Finite Group Databasebeta

← #28482060

Subgroups — #28482060

Order 15104.

940 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837262C211yesmaximal, characteristic
2#21424006C211yesmaximal, characteristic
3#21421975C214yesmaximal, complemented
4C59×C22⋊#95C211yesmaximal, characteristic
5C22×C4⋊Dic59C411yescharacteristic, complemented
6C22×C4⋊Dic59C411yescharacteristic, complemented
7C22×C22⋊Dic59—21no—
8C2×C22⋊(C59⋊C8)—21no—
9C2×C22⋊(C59⋊C8)—21no—
10C2×C22⋊(C59⋊C8)C2212yes—
11#16837262—21no—
12#16837262—21no—
13#16837262C412yescomplemented
14#16837262C2212yes—
15C2×C59⋊#95—21no—
16C24×C4×C59C2211yescharacteristic
17C22×C22⋊C4×C59—21no—
18C2×#95×C59—21no—
19C2×#95×C59C2212yes—
20C23×Dic59—21no—
21C23×Dic59—21no—
22C22×C59⋊C8—22no—
23C2×C4⋊Dic59—21no—
24C2×C4⋊Dic59—21no—
25C2×C4⋊Dic59—42no—
26C2×C4⋊Dic59—42no—
27C2×C4⋊Dic59C2×C412yes—
28C2×C4⋊Dic59C2×C412yes—
29C2×C22⋊Dic59—22no—
30C2×C22⋊Dic59—22no—
31C2×C22⋊Dic59—42no—
32C2×C22⋊Dic59—42no—
33C22⋊(C59⋊C8)—24no—
34C22⋊(C59⋊C8)—42no—
35C22⋊(C59⋊C8)—42no—
36C59⋊#95—22no—
37C59⋊#95—22no—
38C25×C59D411yescharacteristic
39C23×C4×C59—24no—
40C23×C4×C59—22no—
41C23×C4×C59—42no—
42C23×C4×C59—42no—
43C23×C4×C59C2×C411yescharacteristic
44C23×C4×C59C2×C411yescharacteristic
45C23×C4×C59D411yescharacteristic
46C23×C4×C59D411yescharacteristic
47C23×C4×C59D411yescharacteristic
48C23×C4×C59C2311yescharacteristic
49C2×C22⋊C4×C59—24no—
50C2×C22⋊C4×C59—42no—
51C2×C22⋊C4×C59—42no—
52#95×C59—24no—
53#95×C59—42no—
54C24×C59—22no—
55C24×C59—22no—
56C24×C59—22no—
57C24×C59—22no—
58C24×C59—41no—
59C24×C59—41no—
60C24×C59C22⋊C411yescharacteristic
61C24×C59C22⋊C411yescharacteristic
62C24×C59D812yes—
63C24×C59SD1612yes—
64C24×C59C2×D411yescharacteristic
65C22×C4×C59—22no—
66C22×C4×C59—22no—
67C22×C4×C59—22no—
68C22×C4×C59—22no—
69C22×C4×C59—22no—
70C22×C4×C59—22no—
71C22×C4×C59—22no—
72C22×C4×C59—22no—
73C22×C4×C59—22no—
74C22×C4×C59—22no—
75C22×C4×C59—24no—
76C22×C4×C59—41no—
77C22×C4×C59—41no—
78C22×C4×C59—41no—
79C22×C4×C59—41no—
80C22×C4×C59—41no—
81C22×C4×C59—41no—
82C22×C4×C59—41no—
83C22×C4×C59—416no—
84C22×C4×C59—42no—
85C22×C4×C59—42no—
86C22×C4×C59—42no—
87C22×C4×C59—42no—
88C22×C4×C59—42no—
89C22×C4×C59—42no—
90C22×C4×C59C22⋊C411yescharacteristic
91C22×C4×C59C22⋊C411yescharacteristic
92C22×C4×C59C22×C411yescharacteristic
93C22×C4×C59C2×D411yescharacteristic
94C22×C4×C59#4114yes—
95C22×Dic59—22no—
96C22×Dic59—22no—
97C22×Dic59—42no—
98C22×Dic59—42no—
99C22×Dic59—42no—
100C22×Dic59—42no—
101C22×Dic59—42no—
102C22×Dic59—42no—
103C22⋊C4×C59—48no—
104C22⋊Dic59—44no—
105C22⋊Dic59—42no—
106C22⋊Dic59—42no—
107C4⋊Dic59—42no—
108C4⋊Dic59—42no—
109C4⋊Dic59—42no—
110C4⋊Dic59—42no—
111C2×C59⋊C8—42no—
112C2×C59⋊C8—42no—
113C2×C59⋊C8—42no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59—21no—
118C23×C59—21no—
119C23×C59—21no—
120C23×C59—21no—
121C23×C59—21no—
122C23×C59—24no—
123C23×C59—24no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—21no—
127C23×C59—21no—
128C23×C59—21no—
129C23×C59—21no—
130C23×C59—24no—
131C23×C59—24no—
132C23×C59—42no—
133C23×C59—42no—
134C23×C59—44no—
