Finite Group Databasebeta

← #28477315

Subgroups — #28477315

Order 15104.

506 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432427C211yesmaximal, characteristic
2#21424164C211yesmaximal, characteristic, complemented
3#21421918C212yesmaximal, complemented
4#21421916C212yesmaximal, complemented
5C59×#1817C211yesmaximal, characteristic, complemented
6C2×#14273710—21no—
7C2×#14273701C411yescharacteristic
8C2×C22⋊(C59⋊C8)—21no—
9#16837304C411yescharacteristic
10#16837304C2211yescharacteristic
11#16837300C411yescharacteristic
12#16837300C2211yescharacteristic
13#16837293—21no—
14#16837293—21no—
15#16837281—21no—
16#16837262C411yescharacteristic
17#16837157—21no—
18#16837157C2212yes—
19C22×C42×C59C2211yescharacteristic
20C2×C22⋊C8×C59—21no—
21C59×#336—21no—
22C59×#336C2212yes—
23C22×D236C2×C411yescharacteristic
24C22×C22⋊D59—21no—
25C22×C59⋊C8—22no—
26#14273710—44no—
27#14273701—42no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×C4⋊Dic59C2×C411yescharacteristic
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×C22⋊Dic59—21no—
34C2×(C2×D59)⋊C4—21no—
35C2×(C2×D59)⋊C4—21no—
36C2×(C2×D59)⋊C4—21no—
37C2×(C2×D59)⋊C4—21no—
38C2×(C2×D59)⋊C4—21no—
39C22⋊(C59⋊C8)—42no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C23×C4×C59C2×C411yescharacteristic
44C23×C4×C59D411yescharacteristic
45C23×C4×C59D411yescharacteristic
46C22×C8×C59—22no—
47C2×C42×C59—42no—
48C2×C42×C59C2×C411yescharacteristic
49C2×C42×C59D411yescharacteristic
50C2×C42×C59D411yescharacteristic
51C2×C42×C59C2311yescharacteristic
52C22⋊C8×C59—42no—
53C24×C59C22⋊C411yescharacteristic
54C23×D59—21no—
55C22×C4×C59—22no—
56C22×C4×C59—22no—
57C22×C4×C59—22no—
58C22×C4×C59—22no—
59C22×C4×C59—22no—
60C22×C4×C59—22no—
61C22×C4×C59—41no—
62C22×C4×C59—41no—
63C22×C4×C59—41no—
64C22×C4×C59C22⋊C411yescharacteristic
65C22×C4×C59C22⋊C411yescharacteristic
66C22×C4×C59C22⋊C411yescharacteristic
67C22×C4×C59C22×C411yescharacteristic
68C22×C4×C59C2×D411yescharacteristic
69C22×C4×C59C2×D411yescharacteristic
70C2×C22⋊D59—42no—
71C2×C22⋊D59—42no—
72C2×C22⋊D59—42no—
73C22×Dic59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C2×D236—22no—
77C2×D236—41no—
78C2×D236—41no—
79C2×C8×C59—42no—
80C2×C8×C59—42no—
81C2×C8×C59—42no—
82C42×C59—41no—
83C42×C59—41no—
84C42×C59—41no—
85C42×C59—41no—
86C22⋊Dic59—42no—
87(C2×D59)⋊C4—42no—
88(C2×D59)⋊C4—42no—
89(C2×D59)⋊C4—42no—
90(C2×D59)⋊C4—42no—
91(C2×D59)⋊C4—42no—
92C4⋊Dic59—22no—
93C4⋊Dic59—41no—
94C4⋊Dic59—41no—
95Dic59⋊C4—42no—
96Dic59⋊C4—42no—
97C2×C59⋊C8—42no—
98C2×C59⋊C8—42no—
99C2×C59⋊C8—42no—
100C23×C59—21no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59—21no—
104C23×C59—21no—
105C23×C59—21no—
106C23×C59#9912yes—
107C23×C59C2×C22⋊C411yescharacteristic
108C22×D59—41no—
109C22×D59—41no—
110C22×D59—41no—
111C22×D59—41no—
112C22×D59—41no—
113C22×D59—41no—
114C22×D59—41no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—44no—
131C2×C4×C59—44no—
132C2×C4×C59—44no—
133C2×C4×C59#13112yes—
134C2×C4×C59#13512yes—
135C2×C4×C59AGL(1,ℤ/8)12yes—
136C22⋊D59—84no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146D236—82no—
147C8×C59—82no—
148C59⋊C8—82no—
149#7718—591nomaximal, Sylow
150C22×C59—22no—
151C22×C59—22no—
152C22×C59—22no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59#40811yescharacteristic
158C22×C59C2×#9911yescharacteristic
159C22×C59#41311yescharacteristic
160C22×C59#41611yescharacteristic
161C22×C59#41811yescharacteristic
162C22×C59#42111yescharacteristic
163C22×C59#42111yescharacteristic
164C2×D59—81no—
165C2×D59—81no—
166C2×D59—81no—
167C2×D59—81no—
168C2×D59—81no—
169C2×D59—81no—
170C2×D59—81no—
171C4×C59—22no—
172C4×C59—22no—
173C4×C59—22no—
174C4×C59—41no—
175C4×C59—41no—
176C4×C59—41no—
177Dic59—81no—
178Dic59—81no—
179Dic59—81no—
180#2854—591no—
181#1817—591no—
182#1817D5911yescharacteristic, complemented
183#1271—592no—
184#1270—592no—
