Finite Group Databasebeta

← #28492479

Subgroups — #28492479

Order 15104.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837597C211yesmaximal, characteristic
2#21424901C211yesmaximal, characteristic, complemented
3#21424891C211yesmaximal, characteristic, complemented
4C2×#16837154C211yesmaximal, characteristic, complemented
5C2×#16837145C211yesmaximal, characteristic, complemented
6#21421979C211yesmaximal, characteristic, complemented
7C59×#1802C211yesmaximal, characteristic, complemented
8C22×#11745669—21no—
9C2×#14273724C2211yescharacteristic
10#16837597—22no—
11#16837597—22no—
12C2×C4⋊(C59⋊C8)C2211yescharacteristic
13C2×C4⋊(C59⋊C8)C2211yescharacteristic
14C2×#14273647—21no—
15C2×#14273647—21no—
16C2×#14273647—21no—
17C2×C22⋊(C59⋊C8)—21no—
18C2×C22⋊(C59⋊C8)—21no—
19C2×C4×C59⋊C8C2211yescharacteristic
20#16837154—22no—
21#16837145—22no—
22C2×C4×D4×C59C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C2×#102×C59—21no—
25C59×#384C2211yescharacteristic
26C59×#340—21no—
27C22×D236—21no—
28C22×D236—21no—
29C22×D236—21no—
30C2×#11745669—24no—
31C2×#11745669—42no—
32C2×#11745669—42no—
33C22×C59⋊C8—21no—
34C22×C59⋊C8—21no—
35C22×C59⋊C8D411yescharacteristic
36C22×C59⋊C8D411yescharacteristic
37#14273724—21no—
38#14273724—21no—
39#14273724—21no—
40#14273724D412yes—
41C4⋊(C59⋊C8)—21no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)—21no—
44C4⋊(C59⋊C8)D412yes—
45#14273647—24no—
46#14273647—42no—
47#14273647—42no—
48C22⋊(C59⋊C8)—42no—
49C22⋊(C59⋊C8)—42no—
50C4×C59⋊C8—21no—
51C4×C59⋊C8—21no—
52C22×D4×C59D411yescharacteristic
53C23×C4×C59—21no—
54C22×C8×C59—21no—
55C4×D4×C59—21no—
56C4×D4×C59—21no—
57C4×D4×C59—21no—
58C4×D4×C59—21no—
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59—21no—
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59D411yescharacteristic
63C2×C22⋊C4×C59—21no—
64C2×C42×C59C2311yescharacteristic
65C4⋊C8×C59—21no—
66C4⋊C8×C59—21no—
67#102×C59—42no—
68C24×C59—21no—
69C23×D59—41no—
70C2×D4×C59—21no—
71C2×D4×C59—21no—
72C2×D4×C59—21no—
73C2×D4×C59—21no—
74C2×D4×C59—21no—
75C2×D4×C59D812yes—
76C22×C4×C59—21no—
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—41no—
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59C2×D411yescharacteristic
86C22×C4×C59#4111yescharacteristic
87C2×D236—22no—
88C2×D236—22no—
89C2×D236—22no—
90C2×D236—41no—
91C2×D236—41no—
92C2×D236—41no—
93C2×D236—41no—
94C2×D236—41no—
95C2×D236—41no—
96C2×D236—41no—
97C2×D236—41no—
98C2×D236—41no—
99C2×D236—41no—
100C2×D236—41no—
101C2×D236—81no—
102C2×D236—81no—
103C2×C8×C59—41no—
104C2×C8×C59—41no—
105C2×C8×C59—41no—
106C4⋊C4×C59—21no—
107C4⋊C4×C59—21no—
108C4⋊C4×C59—41no—
109C4⋊C4×C59—41no—
110C4⋊C4×C59—41no—
111C4⋊C4×C59—41no—
112C4⋊C4×C59—81no—
113C22⋊C4×C59—41no—
114C22⋊C4×C59—41no—
115C42×C59C2×D411yescharacteristic
116C42×C59C2×D411yescharacteristic
117C42×C59#4111yescharacteristic
118C42×C59#4111yescharacteristic
119#11745669—48no—
120C2×C59⋊C8—21no—
121C2×C59⋊C8—21no—
122C2×C59⋊C8—22no—
123C2×C59⋊C8—21no—
124C2×C59⋊C8—21no—
125C2×C59⋊C8—21no—
126C2×C59⋊C8—41no—
127C2×C59⋊C8—41no—
128C2×C59⋊C8—41no—
129C2×C59⋊C8—41no—
130C2×C59⋊C8—41no—
131C2×C59⋊C8D812yescomplemented
132C23×C59—22no—
133C23×C59—41no—
134C23×C59—41no—
135C23×C59—41no—
136C23×C59—41no—
137C23×C59—41no—
138C23×C59—41no—
139C23×C59#12111yescharacteristic
140C22×D59—42no—
141C22×D59—81no—
142C22×D59—81no—
143C22×D59—81no—
144C22×D59—81no—
145C22×D59—81no—
146C22×D59—81no—
147D4×C59—22no—
148D4×C59—22no—
149D4×C59—41no—