135C23×C59—44no—
136C23×C59—44no—
137C23×C59—44no—
138C23×C59#9912yes—
139C23×C59#10212yes—
140C23×C59#10212yes—
141C23×C59#10412yes—
142C23×C59C2×C22⋊C411yescharacteristic
143C23×C59#12312yes—
144C23×C59C2×D811yescharacteristic
145C23×C59C2×SD1611yescharacteristic
146C23×C59#13712yes—
147C2×C4×C59—28no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—21no—
157C2×C4×C59—44no—
158C2×C4×C59—44no—
159C2×C4×C59—44no—
160C2×C4×C59—44no—
161C2×C4×C59—44no—
162C2×C4×C59—44no—
163C2×C4×C59—44no—
164C2×C4×C59—44no—
165C2×C4×C59—82no—
166C2×C4×C59—82no—
167C2×C4×C59—82no—
168C2×C4×C59—82no—
169C2×C4×C59#9912yes—
170C2×C4×C59#11712yes—
171C2×C4×C59#12312yes—
172C2×Dic59—42no—
173C2×Dic59—42no—
174C2×Dic59—42no—
175C2×Dic59—42no—
176C2×Dic59—42no—
177C2×Dic59—42no—
178C2×Dic59—84no—
179C2×Dic59—84no—
180C59⋊C8—82no—
181#8712—591nomaximal, Sylow
182C22×C59—22no—
183C22×C59—22no—
184C22×C59—22no—
185C22×C59—22no—
186C22×C59—22no—
187C22×C59—21no—
188C22×C59—21no—
189C22×C59—22no—
190C22×C59—22no—
191C22×C59—22no—
192C22×C59—22no—
193C22×C59—22no—
194C22×C59—21no—
195C22×C59—21no—
196C22×C59—22no—
197C22×C59—22no—
198C22×C59—22no—
199C22×C59—48no—
200C22×C59—48no—
201C22×C59—41no—
202C22×C59—41no—
203C22×C59—41no—
204C22×C59—41no—
205C22×C59#32714yes—
206C22×C59#38111yescharacteristic
207C22×C59C2×#9911yescharacteristic
208C22×C59C2×#9911yescharacteristic
209C22×C59C2×#10211yescharacteristic
210C22×C59#41911yescharacteristic
211C22×C59C2×#10411yescharacteristic
212C22×C59#42111yescharacteristic
213C22×C59#48012yes—
214C22×C59#48312yes—
215C4×C59—22no—
216C4×C59—22no—
217C4×C59—22no—
218C4×C59—41no—
219C4×C59—84no—
220Dic59—82no—
221Dic59—82no—
222C2×#380—591no—
223#1779—591no—
224C22⋊#95D5911yescharacteristic
225#1294—594no—
226C2×C59—22no—
227C2×C59—24no—
228C2×C59—22no—
229C2×C59—42no—
230C2×C59C2×#32711yescharacteristic
231C2×C59#150811yescharacteristic
232C2×C59#151111yescharacteristic
233C2×C59#151911yescharacteristic
234C2×C59#181911yescharacteristic
235C2×C59#182311yescharacteristic
236C2×C59#182611yescharacteristic
237C24×C4C2×D5911yescharacteristic
238C22×C4⋊C4—591no—
239C22×C4⋊C4—591no—
240C22×C22⋊C4—21no—
241C22×C22⋊C4—1181no—
242C2×C22⋊C8—592no—
243C2×C22⋊C8—1181no—
244C2×C22⋊C8—1181no—
245#380—592no—
246#380—592no—
247#380—1181no—
248#380—1181no—
249C2×#95—21no—
250C2×#95—1181no—
251C2×#95C2×D5912yes—
252C59#871211yescharacteristic, complemented, Sylow
253C25C22⋊D5911yescharacteristic
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—1181no—
259C23×C4—1181no—
260C23×C4C4×D5911yescharacteristic
261C23×C4C4×D5911yescharacteristic
262C23×C4D23611yescharacteristic
263C23×C4D23611yescharacteristic
264C23×C4C22⋊D5911yescharacteristic
265C23×C4C22×D5911yescharacteristic
266C22×C8—1182no—
267C2×C4⋊C4—592no—
268C2×C4⋊C4—592no—
269C2×C4⋊C4—1181no—
270C2×C4⋊C4—1181no—
271C2×C4⋊C4—2362no—
272C2×C4⋊C4—2362no—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—42no—
275C2×C22⋊C4—42no—
276C2×C22⋊C4—1182no—
277C2×C22⋊C4—1182no—
278C2×C22⋊C4—2362no—
279C2×C22⋊C4—2362no—
280C22⋊C8—1184no—
281C22⋊C8—2362no—
282C22⋊C8—2362no—
