Finite Group Databasebeta

← #28492227

Subgroups — #28492227

Order 15104.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429019C211yesmaximal, characteristic
2#21424252C211yesmaximal, characteristic, complemented
3#21424102C211yesmaximal, characteristic, complemented
4#21424097C211yesmaximal, characteristic
5C2×#16837132C211yesmaximal, characteristic, complemented
6C2×#16837129C211yesmaximal, characteristic
7C59×#1296C211yesmaximal, characteristic, complemented
8C2×#14273707—21no—
9C2×C4×Dic118C2211yescharacteristic
10C2×C4×D236C2211yescharacteristic
11C2×#14273658—22no—
12C2×#14273652—21no—
13C2×#14273649—21no—
14C2×C4×C59⋊C8C2211yescharacteristic
15#16837324—22no—
16#16837303—21no—
17#16837301—21no—
18#16837272C2211yescharacteristic
19#16837259—21no—
20#16837165—21no—
21#16837165—21no—
22#16837132—22no—
23#16837129—22no—
24C2×C4⋊C8×C59C2211yescharacteristic
25C2×C4⋊C8×C59C2211yescharacteristic
26C59×#384C2211yescharacteristic
27C22×Dic118D411yescharacteristic
28C22×D236D411yescharacteristic
29C22×C4×D59—21no—
30C22×C59⋊C8—21no—
31#14273707—42no—
32#14273707—42no—
33C4×Dic118—21no—
34C4×Dic118—21no—
35C4×Dic118—21no—
36C4×Dic118—21no—
37C4×D236—21no—
38C4×D236—21no—
39C4×D236—21no—
40C4×D236—21no—
41C2×C4⋊Dic59—22no—
42C2×C4⋊Dic59—21no—
43C2×C4⋊Dic59—21no—
44C2×C4⋊Dic59—21no—
45C2×C4⋊Dic59D411yescharacteristic
46C2×C4⋊Dic59D411yescharacteristic
47C2×Dic59⋊C4—21no—
48C2×(C2×D59)⋊C4—22no—
49C2×(C2×D59)⋊C4—21no—
50C2×(C2×D59)⋊C4—22no—
51C2×C4×Dic59—21no—
52#14273658—44no—
53#14273652—42no—
54#14273649—42no—
55C4×C59⋊C8—21no—
56C4×C59⋊C8D412yes—
57C59⋊#95—22no—
58C22×C8×C59—21no—
59C22×C8×C59—21no—
60C2×C4⋊C4×C59—21no—
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59D412yes—
63C2×C42×C59C2311yescharacteristic
64C4⋊C8×C59—21no—
65C4⋊C8×C59—21no—
66C4⋊C8×C59—21no—
67C4⋊C8×C59—21no—
68C23×D59—21no—
69C22×C4×C59—22no—
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×Dic59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C22×Dic59—41no—
77C2×D236—21no—
78C2×D236—21no—
79C2×D236—21no—
80C2×D236—21no—
81C2×D236—21no—
82C2×D236SD1612yes—
83C2×C4×D59—41no—
84C2×C4×D59—41no—
85C2×C4×D59—41no—
86C2×C4×D59—41no—
87C2×C4×D59—41no—
88C2×C4×D59—41no—
89C2×Dic118—21no—
90C2×Dic118—21no—
91C2×Dic118—21no—
92C2×Dic118—21no—
93C2×Dic118—21no—
94C2×Dic118SD1612yes—
95C2×C8×C59—41no—
96C2×C8×C59—41no—
97C2×C8×C59—41no—
98C2×C8×C59—41no—
99C2×C8×C59—41no—
100C2×C8×C59—41no—
101C4⋊C4×C59—42no—
102C4⋊C4×C59—41no—
103C4⋊C4×C59—41no—
104C4⋊C4×C59—41no—
105C4⋊C4×C59—41no—
106C42×C59C2×D411yescharacteristic
107C42×C59#4111yescharacteristic
108C42×C59#4111yescharacteristic
109C42×C59#4111yescharacteristic
110(C2×D59)⋊C4—44no—
111(C2×D59)⋊C4—41no—
112(C2×D59)⋊C4—41no—
113(C2×D59)⋊C4—82no—
114C4⋊Dic59—21no—
115C4⋊Dic59—21no—
116C4⋊Dic59—21no—
117C4⋊Dic59—21no—
118C4⋊Dic59—44no—
119C4⋊Dic59—42no—
120C4⋊Dic59—41no—
121C4⋊Dic59—41no—
122C4⋊Dic59—41no—
123C4⋊Dic59—41no—
124Dic59⋊C4—41no—
125Dic59⋊C4—41no—
126C4×Dic59—41no—
127C4×Dic59—41no—
128C2×C59⋊C8—22no—
129C2×C59⋊C8—22no—
130C2×C59⋊C8—22no—
131C23×C59#12011yescharacteristic
132C22×D59—22no—
133C22×D59—41no—
134C22×D59—41no—
135C22×D59—41no—
136C22×D59—41no—
137C22×D59—41no—
138C22×D59—41no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—42no—
142C2×C4×C59—42no—
143C2×C4×C59—42no—
144C2×C4×C59#12111yescharacteristic
145C2×C4×C59#12111yescharacteristic
146C2×C4×C59#12111yescharacteristic
147C2×C4×C59#12311yescharacteristic
