Finite Group Databasebeta

← #34109670

Subgroups — #34109670

Order 20096.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097795C211yesmaximal, characteristic, complemented
2C2×#19097790C211yesmaximal, characteristic, complemented
3#23757836C211yesmaximal, characteristic, complemented
4#23757752C211yesmaximal, characteristic, complemented
5#23757496C211yesmaximal, characteristic, complemented
6#23757494C211yesmaximal, characteristic, complemented
7#23757488C211yesmaximal, characteristic, complemented
8#23757486C211yesmaximal, characteristic, complemented
9#23757472C211yesmaximal, characteristic, complemented
10#23757470C211yesmaximal, characteristic, complemented
11#23757466C211yesmaximal, characteristic, complemented
12#23757298C211yesmaximal, characteristic, complemented
13#23757271C211yesmaximal, characteristic, complemented
14#102×D157C211yesmaximal, characteristic, complemented
15#459×C157C211yesmaximal, characteristic, complemented
16C2×#14578953C2211yescharacteristic
17C2×#14578953C2211yescharacteristic
18C2×D4×D157C2211yescharacteristic
19#19097795—24no—
20#19097790—24no—
21C2×Dic628C2211yescharacteristic, complemented
22C2×#14578943C2211yescharacteristic
23C2×#14578942C2211yescharacteristic
24C2×#14578942C2211yescharacteristic, complemented
25C2×#14578942C2211yescharacteristic, complemented
26C2×#14578939C2211yescharacteristic
27C2×#14578937C2211yescharacteristic
28C2×C8×D157C2211yescharacteristic
29#19097767C2211yescharacteristic
30#19097759C2211yescharacteristic
31#19097758C2211yescharacteristic
32#19097743—21no—
33#19097743—21no—
34#19097739—21no—
35#19097739—21no—
36C4×Dic314C2211yescharacteristic, complemented
37#19097736C2211yescharacteristic, complemented
38D4×Dic157C2211yescharacteristic, complemented
39C4×C22⋊D157—21no—
40#19097731—21no—
41#19097728C2211yescharacteristic
42#19097727—21no—
43C2×#14578933—21no—
44C4⋊C4×D157C2211yescharacteristic
45C4⋊#11929434C2211yescharacteristic, complemented
46#19097700C2211yescharacteristic, complemented
47#19097700C2211yescharacteristic, complemented
48#19097696C2211yescharacteristic, complemented
49#19097694C2211yescharacteristic, complemented
50#19097693C2211yescharacteristic
51#19097692C2211yescharacteristic
52#19097692C2211yescharacteristic, complemented
53#19097691C2211yescharacteristic
54C2×D8×C157C2211yescharacteristic
55C2×D8×C157C2211yescharacteristic, complemented
56#127×C157C2211yescharacteristic
57C4×D4×C157C2211yescharacteristic, complemented
58C4⋊C8×C157C2211yescharacteristic, complemented
59#102×C157C2211yescharacteristic
60#102×C157C2211yescharacteristic, complemented
61C23×D157—21no—
62#14578953—22no—
63#14578953—22no—
64#14578953—22no—
65#14578953D414yescomplemented
66C2×Dic314C2311yescharacteristic
67C2×Dic314C2311yescharacteristic
68C2×D628C2311yescharacteristic
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72C2×C22⋊D157—21no—
73C2×C22⋊D157—21no—
74D4×D157—22no—
75D4×D157—22no—
76C22×Dic157—21no—
77C22×Dic157—21no—
78C22×Dic157—21no—
79C2×C4×D157—21no—
80C2×C4×D157C2311yescharacteristic
81Dic628—22no—
82#14578943—22no—
83#14578942—22no—
84#14578942—22no—
85#14578942—22no—
86#14578939—22no—
87#14578937—22no—
88C2×#11929434C2311yescharacteristic
89C2×#11929434C2311yescharacteristic
90C8×D157—22no—
91C4⋊Dic157C2311yescharacteristic
92#14578933—21no—
93#14578933—21no—
94#14578933—21no—
95#14578933D411yescharacteristic
96#14578933D411yescharacteristic
97C22⋊Dic157—21no—
98C22⋊Dic157—21no—
99C22⋊Dic157—21no—
100#14578931—21no—
101#14578931—21no—
102#14578931D411yescharacteristic
103#14578931D411yescharacteristic
104C4×Dic157—21no—
105C4×Dic157—21no—
106C4×Dic157C2311yescharacteristic
