Finite Group Databasebeta

← #28477964

Subgroups — #28477964

Order 15104.

516 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 91 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#21425659C211yesmaximal, characteristic, complemented
2#21425629C211yesmaximal, characteristic, complemented
3#21425629C211yesmaximal, characteristic, complemented
4#21421919C211yesmaximal, characteristic, complemented
5#21421917C211yesmaximal, characteristic, complemented
6#21421917C211yesmaximal, characteristic, complemented
7C59×#2682C211yesmaximal, characteristic
8C2×#14273658—21no—
9C2×#14273658—21no—
10C2×#14273648—21no—
11C2×#14273648—21no—
12#16837272C2211yescharacteristic
13#16837164—21no—
14#16837164—21no—
15#16837157C2211yescharacteristic
16#16837157C2211yescharacteristic
17#16837157C2211yescharacteristic
18C2×#123×C59—21no—
19C2×#121×C59—21no—
20C59×#396—21no—
21C59×#394—21no—
22C59×#392—21no—
23C59×#390C2211yescharacteristic
24C59×#390C2211yescharacteristic
25C59×#389C2211yescharacteristic
26C59×#385—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#14273658—42no—
34#14273658—42no—
35#14273648—42no—
36#14273648—42no—
37C22×D4×C59—21no—
38C22×D4×C59—21no—
39C22×D4×C59D411yescharacteristic
40C22×D4×C59D411yescharacteristic
41C23×C4×C59—21no—
42#123×C59—42no—
43#123×C59—42no—
44#121×C59—42no—
45#121×C59—42no—
46C2×C4⋊C4×C59—21no—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59D411yescharacteristic
49C2×C4⋊C4×C59D411yescharacteristic
50C2×C4⋊C4×C59D411yescharacteristic
51C2×C4⋊C4×C59D411yescharacteristic
52C2×C22⋊C4×C59—21no—
53C2×C22⋊C4×C59—21no—
54C2×C22⋊C4×C59—21no—
55C2×C22⋊C4×C59—21no—
56C2×C22⋊C4×C59—21no—
57C2×C22⋊C4×C59—21no—
58C2×C22⋊C4×C59—21no—
59C2×C42×C59C2311yescharacteristic
60#95×C59—21no—
61#95×C59—21no—
62C24×C59—21no—
63C24×C59—21no—
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59—21no—
67C2×D4×C59—41no—
68C2×D4×C59—41no—
69C2×D4×C59—41no—
70C2×D4×C59—41no—
71C2×D4×C59—42no—
72C2×D4×C59—42no—
73C2×D4×C59—42no—
74C2×D4×C59—81no—
75C2×D4×C59—81no—
76C2×D4×C59—81no—
77C2×D4×C59SD1612yes—
78C22×C4×C59—21no—
79C22×C4×C59—21no—
80C22×C4×C59—21no—
81C22×C4×C59—21no—
82C22×C4×C59—42no—
83C22×C4×C59—42no—
84C22×C4×C59—81no—
85C22×C4×C59C2×D411yescharacteristic
86C22×C4×C59C2×D411yescharacteristic
87C22×C4×C59C2×D411yescharacteristic
88C22×Dic59—41no—
89C4⋊C4×C59—21no—
90C4⋊C4×C59—42no—
91C4⋊C4×C59—41no—
92C4⋊C4×C59—41no—
93C4⋊C4×C59—41no—
94C4⋊C4×C59—41no—
95C4⋊C4×C59—41no—
96C4⋊C4×C59SD1612yes—
97C22⋊C4×C59—42no—
98C22⋊C4×C59—42no—
99C22⋊C4×C59—41no—
100C22⋊C4×C59—41no—
101C22⋊C4×C59—41no—
102C22⋊C4×C59—41no—
103C22⋊C4×C59—41no—
104C22⋊C4×C59—41no—
105C22⋊C4×C59—41no—
106C22⋊C4×C59—41no—
107C22⋊C4×C59—81no—
108C42×C59—41no—
109C4⋊Dic59—41no—
110C4⋊Dic59—41no—
111C4⋊Dic59—41no—
112C4⋊Dic59—41no—
113C4⋊Dic59—42no—
114C2×C59⋊C8—22no—
115C2×C59⋊C8—22no—
116C2×C59⋊C8—41no—
117C2×C59⋊C8—41no—
118C2×C59⋊C8—41no—
119C2×C59⋊C8—41no—
120C2×C59⋊C8—41no—
121C2×C59⋊C8—41no—
122C2×C59⋊C8—41no—
123C23×C59—22no—
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—41no—
135C23×C59—41no—
136C23×C59—41no—
137C23×C59#12011yescharacteristic
138D4×C59—42no—
139D4×C59—42no—
140D4×C59—81no—
141D4×C59—81no—
142D4×C59—84no—
143D4×C59—84no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—22no—
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×C59—41no—
162C2×C4×C59—84no—
163C2×C4×C59C2×SD1611yescharacteristic
164C2×C4×C59C2×SD1611yescharacteristic
165C2×C4×C59#13511yescharacteristic
166C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C59#13711yescharacteristic
169C2×Dic59—81no—
170C2×Dic59—81no—
171C2×Dic59—81no—
172C59⋊C8—42no—
173C59⋊C8—42no—
174C59⋊C8—81no—
175#7825—591nomaximal, Sylow
176C22×C59—42no—
177C22×C59—42no—
178C22×C59—42no—
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—81no—
189C22×C59—81no—
190C22×C59#45011yescharacteristic
191C22×C59#45011yescharacteristic
192C22×C59#45211yescharacteristic
193C22×C59#45311yescharacteristic
194C22×C59#45311yescharacteristic
195C22×C59#45411yescharacteristic
196C22×C59#45811yescharacteristic
197C4×C59—21no—
198C4×C59—21no—
199C4×C59—21no—
