Finite Group Databasebeta

← #28485115

Subgroups — #28485115

Order 15104.

552 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837732C211yesmaximal, characteristic
2#21425081C211yesmaximal, characteristic
3#21424182C211yesmaximal, characteristic
4#21422667C211yesmaximal, characteristic
5#21421963C211yesmaximal, characteristic
6#21421944C211yesmaximal, characteristic
7C59×#2344C211yesmaximal, characteristic
8C2×#14273706C2211yescharacteristic
9#16837732—22no—
10#16837732—21no—
11#16837732—21no—
12C2×#14273658C412yescomplemented
13C2×#14273650C412yescomplemented
14C2×C22⋊(C59⋊C8)C2211yescharacteristic
15C2×C22⋊(C59⋊C8)C2211yescharacteristic
16#16837262C2211yescharacteristic
17#16837168—21no—
18#16837168—21no—
19#16837164—22no—
20#16837138—22no—
21C2×#117×C59—21no—
22C22×C4⋊C4×C59C2211yescharacteristic
23C59×#389—21no—
24C59×#387—22no—
25C59×#381—21no—
26C59×#380C2211yescharacteristic
27C4×C4⋊C4×C59—21no—
28C4×C22⋊C4×C59C2211yescharacteristic
29C22×Dic118C2×C411yescharacteristic
30C22×C59⋊C8—21no—
31C22×C59⋊C8C2×C412yes—
32#14273706—21no—
33#14273706—21no—
34#14273706—21no—
35#14273706—21no—
36C2×C4⋊Dic59—21no—
37C2×C4⋊Dic59C2×C411yescharacteristic
38C2×Dic59⋊C4—21no—
39C2×C22⋊Dic59—21no—
40C2×C22⋊Dic59—21no—
41#14273658—22no—
42#14273658—22no—
43#14273650—22no—
44#14273650—22no—
45C22⋊(C59⋊C8)—21no—
46C22⋊(C59⋊C8)—21no—
47C22⋊(C59⋊C8)—21no—
48C22⋊(C59⋊C8)—21no—
49C59⋊#95—21no—
50C23×C4×C59—21no—
51C23×C4×C59C2311yescharacteristic
52#117×C59—42no—
53#117×C59—42no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59—22no—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59C2×C412yes—
60C2×C4⋊C4×C59D412yes—
61C2×C4⋊C4×C59D411yescharacteristic
62C2×C4⋊C4×C59D411yescharacteristic
63C2×C22⋊C4×C59—21no—
64C2×C22⋊C4×C59D411yescharacteristic
65C2×C22⋊C4×C59D411yescharacteristic
66C2×C42×C59—22no—
67C2×C42×C59—21no—
68#95×C59—22no—
69#95×C59—22no—
70#95×C59—21no—
71#95×C59D412yes—
72C24×C59C2×D411yescharacteristic
73C22×C4×C59—22no—
74C22×C4×C59—21no—
75C22×C4×C59—21no—
76C22×C4×C59—21no—
77C22×C4×C59—22no—
78C22×C4×C59—21no—
79C22×C4×C59—22no—
80C22×C4×C59—42no—
81C22×C4×C59—41no—
82C22×C4×C59—41no—
83C22×C4×C59—41no—
84C22×C4×C59—41no—
85C22×C4×C59C22×C411yescharacteristic
86C22×C4×C59C2×D411yescharacteristic
87C22×C4×C59C2×D411yescharacteristic
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59#4111yescharacteristic
90C22×C4×C59#4111yescharacteristic
91C22×Dic59—21no—
92C22×Dic59—21no—
93C22×Dic59—41no—
94C2×Dic118—21no—
95C2×Dic118—21no—
96C2×Dic118—42no—
97C4⋊C4×C59—22no—
98C4⋊C4×C59—22no—
99C4⋊C4×C59—21no—
100C4⋊C4×C59—21no—
101C4⋊C4×C59—42no—
102C4⋊C4×C59—44no—
103C4⋊C4×C59C22⋊C412yes—
104C4⋊C4×C59C22⋊C412yes—
105C22⋊C4×C59—21no—
106C22⋊C4×C59—21no—
107C22⋊C4×C59—21no—
108C22⋊C4×C59—41no—
109C22⋊C4×C59—41no—
110C22⋊C4×C59SD1612yes—
111C42×C59—42no—
112C42×C59—44no—
113C22⋊Dic59—41no—
114C22⋊Dic59—41no—
115C22⋊Dic59—41no—
116C22⋊Dic59—41no—
117C4⋊Dic59—21no—
118C4⋊Dic59—21no—
119C4⋊Dic59—42no—
120Dic59⋊C4—41no—
121Dic59⋊C4—41no—
122C2×C59⋊C8—22no—
