Finite Group Databasebeta

← #29589576

Subgroups — #29589576

Order 15616.

398 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 71 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#21450303C211yesmaximal, characteristic
2#21444147C211yesmaximal, characteristic
3#324×D61C211yesmaximal, characteristic
4#21443762C211yesmaximal, characteristic, complemented
5#21443762C211yesmaximal, characteristic, complemented
6#21443753C211yesmaximal, characteristic, complemented
7C61×#1319C211yesmaximal, characteristic, complemented
8C2×#14519753C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10#16839724—21no—
11C22⋊C8×D61—21no—
12#16839703—21no—
13#16839703—21no—
14#16839669C411yescharacteristic
15#16839628C411yescharacteristic
16#16839627C2211yescharacteristic
17#16839624—21no—
18#16839624—21no—
19C4×#11758198C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839487—21no—
23#16839487—21no—
24C61×#391C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C2×#11758189—41no—
31C2×C8×D61—41no—
32#14519753—41no—
33#14519753—41no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196D411yescharacteristic
38C2×#11758196D411yescharacteristic
39C4⋊C4×D61—41no—
40C4⋊C4×D61—41no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C22⋊#92418—21no—
45C22⋊#92418—21no—
46#14519689—41no—
47#14519689—41no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C22×Q8×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2311yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62C23×D61C22⋊C411yescharacteristic
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—41no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—41no—
91C42×C61—41no—
92#11758198—42no—
93#11758198—41no—
94#11758198—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97#11758196—41no—
98#11758196—41no—
99#11758196—42no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C2×#92418—41no—
103C2×#92418—41no—
104#11758189—82no—
105C8×D61—82no—
106C23×C61C2×C22⋊C411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—22no—
110C22×D61—41no—
111C22×D61#9911yescharacteristic
112C22×D61#9911yescharacteristic
113Q8×C61—81no—
114Q8×C61—81no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61#13111yescharacteristic
128C2×C4×C61#13111yescharacteristic
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—42no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C4×D61—41no—
142C4×D61—41no—
143C4×D61—41no—
144C4×D61—41no—
145C4×D61—42no—
146C4×D61—42no—
147C4×D61—81no—
148C4×D61—81no—
149C8×C61—81no—
150C8×C61—81no—
151#92418—81no—
152#92418—81no—
153#11551—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61#40811yescharacteristic
157C22×C61C2×#9911yescharacteristic
158C22×C61#41311yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—42no—
165C2×D61—42no—
166C2×D61#35412yes—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—81no—
172C4×C61—81no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—81no—
177Dic61—81no—
178#2503—611no—
179#1463—611no—
180C2×#324—611no—
181#1324—611no—
182#1324—611no—
183#1319—611no—
184#1319D6111yescharacteristic, complemented
185C2×C61—21no—
186C2×C61—21no—
187C2×C61#146811yescharacteristic
188C2×C61C2×#35411yescharacteristic
189C2×C61#213311yescharacteristic
190D61—22no—
191D61—41no—
192C2×C22⋊Q8—611no—
193C22×C4⋊C4—611no—
194#407—1221no—
195C2×C22⋊C8—1221no—
196#400—1221no—
197#400—1221no—
198#391—611no—
199#391C2×D6111yescharacteristic
200#382—611no—
201#382—611no—
202#381—1221no—
203#381—1221no—
204C4×C22⋊C4—611no—
205#324—611no—
206#324—611no—
207#324—1221no—
208#324—1221no—
209#324C2×D6111yescharacteristic
210#324C2×D6111yescharacteristic
211C61#1155111yescharacteristic, complemented, Sylow
212C22×Q8C4×D6111yescharacteristic
213C23×C4—611no—
214C23×C4—611no—
215C23×C4—611no—
216C2×M16—2441no—
217C22×C8—2441no—
218C22⋊Q8—2441no—
219C22⋊Q8—2441no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—2441no—
226C2×C4⋊C4—2441no—
227C2×C4⋊C4C22×D6111yescharacteristic
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C42—611no—
231C2×C42C4×D6111yescharacteristic
232C22⋊C8—21no—
233C22⋊C8—21no—
234C22⋊C8—1221no—
235C22⋊C8—1221no—
236C22⋊C8—2441no—
237C22⋊C8—2441no—
238#95—21no—
239#95—21no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247C24—611no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—2441no—
268C22×C4—2442no—
269C22×C4—2442no—
270C22×C4C2×C4×D6111yescharacteristic
271C22×C4D4×D6111yescharacteristic
272C22×C4D4×D6111yescharacteristic
273M16—4882no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—4882no—
277C2×C8—2441no—
278C2×C8—2441no—
279C4⋊C4—41no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2442no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C22⋊C4—2442no—
288C42—41no—
289C42—1221no—
290C42—1221no—
291C23—611no—
292C23—611no—
293C23—1222no—
294C23—1221no—
295C23—1221no—
296C23—2441no—
297C23C22⋊C4×D6111yescharacteristic
298Q8—81no—
299Q8—81no—
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—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2442no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451978311yescharacteristic
333C2×C4#1451978511yescharacteristic
334C8—81no—
335C8—81no—
336C8—4881no—
337C8—4881no—
338C22—21no—
339C22—21no—
340C22—612no—
341C22—1221no—
342C22—1221no—
343C22—1221no—
344C22—1221no—
345C22—1221no—
346C22—2442no—
347C22—2442no—
348C22#1683972711yescharacteristic
349C22#99×D6111yescharacteristic
350C22#1683974311yescharacteristic
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—4881no—
358C4—4881no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C2—21no—
363C2—21no—
364C2—1222no—
365C2—2441no—
366C2#2144416411yescharacteristic
367C2#354×D6111yescharacteristic
368C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1319C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1319D61
hypocenterC61#11551
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
4. #21443762C2semidirect
5. #21443762C2semidirect
6. #21443753C2semidirect
7. C61×#1319C2semidirect
184. #1319D61semidirect
211. C61#11551semidirect

Maximal subgroups

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

subgroupindex
#214503032
#214441472
#324×D612
#214437622
#214437532
C61×#13192
#1155161