Finite Group Databasebeta

← #34109793

Subgroups — #34109793

Order 20096.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097792C211yesmaximal, characteristic, complemented
2C2×#19097777C211yesmaximal, characteristic, complemented
3#23757853C211yesmaximal, characteristic, complemented
4#23757852C211yesmaximal, characteristic, complemented
5#23757530C211yesmaximal, characteristic, complemented
6#23757529C211yesmaximal, characteristic, complemented
7#23757525C211yesmaximal, characteristic, complemented
8#23757524C211yesmaximal, characteristic, complemented
9#23757503C211yesmaximal, characteristic, complemented
10#23757502C211yesmaximal, characteristic, complemented
11#23757499C211yesmaximal, characteristic, complemented
12#106×D157C211yesmaximal, characteristic, complemented
13#23757273C211yesmaximal, characteristic, complemented
14#23757271C211yesmaximal, characteristic, complemented
15#465×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578954C2211yescharacteristic
18C2×#14578953C2211yescharacteristic
19#19097792—24no—
20C2×#14578944C2211yescharacteristic
21C2×#14578943C2211yescharacteristic
22C2×#14578939C2211yescharacteristic
23#19097777—24no—
24C2×#14578938C2211yescharacteristic
25C2×#14578937C2211yescharacteristic
26C2×#14578937C2211yescharacteristic
27C2×C8×D157C2211yescharacteristic
28C2×C8×D157C2211yescharacteristic
29#19097751C2211yescharacteristic
30#19097750C2211yescharacteristic
31#19097749—21no—
32#19097748—21no—
33#19097747C2211yescharacteristic
34#19097746—21no—
35#19097746C2211yescharacteristic
36#19097745C2211yescharacteristic
37#19097744—21no—
38#19097744—21no—
39#19097744—21no—
40#19097743—21no—
41#19097742—21no—
42#19097742C2211yescharacteristic
43C4⋊C4×D157C2211yescharacteristic
44C4⋊C4×D157C2211yescharacteristic
45#19097703C2211yescharacteristic
46#19097702C2211yescharacteristic
47#19097702C2211yescharacteristic
48#19097696C2211yescharacteristic
49#19097695C2211yescharacteristic
50#19097694C2211yescharacteristic
51#19097693C2211yescharacteristic
52#19097692C2211yescharacteristic
53#19097691C2211yescharacteristic
54C2×SD16×C157C2211yescharacteristic
55C22×C8×C157C2211yescharacteristic
56C22⋊Q8×C157C2211yescharacteristic
57#121×C157C2211yescharacteristic
58#106×C157C2211yescharacteristic
59#103×C157C2211yescharacteristic
60#102×C157C2211yescharacteristic
61#14578955—22no—
62#14578955—22no—
63#14578954—22no—
64#14578954—22no—
65#14578953—22no—
66#14578953—22no—
67C2×Dic314D411yescharacteristic
68C2×Dic314C2311yescharacteristic
69C2×D628—21no—
70C2×D628—21no—
71C2×D628D411yescharacteristic
72C2×D628C2311yescharacteristic
73C2×C22⋊D157—21no—
74C2×C22⋊D157—21no—
75C2×C22⋊D157—21no—
76C2×C22⋊D157D411yescharacteristic
77C2×C22⋊D157D411yescharacteristic
78C22×Dic157—21no—
79C2×C4×D157—21no—
80C2×C4×D157—21no—
81C2×C4×D157—21no—
82C2×C4×D157C2311yescharacteristic
83C2×C4×D157C2311yescharacteristic
84#14578944—22no—
85#14578943—22no—
86#14578939—22no—
87#14578938—22no—
88#14578937—22no—
89#14578937—22no—
90C2×#11929434C2311yescharacteristic
91C2×#11929434C2311yescharacteristic
92C8×D157—22no—
93C8×D157D414yescomplemented
94C4⋊Dic157—21no—
95C4⋊Dic157C2311yescharacteristic
96C4⋊Dic157C2311yescharacteristic
97#14578933—21no—
98#14578933—21no—
99#14578933—21no—
100#14578933—21no—
101C22⋊Dic157—21no—
102C22⋊Dic157—21no—
103#14578931—21no—
