Finite Group Databasebeta

← #28488975

Subgroups — #28488975

Order 15104.

654 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#16837730C211yesmaximal, characteristic
2#21429911C211yesmaximal, characteristic
3C2×#16837334C211yesmaximal, characteristic
4#21424183C211yesmaximal, characteristic
5C2×#16837127C211yesmaximal, characteristic
6#21421975C211yesmaximal, characteristic
7C2×C59×#328C211yesmaximal, characteristic
8C22×C4⋊Dic59—21no—
9C22×C4⋊Dic59C2211yescharacteristic
10C22×Dic59⋊C4C2211yescharacteristic
11#16837730—22no—
12#16837730—22no—
13C2×#14273658—21no—
14C2×#14273651—21no—
15C2×C22⋊(C59⋊C8)C2211yescharacteristic
16#16837340—21no—
17#16837335—22no—
18#16837334—22no—
19#16837334—22no—
20#16837321—21no—
21#16837274—21no—
22#16837263—21no—
23#16837262C2211yescharacteristic
24C2×C59⋊#95—21no—
25#16837165—22no—
26#16837127—22no—
27C2×C22⋊Q8×C59C2211yescharacteristic
28C2×C22⋊C8×C59C2211yescharacteristic
29C2×#95×C59C2211yescharacteristic
30C59×#328—22no—
31C23×Dic59—21no—
32C23×Dic59D411yescharacteristic
33C23×Dic59D411yescharacteristic
34C22×C59⋊C8—21no—
35C2×C4⋊Dic59—21no—
36C2×C4⋊Dic59—21no—
37C2×C4⋊Dic59—21no—
38C2×C4⋊Dic59—21no—
39C2×C4⋊Dic59—24no—
40C2×C4⋊Dic59—21no—
41C2×C4⋊Dic59—42no—
42C2×C4⋊Dic59—42no—
43C2×C4⋊Dic59D412yes—
44C2×C4⋊Dic59D412yes—
45C2×Dic59⋊C4—21no—
46C2×Dic59⋊C4—21no—
47C2×Dic59⋊C4—21no—
48C2×Dic59⋊C4—21no—
49C2×Dic59⋊C4—21no—
50C2×Dic59⋊C4—21no—
51C2×Dic59⋊C4—22no—
52C2×C22⋊Dic59—21no—
53#14273658—24no—
54#14273651—24no—
55C22⋊(C59⋊C8)—21no—
56C22⋊(C59⋊C8)D412yes—
57C59⋊#95—24no—
58C59⋊#95—22no—
59C59⋊#95—22no—
60C59⋊#95—22no—
61C59⋊#95—21no—
62C22×Q8×C59D411yescharacteristic
63C23×C4×C59—21no—
64C23×C4×C59C2311yescharacteristic
65C22×C8×C59—21no—
66C22⋊Q8×C59—21no—
67C22⋊Q8×C59—21no—
68C22⋊Q8×C59—21no—
69C22⋊Q8×C59—21no—
70C2×C4⋊C4×C59—21no—
71C2×C4⋊C4×C59D411yescharacteristic
72C2×C22⋊C4×C59—21no—
73C22⋊C8×C59—21no—
74C22⋊C8×C59—21no—
75#95×C59—21no—
76#95×C59D412yes—
77C24×C59C2×D411yescharacteristic
78C2×Q8×C59—21no—
79C2×Q8×C59—21no—
80C2×Q8×C59—42no—
81C22×C4×C59—24no—
82C22×C4×C59—22no—
83C22×C4×C59—21no—
84C22×C4×C59—21no—
85C22×C4×C59—42no—
86C22×C4×C59—42no—
87C22×C4×C59—41no—
88C22×C4×C59—41no—
89C22×C4×C59C2×D411yescharacteristic
90C22×C4×C59C2×D411yescharacteristic
91C22×C4×C59C2×D411yescharacteristic
92C22×C4×C59C2×D411yescharacteristic
93C22×C4×C59C2×D411yescharacteristic
94C22×C4×C59#4111yescharacteristic
95C22×Dic59—21no—
96C22×Dic59—21no—
97C22×Dic59—21no—
98C22×Dic59—21no—
99C22×Dic59—21no—
100C22×Dic59—21no—
101C22×Dic59—22no—
102C22×Dic59—21no—
103C22×Dic59—21no—
104C22×Dic59—22no—
105C22×Dic59—21no—
106C22×Dic59—42no—
107C22×Dic59—41no—
108C22×Dic59—41no—
109C22×Dic59—41no—
110C22×Dic59—41no—
111C22×Dic59—41no—
112C22×Dic59—41no—
113C22×Dic59SD1612yes—
114C2×C8×C59—42no—
115C2×C8×C59—41no—
116C4⋊C4×C59—21no—
117C4⋊C4×C59—21no—
118C4⋊C4×C59—41no—
119C4⋊C4×C59—41no—
120C22⋊C4×C59—41no—
121C22⋊C4×C59—41no—
122C22⋊Dic59—41no—
123C22⋊Dic59—41no—
124C4⋊Dic59—22no—
125C4⋊Dic59—22no—
126C4⋊Dic59—48no—
127C4⋊Dic59—41no—
128C4⋊Dic59—41no—
129C4⋊Dic59—42no—
130Dic59⋊C4—41no—
131Dic59⋊C4—41no—
132Dic59⋊C4—41no—
133Dic59⋊C4—41no—
134Dic59⋊C4—82no—
135C2×C59⋊C8—22no—
136C2×C59⋊C8—42no—
137C23×C59—22no—
