Finite Group Databasebeta

← #28506871

Subgroups — #28506871

Order 15104.

430 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837517C211yesmaximal, characteristic
2C2×#16837222C211yesmaximal, characteristic, complemented
3C2×#16837187C211yesmaximal, characteristic, complemented
4C2×#16837186C211yesmaximal, characteristic, complemented
5#21425709C211yesmaximal, characteristic, complemented
6C2×#16837177C211yesmaximal, characteristic, complemented
7C59×#2113C211yesmaximal, characteristic, complemented
8C2×#14273747C411yescharacteristic
9C2×#14273733C2211yescharacteristic
10C2×#14273667C2211yescharacteristic
11C22×C59⋊C16C2211yescharacteristic
12#16837517—22no—
13#16837517—22no—
14C2×#14273662C411yescharacteristic
15C2×#14273654C411yescharacteristic
16C2×#14273653C411yescharacteristic
17C2×C8×Dic59C2211yescharacteristic
18#16837222—22no—
19#16837187—22no—
20#16837186—22no—
21(C2×D59)⋊C16—22no—
22#16837177—22no—
23C2×#131×C59C2211yescharacteristic
24C2×M32×C59C2211yescharacteristic
25C22×C16×C59C2211yescharacteristic
26C59×C22⋊C16—22no—
27C2×#11745685C2×C411yescharacteristic
28#14273747—22no—
29#14273747—22no—
30C2×#11745672C811yescharacteristic
31C2×#11745670C811yescharacteristic
32C2×#11745671C811yescharacteristic
33C2×#11745669C811yescharacteristic
34#14273733—21no—
35#14273733—21no—
36#14273733—21no—
37#14273733—21no—
38C2×#11745664C2×C411yescharacteristic
39C2×#11745659—21no—
40C22×C59⋊C8C2×C411yescharacteristic
41C2×C8×D59—21no—
42C2×C4×Dic59C2×C411yescharacteristic
43#14273667—21no—
44#14273667—21no—
45C2×C59⋊C16—21no—
46C2×C59⋊C16—21no—
47C2×C59⋊C16—21no—
48C2×C59⋊C16D412yes—
49#14273662—22no—
50#14273654—22no—
51#14273653—22no—
52C8×Dic59D412yes—
53C8×Dic59D412yes—
54C2×#41×C59C2×C411yescharacteristic
55#131×C59—21no—
56#131×C59—21no—
57#131×C59—21no—
58#131×C59—21no—
59C2×M16×C59—21no—
60C2×M16×C59C2×C411yescharacteristic
61C22×C8×C59—21no—
62C22×C8×C59C2311yescharacteristic
63M32×C59—21no—
64M32×C59—21no—
65C2×C16×C59—21no—
66C2×C16×C59—21no—
67C2×C16×C59—21no—
68C2×C16×C59D412yes—
69#41×C59—21no—
70#41×C59—21no—
71#41×C59—21no—
72#41×C59—21no—
73C2×Q8×C59C2×C811yescharacteristic
74C2×D4×C59—21no—
75C2×D4×C59C2×C811yescharacteristic
76C22×C4×C59—21no—
77C22×C4×C59C22×C411yescharacteristic
78C2×C22⋊D59—21no—
79C22×Dic59—21no—
80#11745685—21no—
81#11745685—21no—
82#11745685—21no—
83#11745685—21no—
84C2×D236C2×C811yescharacteristic
85C2×C4×D59—21no—
86C2×Dic118C2×C811yescharacteristic
87M16×C59—21no—
88M16×C59—21no—
89M16×C59—41no—
90M16×C59—41no—
91C2×C8×C59—21no—
92C2×C8×C59—41no—
93C2×C8×C59—41no—
94C2×C8×C59C2×D411yescharacteristic
95C2×C8×C59C2×D411yescharacteristic
96C2×C8×C59C2×D411yescharacteristic
97C2×C8×C59C2×D411yescharacteristic
98C2×C8×C59#4111yescharacteristic
99C2×C8×C59#4111yescharacteristic
100#11745672—22no—
101#11745671—22no—
102#11745670—22no—
103#11745669—22no—
104C4×Dic59—21no—
105C4×Dic59C22⋊C412yes—
106#11745664—21no—
107#11745664—21no—
108C2×C59⋊C8—21no—
