Finite Group Databasebeta

← #28507154

Subgroups — #28507154

Order 15104.

598 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837777C211yesmaximal, characteristic
2C2×Dic59⋊C16C211yesmaximal, characteristic, complemented
3C2×#16837204C211yesmaximal, characteristic, complemented
4C2×#16837203C211yesmaximal, characteristic, complemented
5C2×#16837202C211yesmaximal, characteristic, complemented
6#107×Dic59C211yesmaximal, characteristic, complemented
7C2×C59×#357C211yesmaximal, characteristic, complemented
8C22×D472C2211yescharacteristic
9C22×#11745669—21no—
10C2×#14273723—21no—
11C22×C59⋊C16C2211yescharacteristic
12#16837777—22no—
13#16837777C414yescomplemented
14C2×#14273661C2211yescharacteristic
15C2×C8×Dic59C2211yescharacteristic
16C4⋊C4×Dic59—21no—
17Dic59⋊C16—22no—
18#16837204—22no—
19#16837203—22no—
20#16837202—22no—
21#16837164—21no—
22C22×D8×C59C2211yescharacteristic
23C22×C16×C59C2211yescharacteristic
24C2×#107×C59C2211yescharacteristic
25C59×#357—22no—
26C22×D236—21no—
27C22×C22⋊D59—41no—
28C22×C22⋊D59—41no—
29C2×D472—21no—
30C2×D472—21no—
31C2×D472—21no—
32C2×D472—21no—
33C2×D472—21no—
34C2×D472C2×C412yes—
35C2×#11745669—24no—
36C2×#11745669—42no—
37C2×#11745669—42no—
38C22×C59⋊C8D411yescharacteristic
39#14273723—24no—
40#14273723—42no—
41C2×C4⋊Dic59—21no—
42C2×C4×Dic59—41no—
43C2×C4×Dic59D411yescharacteristic
44C2×C59⋊C16—21no—
45C2×C59⋊C16—21no—
46C2×C59⋊C16—21no—
47#14273661—21no—
48#14273661D412yescomplemented
49C8×Dic59C2×C412yes—
50C8×Dic59D412yes—
51C59⋊#95—41no—
52C22×D4×C59—21no—
53C2×D8×C59—21no—
54C2×D8×C59—21no—
55C2×D8×C59—21no—
56C2×D8×C59—21no—
57C2×D8×C59—21no—
58C2×D8×C59C2×C412yes—
59C22×C8×C59C2311yescharacteristic
60C2×C4⋊C4×C59—21no—
61C2×C16×C59—21no—
62C2×C16×C59—21no—
63C2×C16×C59—21no—
64#107×C59—21no—
65#107×C59D412yescomplemented
66C24×C59—41no—
67C23×D59—41no—
68C2×D4×C59—22no—
69C2×D4×C59—41no—
70C2×D4×C59—41no—
71C2×D4×C59—41no—
72C2×D4×C59—41no—
73C2×D4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59C2×D411yescharacteristic
76C2×C22⋊D59—44no—
77C2×C22⋊D59—44no—
78C2×C22⋊D59—82no—
79C2×C22⋊D59—82no—
80C2×C22⋊D59—82no—
81C2×C22⋊D59—82no—
82C22×Dic59—41no—
83C22×Dic59D811yescharacteristic
84C22×Dic59D811yescharacteristic
85C2×D236—22no—
86C2×D236—41no—
87C2×D236—41no—
88C2×D236—41no—
89C2×D236—41no—
90C2×D236—41no—
91D8×C59—22no—
92D8×C59—22no—
93D8×C59—41no—
94D8×C59—41no—
95C2×C8×C59C22×C411yescharacteristic
96C2×C8×C59C2×D411yescharacteristic
97C2×C8×C59C2×D411yescharacteristic
98C2×C8×C59C2×D411yescharacteristic
99C2×C8×C59#4111yescharacteristic
100C2×C8×C59#4111yescharacteristic
101C4⋊C4×C59—22no—
102C4⋊C4×C59—41no—
103#11745669—48no—
104C4⋊Dic59—22no—
105C4⋊Dic59—41no—
106C4×Dic59—82no—
107C4×Dic59C22⋊C412yes—
108C4×Dic59SD1612yes—
109C2×C59⋊C8—21no—
110C2×C59⋊C8—21no—
111C2×C59⋊C8C22⋊C412yes—
112D472—22no—
113D472—22no—
114D472—41no—
115D472—41no—
116C16×C59—41no—
117C59⋊C16—41no—
118C23×C59—42no—
119C23×C59—81no—
120C23×C59—81no—
121C23×C59—81no—
122C23×C59—81no—
123C23×C59—81no—
124C23×C59—81no—
125C23×C59C2×D811yescharacteristic
126C22×D59—42no—
127C22×D59—81no—
128C22×D59—81no—
129C22×D59—81no—
130C22×D59—81no—
131C22×D59—81no—
132C22×D59—81no—
133D4×C59—42no—
134D4×C59—42no—
135D4×C59—81no—
