Finite Group Databasebeta

← #28487796

Subgroups — #28487796

Order 15104.

486 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432473C211yesmaximal, characteristic
2#21424247C211yesmaximal, characteristic
3#21423951C211yesmaximal, characteristic
4C2×#16837149C211yesmaximal, characteristic
5C2×#16837148C211yesmaximal, characteristic
6C2×#16837147C211yesmaximal, characteristic
7C2×C59×#332C211yesmaximal, characteristic
8C2×#14273727C2211yescharacteristic
9C2×C4⋊(C59⋊C8)C2211yescharacteristic
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×Dic59⋊C8—22no—
12C2×#14273637—21no—
13#16837309—21no—
14#16837309—21no—
15#16837307—22no—
16#16837267C414yes—
17C42×Dic59C2211yescharacteristic
18#16837156—21no—
19#16837149—22no—
20#16837148—22no—
21#16837147—22no—
22C2×C4⋊Q8×C59C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C2×C4⋊C8×C59C2211yescharacteristic
25C59×#332—22no—
26C22×Dic118—21no—
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29#14273727—21no—
30#14273727—21no—
31#14273727—21no—
32#14273727—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59C2×C412yes—
35C2×C4×Dic59C2×C412yes—
36C2×C4×Dic59D411yescharacteristic
37C2×C4×Dic59D412yes—
38C2×C4×Dic59D411yescharacteristic
39C4⋊(C59⋊C8)—21no—
40C4⋊(C59⋊C8)—21no—
41C4⋊(C59⋊C8)—21no—
42C4⋊(C59⋊C8)D412yes—
43Dic59⋊C8—44no—
44#14273637—42no—
45C59⋊#95—24no—
46C59⋊#95—24no—
47C22×Q8×C59—21no—
48C22×C8×C59—21no—
49C22×C8×C59—21no—
50C4⋊Q8×C59—21no—
51C4⋊Q8×C59—21no—
52C4⋊Q8×C59—21no—
53C4⋊Q8×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59C2×C412yes—
56C2×C42×C59C2311yescharacteristic
57C4⋊C8×C59—21no—
58C4⋊C8×C59—21no—
59C4⋊C8×C59—21no—
60C4⋊C8×C59D412yes—
61C2×Q8×C59—41no—
62C2×Q8×C59—41no—
63C2×Q8×C59—41no—
64C2×Q8×C59—41no—
65C2×Q8×C59—41no—
66C2×Q8×C59—41no—
67C22×C4×C59—22no—
68C22×C4×C59C22×C411yescharacteristic
69C22×C4×C59C2×D411yescharacteristic
70C22×C4×C59C2×D411yescharacteristic
71C22×Dic59—22no—
72C22×Dic59C22⋊C412yes—
73C22×Dic59C22⋊C412yes—
74C2×Dic118—41no—
75C2×Dic118—41no—
76C2×Dic118—42no—
77C2×Dic118—42no—
78C2×C8×C59—22no—
79C2×C8×C59—41no—
80C2×C8×C59—41no—
81C2×C8×C59—41no—
82C2×C8×C59—42no—
83C4⋊C4×C59—22no—
84C4⋊C4×C59—22no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59—41no—
87C42×C59C2×D411yescharacteristic
88C42×C59C2×D411yescharacteristic
89C42×C59#4111yescharacteristic
90C42×C59#4111yescharacteristic
91C4⋊Dic59—22no—
92C4⋊Dic59—22no—
93C4⋊Dic59—41no—
94C4⋊Dic59—41no—
95C4×Dic59—21no—
96C4×Dic59—21no—
97C4×Dic59—21no—
98C4×Dic59—22no—
99C4×Dic59—22no—
100C4×Dic59—21no—
101C4×Dic59—24no—
102C2×C59⋊C8—22no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8—41no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—42no—
107C23×C59C2×C22⋊C411yescharacteristic
108Q8×C59—81no—
109Q8×C59—81no—
110Q8×C59—81no—
111Q8×C59—81no—
112C2×C4×C59—22no—
113C2×C4×C59—42no—
114C2×C4×C59—42no—
115C2×C4×C59—42no—
116C2×C4×C59C4×D411yescharacteristic
117C2×C4×C59C4×D411yescharacteristic
118C2×C4×C59#12111yescharacteristic
119C2×C4×C59#12111yescharacteristic
120C2×C4×C59#12411yescharacteristic
121C2×C4×C59#12711yescharacteristic
122C2×C4×C59#13511yescharacteristic
123C2×C4×C59#13511yescharacteristic
124C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C59AGL(1,ℤ/8)12yes—
126C2×C4×C59#13711yescharacteristic
127C2×C4×C59#13712yes—
128C2×Dic59—22no—
129C2×Dic59—22no—
130C2×Dic59—22no—
131C2×Dic59—22no—
132C2×Dic59—22no—
133C2×Dic59—42no—
134C2×Dic59—44no—
135C2×Dic59#10114yes—
136Dic118—82no—
137Dic118—81no—
138Dic118—81no—
139C8×C59—42no—
140C8×C59—81no—
141C59⋊C8—42no—
142C59⋊C8—81no—
143#9708—591nomaximal, Sylow
144C22×C59#39011yescharacteristic
145C22×C59C2×#10112yes—
146C22×C59#41611yescharacteristic
147C22×C59#41711yescharacteristic
148C22×C59#41712yes—
149C4×C59—21no—
150C4×C59—21no—
151C4×C59—82no—
152C4×C59#46311yescharacteristic
153C4×C59#46311yescharacteristic
154C4×C59#46411yescharacteristic
155C4×C59#46411yescharacteristic
156C4×C59#48912yes—
157C4×C59#49611yescharacteristic
