Finite Group Databasebeta

← #28507854

Subgroups — #28507854

Order 15104.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837639C211yesmaximal, characteristic
2C2×#16837229C211yesmaximal, characteristic, complemented
3C2×#16837204C211yesmaximal, characteristic, complemented
4C2×#16837202C211yesmaximal, characteristic, complemented
5C2×(C2×D59)⋊C16C211yesmaximal, characteristic, complemented
6#21424122C211yesmaximal, characteristic, complemented
7C59×#1380C211yesmaximal, characteristic, complemented
8C22×D472C2211yescharacteristic
9C22×C8×D59C2211yescharacteristic
10C2×#14273702—21no—
11C22×C59⋊C16C2211yescharacteristic
12#16837639—22no—
13#16837639—22no—
14C2×#14273661C2211yescharacteristic
15C2×#14273647—21no—
16#16837259—21no—
17#16837229—22no—
18#16837204—22no—
19#16837202—22no—
20(C2×D59)⋊C16—22no—
21#16837164—21no—
22C22×C16×C59C2211yescharacteristic
23C2×#107×C59C2211yescharacteristic
24C2×#107×C59C2211yescharacteristic
25C22×D236—21no—
26C22×D236—41no—
27C22×C4×D59D411yescharacteristic
28C2×D472—21no—
29C2×D472—21no—
30C2×D472—21no—
31C2×D472—21no—
32C2×D472—21no—
33C2×D472D412yes—
34C22×C59⋊C8D411yescharacteristic
35C2×C8×D59—21no—
36C2×C8×D59—21no—
37C2×C8×D59—21no—
38C2×C8×D59—21no—
39C2×C8×D59—21no—
40C2×C8×D59—21no—
41#14273702—24no—
42#14273702—42no—
43C2×C4⋊Dic59—21no—
44C2×(C2×D59)⋊C4—41no—
45C2×(C2×D59)⋊C4—41no—
46C2×C59⋊C16—21no—
47C2×C59⋊C16—21no—
48C2×C59⋊C16D412yescomplemented
49#14273661—21no—
50#14273661—21no—
51#14273647—24no—
52C59⋊#95—41no—
53C22×C8×C59C2311yescharacteristic
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C16×C59—21no—
57C2×C16×C59—21no—
58C2×C16×C59—21no—
59#107×C59—21no—
60#107×C59—21no—
61#107×C59—21no—
62#107×C59D412yes—
63C23×D59—41no—
64C23×D59D811yescharacteristic
65C22×C4×C59—41no—
66C22×C4×C59—41no—
67C22×C4×C59C2×D411yescharacteristic
68C22×Dic59—41no—
69C22×Dic59D811yescharacteristic
70C2×D236—22no—
71C2×D236—41no—
72C2×D236—41no—
73C2×D236—41no—
74C2×D236—41no—
75C2×D236—44no—
76C2×D236—41no—
77C2×D236—82no—
78C2×D236—82no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×C4×D59—21no—
83C2×C4×D59—21no—
84C2×C4×D59—21no—
85C2×C8×C59C2×D411yescharacteristic
86C2×C8×C59C2×D411yescharacteristic
87C2×C8×C59C2×D411yescharacteristic
88C2×C8×C59#4111yescharacteristic
89C2×C8×C59#4111yescharacteristic
90C2×C8×C59#4111yescharacteristic
91C4⋊C4×C59—22no—
92C4⋊C4×C59—41no—
93C4⋊C4×C59—41no—
94C4⋊C4×C59—41no—
95(C2×D59)⋊C4—44no—
96(C2×D59)⋊C4—82no—
97C4⋊Dic59—41no—
98C4⋊Dic59—41no—
99C2×C59⋊C8—21no—
100C2×C59⋊C8—21no—
101C2×C59⋊C8—21no—
102D472—22no—
103D472—22no—
104D472—41no—
105D472—41no—
106C8×D59—41no—
107C8×D59—41no—
108C8×D59—41no—
109C8×D59—41no—
110C16×C59—41no—
111C59⋊C16—22no—
112C23×C59C2×D811yescharacteristic
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—42no—
120C22×D59—81no—
121C22×D59—81no—
122C22×D59—81no—
123C22×D59—81no—
124C22×D59—81no—
125C22×D59—81no—
126C22×D59SD3212yes—
127C2×C4×C59—42no—
128C2×C4×C59—81no—
129C2×C4×C59—81no—
130C2×C4×C59—81no—
131C2×C4×C59—81no—
132C2×C4×C59—81no—
133C2×C4×C59#12011yescharacteristic
