Finite Group Databasebeta

← #30608430

Subgroups — #30608430

Order 15616.

344 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462119C211yesmaximal, characteristic, complemented
2#21462095C211yesmaximal, characteristic, complemented
3#21460967C211yesmaximal, characteristic, complemented
4#21460966C211yesmaximal, characteristic, complemented
5#21460946C211yesmaximal, characteristic, complemented
6#21460946C211yesmaximal, characteristic, complemented
7#21456862C211yesmaximal, characteristic
8#16840749—21no—
9D61⋊#99—21no—
10#16840671C2211yescharacteristic
11#16840671C2211yescharacteristic
12#16840670—21no—
13#16840669C2211yescharacteristic
14#16840669C2211yescharacteristic
15#16840666—21no—
16#16840366C411yescharacteristic, complemented
17#16840325C2211yescharacteristic
18#16840149C2211yescharacteristic
19#16840126C411yescharacteristic, complemented
20#16840117C2211yescharacteristic
21#16839975—21no—
22#16839955—21no—
23#16839904—21no—
24#16839894—21no—
25#16839821C411yescharacteristic, complemented
26C61×#493C411yescharacteristic, complemented
27C2×#11758217—41no—
28C2×C22⋊#6923—41no—
29#14519838—21no—
30#14519838—21no—
31#14519837—41no—
32#14519836—21no—
33#14519836—21no—
34#14519835—41no—
35C2×#11758224D411yescharacteristic
36C2×D4×D61D411yescharacteristic
37C2×#11758200—21no—
38C2×#11758199—21no—
39#14519773D411yescharacteristic
40#14519769C2×C411yescharacteristic, complemented
41#14519765C2311yescharacteristic
42#14519764D411yescharacteristic
43#14519758—41no—
44#14519749—41no—
45#14519749—41no—
46#14519748—21no—
47#14519745—41no—
48D4×Dic61—21no—
49#14519734C2×C411yescharacteristic
50#14519706—21no—
51#14519702—21no—
52#14519699—21no—
53#14519698—21no—
54#14519698—21no—
55#14519689—21no—
56#14519688C2×C411yescharacteristic, complemented
57C2×D8×C61—21no—
58C2×D8×C61—21no—
59#127×C61C2×C411yescharacteristic
60#127×C61C2×C411yescharacteristic, complemented
61C4×C8×C61C2×C411yescharacteristic, complemented
62C23×D61—21no—
63C22×#6923—81no—
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61C22⋊C411yescharacteristic
68C2×D4×C61C22⋊C411yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—41no—
73C22×Dic61—21no—
74C22×Dic61—41no—
75#11758224—81no—
76D4×D61—81no—
77C2×D244C2×D411yescharacteristic
78C2×C4×D61C22⋊C411yescharacteristic
79C2×Dic122C2×D411yescharacteristic
80C22⋊#6923—41no—
81C22⋊#6923—41no—
82C22⋊#6923—81no—
83#11758217—41no—
84#11758217—41no—
85#11758217—81no—
86C2×#92420—81no—
87D8×C61—81no—
88D8×C61—81no—
89C2×C8×C61—21no—
90C42×C61C22×C411yescharacteristic
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C22⋊Dic61—41no—
94#11758200—81no—
95#11758199—81no—
96#11758198—21no—
97#11758198—41no—
98C4⋊Dic61—21no—
99#11758196—21no—
100#11758196—41no—
101C4×Dic61C22⋊C411yescharacteristic
102C2×#92418—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—41no—
106C22×D61—21no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—161no—
110C22×D61#9911yescharacteristic
111C2×#6923—81no—
112C2×#6923—81no—
113C2×#6923—162no—
114D4×C61—41no—
115D4×C61—41no—
116D4×C61—41no—
117D4×C61—41no—
118D4×C61—161no—
119D4×C61—161no—
120C2×C4×C61—21no—
121C2×C4×C61C2×C22⋊C411yescharacteristic
122C22⋊D61—81no—
123C22⋊D61—81no—
124C22⋊D61—161no—
125C22⋊D61—161no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—161no—
132C2×Dic61#9911yescharacteristic
133D244—41no—
134C4×D61—41no—
135Dic122—41no—
136#92420—81no—
137#92420—81no—
138C8×C61—41no—
139#92418—41no—
140#13605—611nomaximal, Sylow
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—81no—
144C22×C61—81no—
145C22×C61—81no—
146C22×C61—81no—
147C22×C61—81no—
148C22×C61C2×#9911yescharacteristic
149C2×D61—21no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—82no—
153C2×D61—81no—
154C2×D61—161no—
155#6923—161no—
156#6923—161no—
157C4×C61—21no—
158C4×C61—41no—
159Dic61—21no—
160Dic61—41no—
161Dic61—41no—
162Dic61—81no—