150D4×C59—41no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—41no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—81no—
157C2×C4×C59—81no—
158C2×C4×C59—81no—
159C2×C4×C59—81no—
160C2×C4×C59—81no—
161C2×C4×C59—81no—
162C2×C4×C59—81no—
163C2×C4×C59#12011yescharacteristic
164C2×C4×C59#12111yescharacteristic
165C2×C4×C59#12111yescharacteristic
166C2×C4×C59#12311yescharacteristic
167C2×C4×C59#12311yescharacteristic
168C2×C4×C59#12411yescharacteristic
169C2×C4×C59C2×D811yescharacteristic
170C2×C4×C59C2×D811yescharacteristic
171C2×C4×C59#13511yescharacteristic
172C2×C4×C59#13511yescharacteristic
173C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C59#13711yescharacteristic
177D236—42no—
178D236—42no—
179D236—42no—
180D236—42no—
181D236—82no—
182D236—82no—
183D236—81no—
184D236—81no—
185D236—81no—
186D236—81no—
187C8×C59—81no—
188C59⋊C8—22no—
189C59⋊C8—42no—
190C59⋊C8—41no—
191C59⋊C8—81no—
192#10472—591nomaximal, Sylow
193C22×C59—42no—
194C22×C59—42no—
195C22×C59—42no—
196C22×C59—81no—
197C22×C59—81no—
198C22×C59—81no—
199C22×C59—81no—
200C22×C59#39411yescharacteristic
201C22×C59#45911yescharacteristic
202C22×C59#46311yescharacteristic
203C22×C59#46611yescharacteristic
204C22×C59#46811yescharacteristic
205C22×C59#47111yescharacteristic
206C22×C59#47211yescharacteristic
207C2×D59—82no—
208C2×D59—82no—
209C2×D59—82no—
210C2×D59—161no—
211C2×D59—161no—
212C2×D59—161no—
213C2×D59—161no—
214C4×C59—21no—
215C4×C59—21no—
216C4×C59—81no—
217C4×C59—161no—
218C4×C59#44711yescharacteristic
219C4×C59#45211yescharacteristic
220C4×C59#45911yescharacteristic
221C4×C59#46311yescharacteristic
222C4×C59#46611yescharacteristic
223C4×C59#46911yescharacteristic
224C4×C59#48011yescharacteristic
225C4×C59#48211yescharacteristic
226C2×#459—591no—
227#1957—591no—
228#1954—591no—
229#1802D5911yescharacteristic, complemented
230C2×#335—591no—
231C2×#331—591no—
232#1296—591no—
233C2×C59—82no—
234C2×C59#166711yescharacteristic
235C2×C59#168111yescharacteristic
236C2×C59#168511yescharacteristic
237C2×C59#169711yescharacteristic
238C2×C59#203311yescharacteristic
239C2×C59#205111yescharacteristic
240C2×C59#205411yescharacteristic
241D59—162no—
242C22×D8—1181no—
243C2×#127—591no—
244C2×C4×D4C2×D5911yescharacteristic
245#459—1182no—
246#459—1182no—
247C2×C4⋊C8—591no—
248C2×C4⋊C8—591no—
249C2×C4⋊C8C2×D5911yescharacteristic
250C2×#102—21no—
251C2×#102—1181no—
252C2×#102—1181no—
253C2×#102—1181no—
254C2×C22⋊C8—1181no—
255C2×C22⋊C8—1181no—
256C2×C4×C8—591no—
257#384C2×D5911yescharacteristic
258#340—21no—
259#335—1182no—
260#331—1182no—
261C59#1047211yescharacteristic, complemented, Sylow
262C22×D4—1181no—
263C22×D4—1181no—
264C22×D4—1181no—
265C22×D4C22⋊D5911yescharacteristic
266C23×C4—21no—
267C2×D8—1184no—
268C2×D8—2362no—
269C2×D8—2362no—
270C22×C8—21no—
271C22×C8—591no—
272C22×C8—591no—
273C22×C8—1181no—
274C22×C8—1181no—
275#127—592no—
276#127—1181no—
277#127—1181no—
278#127—1181no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4C22⋊D5911yescharacteristic
287C2×C22⋊C4—21no—
288C2×C42C22×D5911yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—592no—
292C4⋊C8—1181no—
293C4⋊C8—1181no—
294C4⋊C8—1181no—
295#102—42no—
296#102—1184no—
297#102—2362no—
298#102—2362no—
299C22⋊C8—2362no—
300C22⋊C8—2362no—
301C4×C8—1181no—
302C4×C8—1181no—
303C24—21no—
304C24—2361no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—1182no—
311C2×D4—1182no—
312C2×D4—1182no—
313C2×D4—4721no—
314C2×D4—4721no—
315C2×D4—2361no—