134C2×C4×C59#12111yescharacteristic
135C2×C4×C59#12311yescharacteristic
136C2×C4×C59#13511yescharacteristic
137C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C59#13711yescharacteristic
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—81no—
143C2×Dic59—81no—
144C2×Dic59—81no—
145D236—42no—
146D236—42no—
147D236—88no—
148D236—81no—
149D236—81no—
150C4×D59—41no—
151C4×D59—41no—
152C4×D59—41no—
153C4×D59—41no—
154C8×C59#12111yescharacteristic
155C8×C59#12111yescharacteristic
156C8×C59#12311yescharacteristic
157C8×C59#12411yescharacteristic
158C59⋊C8—41no—
159#13381—591nomaximal, Sylow
160C22×C59#44711yescharacteristic
161C22×C59#46611yescharacteristic
162C22×C59#48011yescharacteristic
163C22×C59C2×SD3211yescharacteristic
164C22×C59#50811yescharacteristic
165C22×C59#50911yescharacteristic
166C22×C59#50911yescharacteristic
167C2×D59—22no—
168C2×D59—22no—
169C2×D59—22no—
170C2×D59—41no—
171C2×D59—41no—
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—82no—
175C2×D59—82no—
176C2×D59—82no—
177C2×D59—161no—
178C2×D59—161no—
179C2×D59—161no—
180C2×D59—161no—
181C4×C59—82no—
182C4×C59—161no—
183C4×C59#39411yescharacteristic
184C4×C59#45211yescharacteristic
185C4×C59#46811yescharacteristic
186C4×C59#48211yescharacteristic
187Dic59—41no—
188Dic59—161no—
189C2×#466—591no—
190C2×#367—591no—
191C2×#357—591no—
192C2×#357—591no—
193C2×C22⋊C16—591no—
194#1808—591no—
195#1380D5911yescharacteristic, complemented
196C2×C59#203311yescharacteristic
197C2×C59#218611yescharacteristic
198C2×C59#218711yescharacteristic
199C2×C59#221711yescharacteristic
200C2×C59#221811yescharacteristic
201C2×C59#223311yescharacteristic
202C2×C59#223411yescharacteristic
203D59—42no—
204D59—162no—
205C22×D8—591no—
206C23×C8—591no—
207C2×#121—1181no—
208C22×C16—591no—
209C22×C16C2×D5911yescharacteristic
210#466—1182no—
211#466—1182no—
212C2×#107—591no—
213C2×#107C2×D5911yescharacteristic
214C2×#107C2×D5911yescharacteristic
215C2×#102—1181no—
216#380—1181no—
217#367—1182no—
218#357—1182no—
219#357—1182no—
220C22⋊C16—1182no—
221#340—1181no—
222C59#1338111yescharacteristic, complemented, Sylow
223C22×D4—1181no—
224C22×D4—2361no—
225C23×C4—591no—
226C2×D8—592no—
227C2×D8—1181no—
228C2×D8—1181no—
229C2×D8—1181no—
230C2×D8—1181no—
231C2×D8—1181no—
232C22×C8—591no—
233C22×C8—1181no—
234C22×C8—1181no—
235C22×C8—1181no—
236C22×C8—1181no—
237C22×C8—1181no—
238C22×C8—1181no—
239C22×C8C22×D5911yescharacteristic
240#121—1184no—
241#121—2362no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—1181no—
245C2×C22⋊C4—2361no—
246C2×C22⋊C4—2361no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—592no—
251C2×C16—1181no—
252C2×C16—1181no—
253#107—21no—
254#107—21no—
255#107—21no—
256#107—1181no—
257#107—1181no—
258#107D23612yes—
259#102—1184no—
260#95—2361no—
261C24—591no—
262C24—2361no—
263C2×D4—1182no—
264C2×D4—4722no—
265C2×D4—4722no—
266C2×D4—2364no—
267C2×D4—2361no—
268C2×D4—2361no—
269C2×D4—2361no—
270C2×D4—2361no—
271C2×D4—2361no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—591no—
275C22×C4—1181no—
276C22×C4—1181no—
277C22×C4—1181no—
