C22×C157—21no—
152C22×C157—41no—
153C22×C157—41no—
154C22×C157C22×D411yescharacteristic
155C2×D157—41no—
156C2×D157—41no—
157C2×D157—41no—
158C2×D157—41no—
159C2×D157—41no—
160C2×D157—41no—
161C4×C157—21no—
162C4×C157—22no—
163C4×C157—21no—
164C4×C157—21no—
165C4×C157—21no—
166C4×C157—21no—
167C4×C157—41no—
168C4×C157—41no—
169C4×C157C2×#4111yescharacteristic
170C4×C157C2×#4111yescharacteristic
171Dic157—41no—
172Dic157—41no—
173C2×C157—41no—
174C2×C157—42no—
175C2×C157#52511yescharacteristic
176C2×C157#57611yescharacteristic
177C2×C157#57711yescharacteristic
178D157—81no—
179D157—81no—
180C157#311911yescharacteristic, complemented, Sylow
181#3119—1571nomaximal, Sylow
182#540—1571no—
183#520D15711yescharacteristic, complemented
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#433—1571no—
197C2×#41C2×D15711yescharacteristic
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×Q8C2×D15711yescharacteristic
211C4×Q8C2×D15711yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1571no—
215C4×D4—1571no—
216C4×D4C2×D15711yescharacteristic
217C4×D4C2×D15711yescharacteristic
218#117—21no—
219#117C2×D15711yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D15711yescharacteristic
222#107—1571no—
223#107—1571no—
224#106—1571no—
225#106—1571no—
226C4⋊C8—1571no—
227C4⋊C8—1571no—
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⋊C8—1571no—
237C22⋊C8—1571no—
238#97—1571no—
239C4×C8—1571no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D15711yescharacteristic
243C2×D4—21no—
244C2×D4—3141no—
245C2×D4—3141no—
246C2×D4—3141no—
247C2×D4—3141no—
248C2×D4—1571no—
249C2×D4—1571no—
250C2×D4C22×D15711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—3141no—
256C22×C4—3141no—
257C22×C4C22×D15711yescharacteristic
258SD16—3142no—
259SD16—3142no—
260D8—3142no—
261D8—3142no—
262C2×C8—1571no—
263C2×C8—1571no—
264C2×C8—1571no—
265C2×C8—1571no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—3141no—
270C4⋊C4—3141no—
271C4⋊C4—1571no—
272C4⋊C4—1571no—
273C4⋊C4C22⋊D15711yescharacteristic
274C4⋊C4C22⋊D15711yescharacteristic
275C4⋊C4C22×D15711yescharacteristic
276C4⋊C4C22×D15711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3141no—
280C22⋊C4—3141no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C22⋊C4C22⋊D15711yescharacteristic
284C22⋊C4C22⋊D15711yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D15711yescharacteristic
288C42C22×D15711yescharacteristic
289C23—21no—
290C23—3141no—
291C23—3141no—
292C23C2×C22⋊D15711yescharacteristic
293Q8—21no—
294Q8#1457895412yes—
295D4—24no—
296D4—21no—
297D4—3141no—
298D4—3141no—
299D4—3141no—
300D4—3141no—
301D4—12561no—
302D4—12561no—
303D4—12561no—
304D4—12561no—
305D4#1457895412yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—3141no—
316C2×C4—3141no—
317C2×C4—12561no—
318C2×C4—12561no—
319C2×C4C2×C22⋊D15711yescharacteristic
320C2×C4C2×C22⋊D15711yescharacteristic
321C2×C4C2×C22⋊D15711yescharacteristic
322C2×C4C2×C22⋊D15711yescharacteristic
323C2×C4C2×C22⋊D15711yescharacteristic
324C2×C4C23×D15711yescharacteristic
325C8—3141no—
326C8—3141no—
327C8—3141no—
328C8—3141no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—6281no—
336C22—6281no—
337C22—6281no—
338C22—6281no—
339C22—6281no—
340C22—6281no—
341C22C22×C22⋊D15711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—6281no—
351C4—6281no—
352C4C2×#1457895411yescharacteristic
353C4C2×#1457895411yescharacteristic
354C2—41no—
355C2—42no—
356C2—12561no—
357C2—12561no—
358C2#2375778411yescharacteristic
359C2#2375807611yescharacteristic
360C2#2375808111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#520×C157C2
socleC22×C157C22×D4
hypercenter#520D157
hypocenterC157#3119
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #23757878C2semidirect
2. #23757591C2semidirect
3. #23757586C2semidirect
4. #23757580C2semidirect
5. #23757573C2semidirect
6. #23757473C2semidirect
7. #23757468C2semidirect
8. #23757418C2semidirect
9. #23757418C2semidirect
10. #23757383C2semidirect
11. #23757371C2semidirect
12. C4×#14578941C2semidirect
13. C4×#14578939C2semidirect
14. #23757334C2semidirect
15. #520×C157C2semidirect
180. C157#3119semidirect
183. #520D157semidirect

Maximal subgroups

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

subgroupindex
#237578782
#237575912
#237575862
#237575802
#237575732
#237574732
#237574682
#237574182
#237573832
#237573712
C4×#145789412
C4×#145789392
#237573342
#520×C1572
#3119157