Finite Group Databasebeta

← #28483716

Subgroups — #28483716

Order 15104.

812 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#16837338C211yesmaximal, characteristic
2#21426710C211yesmaximal, characteristic
3#21424187C212yesmaximal, complemented
4#21421976C212yesmaximal, complemented
5C2×C59×#323C211yesmaximal, characteristic
6C22×C4⋊Dic59C2211yescharacteristic
7C22×Dic59⋊C4—21no—
8C22×C22⋊Dic59—21no—
9C22×C22⋊Dic59—21no—
10#16837338—22no—
11#16837338C414yescomplemented
12#16837277—24no—
13#16837262—21no—
14#16837262C2212yes—
15C2×C59⋊#95C2211yescharacteristic
16#16837165—24no—
17C22×C22⋊C4×C59C2211yescharacteristic
18C2×C22⋊C8×C59C2212yes—
19C59×#323—22no—
20C23×Dic59—21no—
21C23×Dic59—21no—
22C23×Dic59—22no—
23C2×C4⋊Dic59—22no—
24C2×C4⋊Dic59—22no—
25C2×C4⋊Dic59—21no—
26C2×C4⋊Dic59—22no—
27C2×C4⋊Dic59C2×C412yescomplemented
28C2×C4⋊Dic59D414yes—
29C2×Dic59⋊C4—24no—
30C2×Dic59⋊C4—44no—
31C2×C22⋊Dic59—22no—
32C2×C22⋊Dic59—24no—
33C2×C22⋊Dic59—22no—
34C2×C22⋊Dic59—44no—
35C2×C22⋊Dic59—42no—
36C2×C22⋊Dic59—42no—
37C59⋊#95—22no—
38C59⋊#95—21no—
39C59⋊#95—22no—
40C59⋊#95C2×C412yescomplemented
41C25×C59D411yescharacteristic
42C23×C4×C59D411yescharacteristic
43C23×C4×C59C2311yescharacteristic
44C22×C8×C59—22no—
45C2×C22⋊C4×C59—22no—
46C2×C22⋊C4×C59—22no—
47C2×C22⋊C4×C59C2×C412yes—
48C2×C22⋊C4×C59D412yes—
49C22⋊C8×C59—22no—
50C22⋊C8×C59—22no—
51C24×C59—21no—
52C24×C59—21no—
53C24×C59—21no—
54C24×C59—21no—
55C24×C59—42no—
56C24×C59—42no—
57C24×C59C22⋊C412yes—
58C24×C59SD1612yes—
59C24×C59Q1612yes—
60C24×C59C2×D411yescharacteristic
61C22×C4×C59—21no—
62C22×C4×C59—21no—
63C22×C4×C59—42no—
64C22×C4×C59—42no—
65C22×C4×C59C22⋊C412yes—
66C22×C4×C59C22×C411yescharacteristic
67C22×C4×C59C2×D412yes—
68C22×C4×C59C2×D411yescharacteristic
69C22×C4×C59#4112yes—
70C22×Dic59—24no—
71C22×Dic59—22no—
72C22×Dic59—22no—
73C22×Dic59—24no—
74C22×Dic59—42no—
75C22×Dic59—41no—
76C22×Dic59—41no—
77C22×Dic59—42no—
78C22×Dic59—44no—
79C22×Dic59—42no—
80C22×Dic59—41no—
81C22×Dic59—41no—
82C22×Dic59—82no—
83C22×Dic59—82no—
84C2×C8×C59—44no—
85C2×C8×C59—42no—
86C22⋊C4×C59—24no—
87C22⋊C4×C59—24no—
88C22⋊Dic59—48no—
89C22⋊Dic59—44no—
90C22⋊Dic59—42no—
91C22⋊Dic59—42no—
92C4⋊Dic59—24no—
93C4⋊Dic59—42no—
94C4⋊Dic59—44no—
95C4⋊Dic59—82no—
96Dic59⋊C4—48no—
97C23×C59—22no—
98C23×C59—22no—
99C23×C59—22no—
100C23×C59—22no—
101C23×C59—22no—
102C23×C59—22no—
103C23×C59—22no—
104C23×C59—22no—
105C23×C59—42no—
106C23×C59—42no—
107C23×C59—44no—
108C23×C59—44no—
109C23×C59—42no—
110C23×C59—42no—
111C23×C59—82no—
112C23×C59—82no—
113C23×C59—81no—
114C23×C59—81no—
115C23×C59#10314yes—
116C23×C59C2×C22⋊C411yescharacteristic
117C23×C59#12011yescharacteristic
118C23×C59#12311yescharacteristic
119C23×C59C2×SD1611yescharacteristic
