Finite Group Databasebeta

← #28487833

Subgroups — #28487833

Order 15104.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432397C211yesmaximal, characteristic
2#21424076C211yesmaximal, characteristic, complemented
3C2×#16837138C212yesmaximal, complemented
4C2×#16837135C212yesmaximal
5C59×#1434C211yesmaximal, characteristic, complemented
6C2×#14273715C411yescharacteristic, complemented
7C2×#14273706C2211yescharacteristic
8C2×#14273701C2211yescharacteristic
9C2×C4⋊(C59⋊C8)—21no—
10C2×C22⋊(C59⋊C8)C2212yes—
11#16837308C411yescharacteristic, complemented
12#16837304C411yescharacteristic, complemented
13#16837293—21no—
14#16837293—21no—
15#16837281—21no—
16#16837281—21no—
17#16837268C411yescharacteristic, complemented
18#16837157—21no—
19#16837138—24no—
20#16837135—24no—
21C22×C42×C59C2211yescharacteristic
22C2×#95×C59—21no—
23C2×#95×C59—21no—
24C2×#95×C59C2212yes—
25C22×Dic118C2×C411yescharacteristic
26C22×D236C2×C411yescharacteristic
27C22×C22⋊D59—21no—
28C22×C59⋊C8—22no—
29#14273715—42no—
30#14273706—22no—
31#14273706—22no—
32#14273701—22no—
33#14273701—22no—
34C2×C4⋊Dic59C2×C411yescharacteristic
35C2×C4⋊Dic59C2×C411yescharacteristic
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)—42no—
44C22⋊(C59⋊C8)—22no—
45C22⋊(C59⋊C8)—22no—
46C59⋊#95—21no—
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—42no—
55C2×C42×C59C2×C411yescharacteristic
56C2×C42×C59C2×C411yescharacteristic
57C2×C42×C59D411yescharacteristic
58C2×C42×C59D411yescharacteristic
59#95×C59—22no—
60#95×C59—42no—
61#95×C59—42no—
62#95×C59D414yes—
63C24×C59C2×D411yescharacteristic
64C23×D59—21no—
65C22×C4×C59—22no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—22no—
69C22×C4×C59—24no—
70C22×C4×C59—41no—
71C22×C4×C59—41no—
72C22×C4×C59—41no—
73C22×C4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59—42no—
76C22×C4×C59—42no—
77C22×C4×C59—42no—
78C22×C4×C59—42no—
79C22×C4×C59—42no—
80C22×C4×C59—42no—
81C22×C4×C59C22⋊C411yescharacteristic
82C22×C4×C59C22⋊C411yescharacteristic
83C22×C4×C59C22⋊C411yescharacteristic
84C22×C4×C59C22⋊C411yescharacteristic
85C22×C4×C59C22×C411yescharacteristic
86C22×C4×C59C2×D411yescharacteristic
87C22×C4×C59C2×D412yes—
88C22×C4×C59#4112yes—
89C2×C22⋊D59—42no—
90C2×C22⋊D59—42no—
91C2×C22⋊D59—41no—
92C2×C22⋊D59—41no—
93C22×Dic59—21no—
94C22×Dic59—21no—
95C22×Dic59—21no—
96C2×D236—22no—
97C2×D236—41no—
98C2×D236—41no—
99C2×Dic118—22no—
100C2×Dic118—41no—
101C2×Dic118—41no—
102C42×C59—22no—
103C42×C59—22no—
104C42×C59—41no—
105C42×C59—41no—
106C22⋊Dic59—42no—
107(C2×D59)⋊C4—42no—
108(C2×D59)⋊C4—42no—
109(C2×D59)⋊C4—42no—
110(C2×D59)⋊C4—42no—
111(C2×D59)⋊C4—41no—
112(C2×D59)⋊C4—41no—
113C4⋊Dic59—22no—
114C4⋊Dic59—22no—
115Dic59⋊C4—41no—
116Dic59⋊C4—41no—
117C2×C59⋊C8—42no—
118C2×C59⋊C8—42no—
119C2×C59⋊C8—42no—
120C23×C59—21no—
121C23×C59—21no—
122C23×C59—21no—
123C23×C59—21no—
124C23×C59C2×C22⋊C411yescharacteristic
125C23×C59#12112yes—
126C23×C59#13512yes—
127C23×C59AGL(1,ℤ/8)11yescharacteristic
128C23×C59#13711yescharacteristic
129C22×D59—41no—
130C22×D59—41no—