123C2×C59⋊C8—42no—
124C2×C59⋊C8—42no—
125C2×C59⋊C8—41no—
126C23×C59—41no—
127C23×C59—41no—
128C23×C59C4×D411yescharacteristic
129C23×C59#12011yescharacteristic
130C23×C59#12111yescharacteristic
131C23×C59C2×SD1611yescharacteristic
132C23×C59#13511yescharacteristic
133C23×C59AGL(1,ℤ/8)11yescharacteristic
134C23×C59#13711yescharacteristic
135C2×C4×C59—22no—
136C2×C4×C59—22no—
137C2×C4×C59—22no—
138C2×C4×C59—22no—
139C2×C4×C59—22no—
140C2×C4×C59—22no—
141C2×C4×C59—41no—
142C2×C4×C59—41no—
143C2×C4×C59—41no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—42no—
147C2×C4×C59—42no—
148C2×C4×C59—41no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—42no—
153C2×C4×C59—42no—
154C2×C4×C59—41no—
155C2×C4×C59—42no—
156C2×C4×C59—41no—
157C2×C4×C59—42no—
158C2×C4×C59—42no—
159C2×C4×C59—41no—
160C2×C4×C59C2×C22⋊C411yescharacteristic
161C2×C4×C59C4×D411yescharacteristic
162C2×C4×C59#12111yescharacteristic
163C2×C4×C59#12311yescharacteristic
164C2×Dic59—41no—
165C2×Dic59—41no—
166C2×Dic59—81no—
167C2×Dic59—81no—
168C2×Dic59—81no—
169C2×Dic59—81no—
170C2×Dic59—81no—
171Dic118—42no—
172Dic118—81no—
173C59⋊C8—42no—
174C59⋊C8—81no—
175#9256—591nomaximal, Sylow
176C22×C59—21no—
177C22×C59—21no—
178C22×C59—21no—
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—21no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59#38611yescharacteristic
187C22×C59C4×SD1611yescharacteristic
188C22×C59#44011yescharacteristic
189C22×C59#45011yescharacteristic
190C22×C59#45211yescharacteristic
191C22×C59#46111yescharacteristic
192C22×C59#46311yescharacteristic
193C4×C59—21no—
194C4×C59—21no—
195C4×C59—21no—
196C4×C59—42no—
197C4×C59—42no—
198C4×C59—42no—
199C4×C59—82no—
200C4×C59—81no—
201C4×C59#41012yes—
202Dic59—81no—
203Dic59—81no—
204Dic59—161no—
205C2×#483—591no—
206#2344D5911yescharacteristic
207#1996—591no—
208#1823—591no—
209#1520—591no—
210#1289—591no—
211#1282—591no—
212C2×C59—21no—
213C2×C59—21no—
214C2×C59—21no—
215C2×C59—21no—
216C2×C59—21no—
217C2×C59—21no—
218C2×C59#187711yescharacteristic
219C2×C59#189911yescharacteristic
220C2×C59#190511yescharacteristic
221C2×C22⋊Q8—591no—
222C2×#117—21no—
223C22×C4⋊C4C2×D5911yescharacteristic
224#483—1182no—
225#483—1181no—
226#483—1181no—
227C2×#106—592no—
228C2×#103—592no—
229C2×C22⋊C8—591no—
230C2×C22⋊C8—591no—
231#389—21no—
232#387—22no—
233#381—21no—
234#380—591no—
235#380C2×D5911yescharacteristic
236C4×C4⋊C4—21no—
237C4×C22⋊C4C2×D5911yescharacteristic
238#342—1181no—
239#342—1181no—
240#340—1182no—
241#328—1182no—
242C59#925611yescharacteristic, complemented, Sylow
243C22×Q8—591no—
244C23×C4—21no—
245C23×C4C22×D5911yescharacteristic
246C22×C8—592no—
247C22×C8—1181no—
248C22⋊Q8—1181no—
249C22⋊Q8—1181no—
250C22⋊Q8—1181no—
251C22⋊Q8—1181no—
252#117—42no—
253#117—42no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—591no—
260C2×C4⋊C4—1181no—
261C2×C4⋊C4—1181no—
262C2×C4⋊C4C4×D5912yes—
263C2×C4⋊C4D23612yes—
264C2×C4⋊C4C22⋊D5911yescharacteristic
265C2×C4⋊C4C22⋊D5911yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—1181no—
