Finite Group Databasebeta

← #29577677

Subgroups — #29577677

Order 15616.

486 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 103 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#21450795C211yesmaximal, characteristic
2#21444442C212yesmaximal
3#21444163C211yesmaximal, characteristic, complemented
4#21443674C212yesmaximal, complemented
5C61×#2983C211yesmaximal, characteristic, complemented
6C2×#14519775C411yescharacteristic
7C2×#14519766C411yescharacteristic
8C2×#14519765C2211yescharacteristic
9#16839819C2212yes—
10#16839684—21no—
11#16839684—21no—
12#16839667C411yescharacteristic
13#16839663C411yescharacteristic
14#16839653—21no—
15#16839653—21no—
16C4×C4⋊Dic61C2211yescharacteristic
17#16839501—24no—
18#16839488—21no—
19#16839488—21no—
20C2×C4×Q8×C61C2211yescharacteristic
21C61×#446—24no—
22C61×#432—21no—
23C61×#432C2212yes—
24C61×#431—21no—
25C22×Dic122C2×C411yescharacteristic
26C22×D244C2×C411yescharacteristic
27#14519775—42no—
28#14519766—42no—
29#14519765—22no—
30#14519765—22no—
31C2×C4⋊Dic61—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C4⋊#92418—22no—
43C22⋊#92418—22no—
44#14519688—22no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×Q8×C61C2×C411yescharacteristic
49C4×Q8×C61—22no—
50C4×Q8×C61—22no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C42×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—22no—
58C4⋊C8×C61—22no—
59C4⋊C8×C61—22no—
60C22⋊C8×C61—22no—
61#97×C61—22no—
62#97×C61D414yes—
63C4×C8×C61—22no—
64C23×D61—21no—
65C2×Q8×C61—22no—
66C2×Q8×C61—22no—
67C2×Q8×C61—41no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C2×D244—22no—
79C2×D244—41no—
80C2×D244—41no—
81C2×Dic122—22no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×C8×C61—24no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—22no—
88C42×C61—21no—
89C42×C61—21no—
90C42×C61—21no—
91C42×C61—21no—
92C42×C61C2×D412yes—
93C42×C61#4112yes—
94#11758198—42no—
95#11758198—42no—
96#11758198—42no—
97#11758198—42no—
98#11758198—41no—
99#11758198—42no—
100#11758198—41no—
101C4⋊Dic61—42no—
102#11758196—42no—
103#11758196—42no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C2×#92418—42no—
107C23×C61C2×C22⋊C411yescharacteristic
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115Q8×C61—44no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61#10012yes—
130C2×C4×C61C4×D412yes—
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61#12112yes—
133C2×C4×C61#12311yescharacteristic
134C2×Dic61—22no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143D244—82no—
144Dic122—82no—
145C8×C61—44no—
146#92418—82no—
147#9448—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61#38611yescharacteristic
151C22×C61C2×#10011yescharacteristic
152C22×C61#41311yescharacteristic
153C2×D61—81no—
154C2×D61—81no—
155C2×D61—81no—
156C2×D61—81no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—81no—
160C4×C61—22no—
161C4×C61—22no—
162C4×C61—22no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168Dic61—42no—
169Dic61—81no—
170Dic61—81no—
171#2983D6111yescharacteristic, complemented
172#2545—611no—
173#1533—612no—
174#1467—611no—
175#1285—612no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61#188411yescharacteristic
179C2×C61#190011yescharacteristic
180C2×C61#191211yescharacteristic
181D61—161no—
182C2×C4⋊Q8—611no—
183C2×#124—611no—
184C2×#124—611no—
185C2×C4×Q8C2×D6111yescharacteristic
186#446—24no—
187#432—21no—
188#432—612no—
189#432C2×D6112yes—
190#431—21no—
191#396—1221no—
192#396—1221no—
193#391—611no—
194#390—611no—
195#388—1221no—
196#388—1221no—
197C4×C4⋊C4—611no—
198#329—1224no—
199#324—1221no—
200#324—1221no—
201C61#944811yescharacteristic, complemented, Sylow
202C22×Q8—611no—
203C22×Q8C4×D6111yescharacteristic
204C22×D4—611no—
205C4⋊Q8—2442no—
206#124—1222no—
207#124—1222no—
208#124—2442no—
209C4×Q8—22no—
210C4×Q8—22no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4C4×D6111yescharacteristic
215C2×C4⋊C4D24411yescharacteristic
216C2×C4⋊C4D24411yescharacteristic
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42C22⋊D6111yescharacteristic
226C2×C42C22⋊D6111yescharacteristic
227C2×C42C22×D6111yescharacteristic
228C4⋊C8—22no—
229C4⋊C8—22no—
230C4⋊C8—22no—
231C4⋊C8—1222no—
232C22⋊C8—22no—
233C22⋊C8—1222no—
234#97—22no—
235#97—1222no—
236#97C22⋊D6114yes—
237C4×C8—22no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24—1221no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—1222no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×D4—1222no—
249C2×D4—2441no—
250C2×D4—2441no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4#1175819811yescharacteristic
255C22×C4#1175819811yescharacteristic
256C22×C4#1175819811yescharacteristic
257C22×C4#1175819811yescharacteristic
258C22×C4C2×C4×D6111yescharacteristic
259C22×C4C2×D24411yescharacteristic
260C22×C4C2×C22⋊D6111yescharacteristic
261C2×C8—24no—
262C2×C8—2442no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C4⋊C4—2442no—
269C22⋊C4—2442no—
270C22⋊C4—2442no—
271C22⋊C4—2442no—
272C22⋊C4—2442no—
273C22⋊C4—2441no—
274C22⋊C4—2442no—
275C22⋊C4—2441no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—2441no—
281C42—2441no—
282C42#1175822212yes—
283C42C2×C22⋊D6112yes—
284C23—2441no—
285C23—2441no—
286C23—2441no—
287C23—2441no—
288C23—2441no—
289C23—2441no—
290C23—2441no—
291C23C2×#1175819811yescharacteristic
292Q8—44no—
293Q8—4882no—
294D4—4882no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—1222no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4#1451969312yes—
318C2×C4C4×C22⋊D6112yes—
319C2×C4#1451974611yescharacteristic
320C2×C4#1451975112yes—
321C2×C4#1451976011yescharacteristic
322C8—44no—
323C8—4882no—
324C22—21no—
325C22—21no—
326C22—4881no—
327C22—4881no—
328C22—4881no—
329C22—4881no—
330C22—4881no—
331C22—4881no—
332C22—4881no—
333C22#1683964111yescharacteristic
334C22C2×#1451969311yescharacteristic
335C22#1683974411yescharacteristic
336C4—22no—
337C4—22no—
338C4—22no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—4881no—
345C4—4881no—
346C4—2442no—
347C2—21no—
348C2—21no—
349C2—9761no—
350C2#2144620211yescharacteristic
351C2#2144628211yescharacteristic
352C2#2144635611yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2983C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#2983D61
hypocenterC61#9448
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
3. #21444163C2semidirect
4. #21443674C2semidirect
5. C61×#2983C2semidirect
171. #2983D61semidirect
201. C61#9448semidirect

Maximal subgroups

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

subgroupindex
#214507952
#214444422
#214441632
#214436742
C61×#29832
#944861