109C2×C59⋊C8C22⋊C412yes—
110C2×C59⋊C8C2×C811yescharacteristic
111C2×C59⋊C8C2×C811yescharacteristic
112C2×C59⋊C8M1612yes—
113#11745659—41no—
114#11745659—41no—
115C8×D59—41no—
116C8×D59—41no—
117C16×C59—22no—
118C16×C59—41no—
119C59⋊C16—22no—
120C59⋊C16—41no—
121C23×C59—21no—
122C23×C59#13111yescharacteristic
123C22×D59—21no—
124Q8×C59—21no—
125Q8×C59—21no—
126D4×C59—21no—
127D4×C59—21no—
128D4×C59—41no—
129D4×C59—41no—
130C2×C4×C59—21no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59C2×C22⋊C411yescharacteristic
134C2×C4×C59C4×D411yescharacteristic
135C2×C4×C59C4×D411yescharacteristic
136C2×C4×C59C22×C811yescharacteristic
137C2×C4×C59C2×M1611yescharacteristic
138C2×C4×C59#13111yescharacteristic
139C22⋊D59—41no—
140C22⋊D59—41no—
141C2×Dic59—22no—
142C2×Dic59—21no—
143C2×Dic59—42no—
144D236—21no—
145D236—21no—
146C4×D59—41no—
147C4×D59—41no—
148Dic118—21no—
149Dic118—21no—
150C8×C59—41no—
151C8×C59#12111yescharacteristic
152C8×C59#12111yescharacteristic
153C8×C59#12411yescharacteristic
154C8×C59#12711yescharacteristic
155C59⋊C8—41no—
156C59⋊C8C22⋊C812yes—
157C59⋊C8C22⋊C812yes—
158#13196—591nomaximal, Sylow
159C22×C59—22no—
160C22×C59—42no—
161C22×C59—41no—
162C22×C59#40811yescharacteristic
163C22×C59C8×D411yescharacteristic
164C22×C59#43611yescharacteristic
165C2×D59—42no—
166C2×D59—41no—
167C4×C59—41no—
168C4×C59#39011yescharacteristic
169C4×C59C2×C22⋊C811yescharacteristic
170C4×C59C8×D411yescharacteristic
171C4×C59#43611yescharacteristic
172Dic59—42no—
173Dic59—41no—
174C2×#443—591no—
175C2×#364—591no—
176C2×#350—591no—
177C2×#350—591no—
178#2113—591no—
179#2113D5911yescharacteristic, complemented
180C2×#346—591no—
181C2×C59—21no—
182C2×C59—21no—
183C2×C59—81no—
184C2×C59#195411yescharacteristic
185C2×C59#217112yes—
186D59—81no—
187C2×#135—591no—
188C2×#131—591no—
189C2×#131C2×D5911yescharacteristic
190C2×M32—591no—
191C2×M32C2×D5911yescharacteristic
192C22×C16—591no—
193C22×C16C2×D5911yescharacteristic
194#443—1182no—
195#443—1182no—
196C2×#108—591no—
197C2×#104—591no—
198C2×#104—591no—
199C2×C4×C8—591no—
200#364—1182no—
201#350—1182no—
202#350—1182no—
203C22⋊C16—22no—
204C22⋊C16—1182no—
205#346—1182no—
206C59#1319611yescharacteristic, complemented, Sylow
207C2×#41—591no—
208C2×#41C4×D5911yescharacteristic
209#135—1182no—
210#135—1182no—
211C2×Q16—591no—
212C2×SD16—591no—
213C2×SD16—591no—
214C2×D8—591no—
215#131—21no—
216#131—21no—
217#131—21no—
218#131—21no—
219#131—1181no—
220#131—1181no—
221#131—1181no—
222#131—1181no—
223C2×M16—21no—
224C2×M16—591no—
225C2×M16—1181no—
226C2×M16C4×D5911yescharacteristic
227C22×C8—21no—
228C22×C8—591no—
229C22×C8—1181no—
230C22×C8C22×D5911yescharacteristic
231C2×C42—591no—
232M32—21no—
233M32—21no—
234M32—1181no—
235M32—1181no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—592no—
240C2×C16—1181no—
241C2×C16—1181no—
242C2×C16—1181no—
243C2×C16C22⋊D5912yes—
244#108—1182no—
245#104—1182no—
246#104—1182no—
247C4×C8—592no—
248C4×C8—592no—
