Finite Group Databasebeta

← #28507864

Subgroups — #28507864

Order 15104.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837640C211yesmaximal, characteristic
2C2×#16837228C211yesmaximal, characteristic, complemented
3C2×#16837206C211yesmaximal, characteristic, complemented
4C2×(C2×D59)⋊C16C211yesmaximal, characteristic
5#21424122C211yesmaximal, characteristic
6#21422187C211yesmaximal, characteristic, complemented
7C2×C59×#358C211yesmaximal, characteristic, complemented
8C22×C8×D59C2211yescharacteristic
9C2×#14273703—21no—
10C22×C59⋊C16C2211yescharacteristic
11#16837640—22no—
12#16837640—22no—
13C2×#14273661C2211yescharacteristic
14C2×#14273661C2211yescharacteristic
15C2×#14273651—21no—
16#16837259—21no—
17#16837228—22no—
18#16837206—22no—
19(C2×D59)⋊C16—22no—
20#16837164—21no—
21C22×Q16×C59C2211yescharacteristic
22C22×C16×C59C2211yescharacteristic
23C2×#107×C59C2211yescharacteristic
24C59×#358—22no—
25C22×C4×D59D411yescharacteristic
26C22×C59⋊C8D411yescharacteristic
27C2×C8×D59—21no—
28C2×C8×D59—21no—
29C2×C8×D59—21no—
30C2×C8×D59—21no—
31C2×C8×D59—21no—
32C2×C8×D59—21no—
33#14273703—24no—
34#14273703—42no—
35C2×C4⋊Dic59—21no—
36C2×C4⋊Dic59—21no—
37C2×Dic59⋊C4—41no—
38C2×(C2×D59)⋊C4—41no—
39C2×(C2×D59)⋊C4—41no—
40C2×C59⋊C16—21no—
41C2×C59⋊C16—21no—
42C2×C59⋊C16—21no—
43#14273661—21no—
44#14273661—21no—
45#14273661—21no—
46#14273661D412yes—
47#14273651—24no—
48C59⋊#95—41no—
49C22×Q8×C59—21no—
50C2×Q16×C59—21no—
51C2×Q16×C59—21no—
52C2×Q16×C59—21no—
53C2×Q16×C59—21no—
54C2×Q16×C59—21no—
55C2×Q16×C59D412yes—
56C22×C8×C59C2311yescharacteristic
57C2×C4⋊C4×C59—21no—
58C2×C16×C59—21no—
59C2×C16×C59—21no—
60C2×C16×C59D412yes—
61#107×C59—21no—
62#107×C59—21no—
63C23×D59D811yescharacteristic
64C2×Q8×C59—22no—
65C2×Q8×C59—41no—
66C2×Q8×C59—41no—
67C2×Q8×C59—41no—
68C2×Q8×C59—41no—
69C2×Q8×C59—41no—
70C22×C4×C59—41no—
71C22×C4×C59—41no—
72C22×C4×C59C2×D411yescharacteristic
73C22×Dic59—41no—
74C22×Dic59—41no—
75C22×Dic59D811yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82Q16×C59—22no—
83Q16×C59—22no—
84Q16×C59—41no—
85Q16×C59—41no—
86C2×C8×C59C2×D411yescharacteristic
87C2×C8×C59C2×D411yescharacteristic
88C2×C8×C59C2×D411yescharacteristic
89C2×C8×C59#4111yescharacteristic
90C2×C8×C59#4111yescharacteristic
91C2×C8×C59#4111yescharacteristic
92C4⋊C4×C59—41no—
93C4⋊C4×C59—41no—
94(C2×D59)⋊C4—44no—
95(C2×D59)⋊C4—82no—
96C4⋊Dic59—22no—
97C4⋊Dic59—41no—
98C4⋊Dic59—41no—
99C4⋊Dic59—41no—
100Dic59⋊C4—44no—
101C2×C59⋊C8—21no—
102C2×C59⋊C8—21no—
103C2×C59⋊C8—21no—
104C8×D59—41no—
105C8×D59—41no—
106C8×D59—41no—
107C8×D59—41no—
108C16×C59—22no—
109C59⋊C16—41no—
110C23×C59C2×D811yescharacteristic
111C22×D59—21no—
112C22×D59—21no—
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59Q3212yes—
118Q8×C59—42no—
119Q8×C59—42no—
120Q8×C59—81no—
121Q8×C59—81no—
122C2×C4×C59—42no—
123C2×C4×C59—81no—
124C2×C4×C59—81no—
125C2×C4×C59—81no—
126C2×C4×C59—81no—
127C2×C4×C59—81no—
128C2×C4×C59#12011yescharacteristic
129C2×C4×C59#12111yescharacteristic
130C2×C4×C59#12311yescharacteristic
131C2×C4×C59#13511yescharacteristic
132C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C59#13711yescharacteristic
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—42no—
138C2×Dic59—81no—
139C2×Dic59—81no—
140C2×Dic59—81no—
141C2×Dic59—81no—
142C2×Dic59—81no—
143C4×D59—41no—
144C4×D59—41no—
145C4×D59—41no—
146C4×D59—41no—
147C8×C59#12111yescharacteristic
148C8×C59#12111yescharacteristic
149C8×C59#12311yescharacteristic
150C8×C59#12411yescharacteristic
151C59⋊C8—41no—
152#13383—591nomaximal, Sylow
153C22×C59#44711yescharacteristic
154C22×C59#46611yescharacteristic
155C22×C59#48011yescharacteristic
156C22×C59C2×Q3211yescharacteristic
157C22×C59#50811yescharacteristic
158C22×C59#50911yescharacteristic
159C22×C59#51011yescharacteristic
160C2×D59—22no—
161C2×D59—22no—
162C2×D59—22no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C4×C59—82no—
168C4×C59—161no—
169C4×C59#39411yescharacteristic
170C4×C59#45211yescharacteristic
171C4×C59#46811yescharacteristic
172C4×C59#48211yescharacteristic
173Dic59—41no—
174Dic59—82no—
175Dic59—161no—
176C2×#467—591no—
177C2×#366—591no—
178C2×#358—591no—
179C2×#358D5911yescharacteristic, complemented
180C2×C22⋊C16—591no—
181#1808—591no—
182#1380—591no—
