Finite Group Databasebeta

← #34103392

Subgroups — #34103392

Order 20096.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic157C211yesmaximal, characteristic
2C2×#19097727C211yesmaximal, characteristic, complemented
3#23757215C211yesmaximal, characteristic, complemented
4#23757209C211yesmaximal, characteristic, complemented
5#23757206C211yesmaximal, characteristic, complemented
6#23757201C211yesmaximal, characteristic, complemented
7#23757201C211yesmaximal, characteristic, complemented
8#23757198C211yesmaximal, characteristic, complemented
9#23757187C211yesmaximal, characteristic
10C4⋊C4×Dic157C211yesmaximal, characteristic, complemented
11#23757124C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic157C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic157C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic157C211yesmaximal, characteristic, complemented
15#394×C157C211yesmaximal, characteristic
16C23×Dic157C2211yescharacteristic
17C23×Dic157C2211yescharacteristic
18D4×Dic157—24no—
19#19097727—24no—
20C2×C4⋊Dic157C2211yescharacteristic
21C2×C4⋊Dic157C2211yescharacteristic
22C2×#14578933C2211yescharacteristic
23C2×#14578933C2211yescharacteristic
24C2×#14578933C2211yescharacteristic
25C2×#14578933C2211yescharacteristic
26C2×C22⋊Dic157C2211yescharacteristic
27C2×C22⋊Dic157C2211yescharacteristic
28C2×C22⋊Dic157C2211yescharacteristic
29C2×C22⋊Dic157C2211yescharacteristic
30C2×C22⋊Dic157C2211yescharacteristic
31C2×C22⋊Dic157C2211yescharacteristic
32C2×C4×Dic157C2211yescharacteristic
33C2×C4×Dic157C2211yescharacteristic
34C2×C4×Dic157C2211yescharacteristic
35C2×C4×Dic157C2211yescharacteristic
36C2×C4×Dic157C2211yescharacteristic
37#19097678C2211yescharacteristic
38#19097678C2211yescharacteristic
39#19097678C2211yescharacteristic
40#19097678C2211yescharacteristic
41#19097678C2211yescharacteristic
42#19097678C2211yescharacteristic
43#19097678C2211yescharacteristic
44#19097678C2211yescharacteristic
45#19097678C2211yescharacteristic
46C22×D4×C157C2211yescharacteristic
47C2×C4⋊C4×C157C2211yescharacteristic
48C2×C22⋊C4×C157C2211yescharacteristic
49C2×C22⋊C4×C157C2211yescharacteristic
50C2×C22⋊C4×C157C2211yescharacteristic
51C2×C22⋊C4×C157C2211yescharacteristic
52#95×C157C2211yescharacteristic
53C22×Dic157—22no—
54C22×Dic157—22no—
55C22×Dic157—22no—
56C22×Dic157—22no—
57C22×Dic157—22no—
58C22×Dic157D414yes—
59C22×Dic157C2311yescharacteristic
60C22×Dic157C2311yescharacteristic
61C22×Dic157C2311yescharacteristic
62C22×Dic157C2311yescharacteristic
63C22×Dic157C2311yescharacteristic
64C22×Dic157C2311yescharacteristic
65C22×Dic157C2311yescharacteristic
66C22×Dic157C2311yescharacteristic
67C4⋊Dic157—22no—
68C4⋊Dic157—22no—
69#14578933—22no—
70#14578933—22no—
71#14578933—22no—
72#14578933—22no—
73C22⋊Dic157—22no—
74C22⋊Dic157—22no—
75C22⋊Dic157—22no—
76C22⋊Dic157—22no—
77C22⋊Dic157—22no—
78C22⋊Dic157—22no—
79C4×Dic157—22no—
80C4×Dic157—22no—
81C4×Dic157—22no—
82C4×Dic157—22no—
83C4×Dic157—22no—
84C24×C157C2311yescharacteristic
85C24×C157C2311yescharacteristic
86C2×D4×C157—22no—
87C2×D4×C157—22no—
88C2×D4×C157—22no—
89C22×C4×C157C2311yescharacteristic
90C22×C4×C157C2311yescharacteristic
91C22×C4×C157C2311yescharacteristic
92C22×C4×C157C2311yescharacteristic