107C2×D4×C157—21no—
108C2×D4×C157—21no—
109C2×D4×C157C2311yescharacteristic
110C2×D4×C157C2311yescharacteristic
111C2×D4×C157C2311yescharacteristic
112C22×C4×C157—21no—
113D8×C157—22no—
114D8×C157—22no—
115C2×C8×C157C2311yescharacteristic
116C2×C8×C157C2311yescharacteristic
117C4⋊C4×C157C2311yescharacteristic
118C22⋊C4×C157—21no—
119C42×C157C2311yescharacteristic
120C22×D157—21no—
121C22×D157—42no—
122C22×D157—81no—
123C22×D157—81no—
124C22×D157C2×D411yescharacteristic
125Dic314—21no—
126Dic314—21no—
127Dic314—21no—
128Dic314C2×D412yes—
129D628—21no—
130D628—21no—
131C22⋊D157—24no—
132C22⋊D157—42no—
133C22⋊D157—42no—
134C22⋊D157—81no—
135C22⋊D157—81no—
136C2×Dic157—21no—
137C2×Dic157—24no—
138C2×Dic157—21no—
139C2×Dic157—21no—
140C2×Dic157—42no—
141C2×Dic157—81no—
142C2×Dic157C2×D411yescharacteristic
143C2×Dic157C2×D411yescharacteristic
144C2×Dic157C2×D411yescharacteristic
145C4×D157—81no—
146C4×D157C2×D412yes—
147C4×D157#4112yes—
148#11929434—21no—
149#11929434—21no—
150C23×C157—21no—
151C23×C157—21no—
152C23×C157—21no—
153D4×C157—21no—
154D4×C157—21no—
155D4×C157—21no—
156D4×C157—21no—
157D4×C157—21no—
158D4×C157—81no—
159D4×C157—81no—
160D4×C157C2×D412yes—
161C2×C4×C157—21no—
162C2×C4×C157—81no—
163C2×C4×C157C2×D411yescharacteristic
164C2×C4×C157C2×D411yescharacteristic
165C2×C4×C157C2411yescharacteristic
166C8×C157—21no—
167C8×C157—21no—
168C22×C157—22no—
169C22×C157—41no—
170C22×C157—41no—
171C22×C157—41no—
172C22×C157—41no—
173C22×C157—41no—
174C22×C157—41no—
175C22×C157—41no—
176C22×C157—41no—
177C22×C157C22×D411yescharacteristic
178C2×D157—21no—
179C2×D157—21no—
180C2×D157—41no—
181C2×D157—41no—
182C2×D157—41no—
183C2×D157—84no—
184C2×D157#12112yes—
185C4×C157—21no—
186C4×C157—21no—
187C4×C157—41no—
188C4×C157C22×D411yescharacteristic
189C4×C157C2×#4111yescharacteristic
190Dic157—22no—
191Dic157—21no—
192Dic157—21no—
193Dic157—41no—
194Dic157—41no—
195Dic157#12112yes—
196C2×C157—42no—
197C2×C157—81no—
198C2×C157—81no—
199C2×C157C2×#12111yescharacteristic
200C2×C157#57611yescharacteristic
201C2×C157#57711yescharacteristic
202D157—22no—
203D157—81no—
204C157#304511yescharacteristic, complemented, Sylow
205#3045—1571nomaximal, Sylow
206C2×AGL(1,ℤ/8)—1571no—
207C2×#135—1571no—
208#535—1571no—
209#520—1571no—
210#464—1571no—
211#464—1571no—
212#463—1571no—
213#463—1571no—
214#460—1571no—
215#460—1571no—
216#459—1571no—
217#459D15711yescharacteristic, complemented
218#424—1571no—
219#417—1571no—
220C2×#102—1571no—
221C2×#41—1571no—
222C2×#41—1571no—
223C22×D4—1571no—
224AGL(1,ℤ/8)—3144no—
225#135—3144no—
226C2×Q16—1571no—
227C2×SD16—1571no—
228C2×SD16—1571no—
229C2×SD16—1571no—
230C2×SD16—1571no—
231C2×D8—1571no—
232C2×D8C2×D15711yescharacteristic
233C2×D8C2×D15711yescharacteristic, complemented
234C2×M16—1571no—
235C22×C8—1571no—
236#127—1571no—
237#127C2×D15711yescharacteristic
238#124—1571no—
239#124—1571no—
240#121—3141no—
241#121—3141no—
242#120—3141no—
243#120—3141no—
244C4×Q8—1571no—
245C4×Q8—1571no—
246C4×D4—3141no—
247C4×D4—3141no—
248C4×D4—1571no—
249C4×D4C2×D15711yescharacteristic, complemented
250#117—3141no—
251#117—1571no—
252C2×C4⋊C4—3141no—
253C2×C4⋊C4—1571no—
254C4⋊C8—1571no—
255C4⋊C8—1571no—
256C4⋊C8—1571no—
257C4⋊C8C2×D15711yescharacteristic, complemented
258#103—1571no—
259#103—1571no—
260#102—1571no—
261#102—1571no—
262#102—1571no—
263#102—1571no—
264#102C2×D15711yescharacteristic
265#102C2×D15711yescharacteristic, complemented
266C24—3141no—
267#41—3142no—
268#41—3142no—
269#41—3142no—
270#41—1574no—
271C2×Q8—1571no—
272C2×Q8—1571no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—3141no—
276C2×D4—3141no—
