Finite Group Databasebeta

← #28488976

Subgroups — #28488976

Order 15104.

654 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837732C211yesmaximal, characteristic
2#21429909C211yesmaximal, characteristic
3#21424182C211yesmaximal, characteristic
4C2×#16837138C211yesmaximal, characteristic
5C2×#16837128C211yesmaximal, characteristic
6#21421975C211yesmaximal, characteristic
7C2×C59×#398C211yesmaximal, characteristic
8C2×#14273706C2211yescharacteristic
9#16837732—22no—
10#16837732—22no—
11C2×#14273658—21no—
12C2×#14273650—21no—
13C2×C22⋊(C59⋊C8)C2211yescharacteristic
14C2×C22⋊(C59⋊C8)C2211yescharacteristic
15#16837341—21no—
16#16837335—22no—
17#16837322—21no—
18#16837275—21no—
19#16837265—21no—
20#16837262C2211yescharacteristic
21#16837164—22no—
22#16837138—22no—
23#16837128—22no—
24C22×C4⋊C4×C59—21no—
25C22×C4⋊C4×C59C2211yescharacteristic
26C22×C4⋊C4×C59C2211yescharacteristic
27C59×#398—22no—
28C59×#398—22no—
29C2×#95×C59—21no—
30C2×#95×C59C2211yescharacteristic
31C22×Dic118D411yescharacteristic
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34#14273706—21no—
35#14273706—21no—
36#14273706—21no—
37#14273706—21no—
38C2×C4⋊Dic59D411yescharacteristic
39C2×C4⋊Dic59D412yes—
40C2×Dic59⋊C4—21no—
41C2×Dic59⋊C4—22no—
42C2×C22⋊Dic59—21no—
43C2×C22⋊Dic59—21no—
44#14273658—24no—
45#14273650—24no—
46C22⋊(C59⋊C8)—21no—
47C22⋊(C59⋊C8)—21no—
48C22⋊(C59⋊C8)—21no—
49C22⋊(C59⋊C8)D412yes—
50C59⋊#95—22no—
51C59⋊#95—22no—
52C59⋊#95—22no—
53C59⋊#95—21no—
54C23×C4×C59—21no—
55C23×C4×C59—21no—
56C23×C4×C59D411yescharacteristic
57C23×C4×C59D411yescharacteristic
58C23×C4×C59C2311yescharacteristic
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59—21no—
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59—21no—
63C2×C4⋊C4×C59—24no—
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59—21no—
66C2×C4⋊C4×C59—21no—
67C2×C4⋊C4×C59—21no—
68C2×C4⋊C4×C59—21no—
69C2×C4⋊C4×C59—21no—
70C2×C4⋊C4×C59—21no—
71C2×C4⋊C4×C59—42no—
72C2×C4⋊C4×C59—42no—
73C2×C4⋊C4×C59D412yes—
74#95×C59—24no—
75#95×C59—21no—
76#95×C59D412yes—
77C24×C59C2×D411yescharacteristic
78C22×C4×C59—24no—
79C22×C4×C59—22no—
80C22×C4×C59—21no—
81C22×C4×C59—21no—
82C22×C4×C59—21no—
83C22×C4×C59—21no—
84C22×C4×C59—21no—
85C22×C4×C59—21no—
86C22×C4×C59—21no—
87C22×C4×C59—22no—
88C22×C4×C59—21no—
89C22×C4×C59—21no—
90C22×C4×C59—42no—
91C22×C4×C59—42no—
92C22×C4×C59—41no—
93C22×C4×C59—41no—
94C22×C4×C59—42no—
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×C59SD1612yes—
102C22×C4×C59C2×D411yescharacteristic
103C22×C4×C59C2×D411yescharacteristic
104C22×C4×C59C2×D411yescharacteristic
105C22×C4×C59C2×D411yescharacteristic
106C22×C4×C59C2×D411yescharacteristic
107C22×C4×C59#4111yescharacteristic
108C22×Dic59—21no—
109C22×Dic59—22no—
110C22×Dic59—21no—
111C2×Dic118—21no—
112C2×Dic118—21no—
113C2×Dic118—42no—
114C4⋊C4×C59—22no—
115C4⋊C4×C59—22no—
116C4⋊C4×C59—48no—
117C4⋊C4×C59—41no—
118C4⋊C4×C59—41no—
119C4⋊C4×C59—41no—
120C4⋊C4×C59—41no—
121C4⋊C4×C59—41no—
122C4⋊C4×C59—41no—
123C22⋊Dic59—41no—
124C22⋊Dic59—41no—
125C22⋊Dic59—41no—
126C22⋊Dic59—41no—
127C4⋊Dic59—21no—
128C4⋊Dic59—21no—
129C4⋊Dic59—42no—
130Dic59⋊C4—41no—
131Dic59⋊C4—41no—
132Dic59⋊C4—82no—
133C2×C59⋊C8—22no—
134C2×C59⋊C8—42no—
135C2×C59⋊C8—42no—
136C2×C59⋊C8—41no—
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
146C2×C4×C59—22no—
147C2×C4×C59—22no—
148C2×C4×C59—24no—
149C2×C4×C59—22no—
150C2×C4×C59—22no—
151C2×C4×C59—22no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—44no—
157C2×C4×C59—44no—
158C2×C4×C59—42no—
159C2×C4×C59—41no—
160C2×C4×C59—41no—
161C2×C4×C59—42no—
162C2×C4×C59—41no—
163C2×C4×C59—41no—
164C2×C4×C59—42no—
165C2×C4×C59—42no—
166C2×C4×C59—41no—
167C2×C4×C59—42no—
168C2×C4×C59—42no—
169C2×C4×C59—42no—
170C2×C4×C59—81no—
171C2×C4×C59—81no—
172C2×C4×C59—81no—
173C2×C4×C59—81no—
174C2×C4×C59—81no—
175C2×C4×C59#12011yescharacteristic
176C2×C4×C59#12111yescharacteristic
177C2×C4×C59#12111yescharacteristic
178C2×C4×C59#12711yescharacteristic
179C2×Dic59—41no—
180C2×Dic59—41no—
181C2×Dic59—42no—
