Finite Group Databasebeta

← #28477781

Subgroups — #28477781

Order 15104.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21425624C211yesmaximal, characteristic, complemented
2#21425504C211yesmaximal, characteristic, complemented
3#21425499C211yesmaximal, characteristic, complemented
4#21421922C211yesmaximal, characteristic, complemented
5#21421917C211yesmaximal, characteristic, complemented
6#21421917C211yesmaximal, characteristic, complemented
7C59×#2733C211yesmaximal, characteristic
8C2×#14273660—21no—
9C2×#14273651—21no—
10C2×#14273648—21no—
11C2×#14273648—21no—
12#16837272C2211yescharacteristic
13#16837164—21no—
14#16837164—21no—
15#16837157C2211yescharacteristic
16#16837157C2211yescharacteristic
17#16837157C2211yescharacteristic
18C2×#124×C59—21no—
19C59×#394—21no—
20C59×#392—21no—
21C59×#392—21no—
22C59×#391C2211yescharacteristic
23C59×#390C2211yescharacteristic
24C59×#390C2211yescharacteristic
25C59×#388—21no—
26C59×#388—21no—
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59—21no—
33#14273660—42no—
34#14273651—42no—
35#14273648—42no—
36#14273648—42no—
37C22×Q8×C59D411yescharacteristic
38C22×D4×C59—21no—
39C22×D4×C59—21no—
40C22×D4×C59D411yescharacteristic
41C22×D4×C59D411yescharacteristic
42#124×C59—42no—
43#124×C59—42no—
44C2×C4⋊C4×C59D411yescharacteristic
45C2×C4⋊C4×C59D411yescharacteristic
46C2×C4⋊C4×C59D411yescharacteristic
47C2×C22⋊C4×C59—21no—
48C2×C22⋊C4×C59—21no—
49C2×C22⋊C4×C59—21no—
50C2×C22⋊C4×C59—21no—
51C2×C22⋊C4×C59—21no—
52C2×C22⋊C4×C59—21no—
53C2×C22⋊C4×C59—21no—
54C2×C22⋊C4×C59—21no—
55C2×C42×C59—21no—
56C2×C42×C59C2311yescharacteristic
57#95×C59—21no—
58#95×C59—21no—
59#95×C59—21no—
60C24×C59—21no—
61C24×C59—21no—
62C2×Q8×C59—21no—
63C2×Q8×C59—41no—
64C2×Q8×C59—41no—
65C2×Q8×C59D812yes—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—21no—
70C2×D4×C59—41no—
71C2×D4×C59—41no—
72C2×D4×C59—41no—
73C2×D4×C59—41no—
74C2×D4×C59—42no—
75C2×D4×C59—81no—
76C2×D4×C59—81no—
77C2×D4×C59—81no—
78C2×D4×C59—81no—
79C2×D4×C59—81no—
80C22×C4×C59—21no—
81C22×C4×C59—21no—
82C22×C4×C59—21no—
83C22×C4×C59—21no—
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59C2×D411yescharacteristic
86C22×C4×C59C2×D411yescharacteristic
87C22×Dic59—41no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C22⋊C4×C59—42no—
92C22⋊C4×C59—42no—
93C22⋊C4×C59—41no—
94C22⋊C4×C59—41no—
95C22⋊C4×C59—41no—
96C22⋊C4×C59—41no—
97C22⋊C4×C59—41no—
98C22⋊C4×C59—41no—
99C22⋊C4×C59—41no—
100C22⋊C4×C59—41no—
101C22⋊C4×C59—81no—
102C22⋊C4×C59—81no—
103C42×C59—41no—
104C42×C59—42no—
105C4⋊Dic59—41no—
106C4⋊Dic59—41no—
107C4⋊Dic59—41no—
108C4⋊Dic59—41no—
109C4⋊Dic59—41no—
110C4⋊Dic59—41no—
111C2×C59⋊C8—22no—
112C2×C59⋊C8—41no—
113C2×C59⋊C8—41no—
114C2×C59⋊C8—41no—
115C2×C59⋊C8—41no—
116C2×C59⋊C8—41no—
117C2×C59⋊C8—41no—
118C2×C59⋊C8—41no—
119C2×C59⋊C8—41no—
120C23×C59—41no—
121C23×C59—41no—
122C23×C59—41no—
123C23×C59—41no—
124C23×C59—41no—
125C23×C59—41no—
126C23×C59—41no—
127C23×C59—41no—
128C23×C59—41no—
129C23×C59—41no—
130C23×C59—41no—
131C23×C59—41no—
132C23×C59—41no—
133C23×C59—41no—
134C23×C59#12011yescharacteristic
135Q8×C59—42no—
136Q8×C59—81no—
137D4×C59—42no—
138D4×C59—42no—
139D4×C59—81no—
140D4×C59—81no—
141D4×C59—84no—
142D4×C59—84no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—22no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—41no—
157C2×C4×C59—41no—
158C2×C4×C59—41no—
159C2×C4×C59—41no—
160C2×C4×C59—41no—
161C2×C4×C59C2×D811yescharacteristic
162C2×C4×C59#13511yescharacteristic
163C2×C4×C59#13511yescharacteristic
164C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C59#13711yescharacteristic
167C2×Dic59—81no—
168C2×Dic59—81no—
169C2×Dic59—81no—
170C59⋊C8—42no—
171C59⋊C8—81no—
172C59⋊C8—81no—
173#7796—591nomaximal, Sylow
174C22×C59—81no—
175C22×C59—81no—
176C22×C59—81no—
177C22×C59—81no—
178C22×C59—81no—
179C22×C59—81no—
180C22×C59—81no—
181C22×C59—81no—
182C22×C59—81no—
183C22×C59—81no—
184C22×C59—81no—
185C22×C59—81no—
186C22×C59—81no—
187C22×C59—81no—
188C22×C59#44711yescharacteristic
189C22×C59#44911yescharacteristic
190C22×C59#45211yescharacteristic
191C22×C59#45311yescharacteristic