268C2×C22⋊C4—1181no—
269C2×C22⋊C4C22⋊D5911yescharacteristic
270C2×C22⋊C4C22⋊D5911yescharacteristic
271C2×C42—22no—
272C2×C42—21no—
273#106—1182no—
274#106—1182no—
275#103—1182no—
276#103—1182no—
277C22⋊C8—1181no—
278C22⋊C8—1181no—
279C22⋊C8—1181no—
280C22⋊C8—1181no—
281#95—22no—
282#95—22no—
283#95—21no—
284#95—1181no—
285#95C22⋊D5912yes—
286C24C2×C22⋊D5911yescharacteristic
287C2×Q8—1181no—
288C2×Q8—1181no—
289C2×Q8—2362no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—42no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—1181no—
303C22×C4—1181no—
304C22×C4—2361no—
305C22×C4C2×C4×D5911yescharacteristic
306C22×C4C2×D23611yescharacteristic
307C22×C4#1174568511yescharacteristic
308C22×C4#1174568511yescharacteristic
309C22×C4C2×C22⋊D5911yescharacteristic
310C22×C4C2×C22⋊D5911yescharacteristic
311C2×C8—1182no—
312C2×C8—2362no—
313C2×C8—2361no—
314C2×C8—2362no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—44no—
320C4⋊C4—42no—
321C4⋊C4—1181no—
322C4⋊C4—1181no—
323C4⋊C4—2362no—
324C4⋊C4—2361no—
325C4⋊C4—2361no—
326C4⋊C4(C2×D59)⋊C412yes—
327C4⋊C4(C2×D59)⋊C412yes—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—2361no—
334C22⋊C4—2361no—
335C22⋊C4—2361no—
336C22⋊C4—2361no—
337C22⋊C4#1174567012yes—
338C42—44no—
339C42—42no—
340C23—41no—
341C23—41no—
342C23C4×C22⋊D5911yescharacteristic
343C23#1427369611yescharacteristic
344C23#1427370111yescharacteristic
345C23C2×#1174567011yescharacteristic
346C23#1427374711yescharacteristic
347C23#1427375311yescharacteristic
348C23#1427375711yescharacteristic
349Q8—4721no—
350Q8—2362no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—4721no—
377C2×C4—4721no—
378C2×C4—4721no—
379C2×C4—4721no—
380C2×C4—4721no—
381C2×C4—2361no—
382C2×C4—2361no—
383C2×C4C2×(C2×D59)⋊C411yescharacteristic
384C2×C4C4×C22⋊D5911yescharacteristic
385C2×C4#1427370111yescharacteristic
386C2×C4#1427371011yescharacteristic
387C8—4721no—
388C8—2362no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22#1683728111yescharacteristic
400C22C4×#1174567011yescharacteristic
401C22#1683750211yescharacteristic
402C22#1683755311yescharacteristic
403C22#1683756411yescharacteristic
404C22#1683760711yescharacteristic
405C22#1683761711yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—42no—
410C4—42no—
411C4—42no—
412C4—82no—
413C4—81no—
414C4—9441no—
415C4—4721no—
416C4—4721no—
417C4#1683737512yes—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2#2142443011yescharacteristic
425C2#2142455411yescharacteristic
426C2#2142459011yescharacteristic
subgroupG/H
centerC22#16837281
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#2344C2
socleC22×C59#386
prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenter#2344D59
hypocenterC59#9256
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
12. C2×#14273658C4semidirect
13. C2×#14273650C4semidirect
242. C59#9256semidirect

Maximal subgroups

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

subgroupindex
C2×#168377322
#214250812
#214241822
#214226672
#214219632
#214219442
C59×#23442
#925659