182C2×Dic59—42no—
183C2×Dic59—42no—
184C2×Dic59—42no—
185C2×Dic59—42no—
186Dic118—42no—
187Dic118—81no—
188C59⋊C8—42no—
189C59⋊C8—81no—
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—42no—
214C4×C59—82no—
215C4×C59—81no—
216Dic59—82no—
217Dic59—81no—
218Dic59—81no—
219C2×#483—591no—
220#2627—591no—
221C2×#398D5911yescharacteristic
222#1823—591no—
223C2×#328—591no—
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⋊Q8—591no—
236C22×C4⋊C4—21no—
237C22×C4⋊C4C2×D5911yescharacteristic
238C22×C4⋊C4C2×D5911yescharacteristic
239#483—1182no—
240#483—1182no—
241C2×#106—1181no—
242C2×#103—1181no—
243C2×C22⋊C8—591no—
244C2×C22⋊C8—591no—
245#400—1181no—
246#398—22no—
247#398—22no—
248#398—1182no—
249#395—1181no—
250#385—1181no—
251#381—1181no—
252#380—591no—
253C2×#95—21no—
254C2×#95C2×D5911yescharacteristic
255#340—1182no—
256#328—1182no—
257#324—1182no—
258C59#992711yescharacteristic, complemented, Sylow
259C22×Q8—591no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4C22⋊D5911yescharacteristic
263C23×C4C22⋊D5911yescharacteristic
264C23×C4C22×D5911yescharacteristic
265C22×C8—1181no—
266C22×C8—1181no—
267C22⋊Q8—1181no—
268C22⋊Q8—1181no—
269C22⋊Q8—1181no—
270C22⋊Q8—1181no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—591no—
286C2×C4⋊C4—592no—
287C2×C4⋊C4—1182no—
288C2×C4⋊C4—1181no—
289C2×C4⋊C4C22⋊D5912yes—
290C2×C22⋊C4—1181no—
291C2×C22⋊C4—1181no—
292#106—1184no—
293#103—1184no—
294C22⋊C8—592no—
295C22⋊C8—1181no—
296C22⋊C8—1181no—
297C22⋊C8—1181no—
298#95—24no—
299#95—21no—
300#95—1182no—
301#95—1182no—
302#95—1182no—
303#95—1181no—
304#95C22⋊D5912yes—
305C24C2×C22⋊D5911yescharacteristic
306C2×Q8—1181no—
307C2×Q8—1181no—
308C2×Q8—2362no—
309C22×C4—24no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—1182no—
333C22×C4—1181no—
334C22×C4—1181no—
335C22×C4#1174567012yes—
336C22×C4D4×D5911yescharacteristic
337C22×C4D4×D5911yescharacteristic
338C22×C4D4×D5911yescharacteristic
339C22×C4#1174568711yescharacteristic
340C22×C4C2×C22⋊D5911yescharacteristic
341C22×C4C2×C22⋊D5911yescharacteristic
342C2×C8—1182no—
343C2×C8—2362no—
344C2×C8—2361no—
345C2×C8—2362no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—48no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—1181no—
356C4⋊C4—1181no—
357C4⋊C4—4722no—
358C4⋊C4—2362no—
359C4⋊C4—2361no—
360C4⋊C4—2361no—
361C22⋊C4—2361no—
362C22⋊C4—2361no—
363C22⋊C4—2361no—
364C22⋊C4—2361no—
365C23—22no—
366C23—22no—
367C23#1427369511yescharacteristic
368C23#1427369611yescharacteristic
369C23#1427369911yescharacteristic
370C23C2×#1174567011yescharacteristic
371C23#1427374711yescharacteristic
372C23#1427375311yescharacteristic
373C23#1427375711yescharacteristic
374Q8—4721no—
375Q8—2362no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—2362no—
406C2×C4—2361no—
407C2×C4—2361no—
408C2×C4—2362no—
409C2×C4—2362no—
410C2×C4—2362no—
411C2×C4—2362no—
412C2×C4#1427369511yescharacteristic
413C2×C4#1427369811yescharacteristic
414C2×C4#1427369911yescharacteristic
415C2×C4#1427372311yescharacteristic
416C8—4721no—
417C8—2362no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22#1683731011yescharacteristic
427C22#1683754011yescharacteristic
428C22#1683754511yescharacteristic
429C22#1683755311yescharacteristic
430C22#1683756411yescharacteristic
431C22#1683758412yes—
432C22#1683759112yes—
433C22#1683762911yescharacteristic
434C22#1683764611yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—44no—
440C4—42no—
441C4—81no—
442C4—82no—
443C4—4721no—
444C4—4721no—
445C4—4722no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2#2142309112yes—
451C2#2142310312yes—
452C2#2142509911yescharacteristic
453C2#2142513211yescharacteristic
454C2#2142522411yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC2×C59×#398C2
socleC23×C59#120
prime radicalC24×C59C2×D4
hypercenterC2×#398D59
hypocenterC59#9927
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#398

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×#168377322
#214299092
#214241822
C2×#168371382
C2×#168371282
#214219752
C2×C59×#3982
#992759