93C22×C4×C157C2311yescharacteristic
94C4⋊C4×C157—22no—
95C22⋊C4×C157—22no—
96C22⋊C4×C157—22no—
97C22⋊C4×C157—22no—
98C22⋊C4×C157—22no—
99C2×Dic157—21no—
100C2×Dic157—21no—
101C2×Dic157—21no—
102C2×Dic157—21no—
103C2×Dic157—28no—
104C2×Dic157—21no—
105C2×Dic157—21no—
106C2×Dic157—21no—
107C2×Dic157—21no—
108C2×Dic157—21no—
109C2×Dic157—21no—
110C2×Dic157—21no—
111C2×Dic157—21no—
112C2×Dic157—21no—
113C2×Dic157—21no—
114C2×Dic157—21no—
115C2×Dic157—21no—
116C2×Dic157—21no—
117C2×Dic157—21no—
118C2×Dic157—21no—
119C2×Dic157—44no—
120C2×Dic157C2×D412yes—
121C2×Dic157C2×D412yes—
122C2×Dic157#4112yes—
123C2×Dic157#4112yes—
124C2×Dic157#4112yes—
125C23×C157—21no—
126C23×C157—21no—
127C23×C157—21no—
128C23×C157—21no—
129C23×C157—21no—
130C23×C157—21no—
131C23×C157—21no—
132C23×C157—21no—
133C23×C157—21no—
134C23×C157—21no—
135C23×C157—21no—
136C23×C157—21no—
137C23×C157C2×D412yes—
138C23×C157#4112yes—
139C23×C157C2411yescharacteristic
140D4×C157—28no—
141C2×C4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—21no—
146C2×C4×C157—21no—
147C2×C4×C157—21no—
148C2×C4×C157—21no—
149C2×C4×C157—21no—
150C2×C4×C157—21no—
151C2×C4×C157—21no—
152C2×C4×C157—21no—
153C2×C4×C157—21no—
154C2×C4×C157#4112yes—
155C2×C4×C157#4112yes—
156C22×C157—22no—
157C22×C157—22no—
158C22×C157—22no—
159C22×C157—22no—
160C22×C157—22no—
161C22×C157—22no—
162C22×C157—41no—
163C22×C157—41no—
164C22×C157—41no—
165C22×C157—41no—
166C22×C157—41no—
167C22×C157—41no—
168C22×C157—41no—
169C22×C157—41no—
170C22×C157C22×D411yescharacteristic
171C22×C157C2×#4111yescharacteristic
172C22×C157C2×#4111yescharacteristic
173C22×C157C2×#4111yescharacteristic
174C22×C157C2×#4111yescharacteristic
175C22×C157C2×#4111yescharacteristic
176C22×C157C2×#4111yescharacteristic
177C4×C157—22no—
178C4×C157—22no—
179C4×C157—41no—
180C4×C157—41no—
181C4×C157—41no—
182Dic157—22no—
183Dic157—22no—
184Dic157—41no—
185Dic157—41no—
186Dic157—41no—
187Dic157—41no—
188Dic157—41no—
189Dic157#12314yes—
190C2×C157—42no—
191C2×C157—42no—
192C2×C157C2×#12311yescharacteristic
193C2×C157#52511yescharacteristic
194C2×C157#52911yescharacteristic
195C2×C157#52911yescharacteristic
196C2×C157#52911yescharacteristic
197C2×C157#52911yescharacteristic
198C2×C157#53211yescharacteristic
199C157#239511yescharacteristic, complemented, Sylow
200#2395—1571nomaximal, Sylow
201C2×C4×D4—1571no—
202C2×#117—1571no—
203#400—1571no—
204#399—1571no—
205#398—1571no—
206#397—1571no—
207#397—1571no—
208#397—1571no—
209#394—1571no—
210#394D15711yescharacteristic
211C4×C4⋊C4—1571no—
212C4×C4⋊C4—1571no—
213C4×C22⋊C4—1571no—
214C4×C22⋊C4—1571no—
215C4×C22⋊C4—1571no—
216C22×D4C2×D15711yescharacteristic
217C23×C4—1571no—
218C23×C4—1571no—
219C4×D4—3144no—
220#117—3144no—
221C2×C4⋊C4—1571no—
222C2×C4⋊C4—1571no—
223C2×C4⋊C4—1571no—
224C2×C4⋊C4—1571no—
225C2×C4⋊C4—1571no—
226C2×C4⋊C4—1571no—
227C2×C4⋊C4C2×D15711yescharacteristic
228C2×C22⋊C4—1571no—
229C2×C22⋊C4—1571no—
230C2×C22⋊C4—1571no—
231C2×C22⋊C4—1571no—
232C2×C22⋊C4—1571no—
233C2×C22⋊C4—1571no—
234C2×C22⋊C4C2×D15711yescharacteristic
235C2×C22⋊C4C2×D15711yescharacteristic
236C2×C22⋊C4C2×D15711yescharacteristic
237C2×C22⋊C4C2×D15711yescharacteristic
238C2×C42—1571no—
239C2×C42—1571no—
240C2×C42—1571no—
241C2×C42—1571no—