185C2×C59—42no—
186C2×C59#146811yescharacteristic
187C2×C59#148211yescharacteristic
188C2×C59#149611yescharacteristic
189C2×C59#151011yescharacteristic
190C2×C59#151611yescharacteristic
191C2×C59#153511yescharacteristic
192C2×C59#155311yescharacteristic
193D59—161no—
194C2×#123—1181no—
195C2×#121—591no—
196C22×C42C2×D5911yescharacteristic
197C2×C22⋊C8—21no—
198C2×C22⋊C8—1181no—
199#390—591no—
200#390—591no—
201#389—591no—
202#389—591no—
203#388—1181no—
204#388—1181no—
205#386—1181no—
206#380—591no—
207#336—21no—
208#336—592no—
209#336—1181no—
210#336C2×D5912yes—
211C59#771811yescharacteristic, complemented, Sylow
212C22×D4—591no—
213C22×D4—1181no—
214C23×C4C4×D5911yescharacteristic
215C23×C4D23611yescharacteristic
216C23×C4C22⋊D5911yescharacteristic
217C22×C8—22no—
218C22×C8—1182no—
219#123—2364no—
220#121—2362no—
221C2×C4⋊C4—591no—
222C2×C4⋊C4—591no—
223C2×C4⋊C4—591no—
224C2×C4⋊C4—1181no—
225C2×C4⋊C4—1181no—
226C2×C22⋊C4—1181no—
227C2×C22⋊C4—1181no—
228C2×C22⋊C4—1181no—
229C2×C22⋊C4—1181no—
230C2×C22⋊C4—1181no—
231C2×C22⋊C4—1181no—
232C2×C42—42no—
233C2×C42C4×D5911yescharacteristic
234C2×C42D23611yescharacteristic
235C2×C42C22⋊D5911yescharacteristic
236C2×C42C22×D5911yescharacteristic
237C22⋊C8—42no—
238C22⋊C8—2362no—
239#95—1181no—
240#95—1181no—
241#95—1181no—
242C24—1181no—
243C24(C2×D59)⋊C411yescharacteristic
244C2×D4—1182no—
245C2×D4—2361no—
246C2×D4—2361no—
247C2×D4—2362no—
248C2×D4—2362no—
249C2×D4—2362no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4(C2×D59)⋊C411yescharacteristic
263C22×C4(C2×D59)⋊C411yescharacteristic
264C22×C4(C2×D59)⋊C411yescharacteristic
265C22×C4C2×C4×D5911yescharacteristic
266C22×C4C2×D23611yescharacteristic
267C22×C4C2×C22⋊D5911yescharacteristic
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—2362no—
272C2×C8—2362no—
273C2×C8—2362no—
274C4⋊C4—1182no—
275C4⋊C4—2361no—
276C4⋊C4—2361no—
277C4⋊C4—2362no—
278C4⋊C4—2362no—
279C22⋊C4—2362no—
280C22⋊C4—2362no—
281C22⋊C4—2362no—
282C22⋊C4—2362no—
283C22⋊C4—2362no—
284C22⋊C4—2362no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—41no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—2361no—
296C23—2361no—
297C23—2361no—
298C23—2361no—
299C23—2361no—
300C23—2361no—
301C23—2361no—
302C23#1427364112yes—
303C23C2×(C2×D59)⋊C411yescharacteristic
304D4—4722no—
305D4—4724no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4—2361no—
328C2×C4—2361no—
329C2×C4—2361no—
330C2×C4—2361no—
331C2×C4—2361no—
332C2×C4—2361no—
333C2×C4#1427373312yes—
334C2×C4#1427374712yes—
335C2×C4#1427375512yes—
336C8—82no—
337C8—4722no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—4721no—
346C22—4721no—
347C22—4721no—
348C22—4721no—
349C22—4721no—
350C22—4721no—
351C22—4721no—
352C22#1683736811yescharacteristic
353C22C2×#1427364111yescharacteristic
354C22#1683738411yescharacteristic
355C22#1683739611yescharacteristic
356C22#1683740811yescharacteristic
357C22#1683741811yescharacteristic
358C22#1683742011yescharacteristic
359C4—22no—
360C4—22no—
361C4—22no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—4721no—
366C4—4721no—
367C4—4721no—
368C2—42no—
369C2—9441no—
370C2#2142244211yescharacteristic
371C2#2142250211yescharacteristic
372C2#2142256611yescharacteristic
373C2#2142262611yescharacteristic
374C2#2142265011yescharacteristic
375C2#2142272511yescharacteristic
376C2#2142280211yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1817C2
socleC23×C59C2×C22⋊C4
prime radicalC2×#14273701C4
cosocleC2×C42×C59C23
hypercenter#1817D59
hypocenterC59#7718
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #21424164C2semidirect
3. #21421918C2semidirect
4. #21421916C2semidirect
5. C59×#1817C2semidirect
182. #1817D59semidirect
211. C59#7718semidirect

Maximal subgroups

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

subgroupindex
#214324272
#214241642
#214219182
#214219162
C59×#18172
#771859