Finite Group Databasebeta

← #34100586

Subgroups — #34100586

Order 20096.

598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097739C211yesmaximal, characteristic
2C2×C22⋊C4×D157C211yesmaximal, characteristic, complemented
3C2×#19097686C211yesmaximal, characteristic, complemented
4#23757128C211yesmaximal, characteristic, complemented
5#23757039C211yesmaximal, characteristic, complemented
6#23757039C211yesmaximal, characteristic, complemented
7C2×#99×C157C211yesmaximal, characteristic, complemented
8C24×D157C2211yescharacteristic
9C22×C22⋊D157C412yescomplemented
10C22×C4×D157—21no—
11#19097739—21no—
12#19097739—22no—
13#19097739—21no—
14C2×C22⋊Dic157C2211yescharacteristic
15C2×C22⋊Dic157C2211yescharacteristic
16C2×C22⋊Dic157C2211yescharacteristic
17C2×#14578931—21no—
18C2×#14578931—22no—
19C2×#14578931C412yescomplemented
20C22⋊C4×D157—22no—
21C22⋊C4×D157—22no—
22#19097686—22no—
23C22×D4×C157C2211yescharacteristic
24C2×C22⋊C4×C157C2211yescharacteristic
25C2×C22⋊C4×C157C2211yescharacteristic
26#99×C157—22no—
27C23×D157—21no—
28C23×D157—21no—
29C23×D157—21no—
30C23×D157—21no—
31C23×D157—44no—
32C23×D157C2×C412yes—
33C23×D157D411yescharacteristic
34C23×D157D412yes—
35C23×D157D411yescharacteristic
36C2×C22⋊D157—22no—
37C2×C22⋊D157—22no—
38C2×C22⋊D157—44no—
39C22×Dic157—21no—
40C22×Dic157—21no—
41C22×Dic157C2×C412yescomplemented
42C2×C4×D157—24no—
43C2×C4×D157—44no—
44C22⋊Dic157—21no—
45C22⋊Dic157—21no—
46C22⋊Dic157—21no—
47C22⋊Dic157—21no—
48C22⋊Dic157—21no—
49C22⋊Dic157D412yescomplemented
50#14578931—24no—
51#14578931—22no—
52#14578931—22no—
53#14578931—44no—
54C24×C157C2×C411yescharacteristic, complemented
55C24×C157C2311yescharacteristic
56C2×D4×C157—21no—
57C2×D4×C157—21no—
58C2×D4×C157—21no—
59C2×D4×C157—21no—
60C2×D4×C157—21no—
61C2×D4×C157—21no—
62C22×C4×C157—21no—
63C22×C4×C157—21no—
64C22×C4×C157C2×C411yescharacteristic, complemented
65C22⋊C4×C157—21no—
66C22⋊C4×C157—21no—
67C22⋊C4×C157—21no—
68C22⋊C4×C157D412yescomplemented
69C22×D157—21no—
70C22×D157—21no—
71C22×D157—24no—
72C22×D157—22no—
73C22×D157—22no—
74C22×D157—21no—
75C22×D157—22no—
76C22×D157—22no—
77C22×D157—21no—
78C22×D157—24no—
79C22×D157—24no—
80C22×D157—42no—
81C22×D157—42no—
82C22×D157—42no—
83C22×D157—44no—
84C22×D157—44no—
85C22×D157—44no—
86C22×D157—44no—
87C22×D157C22⋊C412yes—
88C22×D157C22⋊C412yes—
89C22⋊D157—44no—
90C22⋊D157—44no—
91C2×Dic157—22no—
92C2×Dic157—22no—
93C2×Dic157—42no—
94C2×Dic157—42no—
95C2×Dic157—42no—
96C2×Dic157—41no—
97C4×D157—48no—
98C23×C157—21no—
99C23×C157—21no—
100C23×C157—21no—
101C23×C157—42no—
102C23×C157—42no—
103C23×C157C22×C411yescharacteristic
104C23×C157C2×D411yescharacteristic
105C23×C157C2×D411yescharacteristic
106C23×C157C2×D411yescharacteristic
107C23×C157C2×D411yescharacteristic
108C23×C157#4111yescharacteristic
109C23×C157#4111yescharacteristic
110D4×C157—41no—
111D4×C157—41no—
112D4×C157—41no—
113D4×C157—41no—
114C2×C4×C157—21no—
115C2×C4×C157—21no—
116C2×C4×C157—21no—
117C2×C4×C157—22no—
118C2×C4×C157—42no—
119C2×C4×C157—42no—
120C2×C4×C157—41no—
121C22×C157—22no—
122C22×C157—22no—
123C22×C157—22no—
124C22×C157—41no—
125C22×C157—41no—
126C22×C157—41no—
127C22×C157—41no—
128C22×C157—41no—
129C22×C157—42no—
130C22×C157—81no—
131C22×C157—81no—
132C22×C157C2×C22⋊C411yescharacteristic
133C22×C157C4×D411yescharacteristic
134C22×C157C4×D411yescharacteristic
135C22×C157#12011yescharacteristic
136C22×C157#12111yescharacteristic
137C22×C157#12111yescharacteristic
138C22×C157#12311yescharacteristic
139C2×D157—24no—
140C2×D157—24no—
141C2×D157—22no—
142C2×D157—22no—
143C2×D157—22no—
144C2×D157—22no—
145C2×D157—22no—
146C2×D157—44no—
147C2×D157—44no—
148C2×D157—44no—
149C2×D157—44no—
150C2×D157—42no—
151C2×D157—42no—
152C2×D157#9914yescomplemented
153C4×C157—42no—
154C4×C157—41no—
155C4×C157—81no—
156Dic157—42no—
157Dic157—42no—
158Dic157—81no—
159C2×C157—21no—
160C2×C157—21no—
161C2×C157—21no—
162C2×C157—21no—
163C2×C157—21no—
164C2×C157—21no—
165C2×C157—81no—
166C2×C157#38611yescharacteristic
