Finite Group Databasebeta

← #28482923

Subgroups — #28482923

Order 15104.

530 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21427047C211yesmaximal, characteristic
2#21424857C211yesmaximal, characteristic, complemented
3#21424093C211yesmaximal, characteristic
4C2×#16837131C211yesmaximal, characteristic
5#21421979C211yesmaximal, characteristic, complemented
6#21421936C211yesmaximal, characteristic, complemented
7C59×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D236C2211yescharacteristic
9C2×#14273685—21no—
10C2×#14273658—21no—
11C2×C4⋊(C59⋊C8)C2211yescharacteristic
12C2×C4⋊(C59⋊C8)C2211yescharacteristic
13C2×#14273647—21no—
14#16837303—21no—
15#16837292—22no—
16#16837259—21no—
17C4⋊C4×Dic59—21no—
18C4×C4⋊Dic59C2211yescharacteristic
19#16837164—21no—
20#16837164—21no—
21#16837131C414yescomplemented
22C2×C4×C8×C59C2211yescharacteristic
23C59×#384C2211yescharacteristic
24C59×#384C2211yescharacteristic
25C59×#340—22no—
26C22×D236D411yescharacteristic
27C22×C4×D59—21no—
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30C4×D236—21no—
31C4×D236—21no—
32C4×D236C2×C412yes—
33C4×D236Q812yes—
34#14273685—42no—
35#14273685—42no—
36C2×C4⋊Dic59D411yescharacteristic
37C2×C4⋊Dic59D411yescharacteristic
38C2×C4⋊Dic59D411yescharacteristic
39C2×(C2×D59)⋊C4—21no—
40C2×(C2×D59)⋊C4—22no—
41C2×(C2×D59)⋊C4—22no—
42C2×C4×Dic59—22no—
43C2×C4×Dic59—21no—
44#14273658—42no—
45C4⋊(C59⋊C8)—21no—
46C4⋊(C59⋊C8)—21no—
47C4⋊(C59⋊C8)—21no—
48C4⋊(C59⋊C8)C2×C412yes—
49#14273647—42no—
50C59⋊#95—22no—
51C59⋊#95—21no—
52C22×C8×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59D412yes—
59C2×C42×C59C2311yescharacteristic
60C4×C8×C59—21no—
61C4×C8×C59C2×C412yes—
62C23×D59—21no—
63C22×C4×C59—22no—
64C22×C4×C59—41no—
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59—21no—
71C2×D236—21no—
72C2×D236—21no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236C4⋊C412yes—
77C2×C4×D59—22no—
78C2×C4×D59—22no—
79C2×C4×D59—41no—
80C2×C4×D59—41no—
81C2×C4×D59—41no—
82C2×C4×D59—41no—
83C2×C8×C59—22no—
84C2×C8×C59—41no—
85C2×C8×C59—41no—
86C4⋊C4×C59—42no—
87C4⋊C4×C59—42no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C4⋊C4×C59—41no—
92C4⋊C4×C59—41no—
93C4⋊C4×C59—41no—
94C4⋊C4×C59—41no—
95C4⋊C4×C59—41no—
96C42×C59C22×C411yescharacteristic
97C42×C59C2×Q811yescharacteristic
98C42×C59#4111yescharacteristic
99C42×C59#4111yescharacteristic
100(C2×D59)⋊C4—22no—
101(C2×D59)⋊C4—22no—
102(C2×D59)⋊C4—44no—
103(C2×D59)⋊C4—82no—
104C4⋊Dic59—21no—
105C4⋊Dic59—21no—
106C4⋊Dic59—21no—
107C4⋊Dic59—21no—
108C4⋊Dic59C4⋊C412yes—
109C4⋊Dic59SD1612yes—
110C4×Dic59—44no—
111C4×Dic59—41no—
112C4×Dic59—41no—
113C2×C59⋊C8—22no—
114C2×C59⋊C8—41no—
115C2×C59⋊C8—41no—
116C2×C59⋊C8—41no—
117C2×C59⋊C8—41no—
118C2×C59⋊C8—41no—
119C23×C59#12011yescharacteristic
120C22×D59—22no—
121C22×D59—41no—
122C22×D59—41no—
123C22×D59—41no—
124C22×D59—41no—
125C22×D59—41no—
126C22×D59—41no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—42no—
130C2×C4×C59—42no—
131C2×C4×C59—42no—
132C2×C4×C59—81no—
133C2×C4×C59—81no—
134C2×C4×C59—81no—
135C2×C4×C59C2×C4⋊C411yescharacteristic
136C2×C4×C59C4×D411yescharacteristic
137C2×C4×C59C4×D411yescharacteristic
138C2×C4×C59C22⋊Q811yescharacteristic
