Finite Group Databasebeta

← #28481859

Subgroups — #28481859

Order 15104.

454 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#11745685C211yesmaximal, characteristic
2#21424117C212yesmaximal
3#21422855C211yesmaximal, characteristic, complemented
4#21421999C212yesmaximal, complemented
5C4×#107×C59C211yesmaximal, characteristic, complemented
6C4×#11745685C2211yescharacteristic
7C8×Dic118C411yescharacteristic, complemented
8C8×Dic118C411yescharacteristic, complemented
9C8×D236C411yescharacteristic, complemented
10C8×D236C411yescharacteristic, complemented
11C8×C22⋊D59—21no—
12C8×C22⋊D59—21no—
13#16837455C2211yescharacteristic
14#16837453—21no—
15#16837426C2212yes—
16C2×#14273655—22no—
17C4×C8×D59—21no—
18#16837162—22no—
19#16837155—21no—
20#16837155—21no—
21C2×#107×C59—21no—
22C2×C4×C8×C59C2211yescharacteristic
23C4×C4⋊C4×C59C2212yes—
24C59×#340—21no—
25C2×#11745685D411yescharacteristic
26C2×#11745664—22no—
27C2×C8×D59—21no—
28C2×C8×D59—21no—
29C4×Dic118C2×C411yescharacteristic
30C4×Dic118Q811yescharacteristic
31C4×D236C2×C411yescharacteristic
32C4×D236Q811yescharacteristic
33C4×C22⋊D59—21no—
34C4×C22⋊D59—21no—
35#14273686D411yescharacteristic
36#14273684—21no—
37C42×D59—21no—
38C4⋊(C59⋊C8)—22no—
39C4⋊(C59⋊C8)—22no—
40C4⋊(C59⋊C8)C2×C411yescharacteristic
41C4⋊(C59⋊C8)C2×C411yescharacteristic
42Dic59⋊C8—21no—
43Dic59⋊C8—21no—
44#14273655—44no—
45C22⋊(C59⋊C8)—21no—
46(C2×D59)⋊C8—21no—
47(C2×D59)⋊C8—21no—
48C4×C59⋊C8—21no—
49C8×Dic59—21no—
50C8×Dic59—21no—
51C22×C8×C59D411yescharacteristic
52C22×C8×C59D411yescharacteristic
53C2×C4⋊C4×C59—22no—
54C2×C42×C59—22no—
55C2×C42×C59C2311yescharacteristic
56#107×C59—24no—
57C4×C8×C59C2×C411yescharacteristic
58C4×C8×C59C2×C411yescharacteristic
59C4×C8×C59D411yescharacteristic
60C4×C8×C59D411yescharacteristic
61#95×C59—22no—
62C22×C4×C59—42no—
63C22×C4×C59C2×D411yescharacteristic
64C22×C4×C59C2×D411yescharacteristic
65C22×C4×C59#4111yescharacteristic
66C2×C22⋊D59—21no—
67#11745685—21no—
68#11745685—21no—
69#11745685D812yes—
70#11745685Q1612yes—
71C2×D236C4⋊C411yescharacteristic
72C2×C4×D59—21no—
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×Dic118C4⋊C411yescharacteristic
76C2×C8×C59—22no—
77C2×C8×C59—41no—
78C2×C8×C59C22⋊C411yescharacteristic
79C2×C8×C59C22⋊C411yescharacteristic
80C2×C8×C59C22⋊C411yescharacteristic
81C2×C8×C59C22⋊C411yescharacteristic
82C4⋊C4×C59—24no—
83C4⋊C4×C59—42no—
84C42×C59—42no—
85C42×C59—42no—
86C42×C59C22×C411yescharacteristic
87C42×C59C2×D411yescharacteristic
88C42×C59C2×Q811yescharacteristic
89C42×C59#4111yescharacteristic
90C22⋊Dic59—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93C4⋊Dic59C4⋊C411yescharacteristic
94C4⋊Dic59C4⋊C411yescharacteristic
95Dic59⋊C4—21no—
96Dic59⋊C4—21no—
97C4×Dic59—21no—
98C4×Dic59—21no—
99C4×Dic59—21no—
100#11745664—42no—
101#11745664—42no—
102C2×C59⋊C8—21no—
103C2×C59⋊C8—21no—
104C2×C59⋊C8—42no—
105C8×D59—42no—
106C8×D59—42no—
107C23×C59#12111yescharacteristic