183C2×C59#203311yescharacteristic
184C2×C59#218611yescharacteristic
185C2×C59#218811yescharacteristic
186C2×C59#221611yescharacteristic
187C2×C59#222011yescharacteristic
188C2×C59#223611yescharacteristic
189C2×C59#223711yescharacteristic
190D59—42no—
191C22×Q16C2×D5911yescharacteristic
192C23×C8—591no—
193C2×C22⋊Q8—1181no—
194C22×C16—591no—
195C22×C16C2×D5911yescharacteristic
196#467—1182no—
197#467—1182no—
198C2×#107—591no—
199C2×#107—591no—
200C2×#107C2×D5911yescharacteristic
201C2×#103—1181no—
202#380—1181no—
203#366—1182no—
204#358—22no—
205#358—1182no—
206C22⋊C16—1182no—
207#340—1181no—
208C59#1338311yescharacteristic, complemented, Sylow
209C22×Q8—21no—
210C23×C4—591no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16D23612yes—
217C22×C8—591no—
218C22×C8—1181no—
219C22×C8—1181no—
220C22×C8—1181no—
221C22×C8—1181no—
222C22×C8—1181no—
223C22×C8—1181no—
224C22×C8C22×D5911yescharacteristic
225C22⋊Q8—1184no—
226C22⋊Q8—2362no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—1181no—
229C2×C4⋊C4—1181no—
230C2×C4⋊C4—2361no—
231C2×C22⋊C4—2361no—
232C2×C22⋊C4—2361no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—1181no—
236C2×C16—1181no—
237C2×C16—1181no—
238C2×C16C22⋊D5912yes—
239#107—21no—
240#107—21no—
241#107—592no—
242#107—1181no—
243#107—1181no—
244#107—1181no—
245#103—1184no—
246#95—2361no—
247C24—591no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—591no—
257C22×C4—1181no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4—1181no—
263C22×C4—2361no—
264C22×C4—2361no—
265C22×C4D4×D5911yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—41no—
269Q16—41no—
270C2×C8—1181no—
271C2×C8—1181no—
272C2×C8—1181no—
273C2×C8—2361no—
274C2×C8—2361no—
275C2×C8—2361no—
276C2×C8—2361no—
277C2×C8C2×D23611yescharacteristic
278C2×C8#1174568511yescharacteristic
279C2×C8D4×D5911yescharacteristic
280C2×C8#1174568711yescharacteristic
281C2×C8#1174568711yescharacteristic
282C2×C8C2×C22⋊D5911yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—1182no—
286C4⋊C4—2364no—
287C4⋊C4—2361no—
288C4⋊C4—2361no—
289C4⋊C4—2361no—
290C22⋊C4—4722no—
291C22⋊C4—2364no—
292C16—22no—
293C16—2361no—
294C23—592no—
295C23—1181no—
296C23—1181no—
297C23—1181no—
298C23—1181no—
299C23—1181no—
300C23—1181no—
301C23D8×D5911yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—4721no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4—4721no—
319C2×C4—4721no—
320C2×C4—2362no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4—2361no—
325C2×C4#1427369711yescharacteristic
326C2×C4#1427369811yescharacteristic
327C2×C4#1427370911yescharacteristic
328C2×C4#1427374611yescharacteristic
329C2×C4#1427375411yescharacteristic
330C2×C4#1427375611yescharacteristic
331C8—2361no—
332C8#1427369911yescharacteristic
333C8#1427370111yescharacteristic
334C8#1427371111yescharacteristic
335C8#1427371311yescharacteristic
336C22—1182no—
337C22—1182no—
338C22—1182no—
339C22—2361no—
340C22—2361no—
341C22—2361no—
342C22—2361no—
343C22#1683753711yescharacteristic
344C22#1683763511yescharacteristic
345C22#1683771411yescharacteristic
346C22Q32×D5911yescharacteristic
347C22#1683783511yescharacteristic
348C22#1683783911yescharacteristic
349C22#1683784111yescharacteristic
350C4—82no—
351C4—161no—
352C4—9441no—
353C4—4722no—
354C4—2361no—
355C4#1683731811yescharacteristic
356C4#1683756511yescharacteristic
357C4#1683764511yescharacteristic
358C4#1683772411yescharacteristic
359C2—2362no—
360C2#2142527711yescharacteristic
361C2#2142602211yescharacteristic
362C2#2142603111yescharacteristic
363C2#2142618411yescharacteristic
364C2#2142620611yescharacteristic
365C2#2142629711yescharacteristic
366C2#2142630311yescharacteristic
subgroupG/H
centerC23D8×D59
commutator, cosocleC22×C8×C59C23
FrattiniC22×C8C22×D59
FittingC2×C59×#358C2
socleC23×C59C2×D8
prime radicalC23×D59D8
hypercenterC2×#358D59
hypocenterC59#13383
LCSG ▷ C22×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#16837228C2semidirect
3. C2×#16837206C2semidirect
6. #21422187C2semidirect
7. C2×C59×#358C2semidirect
179. C2×#358D59semidirect
208. C59#13383semidirect

Maximal subgroups

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

subgroupindex
C2×#168376402
C2×#168372282
C2×#168372062
C2×(C2×D59)⋊C162
#214241222
#214221872
C2×C59×#3582
#1338359