136D4×C59—81no—
137C2×C4×C59—42no—
138C2×C4×C59—81no—
139C2×C4×C59—81no—
140C2×C4×C59C2×C22⋊C411yescharacteristic
141C2×C4×C59#12111yescharacteristic
142C2×C4×C59#12111yescharacteristic
143C2×C4×C59C2×SD1611yescharacteristic
144C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
146C22⋊D59—88no—
147C22⋊D59—88no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—42no—
151C2×Dic59—81no—
152C2×Dic59—81no—
153C2×Dic59#10212yes—
154C2×Dic59#10212yes—
155C2×Dic59D1612yes—
156C2×Dic59SD3212yes—
157D236—42no—
158D236—42no—
159D236—81no—
160D236—81no—
161C8×C59C4×D411yescharacteristic
162C8×C59C4×D411yescharacteristic
163C8×C59#12411yescharacteristic
164C8×C59#12711yescharacteristic
165C59⋊C8—22no—
166#13252—591nomaximal, Sylow
167C22×C59—82no—
168C22×C59—82no—
169C22×C59—82no—
170C22×C59—161no—
171C22×C59—161no—
172C22×C59—161no—
173C22×C59—161no—
174C22×C59C2×#10211yescharacteristic
175C22×C59#45911yescharacteristic
176C22×C59#45911yescharacteristic
177C22×C59C2×D1611yescharacteristic
178C22×C59C2×SD3211yescharacteristic
179C22×C59#50911yescharacteristic
180C22×C59#50911yescharacteristic
181C2×D59—82no—
182C2×D59—82no—
183C2×D59—82no—
184C2×D59—161no—
185C2×D59—161no—
186C2×D59—161no—
187C2×D59—161no—
188C4×C59—82no—
189C4×C59#39011yescharacteristic
190C4×C59#41811yescharacteristic
191C4×C59#46011yescharacteristic
192C4×C59#46011yescharacteristic
193Dic59—22no—
194Dic59—82no—
195Dic59#35714yescomplemented
196C2×#493—591no—
197C2×C4⋊C16—591no—
198C2×#357—591no—
199C2×#357—591no—
200C2×#357—591no—
201C2×#357D5911yescharacteristic, complemented
202C4×#107—591no—
203C2×C59—162no—
204C2×C59#198211yescharacteristic
205C2×C59C2×#35711yescharacteristic
206C2×C59#214011yescharacteristic
207C2×C59#220611yescharacteristic
208C2×C59#220611yescharacteristic
209C2×C59#220711yescharacteristic
210C2×C59#220711yescharacteristic
211D59—162no—
212C22×D8—591no—
213C22×D8—1181no—
214C22×D8C2×D5911yescharacteristic
215C2×#127—1181no—
216C22×C16—591no—
217C22×C16C2×D5911yescharacteristic
218#493—594no—
219#493—1182no—
220C2×#107—591no—
221C2×#107C2×D5911yescharacteristic
222C2×C4×C8—591no—
223C4×C4⋊C4—1181no—
224C4⋊C16—1182no—
225#357—22no—
226#357—1182no—
227#357—1182no—
228#357—1182no—
229#340—1181no—
230C59#1325211yescharacteristic, complemented, Sylow
231C22×D4—21no—
232C22×D4—1181no—
233C22×D4—2361no—
234C22×D4—2361no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8—21no—
240C2×D8—592no—
241C2×D8—1184no—
242C2×D8—1181no—
243C2×D8—1181no—
244C2×D8—1181no—
245C2×D8—1181no—
246C2×D8—1181no—
247C2×D8—2362no—
248C2×D8—2362no—
249C2×D8C4×D5912yes—
250C22×C8—591no—
251C22×C8C22×D5911yescharacteristic
252#127—1184no—
253#127—2362no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—1181no—
256C2×C42—591no—
257C2×C42—2361no—
258C2×C16—21no—
259C2×C16—21no—
260C2×C16—21no—
261C2×C16—1181no—
262C2×C16—1181no—
263C2×C16—1181no—
264#107—21no—
265#107—592no—
266#107—1181no—
267#107C22⋊D5912yescomplemented
268C4×C8—592no—
269C4×C8—592no—
270#95—2361no—
271C24—41no—
272C24—2361no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—1182no—
280C2×D4—4722no—
281C2×D4—4722no—
282C2×D4—4722no—
283C2×D4—4722no—
284C2×D4—2364no—
285C2×D4—2364no—
286C2×D4—2361no—
287C2×D4—2361no—