148C2×C4×C59#12311yescharacteristic
149C2×C4×C59#12411yescharacteristic
150C2×C4×C59C2×SD1611yescharacteristic
151C2×C4×C59C2×SD1611yescharacteristic
152C2×C4×C59#13511yescharacteristic
153C2×C4×C59#13511yescharacteristic
154C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C59#13711yescharacteristic
157C2×C4×C59#13711yescharacteristic
158C2×Dic59—22no—
159C2×Dic59—41no—
160C2×Dic59—41no—
161C2×Dic59—41no—
162C2×Dic59—41no—
163C2×Dic59—41no—
164C2×Dic59—41no—
165C2×Dic59—41no—
166C2×Dic59—41no—
167C2×Dic59—81no—
168C2×Dic59—81no—
169C2×Dic59—81no—
170D236—22no—
171D236—22no—
172D236—41no—
173D236—41no—
174C4×D59—81no—
175C4×D59—81no—
176C4×D59—81no—
177C4×D59—81no—
178Dic118—22no—
179Dic118—22no—
180Dic118—41no—
181Dic118—41no—
182C8×C59—81no—
183C8×C59—81no—
184C59⋊C8—24no—
185#10435—591nomaximal, Sylow
186C22×C59#39411yescharacteristic
187C22×C59#44811yescharacteristic
188C22×C59#44911yescharacteristic
189C22×C59#45011yescharacteristic
190C22×C59#45211yescharacteristic
191C22×C59#45311yescharacteristic
192C22×C59#45611yescharacteristic
193C2×D59—42no—
194C2×D59—42no—
195C2×D59—42no—
196C2×D59—81no—
197C2×D59—81no—
198C2×D59—81no—
199C2×D59—81no—
200C4×C59—21no—
201C4×C59—21no—
202C4×C59—82no—
203C4×C59#46511yescharacteristic
204C4×C59#46511yescharacteristic
205C4×C59#46911yescharacteristic
206C4×C59#47011yescharacteristic
207C4×C59#48111yescharacteristic
208C4×C59#48211yescharacteristic
209C4×C59#48311yescharacteristic
210C4×C59#48511yescharacteristic
211Dic59—42no—
212Dic59—81no—
213Dic59—81no—
214Dic59—161no—
215#2538—591no—
216#1844—591no—
217#1803—591no—
218#1802—591no—
219C2×Q8⋊C8—591no—
220C2×D4⋊C8—591no—
221#1296D5911yescharacteristic, complemented
222C2×C59#162211yescharacteristic
223C2×C59#163111yescharacteristic
224C2×C59#165111yescharacteristic
225C2×C59#165211yescharacteristic
226C2×C59#203411yescharacteristic
227C2×C59#203511yescharacteristic
228C2×C59#203911yescharacteristic
229D59—82no—
230C2×C22⋊Q8—1181no—
231C2×C4×Q8—591no—
232C2×C4×D4—591no—
233C2×#106—1182no—
234C2×C4⋊C8C2×D5911yescharacteristic
235C2×C4⋊C8C2×D5911yescharacteristic
236C2×#103—1181no—
237C2×#102—1181no—
238C2×C4×C8—591no—
239#396—1182no—
240#390—1181no—
241#389—1181no—
242#384—591no—
243#384C2×D5911yescharacteristic
244#380—1181no—
245#340—1181no—
246#340—1181no—
247Q8⋊C8—1182no—
248D4⋊C8—1182no—
249C59#1043511yescharacteristic, complemented, Sylow
250C22×Q8—591no—
251C22×D4—591no—
252C23×C4—1181no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—1181no—
256C22⋊Q8—2362no—
257C22⋊Q8—2362no—
258C4×Q8—1181no—
259C4×Q8—1181no—
260C4×Q8—1181no—
261C4×Q8—1181no—
262C4×D4—1181no—
263C4×D4—1181no—
264C4×D4—1181no—
265C4×D4—1181no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—591no—
269C2×C4⋊C4—591no—
270C2×C4⋊C4—1182no—
271C2×C4⋊C4—1181no—
272C2×C4⋊C4—1181no—
273C2×C4⋊C4—1181no—
274C2×C4⋊C4—1181no—
275C2×C4⋊C4D23612yes—
276C2×C22⋊C4—1182no—
277C2×C22⋊C4—1182no—
278C2×C22⋊C4—1181no—
279C2×C42—1181no—
280C2×C42C22×D5911yescharacteristic
281#106—2364no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286#103—2362no—
287#102—2362no—
288C4×C8—592no—
289C4×C8—1181no—
290#95—1182no—
291C24—1181no—
292C2×Q8—592no—
293C2×Q8—1181no—
294C2×Q8—1181no—
295C2×Q8—1181no—
296C2×Q8—1181no—
297C2×Q8—1181no—
298C2×D4—592no—
299C2×D4—1181no—
300C2×D4—1181no—
301C2×D4—1181no—
302C2×D4—1181no—
303C2×D4—1181no—
304C22×C4—22no—
305C22×C4—1181no—
306C22×C4—1181no—