249#41—21no—
250#41—21no—
251#41—21no—
252#41—21no—
253#41—1181no—
254#41—1181no—
255#41—1181no—
256#41—1181no—
257C2×Q8—591no—
258C2×Q8C8×D5911yescharacteristic
259C2×D4—21no—
260C2×D4—591no—
261C2×D4—1181no—
262C2×D4C8×D5911yescharacteristic
263C22×C4—21no—
264C22×C4—1181no—
265C22×C4—1181no—
266C22×C4C2×C4×D5911yescharacteristic
267Q16—1182no—
268SD16—1182no—
269SD16—1182no—
270D8—1182no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—1181no—
276M16—1181no—
277M16—2361no—
278M16—2361no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—592no—
283C2×C8—591no—
284C2×C8—591no—
285C2×C8—592no—
286C2×C8—1181no—
287C2×C8—2361no—
288C2×C8—2361no—
289C2×C8#1174568511yescharacteristic
290C2×C8D4×D5911yescharacteristic
291C2×C8D4×D5911yescharacteristic
292C2×C8D4×D5911yescharacteristic
293C2×C8#1174568711yescharacteristic
294C2×C8C2×C22⋊D5911yescharacteristic
295C42—592no—
296C42—1181no—
297C16—22no—
298C16—41no—
299C16—1182no—
300C16—2361no—
301C23—21no—
302C23—1181no—
303C23#1427373311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1181no—
307Q8—1181no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—1181no—
313D4—1181no—
314D4—2361no—
315D4—2361no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—1181no—
320C2×C4—1182no—
321C2×C4—2362no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4C22⋊C4×D5911yescharacteristic
325C2×C4(C22⋊D59)⋊C411yescharacteristic
326C2×C4C4×C22⋊D5911yescharacteristic
327C2×C4C2×C8×D5911yescharacteristic
328C2×C4M16×D5911yescharacteristic
329C2×C4#1427373511yescharacteristic
330C8—41no—
331C8—592no—
332C8—592no—
333C8—2361no—
334C8#1427369911yescharacteristic
335C8#1427370011yescharacteristic
336C8#1427371311yescharacteristic
337C8#1427372311yescharacteristic
338C22—22no—
339C22—42no—
340C22—41no—
341C22—2362no—
342C22—2361no—
343C22#1683736711yescharacteristic
344C22C8×C22⋊D5911yescharacteristic
345C22#1683747711yescharacteristic
346C4—41no—
347C4—2362no—
348C4—2361no—
349C4#1683730211yescharacteristic
350C4C22⋊C8×D5911yescharacteristic
351C4(C22⋊D59)⋊C811yescharacteristic
352C4#1683747811yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2—4721no—
357C2#2142488811yescharacteristic
358C2#2142593612yes—
subgroupG/H
centerC2×C8C2×C22⋊D59
commutatorC2×C4×C59C22×C8
FrattiniC22×C8C22×D59
FittingC59×#2113C2
socleC22×C59C8×D4
prime radicalC2×#14273747C4
cosocleC22×C8×C59C23
hypercenter#2113D59
hypocenterC59#13196
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ #2113

Complements

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

NH ≅ G/Ntype
2. C2×#16837222C2semidirect
3. C2×#16837187C2semidirect
4. C2×#16837186C2semidirect
5. #21425709C2semidirect
6. C2×#16837177C2semidirect
7. C59×#2113C2semidirect
179. #2113D59semidirect
206. C59#13196semidirect

Maximal subgroups

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

subgroupindex
C2×#168375172
C2×#168372222
C2×#168371872
C2×#168371862
#214257092
C2×#168371772
C59×#21132
#1319659