Finite Group Databasebeta

← #28477222

Subgroups — #28477222

Order 15104.

532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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#21432426C211yesmaximal, characteristic
2#21424075C211yesmaximal, characteristic, complemented
3#21423857C211yesmaximal, characteristic, complemented
4#21421920C211yesmaximal, characteristic, complemented
5#21421918C211yesmaximal, characteristic, complemented
6#21421917C211yesmaximal, characteristic, complemented
7C59×#1270C211yesmaximal, characteristic, complemented
8C2×#14273709—21no—
9C2×#14273698C411yescharacteristic
10C2×C42×D59C2211yescharacteristic
11C2×Dic59⋊C8—21no—
12C2×(C2×D59)⋊C8—21no—
13C2×(C2×D59)⋊C8—21no—
14C2×#14273637—21no—
15#16837305C411yescharacteristic
16#16837301C411yescharacteristic
17#16837300C2211yescharacteristic
18#16837296—21no—
19#16837295—21no—
20#16837278—21no—
21#16837259C411yescharacteristic
22#16837157C2211yescharacteristic
23#16837157C2211yescharacteristic
24C59×#390C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×C22⋊D59—21no—
28C22×C4×D59C2×C411yescharacteristic
29C22×C4×D59D411yescharacteristic
30C22×C4×D59D411yescharacteristic
31C22×C59⋊C8—21no—
32C22×C59⋊C8—21no—
33#14273709—42no—
34#14273709—42no—
35#14273698—42no—
36C2×C4⋊Dic59—21no—
37C2×C4⋊Dic59C2×C411yescharacteristic
38C2×C4⋊Dic59C2×C411yescharacteristic
39C2×Dic59⋊C4—21no—
40C2×C22⋊Dic59—21no—
41C2×C22⋊Dic59—21no—
42C2×C22⋊Dic59—21no—
43C2×(C2×D59)⋊C4—21no—
44C2×C4×Dic59C2×C411yescharacteristic
45C2×C4×Dic59D411yescharacteristic
46C2×C4×Dic59D411yescharacteristic
47C42×D59—42no—
48Dic59⋊C8—42no—
49(C2×D59)⋊C8—24no—
50(C2×D59)⋊C8—42no—
51#14273637—42no—
52C59⋊#95—21no—
53C59⋊#95—21no—
54C59⋊#95—21no—
55C22×D4×C59C2×C411yescharacteristic
56C22×C8×C59—21no—
57C22×C8×C59—21no—
58C2×C4⋊C4×C59C2×C411yescharacteristic
59C2×C22⋊C4×C59—21no—
60C2×C22⋊C4×C59—21no—
61C2×C42×C59C2311yescharacteristic
62C24×C59—21no—
63C23×D59C22⋊C411yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59—41no—
67C2×D4×C59—41no—
68C22×C4×C59—21no—
69C22×C4×C59C22×C411yescharacteristic
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C2×C22⋊D59—42no—
73C2×C22⋊D59—42no—
74C2×C22⋊D59—42no—
75C22×Dic59—21no—
76C22×Dic59—21no—
77C22×Dic59C22⋊C411yescharacteristic
78C22×Dic59C22⋊C411yescharacteristic
79C22×Dic59C22⋊C411yescharacteristic
80C2×C4×D59—22no—
81C2×C4×D59—21no—
82C2×C4×D59—21no—
83C2×C4×D59—21no—
84C2×C4×D59—21no—
85C2×C4×D59—21no—
86C2×C4×D59—21no—
87C2×C4×D59—22no—
88C2×C4×D59—41no—
89C2×C4×D59—41no—
90C2×C4×D59—41no—
91C2×C4×D59—41no—
92C2×C8×C59—22no—
93C2×C8×C59—41no—
94C2×C8×C59—41no—
95C2×C8×C59—41no—
96C2×C8×C59—41no—
97C2×C8×C59—41no—
98C4⋊C4×C59—41no—
99C22⋊C4×C59—41no—
100C22⋊C4×C59—41no—
101C22⋊C4×C59—41no—
102C22⋊C4×C59—41no—
103C42×C59—41no—
104C22⋊Dic59—42no—
105C22⋊Dic59—42no—
106C22⋊Dic59—42no—
107(C2×D59)⋊C4—42no—
108C4⋊Dic59—21no—
109C4⋊Dic59—21no—
110C4⋊Dic59—42no—
111C4⋊Dic59—41no—
112Dic59⋊C4—41no—
113Dic59⋊C4—41no—
114C4×Dic59—22no—
115C4×Dic59—22no—
116C4×Dic59—41no—
117C2×C59⋊C8—22no—
118C2×C59⋊C8—41no—
119C2×C59⋊C8—41no—
120C2×C59⋊C8—41no—
121C2×C59⋊C8—41no—
122C2×C59⋊C8—41no—
123C23×C59—41no—
124C23×C59—41no—
125C23×C59—41no—