316C2×D4—2361no—
317C2×D4—2361no—
318C2×D4—2361no—
319C2×D4—2361no—
320C2×D4—2361no—
321C2×D4—2361no—
322C2×D4—2361no—
323C2×D4—2361no—
324C2×D4—2361no—
325C2×D4—2361no—
326C2×D4#1174566912yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4D4×D5911yescharacteristic
336C22×C4#1174568711yescharacteristic
337C22×C4C2×C22⋊D5911yescharacteristic
338D8—2368no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—592no—
343C2×C8—1181no—
344C2×C8—1181no—
345C2×C8—1182no—
346C2×C8—1181no—
347C2×C8—1181no—
348C2×C8—1181no—
349C2×C8—2361no—
350C2×C8—2361no—
351C2×C8—2361no—
352C2×C8—2361no—
353C2×C8—2361no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—81no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42#1174568511yescharacteristic
364C42#1174568511yescharacteristic
365C42D4×D5911yescharacteristic
366C42D4×D5911yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—4721no—
375C23—4721no—
376C23—4721no—
377C23—4721no—
378C23—4721no—
379C23—4721no—
380C23—2362no—
381C23#1427369911yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—41no—
386D4—4722no—
387D4—4722no—
388D4—4721no—
389D4—4721no—
390D4—4721no—
391D4—4721no—
392D4—2362no—
393D4—2362no—
394D4—2362no—
395D4—2362no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4#1427369511yescharacteristic
409C2×C4#1427370011yescharacteristic
410C2×C4#1427370011yescharacteristic
411C2×C4#1427370911yescharacteristic
412C2×C4#1427371011yescharacteristic
413C2×C4#1427371311yescharacteristic
414C2×C4D8×D5911yescharacteristic
415C2×C4C2×#1174566911yescharacteristic
416C2×C4#1427374711yescharacteristic
417C2×C4#1427374811yescharacteristic
418C2×C4#1427375111yescharacteristic
419C2×C4#1427375211yescharacteristic
420C2×C4#1427375411yescharacteristic
421C2×C4#1427375811yescharacteristic
422C8—81no—
423C8—1182no—
424C8—4721no—
425C8—2361no—
426C8—2362no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—9441no—
435C22—9441no—
436C22—9441no—
437C22—9441no—
438C22—4722no—
439C22—4722no—
440C22—4722no—
441C22#1683731711yescharacteristic
442C22#1683759511yescharacteristic
443C22#1683761911yescharacteristic
444C22#1683763611yescharacteristic
445C22#1683765011yescharacteristic
446C22#1683766711yescharacteristic
447C22#1683767011yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—161no—
452C4#1683753511yescharacteristic
453C4#1683756211yescharacteristic
454C4#1683759611yescharacteristic
455C4#1683761611yescharacteristic
456C4#1683763711yescharacteristic
457C4#1683765411yescharacteristic
458C4#1683771511yescharacteristic
459C4#1683772611yescharacteristic
460C2—82no—
461C2—9442no—
462C2#2142344911yescharacteristic
463C2#2142353511yescharacteristic
464C2#2142356311yescharacteristic
465C2#2142363111yescharacteristic
466C2#2142527811yescharacteristic
467C2#2142538611yescharacteristic
468C2#2142540511yescharacteristic
subgroupG/H
centerC23#14273699
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1802C2
socleC23×C59#121
prime radicalC2×#16837597C2
hypercenter#1802D59
hypocenterC59#10472
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #21424901C2semidirect
3. #21424891C2semidirect
4. C2×#16837154C2semidirect
5. C2×#16837145C2semidirect
6. #21421979C2semidirect
7. C59×#1802C2semidirect
131. C2×C59⋊C8D8semidirect
229. #1802D59semidirect
261. C59#10472semidirect

Maximal subgroups

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

subgroupindex
C2×#168375972
#214249012
#214248912
C2×#168371542
C2×#168371452
#214219792
C59×#18022
#1047259