Finite Group Databasebeta

← #28484257

Subgroups — #28484257

Order 15104.

694 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×#16837455C211yesmaximal, characteristic, complemented
2#21432427C211yesmaximal, characteristic
3C2×#16837135C212yesmaximal
4#21421975C212yesmaximal, complemented
5C59×#1434C211yesmaximal, characteristic, complemented
6C2×#14273710—21no—
7C2×#14273701C2211yescharacteristic
8#16837455—24no—
9C2×C4⋊(C59⋊C8)—21no—
10C2×C22⋊(C59⋊C8)C2212yes—
11C2×C4×C59⋊C8—21no—
12#16837304C411yescharacteristic, complemented
13#16837304C411yescharacteristic, complemented
14#16837300C411yescharacteristic, complemented
15#16837300C411yescharacteristic, complemented
16#16837293—21no—
17#16837293—21no—
18#16837281—21no—
19#16837262C2211yescharacteristic
20#16837135—24no—
21C22×C42×C59C2211yescharacteristic
22C2×#95×C59—21no—
23C2×#95×C59—21no—
24C2×#95×C59C2212yes—
25C22×D236C2×C411yescharacteristic
26C22×C22⋊D59—21no—
27C22×C59⋊C8—22no—
28#14273710—42no—
29#14273710—42no—
30#14273701—22no—
31#14273701—22no—
32C2×C4⋊Dic59C2×C411yescharacteristic
33C2×C4⋊Dic59C2×C411yescharacteristic
34C2×C4⋊Dic59C2×C411yescharacteristic
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4—21no—
37C2×C22⋊Dic59—21no—
38C2×(C2×D59)⋊C4—21no—
39C2×(C2×D59)⋊C4—21no—
40C2×(C2×D59)⋊C4—21no—
41C2×(C2×D59)⋊C4—21no—
42C2×(C2×D59)⋊C4—21no—
43C4⋊(C59⋊C8)—24no—
44C22⋊(C59⋊C8)—22no—
45C22⋊(C59⋊C8)D414yes—
46C4×C59⋊C8—24no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C23×C4×C59—22no—
51C23×C4×C59D411yescharacteristic
52C23×C4×C59D411yescharacteristic
53C23×C4×C59C2311yescharacteristic
54C2×C42×C59—22no—
55C2×C42×C59—22no—
56C2×C42×C59C2×C411yescharacteristic
57C2×C42×C59C2×C411yescharacteristic
58C2×C42×C59D411yescharacteristic
59C2×C42×C59D411yescharacteristic
60#95×C59—24no—
61#95×C59—22no—
62#95×C59—22no—
63#95×C59—42no—
64C24×C59C2×D411yescharacteristic
65C23×D59—21no—
66C22×C4×C59—22no—
67C22×C4×C59—22no—
68C22×C4×C59—22no—
69C22×C4×C59—22no—
70C22×C4×C59—24no—
71C22×C4×C59—41no—
72C22×C4×C59—41no—
73C22×C4×C59—41no—
74C22×C4×C59—42no—
75C22×C4×C59—42no—
76C22×C4×C59—42no—
77C22×C4×C59—42no—
78C22×C4×C59—42no—
79C22×C4×C59—42no—
80C22×C4×C59C22⋊C411yescharacteristic
81C22×C4×C59C22⋊C411yescharacteristic
82C22×C4×C59C22⋊C411yescharacteristic
83C22×C4×C59C22⋊C411yescharacteristic
84C22×C4×C59D812yes—
85C22×C4×C59SD1612yes—
86C22×C4×C59C22×C411yescharacteristic
87C22×C4×C59C2×D411yescharacteristic
88C22×C4×C59C2×D412yes—
89C22×C4×C59#4112yes—
90C2×C22⋊D59—42no—
91C2×C22⋊D59—41no—
92C2×C22⋊D59—41no—
93C2×C22⋊D59—42no—
94C22×Dic59—21no—
95C22×Dic59—21no—
96C22×Dic59—21no—
97C2×D236—22no—
98C2×D236—41no—
99C2×D236—41no—
100C42×C59—22no—
101C42×C59—22no—
102C42×C59—21no—
103C42×C59—21no—
104C42×C59—21no—
105C42×C59—21no—
106C22⋊Dic59—41no—
107C22⋊Dic59—41no—
108(C2×D59)⋊C4—42no—
109(C2×D59)⋊C4—42no—
110(C2×D59)⋊C4—42no—
111(C2×D59)⋊C4—42no—
112(C2×D59)⋊C4—41no—
113(C2×D59)⋊C4—41no—
114C4⋊Dic59—22no—
115C4⋊Dic59—41no—
116C4⋊Dic59—41no—
117Dic59⋊C4—42no—
118Dic59⋊C4—42no—
119C2×C59⋊C8—24no—
120C2×C59⋊C8—42no—
121C2×C59⋊C8—42no—
122C23×C59—21no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59C2×C22⋊C411yescharacteristic
127C23×C59#12112yes—
