Finite Group Databasebeta

← #30599392

Subgroups — #30599392

Order 15616.

498 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461683C211yesmaximal, characteristic
2#21461058C211yesmaximal, characteristic
3#21460717C212yesmaximal, complemented
4#21460672C212yesmaximal, complemented
5#21448723C211yesmaximal, characteristic
6#16840779C2212yes—
7#16840765C2212yes—
8C2×#14519837—21no—
9#16840642—21no—
10#16840606—21no—
11#16840605—21no—
12C2×C4×C22⋊D61C2211yescharacteristic
13C2×#14519737—21no—
14#16839657—21no—
15#16839634—21no—
16#16839633—21no—
17#16839626C2211yescharacteristic
18#16839621C411yescharacteristic
19#16839613C2211yescharacteristic
20C2×#14519684C411yescharacteristic
21#95×D61C411yescharacteristic
22C61×#380C411yescharacteristic
23C2×#11758217—22no—
24#14519844—22no—
25#14519844—22no—
26C4⋊#92420—22no—
27#14519837—42no—
28C22⋊#92420—22no—
29C4×#92420—22no—
30C22×C22⋊D61D411yescharacteristic
31C23×Dic61—21no—
32C22×C4×D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C4×C22⋊D61—22no—
35C4×C22⋊D61—22no—
36#14519737—42no—
37#14519737—42no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61D411yescharacteristic
43C2×#11758198—21no—
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61C2311yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51#14519684C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55#95×C61C2×C411yescharacteristic
56#95×C61C2×C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C23×D61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—81no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C2×C22⋊D61—22no—
67C2×C22⋊D61—22no—
68C2×C22⋊D61D812yes—
69C2×C22⋊D61SD1612yes—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—42no—
73C22×Dic61—42no—
74C22×Dic61—81no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82C2×C4×D61—81no—
83C2×C4×D61—81no—
84#11758217—42no—
85#11758217—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C4⋊C4×C61—81no—
89C22⋊C4×C61—42no—
90C22⋊Dic61—22no—
91#11758198—22no—
92#11758198—42no—
93#11758196—22no—
94#11758196—42no—
95#11758196—41no—
96#11758196—41no—
97#11758196—81no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61#4112yes—
101C4×Dic61#4112yes—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61#10212yes—
107C23×C61C2×C22⋊C411yescharacteristic
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61#10212yes—
113C2×C4×C61—21no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—81no—
123C2×C4×C61—81no—
124C2×C4×C61#11711yescharacteristic
125C2×C4×C61#11711yescharacteristic
126C22⋊D61—24no—
127C22⋊D61—24no—
128C2×Dic61—22no—
129C2×Dic61—21no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—84no—
138C2×Dic61#12312yes—
139C2×Dic61#12312yes—
140C2×Dic61C2×D811yescharacteristic
141C2×Dic61C2×SD1611yescharacteristic
142C2×Dic61#13712yes—
143C4×D61—81no—
144C4×D61—81no—
145C4×D61—84no—
146#92420—82no—
147#92420—82no—
148#8764—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—22no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61#38111yescharacteristic
157C22×C61C2×#10211yescharacteristic
158C22×C61#41911yescharacteristic
159C2×D61—22no—
160C2×D61—42no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—42no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—81no—
168C4×C61—81no—
169Dic61—22no—
170Dic61—42no—
171Dic61—41no—
172Dic61—81no—
173Dic61#48012yes—
174Dic61#48312yes—
175#2349—611no—
176#1800—611no—
177#1460—611no—
178#1303—612no—
179#1286—612no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—42no—
183C2×C61#182311yescharacteristic
184C2×C61#182711yescharacteristic
185C2×C61#182911yescharacteristic
186D61—42no—
187C2×C4×D4—611no—
188C2×C4×D4—1221no—
189#431—612no—
190#423—612no—
191C2×#100—1221no—
192#389—1221no—
193#385—1221no—
194#385—1221no—
195#382—611no—
196#380—611no—
197#380#692311yescharacteristic
198C4×C4⋊C4—611no—
199C2×#95—611no—
200C2×#95—611no—
201#343—1221no—
202#323—1221no—
203#323—1221no—
204C61#876411yescharacteristic, complemented, Sylow
205C22×D4—611no—
206C23×C4—611no—
207C23×C4—1221no—
208C23×C4—1221no—
209C23×C4C2×#692311yescharacteristic
210C2×M16—1222no—
211C4×D4—1222no—
212C4×D4—1222no—
213C4×D4—2442no—
214C4×D4—2442no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4—1221no—
224C2×C42—611no—
225C2×C42—1221no—
226C4⋊C8—1222no—
227C4⋊C8—1222no—
228C4⋊C8—1222no—
229#100—2442no—
230C22⋊C8—1222no—
231C4×C8—1222no—
232#95—611no—
233#95—611no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95C2×#692311yescharacteristic
238#95C2×#692311yescharacteristic
239C24—611no—
240C24C22⋊#692311yescharacteristic
241C2×D4—612no—
242C2×D4—612no—
243C2×D4—1222no—
244C2×D4—1222no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—81no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—4881no—
258C22×C4—4881no—
259C22×C4—4881no—
260C22×C4—2442no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4—2442no—
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22×#692311yescharacteristic
266M16—2442no—
267M16—2442no—
268C2×C8—2442no—
269C2×C8—2442no—
270C4⋊C4—81no—
271C4⋊C4—1222no—
272C4⋊C4—4881no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2442no—
276C22⋊C4—42no—
277C22⋊C4—1222no—
278C22⋊C4—1222no—
279C22⋊C4—2442no—
280C42—612no—
281C42—612no—
282C42—2441no—
283C42—2441no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—612no—
289C23—1221no—
290C23—1221no—
291C23—2441no—
292C23—2441no—
293C23#1451983912yes—
294C23C2×C22⋊#692311yescharacteristic
295D4—1224no—
296D4—1224no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—612no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—612no—
312C2×C4—612no—
313C2×C4—1222no—
314C2×C4—1221no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4884no—
318C2×C4—4884no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4#1451985611yescharacteristic
327C2×C4#1451985611yescharacteristic
328C8—4882no—
329C8—4882no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—1222no—
338C22—2442no—
339C22—2442no—
340C22—2441no—
341C22—2441no—
342C22#1684070511yescharacteristic
343C22C2×#1451983911yescharacteristic
344C22#1684075511yescharacteristic
345C4—21no—
346C4—21no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—612no—
351C4—612no—
352C4—1222no—
353C4—4881no—
354C4—2442no—
355C4—2441no—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—2442no—
360C2#2146172211yescharacteristic
361C2#2146172911yescharacteristic
362C2#2146173211yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC22×C61#381
prime radicalC22×C22⋊D61D4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#8764
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460717C2semidirect
4. #21460672C2semidirect
204. C61#8764semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214610582
#214607172
#214606722
#214487232
#876461