131C22×D59—41no—
132C22×D59—41no—
133C22×D59—41no—
134C22×D59—41no—
135C22×D59—41no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
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—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—42no—
152C2×C4×C59—42no—
153C2×C4×C59—44no—
154C2×C4×C59—42no—
155C2×C4×C59—42no—
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#9912yes—
164C2×C4×C59C4×D412yes—
165C2×C4×C59#12411yescharacteristic
166C2×C4×C59#12711yescharacteristic
167C22⋊D59—82no—
168C22⋊D59—82no—
169C2×Dic59—41no—
170C2×Dic59—41no—
171C2×Dic59—41no—
172C2×Dic59—41no—
173C2×Dic59—41no—
174C2×Dic59—41no—
175C2×Dic59—41no—
176C2×Dic59—41no—
177C2×Dic59—41no—
178D236—82no—
179Dic118—82no—
180C59⋊C8—82no—
181#9716—591nomaximal, Sylow
182C22×C59—22no—
183C22×C59—22no—
184C22×C59—21no—
185C22×C59—21no—
186C22×C59—21no—
187C22×C59—21no—
188C22×C59—22no—
189C22×C59—22no—
190C22×C59#39011yescharacteristic
191C22×C59C2×#9911yescharacteristic
192C22×C59#41011yescharacteristic
193C22×C59#41611yescharacteristic
194C22×C59#41711yescharacteristic
195C22×C59#42111yescharacteristic
196C22×C59#42111yescharacteristic
197C22×C59#46312yes—
198C22×C59#46412yes—
199C2×D59—81no—
200C2×D59—81no—
201C2×D59—81no—
202C2×D59—81no—
203C2×D59—81no—
204C2×D59—81no—
205C2×D59—81no—
206C4×C59—21no—
207C4×C59—22no—
208C4×C59—21no—
209C4×C59—22no—
210C4×C59—41no—
211C4×C59—41no—
212C4×C59—41no—
213C4×C59—84no—
214Dic59—81no—
215Dic59—81no—
216Dic59—81no—
217#2850—591no—
218#1797—591no—
219C2×#328—592no—
220C2×#327—592no—
221#1434D5911yescharacteristic, complemented
222C2×C59—22no—
223C2×C59—22no—
224C2×C59#151211yescharacteristic
225C2×C59#151311yescharacteristic
226C2×C59#151611yescharacteristic
227C2×C59#152111yescharacteristic
228C2×C59#196311yescharacteristic
229C2×C59#196411yescharacteristic
230C2×C59#198311yescharacteristic
231D59—161no—
232C2×#124—591no—
233C2×C22⋊Q8—591no—
234C2×#121—591no—
235C22×C42C2×D5911yescharacteristic
236C2×C4⋊C8—1181no—
237C2×C22⋊C8—592no—
238#391—591no—
239#390—591no—
240#388—1181no—
241#388—1181no—
242#386—1181no—
243#386—1181no—
244#382—591no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95C2×D5912yes—
248#336—1181no—
249#328—1184no—
250#327—1184no—
251C59#971611yescharacteristic, complemented, Sylow
252C22×Q8—591no—
253C22×D4—591no—
254C22×D4—1181no—
255C23×C4—22no—
256C23×C4C22⋊D5911yescharacteristic
257C23×C4C22⋊D5911yescharacteristic
258C23×C4C22×D5911yescharacteristic
259C22×C8—1182no—
260#124—2362no—
261C22⋊Q8—1182no—
262C22⋊Q8—1182no—
263#121—1182no—
264#121—1182no—
265C2×C4⋊C4—591no—
266C2×C4⋊C4—591no—
267C2×C4⋊C4—1181no—
268C2×C22⋊C4—1181no—
269C2×C22⋊C4—1181no—
270C2×C22⋊C4—1181no—
271C2×C22⋊C4—1181no—
272C2×C22⋊C4—1181no—
273C2×C22⋊C4—1181no—
274C2×C42—42no—
275C2×C42C4×D5911yescharacteristic
276C2×C42C4×D5911yescharacteristic
277C2×C42D23611yescharacteristic
278C2×C42D23611yescharacteristic
279C4⋊C8—2362no—
280C22⋊C8—1182no—
281C22⋊C8—1182no—
282#95—22no—
283#95—42no—
284#95—42no—
285#95—1181no—
286#95—1181no—
287#95—1181no—
