Finite Group Databasebeta

← #29583154

Subgroups — #29583154

Order 15616.

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

normal subgroups only

This group has 364 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#21449127C211yesmaximal, characteristic
2#21446801C211yesmaximal, characteristic
3#21444318C211yesmaximal, characteristic
4#21443722C211yesmaximal, characteristic
5#21443721C211yesmaximal, characteristic
6#21443647C211yesmaximal, characteristic
7C61×#1503C211yesmaximal, characteristic
8#16839815C2211yescharacteristic
9#16839786C2211yescharacteristic
10#16839704—21no—
11#16839701—21no—
12#16839695—21no—
13#16839694—21no—
14C4×#11758196—21no—
15C4×C4⋊Dic61—21no—
16C4×C4⋊Dic61C2211yescharacteristic
17#16839608C2211yescharacteristic
18#16839521—21no—
19#16839521—21no—
20#16839499—21no—
21#16839499—21no—
22C61×#533C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C4×C4⋊C4×C61C2211yescharacteristic
25C61×#328—21no—
26C61×#328—21no—
27C2×#11758194—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C22⋊#92418—21no—
40C4×#92418—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684D411yescharacteristic
48#14519684D411yescharacteristic
49C4⋊Q8×C61Q811yescharacteristic
50C4⋊Q8×C61Q811yescharacteristic
51#125×C61—21no—
52C22⋊Q8×C61—21no—
53C22⋊Q8×C61—21no—
54C4×Q8×C61—21no—
55C4×Q8×C61—21no—
56#117×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C42×C61—21no—
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C4×C8×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C2×Q8×C61—21no—
66C2×Q8×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C2×C8×C61—41no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C42×C61—41no—
86C42×C61—41no—
87C42×C61—41no—
88C42×C61C2×Q811yescharacteristic
89C42×C61#4111yescharacteristic
90C42×C61#4111yescharacteristic
91C42×C61#4111yescharacteristic
92C4⋊Dic61—42no—
93C4⋊Dic61—42no—
94C4⋊Dic61—42no—
95#11758196—42no—
96#11758196—42no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103#11758194—41no—
104#11758194—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61#12011yescharacteristic
108Q8×C61—81no—
109Q8×C61—81no—
110C2×C4×C61—22no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61C22⋊Q811yescharacteristic
121C2×C4×C61C22⋊Q811yescharacteristic
122C2×C4×C61C22⋊Q811yescharacteristic
123C2×C4×C61#12411yescharacteristic
124C2×C4×C61#12411yescharacteristic
125C2×C4×C61#12411yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61#13511yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×Dic61—22no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C8×C61—81no—
143#92418—81no—
144#92418—81no—
145#10373—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61#39311yescharacteristic
149C22×C61#45211yescharacteristic
150C22×C61#45211yescharacteristic
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—42no—
156C4×C61—81no—
157C4×C61—81no—
158C4×C61—81no—
159C4×C61#47911yescharacteristic
160C4×C61#47911yescharacteristic
161C4×C61#48811yescharacteristic
162C4×C61#49111yescharacteristic
163Dic61—42no—
164Dic61—81no—
165Dic61—81no—
166Dic61—81no—
167#2402—611no—
168#1995—611no—
169#1503—611no—
170#1503D6111yescharacteristic
171#1303—611no—
172#1303—611no—
173#1274—611no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#202611yescharacteristic
177C2×C61#203111yescharacteristic
178C2×C61#203111yescharacteristic
179#533C2×D6111yescharacteristic
180#431—611no—
181#431C2×D6111yescharacteristic
182#423—611no—
183#400—1221no—
184#400—1221no—
185#398—1221no—
186#398—1221no—
187C4×C4⋊C4—611no—
188C4×C4⋊C4—1221no—
189C4×C4⋊C4—1221no—
190C4×C4⋊C4C2×D6111yescharacteristic
191#376—611no—
192#339—1221no—
193#339—1221no—
194#328—21no—
195#328—21no—
196#328—1221no—
197#328—1221no—
198C61#1037311yescharacteristic, complemented, Sylow
199C2×M16—1221no—
200C4⋊Q8Dic12211yescharacteristic
201C4⋊Q8Dic12211yescharacteristic
202#125—21no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207#117—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C42—21no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42—1221no—
218C2×C42C22×D6111yescharacteristic
219C4⋊C8—21no—
220C4⋊C8—1221no—
221C4⋊C8—1221no—
222C4⋊C8—1221no—
223C22⋊C8—21no—
224C22⋊C8—1221no—
225C4×C8—21no—
226C4×C8—1221no—
227#95—611no—
228#95—611no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95C22⋊D6111yescharacteristic
236#95C22⋊D6111yescharacteristic
237C2×Q8—21no—
238C2×Q8—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4D4×D6111yescharacteristic
246C22×C4D4×D6111yescharacteristic
247C22×C4C2×C22⋊D6111yescharacteristic
248M16—2441no—
249M16—2441no—
250C2×C8—41no—
251C2×C8—2441no—
252C2×C8—2441no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—42no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—2442no—
261C4⋊C4—2442no—
262C4⋊C4—2442no—
263C4⋊C4—2442no—
264C4⋊C4—2442no—
265C22⋊C4—41no—
266C42—41no—
267C42—41no—
268C42—41no—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C42—2441no—
274C42—2441no—
275C42C2×Dic12211yescharacteristic
276C42#1175822211yescharacteristic
277C42#1175822411yescharacteristic
278C42#1175822411yescharacteristic
279C23#1451974511yescharacteristic
280Q8—81no—
281Q8—81no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—1222no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4#1451975411yescharacteristic
305C2×C4#1451975411yescharacteristic
306C2×C4#1451975611yescharacteristic
307C2×C4#1451976311yescharacteristic
308C2×C4#1451976311yescharacteristic
309C2×C4#1451976411yescharacteristic
310C2×C4#1451979811yescharacteristic
311C2×C4#1451980011yescharacteristic
312C2×C4#1451980611yescharacteristic
313C2×C4#1451980911yescharacteristic
314C8—81no—
315C8—4881no—
316C8—4881no—
317C22—21no—
318C22—21no—
319C22#1683967411yescharacteristic
320C22#1683992111yescharacteristic
321C22#1683992311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—4881no—
331C4—4881no—
332C4—4881no—
333C4—2442no—
334C4#1684006711yescharacteristic
335C4#1684007111yescharacteristic
336C4#1684011811yescharacteristic
337C4#1684012911yescharacteristic
338C2—21no—
339C2—21no—
340C2#2144696811yescharacteristic
341C2#2144699111yescharacteristic
342C2#2144699311yescharacteristic
subgroupG/H
centerC2×C4#14519763
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1503C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#1503D61
hypocenterC61#10373
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
198. C61#10373semidirect

Maximal subgroups

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

subgroupindex
#214491272
#214468012
#214443182
#214437222
#214437212
#214436472
C61×#15032
#1037361