Finite Group Databasebeta

← #28492485

Subgroups — #28492485

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×#16837594C211yesmaximal, characteristic
2#21424890C211yesmaximal, characteristic, complemented
3#21424093C211yesmaximal, characteristic, complemented
4C2×#16837153C211yesmaximal, characteristic, complemented
5C2×#16837146C211yesmaximal, characteristic, complemented
6#21421979C211yesmaximal, characteristic, complemented
7C59×#1957C211yesmaximal, characteristic, complemented
8C22×#11745669—21no—
9C2×C4×D236C2211yescharacteristic
10#16837594—22no—
11#16837594—22no—
12C2×C4⋊(C59⋊C8)C2211yescharacteristic
13C2×C4⋊(C59⋊C8)C2211yescharacteristic
14C2×C4⋊(C59⋊C8)C2211yescharacteristic
15C2×#14273648—21no—
16C2×#14273647—21no—
17C2×(C2×D59)⋊C8—21no—
18C2×(C2×D59)⋊C8—21no—
19#16837164—21no—
20#16837153—22no—
21#16837146—22no—
22C2×#127×C59C2211yescharacteristic
23C2×#102×C59—21no—
24C2×#102×C59—21no—
25C2×C4×C8×C59C2211yescharacteristic
26C59×#384C2211yescharacteristic
27C22×D236D411yescharacteristic
28C22×C4×D59—21no—
29C2×#11745669—24no—
30C2×#11745669—42no—
31C2×#11745669—42no—
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34C22×C59⋊C8—21no—
35C4×D236—21no—
36C4×D236—21no—
37C4×D236—21no—
38C4×D236—21no—
39C2×C4⋊Dic59D411yescharacteristic
40C2×(C2×D59)⋊C4—21no—
41C4⋊(C59⋊C8)—21no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)—21no—
44C4⋊(C59⋊C8)—21no—
45C4⋊(C59⋊C8)—21no—
46C4⋊(C59⋊C8)D412yes—
47#14273648—24no—
48#14273647—42no—
49(C2×D59)⋊C8—42no—
50(C2×D59)⋊C8—42no—
51C22×D4×C59—21no—
52C22×D4×C59—21no—
53C22×D4×C59—21no—
54C22×C8×C59D411yescharacteristic
55C22×C8×C59D411yescharacteristic
56#127×C59—21no—
57#127×C59—21no—
58#127×C59—21no—
59#127×C59D412yes—
60C2×C4⋊C4×C59—21no—
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59—21no—
63C2×C42×C59C2311yescharacteristic
64#102×C59—42no—
65#102×C59—42no—
66C4×C8×C59—21no—
67C4×C8×C59—21no—
68C24×C59—41no—
69C23×D59—21no—
70C2×D4×C59—22no—
71C2×D4×C59—22no—
72C2×D4×C59—22no—
73C2×D4×C59—41no—
74C2×D4×C59—41no—
75C2×D4×C59—41no—
76C2×D4×C59—41no—
77C2×D4×C59—41no—
78C2×D4×C59—41no—
79C2×D4×C59—41no—
80C2×D4×C59—41no—
81C2×D4×C59—41no—
82C2×D4×C59—41no—
83C2×D4×C59—41no—
84C2×D4×C59—81no—
85C2×D4×C59—81no—
86C22×C4×C59—41no—
87C22×C4×C59C2×D411yescharacteristic
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59#4111yescharacteristic
90C22×Dic59—21no—
91C2×D236—21no—
92C2×D236—21no—
93C2×D236—21no—
94C2×D236—21no—
95C2×D236—21no—
96C2×D236SD1612yes—
97C2×C4×D59—41no—
98C2×C4×D59—41no—
99C2×C4×D59—41no—
100C2×C4×D59—41no—
101C2×C4×D59—41no—
102C2×C4×D59—41no—
103C2×C8×C59—21no—
104C2×C8×C59—21no—
105C2×C8×C59—21no—
106C2×C8×C59—21no—
107C2×C8×C59—21no—
108C2×C8×C59D812yescomplemented
109C4⋊C4×C59—41no—
110C4⋊C4×C59—41no—
111C4⋊C4×C59—41no—
112C4⋊C4×C59—41no—
113C4⋊C4×C59—81no—
114C42×C59C2×D411yescharacteristic
115C42×C59C2×D411yescharacteristic
116C42×C59#4111yescharacteristic
117C42×C59#4111yescharacteristic
118#11745669—48no—
119(C2×D59)⋊C4—41no—
120(C2×D59)⋊C4—41no—
121C4⋊Dic59—21no—
122C4⋊Dic59—21no—
123C2×C59⋊C8—22no—
124C2×C59⋊C8—41no—
125C2×C59⋊C8—41no—
126C2×C59⋊C8—41no—
127C2×C59⋊C8—41no—
128C2×C59⋊C8—41no—
129C2×C59⋊C8—41no—
130C2×C59⋊C8—41no—
131C2×C59⋊C8—41no—
132C23×C59—42no—
133C23×C59—81no—
134C23×C59—81no—
135C23×C59—81no—
136C23×C59—81no—
137C23×C59—81no—
138C23×C59—81no—
139C23×C59#12111yescharacteristic
140C22×D59—22no—
141C22×D59—41no—
142C22×D59—41no—
143C22×D59—41no—
144C22×D59—41no—
145C22×D59—41no—
146C22×D59—41no—
147D4×C59—42no—
148D4×C59—42no—
149D4×C59—42no—