138C23×C59—22no—
139C23×C59#12011yescharacteristic
140C23×C59#12011yescharacteristic
141C23×C59#12111yescharacteristic
142C23×C59C2×SD1611yescharacteristic
143C23×C59#13511yescharacteristic
144C23×C59AGL(1,ℤ/8)11yescharacteristic
145C23×C59#13711yescharacteristic
146Q8×C59—42no—
147Q8×C59—81no—
148C2×C4×C59—22no—
149C2×C4×C59—22no—
150C2×C4×C59—24no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—41no—
155C2×C4×C59—44no—
156C2×C4×C59—44no—
157C2×C4×C59—42no—
158C2×C4×C59—42no—
159C2×C4×C59—41no—
160C2×C4×C59—41no—
161C2×C4×C59—42no—
162C2×C4×C59—42no—
163C2×C4×C59#12011yescharacteristic
164C2×C4×C59#12111yescharacteristic
165C2×C4×C59#12111yescharacteristic
166C2×C4×C59#12711yescharacteristic
167C2×Dic59—22no—
168C2×Dic59—22no—
169C2×Dic59—22no—
170C2×Dic59—41no—
171C2×Dic59—41no—
172C2×Dic59—41no—
173C2×Dic59—41no—
174C2×Dic59—42no—
175C2×Dic59—41no—
176C2×Dic59—42no—
177C2×Dic59—42no—
178C2×Dic59—42no—
179C2×Dic59—42no—
180C2×Dic59—42no—
181C2×Dic59—42no—
182C2×Dic59—42no—
183C2×Dic59—81no—
184C2×Dic59—81no—
185C2×Dic59—81no—
186C2×Dic59—81no—
187C2×Dic59—81no—
188C8×C59—81no—
189C59⋊C8—42no—
190#9927—591nomaximal, Sylow
191C22×C59—22no—
192C22×C59—22no—
193C22×C59—22no—
194C22×C59—22no—
195C22×C59—21no—
196C22×C59—21no—
197C22×C59—21no—
198C22×C59—21no—
199C22×C59#39211yescharacteristic
200C22×C59#44811yescharacteristic
201C22×C59#44911yescharacteristic
202C22×C59#45011yescharacteristic
203C22×C59#45211yescharacteristic
204C22×C59#45612yes—
205C22×C59#45812yes—
206C22×C59#46511yescharacteristic
207C22×C59#46811yescharacteristic
208C4×C59—21no—
209C4×C59—21no—
210C4×C59—21no—
211C4×C59—21no—
212C4×C59—44no—
213C4×C59—81no—
214C4×C59—81no—
215Dic59—42no—
216Dic59—82no—
217Dic59—82no—
218Dic59—81no—
219C2×#483—591no—
220#2627—591no—
221C2×#398—591no—
222#1823—591no—
223C2×#328D5911yescharacteristic
224C2×#324—591no—
225#1294—591no—
226C2×C59—21no—
227C2×C59—21no—
228C2×C59—21no—
229C2×C59—21no—
230C2×C59#160912yes—
231C2×C59#161112yes—
232C2×C59#200011yescharacteristic
233C2×C59#200511yescharacteristic
234C2×C59#202211yescharacteristic
235C2×C22⋊Q8C2×D5911yescharacteristic
236C22×C4⋊C4—591no—
237C22×C4⋊C4—591no—
238C22×C4⋊C4—1181no—
239#483—1182no—
240#483—1182no—
241C2×#106—1181no—
242C2×#103—1181no—
243C2×C22⋊C8—591no—
244C2×C22⋊C8C2×D5911yescharacteristic
245#400—1181no—
246#398—1182no—
247#398—1182no—
248#398—1182no—
249#395—1181no—
250#385—1181no—
251#381—1181no—
252#380—591no—
253C2×#95—1181no—
254C2×#95C2×D5911yescharacteristic
255#340—1182no—
256#328—22no—
257#324—1182no—
258C59#992711yescharacteristic, complemented, Sylow
259C22×Q8D23611yescharacteristic
260C23×C4—21no—
261C23×C4—591no—
262C23×C4—591no—
263C23×C4—1181no—
264C23×C4C22×D5911yescharacteristic
265C22×C8—21no—
266C22×C8—1181no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—592no—
273C2×C4⋊C4—592no—
274C2×C4⋊C4—1181no—
275C2×C4⋊C4—1181no—
276C2×C4⋊C4—1181no—
277C2×C4⋊C4—1181no—
278C2×C4⋊C4—1182no—
279C2×C4⋊C4—1184no—
280C2×C4⋊C4—1181no—
281C2×C4⋊C4—1181no—
282C2×C4⋊C4—1181no—
283C2×C4⋊C4—1181no—
284C2×C4⋊C4—1181no—
285C2×C4⋊C4—1181no—
286C2×C4⋊C4—1181no—
287C2×C4⋊C4—2362no—
288C2×C4⋊C4—2362no—
289C2×C4⋊C4D23611yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—1181no—
292#106—1184no—