139C2×C4×C59C22⋊Q811yescharacteristic
140C2×C4×C59#12311yescharacteristic
141C2×C4×C59C2×SD1611yescharacteristic
142C2×C4×C59#13511yescharacteristic
143C2×C4×C59#13511yescharacteristic
144C2×C4×C59#13511yescharacteristic
145C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C59#13711yescharacteristic
149C2×Dic59—22no—
150C2×Dic59—22no—
151C2×Dic59—41no—
152C2×Dic59—41no—
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—41no—
156C2×Dic59—41no—
157C2×Dic59—41no—
158D236—22no—
159D236—22no—
160D236—41no—
161D236—41no—
162C4×D59—42no—
163C4×D59—42no—
164C4×D59—42no—
165C4×D59—42no—
166C8×C59—42no—
167C59⋊C8—42no—
168C59⋊C8—81no—
169#8893—591nomaximal, Sylow
170C22×C59#38511yescharacteristic
171C22×C59#44911yescharacteristic
172C22×C59#44911yescharacteristic
173C22×C59#45011yescharacteristic
174C22×C59#45211yescharacteristic
175C22×C59#45411yescharacteristic
176C22×C59#45511yescharacteristic
177C2×D59—42no—
178C2×D59—42no—
179C2×D59—42no—
180C2×D59—81no—
181C2×D59—81no—
182C2×D59—81no—
183C2×D59—81no—
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—82no—
187C4×C59—161no—
188C4×C59#42711yescharacteristic
189C4×C59#42811yescharacteristic
190C4×C59C4×SD1611yescharacteristic
191C4×C59#44211yescharacteristic
192C4×C59#47611yescharacteristic
193C4×C59#47811yescharacteristic
194C4×C59#48211yescharacteristic
195C4×C59#48511yescharacteristic
196Dic59—42no—
197Dic59—42no—
198Dic59—81no—
199#2354—591no—
200#1948—591no—
201#1834D5911yescharacteristic, complemented
202#1802—591no—
203C2×D4⋊C8—591no—
204#1296—591no—
205#1279—591no—
206C2×C59#162811yescharacteristic
207C2×C59#163511yescharacteristic
208C2×C59#164211yescharacteristic
209C2×C59#164611yescharacteristic
210C2×C59#185411yescharacteristic
211C2×C59#186011yescharacteristic
212C2×C59#186411yescharacteristic
213D59—82no—
214C2×C4×D4—591no—
215C2×#117—1181no—
216C2×#106—1181no—
217C2×C4⋊C8—591no—
218C2×C4⋊C8—591no—
219C2×#102—1181no—
220C2×C4×C8C2×D5911yescharacteristic
221#390—1181no—
222#388—1182no—
223#384C2×D5911yescharacteristic
224#384C2×D5911yescharacteristic
225#380—1181no—
226C4×C4⋊C4—591no—
227C4×C4⋊C4—1181no—
228#340—22no—
229#340—1181no—
230#340—1181no—
231D4⋊C8—594no—
232C59#889311yescharacteristic, complemented, Sylow
233C22×D4—591no—
234C23×C4—1181no—
235C22×C8—21no—
236C22×C8—1181no—
237C22×C8—1181no—
238C4×D4—592no—
239C4×D4—592no—
240C4×D4—1181no—
241C4×D4—1181no—
242#117—2362no—
243#117—2362no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—591no—
250C2×C4⋊C4—591no—
251C2×C4⋊C4—591no—
252C2×C4⋊C4C22⋊D5912yes—
253C2×C22⋊C4—1181no—
254C2×C22⋊C4—1182no—
255C2×C22⋊C4—1182no—
256C2×C42—1182no—
257C2×C42—1181no—
258C2×C42C22×D5911yescharacteristic
259#106—2362no—
260C4⋊C8—592no—
261C4⋊C8—1181no—
262C4⋊C8—1181no—
263C4⋊C8—1181no—
264#102—2362no—
265C4×C8—21no—
266C4×C8C4×D5912yes—
267#95—1182no—
268#95—1181no—
269C24—1181no—
270C2×D4—592no—
271C2×D4—1181no—
272C2×D4—1181no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1181no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—1181no—
279C22×C4—1181no—
280C22×C4—1182no—
281C22×C4—1182no—
282C22×C4—1181no—
283C22×C4—2361no—
284C22×C4—2361no—
285C22×C4—2361no—
286C22×C4—2361no—
287C22×C4D4×D5911yescharacteristic
