Finite Group Databasebeta

← #28478951

Subgroups — #28478951

Order 15104.

524 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
1#21432724C211yesmaximal, characteristic
2C2×#16837457C211yesmaximal, characteristic
3#432×D59C211yesmaximal, characteristic
4#21421996C211yesmaximal, characteristic, complemented
5#21421995C211yesmaximal, characteristic, complemented
6#21421994C211yesmaximal, characteristic, complemented
7C59×#1302C211yesmaximal, characteristic, complemented
8C2×C42×D59C2211yescharacteristic
9#16837459C2211yescharacteristic
10#16837458—21no—
11#16837458C412yes—
12#16837457—21no—
13#16837457—21no—
14#16837457—21no—
15#16837457C412yes—
16#16837457C412yes—
17#16837456—21no—
18#16837456C412yes—
19#16837455C2211yescharacteristic
20#16837453—21no—
21#16837424—21no—
22C2×Dic59⋊C8—21no—
23C4⋊C8×D59C412yes—
24#16837364C412yes—
25C2×(C2×D59)⋊C8—21no—
26C22⋊C8×D59—21no—
27C4×#11745659—21no—
28C2×#14273638C2211yescharacteristic
29#97×D59—21no—
30C59×#432C2211yescharacteristic
31C59×#431C2211yescharacteristic
32C2×#97×C59C2211yescharacteristic
33C22×C4×D59C2×C411yescharacteristic
34C22×C4×D59D411yescharacteristic
35C22×C4×D59Q811yescharacteristic
36C2×#11745659—22no—
37C22×C59⋊C8—21no—
38C2×C8×D59—22no—
39C2×C4×Dic59C2×C411yescharacteristic
40C2×C4×Dic59D411yescharacteristic
41C2×C4×Dic59Q811yescharacteristic
42C42×D59C2×C411yescharacteristic
43C42×D59C2×C411yescharacteristic
44C42×D59C2×C411yescharacteristic
45C42×D59C2×C411yescharacteristic
46C42×D59D411yescharacteristic
47C42×D59D411yescharacteristic
48C42×D59D411yescharacteristic
49C42×D59D411yescharacteristic
50C4⋊(C59⋊C8)—21no—
51C4⋊(C59⋊C8)C2×C412yes—
52Dic59⋊C8—22no—
53Dic59⋊C8—22no—
54Dic59⋊C8—22no—
55Dic59⋊C8—22no—
56C22⋊(C59⋊C8)—21no—
57C22⋊(C59⋊C8)C2×C412yes—
58(C2×D59)⋊C8—22no—
59(C2×D59)⋊C8—22no—
60(C2×D59)⋊C8—22no—
61(C2×D59)⋊C8—22no—
62#14273638—21no—
63#14273638—21no—
64#14273638C2×C412yes—
65#14273637—22no—
66#14273637—22no—
67C4×C59⋊C8—21no—
68C22×C8×C59—21no—
69C2×C42×C59C2311yescharacteristic
70C4⋊C8×C59—21no—
71C4⋊C8×C59C2×C412yes—
72C22⋊C8×C59—21no—
73C22⋊C8×C59C2×C412yes—
74#97×C59—21no—
75#97×C59—21no—
76#97×C59C2×C412yes—
77C4×C8×C59—21no—
78C23×D59C4⋊C411yescharacteristic
79C22×C4×C59C22×C411yescharacteristic
80C22×C4×C59C2×D411yescharacteristic
81C22×C4×C59C2×Q811yescharacteristic
82C22×Dic59C4⋊C411yescharacteristic
83C22×Dic59C4⋊C411yescharacteristic
84C22×Dic59C4⋊C411yescharacteristic
85C2×C4×D59—42no—
86C2×C4×D59—42no—
87C2×C4×D59—42no—
88C2×C4×D59C4211yescharacteristic
89C2×C4×D59C4211yescharacteristic
90C2×C4×D59C22⋊C411yescharacteristic
91C2×C4×D59C22⋊C411yescharacteristic
92C2×C4×D59C22⋊C411yescharacteristic
93C2×C4×D59C22⋊C411yescharacteristic
94C2×C4×D59C22⋊C411yescharacteristic
95C2×C4×D59C22⋊C411yescharacteristic
96C2×C4×D59C4⋊C411yescharacteristic
97C2×C4×D59C4⋊C411yescharacteristic
98C2×C4×D59C4⋊C411yescharacteristic
99C2×C4×D59C4⋊C411yescharacteristic
100C2×C8×C59—22no—
101C2×C8×C59—22no—
102C2×C8×C59—22no—
103C2×C8×C59—42no—
104C42×C59C22×C411yescharacteristic
105C42×C59C22×C411yescharacteristic
106C42×C59C2×D411yescharacteristic
107C42×C59C2×D411yescharacteristic
108C4×Dic59C4211yescharacteristic
109C4×Dic59C4211yescharacteristic