288#95—1181no—
289#95D23614yes—
290C24—1181no—
291C24C2×C22⋊D5911yescharacteristic
292C2×Q8—1182no—
293C2×Q8—2361no—
294C2×Q8—2361no—
295C2×D4—1182no—
296C2×D4—2361no—
297C2×D4—2361no—
298C2×D4—2362no—
299C2×D4—2362no—
300C2×D4—2361no—
301C2×D4—2361no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—1181no—
319C22×C4—1181no—
320C22×C4—1181no—
321C22×C4(C2×D59)⋊C411yescharacteristic
322C22×C4(C2×D59)⋊C411yescharacteristic
323C22×C4(C2×D59)⋊C411yescharacteristic
324C22×C4(C2×D59)⋊C411yescharacteristic
325C22×C4C2×C4×D5911yescharacteristic
326C22×C4C2×D23611yescharacteristic
327C22×C4C2×D23612yes—
328C22×C4#1174568512yes—
329C2×C8—2362no—
330C2×C8—2362no—
331C2×C8—2362no—
332C4⋊C4—1182no—
333C4⋊C4—1182no—
334C4⋊C4—2361no—
335C4⋊C4—2361no—
336C22⋊C4—2362no—
337C22⋊C4—2362no—
338C22⋊C4—2362no—
339C22⋊C4—2362no—
340C22⋊C4—2362no—
341C22⋊C4—2361no—
342C22⋊C4—2361no—
343C42—22no—
344C42—22no—
345C42—41no—
346C42—41no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—2361no—
352C23—2361no—
353C23—2361no—
354C23—2361no—
355C23—2361no—
356C23—2361no—
357C23—2361no—
358C23C2×(C2×D59)⋊C411yescharacteristic
359C23#1427370112yes—
360C23#1427374712yes—
361C23#1427375311yescharacteristic
362C23#1427375811yescharacteristic
363Q8—4722no—
364D4—4722no—
365D4—4722no—
366D4—4722no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
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—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
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#1427364112yes—
404C2×C4C4×D23612yes—
405C2×C4#1427371511yescharacteristic
406C2×C4#1427372411yescharacteristic
407C8—4722no—
408C22—22no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—22no—
415C22—22no—
416C22—4721no—
417C22—4721no—
418C22—4721no—
419C22—4721no—
420C22—4721no—
421C22—4721no—
422C22—4721no—
423C22#1683730411yescharacteristic
424C22C2×#1427364111yescharacteristic
425C22#1683737511yescharacteristic
426C22#1683739611yescharacteristic
427C22#1683740111yescharacteristic
428C22#1683742011yescharacteristic
429C22#1683742011yescharacteristic
430C22#1683761712yes—
431C22#1683762412yes—
432C4—21no—
433C4—22no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—84no—
440C4—4721no—
441C4—4721no—
442C4—4721no—
443C2—22no—
444C2—22no—
445C2—9441no—
446C2#2142263211yescharacteristic
447C2#2142263711yescharacteristic
448C2#2142265011yescharacteristic
449C2#2142267111yescharacteristic
450C2#2142492811yescharacteristic
451C2#2142493211yescharacteristic
452C2#2142502811yescharacteristic
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#9716
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
2. #21424076C2semidirect
3. C2×#16837138C2semidirect
5. C59×#1434C2semidirect
6. C2×#14273715C4semidirect
11. #16837308C4semidirect
12. #16837304C4semidirect
17. #16837268C4semidirect
221. #1434D59semidirect
251. C59#9716semidirect

Maximal subgroups

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

subgroupindex
#214323972
#214240762
C2×#168371382
C2×#168371352
C59×#14342
#971659