108C22×D59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—41no—
112C2×C4×C59—44no—
113C2×C4×C59—82no—
114C2×C4×C59—82no—
115C2×C4×C59C2×C22⋊C411yescharacteristic
116C2×C4×C59C2×C4⋊C411yescharacteristic
117C2×C4×C59#11711yescharacteristic
118C2×C4×C59#12111yescharacteristic
119C2×C4×C59C22⋊Q811yescharacteristic
120C2×C4×C59C22⋊Q811yescharacteristic
121C2×C4×C59C2×D811yescharacteristic
122C2×C4×C59C2×Q1611yescharacteristic
123C2×C4×C59#13511yescharacteristic
124C2×C4×C59#13511yescharacteristic
125C22⋊D59—22no—
126C22⋊D59—22no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130D236—21no—
131D236#10712yescomplemented
132C4×D59—22no—
133C4×D59—22no—
134C4×D59—42no—
135C4×D59—41no—
136C4×D59—41no—
137Dic118—21no—
138Dic118#10712yescomplemented
139C8×C59—21no—
140C8×C59—21no—
141C8×C59—21no—
142C8×C59#10412yescomplemented
143C59⋊C8—41no—
144C59⋊C8—41no—
145C59⋊C8—82no—
146#8667—591nomaximal, Sylow
147C22×C59—21no—
148C22×C59—21no—
149C22×C59#38011yescharacteristic
150C22×C59#46611yescharacteristic
151C22×C59#46711yescharacteristic
152C2×D59—22no—
153C2×D59—41no—
154C2×D59—41no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—84no—
159C4×C59C2×#10411yescharacteristic
160C4×C59#42111yescharacteristic
161C4×C59C2×#10711yescharacteristic
162C4×C59#42711yescharacteristic
163C4×C59#46611yescharacteristic
164C4×C59#46711yescharacteristic
165Dic59—22no—
166Dic59—41no—
167Dic59—41no—
168C8×#41—591no—
169#1806—592no—
170C4×#107D5911yescharacteristic, complemented
171#1567—591no—
172#1303—592no—
173C2×C59—21no—
174C2×C59—21no—
175C2×C59#180611yescharacteristic
176C2×C59#180811yescharacteristic
177C2×C59#181411yescharacteristic
178D59—42no—
179C4×#41—591no—
180C8×Q8—591no—
181C8×Q8—591no—
182C8×D4—591no—
183C8×D4—591no—
184C8×D4—1181no—
185C8×D4—1181no—
186#431—591no—
187#431—1181no—
188C2×#107—21no—
189#423—592no—
190C2×#104—1182no—
191C2×C4×C8—1181no—
192C2×C4×C8C2×D5911yescharacteristic
193C4×C4⋊C4C2×D5912yes—
194#340—21no—
195#339—1182no—
196#335—1181no—
197#335—1181no—
198C59#866711yescharacteristic, complemented, Sylow
199C2×#41—591no—
200C2×M16—1182no—
201C22×C8—1181no—
202C22×C8—1181no—
203C22×C8C22⋊D5911yescharacteristic
204C22×C8C22⋊D5911yescharacteristic
205C4×Q8—591no—
206C4×Q8—591no—
207C4×D4—591no—
208C4×D4—591no—
209C4×D4—1181no—
210C4×D4—1181no—
211#117—591no—
212#117—1181no—
213C2×C4⋊C4—22no—
214C2×C42—22no—
215C2×C42—1181no—
216C2×C42C22×D5911yescharacteristic
217#107—24no—
218C4⋊C8—591no—
219C4⋊C8—591no—
220C4⋊C8—1181no—
221C4⋊C8—1181no—
222C4⋊C8—1182no—
223C4⋊C8—1182no—
224#104—2364no—
225C22⋊C8—1181no—
226C22⋊C8—1181no—
227C22⋊C8—1181no—
228C4×C8—1181no—
229C4×C8—1181no—
230C4×C8—1181no—
231C4×C8C4×D5911yescharacteristic
232C4×C8C4×D5911yescharacteristic
233C4×C8D23611yescharacteristic
234C4×C8D23611yescharacteristic
235#95—22no—
236#41—592no—
237#41—592no—
238#41—1181no—
239#41—1181no—
240C2×Q8—591no—
241C2×D4—591no—
242C2×D4—1181no—
243C22×C4—42no—
244C22×C4—1181no—
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4D4×D5911yescharacteristic