200C4×C59—21no—
201C4×C59—21no—
202C4×C59—21no—
203C4×C59—42no—
204C4×C59—81no—
205C4×C59—81no—
206C4×C59—81no—
207Dic59—161no—
208#2682D5911yescharacteristic
209#2100—591no—
210#2094—591no—
211#2094—591no—
212#1271—591no—
213#1270—591no—
214#1270—591no—
215C2×C59—82no—
216C2×C59—161no—
217C2×C59#161311yescharacteristic
218C2×C59#161611yescharacteristic
219C2×C59#161811yescharacteristic
220C2×C59#162911yescharacteristic
221C2×C59#163111yescharacteristic
222C2×C59#163511yescharacteristic
223C2×C59#165611yescharacteristic
224C2×#123—21no—
225C2×#121—21no—
226C2×#106—1181no—
227C2×#106—1181no—
228C2×#102—1181no—
229C2×#102—1181no—
230#396—21no—
231#394—21no—
232#392—21no—
233#390C2×D5911yescharacteristic
234#390C2×D5911yescharacteristic
235#389C2×D5911yescharacteristic
236#385—21no—
237#384—591no—
238#340—1181no—
239#340—1181no—
240#336—591no—
241#336—591no—
242#336—591no—
243C59#782511yescharacteristic, complemented, Sylow
244C22×D4—21no—
245C22×D4—21no—
246C22×D4C22⋊D5911yescharacteristic
247C22×D4C22⋊D5911yescharacteristic
248C23×C4—21no—
249C22×C8—1181no—
250C22×C8—1181no—
251C22×C8—1181no—
252#123—42no—
253#123—42no—
254#121—42no—
255#121—42no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—1181no—
259C2×C4⋊C4—1181no—
260C2×C4⋊C4—1181no—
261C2×C4⋊C4C22⋊D5911yescharacteristic
262C2×C4⋊C4C22⋊D5911yescharacteristic
263C2×C4⋊C4C22⋊D5911yescharacteristic
264C2×C4⋊C4C22⋊D5911yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C42C22×D5911yescharacteristic
273#106—2362no—
274#106—2362no—
275#102—2362no—
276#102—2362no—
277#95—21no—
278#95—21no—
279C24—21no—
280C24—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4#1174567012yes—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—81no—
302C22×C4—2361no—
303C22×C4C2×C22⋊D5911yescharacteristic
304C22×C4C2×C22⋊D5911yescharacteristic
305C22×C4C2×C22⋊D5911yescharacteristic
306C2×C8—1182no—
307C2×C8—1182no—
308C2×C8—2361no—
309C2×C8—2361no—
310C2×C8—2361no—
311C2×C8—2361no—
312C2×C8—2361no—
313C2×C8—2361no—
314C2×C8—2361no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—2361no—
323C4⋊C4—2361no—
324C4⋊C4—2361no—
325C4⋊C4—2361no—
326C4⋊C4—2362no—
327C4⋊C4#1174567012yes—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—81no—
339C42—41no—
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23#1427369611yescharacteristic
355D4—42no—
356D4—42no—
357D4—81no—
358D4—81no—
359D4—84no—
360D4—84no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
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—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—84no—
380C2×C4—4721no—
381C2×C4—4721no—
382C2×C4—4721no—
383C2×C4C2×#1174567011yescharacteristic
384C2×C4C2×#1174567011yescharacteristic
385C2×C4#1427374711yescharacteristic
386C2×C4#1427375311yescharacteristic
387C2×C4#1427375311yescharacteristic
388C2×C4#1427375711yescharacteristic
389C8—4721no—
390C8—2362no—
391C8—2362no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22#1683755311yescharacteristic
407C22#1683755311yescharacteristic
408C22#1683756411yescharacteristic
409C22#1683757011yescharacteristic
410C22#1683757011yescharacteristic
411C22#1683757511yescharacteristic
412C22#1683759211yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—9441no—
424C2—82no—
425C2—161no—
426C2#2142311611yescharacteristic
427C2#2142313311yescharacteristic
428C2#2142314411yescharacteristic
429C2#2142321211yescharacteristic
430C2#2142322311yescharacteristic
431C2#2142324711yescharacteristic
432C2#2142338911yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
Fitting, prime radicalC59×#2682C2
socleC23×C59#120
hypercenter#2682D59
hypocenterC59#7825
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2682

Complements

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

NH ≅ G/Ntype
1. #21425659C2semidirect
2. #21425629C2semidirect
3. #21425629C2semidirect
4. #21421919C2semidirect
5. #21421917C2semidirect
6. #21421917C2semidirect
243. C59#7825semidirect

Maximal subgroups

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

subgroupindex
#214256592
#214256292
#214219192
#214219172
C59×#26822
#782559