150D4×C59—42no—
151D4×C59—82no—
152D4×C59—82no—
153D4×C59—81no—
154D4×C59—81no—
155D4×C59—81no—
156D4×C59—81no—
157C2×C4×C59—21no—
158C2×C4×C59—21no—
159C2×C4×C59—81no—
160C2×C4×C59—81no—
161C2×C4×C59—81no—
162C2×C4×C59#12011yescharacteristic
163C2×C4×C59#12111yescharacteristic
164C2×C4×C59#12111yescharacteristic
165C2×C4×C59#12311yescharacteristic
166C2×C4×C59#12311yescharacteristic
167C2×C4×C59#12411yescharacteristic
168C2×C4×C59C2×D811yescharacteristic
169C2×C4×C59C2×SD1611yescharacteristic
170C2×C4×C59#13511yescharacteristic
171C2×C4×C59#13511yescharacteristic
172C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
176C2×Dic59—41no—
177C2×Dic59—41no—
178C2×Dic59—41no—
179D236—22no—
180D236—22no—
181D236—41no—
182D236—41no—
183C4×D59—81no—
184C4×D59—81no—
185C4×D59—81no—
186C4×D59—81no—
187C8×C59—22no—
188C8×C59—41no—
189C59⋊C8—42no—
190C59⋊C8—81no—
191C59⋊C8—81no—
192#10473—591nomaximal, Sylow
193C22×C59—82no—
194C22×C59—82no—
195C22×C59—82no—
196C22×C59—161no—
197C22×C59—161no—
198C22×C59—161no—
199C22×C59—161no—
200C22×C59#39411yescharacteristic
201C22×C59#45911yescharacteristic
202C22×C59#46311yescharacteristic
203C22×C59#46511yescharacteristic
204C22×C59#46911yescharacteristic
205C22×C59#47111yescharacteristic
206C22×C59#47211yescharacteristic
207C2×D59—42no—
208C2×D59—42no—
209C2×D59—42no—
210C2×D59—81no—
211C2×D59—81no—
212C2×D59—81no—
213C2×D59—81no—
214C4×C59—21no—
215C4×C59—21no—
216C4×C59—161no—
217C4×C59#44911yescharacteristic
218C4×C59#45011yescharacteristic
219C4×C59#45911yescharacteristic
220C4×C59#46311yescharacteristic
221C4×C59#46611yescharacteristic
222C4×C59#46911yescharacteristic
223C4×C59#48111yescharacteristic
224C4×C59#48211yescharacteristic
225Dic59—81no—
226C2×#459—591no—
227#1957D5911yescharacteristic, complemented
228#1954—591no—
229#1802—591no—
230C2×#334—591no—
231C2×#331—591no—
232#1296—591no—
233C2×C59—162no—
234C2×C59#166511yescharacteristic
235C2×C59#167711yescharacteristic
236C2×C59#168711yescharacteristic
237C2×C59#170111yescharacteristic
238C2×C59#203411yescharacteristic
239C2×C59#205111yescharacteristic
240C2×C59#205411yescharacteristic
241D59—82no—
242C22×D8—1181no—
243C2×#127C2×D5911yescharacteristic
244C2×C4×D4—591no—
245#459—1182no—
246#459—1182no—
247C2×C4⋊C8—591no—
248C2×C4⋊C8—591no—
249C2×C4⋊C8—591no—
250C2×#102—21no—
251C2×#102—21no—
252C2×#102—1181no—
253C2×#102—1181no—
254C2×C22⋊C8—1181no—
255C2×C22⋊C8—1181no—
256C2×C4×C8C2×D5911yescharacteristic
257#384C2×D5911yescharacteristic
258#340—1181no—
259#334—1182no—
260#331—1182no—
261C59#1047311yescharacteristic, complemented, Sylow
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—591no—
266C23×C4—1181no—
267C2×D8—1184no—
268C2×D8—2362no—
269C2×D8—2362no—
270C22×C8—1181no—
271C22×C8—1181no—
272C22×C8—1181no—
273C22×C8C22⋊D5911yescharacteristic
274C22×C8C22⋊D5911yescharacteristic
275#127—21no—
276#127—21no—
277#127—21no—
278#127D23612yes—
279C4×D4—1181no—
280C4×D4—1181no—
281C4×D4—1181no—
282C4×D4—1181no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—591no—
287C2×C22⋊C4—1181no—
288C2×C42C22×D5911yescharacteristic
289C4⋊C8—592no—
290C4⋊C8—1181no—
291C4⋊C8—1181no—
292C4⋊C8—1181no—
293C4⋊C8—1181no—
294C4⋊C8—1181no—
295#102—42no—
296#102—42no—
297#102—1184no—
298#102—2362no—
299C22⋊C8—2362no—
300C22⋊C8—2362no—
301C4×C8—21no—
302C4×C8—21no—
303C24—41no—
304C24—1181no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—81no—
320C2×D4—81no—
321C2×D4—592no—
322C2×D4—1181no—
323C2×D4—1181no—
324C2×D4—1181no—
325C2×D4—1181no—
326C2×D4—1181no—
327C22×C4—41no—
328C22×C4—1181no—
