Finite Group Databasebeta

← #29568647

Subgroups — #29568647

Order 15616.

388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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#21454178C211yesmaximal, characteristic
2#21445961C211yesmaximal, characteristic
3#21445934C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic
5#21443642C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519767—21no—
9C2×#14519706—21no—
10#16839661C411yescharacteristic
11#16839660C2211yescharacteristic
12#16839659—21no—
13#16839658C411yescharacteristic
14#16839657—21no—
15#16839631C411yescharacteristic
16#16839631C411yescharacteristic
17#16839626—21no—
18C42×Dic61C2211yescharacteristic
19#16839517C2211yescharacteristic
20#16839517C2211yescharacteristic
21#16839516—21no—
22#16839516—21no—
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×#92418—21no—
28C22×#92418—21no—
29#14519767—42no—
30#14519767—42no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C22×C8×C61—21no—
51C22×C8×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#95×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C2×C8×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C42×C61—41no—
80C4⋊Dic61—21no—
81C4⋊Dic61—21no—
82C4⋊Dic61—42no—
83C4⋊Dic61—41no—
84#11758196—42no—
85#11758196—42no—
86#11758196—42no—
87#11758196—42no—
88#11758196—42no—
89#11758196—41no—
90#11758196—41no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—22no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C4×Dic61SD1612yes—
99C4×Dic61Q1612yes—
100C2×#92418—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C23×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
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#13111yescharacteristic
120C2×C4×C61#13111yescharacteristic
121C2×C4×C61C2×SD1611yescharacteristic
122C2×C4×C61C2×Q1611yescharacteristic
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61#10112yes—
141C2×Dic61#10312yes—
142C2×Dic61#10312yes—
143C8×C61—81no—
144C8×C61—81no—
145#92418—81no—
146#92418—81no—
147#7720—611nomaximal, Sylow
148C22×C61#40811yescharacteristic
149C22×C61#41011yescharacteristic
150C22×C61C2×#10111yescharacteristic
151C22×C61C2×#10311yescharacteristic
152C22×C61#41811yescharacteristic
153C22×C61#42111yescharacteristic
154C22×C61#42111yescharacteristic
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—81no—
162C4×C61—81no—
163Dic61—22no—
164Dic61—22no—
165Dic61—22no—
166Dic61—41no—
167Dic61—81no—
168Dic61—81no—
169#2859—611no—
170#1839—611no—
171#1831—611no—
172#1271—611no—
173#1271—611no—
174#1271—611no—
175#1271D6111yescharacteristic
176C2×C61#147011yescharacteristic
177C2×C61#148111yescharacteristic
178C2×C61#149611yescharacteristic
179C2×C61#151411yescharacteristic
180C2×C61#151811yescharacteristic
181C2×C61#153411yescharacteristic
182C2×C61#154911yescharacteristic
183C2×#125—1221no—
184C2×C4⋊C8—1221no—
185#389—611no—
186#389—611no—
187#389—611no—
188#389—1221no—
189#389—1221no—
190#389C2×D6111yescharacteristic
191#384—611no—
192#384—611no—
193#382—1221no—
194C43—611no—
195#336—611no—
196#336—611no—
197#336—1221no—
198#336—1221no—
199#336—1221no—
200#336C2×D6111yescharacteristic
201#336C2×D6111yescharacteristic
202C61#772011yescharacteristic, complemented, Sylow
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—1221no—
206C22×C8—1221no—
207#125—2442no—
208#125—2442no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4C4×D6111yescharacteristic
220C2×C4⋊C4C4×D6111yescharacteristic
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42C22×D6111yescharacteristic
228C4⋊C8—2442no—
229#95—21no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4C2×C4×D6111yescharacteristic
242C22×C4D4×D6111yescharacteristic
243C22×C4D4×D6111yescharacteristic
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—2441no—
251C2×C8—2441no—
252C2×C8—2441no—
253C2×C8—2441no—
254C2×C8—2441no—
255C2×C8—2441no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—2441no—
264C4⋊C4—2442no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C4⋊C4—2442no—
269C4⋊C4—2442no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C42—41no—
273C42—612no—
274C42—612no—
275C42—1222no—
276C42—1221no—
277C42—1221no—
278C42—1221no—
279C42—1221no—
280C42—2441no—
281C42—2441no—
282C23C22⋊C4×D6111yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—612no—
296C2×C4—612no—
297C2×C4—612no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4#1451978311yescharacteristic
314C2×C4#1451978511yescharacteristic
315C2×C4SD16×D6111yescharacteristic
316C2×C4Q16×D6111yescharacteristic
317C2×C4#1451980111yescharacteristic
318C2×C4#1451980411yescharacteristic
319C8—81no—
320C8—81no—
321C8—4881no—
322C8—4881no—
323C22#1683972711yescharacteristic
324C22#1683973411yescharacteristic
325C22#101×D6111yescharacteristic
326C22#103×D6111yescharacteristic
327C22#1683976511yescharacteristic
328C22#1683977711yescharacteristic
329C22#1683977711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—1222no—
339C4—1222no—
340C4—1222no—
341C4—4881no—
342C4—4881no—
343C4—2441no—
344C2#2144417311yescharacteristic
345C2#2144422011yescharacteristic
346C2#2144428611yescharacteristic
347C2#2144436411yescharacteristic
348C2#2144438111yescharacteristic
349C2#2144444411yescharacteristic
350C2#2144450211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7720
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
202. C61#7720semidirect

Maximal subgroups

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

subgroupindex
#214541782
#214459612
#214459342
#214436432
#214436422
#214436412
C61×#12712
#772061