110C4×Dic59C22⋊C411yescharacteristic
111C4×Dic59C22⋊C411yescharacteristic
112C4×Dic59C22⋊C411yescharacteristic
113C4×Dic59C22⋊C411yescharacteristic
114C4×Dic59C22⋊C411yescharacteristic
115C4×Dic59C22⋊C411yescharacteristic
116C4×Dic59C4⋊C411yescharacteristic
117C4×Dic59C4⋊C411yescharacteristic
118C4×Dic59C4⋊C411yescharacteristic
119C4×Dic59C4⋊C411yescharacteristic
120C2×C59⋊C8—22no—
121C2×C59⋊C8—22no—
122C2×C59⋊C8—22no—
123C2×C59⋊C8—42no—
124#11745659—44no—
125C8×D59—44no—
126C23×C59C2×C4⋊C411yescharacteristic
127C22×D59—22no—
128C22×D59—22no—
129C22×D59—41no—
130C22×D59#9511yescharacteristic
131C22×D59#9511yescharacteristic
132C2×C4×C59—22no—
133C2×C4×C59—22no—
134C2×C4×C59—41no—
135C2×C4×C59C2×C4211yescharacteristic
136C2×C4×C59C2×C22⋊C411yescharacteristic
137C2×C4×C59C2×C22⋊C411yescharacteristic
138C2×C4×C59C2×C22⋊C411yescharacteristic
139C2×C4×C59C2×C4⋊C411yescharacteristic
140C2×C4×C59C2×C4⋊C411yescharacteristic
141C2×Dic59—22no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59#9511yescharacteristic
145C2×Dic59#9511yescharacteristic
146C2×Dic59#9511yescharacteristic
147C2×Dic59#9511yescharacteristic
148C2×Dic59#9511yescharacteristic
149C2×Dic59#9511yescharacteristic
150C4×D59—22no—
151C4×D59—22no—
152C4×D59—22no—
153C4×D59—22no—
154C4×D59—41no—
155C4×D59—41no—
156C4×D59—41no—
157C4×D59—41no—
158C4×D59—41no—
159C4×D59—41no—
160C4×D59—41no—
161C4×D59—41no—
162C8×C59—42no—
163C8×C59—42no—
164C8×C59—42no—
165C59⋊C8—42no—
166C59⋊C8—42no—
167C59⋊C8—42no—
168#8085—591nomaximal, Sylow
169C22×C59—21no—
170C22×C59—21no—
171C22×C59C2×#9511yescharacteristic
172C22×C59#43012yes—
173C2×D59—21no—
174C2×D59—21no—
175C2×D59—21no—
176C2×D59—21no—
177C2×D59—21no—
178C2×D59—44no—
179C2×D59#34412yes—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59—21no—
183C4×C59—21no—
184C4×C59—21no—
185C4×C59#42112yes—
186Dic59—21no—
187Dic59—21no—
188Dic59—21no—
189Dic59—21no—
190Dic59—21no—
191Dic59—21no—
192#2920—591no—
193C2×#432—591no—
194C2×#432—591no—
195#1302—591no—
196#1302—591no—
197#1302—591no—
198#1302D5911yescharacteristic, complemented
199C2×C59—22no—
200C2×C59#173311yescharacteristic
201C2×C59#173811yescharacteristic
202C2×C59C2×#34411yescharacteristic
203D59—22no—
204D59—41no—
205C22×C42—591no—
206#432—592no—
207#432—592no—
208#432—592no—
209#432—591no—
210#432—592no—
211#432—1181no—
212#432—1181no—
213#432—1181no—
214#432—1181no—
215#432—1181no—
216#432C2×D5911yescharacteristic
217#431—591no—
218#431—1181no—
219#431C2×D5911yescharacteristic
220#423—1181no—
221C2×C4⋊C8—592no—
222C2×C4⋊C8—1181no—
223#407—592no—
224C2×C22⋊C8—1181no—
225C2×C22⋊C8—1181no—
226C4×M16—1181no—
227C2×#97—591no—
228C2×#97—1181no—
229C2×#97C2×D5911yescharacteristic
230C59#808511yescharacteristic, complemented, Sylow
231C23×C4—591no—
232C23×C4—591no—
233C23×C4—591no—
234C2×M16—1182no—
235C22×C8—21no—
236C22×C8—1182no—
237C22×C8—1181no—
238C2×C42—591no—
239C2×C42—591no—
240C2×C42—591no—
241C2×C42—591no—
242C2×C42—591no—
243C2×C42—591no—
244C2×C42—591no—
245C2×C42—591no—
246C2×C42—591no—
247C2×C42—591no—
248C2×C42—591no—
249C2×C42C22×D5911yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—592no—
252C4⋊C8—1182no—
253C4⋊C8—1182no—
