Finite Group Databasebeta

← #28482801

Subgroups — #28482801

Order 15104.

464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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#21433146C211yesmaximal, characteristic
2#21424396C211yesmaximal, characteristic
3#21424300C211yesmaximal, characteristic, complemented
4#21424281C211yesmaximal, characteristic, complemented
5#21422585C211yesmaximal, characteristic
6#21421944C211yesmaximal, characteristic, complemented
7C59×#1297C211yesmaximal, characteristic, complemented
8C22×#11745664C2211yescharacteristic
9#16837913C2211yescharacteristic
10#16837478—21no—
11#16837471—21no—
12#16837470—21no—
13(C22⋊D59)⋊C8—21no—
14#16837460—21no—
15C2×#14273662—21no—
16C2×C4⋊(C59⋊C8)—21no—
17C2×#14273655—21no—
18#16837367—21no—
19C2×C22⋊(C59⋊C8)C2211yescharacteristic
20C2×C22⋊(C59⋊C8)C2211yescharacteristic
21#16837166—21no—
22#16837162—21no—
23#16837157—21no—
24#16837138C411yescharacteristic, complemented
25#16837138C411yescharacteristic, complemented
26#16837135C411yescharacteristic, complemented
27#16837135C411yescharacteristic, complemented
28C59×#407C2211yescharacteristic
29C4×C22⋊C4×C59C2211yescharacteristic
30C4×C22⋊C4×C59C2211yescharacteristic
31C2×#11745685D411yescharacteristic
32C2×#11745664—21no—
33C2×#11745664—21no—
34C2×#11745664—42no—
35C2×#11745659—21no—
36C22×C59⋊C8—21no—
37C22×C59⋊C8—21no—
38C22×C59⋊C8D411yescharacteristic
39C22×C59⋊C8D411yescharacteristic
40C2×C8×D59—21no—
41#14273710—21no—
42#14273706C2×C411yescharacteristic
43#14273706Q811yescharacteristic
44#14273701C2×C411yescharacteristic
45#14273701Q811yescharacteristic
46#14273696—21no—
47C4×C22⋊D59—21no—
48C4×C22⋊D59—21no—
49#14273686D411yescharacteristic
50#14273662—42no—
51C4⋊(C59⋊C8)—42no—
52Dic59⋊C8—21no—
53Dic59⋊C8—21no—
54#14273655—42no—
55C22⋊(C59⋊C8)—21no—
56C22⋊(C59⋊C8)—21no—
57C22⋊(C59⋊C8)—21no—
58C22⋊(C59⋊C8)C2×C411yescharacteristic
59C22⋊(C59⋊C8)C2×C411yescharacteristic
60(C2×D59)⋊C8—21no—
61(C2×D59)⋊C8—21no—
62#14273637—21no—
63C8×Dic59—21no—
64C23×C4×C59C2311yescharacteristic
65C2×M16×C59D411yescharacteristic
66C2×M16×C59D411yescharacteristic
67C2×C22⋊C4×C59—21no—
68C2×C22⋊C4×C59—21no—
69C2×C42×C59—21no—
70C2×C42×C59—21no—
71C22⋊C8×C59—21no—
72C22⋊C8×C59—21no—
73#95×C59—21no—
74#95×C59C2×C411yescharacteristic
75#95×C59C2×C411yescharacteristic
76C24×C59#4111yescharacteristic
77C22×C4×C59—21no—
78C22×C4×C59—21no—
79C22×C4×C59—41no—
80C22×C4×C59—41no—
81C22×C4×C59—41no—
82C22×C4×C59C22×C411yescharacteristic
83C22×C4×C59C2×D411yescharacteristic
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59C2×D411yescharacteristic
86C22×C4×C59C2×Q811yescharacteristic
87C22×C4×C59#4111yescharacteristic
88C2×C22⋊D59—21no—
89C2×C22⋊D59—21no—
90C2×C22⋊D59—21no—
91#11745685—41no—
92#11745685—41no—
93C2×D236C4⋊C411yescharacteristic
94C2×C4×D59—21no—
95C2×Dic118C4⋊C411yescharacteristic
96M16×C59—41no—
97M16×C59—41no—
98C2×C8×C59—21no—
99C2×C8×C59—21no—
100C22⋊C4×C59—22no—
101C22⋊C4×C59—42no—
102C22⋊C4×C59—41no—
103C42×C59—41no—
104C42×C59—41no—
105C42×C59—41no—
106C42×C59—41no—
107C22⋊Dic59—21no—
108C22⋊Dic59—21no—
109C22⋊Dic59—21no—
110(C2×D59)⋊C4—21no—
111(C2×D59)⋊C4—21no—
112C4⋊Dic59C4⋊C411yescharacteristic