158C4×C59#49711yescharacteristic
159Dic59—24no—
160Dic59—42no—
161Dic59—82no—
162#2862—591no—
163#1842—591no—
164#1767—591no—
165C2×#332—591no—
166C2×#332—591no—
167C2×#332—591no—
168C2×#332D5911yescharacteristic
169C2×C59#155212yes—
170C2×C59#156112yes—
171C2×C59#195911yescharacteristic
172C2×C59#196611yescharacteristic
173C2×C59#198311yescharacteristic
174C2×C4⋊Q8—591no—
175C2×C4⋊Q8C2×D5911yescharacteristic
176C2×C4⋊C8—591no—
177C2×C4⋊C8—591no—
178C2×C4⋊C8—1182no—
179C2×C4⋊C8C2×D5911yescharacteristic
180C2×C4⋊C8C2×D5911yescharacteristic
181C2×#97—1181no—
182#391—1182no—
183#391—1181no—
184#391—1181no—
185#382—594no—
186C43—591no—
187#336—1181no—
188#332—22no—
189#332—1182no—
190#332—1182no—
191#332—1182no—
192C59#970811yescharacteristic, complemented, Sylow
193C22×Q8—21no—
194C22×Q8—1181no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—1181no—
198C22×C8—1181no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—1181no—
204C4⋊Q8—1181no—
205C4⋊Q8—1181no—
206C4⋊Q8—1181no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—592no—
209C2×C4⋊C4—1181no—
210C2×C4⋊C4C4×D5912yes—
211C2×C42—592no—
212C2×C42—591no—
213C2×C42—591no—
214C2×C42—592no—
215C2×C42C22×D5911yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—592no—
220C4⋊C8—1181no—
221C4⋊C8—1181no—
222C4⋊C8—1181no—
223C4⋊C8—2364no—
224C4⋊C8C22⋊D5912yes—
225#97—2362no—
226#95—1184no—
227#95—1184no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—2361no—
235C2×Q8—2361no—
236C2×Q8—2362no—
237C2×Q8—2362no—
238C22×C4—22no—
239C22×C4—592no—
240C22×C4—592no—
241C22×C4—1182no—
242C22×C4C2×C4×D5911yescharacteristic
243C22×C4D4×D5911yescharacteristic
244C22×C4D4×D5911yescharacteristic
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—42no—
250C2×C8—1182no—
251C2×C8—2361no—
252C2×C8—2362no—
253C2×C8—2361no—
254C2×C8—2361no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—1182no—
260C4⋊C4—1182no—
261C4⋊C4—2361no—
262C4⋊C4—2361no—
263C42—1184no—
264C42—1181no—
265C42—1181no—
266C42—1181no—
267C42—1182no—
268C42—1181no—
269C42—1182no—
270C42#1174568511yescharacteristic
271C42D4×D5911yescharacteristic
272C42#1174568711yescharacteristic
273C42C2×C22⋊D5911yescharacteristic
274C23C22⋊C4×D5911yescharacteristic
275Q8—81no—
276Q8—81no—
277Q8—81no—
278Q8—81no—
279Q8—4722no—
280Q8—4721no—
281Q8—4721no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—594no—
287C2×C4—1182no—
288C2×C4—1182no—
289C2×C4—1182no—
290C2×C4—1182no—
291C2×C4—1182no—
292C2×C4—2364no—
293C2×C4—2362no—
294C2×C4(C22⋊D59)⋊C411yescharacteristic
295C2×C4C4×C22⋊D5911yescharacteristic
296C2×C4#1427369911yescharacteristic
297C2×C4#1427370011yescharacteristic
298C2×C4#1427371311yescharacteristic
299C2×C4#1427372311yescharacteristic
300C2×C4#1427374611yescharacteristic
301C2×C4#1427374811yescharacteristic
302C2×C4#1427375111yescharacteristic
303C2×C4#1427375412yes—
304C2×C4#1427375611yescharacteristic
305C2×C4#1427375912yes—
306C8—42no—
307C8—81no—
308C8—4721no—
309C8—2362no—
310C22#1683730211yescharacteristic
311C22#101×D5912yes—
312C22#1683739511yescharacteristic
313C22#1683740011yescharacteristic
314C22#1683740212yes—
315C4—21no—
316C4—21no—
317C4—82no—
318C4—1184no—
319C4—4722no—
320C4—2362no—
321C4#1683761511yescharacteristic
322C4#1683761611yescharacteristic
323C4#1683762211yescharacteristic
324C4#1683762311yescharacteristic
325C4#1683776312yes—
326C4#1683778811yescharacteristic
327C4#1683779511yescharacteristic
328C2#2142279312yes—
329C2#2142283212yes—
330C2#2142490911yescharacteristic
331C2#2142493811yescharacteristic
332C2#2142502711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC2×C59×#332C2
socle, prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#332D59
hypocenterC59#9708
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
192. C59#9708semidirect

Maximal subgroups

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

subgroupindex
#214324732
#214242472
#214239512
C2×#168371492
C2×#168371482
C2×#168371472
C2×C59×#3322
#970859