254C4⋊C8—1182no—
255C4⋊C8—1182no—
256C4⋊C8—1181no—
257C4⋊C8C4×D5912yes—
258C22⋊C8—21no—
259C22⋊C8—592no—
260C22⋊C8—1182no—
261C22⋊C8—1182no—
262C22⋊C8—1182no—
263C22⋊C8—1182no—
264C22⋊C8—1181no—
265C22⋊C8C4×D5912yes—
266#97—21no—
267#97—21no—
268#97—592no—
269#97—1182no—
270#97—1182no—
271#97—1181no—
272#97—1181no—
273#97C4×D5912yes—
274C4×C8—21no—
275C4×C8—1181no—
276C24—591no—
277C22×C4—591no—
278C22×C4—591no—
279C22×C4—591no—
280C22×C4—591no—
281C22×C4—591no—
282C22×C4—591no—
283C22×C4—591no—
284C22×C4—591no—
285C22×C4—591no—
286C22×C4—591no—
287C22×C4—591no—
288C22×C4—591no—
289C22×C4—591no—
290C22×C4—591no—
291C22×C4—591no—
292C22×C4—2362no—
293C22×C4—2362no—
294C22×C4—2362no—
295C22×C4C2×C4×D5911yescharacteristic
296C22×C4D4×D5911yescharacteristic
297C22×C4Q8×D5911yescharacteristic
298M16—2364no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—1182no—
304C2×C8—1182no—
305C2×C8—1182no—
306C2×C8—2364no—
307C2×C8—2362no—
308C42—591no—
309C42—591no—
310C42—591no—
311C42—591no—
312C42—591no—
313C42—591no—
314C42—591no—
315C42—591no—
316C42—591no—
317C42—591no—
318C42—591no—
319C42—591no—
320C42C2×C4×D5911yescharacteristic
321C42C2×C4×D5911yescharacteristic
322C42D4×D5911yescharacteristic
323C42D4×D5911yescharacteristic
324C23—591no—
325C23—591no—
326C23—1182no—
327C23—1182no—
328C23—2361no—
329C23C4⋊C4×D5911yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—591no—
334C2×C4—591no—
335C2×C4—591no—
336C2×C4—591no—
337C2×C4—591no—
338C2×C4—591no—
339C2×C4—1182no—
340C2×C4—1182no—
341C2×C4—1182no—
342C2×C4—1182no—
343C2×C4—1182no—
344C2×C4—2361no—
345C2×C4—2361no—
346C2×C4—2361no—
347C2×C4—2361no—
348C2×C4—2361no—
349C2×C4—2361no—
350C2×C4—2361no—
351C2×C4—2361no—
352C2×C4—2361no—
353C2×C4—2361no—
354C2×C4C42×D5911yescharacteristic
355C2×C4C22⋊C4×D5911yescharacteristic
356C2×C4C22⋊C4×D5911yescharacteristic
357C2×C4C22⋊C4×D5911yescharacteristic
358C2×C4C4⋊C4×D5911yescharacteristic
359C2×C4C4⋊C4×D5911yescharacteristic
360C8—42no—
361C8—42no—
362C8—42no—
363C8—2362no—
364C8—2362no—
365C8—2362no—
366C22—21no—
367C22—21no—
368C22—592no—
369C22—1181no—
370C22—1181no—
371C22—1181no—
372C22—1181no—
373C22—1181no—
374C22—2364no—
375C22#95×D5911yescharacteristic
376C22#1683744912yes—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—1181no—
383C4—1181no—
384C4—1181no—
385C4—1181no—
386C4—1181no—
387C4—1181no—
388C4#1683741712yes—
389C2—22no—
390C2—1182no—
391C2—2361no—
392C2#2142380411yescharacteristic
393C2#2142382111yescharacteristic
394C2#344×D5911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D59
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC59×#1302C2
socleC22×C59C2×#95
prime radicalC23×D59C4⋊C4
cosocleC2×C42×C59C23
hypercenter#1302D59
hypocenterC59#8085
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1302

Complements

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

NH ≅ G/Ntype
4. #21421996C2semidirect
5. #21421995C2semidirect
6. #21421994C2semidirect
7. C59×#1302C2semidirect
198. #1302D59semidirect
230. C59#8085semidirect

Maximal subgroups

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

subgroupindex
#214327242
C2×#168374572
#432×D592
#214219962
#214219952
#214219942
C59×#13022
#808559