128C23×C59C2×D811yescharacteristic
129C23×C59C2×SD1611yescharacteristic
130C23×C59#13512yes—
131C22×D59—41no—
132C22×D59—41no—
133C22×D59—41no—
134C22×D59—41no—
135C22×D59—41no—
136C22×D59—41no—
137C22×D59—41no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—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—24no—
149C2×C4×C59—24no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—42no—
154C2×C4×C59—42no—
155C2×C4×C59—44no—
156C2×C4×C59—44no—
157C2×C4×C59—44no—
158C2×C4×C59—44no—
159C2×C4×C59—82no—
160C2×C4×C59—82no—
161C2×C4×C59—82no—
162C2×C4×C59—82no—
163C2×C4×C59#10212yes—
164C2×C4×C59#10212yes—
165C2×C4×C59#10412yes—
166C2×C4×C59C4×D412yes—
167C2×C4×C59#12011yescharacteristic
168C2×C4×C59#12311yescharacteristic
169C22⋊D59—82no—
170C22⋊D59—82no—
171C2×Dic59—41no—
172C2×Dic59—41no—
173C2×Dic59—41no—
174C2×Dic59—41no—
175C2×Dic59—41no—
176C2×Dic59—41no—
177C2×Dic59—41no—
178C2×Dic59—41no—
179C2×Dic59—41no—
180D236—82no—
181C59⋊C8—44no—
182#9114—591nomaximal, Sylow
183C22×C59—22no—
184C22×C59—22no—
185C22×C59—22no—
186C22×C59—21no—
187C22×C59—21no—
188C22×C59—21no—
189C22×C59—21no—
190C22×C59—22no—
191C22×C59#38611yescharacteristic
192C22×C59#41011yescharacteristic
193C22×C59#41011yescharacteristic
194C22×C59C2×#10211yescharacteristic
195C22×C59#41611yescharacteristic
196C22×C59C2×#10411yescharacteristic
197C22×C59#42111yescharacteristic
198C22×C59#46512yes—
199C22×C59#46612yes—
200C2×D59—81no—
201C2×D59—81no—
202C2×D59—81no—
203C2×D59—81no—
204C2×D59—81no—
205C2×D59—81no—
206C2×D59—81no—
207C4×C59—22no—
208C4×C59—22no—
209C4×C59—22no—
210C4×C59—21no—
211C4×C59—22no—
212C4×C59—21no—
213C4×C59—41no—
214C4×C59—84no—
215Dic59—81no—
216Dic59—81no—
217Dic59—81no—
218C2×#431—591no—
219#2854—591no—
220C2×#327—592no—
221#1434D5911yescharacteristic, complemented
222#1294—592no—
223C2×C59—22no—
224C2×C59—22no—
225C2×C59#150011yescharacteristic
226C2×C59#150211yescharacteristic
227C2×C59#151711yescharacteristic
228C2×C59#152111yescharacteristic
229C2×C59#187111yescharacteristic
230C2×C59#189311yescharacteristic
231C2×C59#189911yescharacteristic
232D59—161no—
233C2×#123—1181no—
234C2×#121—591no—
235C22×C42C2×D5911yescharacteristic
236#431—1184no—
237C2×C4⋊C8—1181no—
238C2×C22⋊C8—592no—
239C2×C4×C8—1181no—
240#390—591no—
241#390—591no—
242#389—591no—
243#389—591no—
244#388—1181no—
245#388—1181no—
246#386—1181no—
247#380—591no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95C2×D5912yes—
251#327—1184no—
252C59#911411yescharacteristic, complemented, Sylow
253C22×D4—591no—
254C22×D4—1181no—
255C23×C4—22no—
256C23×C4C22⋊D5911yescharacteristic
257C23×C4C22⋊D5911yescharacteristic
258C23×C4C22×D5911yescharacteristic
259C22×C8—1182no—
260#123—2362no—
261#123—2362no—
262#121—1182no—
263#121—1182no—
264C2×C4⋊C4—591no—
265C2×C4⋊C4—591no—
266C2×C4⋊C4—591no—
267C2×C4⋊C4—1181no—
268C2×C4⋊C4—1181no—
269C2×C22⋊C4—1181no—
270C2×C22⋊C4—1181no—
271C2×C22⋊C4—1181no—
272C2×C22⋊C4—1181no—
273C2×C22⋊C4—1181no—
274C2×C22⋊C4—1181no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42C4×D5911yescharacteristic
278C2×C42C4×D5911yescharacteristic
279C2×C42D23611yescharacteristic
280C2×C42D23611yescharacteristic
281C4⋊C8—1184no—
282C22⋊C8—594no—
283C22⋊C8—1182no—
284C4×C8—1184no—