329C22×C4—2361no—
330C22×C4—2361no—
331C22×C4—2361no—
332C22×C4—2361no—
333C22×C4—2361no—
334C22×C4—2361no—
335C22×C4D4×D5911yescharacteristic
336C22×C4#1174568711yescharacteristic
337C22×C4C2×C22⋊D5911yescharacteristic
338D8—2368no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—1182no—
345C2×C8—2361no—
346C2×C8—2361no—
347C2×C8—2361no—
348C2×C8—2361no—
349C2×C8—2361no—
350C2×C8—2361no—
351C2×C8—2361no—
352C2×C8—2361no—
353C2×C8#1174566912yescomplemented
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—81no—
359C4⋊C4—1181no—
360C4⋊C4—1181no—
361C22⋊C4—2361no—
362C22⋊C4—2361no—
363C42C2×D23611yescharacteristic
364C42#1174568511yescharacteristic
365C42D4×D5911yescharacteristic
366C42#1174568711yescharacteristic
367C23—42no—
368C23—81no—
369C23—81no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23—81no—
374C23—1182no—
375C23—2361no—
376C23—2361no—
377C23—2361no—
378C23—2361no—
379C23—2361no—
380C23—2361no—
381C23#1427369811yescharacteristic
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392D4—1182no—
393D4—1182no—
394D4—2361no—
395D4—2361no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—4721no—
402C2×C4—4721no—
403C2×C4—4721no—
404C2×C4—4721no—
405C2×C4—2361no—
406C2×C4—2361no—
407C2×C4—2361no—
408C2×C4#1427369711yescharacteristic
409C2×C4#1427369911yescharacteristic
410C2×C4#1427370111yescharacteristic
411C2×C4#1427370911yescharacteristic
412C2×C4#1427371111yescharacteristic
413C2×C4#1427371311yescharacteristic
414C2×C4C2×#1174566911yescharacteristic
415C2×C4SD16×D5911yescharacteristic
416C2×C4#1427374711yescharacteristic
417C2×C4#1427374811yescharacteristic
418C2×C4#1427375111yescharacteristic
419C2×C4#1427375111yescharacteristic
420C2×C4#1427375211yescharacteristic
421C2×C4#1427375311yescharacteristic
422C8—22no—
423C8—41no—
424C8—4721no—
425C8—4721no—
426C8—2362no—
427C22—82no—
428C22—82no—
429C22—82no—
430C22—161no—
431C22—161no—
432C22—161no—
433C22—161no—
434C22—4721no—
435C22—4721no—
436C22—4721no—
437C22—4721no—
438C22—2362no—
439C22—2362no—
440C22—2362no—
441C22#1683731811yescharacteristic
442C22#1683759411yescharacteristic
443C22#1683761411yescharacteristic
444C22#1683762811yescharacteristic
445C22#1683765211yescharacteristic
446C22#1683766211yescharacteristic
447C22#1683766911yescharacteristic
448C4—21no—
449C4—21no—
450C4—161no—
451C4—4721no—
452C4#1683754811yescharacteristic
453C4#1683755411yescharacteristic
454C4#1683759711yescharacteristic
455C4#1683761711yescharacteristic
456C4#1683763611yescharacteristic
457C4#1683765311yescharacteristic
458C4#1683771911yescharacteristic
459C4#1683772511yescharacteristic
460C2—162no—
461C2—4722no—
462C2#2142343411yescharacteristic
463C2#2142350211yescharacteristic
464C2#2142357211yescharacteristic
465C2#2142365411yescharacteristic
466C2#2142528411yescharacteristic
467C2#2142538911yescharacteristic
468C2#2142540611yescharacteristic
subgroupG/H
centerC23#14273698
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1957C2
socleC23×C59#121
prime radicalC2×#16837594C2
hypercenter#1957D59
hypocenterC59#10473
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #21424890C2semidirect
3. #21424093C2semidirect
4. C2×#16837153C2semidirect
5. C2×#16837146C2semidirect
6. #21421979C2semidirect
7. C59×#1957C2semidirect
108. C2×C8×C59D8semidirect
227. #1957D59semidirect
261. C59#10473semidirect
353. C2×C8#11745669semidirect

Maximal subgroups

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

subgroupindex
C2×#168375942
#214248902
#214240932
C2×#168371532
C2×#168371462
#214219792
C59×#19572
#1047359