192C22×C59#45511yescharacteristic
193C22×C59#45511yescharacteristic
194C22×C59#45811yescharacteristic
195C4×C59—21no—
196C4×C59—21no—
197C4×C59—21no—
198C4×C59—21no—
199C4×C59—21no—
200C4×C59—21no—
201C4×C59—42no—
202C4×C59—81no—
203C4×C59—81no—
204C4×C59—81no—
205Dic59—161no—
206#2733D5911yescharacteristic
207#2093—591no—
208#2072—591no—
209#2071—591no—
210#1272—591no—
211#1270—591no—
212#1270—591no—
213C2×C59—161no—
214C2×C59—161no—
215C2×C59#160711yescharacteristic
216C2×C59#161211yescharacteristic
217C2×C59#161811yescharacteristic
218C2×C59#162111yescharacteristic
219C2×C59#164111yescharacteristic
220C2×C59#164611yescharacteristic
221C2×C59#165911yescharacteristic
222C2×#124—21no—
223C2×#107—1181no—
224C2×#103—1181no—
225C2×#102—1181no—
226C2×#102—1181no—
227#394—21no—
228#392—21no—
229#392—21no—
230#391C2×D5911yescharacteristic
231#390C2×D5911yescharacteristic
232#390C2×D5911yescharacteristic
233#388—21no—
234#388—21no—
235#384—591no—
236#340—1181no—
237#340—1181no—
238#336—591no—
239#336—591no—
240#336—591no—
241C59#779611yescharacteristic, complemented, Sylow
242C22×Q8C22⋊D5911yescharacteristic
243C22×D4—21no—
244C22×D4—21no—
245C22×D4C22⋊D5911yescharacteristic
246C22×D4C22⋊D5911yescharacteristic
247C22×C8—1181no—
248C22×C8—1181no—
249C22×C8—1181no—
250#124—42no—
251#124—42no—
252C2×C4⋊C4—1181no—
253C2×C4⋊C4—1181no—
254C2×C4⋊C4—1181no—
255C2×C4⋊C4C22⋊D5911yescharacteristic
256C2×C4⋊C4C22⋊D5911yescharacteristic
257C2×C4⋊C4C22⋊D5911yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C42—21no—
267C2×C42C22×D5911yescharacteristic
268#107—2362no—
269#103—2362no—
270#102—2362no—
271#102—2362no—
272#95—21no—
273#95—21no—
274#95—21no—
275C24—21no—
276C24—21no—
277C2×Q8—21no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8#1174566912yes—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—81no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4—81no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—2361no—
300C22×C4C2×C22⋊D5911yescharacteristic
301C22×C4C2×C22⋊D5911yescharacteristic
302C22×C4C2×C22⋊D5911yescharacteristic
303C2×C8—1182no—
304C2×C8—2361no—
305C2×C8—2361no—
306C2×C8—2361no—
307C2×C8—2361no—
308C2×C8—2361no—
309C2×C8—2361no—
310C2×C8—2361no—
311C2×C8—2361no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—2361no—
316C4⋊C4—2361no—
317C4⋊C4—2361no—
318C4⋊C4—2361no—
319C4⋊C4—2361no—
320C4⋊C4—2361no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C42—41no—
334C42—42no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23#1427369611yescharacteristic
350Q8—42no—
351Q8—81no—
352D4—42no—
353D4—42no—
354D4—81no—
355D4—81no—
356D4—84no—
357D4—84no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—4721no—
377C2×C4—4721no—
378C2×C4—4721no—
379C2×C4C2×#1174566911yescharacteristic
380C2×C4#1427374711yescharacteristic
381C2×C4#1427374711yescharacteristic
382C2×C4#1427375211yescharacteristic
383C2×C4#1427375311yescharacteristic
384C2×C4#1427375711yescharacteristic
385C8—4721no—
386C8—4721no—
387C8—2362no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22#1683753611yescharacteristic
403C22#1683754711yescharacteristic
404C22#1683756411yescharacteristic
405C22#1683757011yescharacteristic
406C22#1683758011yescharacteristic
407C22#1683758011yescharacteristic
408C22#1683759211yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4—9441no—
420C2—161no—
421C2—161no—
422C2#2142308211yescharacteristic
423C2#2142311011yescharacteristic
424C2#2142314411yescharacteristic
425C2#2142316111yescharacteristic
426C2#2142328911yescharacteristic
427C2#2142332411yescharacteristic
428C2#2142340211yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
Fitting, prime radicalC59×#2733C2
socleC23×C59#120
hypercenter#2733D59
hypocenterC59#7796
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #21425624C2semidirect
2. #21425504C2semidirect
3. #21425499C2semidirect
4. #21421922C2semidirect
5. #21421917C2semidirect
6. #21421917C2semidirect
241. C59#7796semidirect

Maximal subgroups

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

subgroupindex
#214256242
#214255042
#214254992
#214219222
#214219172
C59×#27332
#779659