277C2×D4—3142no—
278C2×D4—3142no—
279C2×D4—3141no—
280C2×D4—3141no—
281C2×D4—3141no—
282C2×D4—1571no—
283C2×D4C22×D15711yescharacteristic
284C2×D4C22×D15711yescharacteristic
285C2×D4C22×D15711yescharacteristic
286C22×C4—21no—
287C22×C4—3141no—
288C22×C4—3141no—
289C22×C4—3141no—
290C22×C4—3141no—
291C22×C4—1571no—
292Q16—3142no—
293SD16—3142no—
294SD16—3142no—
295SD16—3142no—
296SD16—3142no—
297D8—22no—
298D8—22no—
299D8—3142no—
300M16—3142no—
301C2×C8—3142no—
302C2×C8—1571no—
303C2×C8—1571no—
304C2×C8C22×D15711yescharacteristic
305C2×C8C22×D15711yescharacteristic
306C4⋊C4—3141no—
307C4⋊C4—3141no—
308C4⋊C4—3141no—
309C4⋊C4—1571no—
310C4⋊C4—1571no—
311C4⋊C4—1571no—
312C4⋊C4C22×D15711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—3141no—
315C22⋊C4—3141no—
316C22⋊C4—3141no—
317C22⋊C4—3141no—
318C22⋊C4—3141no—
319C22⋊C4—1571no—
320C22⋊C4—1571no—
321C42—3141no—
322C42—3141no—
323C42—1571no—
324C42C22×D15711yescharacteristic
325C23—21no—
326C23—21no—
327C23—21no—
328C23—3141no—
329C23—6282no—
330C23—1571no—
331C23—12561no—
332C23—12561no—
333Q8—3141no—
334Q8—3141no—
335Q8—3141no—
336Q8—1572no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—81no—
343D4—81no—
344D4—3144no—
345D4—3141no—
346D4—3141no—
347D4—6282no—
348D4—6282no—
349D4—12561no—
350D4—12561no—
351D4D4×D15712yes—
352C2×C4—21no—
353C2×C4—81no—
354C2×C4—3141no—
355C2×C4—3144no—
356C2×C4—3141no—
357C2×C4—3141no—
358C2×C4—6282no—
359C2×C4—1571no—
360C2×C4—1571no—
361C2×C4—1571no—
362C2×C4—1572no—
363C2×C4—1572no—
364C2×C4—12561no—
365C2×C4—12561no—
366C2×C4D4×D15711yescharacteristic
367C2×C4D4×D15711yescharacteristic
368C2×C4C23×D15711yescharacteristic
369C8—21no—
370C8—21no—
371C8—3141no—
372C8—3141no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—3141no—
383C22—3141no—
384C22—6281no—
385C22—6281no—
386C22—6281no—
387C22—1572no—
388C22—12564no—
389C22C2×D4×D15711yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—3141no—
394C4—3142no—
395C4—3141no—
396C4—6281no—
397C4—6281no—
398C4—1572no—
399C4C2×D4×D15711yescharacteristic
400C4#41×D15711yescharacteristic
401C2—42no—
402C2—81no—
403C2—81no—
404C2—3142no—
405C2—12561no—
406C2#121×D15711yescharacteristic
407C2#2375807411yescharacteristic
408C2#2375808311yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#459×C157C2
socleC22×C157C22×D4
hypercenter#459D157
hypocenterC157#3045
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#19097795C2semidirect
2. C2×#19097790C2semidirect
3. #23757836C2semidirect
4. #23757752C2semidirect
5. #23757496C2semidirect
6. #23757494C2semidirect
7. #23757488C2semidirect
8. #23757486C2semidirect
9. #23757472C2semidirect
10. #23757470C2semidirect
11. #23757466C2semidirect
12. #23757298C2semidirect
13. #23757271C2semidirect
14. #102×D157C2semidirect
15. #459×C157C2semidirect
21. C2×Dic628C22semidirect
24. C2×#14578942C22semidirect
25. C2×#14578942C22semidirect
36. C4×Dic314C22semidirect
37. #19097736C22semidirect
38. D4×Dic157C22semidirect
45. C4⋊#11929434C22semidirect
46. #19097700C22semidirect
47. #19097700C22semidirect
48. #19097696C22semidirect
49. #19097694C22semidirect
52. #19097692C22semidirect
55. C2×D8×C157C22semidirect
57. C4×D4×C157C22semidirect
58. C4⋊C8×C157C22semidirect
60. #102×C157C22semidirect
65. #14578953D4semidirect
204. C157#3045semidirect
217. #459D157semidirect
233. C2×D8C2×D157semidirect
249. C4×D4C2×D157semidirect
257. C4⋊C8C2×D157semidirect
265. #102C2×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977952
C2×#190977902
#237578362
#237577522
#237574962
#237574942
#237574882
#237574862
#237574722
#237574702
#237574662
#237572982
#237572712
#102×D1572
#459×C1572
#3045157