288C2×D4—2361no—
289C2×D4—2361no—
290C2×D4—2361no—
291C22×C4—41no—
292C22×C4—591no—
293C22×C4—591no—
294C22×C4—2361no—
295C22×C4D4×D5911yescharacteristic
296D8—22no—
297D8—22no—
298D8—41no—
299D8—41no—
300D8—1182no—
301D8—1182no—
302D8—2368no—
303D8—2361no—
304D8—2361no—
305C2×C8—592no—
306C2×C8—1181no—
307C2×C8—1181no—
308C2×C8C2×C4×D5911yescharacteristic
309C2×C8#1174568511yescharacteristic
310C2×C8D4×D5911yescharacteristic
311C2×C8D4×D5911yescharacteristic
312C2×C8#1174568711yescharacteristic
313C2×C8C2×C22⋊D5911yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—1182no—
317C4⋊C4—2361no—
318C42—592no—
319C42—592no—
320C42—4722no—
321C16—41no—
322C16—2361no—
323C23—42no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—4721no—
331C23—4721no—
332C23—4721no—
333C23—4721no—
334C23—4721no—
335C23—4721no—
336C23—2362no—
337C23D8×D5911yescharacteristic
338D4—42no—
339D4—42no—
340D4—81no—
341D4—81no—
342D4—4728no—
343D4—4728no—
344D4—4721no—
345D4—4721no—
346D4—2362no—
347D4—2362no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—592no—
352C2×C4—592no—
353C2×C4—592no—
354C2×C4—592no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—4721no—
358C2×C4—4721no—
359C2×C4—2362no—
360C2×C4C22⋊C4×D5911yescharacteristic
361C2×C4#1427369911yescharacteristic
362C2×C4#1427370011yescharacteristic
363C2×C4SD16×D5911yescharacteristic
364C2×C4#1427375111yescharacteristic
365C2×C4#1427375411yescharacteristic
366C8—1182no—
367C8(C22⋊D59)⋊C411yescharacteristic
368C8C4×C22⋊D5911yescharacteristic
369C8#1427371311yescharacteristic
370C8#1427372311yescharacteristic
371C22—82no—
372C22—82no—
373C22—82no—
374C22—161no—
375C22—161no—
376C22—161no—
377C22—161no—
378C22—9441no—
379C22—9441no—
380C22—9441no—
381C22—9441no—
382C22—4722no—
383C22—4722no—
384C22—4722no—
385C22#102×D5911yescharacteristic
386C22#1683759511yescharacteristic
387C22#1683759611yescharacteristic
388C22D16×D5911yescharacteristic
389C22SD32×D5911yescharacteristic
390C22#1683783611yescharacteristic
391C22#1683783911yescharacteristic
392C4—82no—
393C4—594no—
394C4—1182no—
395C4—4722no—
396C4#1683730211yescharacteristic
397C4#1683740511yescharacteristic
398C4#1683760011yescharacteristic
399C4#1683760111yescharacteristic
400C2—162no—
401C2—9442no—
402C2#2142502111yescharacteristic
403C2#357×D5911yescharacteristic
404C2#2142581011yescharacteristic
405C2#2142612911yescharacteristic
406C2#2142613011yescharacteristic
407C2#2142613411yescharacteristic
408C2#2142613511yescharacteristic
subgroupG/H
centerC23D8×D59
commutatorC2×C8×C59C22×C4
FrattiniC22×C8C22×D59
FittingC2×C59×#357C2
socleC23×C59C2×D8
prime radicalC2×#16837777C2
cosocleC22×C8×C59C23
hypercenterC2×#357D59
hypocenterC59#13252
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×Dic59⋊C16C2semidirect
3. C2×#16837204C2semidirect
4. C2×#16837203C2semidirect
5. C2×#16837202C2semidirect
6. #107×Dic59C2semidirect
7. C2×C59×#357C2semidirect
13. #16837777C4semidirect
48. #14273661D4semidirect
65. #107×C59D4semidirect
195. Dic59#357semidirect
201. C2×#357D59semidirect
230. C59#13252semidirect
267. #107C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168377772
C2×Dic59⋊C162
C2×#168372042
C2×#168372032
C2×#168372022
#107×Dic592
C2×C59×#3572
#1325259