Finite Group Databasebeta

← #34100970

Subgroups — #34100970

Order 20096.

408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 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×#19097743C211yesmaximal, characteristic
2C2×#19097686C211yesmaximal, characteristic, complemented
3C2×#19097685C211yesmaximal, characteristic, complemented
4C2×#19097685C211yesmaximal, characteristic, complemented
5#23757131C211yesmaximal, characteristic, complemented
6C22⋊C4×Dic157C211yesmaximal, characteristic, complemented
7C2×#99×C157C211yesmaximal, characteristic, complemented
8C22×C22⋊D157C411yescharacteristic, complemented
9C22×C22⋊D157C2211yescharacteristic
10C23×Dic157C2211yescharacteristic
11#19097743—21no—
12#19097743—21no—
13#19097743—21no—
14#19097743—21no—
15C2×#14578933—21no—
16C2×#14578933C411yescharacteristic, complemented
17C2×C22⋊Dic157C411yescharacteristic, complemented
18C2×C22⋊Dic157C2211yescharacteristic
19C2×C22⋊Dic157C2211yescharacteristic
20C2×#14578931C411yescharacteristic, complemented
21C2×C4×Dic157—21no—
22#19097686—22no—
23#19097685—22no—
24#19097685—22no—
25#19097678—21no—
26#19097678—21no—
27C22×D4×C157C2211yescharacteristic
28C2×C22⋊C4×C157C2211yescharacteristic
29C2×C22⋊C4×C157C2211yescharacteristic
30#99×C157—22no—
31C23×D157C2×C411yescharacteristic
32C2×C22⋊D157—21no—
33C2×C22⋊D157—21no—
34C2×C22⋊D157—21no—
35C2×C22⋊D157—21no—
36C2×C22⋊D157—21no—
37C2×C22⋊D157—21no—
38C2×C22⋊D157—21no—
39C2×C22⋊D157—21no—
40C2×C22⋊D157—42no—
41C22×Dic157—21no—
42C22×Dic157—21no—
43C22×Dic157—42no—
44C22×Dic157C2×C411yescharacteristic
45C22×Dic157C2×C411yescharacteristic
46C22×Dic157C2×C411yescharacteristic
47C22×Dic157D411yescharacteristic
48C22×Dic157D411yescharacteristic
49C22×Dic157D411yescharacteristic
50C22×Dic157D411yescharacteristic
51#14578933—21no—
52#14578933—21no—
53#14578933—42no—
54C22⋊Dic157—21no—
55C22⋊Dic157—21no—
56C22⋊Dic157—21no—
57C22⋊Dic157—21no—
58C22⋊Dic157—21no—
59C22⋊Dic157D412yescomplemented
60#14578931—21no—
61#14578931—21no—
62C4×Dic157—42no—
63C24×C157C2×C411yescharacteristic
64C24×C157C2311yescharacteristic
65C2×D4×C157—21no—
66C2×D4×C157—21no—
67C2×D4×C157—21no—
68C2×D4×C157—21no—
69C2×D4×C157—21no—
70C2×D4×C157—21no—
71C22×C4×C157—21no—
72C22×C4×C157—21no—
73C22×C4×C157C2×C411yescharacteristic
74C22⋊C4×C157—21no—
75C22⋊C4×C157—21no—
76C22⋊C4×C157—21no—
77C22⋊C4×C157D412yescomplemented
78C22×D157—21no—
79C22×D157—21no—
80C22×D157—21no—
81C22×D157—41no—
82C22×D157—41no—
83C22⋊D157—42no—
84C22⋊D157—41no—
85C22⋊D157—41no—
86C22⋊D157—41no—
87C22⋊D157—41no—
88C22⋊D157—42no—
89C2×Dic157—22no—
90C2×Dic157—22no—
91C2×Dic157—22no—
92C2×Dic157—21no—
93C2×Dic157—21no—
94C2×Dic157—21no—
95C2×Dic157—22no—
96C2×Dic157—41no—
97C2×Dic157—41no—
98C2×Dic157—41no—
99C2×Dic157—41no—
100C2×Dic157—41no—
101C2×Dic157—41no—
102C2×Dic157—41no—
103C2×Dic157—41no—
104C2×Dic157C22⋊C411yescharacteristic