104#14578931—21no—
105#14578931—21no—
106#14578931—21no—
107C2×Q8×C157C2311yescharacteristic
108C2×D4×C157—21no—
109C2×D4×C157C2311yescharacteristic
110C22×C4×C157C2311yescharacteristic
111SD16×C157—22no—
112C2×C8×C157—22no—
113C2×C8×C157C2311yescharacteristic
114C2×C8×C157C2311yescharacteristic
115C4⋊C4×C157—21no—
116C4⋊C4×C157C2311yescharacteristic
117C4⋊C4×C157C2311yescharacteristic
118C22⋊C4×C157—21no—
119C22⋊C4×C157—21no—
120C22×D157—21no—
121C22×D157C2×D411yescharacteristic
122C22×D157C2×D411yescharacteristic
123Dic314—22no—
124Dic314—21no—
125Dic314—21no—
126D628—22no—
127D628—21no—
128D628—21no—
129D628—42no—
130D628—81no—
131C22⋊D157—22no—
132C22⋊D157—22no—
133C22⋊D157—42no—
134C22⋊D157—81no—
135C22⋊D157—81no—
136C2×Dic157—21no—
137C2×Dic157—21no—
138C2×Dic157—21no—
139C2×Dic157—42no—
140C2×Dic157C2×D411yescharacteristic
141C2×Dic157C2×D411yescharacteristic
142C4×D157—21no—
143C4×D157—21no—
144C4×D157—42no—
145C4×D157—81no—
146C4×D157—81no—
147C4×D157C2×D412yes—
148C4×D157#4112yes—
149#11929434—21no—
150#11929434C2×D412yes—
151C23×C157—21no—
152C23×C157C2×D411yescharacteristic
153Q8×C157—21no—
154Q8×C157—21no—
155D4×C157—21no—
156D4×C157—21no—
157D4×C157—81no—
158C2×C4×C157—21no—
159C2×C4×C157—21no—
160C2×C4×C157—21no—
161C2×C4×C157—21no—
162C2×C4×C157—21no—
163C2×C4×C157C2×D411yescharacteristic
164C2×C4×C157C2411yescharacteristic
165C8×C157—21no—
166C8×C157C2×D412yes—
167C22×C157—21no—
168C22×C157—21no—
169C22×C157—21no—
170C22×C157—41no—
171C22×C157—41no—
172C22×C157—41no—
173C22×C157C22×D411yescharacteristic
174C2×D157—21no—
175C2×D157—21no—
176C2×D157—21no—
177C2×D157—21no—
178C2×D157—21no—
179C2×D157—41no—
180C2×D157—41no—
181C2×D157—41no—
182C2×D157#12112yes—
183C4×C157—21no—
184C4×C157—41no—
185C4×C157—41no—
186C4×C157—41no—
187C4×C157C22×D411yescharacteristic
188C4×C157C2×#4111yescharacteristic
189Dic157—21no—
190Dic157—41no—
191Dic157—41no—
192Dic157—41no—
193Dic157#12112yes—
194C2×C157—41no—
195C2×C157—81no—
196C2×C157C2×#12111yescharacteristic
197C2×C157#57711yescharacteristic
198C2×C157#57711yescharacteristic
199D157—22no—
200D157—41no—
201D157—81no—
202C157#306011yescharacteristic, complemented, Sylow
203#3060—1571nomaximal, Sylow
204C2×#135—1571no—
205C2×#131—1571no—
206#537—1571no—
207#537—1571no—
208#470—1571no—
209#470—1571no—
210#469—1571no—
211#469—1571no—
212#465—1571no—
213#465—1571no—
214#465—1571no—
215#465D15711yescharacteristic, complemented
216C2×#106—1571no—
217#417—1571no—
218#417—1571no—
219C2×#41—1571no—
220C2×#41—1571no—
221C2×#41—1571no—
222#135—3144no—
223C2×Q16—1571no—
224C2×SD16—1571no—
225C2×SD16C2×D15711yescharacteristic
226C2×D8—1571no—
227#131—3144no—
228C2×M16—1571no—
229C2×M16—1571no—
230C2×M16—1571no—
231C22×C8—1571no—
232C22×C8—1571no—
233C22×C8C2×D15711yescharacteristic
234C22⋊Q8—3141no—
235C22⋊Q8—3141no—
236C22⋊Q8—1571no—
237C22⋊Q8—1571no—
238C22⋊Q8—1571no—
239C22⋊Q8C2×D15711yescharacteristic
240#121—3141no—
241#121—3141no—
242#121—3141no—
243#121—3141no—
244#121—3141no—
245#121—3141no—
246#121—1571no—
247#121—1571no—
248#121—1571no—
249#121C2×D15711yescharacteristic
250C2×C4⋊C4—1571no—
251C2×C4⋊C4—1571no—
252#106—1571no—
253#106—1571no—
254#106—1571no—
255#106C2×D15711yescharacteristic
256#103—1571no—
257#103—1571no—
258#103—1571no—
259#103C2×D15711yescharacteristic
260#102—1571no—