167C2×C157C2×#9912yes—
168D157—24no—
169D157—42no—
170C157#189811yescharacteristic, complemented, Sylow
171#1898—1571nomaximal, Sylow
172C2×#120—1571no—
173C22×C22⋊C4—1571no—
174C2×#99—1571no—
175C2×#99D15711yescharacteristic, complemented
176#379—1571no—
177#342—1571no—
178#342—1571no—
179C25—1571no—
180C22×D4—1572no—
181C22×D4C2×D15711yescharacteristic
182C23×C4—3141no—
183#120—3141no—
184#120—3142no—
185#120—3141no—
186C2×C22⋊C4—3142no—
187C2×C22⋊C4—3141no—
188C2×C22⋊C4—3142no—
189C2×C22⋊C4—3142no—
190C2×C22⋊C4—1571no—
191C2×C22⋊C4—1571no—
192C2×C22⋊C4—1572no—
193C2×C22⋊C4—1571no—
194C2×C22⋊C4C2×D15711yescharacteristic
195C2×C22⋊C4C2×D15711yescharacteristic
196#99—22no—
197#99—3142no—
198C24—3141no—
199C24—3141no—
200C24—3141no—
201C24—3141no—
202C24—6284no—
203C24—1571no—
204C24—1572no—
205C24—1572no—
206C24—1571no—
207C24C4×D15711yescharacteristic, complemented
208C24C22×D15711yescharacteristic
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—21no—
215C2×D4—3142no—
216C2×D4—3142no—
217C2×D4—6284no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—3144no—
221C22×C4—3141no—
222C22×C4—3141no—
223C22×C4—6284no—
224C22×C4—1572no—
225C22×C4C4×D15711yescharacteristic, complemented
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—3144no—
230C22⋊C4—3142no—
231C22⋊C4—3142no—
232C22⋊C4—3141no—
233C22⋊C4—3141no—
234C22⋊C4—3141no—
235C22⋊C4—3141no—
236C22⋊C4—3141no—
237C22⋊C4—6284no—
238C22⋊C4—1572no—
239C22⋊C4C22⋊D15712yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—42no—
244C23—42no—
245C23—3144no—
246C23—3144no—
247C23—3144no—
248C23—3141no—
249C23—3141no—
250C23—3142no—
251C23—3142no—
252C23—3141no—
253C23—3142no—
254C23—3142no—
255C23—3141no—
256C23—6282no—
257C23—6282no—
258C23—6282no—
259C23—6284no—
260C23—6284no—
261C23—6284no—
262C23—6284no—
263C23—1572no—
264C23—1572no—
265C23C2×C4×D15711yescharacteristic
266C23D4×D15711yescharacteristic
267C23D4×D15711yescharacteristic
268C23D4×D15711yescharacteristic
269C23C2×C22⋊D15711yescharacteristic
270C23#1457895311yescharacteristic
271C23#1457895411yescharacteristic
272D4—41no—
273D4—41no—
274D4—41no—
275D4—41no—
276D4—6284no—
277D4—6284no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—3142no—
286C2×C4—3142no—
287C2×C4—6288no—
288C2×C4—6282no—
289C2×C4—6282no—
290C2×C4—6282no—
291C2×C4—6281no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22—42no—
301C22—81no—
302C22—81no—
303C22—3144no—
304C22—3144no—
305C22—3142no—
306C22—3142no—
307C22—3142no—
308C22—3142no—
309C22—3142no—
310C22—6284no—
311C22—6284no—
312C22—6284no—
313C22—6284no—
314C22—6282no—
315C22—6282no—
316C22—1574no—
317C22C22⋊C4×D15711yescharacteristic
318C22#1909773111yescharacteristic
319C22C4×C22⋊D15711yescharacteristic
320C22#1909773911yescharacteristic
321C22#1909774211yescharacteristic
322C22#1909774411yescharacteristic
323C22#1909775311yescharacteristic
324C4—42no—
325C4—41no—
326C4—81no—
327C4—6282no—
328C4—6282no—
329C4—12561no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2—21no—
335C2—21no—
336C2—81no—
337C2—3144no—
338C2—6282no—
339C2#2375714911yescharacteristic
340C2#99×D15712yes—
subgroupG/H
centerC22C22⋊C4×D157
commutatorC23×C157C22×C4
FrattiniC24C22×D157
FittingC2×#99×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC2×#19097739C2
cosocleC24×C157C23
hypercenterC2×#99D157
hypocenterC157#1898
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D157C2semidirect
3. C2×#19097686C2semidirect
4. #23757128C2semidirect
5. #23757039C2semidirect
6. #23757039C2semidirect
7. C2×#99×C157C2semidirect
9. C22×C22⋊D157C4semidirect
19. C2×#14578931C4semidirect
41. C22×Dic157C2×C4semidirect
49. C22⋊Dic157D4semidirect
54. C24×C157C2×C4semidirect
64. C22×C4×C157C2×C4semidirect
68. C22⋊C4×C157D4semidirect
152. C2×D157#99semidirect
170. C157#1898semidirect
175. C2×#99D157semidirect
207. C24C4×D157semidirect
225. C22×C4C4×D157semidirect
239. C22⋊C4C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977392
C2×C22⋊C4×D1572
C2×#190976862
#237571282
#237570392
C2×#99×C1572
#1898157