278C22×C4—1181no—
279C22×C4—1181no—
280C22×C4—1181no—
281C22×C4—2361no—
282C22×C4D4×D5911yescharacteristic
283D8—1182no—
284D8—1182no—
285D8—2361no—
286D8—2361no—
287C2×C8—1181no—
288C2×C8—1181no—
289C2×C8—1181no—
290C2×C8—2361no—
291C2×C8—2361no—
292C2×C8—2361no—
293C2×C8—2361no—
294C2×C8C2×D23611yescharacteristic
295C2×C8#1174568511yescharacteristic
296C2×C8#1174568511yescharacteristic
297C2×C8D4×D5911yescharacteristic
298C2×C8D4×D5911yescharacteristic
299C2×C8#1174568911yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—2361no—
305C4⋊C4—2361no—
306C22⋊C4—4722no—
307C22⋊C4—2364no—
308C16—41no—
309C16—1182no—
310C23—592no—
311C23—1181no—
312C23—1181no—
313C23—1181no—
314C23—1181no—
315C23—1181no—
316C23—1181no—
317C23—4721no—
318C23—4721no—
319C23—4721no—
320C23—4721no—
321C23—4721no—
322C23—4721no—
323C23—2362no—
324C23D8×D5911yescharacteristic
325D4—4728no—
326D4—4721no—
327D4—4721no—
328D4—2362no—
329D4—2362no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—4721no—
340C2×C4—4721no—
341C2×C4—4721no—
342C2×C4—2361no—
343C2×C4—2361no—
344C2×C4—2361no—
345C2×C4—2361no—
346C2×C4#1427369711yescharacteristic
347C2×C4#1427370011yescharacteristic
348C2×C4#1427371211yescharacteristic
349C2×C4#1427374811yescharacteristic
350C2×C4#1427375411yescharacteristic
351C2×C4#1427375911yescharacteristic
352C8—2361no—
353C8#1427370011yescharacteristic
354C8#1427370211yescharacteristic
355C8#1427371211yescharacteristic
356C8#1427371511yescharacteristic
357C22—1182no—
358C22—1182no—
359C22—1182no—
360C22—9441no—
361C22—9441no—
362C22—9441no—
363C22—9441no—
364C22—4722no—
365C22—4722no—
366C22—4722no—
367C22—2361no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22#1683753711yescharacteristic
372C22#1683763711yescharacteristic
373C22#1683771711yescharacteristic
374C22SD32×D5911yescharacteristic
375C22#1683783511yescharacteristic
376C22#1683783611yescharacteristic
377C22#1683783911yescharacteristic
378C4—82no—
379C4—161no—
380C4—9441no—
381C4—2361no—
382C4#1683732011yescharacteristic
383C4#1683756711yescharacteristic
384C4#1683765111yescharacteristic
385C4#1683772811yescharacteristic
386C2—9442no—
387C2—2362no—
388C2#2142528111yescharacteristic
389C2#2142602211yescharacteristic
390C2#2142602611yescharacteristic
391C2#2142619511yescharacteristic
392C2#2142619811yescharacteristic
393C2#2142628311yescharacteristic
394C2#2142629011yescharacteristic
subgroupG/H
centerC23D8×D59
commutator, cosocleC22×C8×C59C23
FrattiniC22×C8C22×D59
FittingC59×#1380C2
socleC23×C59C2×D8
prime radicalC2×#16837639C2
hypercenter#1380D59
hypocenterC59#13381
LCSG ▷ C22×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#16837229C2semidirect
3. C2×#16837204C2semidirect
4. C2×#16837202C2semidirect
5. C2×(C2×D59)⋊C16C2semidirect
6. #21424122C2semidirect
7. C59×#1380C2semidirect
48. C2×C59⋊C16D4semidirect
195. #1380D59semidirect
222. C59#13381semidirect

Maximal subgroups

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

subgroupindex
C2×#168376392
C2×#168372292
C2×#168372042
C2×#168372022
C2×(C2×D59)⋊C162
#214241222
C59×#13802
#1338159