163#3220—611no—
164#2134—611no—
165#2127—611no—
166#1414—611no—
167#1414—611no—
168#1406—611no—
169#1406—611no—
170C2×C61—21no—
171C2×C61—81no—
172C2×C61—81no—
173C2×C61—161no—
174C2×C61#212711yescharacteristic
175D61—41no—
176D61—81no—
177#540—611no—
178#535—611no—
179#496—611no—
180#493#692311yescharacteristic, complemented
181#490—611no—
182#488—611no—
183#463—1221no—
184#459—1221no—
185#449—1221no—
186#447—1221no—
187#433—611no—
188#413—1221no—
189C2×#99—1221no—
190#355—611no—
191#355—611no—
192#355—1221no—
193#354—611no—
194#354—611no—
195#353—1221no—
196C61#1360511yescharacteristic, complemented, Sylow
197C2×#41—611no—
198C22×D4—611no—
199C2×SD16—1221no—
200C2×D8—21no—
201C2×D8—21no—
202C2×D8—1221no—
203C2×M16—2441no—
204#127—611no—
205#127C2×#692311yescharacteristic
206#127C2×#692311yescharacteristic, complemented
207#125—611no—
208#124—611no—
209#124—611no—
210#123—2441no—
211#121—1221no—
212#121—2441no—
213#121—2441no—
214#120—2441no—
215C4×D4—1221no—
216#117—611no—
217C2×C22⋊C4—2441no—
218C4⋊C8—1221no—
219#103—1221no—
220#102—1221no—
221#102—1221no—
222#102—1221no—
223#101—1221no—
224#101—1221no—
225#100—2441no—
226#99—1221no—
227#99—1221no—
228#99—2441no—
229C22⋊C8—1221no—
230#97—611no—
231C4×C8C2×#692311yescharacteristic, complemented
232C24—1221no—
233#41—4881no—
234C2×Q8—611no—
235C2×D4—21no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—611no—
239C2×D4—1221no—
240C2×D4—1221no—
241C2×D4—4881no—
242C2×D4—2441no—
243C2×D4—2441no—
244C2×D4C22⋊#692311yescharacteristic
245C2×D4C22⋊#692311yescharacteristic
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—4881no—
249C22×C4—2441no—
250SD16—4881no—
251D8—81no—
252D8—81no—
253D8—4881no—
254M16—4881no—
255M16—2441no—
256M16—2441no—
257C2×C8—21no—
258C2×C8—1221no—
259C2×C8—4881no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—2441no—
263C22⋊C4—1221no—
264C22⋊C4—4881no—
265C22⋊C4—2441no—
266C22⋊C4—2441no—
267C22⋊C4—2441no—
268C22⋊C4—2441no—
269C22⋊C4—2441no—
270C22⋊C4—2441no—
271C42—611no—
272C42C22×#692311yescharacteristic
273C23—21no—
274C23—21no—
275C23—41no—
276C23—611no—
277C23—1221no—
278C23—9761no—
279C23—2441no—
280C23—2441no—
281Q8—2441no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—41no—
286D4—161no—
287D4—161no—
288D4—9761no—
289D4—9761no—
290D4—4881no—
291D4—4881no—
292D4—2441no—
293C2×C4—21no—
294C2×C4—611no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—9762no—
298C2×C4—9761no—
299C2×C4—4881no—
300C2×C4—4881no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4C2×C22⋊#692311yescharacteristic
306C8—41no—
307C8—4881no—
308C8—4881no—
309C8—2441no—
310C22—41no—
311C22—41no—
312C22—81no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22—1221no—
318C22—9761no—
319C22—4881no—
320C22—4882no—
321C22—2441no—
322C22—2441no—
323C22D61⋊#9911yescharacteristic
324C4—21no—
325C4—41no—
326C4—1221no—
327C4—9761no—
328C4—9761no—
329C4—4881no—
330C4—2441no—
331C4—2441no—
332C2—21no—
333C2—81no—
334C2—81no—
335C2—161no—
336C2—4881no—
337C2—2441no—
338C2#2146209511yescharacteristic
subgroupG/H
centerC2#21462095
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#493C4
socleC2×C61#2127
prime radical#21456862C2
cosocle#14519765C23
hypercenter#493#6923
hypocenterC61#13605
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #21462119C2semidirect
2. #21462095C2semidirect
3. #21460967C2semidirect
4. #21460966C2semidirect
5. #21460946C2semidirect
6. #21460946C2semidirect
16. #16840366C4semidirect
19. #16840126C4semidirect
25. #16839821C4semidirect
26. C61×#493C4semidirect
40. #14519769C2×C4semidirect
56. #14519688C2×C4semidirect
60. #127×C61C2×C4semidirect
61. C4×C8×C61C2×C4semidirect
180. #493#6923semidirect
196. C61#13605semidirect
206. #127C2×#6923semidirect
231. C4×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214621192
#214620952
#214609672
#214609662
#214609462
#214568622
#1360561