285#95—24no—
286#95—22no—
287#95—22no—
288#95—42no—
289#95—1181no—
290#95—1181no—
291#95—1181no—
292C24—1181no—
293C24C2×C22⋊D5911yescharacteristic
294C2×D4—1182no—
295C2×D4—2361no—
296C2×D4—2361no—
297C2×D4—2362no—
298C2×D4—2361no—
299C2×D4—2361no—
300C2×D4—2362no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—1181no—
316C22×C4—1181no—
317C22×C4—1181no—
318C22×C4(C2×D59)⋊C411yescharacteristic
319C22×C4(C2×D59)⋊C411yescharacteristic
320C22×C4(C2×D59)⋊C411yescharacteristic
321C22×C4(C2×D59)⋊C411yescharacteristic
322C22×C4#1174566912yes—
323C22×C4#1174567112yes—
324C22×C4C2×C4×D5911yescharacteristic
325C22×C4C2×D23611yescharacteristic
326C22×C4D4×D5912yes—
327C22×C4#1174568712yes—
328C2×C8—1184no—
329C2×C8—2362no—
330C2×C8—2362no—
331C4⋊C4—1182no—
332C4⋊C4—2361no—
333C4⋊C4—2361no—
334C4⋊C4—2362no—
335C4⋊C4—2362no—
336C22⋊C4—2362no—
337C22⋊C4—2361no—
338C22⋊C4—2361no—
339C22⋊C4—2362no—
340C22⋊C4—2362no—
341C22⋊C4—2362no—
342C22⋊C4—2361no—
343C22⋊C4—2361no—
344C42—22no—
345C42—22no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—2361no—
355C23—2361no—
356C23—2361no—
357C23—2361no—
358C23—2361no—
359C23—2361no—
360C23—2361no—
361C23C2×(C2×D59)⋊C411yescharacteristic
362C23#1427369912yes—
363C23C2×#1174566911yescharacteristic
364C23C2×#1174567111yescharacteristic
365C23#1427374712yes—
366D4—4722no—
367D4—4722no—
368D4—4722no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—2361no—
395C2×C4—2361no—
396C2×C4—2361no—
397C2×C4—2361no—
398C2×C4—2361no—
399C2×C4—2361no—
400C2×C4—2361no—
401C2×C4—2361no—
402C2×C4—2361no—
403C2×C4#1427364712yes—
404C2×C4#1427364712yes—
405C2×C4#1427365512yes—
406C2×C4(C22⋊D59)⋊C412yes—
407C2×C4#1427369711yescharacteristic
408C2×C4#1427371111yescharacteristic
409C8—2364no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—21no—
418C22—4721no—
419C22—4721no—
420C22—4721no—
421C22—4721no—
422C22—4721no—
423C22—4721no—
424C22—4721no—
425C22#1683727911yescharacteristic
426C22#1683737511yescharacteristic
427C22#1683737511yescharacteristic
428C22C2×#1427364711yescharacteristic
429C22#1683739611yescharacteristic
430C22C2×#1427365511yescharacteristic
431C22#1683742011yescharacteristic
432C22#1683763312yes—
433C22#1683763612yes—
434C4—22no—
435C4—22no—
436C4—22no—
437C4—21no—
438C4—22no—
439C4—21no—
440C4—41no—
441C4—84no—
442C4—4721no—
443C4—4721no—
444C4—4721no—
445C2—22no—
446C2—22no—
447C2—9441no—
448C2#2142258011yescharacteristic
449C2#2142259011yescharacteristic
450C2#2142265511yescharacteristic
451C2#2142267111yescharacteristic
452C2#2142439611yescharacteristic
453C2#2142452211yescharacteristic
454C2#2142455211yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1434C2
socleC23×C59C2×C22⋊C4
prime radicalC2×#14273701C22
cosocleC23×C4×C59C23
hypercenter#1434D59
hypocenterC59#9114
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#16837455C2semidirect
4. #21421975C2semidirect
5. C59×#1434C2semidirect
12. #16837304C4semidirect
13. #16837304C4semidirect
14. #16837300C4semidirect
15. #16837300C4semidirect
221. #1434D59semidirect
252. C59#9114semidirect

Maximal subgroups

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

subgroupindex
C2×#168374552
#214324272
C2×#168371352
#214219752
C59×#14342
#911459