288C22×C4D4×D5911yescharacteristic
289C22×C4C2×C22⋊D5911yescharacteristic
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—1182no—
294C2×C8—2361no—
295C2×C8—2361no—
296C2×C8—2361no—
297C2×C8—2361no—
298C2×C8—2361no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—592no—
310C4⋊C4—592no—
311C4⋊C4—1181no—
312C4⋊C4—1181no—
313C4⋊C4—1181no—
314C4⋊C4—1181no—
315C22⋊C4—1182no—
316C22⋊C4—1182no—
317C22⋊C4—4722no—
318C22⋊C4—2364no—
319C42—2364no—
320C42—2361no—
321C42—2361no—
322C42C2×C4×D5911yescharacteristic
323C42#1174568511yescharacteristic
324C42Q8×D5911yescharacteristic
325C42#1174568911yescharacteristic
326C23—1182no—
327C23—2361no—
328C23—2361no—
329C23—2361no—
330C23—2361no—
331C23—2361no—
332C23—2361no—
333C23#1427369511yescharacteristic
334D4—1182no—
335D4—1182no—
336D4—2361no—
337D4—2361no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—1182no—
347C2×C4—1182no—
348C2×C4—2361no—
349C2×C4—2361no—
350C2×C4—2361no—
351C2×C4—2361no—
352C2×C4—2361no—
353C2×C4—2361no—
354C2×C4—2361no—
355C2×C4—2362no—
356C2×C4—2362no—
357C2×C4—2362no—
358C2×C4—2362no—
359C2×C4C4⋊C4×D5911yescharacteristic
360C2×C4C4×C22⋊D5911yescharacteristic
361C2×C4#1427368911yescharacteristic
362C2×C4#1427370311yescharacteristic
363C2×C4#1427370511yescharacteristic
364C2×C4#1427371211yescharacteristic
365C2×C4SD16×D5911yescharacteristic
366C2×C4#1427374611yescharacteristic
367C2×C4#1427374811yescharacteristic
368C2×C4#1427375011yescharacteristic
369C2×C4#1427375111yescharacteristic
370C2×C4#1427375411yescharacteristic
371C2×C4#1427375411yescharacteristic
372C2×C4#1427375911yescharacteristic
373C8—42no—
374C8—4721no—
375C8—2362no—
376C22—4721no—
377C22—4721no—
378C22—4721no—
379C22—4721no—
380C22—2362no—
381C22—2362no—
382C22—2362no—
383C22#1683727311yescharacteristic
384C22#1683754411yescharacteristic
385C22#1683754611yescharacteristic
386C22#1683755111yescharacteristic
387C22#1683756311yescharacteristic
388C22#1683757411yescharacteristic
389C22#1683757911yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—161no—
394C4—4721no—
395C4—2362no—
396C4—2362no—
397C4#1683743911yescharacteristic
398C4#1683744311yescharacteristic
399C4#1683748911yescharacteristic
400C4#1683751311yescharacteristic
401C4#1683769111yescharacteristic
402C4#1683770111yescharacteristic
403C4#1683772911yescharacteristic
404C4#1683774511yescharacteristic
405C2—4722no—
406C2#2142320311yescharacteristic
407C2#2142324411yescharacteristic
408C2#2142329311yescharacteristic
409C2#2142332111yescharacteristic
410C2#2142429211yescharacteristic
411C2#2142432811yescharacteristic
412C2#2142435411yescharacteristic
subgroupG/H
centerC23#14273695
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1834C2
socleC23×C59#120
prime radicalC22×D236D4
cosocleC2×C42×C59C23
hypercenter#1834D59
hypocenterC59#8893
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #21424857C2semidirect
5. #21421979C2semidirect
6. #21421936C2semidirect
7. C59×#1834C2semidirect
21. #16837131C4semidirect
201. #1834D59semidirect
232. C59#8893semidirect

Maximal subgroups

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

subgroupindex
#214270472
#214248572
#214240932
C2×#168371312
#214219792
#214219362
C59×#18342
#889359