307C22×C4—1181no—
308C22×C4—2361no—
309C22×C4—2361no—
310C22×C4—2361no—
311C22×C4—2361no—
312C22×C4—2361no—
313C22×C4—2361no—
314C22×C4—2361no—
315C22×C4C2×D23611yescharacteristic
316C22×C4D4×D5911yescharacteristic
317C22×C4D4×D5911yescharacteristic
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—1182no—
325C2×C8—1182no—
326C2×C8—1182no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—1181no—
333C4⋊C4—1181no—
334C4⋊C4—1181no—
335C4⋊C4—1181no—
336C4⋊C4—2362no—
337C4⋊C4—2364no—
338C4⋊C4—2361no—
339C4⋊C4—2361no—
340C4⋊C4—2361no—
341C4⋊C4—2361no—
342C4⋊C4—2361no—
343C4⋊C4—2361no—
344C22⋊C4—4722no—
345C22⋊C4—2364no—
346C22⋊C4—2361no—
347C22⋊C4—2361no—
348C42—2361no—
349C42—2361no—
350C42#1174568511yescharacteristic
351C42#1174568511yescharacteristic
352C42D4×D5911yescharacteristic
353C42#1174568911yescharacteristic
354C23—1182no—
355C23—2361no—
356C23—2361no—
357C23—2361no—
358C23—2361no—
359C23—2361no—
360C23—2361no—
361C23#1427369711yescharacteristic
362Q8—1182no—
363Q8—1182no—
364Q8—2361no—
365Q8—2361no—
366D4—1182no—
367D4—1182no—
368D4—2361no—
369D4—2361no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—1182no—
376C2×C4—4721no—
377C2×C4—4721no—
378C2×C4—4721no—
379C2×C4—4721no—
380C2×C4—4721no—
381C2×C4—4721no—
382C2×C4—4721no—
383C2×C4—2361no—
384C2×C4—2361no—
385C2×C4—2361no—
386C2×C4—2361no—
387C2×C4—2361no—
388C2×C4—2361no—
389C2×C4—2361no—
390C2×C4—2361no—
391C2×C4#1427370011yescharacteristic
392C2×C4#1427370011yescharacteristic
393C2×C4#1427370211yescharacteristic
394C2×C4#1427371211yescharacteristic
395C2×C4#1427371211yescharacteristic
396C2×C4#1427371511yescharacteristic
397C2×C4SD16×D5911yescharacteristic
398C2×C4SD16×D5911yescharacteristic
399C2×C4#1427374611yescharacteristic
400C2×C4#1427375011yescharacteristic
401C2×C4#1427375111yescharacteristic
402C2×C4#1427375411yescharacteristic
403C2×C4#1427375611yescharacteristic
404C2×C4#1427375911yescharacteristic
405C8—81no—
406C8—81no—
407C8—1184no—
408C22—4721no—
409C22—4721no—
410C22—4721no—
411C22—4721no—
412C22—2362no—
413C22—2362no—
414C22—2362no—
415C22#1683732011yescharacteristic
416C22#1683754211yescharacteristic
417C22#1683755011yescharacteristic
418C22#1683755411yescharacteristic
419C22#1683756511yescharacteristic
420C22#1683757211yescharacteristic
421C22#1683758711yescharacteristic
422C4—21no—
423C4—21no—
424C4—82no—
425C4—9441no—
426C4—4721no—
427C4—4721no—
428C4—2362no—
429C4#1683763011yescharacteristic
430C4#1683763411yescharacteristic
431C4#1683765411yescharacteristic
432C4#1683765911yescharacteristic
433C4#1683772211yescharacteristic
434C4#1683772911yescharacteristic
435C4#1683773411yescharacteristic
436C4#1683774511yescharacteristic
437C2—4722no—
438C2#2142316911yescharacteristic
439C2#2142322411yescharacteristic
440C2#2142336011yescharacteristic
441C2#2142336711yescharacteristic
442C2#2142528811yescharacteristic
443C2#2142529511yescharacteristic
444C2#2142532111yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1296C2
socleC23×C59#120
prime radicalC22×D236D4
hypercenter#1296D59
hypocenterC59#10435
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21424252C2semidirect
3. #21424102C2semidirect
5. C2×#16837132C2semidirect
7. C59×#1296C2semidirect
221. #1296D59semidirect
249. C59#10435semidirect

Maximal subgroups

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

subgroupindex
#214290192
#214242522
#214241022
#214240972
C2×#168371322
C2×#168371292
C59×#12962
#1043559