Finite Group Databasebeta

← #29589587

Subgroups — #29589587

Order 15616.

440 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 83 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#21450307C211yesmaximal, characteristic
2#21444149C211yesmaximal, characteristic, complemented
3#21443762C212yesmaximal, complemented
4#21443750C212yesmaximal, complemented
5C2×C61×#324C211yesmaximal, characteristic, complemented
6C2×#14519751C411yescharacteristic
7#16839726—21no—
8#16839688—21no—
9#16839688—21no—
10#16839663C411yescharacteristic
11#16839663C2211yescharacteristic
12#16839641—21no—
13#16839641—21no—
14#16839627C411yescharacteristic
15#16839627C2211yescharacteristic
16C4×C22⋊Dic61C411yescharacteristic
17#16839488—21no—
18#16839488C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C2×#11758194—41no—
26#14519751—41no—
27#14519751—41no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C22⋊Dic61—21no—
30C2×#11758198—21no—
31C2×#11758198—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61C2×C411yescharacteristic
37C22⋊#92418—22no—
38C22⋊#92418—41no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C22×C8×C61—41no—
48C2×C4⋊C4×C61—41no—
49C2×C4⋊C4×C61—41no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61C2311yescharacteristic
54C22⋊C8×C61—22no—
55C22⋊C8×C61—41no—
56C24×C61C22⋊C411yescharacteristic
57C23×D61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61—41no—
66C22×C4×C61—81no—
67C22×C4×C61—81no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C2×D244—22no—
82C2×D244—41no—
83C2×D244—41no—
84C2×C8×C61—42no—
85C2×C8×C61—82no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C22⋊Dic61—42no—
91#11758198—42no—
92#11758198—81no—
93#11758198—81no—
94#11758198—81no—
95#11758198—81no—
96C4⋊Dic61—41no—
97C4×Dic61—22no—
98C4×Dic61—41no—
99#11758194—82no—
100C2×#92418—42no—
101C23×C61—22no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—41no—
105C23×C61#9911yescharacteristic
106C23×C61#9911yescharacteristic
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—
115C2×C4×C61—21no—
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—42no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61#13112yes—
135C22⋊D61—82no—
136C22⋊D61—82no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146D244—82no—
147C8×C61—82no—
148#92418—82no—
149#11553—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—42no—
158C22×C61—42no—
159C22×C61#35512yes—
160C22×C61#40811yescharacteristic
161C22×C61C2×#9911yescharacteristic
162C22×C61#41311yescharacteristic
163C2×D61—81no—
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C4×C61—22no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—41no—
176Dic61—81no—
177Dic61—81no—
178Dic61—81no—
179#2504—611no—
180#1463—611no—
181C2×#324D6111yescharacteristic, complemented
182#1324—612no—
183#1318—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—22no—
187C2×C61—41no—
188C2×C61#146811yescharacteristic
189C2×C61#212711yescharacteristic
190C2×C61C2×#35511yescharacteristic
191D61—161no—
192C2×#121—611no—
193C22×C4⋊C4C2×D6111yescharacteristic
194#407—1221no—
195C2×C22⋊C8—21no—
196#397—1221no—
197#397—1221no—
198#390—611no—
199#390—611no—
200#386—1221no—
201#386—1221no—
202#382—611no—
203#382—611no—
204C4×C22⋊C4—611no—
205#324—21no—
206#324—612no—
207#324—1221no—
208#324C2×D6112yes—
209C61#1155311yescharacteristic, complemented, Sylow
210C22×D4—611no—
211C22×D4—1221no—
212C23×C4C4×D6111yescharacteristic
213C23×C4D24411yescharacteristic
214C23×C4C22⋊D6111yescharacteristic
215C2×M16—2441no—
216C22×C8—41no—
217#121—2441no—
218#121—2441no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4C4×D6111yescharacteristic
223C2×C4⋊C4D24411yescharacteristic
224C2×C4⋊C4C22⋊D6111yescharacteristic
225C2×C4⋊C4C22×D6111yescharacteristic
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C42—611no—
233C2×C42—611no—
234C22⋊C8—22no—
235C22⋊C8—41no—
236C22⋊C8—1222no—
237C22⋊C8—2441no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243C24—1221no—
244C24#1175819811yescharacteristic
245C2×D4—1222no—
246C2×D4—2441no—
247C2×D4—2441no—
248C2×D4—2442no—
249C2×D4—2442no—
250C2×D4—2441no—
251C2×D4—2441no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4#1175819811yescharacteristic
266C22×C4#1175819811yescharacteristic
267C22×C4#1175819811yescharacteristic
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4C2×D24411yescharacteristic
270C22×C4C2×C22⋊D6111yescharacteristic
271M16—4882no—
272C2×C8—42no—
273C2×C8—82no—
274C2×C8—2442no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—2441no—
280C22⋊C4—4881no—
281C22⋊C4—4881no—
282C22⋊C4—4881no—
283C22⋊C4—4881no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C42—1222no—
287C42—2441no—
288C23—21no—
289C23—21no—
290C23—22no—
291C23—41no—
292C23—2441no—
293C23—2441no—
294C23—2441no—
295C23—2441no—
296C23—2441no—
297C23—2441no—
298C23—2441no—
299C23#1451969111yescharacteristic
300C23#1451969111yescharacteristic
301C23C2×#1175819811yescharacteristic
302D4—4882no—
303D4—4882no—
304D4—4882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4#1451978312yes—
334C8—82no—
335C8—4882no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—4881no—
346C22—4881no—
347C22—4881no—
348C22—4881no—
349C22—4881no—
350C22—4881no—
351C22—4881no—
352C22#1683955812yes—
353C22#1683972811yescharacteristic
354C22C2×#1451969111yescharacteristic
355C22#1683974411yescharacteristic
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—4881no—
363C4—4881no—
364C4—4881no—
365C2—21no—
366C2—21no—
367C2—22no—
368C2—41no—
369C2—9761no—
370C2#2144416511yescharacteristic
371C2#2144748611yescharacteristic
372C2C2×#1683955811yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC2×C61×#324C2
socleC22×C61C2×#99
prime radicalC2×#14519751C4
cosocleC2×C4⋊C4×C61C23
hypercenterC2×#324D61
hypocenterC61#11553
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #21444149C2semidirect
3. #21443762C2semidirect
4. #21443750C2semidirect
5. C2×C61×#324C2semidirect
181. C2×#324D61semidirect
209. C61#11553semidirect

Maximal subgroups

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

subgroupindex
#214503072
#214441492
#214437622
#214437502
C2×C61×#3242
#1155361