Finite Group Databasebeta

← #29583155

Subgroups — #29583155

Order 15616.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#21446799C211yesmaximal, characteristic
3#21444319C211yesmaximal, characteristic
4#21444317C211yesmaximal, characteristic
5#21443720C211yesmaximal, characteristic
6#21443647C211yesmaximal, characteristic
7C61×#1303C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16839815C2211yescharacteristic
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#16839523—21no—
19#16839523—21no—
20#16839500—21no—
21#16839500—21no—
22#16839498—21no—
23#16839498—21no—
24C61×#431C2211yescharacteristic
25C61×#423C2211yescharacteristic
26C4×C4⋊C4×C61C2211yescharacteristic
27#14519777Q811yescharacteristic
28#14519777Q811yescharacteristic
29#14519769—21no—
30#14519756—21no—
31#14519756—21no—
32C4×Dic122—21no—
33C4×Dic122—21no—
34#14519736—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C4⋊#92418—21no—
44C22⋊#92418—21no—
45C4×#92418—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684D411yescharacteristic
53#14519684D411yescharacteristic
54C2×M16×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C42×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C4×C8×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C2×Dic122—21no—
75C2×Dic122—21no—
76M16×C61—41no—
77M16×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C4⋊C4×C61—42no—
81C42×C61—41no—
82C42×C61—41no—
83C42×C61C2×Q811yescharacteristic
84C42×C61#4111yescharacteristic
85C42×C61#4111yescharacteristic
86C42×C61#4111yescharacteristic
87C22⋊Dic61—41no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—42no—
93C4⋊Dic61—42no—
94C4⋊Dic61—42no—
95#11758196—42no—
96#11758196—42no—
97#11758196—41no—
98#11758196—41no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C2×#92418—41no—
107C23×C61#12011yescharacteristic
108C2×C4×C61—22no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61C22⋊Q811yescharacteristic
117C2×C4×C61C22⋊Q811yescharacteristic
118C2×C4×C61C22⋊Q811yescharacteristic
119C2×C4×C61#12411yescharacteristic
120C2×C4×C61#12411yescharacteristic
121C2×C4×C61#12411yescharacteristic
122C2×C4×C61#13511yescharacteristic
123C2×C4×C61#13511yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×Dic61—22no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
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—
140Dic122—81no—
141Dic122—81no—
142C8×C61—81no—
143C8×C61—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#47911yescharacteristic
158C4×C61#47911yescharacteristic
159C4×C61#48811yescharacteristic
160C4×C61#49111yescharacteristic
161Dic61—42no—
162Dic61—81no—
163Dic61—81no—
164Dic61—81no—
165Dic61—81no—
166Dic61—81no—
167#2402—611no—
168#1995—611no—
169#1503—611no—
170#1503—611no—
171#1303—611no—
172#1303D6111yescharacteristic
173#1274—611no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#202611yescharacteristic
177C2×C61#203111yescharacteristic
178C2×C61#203111yescharacteristic
179#533—611no—
180#431—611no—
181#431C2×D6111yescharacteristic
182#423C2×D6111yescharacteristic
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—1221no—
195#328—1221no—
196#328—1221no—
197#328—1221no—
198C61#1037311yescharacteristic, complemented, Sylow
199C2×M16—21no—
200C4⋊Q8—611no—
201C4⋊Q8—611no—
202#125—1221no—
203C22⋊Q8—1221no—
204C22⋊Q8—1221no—
205C4×Q8—1221no—
206C4×Q8—1221no—
207#117—1221no—
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—21no—
221C4⋊C8—21no—
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#95D24411yescharacteristic
236#95D24411yescharacteristic
237C2×Q8—1221no—
238C2×Q8—1221no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4C2×D24411yescharacteristic
246C22×C4D4×D6111yescharacteristic
247C22×C4D4×D6111yescharacteristic
248M16—41no—
249M16—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—2441no—
253C4⋊C4—42no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—2442no—
259C4⋊C4—2442no—
260C4⋊C4—2442no—
261C4⋊C4—2442no—
262C4⋊C4—2442no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C22⋊C4—2441no—
266C42—41no—
267C42—41no—
268C42—1221no—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C42—2441no—
273C42—2441no—
274C42—2441no—
275C42#1175822211yescharacteristic
276C42#1175822211yescharacteristic
277C42#1175822411yescharacteristic
278C42Q8×D6111yescharacteristic
279C23#1451974711yescharacteristic
280Q8—4881no—
281Q8—4881no—
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—1222no—
291C2×C4—2441no—
292C2×C4—2441no—
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#1451975511yescharacteristic
305C2×C4#1451975511yescharacteristic
306C2×C4#1451975711yescharacteristic
307C2×C4#1451976311yescharacteristic
308C2×C4#1451976311yescharacteristic
309C2×C4#1451976511yescharacteristic
310C2×C4#1451979611yescharacteristic
311C2×C4#1451979811yescharacteristic
312C2×C4#1451980611yescharacteristic
313C2×C4#1451980911yescharacteristic
314C8—81no—
315C8—81no—
316C8—4881no—
317C22—21no—
318C22—21no—
319C22#1683967511yescharacteristic
320C22#1683992511yescharacteristic
321C22#1683992711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—81no—
328C4—4881no—
329C4—4881no—
330C4—4881no—
331C4—4881no—
332C4—4881no—
333C4—2442no—
334C4#1684006811yescharacteristic
335C4#1684007211yescharacteristic
336C4#1684011511yescharacteristic
337C4#1684012911yescharacteristic
338C2—21no—
339C2—21no—
340C2#2144696911yescharacteristic
341C2#2144699211yescharacteristic
342C2#2144699411yescharacteristic
subgroupG/H
centerC2×C4#14519763
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#1303D61
hypocenterC61#10373
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

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
#214467992
#214443192
#214443172
#214437202
#214436472
C61×#13032
#1037361