293#103—1184no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—592no—
297C22⋊C8—1181no—
298#95—21no—
299#95—1184no—
300#95—1182no—
301#95—1182no—
302#95—1182no—
303#95—1181no—
304#95C22⋊D5912yes—
305C24D4×D5911yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—42no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—592no—
318C22×C4—1181no—
319C22×C4—1181no—
320C22×C4—1181no—
321C22×C4—1181no—
322C22×C4—1181no—
323C22×C4—1181no—
324C22×C4—1181no—
325C22×C4—1181no—
326C22×C4—1182no—
327C22×C4—1182no—
328C22×C4—1181no—
329C22×C4—2361no—
330C22×C4—2361no—
331C22×C4—2361no—
332C22×C4—2361no—
333C22×C4—2361no—
334C22×C4—2361no—
335C22×C4—2362no—
336C22×C4C2×D23611yescharacteristic
337C22×C4#1174568511yescharacteristic
338C22×C4D4×D5911yescharacteristic
339C22×C4D4×D5911yescharacteristic
340C22×C4D4×D5911yescharacteristic
341C22×C4C2×C22⋊D5911yescharacteristic
342C2×C8—42no—
343C2×C8—41no—
344C2×C8—1182no—
345C2×C8—2362no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—1182no—
351C4⋊C4—1182no—
352C4⋊C4—4722no—
353C4⋊C4—2362no—
354C4⋊C4—2368no—
355C4⋊C4—2361no—
356C4⋊C4—2361no—
357C4⋊C4—2361no—
358C4⋊C4—2361no—
359C4⋊C4—2361no—
360C4⋊C4—2361no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—2361no—
364C22⋊C4—2361no—
365C23—22no—
366C23—22no—
367C23#1427369511yescharacteristic
368C23#1427369711yescharacteristic
369C23#1427370011yescharacteristic
370C23SD16×D5911yescharacteristic
371C23#1427375011yescharacteristic
372C23#1427375411yescharacteristic
373C23#1427375911yescharacteristic
374Q8—42no—
375Q8—81no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—1182no—
392C2×C4—1182no—
393C2×C4—1182no—
394C2×C4—4721no—
395C2×C4—4721no—
396C2×C4—4721no—
397C2×C4—4721no—
398C2×C4—4721no—
399C2×C4—2362no—
400C2×C4—2362no—
401C2×C4—2362no—
402C2×C4—2362no—
403C2×C4—2362no—
404C2×C4—2361no—
405C2×C4—2362no—
406C2×C4—2362no—
407C2×C4—2362no—
408C2×C4—2361no—
409C2×C4—2361no—
410C2×C4—2361no—
411C2×C4—2361no—
412C2×C4#1427369711yescharacteristic
413C2×C4#1427370011yescharacteristic
414C2×C4#1427370111yescharacteristic
415C2×C4#1427372311yescharacteristic
416C8—81no—
417C8—2362no—
418C22—22no—
419C22—22no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—22no—
425C22—22no—
426C22#1683731111yescharacteristic
427C22#1683754211yescharacteristic
428C22#1683755011yescharacteristic
429C22#1683755111yescharacteristic
430C22#1683756311yescharacteristic
431C22#1683758612yes—
432C22#1683759312yes—
433C22#1683763411yescharacteristic
434C22#1683765111yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—44no—
440C4—81no—
441C4—81no—
442C4—4721no—
443C4—4722no—
444C4—4722no—
445C4—2362no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2#2142309612yes—
451C2#2142310512yes—
452C2#2142509811yescharacteristic
453C2#2142513111yescharacteristic
454C2#2142522611yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC2×C59×#328C2
socleC23×C59#120
prime radicalC24×C59C2×D4
hypercenterC2×#328D59
hypocenterC59#9927
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
258. C59#9927semidirect

Maximal subgroups

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

subgroupindex
C2×#168377302
#214299112
C2×#168373342
#214241832
C2×#168371272
#214219752
C2×C59×#3282
#992759