283#95—24no—
284#95—42no—
285#95—1182no—
286#95—1182no—
287C24—22no—
288C24—22no—
289C24—22no—
290C24—22no—
291C24—41no—
292C24—41no—
293C24(C2×D59)⋊C411yescharacteristic
294C24(C2×D59)⋊C411yescharacteristic
295C24#1174566912yes—
296C24#1174567112yes—
297C24C2×C22⋊D5911yescharacteristic
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—416no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—1182no—
324C22×C4—1182no—
325C22×C4—2362no—
326C22×C4—2362no—
327C22×C4—2362no—
328C22×C4—2362no—
329C22×C4—2362no—
330C22×C4—2362no—
331C22×C4(C2×D59)⋊C411yescharacteristic
332C22×C4(C2×D59)⋊C411yescharacteristic
333C22×C4C2×C4×D5911yescharacteristic
334C22×C4C2×D23611yescharacteristic
335C22×C4#1174568714yes—
336C2×C8—2362no—
337C2×C8—2362no—
338C2×C8—2362no—
339C4⋊C4—2362no—
340C4⋊C4—2362no—
341C4⋊C4—2362no—
342C4⋊C4—2362no—
343C22⋊C4—48no—
344C22⋊C4—2364no—
345C22⋊C4—2362no—
346C22⋊C4—2362no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—24no—
356C23—24no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—24no—
361C23—24no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—42no—
366C23—42no—
367C23—44no—
368C23—44no—
369C23—44no—
370C23—44no—
371C23#1427364112yes—
372C23#1427364712yes—
373C23#1427364712yes—
374C23#1427365512yes—
375C23C2×(C2×D59)⋊C411yescharacteristic
376C23#1427370812yes—
377C23C2×#1174566911yescharacteristic
378C23C2×#1174567111yescharacteristic
379C23#1427375712yes—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—4724no—
403C2×C4—4724no—
404C2×C4—2362no—
405C2×C4—2362no—
406C2×C4—2362no—
407C2×C4—2362no—
408C2×C4—2362no—
409C2×C4—2362no—
410C2×C4#1427364112yes—
411C2×C4#1427368312yes—
412C2×C4#1427371112yes—
413C8—4722no—
414C22—22no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—21no—
424C22—22no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—48no—
432C22—48no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22#1683713514yes—
438C22#1683726311yescharacteristic
439C22C2×#1427364111yescharacteristic
440C22C2×#1427364111yescharacteristic
441C22C2×#1427364711yescharacteristic
442C22#1683741011yescharacteristic
443C22C2×#1427365511yescharacteristic
444C22#1683742011yescharacteristic
445C22#1683771312yes—
446C22#1683773012yes—
447C4—22no—
448C4—22no—
449C4—22no—
450C4—41no—
451C4—84no—
452C4—4722no—
453C4—4722no—
454C2—22no—
455C2—24no—
456C2—22no—
457C2—42no—
458C2C2×#1683713511yescharacteristic
459C2#2142261511yescharacteristic
460C2#2142262811yescharacteristic
461C2#2142266311yescharacteristic
462C2#2142416811yescharacteristic
463C2#2142418011yescharacteristic
464C2#2142419611yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×C22⋊#95C2
socleC23×C59C2×C22⋊C4
prime radicalC25×C59D4
cosocleC23×C4×C59C23
hypercenterC22⋊#95D59
hypocenterC59#8712
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. #21421975C2semidirect
5. C22×C4⋊Dic59C4semidirect
6. C22×C4⋊Dic59C4semidirect
13. #16837262C4semidirect
252. C59#8712semidirect

Maximal subgroups

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

subgroupindex
C2×#168372622
#214240062
#214219752
C59×C22⋊#952
#871259