261#102—1571no—
262#102—1571no—
263#102C2×D15711yescharacteristic
264#41—3142no—
265#41—3142no—
266#41—3142no—
267#41—3142no—
268#41—3142no—
269#41—3142no—
270C2×Q8—1571no—
271C2×Q8—1571no—
272C2×Q8C22×D15711yescharacteristic
273C2×D4—21no—
274C2×D4—3141no—
275C2×D4—3141no—
276C2×D4—3141no—
277C2×D4—3141no—
278C2×D4—3141no—
279C2×D4—1571no—
280C2×D4—1571no—
281C2×D4—1571no—
282C2×D4—1571no—
283C2×D4C22×D15711yescharacteristic
284C22×C4—3141no—
285C22×C4—3141no—
286C22×C4—3141no—
287C22×C4—3141no—
288C22×C4—1571no—
289C22×C4—1571no—
290C22×C4C22×D15711yescharacteristic
291Q16—3142no—
292SD16—22no—
293SD16—3142no—
294D8—3142no—
295M16—3142no—
296M16—3142no—
297M16—3142no—
298C2×C8—22no—
299C2×C8—3142no—
300C2×C8—1571no—
301C2×C8—1571no—
302C2×C8—1574no—
303C2×C8C22×D15711yescharacteristic
304C2×C8C22×D15711yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—3141no—
307C4⋊C4—3141no—
308C4⋊C4—3141no—
309C4⋊C4—3141no—
310C4⋊C4—3141no—
311C4⋊C4—1571no—
312C4⋊C4—1571no—
313C4⋊C4C22×D15711yescharacteristic
314C4⋊C4C22×D15711yescharacteristic
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—3141no—
318C22⋊C4—3141no—
319C22⋊C4—3141no—
320C22⋊C4—3141no—
321C22⋊C4—3141no—
322C22⋊C4—3141no—
323C23—21no—
324C23—3141no—
325C23—1571no—
326C23—1571no—
327C23D4×D15711yescharacteristic
328Q8—21no—
329Q8—21no—
330Q8—3142no—
331Q8—3141no—
332Q8—3141no—
333D4—21no—
334D4—21no—
335D4—81no—
336D4—3142no—
337D4—3142no—
338D4—3142no—
339D4—3141no—
340D4—3141no—
341D4—6282no—
342D4—6282no—
343D4—12561no—
344D4—12561no—
345D4—12561no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3141no—
352C2×C4—3141no—
353C2×C4—3141no—
354C2×C4—3141no—
355C2×C4—3141no—
356C2×C4—6282no—
357C2×C4—6282no—
358C2×C4—1571no—
359C2×C4—1571no—
360C2×C4—1572no—
361C2×C4—1572no—
362C2×C4—12561no—
363C2×C4—12561no—
364C2×C4D4×D15711yescharacteristic
365C2×C4C23×D15711yescharacteristic
366C8—21no—
367C8—3141no—
368C8—1572no—
369C8D4×D15712yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—3141no—
377C22—3141no—
378C22—3141no—
379C22—3141no—
380C22—3141no—
381C22—6281no—
382C22—6281no—
383C22—6281no—
384C22—1572no—
385C22C2×D4×D15711yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—3141no—
391C4—6281no—
392C4—6281no—
393C4—6281no—
394C4—1572no—
395C4C2×D4×D15711yescharacteristic
396C4#41×D15711yescharacteristic
397C2—41no—
398C2—81no—
399C2—3142no—
400C2—6281no—
401C2—12561no—
402C2#121×D15711yescharacteristic
403C2#2375807911yescharacteristic
404C2#2375808011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#465×C157C2
socleC22×C157C22×D4
hypercenter#465D157
hypocenterC157#3060
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#19097792C2semidirect
2. C2×#19097777C2semidirect
3. #23757853C2semidirect
4. #23757852C2semidirect
5. #23757530C2semidirect
6. #23757529C2semidirect
7. #23757525C2semidirect
8. #23757524C2semidirect
9. #23757503C2semidirect
10. #23757502C2semidirect
11. #23757499C2semidirect
12. #106×D157C2semidirect
13. #23757273C2semidirect
14. #23757271C2semidirect
15. #465×C157C2semidirect
93. C8×D157D4semidirect
202. C157#3060semidirect
215. #465D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977922
C2×#190977772
#237578532
#237578522
#237575302
#237575292
#237575252
#237575242
#237575032
#237575022
#237574992
#106×D1572
#237572732
#237572712
#465×C1572
#3060157