126C23×C59—41no—
127C23×C59—41no—
128C23×C59—41no—
129C23×C59—41no—
130C23×C59C2×C22⋊C411yescharacteristic
131C22×D59—21no—
132C22×D59—21no—
133C22×D59—21no—
134C22×D59—21no—
135C22×D59—21no—
136C22×D59—21no—
137C22×D59#10412yes—
138D4×C59—81no—
139D4×C59—81no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59#13111yescharacteristic
150C2×C4×C59#13111yescharacteristic
151C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C59#13711yescharacteristic
155C22⋊D59—84no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158C2×Dic59—21no—
159C2×Dic59—21no—
160C2×Dic59—21no—
161C2×Dic59—21no—
162C2×Dic59—21no—
163C2×Dic59—21no—
164C2×Dic59—41no—
165C2×Dic59—41no—
166C2×Dic59—41no—
167C2×Dic59—41no—
168C2×Dic59—41no—
169C2×Dic59—41no—
170C2×Dic59#9912yes—
171C4×D59—42no—
172C4×D59—42no—
173C4×D59—42no—
174C4×D59—42no—
175C4×D59—42no—
176C4×D59—42no—
177C8×C59—42no—
178C8×C59—81no—
179C59⋊C8—42no—
180C59⋊C8—81no—
181#7698—591nomaximal, Sylow
182C22×C59—81no—
183C22×C59—81no—
184C22×C59—81no—
185C22×C59—81no—
186C22×C59—81no—
187C22×C59—81no—
188C22×C59—81no—
189C22×C59#40811yescharacteristic
190C22×C59C2×#9911yescharacteristic
191C22×C59#41311yescharacteristic
192C22×C59#41711yescharacteristic
193C22×C59#41811yescharacteristic
194C22×C59C2×#10411yescharacteristic
195C22×C59#42111yescharacteristic
196C2×D59—22no—
197C2×D59—22no—
198C2×D59—22no—
199C2×D59—41no—
200C2×D59—41no—
201C2×D59—41no—
202C2×D59—41no—
203C4×C59—21no—
204C4×C59—21no—
205C4×C59—21no—
206C4×C59—21no—
207C4×C59—21no—
208C4×C59—21no—
209C4×C59—81no—
210Dic59—22no—
211Dic59—41no—
212Dic59—41no—
213Dic59—81no—
214Dic59—81no—
215#2854—591no—
216#1797—591no—
217#1749—591no—
218#1271—591no—
219#1271—591no—
220#1270—591no—
221#1270D5911yescharacteristic, complemented
222C2×C59—161no—
223C2×C59#146811yescharacteristic
224C2×C59#148311yescharacteristic
225C2×C59#149611yescharacteristic
226C2×C59#150711yescharacteristic
227C2×C59#151311yescharacteristic
228C2×C59#153211yescharacteristic
229C2×C59#155711yescharacteristic
230D59—42no—
231C2×#123—1181no—
232C2×#121—591no—
233C22×C42—591no—
234C2×C4⋊C8—1181no—
235C2×C22⋊C8—1181no—
236C2×C22⋊C8—1181no—
237C2×#97—1181no—
238#390—591no—
239#390C2×D5911yescharacteristic
240#389—591no—
241#389—591no—
242#388—1181no—
243#388—1181no—
244#386—1181no—
245#380—591no—
246#336—591no—
247#336—591no—
248#336C2×D5911yescharacteristic
249#336C2×D5911yescharacteristic
250C59#769811yescharacteristic, complemented, Sylow
251C22×D4—1181no—
252C22×D4C4×D5911yescharacteristic
253C23×C4—591no—
254C23×C4—591no—
255C23×C4—591no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—1181no—
259C22×C8—1181no—
260#123—2362no—
261#123—2362no—
262#121—2362no—
263C2×C4⋊C4—591no—
264C2×C4⋊C4—591no—
265C2×C4⋊C4—1181no—
266C2×C4⋊C4—1181no—
267C2×C4⋊C4C4×D5911yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—1181no—
271C2×C22⋊C4—1181no—
272C2×C22⋊C4—1181no—
273C2×C22⋊C4—1181no—
274C2×C42—591no—
275C2×C42—591no—
276C2×C42—591no—
277C2×C42—2362no—
278C2×C42C22×D5911yescharacteristic
279C4⋊C8—2362no—
280C22⋊C8—1184no—
281C22⋊C8—2362no—
282#97—2362no—
283#95—1181no—
284#95—1181no—
285#95—1181no—
286C24—21no—
287C24—591no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—2362no—