105C2×Dic157C22⋊C411yescharacteristic
106C2×Dic157C22⋊C411yescharacteristic
107C2×Dic157C22⋊C411yescharacteristic
108C23×C157—21no—
109C23×C157—21no—
110C23×C157—21no—
111C23×C157—41no—
112C23×C157—41no—
113C23×C157—41no—
114C23×C157—41no—
115C23×C157C22×C411yescharacteristic
116C23×C157C2×D411yescharacteristic
117C23×C157C2×D411yescharacteristic
118C23×C157C2×D411yescharacteristic
119C23×C157C2×D411yescharacteristic
120C23×C157#4111yescharacteristic
121C23×C157#4111yescharacteristic
122D4×C157—41no—
123D4×C157—41no—
124D4×C157—41no—
125D4×C157—41no—
126C2×C4×C157—21no—
127C2×C4×C157—21no—
128C2×C4×C157—21no—
129C2×C4×C157—22no—
130C2×C4×C157—41no—
131C2×C4×C157—41no—
132C2×C4×C157—41no—
133C2×C4×C157—41no—
134C2×C4×C157—41no—
135C22×C157—21no—
136C22×C157—21no—
137C22×C157—21no—
138C22×C157—21no—
139C22×C157—21no—
140C22×C157—21no—
141C22×C157—41no—
142C22×C157—41no—
143C22×C157—41no—
144C22×C157—41no—
145C22×C157—41no—
146C22×C157—41no—
147C22×C157—41no—
148C22×C157—81no—
149C22×C157—81no—
150C22×C157C2×C22⋊C411yescharacteristic
151C22×C157C4×D411yescharacteristic
152C22×C157C4×D411yescharacteristic
153C22×C157#12111yescharacteristic
154C22×C157#12111yescharacteristic
155C22×C157#12411yescharacteristic
156C22×C157#12711yescharacteristic
157C2×D157—41no—
158C2×D157—41no—
159C2×D157—41no—
160C2×D157—81no—
161C2×D157—81no—
162C4×C157—42no—
163C4×C157—41no—
164C4×C157—81no—
165Dic157—21no—
166Dic157—21no—
167Dic157—21no—
168Dic157—42no—
169Dic157—41no—
170Dic157—81no—
171Dic157#9912yescomplemented
172C2×C157—21no—
173C2×C157—21no—
174C2×C157—21no—
175C2×C157—21no—
176C2×C157—21no—
177C2×C157—21no—
178C2×C157—81no—
179C2×C157#39011yescharacteristic
180C2×C157C2×#9911yescharacteristic
181C2×C157#41011yescharacteristic
182D157—81no—
183C157#196411yescharacteristic, complemented, Sylow
184#1964—1571nomaximal, Sylow
185C2×#121—1571no—
186C2×#99—1571no—
187C2×#99—1571no—
188C2×#99—1571no—
189C2×#99D15711yescharacteristic, complemented
190#380—1571no—
191C4×C22⋊C4—1571no—
192C22×D4—1571no—
193C22×D4—1571no—
194C22×D4C2×D15711yescharacteristic
195C23×C4—1571no—
196#121—3141no—
197#121—3141no—
198#121—3141no—
199#121—3141no—
200C2×C4⋊C4—3141no—
201C2×C4⋊C4—1571no—
202C2×C22⋊C4—1571no—
203C2×C22⋊C4—1571no—
204C2×C22⋊C4—1571no—
205C2×C22⋊C4—1571no—
206C2×C22⋊C4C2×D15711yescharacteristic
207C2×C22⋊C4C2×D15711yescharacteristic
208C2×C42—3141no—
209#99—22no—
210#99—3142no—
211#99—3142no—
212#99—3142no—
213#95—3141no—
214#95—3141no—
215C24—1571no—
216C24C4×D15711yescharacteristic
217C24C22×D15711yescharacteristic
218C2×D4—21no—
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4—21no—
224C2×D4—3141no—
225C2×D4—3141no—
226C2×D4—3141no—
227C2×D4—3141no—
228C2×D4—3141no—
229C2×D4—3141no—
230C2×D4—3141no—
231C2×D4—3141no—
232C2×D4—6282no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—3141no—
236C22×C4—3141no—
237C22×C4—6282no—