113C4⋊Dic59C4⋊C411yescharacteristic
114Dic59⋊C4—21no—
115Dic59⋊C4—21no—
116C4×Dic59—21no—
117#11745664—22no—
118#11745664—22no—
119#11745664—41no—
120#11745664—41no—
121C2×C59⋊C8—22no—
122C2×C59⋊C8—21no—
123C2×C59⋊C8—21no—
124C2×C59⋊C8—21no—
125C2×C59⋊C8—21no—
126C2×C59⋊C8—41no—
127C2×C59⋊C8—41no—
128C2×C59⋊C8—41no—
129C2×C59⋊C8—41no—
130C2×C59⋊C8—41no—
131C2×C59⋊C8—41no—
132#11745659—81no—
133C8×D59—81no—
134C23×C59—21no—
135C23×C59—21no—
136C23×C59—41no—
137C23×C59—41no—
138C23×C59C4×D411yescharacteristic
139C23×C59C22⋊Q811yescharacteristic
140C23×C59#12311yescharacteristic
141C22×D59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—22no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—41no—
155C2×C4×C59—42no—
156C2×C4×C59—41no—
157C2×C4×C59—41no—
158C2×C4×C59—81no—
159C2×C4×C59—81no—
160C2×C4×C59C2×C4⋊C411yescharacteristic
161C2×C4×C59C4×D411yescharacteristic
162C2×C4×C59#12011yescharacteristic
163C2×C4×C59C22⋊Q811yescharacteristic
164C22⋊D59—41no—
165C22⋊D59—41no—
166C22⋊D59—81no—
167C22⋊D59—81no—
168C2×Dic59—21no—
169C2×Dic59—21no—
170C2×Dic59—21no—
171D236—41no—
172C4×D59—41no—
173C4×D59—41no—
174Dic118—41no—
175C8×C59—41no—
176C8×C59—41no—
177C59⋊C8—41no—
178C59⋊C8—41no—
179C59⋊C8—41no—
180C59⋊C8—42no—
181C59⋊C8—41no—
182#8875—591nomaximal, Sylow
183C22×C59—21no—
184C22×C59—21no—
185C22×C59—21no—
186C22×C59—21no—
187C22×C59—21no—
188C22×C59—21no—
189C22×C59—21no—
190C22×C59—21no—
191C22×C59—81no—
192C22×C59—81no—
193C22×C59#38511yescharacteristic
194C22×C59#44311yescharacteristic
195C22×C59#44411yescharacteristic
196C2×D59—41no—
197C2×D59—41no—
198C2×D59—41no—
199C4×C59—21no—
200C4×C59—21no—
201C4×C59—21no—
202C4×C59—42no—
203C4×C59—81no—
204C4×C59—82no—
205C4×C59B(4,𝔽2)11yescharacteristic
206C4×C59#45811yescharacteristic
207Dic59—41no—
208Dic59—41no—
209Dic59—41no—
210#2976—591no—
211#1871—591no—
212#1855—591no—
213#1851—591no—
214#1501—591no—
215#1297D5911yescharacteristic, complemented
216#1282—591no—
217C2×C59—21no—
218C2×C59—21no—
219C2×C59—41no—
220C2×C59—41no—
221C2×C59#186111yescharacteristic
222C2×C59#186611yescharacteristic
223C2×C59#186711yescharacteristic
224D59—81no—
225C22×M16—591no—
226#525—591no—
227#436—1181no—
228#435—1181no—
229#435—1181no—
230C8×D4—1181no—
231#433—1181no—
232C2×#108—1181no—
233C2×C4⋊C8—1181no—
234C2×#104—1181no—
235#408—1181no—
236#407C2×D5911yescharacteristic
237C2×C22⋊C8—591no—
238C2×C22⋊C8—591no—
239C4×C22⋊C4C2×D5911yescharacteristic
240C4×C22⋊C4C2×D5911yescharacteristic
241#341—1181no—
242#339—1181no—
243#336—1181no—
244#328—591no—
245#328—591no—
246#327—591no—
247#327—591no—
248C59#887511yescharacteristic, complemented, Sylow
249C2×#41—591no—
250C23×C4C22×D5911yescharacteristic
251C2×M16—1181no—
252C2×M16—1181no—
253C2×M16—1181no—
254C2×M16—2362no—
255C2×M16D23611yescharacteristic
256C2×M16D23611yescharacteristic
257C22×C8—591no—
258C22×C8—591no—
259C22×C8—1181no—
260C22×C8—1181no—
261C22×C8—1181no—
262#123—1181no—
263C22⋊Q8—591no—
264C22⋊Q8—591no—
265#121—591no—
266#121—591no—
267#120—1181no—
268C4×D4—1181no—
269C4×D4—1181no—
270#117—591no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C42—21no—
274C2×C42—21no—
275#108—2362no—
276C4⋊C8—1181no—
277C4⋊C8—1181no—
278C4⋊C8—2362no—