248C22×C4#1174568711yescharacteristic
249C22×C4C2×C22⋊D5911yescharacteristic
250M16—2362no—
251M16—2362no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—1181no—
255C2×C8—1181no—
256C2×C8—2362no—
257C2×C8—2362no—
258C2×C8—2362no—
259C2×C8(C2×D59)⋊C411yescharacteristic
260C2×C8(C2×D59)⋊C411yescharacteristic
261C2×C8(C2×D59)⋊C411yescharacteristic
262C2×C8(C2×D59)⋊C411yescharacteristic
263C4⋊C4—24no—
264C4⋊C4—42no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C22⋊C4—1181no—
270C22⋊C4—1181no—
271C22⋊C4—1181no—
272C42—42no—
273C42—42no—
274C42—1181no—
275C42—1181no—
276C42—1181no—
277C42C2×C4×D5911yescharacteristic
278C42C2×D23611yescharacteristic
279C42Q8×D5911yescharacteristic
280C42#1174568911yescharacteristic
281C23—1181no—
282C23#1427369811yescharacteristic
283Q8—592no—
284Q8—1181no—
285D4—592no—
286D4—1182no—
287D4—1182no—
288D4—1181no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—44no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—1181no—
296C2×C4—1182no—
297C2×C4—1182no—
298C2×C4—1181no—
299C2×C4—1181no—
300C2×C4—2362no—
301C2×C4—2361no—
302C2×C4—2361no—
303C2×C4C2×(C2×D59)⋊C411yescharacteristic
304C2×C4C4⋊C4×D5911yescharacteristic
305C2×C4#1427368511yescharacteristic
306C2×C4#1427370211yescharacteristic
307C2×C4#1427370311yescharacteristic
308C2×C4#1427370711yescharacteristic
309C2×C4D8×D5911yescharacteristic
310C2×C4Q16×D5911yescharacteristic
311C2×C4#1427374611yescharacteristic
312C2×C4#1427375011yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—4722no—
317C8—2361no—
318C8—2361no—
319C8#1427365512yescomplemented
320C22—21no—
321C22—21no—
322C22—1182no—
323C22—2361no—
324C22—2361no—
325C22#1683725911yescharacteristic
326C22#1683763511yescharacteristic
327C22#1683764011yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—84no—
332C4—1182no—
333C4—2361no—
334C4—2361no—
335C4C2×#1427365511yescharacteristic
336C4#1683742011yescharacteristic
337C4#107×D5911yescharacteristic
338C4#1683743911yescharacteristic
339C4#1683763911yescharacteristic
340C4#1683764411yescharacteristic
341C2—21no—
342C2—21no—
343C2—2362no—
344C2#2142411711yescharacteristic
345C2#2142412211yescharacteristic
346C2#2142414711yescharacteristic
subgroupG/H
centerC2×C4#14273702
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC4×#107×C59C2
socleC22×C59#380
prime radicalC2×#11745685D4
cosocleC2×C42×C59C23
hypercenterC4×#107D59
hypocenterC59#8667
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
3. #21422855C2semidirect
4. #21421999C2semidirect
5. C4×#107×C59C2semidirect
7. C8×Dic118C4semidirect
8. C8×Dic118C4semidirect
9. C8×D236C4semidirect
10. C8×D236C4semidirect
131. D236#107semidirect
138. Dic118#107semidirect
142. C8×C59#104semidirect
170. C4×#107D59semidirect
198. C59#8667semidirect
319. C8#14273655semidirect

Maximal subgroups

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

subgroupindex
C8×#117456852
#214241172
#214228552
#214219992
C4×#107×C592
#866759