238C22×C4—1571no—
239C22×C4—1571no—
240C22×C4—1571no—
241C22×C4—1571no—
242C22×C4—1571no—
243C22×C4—1571no—
244C22×C4—1571no—
245C22×C4C4×D15711yescharacteristic
246C4⋊C4—3141no—
247C4⋊C4—3141no—
248C4⋊C4—6282no—
249C22⋊C4—21no—
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—3141no—
253C22⋊C4—3141no—
254C22⋊C4—3141no—
255C22⋊C4—3141no—
256C22⋊C4—3141no—
257C22⋊C4—3141no—
258C22⋊C4—3141no—
259C22⋊C4—1572no—
260C22⋊C4C22⋊D15712yescomplemented
261C42—6282no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—3141no—
270C23—3141no—
271C23—3141no—
272C23—6281no—
273C23—6281no—
274C23C2×C4×D15711yescharacteristic
275C23D4×D15711yescharacteristic
276C23D4×D15711yescharacteristic
277C23D4×D15711yescharacteristic
278C23C2×C22⋊D15711yescharacteristic
279C23#1457895311yescharacteristic
280C23#1457895411yescharacteristic
281D4—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—6282no—
286D4—6281no—
287D4—6281no—
288D4—6281no—
289D4—6281no—
290D4—6282no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—3142no—
301C2×C4—3142no—
302C2×C4—3142no—
303C2×C4—3141no—
304C2×C4—3141no—
305C2×C4—3141no—
306C2×C4—3142no—
307C2×C4—6281no—
308C2×C4—6281no—
309C2×C4—6281no—
310C2×C4—6281no—
311C2×C4—6281no—
312C2×C4—6281no—
313C2×C4—6281no—
314C2×C4—6281no—
315C2×C4—1571no—
316C2×C4—1571no—
317C2×C4—1571no—
318C2×C4—1571no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—6281no—
335C22—6281no—
336C22—6281no—
337C22—12561no—
338C22—12561no—
339C22C22⋊C4×D15711yescharacteristic
340C22#1909773111yescharacteristic
341C22C4×C22⋊D15711yescharacteristic
342C22#1909774311yescharacteristic
343C22#1909774411yescharacteristic
344C22#1909775711yescharacteristic
345C22#1909776711yescharacteristic
346C4—42no—
347C4—41no—
348C4—81no—
349C4—3141no—
350C4—3141no—
351C4—3141no—
352C4—6282no—
353C4—6281no—
354C4—1572no—
355C4—12561no—
356C2—21no—
357C2—21no—
358C2—21no—
359C2—21no—
360C2—21no—
361C2—21no—
362C2—81no—
363C2—12561no—
364C2#2375717311yescharacteristic
365C2#99×D15711yescharacteristic
366C2#2375724511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC23×C157C22×C4
FrattiniC24C22×D157
FittingC2×#99×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC2×#19097743C2
cosocleC24×C157C23
hypercenterC2×#99D157
hypocenterC157#1964
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×#19097686C2semidirect
3. C2×#19097685C2semidirect
4. C2×#19097685C2semidirect
5. #23757131C2semidirect
6. C22⋊C4×Dic157C2semidirect
7. C2×#99×C157C2semidirect
8. C22×C22⋊D157C4semidirect
16. C2×#14578933C4semidirect
17. C2×C22⋊Dic157C4semidirect
20. C2×#14578931C4semidirect
59. C22⋊Dic157D4semidirect
77. C22⋊C4×C157D4semidirect
171. Dic157#99semidirect
183. C157#1964semidirect
189. C2×#99D157semidirect
260. C22⋊C4C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977432
C2×#190976862
C2×#190976852
#237571312
C22⋊C4×Dic1572
C2×#99×C1572
#1964157