Finite Group Databasebeta

← #29583773

Subgroups — #29583773

Order 15616.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#21455612C211yesmaximal, characteristic
2#21445830C211yesmaximal, characteristic
3#21444589C211yesmaximal, characteristic, complemented
4#21444383C211yesmaximal, characteristic, complemented
5#21444139C211yesmaximal, characteristic
6#21443678C211yesmaximal, characteristic, complemented
7C61×#1542C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16840059—22no—
10#16840049—21no—
11#16840039—21no—
12#16839815C2211yescharacteristic
13#16839805—21no—
14#16839786C2211yescharacteristic
15#16839766—21no—
16C2×#14519699—21no—
17#16839628C2211yescharacteristic
18#16839525—21no—
19#16839512—22no—
20#16839499—22no—
21#16839485—22no—
22C61×#533C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C61×#333—21no—
26C61×#332—21no—
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C2×#11758194—21no—
30C4×D244—21no—
31C4×D244—21no—
32C4×D244—21no—
33C4×D244—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758198—21no—
37#14519710—22no—
38#14519708—22no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41C4⋊#92418D412yes—
42#14519699—42no—
43#14519697—22no—
44#14519697—22no—
45C22⋊#92418D412yes—
46C4×#92418—21no—
47#14519684—21no—
48#14519684—21no—
49C22×C8×C61—21no—
50C4⋊Q8×C61D411yescharacteristic
51C4⋊Q8×C61D411yescharacteristic
52#125×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—21no—
55C4×Q8×C61—21no—
56C4×Q8×C61—21no—
57#117×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C4×C8×C61—21no—
64C23×D61—21no—
65C2×Q8×C61—21no—
66C2×Q8×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—41no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244SD1612yes—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—82no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C42×C61—41no—
93C42×C61C2×D411yescharacteristic
94C42×C61C2×D411yescharacteristic
95C42×C61#4111yescharacteristic
96C42×C61#4111yescharacteristic
97#11758198—41no—
98#11758198—41no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103#11758194—41no—
104#11758194—41no—
105C2×#92418—22no—
106C2×#92418—22no—
107C23×C61#12111yescharacteristic
108C22×D61—22no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—81no—
112C22×D61—81no—
113Q8×C61—81no—
114Q8×C61—81no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61#12011yescharacteristic
120C2×C4×C61#12111yescharacteristic
121C2×C4×C61#12111yescharacteristic
122C2×C4×C61#12311yescharacteristic
123C2×C4×C61#12311yescharacteristic
124C2×C4×C61#12411yescharacteristic
125C2×C4×C61C2×SD1611yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61#13711yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C2×Dic61—41no—
130C2×Dic61—81no—
131C2×Dic61—81no—
132C2×Dic61—81no—
133C2×Dic61—81no—
134D244—22no—
135D244—22no—
136D244—41no—
137D244—41no—
138C4×D61—82no—
139C4×D61—82no—
140C8×C61—81no—
141C8×C61—81no—
142#92418—42no—
143#92418—42no—
144#10468—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61#39411yescharacteristic
148C22×C61#46511yescharacteristic
149C22×C61#47011yescharacteristic
150C2×D61—42no—
151C2×D61—82no—
152C2×D61—81no—
153C2×D61—81no—
154C2×D61—82no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—81no—
160C4×C61—81no—
161C4×C61#44811yescharacteristic
162C4×C61#45211yescharacteristic
163C4×C61#48311yescharacteristic
164C4×C61#48511yescharacteristic
165Dic61—81no—
166Dic61—161no—
167#3077—611no—
168#1804—611no—
169#1570—611no—
170#1542D6111yescharacteristic, complemented
171#1518—611no—
172#1460—611no—
173#1286—611no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#203511yescharacteristic
177C2×C61#204811yescharacteristic
