Finite Group Databasebeta

← #29575082

Subgroups — #29575082

Order 15616.

534 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 107 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#21449103C211yesmaximal, characteristic
2C4×#14519694C211yesmaximal, characteristic
3#21444265C212yesmaximal, complemented
4#21443711C212yesmaximal, complemented
5C61×#2973C211yesmaximal, characteristic
6C2×C4×Dic122C2211yescharacteristic
7C2×#14519694—21no—
8C4×#11758194C2212yes—
9#16839700—21no—
10#16839687C411yescharacteristic
11#16839687C411yescharacteristic
12#16839676—21no—
13#16839674C411yescharacteristic
14#16839674C411yescharacteristic
15C4×C22⋊Dic61—21no—
16C4×C22⋊Dic61—21no—
17#16839608C2211yescharacteristic
18#16839531—21no—
19#16839492—24no—
20C2×C4×D4×C61C2211yescharacteristic
21C61×#435—24no—
22C61×#432C2212yes—
23C61×#407—21no—
24C2×C22⋊C8×C61—21no—
25C22×Dic122C2×C411yescharacteristic
26C2×#11758194—22no—
27C4×Dic122—22no—
28C4×Dic122—22no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37#14519694—24no—
38#14519688—22no—
39C4×#92418—22no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684C2×C411yescharacteristic
46#14519684C2×C411yescharacteristic
47C22×D4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C23×C4×C61D411yescharacteristic
50C2×M16×C61—22no—
51C22×C8×C61—22no—
52C4×D4×C61—22no—
53C4×D4×C61—22no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61C2×C411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61D414yes—
59C22⋊C8×C61—22no—
60C22⋊C8×C61—22no—
61C22⋊C8×C61—22no—
62#97×C61—22no—
63C24×C61C22⋊C411yescharacteristic
64C24×C61C22⋊C411yescharacteristic
65C2×D4×C61—22no—
66C2×D4×C61—22no—
67C2×D4×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—42no—
73C22×C4×C61—42no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C2×Dic122—22no—
84C2×Dic122—42no—
85M16×C61—82no—
86C2×C8×C61—24no—
87C2×C8×C61—82no—
88C4⋊C4×C61—22no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—22no—
91C42×C61C2×D412yes—
92C42×C61#4112yes—
93C22⋊Dic61—42no—
94C22⋊Dic61—42no—
95C22⋊Dic61—42no—
96C22⋊Dic61—42no—
97C4⋊Dic61—22no—
98#11758196—42no—
99C4×Dic61—42no—
100C4×Dic61—41no—
101C4×Dic61—41no—
102#11758194—24no—
103#11758194—42no—
104C2×#92418—42no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61#10412yes—
115C23×C61C2×C22⋊C411yescharacteristic
116D4×C61—44no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61C4×D412yes—
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12112yes—
132C2×C4×C61#12311yescharacteristic
133C2×Dic61—22no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145Dic122—24no—
146Dic122—42no—
147C8×C61—44no—
148#92418—44no—
149#9029—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—22no—
153C22×C61—42no—
154C22×C61—42no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61#38611yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C22×C61#42111yescharacteristic
165C4×C61—22no—
166C4×C61—21no—
167C4×C61—22no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61#45512yes—
171Dic61—42no—
172Dic61—81no—
173Dic61—81no—
174Dic61—81no—
175#2973D6111yescharacteristic
176#2398—611no—
177C4×#100—611no—
178#1491—612no—
179#1300—612no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—42no—
183C2×C61—81no—
184C2×C61#187111yescharacteristic
185C2×C61#188511yescharacteristic
186C2×C61#189111yescharacteristic
187C2×C4×Q8—611no—
188C2×C4×D4C2×D6111yescharacteristic
189#435—24no—
190#432C2×D6112yes—
191C2×#100—1221no—
192#407—21no—
193C2×C22⋊C8—21no—
194C4×M16—612no—
195#400—1221no—
196#397—611no—
197#397—611no—
198#394—1221no—
199#393—611no—
200#393—611no—
201C4×C22⋊C4—1221no—
202C4×C22⋊C4—1221no—
203#376—611no—
204#343—1221no—
205Q8⋊C8—1224no—
206C61#902911yescharacteristic, complemented, Sylow
207C22×Q8—611no—
208C22×D4D24411yescharacteristic
209C23×C4C22⋊D6111yescharacteristic
210C23×C4C22⋊D6111yescharacteristic
211C2×M16—22no—
212C2×M16—1222no—
213C22×C8—22no—
214C4×Q8—1222no—
215C4×Q8—1222no—
216C4×D4—22no—
217C4×D4—22no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4D24411yescharacteristic
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4C4×D6111yescharacteristic
226C2×C22⋊C4C4×D6111yescharacteristic
227C2×C42—1221no—
228C2×C42—1221no—
229C2×C42C22×D6111yescharacteristic
230C4⋊C8C22⋊D6114yes—
231#100—1224no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235#97—22no—
236#97—1222no—
237C4×C8—1222no—
238#95—611no—
239#95—611no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245C24#1175819811yescharacteristic
246C24#1175819811yescharacteristic
247C2×Q8—1222no—
248C2×Q8—2442no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4#1175819811yescharacteristic
263C22×C4#1175819811yescharacteristic
264C22×C4C2×C4×D6111yescharacteristic
265C22×C4C2×D24411yescharacteristic
266C22×C4C2×C22⋊D6111yescharacteristic
267M16—82no—
268M16—1224no—
269M16—2442no—
270C2×C8—24no—
271C2×C8—82no—
272C2×C8—2442no—
273C4⋊C4—22no—
274C4⋊C4—1222no—
275C4⋊C4—2442no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—2442no—
279C22⋊C4—2442no—
280C22⋊C4—2442no—
281C22⋊C4—2442no—
282C42—2442no—
283C42—2441no—
284C42—2441no—
285C42#1175822212yes—
286C42C2×C22⋊D6112yes—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#1451970312yes—
297C23C2×#1175819811yescharacteristic
298Q8—1224no—
299Q8—2442no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—1222no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4C4×C22⋊D6112yes—
326C2×C4#1451974611yescharacteristic
327C2×C4#1451975112yes—
328C2×C4#1451976011yescharacteristic
329C8—44no—
330C8—2444no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22#1683964111yescharacteristic
344C22C2×#1451970311yescharacteristic
345C22#1683977811yescharacteristic
346C4—21no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—4881no—
352C4—4881no—
353C4—4881no—
354C4—2442no—
355C4#1683994012yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#2144612111yescharacteristic
361C2#2144620711yescharacteristic
362C2#2144623711yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2973C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#2973D61
hypocenterC61#9029
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
3. #21444265C2semidirect
4. #21443711C2semidirect
206. C61#9029semidirect

Maximal subgroups

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

subgroupindex
#214491032
C4×#145196942
#214442652
#214437112
C61×#29732
#902961