120C23×C59C2×Q1611yescharacteristic
121C23×C59AGL(1,ℤ/8)11yescharacteristic
122C23×C59#13711yescharacteristic
123C2×C4×C59—24no—
124C2×C4×C59—22no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—42no—
128C2×C4×C59—42no—
129C2×C4×C59—42no—
130C2×C4×C59—81no—
131C2×C4×C59C4×D412yes—
132C2×C4×C59#12112yes—
133C2×Dic59—24no—
134C2×Dic59—44no—
135C2×Dic59—44no—
136C2×Dic59—42no—
137C2×Dic59—42no—
138C2×Dic59—42no—
139C2×Dic59—42no—
140C2×Dic59—42no—
141C2×Dic59—44no—
142C2×Dic59—44no—
143C2×Dic59—44no—
144C2×Dic59—82no—
145C2×Dic59—88no—
146C2×Dic59—82no—
147C8×C59—82no—
148#9021—591nomaximal, Sylow
149C22×C59—22no—
150C22×C59—22no—
151C22×C59—22no—
152C22×C59—22no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—24no—
158C22×C59—44no—
159C22×C59—44no—
160C22×C59—44no—
161C22×C59—42no—
162C22×C59—42no—
163C22×C59—82no—
164C22×C59—82no—
165C22×C59—82no—
166C22×C59#38611yescharacteristic
167C22×C59C2×#10311yescharacteristic
168C22×C59#41711yescharacteristic
169C22×C59#45011yescharacteristic
170C22×C59#45111yescharacteristic
171C22×C59#45312yes—
172C22×C59#45812yes—
173C22×C59#48311yescharacteristic
174C22×C59#48411yescharacteristic
175C4×C59—22no—
176C4×C59—22no—
177C4×C59—42no—
178Dic59—44no—
179Dic59—84no—
180Dic59—82no—
181C2×#399—591no—
182#2315—591no—
183#1824—592no—
184C2×#323D5911yescharacteristic
185#1294—592no—
186C2×C59—21no—
187C2×C59—21no—
188C2×C59—21no—
189C2×C59—21no—
190C2×C59—44no—
191C2×C59#161312yes—
192C2×C59#161412yes—
193C2×C59#187211yescharacteristic
194C2×C59#188711yescharacteristic
195C2×C59#189011yescharacteristic
196C22×C4⋊C4—591no—
197C22×C4⋊C4—1181no—
198C22×C22⋊C4—1181no—
199C22×C22⋊C4—1181no—
200C22×C22⋊C4C2×D5911yescharacteristic
201C2×C22⋊C8C2×D5912yes—
202#399—594no—
203#399—1182no—
204#385—1184no—
205#380—592no—
206#380—1181no—
207C2×#95—591no—
208#340—1184no—
209#323—22no—
210C59#902111yescharacteristic, complemented, Sylow
211C25D23611yescharacteristic
212C23×C4—1181no—
213C23×C4—1182no—
214C23×C4—1181no—
215C23×C4D23611yescharacteristic
216C23×C4C22×D5911yescharacteristic
217C22×C8—22no—
218C2×C4⋊C4—592no—
219C2×C4⋊C4—594no—
220C2×C4⋊C4—1182no—
221C2×C4⋊C4—1182no—
222C2×C4⋊C4—1182no—
223C2×C4⋊C4—1184no—
224C2×C4⋊C4—1181no—
225C2×C4⋊C4—2364no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—1182no—
229C2×C22⋊C4—1184no—
230C2×C22⋊C4—1182no—
231C2×C22⋊C4—2364no—
232C2×C22⋊C4—2362no—
233C2×C22⋊C4—2362no—
234C2×C22⋊C4C4×D5912yes—
235C2×C22⋊C4C22⋊D5912yes—
236C22⋊C8—22no—
237C22⋊C8—22no—
238#95—592no—
239#95—1182no—
240#95—1182no—
241#95—1181no—
242C24—21no—
243C24—21no—
244C24—21no—
245C24—21no—
246C24—42no—
247C24—42no—
248C24#1174566012yes—
249C24Dic23612yes—
250C24(C2×D59)⋊C412yes—