178C2×C61#205311yescharacteristic
179D61—82no—
180#533C2×D6111yescharacteristic
181C2×C4×D4—611no—
182#478—1222no—
183#476—1221no—
184#474—1221no—
185#431—611no—
186#431C2×D6111yescharacteristic
187#428—1221no—
188#423—611no—
189C2×C4⋊C8C2×D6111yescharacteristic
190#418—1221no—
191C2×#102—1221no—
192#382—611no—
193#340—1221no—
194#334—1222no—
195#333—21no—
196#332—21no—
197#328—1222no—
198#323—1222no—
199C61#1046811yescharacteristic, complemented, Sylow
200C22×D4—611no—
201C23×C4—1221no—
202C2×M16—1221no—
203C22×C8—21no—
204C4⋊Q8C22⋊D6111yescharacteristic
205C4⋊Q8C22⋊D6111yescharacteristic
206#125—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×D4—1221no—
212C4×D4—1221no—
213C4×D4—1221no—
214C4×D4—1221no—
215#117—21no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C42C22×D6111yescharacteristic
220#107—1222no—
221#106—1222no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—612no—
226C4⋊C8—1221no—
227C4⋊C8—1221no—
228#102—1222no—
229#102—1222no—
230#102—2442no—
231C22⋊C8—21no—
232C22⋊C8—612no—
233C4×C8—21no—
234C4×C8—1221no—
235#95—1221no—
236#95—1221no—
237C24—1221no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×D4—612no—
241C2×D4—1221no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4—1221no—
246C22×C4—1221no—
247C22×C4—4882no—
248C22×C4—2441no—
249C22×C4—2441no—
250C22×C4—2441no—
251C22×C4#1175822211yescharacteristic
252C22×C4D4×D6111yescharacteristic
253C22×C4D4×D6111yescharacteristic
254M16—2441no—
255M16—2441no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—1222no—
261C2×C8—1222no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C22⋊C4—41no—
273C22⋊C4—2441no—
274C22⋊C4—2441no—
275C42—41no—
276C42#1175822211yescharacteristic
277C42D4×D6111yescharacteristic
278C42#1175822411yescharacteristic
279C42C2×C22⋊D6111yescharacteristic
280C23—1222no—
281C23—4881no—
282C23—4881no—
283C23—2441no—
284C23—2441no—
285C23#1451975011yescharacteristic
286Q8—81no—
287Q8—81no—
288D4—1222no—
289D4—1222no—
290D4—2441no—
291D4—2441no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—4882no—
297C2×C4—4882no—
298C2×C4—4881no—
299C2×C4—4881no—
300C2×C4—4881no—
301C2×C4—4881no—
302C2×C4—2441no—
303C2×C4#1451974511yescharacteristic
304C2×C4#1451974911yescharacteristic
305C2×C4#1451975011yescharacteristic
306C2×C4#1451975911yescharacteristic
307C2×C4#1451976011yescharacteristic
308C2×C4#1451976311yescharacteristic
309C2×C4SD16×D6111yescharacteristic
310C2×C4#1451980011yescharacteristic
311C2×C4#1451980611yescharacteristic
312C2×C4#1451980911yescharacteristic
313C8—81no—
314C8—81no—
315C8—2442no—
316C8—2442no—
317C22—21no—
318C22—21no—
319C22—4882no—
320C22—4882no—
321C22—4881no—
322C22—4881no—
323C22—2442no—
324C22#1683967711yescharacteristic
325C22#1683999411yescharacteristic
326C22#1684001911yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—9761no—
334C4—4881no—
335C4#1683989911yescharacteristic
336C4#1683992311yescharacteristic
337C4#1684009111yescharacteristic
338C4#1684010211yescharacteristic
339C2—21no—
340C2—21no—
341C2—4882no—
342C2#2144701311yescharacteristic
343C2#2144709211yescharacteristic
344C2#2144712311yescharacteristic
subgroupG/H
centerC22#16839677
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1542C2
socleC22×C61#394
prime radicalC22×D244D4
hypercenter#1542D61
hypocenterC61#10468
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
3. #21444589C2semidirect
4. #21444383C2semidirect
6. #21443678C2semidirect
7. C61×#1542C2semidirect
170. #1542D61semidirect
199. C61#10468semidirect

Maximal subgroups

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

subgroupindex
#214556122
#214458302
#214445892
#214443832
#214441392
#214436782
C61×#15422
#1046861