293C2×D4—2362no—
294C2×D4—2362no—
295C22×C4—21no—
296C22×C4—591no—
297C22×C4—591no—
298C22×C4—591no—
299C22×C4—1182no—
300C22×C4—1182no—
301C22×C4—1181no—
302C22×C4—1181no—
303C22×C4—1181no—
304C22×C4—1181no—
305C22×C4—1181no—
306C22×C4—1181no—
307C22×C4—1181no—
308C22×C4—1181no—
309C22×C4—2361no—
310C22×C4—2361no—
311C22×C4—2361no—
312C22×C4—2361no—
313C22×C4C2×C4×D5911yescharacteristic
314C22×C4D4×D5911yescharacteristic
315C22×C4D4×D5911yescharacteristic
316C2×C8—22no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—1182no—
323C2×C8—2361no—
324C2×C8—2361no—
325C2×C8—2361no—
326C2×C8—2361no—
327C2×C8—2361no—
328C4⋊C4—41no—
329C4⋊C4—1181no—
330C4⋊C4—1181no—
331C4⋊C4—2361no—
332C4⋊C4—2362no—
333C4⋊C4—2361no—
334C4⋊C4—2361no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—2362no—
340C22⋊C4—2362no—
341C22⋊C4—2362no—
342C22⋊C4—2362no—
343C42—41no—
344C42—1182no—
345C42—1182no—
346C42—2361no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—592no—
355C23—1181no—
356C23—1181no—
357C23—1181no—
358C23—1181no—
359C23—1181no—
360C23—1181no—
361C23C22⋊C4×D5911yescharacteristic
362D4—81no—
363D4—81no—
364D4—4724no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—592no—
375C2×C4—1181no—
376C2×C4—1181no—
377C2×C4—1181no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—1181no—
381C2×C4—1181no—
382C2×C4—1181no—
383C2×C4—2362no—
384C2×C4—2362no—
385C2×C4—2362no—
386C2×C4—2362no—
387C2×C4—2362no—
388C2×C4—2362no—
389C2×C4—2361no—
390C2×C4—2361no—
391C2×C4—2361no—
392C2×C4—2361no—
393C2×C4—2361no—
394C2×C4—2361no—
395C2×C4#1427373311yescharacteristic
396C2×C4#1427373511yescharacteristic
397C2×C4#1427375111yescharacteristic
398C2×C4#1427375111yescharacteristic
399C2×C4#1427375411yescharacteristic
400C2×C4#1427375611yescharacteristic
401C8—42no—
402C8—81no—
403C8—4721no—
404C8—2362no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—1182no—
413C22—1182no—
414C22—1182no—
415C22—2361no—
416C22—2361no—
417C22—2361no—
418C22—2361no—
419C22#1683736711yescharacteristic
420C22#99×D5911yescharacteristic
421C22#1683738311yescharacteristic
422C22#1683740011yescharacteristic
423C22#1683740511yescharacteristic
424C22#104×D5911yescharacteristic
425C22#1683741711yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—81no—
433C4—1182no—
434C4—4721no—
435C4—4721no—
436C4—2361no—
437C4—2361no—
438C2—161no—
439C2—2362no—
440C2#2142244111yescharacteristic
441C2#2142250611yescharacteristic
442C2#2142256311yescharacteristic
443C2#2142261011yescharacteristic
444C2#2142263611yescharacteristic
445C2#2142271311yescharacteristic
446C2#2142281511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1270C2
socleC23×C59C2×C22⋊C4
prime radicalC2×#14273698C4
cosocleC2×C42×C59C23
hypercenter#1270D59
hypocenterC59#7698
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21424075C2semidirect
3. #21423857C2semidirect
4. #21421920C2semidirect
5. #21421918C2semidirect
6. #21421917C2semidirect
7. C59×#1270C2semidirect
221. #1270D59semidirect
250. C59#7698semidirect

Maximal subgroups

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

subgroupindex
#214324262
#214240752
#214238572
#214219202
#214219182
#214219172
C59×#12702
#769859