242C2×C42—1571no—
243#95—1571no—
244#95—1571no—
245#95—1571no—
246#95—1571no—
247#95—1571no—
248#95—1571no—
249#95—1571no—
250#95—1571no—
251#95—1571no—
252#95C2×D15711yescharacteristic
253C24C22×D15711yescharacteristic
254C24C22×D15711yescharacteristic
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C22×C4—3142no—
259C22×C4—3142no—
260C22×C4—3142no—
261C22×C4—3142no—
262C22×C4—3142no—
263C22×C4—1571no—
264C22×C4—1571no—
265C22×C4—1571no—
266C22×C4—1571no—
267C22×C4—1571no—
268C22×C4—1574no—
269C22×C4—1571no—
270C22×C4—1571no—
271C22×C4—1571no—
272C22×C4C22×D15711yescharacteristic
273C22×C4C22×D15711yescharacteristic
274C22×C4C22×D15711yescharacteristic
275C22×C4C22×D15711yescharacteristic
276C22×C4C22×D15711yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—3142no—
279C4⋊C4—3142no—
280C4⋊C4—3142no—
281C4⋊C4—3142no—
282C4⋊C4—3142no—
283C4⋊C4—3142no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—3142no—
289C22⋊C4—3142no—
290C22⋊C4—3142no—
291C22⋊C4—3142no—
292C22⋊C4—3142no—
293C22⋊C4—3142no—
294C42—3142no—
295C42—3142no—
296C42—3142no—
297C42—3142no—
298C42—3142no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23D4×D15712yes—
312C23#1457895312yes—
313C23C23×D15711yescharacteristic
314D4—28no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—3141no—
329C2×C4—3141no—
330C2×C4—3141no—
331C2×C4—3141no—
332C2×C4—3148no—
333C2×C4—3141no—
334C2×C4—3141no—
335C2×C4—3141no—
336C2×C4—3141no—
337C2×C4—3141no—
338C2×C4—3141no—
339C2×C4—3141no—
340C2×C4—3141no—
341C2×C4—3141no—
342C2×C4—3141no—
343C2×C4—3141no—
344C2×C4—3141no—
345C2×C4—3141no—
346C2×C4—3141no—
347C2×C4—3141no—
348C2×C4—6284no—
349C2×C4—1572no—
350C2×C4—1572no—
351C2×C4—1572no—
352C2×C4—1572no—
353C2×C4—1572no—
354C2×C4#1457895312yes—
355C2×C4#1457895312yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C2×D4×D15711yescharacteristic
371C22#41×D15711yescharacteristic
372C22#41×D15711yescharacteristic
373C22#41×D15711yescharacteristic
374C22C2×#1457895311yescharacteristic
375C22C2×#1457895311yescharacteristic
376C22C2×#1457895311yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3142no—
383C4—3142no—
384C4—6281no—
385C4—6281no—
386C4—6281no—
387C4—6281no—
388C4—6281no—
389C4—1574no—
390C2—42no—
391C2—42no—
392C2#123×D15711yescharacteristic
393C2#2375777911yescharacteristic
394C2#2375780011yescharacteristic
395C2#2375780211yescharacteristic
396C2#2375780411yescharacteristic
397C2#2375780411yescharacteristic
398C2#2375781811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutator, socle, cosocleC23×C157C24
Fitting#394×C157C2
prime radicalC22×D4×C157C22
hypercenter#394D157
hypocenterC157#2395
LCSG ▷ C23×C157 ▷ C157
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#19097727C2semidirect
3. #23757215C2semidirect
4. #23757209C2semidirect
5. #23757206C2semidirect
6. #23757201C2semidirect
7. #23757201C2semidirect
8. #23757198C2semidirect
10. C4⋊C4×Dic157C2semidirect
11. #23757124C2semidirect
12. C22⋊C4×Dic157C2semidirect
13. C22⋊C4×Dic157C2semidirect
14. C22⋊C4×Dic157C2semidirect
199. C157#2395semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1572
C2×#190977272
#237572152
#237572092
#237572062
#237572012
#237571982
#237571872
C4⋊C4×Dic1572
#237571242
C22⋊C4×Dic1572
#394×C1572
#2395157