279#104—2362no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—591no—
283C22⋊C8—591no—
284C22⋊C8—1181no—
285C22⋊C8—1181no—
286C22⋊C8—1181no—
287C22⋊C8—1181no—
288C22⋊C8—1181no—
289#97—1181no—
290C4×C8—1181no—
291#95—21no—
292#95C4×D5911yescharacteristic
293#95C4×D5911yescharacteristic
294C24#1174568711yescharacteristic
295#41—2361no—
296#41—2361no—
297C2×Q8—591no—
298C2×D4—591no—
299C2×D4—1181no—
300C2×D4—1181no—
301C2×D4—1181no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—1181no—
308C22×C4C2×C4×D5911yescharacteristic
309C22×C4C2×D23611yescharacteristic
310C22×C4#1174568511yescharacteristic
311C22×C4D4×D5911yescharacteristic
312C22×C4D4×D5911yescharacteristic
313C22×C4Q8×D5911yescharacteristic
314M16—41no—
315M16—41no—
316M16—1182no—
317M16—1182no—
318M16—4721no—
319M16—2361no—
320M16—2361no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—1182no—
324C2×C8—1181no—
325C2×C8—1181no—
326C2×C8—1181no—
327C2×C8—1181no—
328C2×C8—4721no—
329C2×C8—2361no—
330C2×C8—2361no—
331C2×C8—2361no—
332C2×C8—2361no—
333C2×C8—2361no—
334C2×C8—2361no—
335C4⋊C4—591no—
336C4⋊C4—591no—
337C4⋊C4—1181no—
338C4⋊C4—1181no—
339C22⋊C4—22no—
340C22⋊C4—42no—
341C22⋊C4—41no—
342C22⋊C4—1181no—
343C22⋊C4—1181no—
344C22⋊C4—1181no—
345C22⋊C4—1181no—
346C22⋊C4—1181no—
347C42—41no—
348C42—41no—
349C42—41no—
350C42—41no—
351C42—1181no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—1181no—
357C23(C22⋊D59)⋊C411yescharacteristic
358C23#1427370711yescharacteristic
359C23#1427370911yescharacteristic
360Q8—2361no—
361D4—4721no—
362D4—4721no—
363D4—2361no—
364D4—2361no—
365D4—2361no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—1181no—
385C2×C4—1181no—
386C2×C4—1181no—
387C2×C4—2361no—
388C2×C4—2361no—
389C2×C4C4⋊C4×D5911yescharacteristic
390C2×C4C4×D23611yescharacteristic
391C2×C4#1427369711yescharacteristic
392C2×C4#1427370511yescharacteristic
393C8—41no—
394C8—41no—
395C8—2361no—
396C8—2361no—
397C8—2362no—
398C8—2361no—
399C8—2361no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—81no—
409C22—81no—
410C22—2361no—
411C22—2361no—
412C22—2361no—
413C22#1683727611yescharacteristic
414C22#1683751611yescharacteristic
415C22#1683752111yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—81no—
421C4—82no—
422C4—2361no—
423C4—2361no—
424C4—2361no—
425C4#1683759011yescharacteristic
426C4#1683759311yescharacteristic
427C2—21no—
428C2—21no—
429C2—41no—
430C2—41no—
431C2—4721no—
432C2#2142433711yescharacteristic
433C2#2142437211yescharacteristic
434C2#2142437811yescharacteristic
subgroupG/H
centerC2×C4#14273697
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1297C2
socleC22×C59#385
prime radical#16837913C22
cosocleC23×C4×C59C23
hypercenter#1297D59
hypocenterC59#8875
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
3. #21424300C2semidirect
4. #21424281C2semidirect
6. #21421944C2semidirect
7. C59×#1297C2semidirect
24. #16837138C4semidirect
25. #16837138C4semidirect
26. #16837135C4semidirect
27. #16837135C4semidirect
215. #1297D59semidirect
248. C59#8875semidirect

Maximal subgroups

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

subgroupindex
#214331462
#214243962
#214243002
#214242812
#214225852
#214219442
C59×#12972
#887559