251C24C2×D23611yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—1184no—
257C22×C4—1182no—
258C22×C4—1182no—
259C22×C4—1184no—
260C22×C4—4722no—
261C22×C4—4722no—
262C22×C4—2362no—
263C22×C4—2364no—
264C22×C4—2362no—
265C22×C4—2361no—
266C22×C4—2361no—
267C22×C4—2362no—
268C22×C4—2361no—
269C22×C4—2361no—
270C22×C4(C2×D59)⋊C412yes—
271C22×C4C2×C4×D5911yescharacteristic
272C22×C4D4×D5912yes—
273C22×C4#1174568712yes—
274C22×C4C2×C22⋊D5911yescharacteristic
275C2×C8—44no—
276C2×C8—42no—
277C4⋊C4—1184no—
278C4⋊C4—4722no—
279C4⋊C4—2364no—
280C4⋊C4—2368no—
281C4⋊C4—2362no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—2368no—
285C22⋊C4—2364no—
286C22⋊C4—2362no—
287C22⋊C4—2362no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—42no—
297C23—44no—
298C23—44no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—82no—
303C23—82no—
304C23—81no—
305C23—81no—
306C23#1427365214yes—
307C23C2×(C2×D59)⋊C411yescharacteristic
308C23#1427369711yescharacteristic
309C23#1427371111yescharacteristic
310C23C2×#1174566011yescharacteristic
311C23C2×Dic23611yescharacteristic
312C23#1427375511yescharacteristic
313C23#1427376011yescharacteristic
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—1184no—
323C2×C4—4722no—
324C2×C4—4728no—
325C2×C4—4722no—
326C2×C4—2362no—
327C2×C4—2362no—
328C2×C4—2362no—
329C2×C4—2364no—
330C2×C4—2364no—
331C2×C4—2364no—
332C2×C4—2364no—
333C2×C4—2364no—
334C2×C4—2362no—
335C2×C4—2362no—
336C2×C4(C22⋊D59)⋊C412yes—
337C2×C4#1427369912yes—
338C8—82no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—24no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22#1683727911yescharacteristic
357C22C2×#1427365211yescharacteristic
358C22#1683740411yescharacteristic
359C22#1683755511yescharacteristic
360C22#1683756011yescharacteristic
361C22#1683757212yes—
362C22#1683759312yes—
363C22#1683773311yescharacteristic
364C22#1683773811yescharacteristic
365C4—22no—
366C4—22no—
367C4—42no—
368C4—4724no—
369C4—4722no—
370C4—2364no—
371C2—21no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—44no—
376C2#2142311812yes—
377C2#2142312312yes—
378C2#2142440111yescharacteristic
379C2#2142449211yescharacteristic
380C2#2142450711yescharacteristic
subgroupG/H
centerC23#14273697
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#323C2
socleC23×C59#120
prime radicalC25×C59D4
cosocleC23×C4×C59C23
hypercenterC2×#323D59
hypocenterC59#9021
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
3. #21424187C2semidirect
4. #21421976C2semidirect
11. #16837338C4semidirect
27. C2×C4⋊Dic59C2×C4semidirect
40. C59⋊#95C2×C4semidirect
210. C59#9021semidirect

Maximal subgroups

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

subgroupindex
C2×#168373382
#214267102
#214241872
#214219762
C2×C59×#3232
#902159