Finite Group Databasebeta

← #30604332

Subgroups — #30604332

Order 15616.

480 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461075C211yesmaximal, characteristic
2#21461055C211yesmaximal, characteristic
3#21460762C212yesmaximal, complemented
4#21460761C212yesmaximal, complemented
5#21450770C211yesmaximal, characteristic
6#16840732—21no—
7C2×C22⋊#92420—21no—
8#16840607C2212yes—
9#16840607C2212yes—
10#16840605—21no—
11#16840605—21no—
12C2×#14519776C411yescharacteristic
13C2×#14519754—21no—
14C2×#14519754—21no—
15C2×D4×Dic61C2211yescharacteristic
16#16839698—21no—
17#16839698—21no—
18#16839665C411yescharacteristic
19#16839632C2211yescharacteristic
20#16839631C2211yescharacteristic
21C4×#11758196C411yescharacteristic
22C61×#390C411yescharacteristic
23C2×#11758217—41no—
24C22×#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C22⋊#92420—41no—
29C22×Dic122—21no—
30C23×Dic61D411yescharacteristic
31C23×Dic61D411yescharacteristic
32#14519776—41no—
33#14519776—41no—
34#14519754—44no—
35#14519754—44no—
36D4×Dic61—41no—
37D4×Dic61—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61C2311yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61D411yescharacteristic
49C2×C22⋊Dic61D411yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52#14519684—21no—
53C22×D4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C42×C61C2×C411yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C24×C61C22⋊C411yescharacteristic
60C2×D4×C61—22no—
61C2×D4×C61—22no—
62C2×D4×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—42no—
73C22×Dic61—42no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×Dic122—42no—
79C2×Dic122—42no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82#11758217—82no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—82no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C22⋊C4×C61—42no—
89C42×C61—22no—
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92C22⋊Dic61—42no—
93C22⋊Dic61—42no—
94C4⋊Dic61—41no—
95C4⋊Dic61—42no—
96C4⋊Dic61—42no—
97C4⋊Dic61—41no—
98#11758196—24no—
99#11758196—42no—
100#11758196—42no—
101#11758196—42no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—22no—
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#10112yes—
115C23×C61C2×C22⋊C411yescharacteristic
116D4×C61—44no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61#13112yes—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143C2×Dic61#9911yescharacteristic
144C2×Dic61#9911yescharacteristic
145Dic122—82no—
146Dic122—82no—
147#92420—82no—
148#92420—82no—
149#11570—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#40811yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C22×C61C2×#10111yescharacteristic
165C4×C61—22no—
166C4×C61—42no—
167C4×C61—81no—
168Dic61—21no—
169Dic61—42no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—81no—
174Dic61#35312yes—
175#2542—611no—
176#1465—611no—
177#1459—611no—
178#1325—612no—
179#1325—612no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—42no—
183C2×C61—81no—
184C2×C61#147211yescharacteristic
185C2×C61C2×#35311yescharacteristic
186C2×C61#213511yescharacteristic
187C2×C4⋊Q8—611no—
188C2×C22⋊Q8—1221no—
189C2×C22⋊Q8—1221no—
190C2×C4×D4—611no—
191#407—1221no—
192C2×C22⋊C8—1221no—
193#399—1221no—
194#399—1221no—
195#390—611no—
196#390#692311yescharacteristic
197#384—611no—
198#384—611no—
199C4×C4⋊C4—611no—
200#324—612no—
201#324—612no—
202#323—1221no—
203#323—1221no—
204C61#1157011yescharacteristic, complemented, Sylow
205C22×Q8—1221no—
206C22×D4C2×#692311yescharacteristic
207C23×C4—611no—
208C23×C4—611no—
209C2×M16—2441no—
210C22×C8—2441no—
211C4⋊Q8—2441no—
212C4⋊Q8—2441no—
213C22⋊Q8—2444no—
214C22⋊Q8—2444no—
215C4×D4—2441no—
216C4×D4—2441no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4C2×#692311yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42C2×#692311yescharacteristic
235C22⋊C8—1222no—
236C22⋊C8—1222no—
237C22⋊C8—2441no—
238C22⋊C8—2441no—
239#95—1221no—
240C24C22⋊#692311yescharacteristic
241C24C22⋊#692311yescharacteristic
242C2×Q8—2441no—
243C2×Q8—2441no—
244C2×Q8—2442no—
245C2×Q8—2442no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4C22×#692311yescharacteristic
264M16—4882no—
265C2×C8—4882no—
266C2×C8—2442no—
267C2×C8—2442no—
268C4⋊C4—41no—
269C4⋊C4—1224no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2442no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C4⋊C4—2442no—
276C4⋊C4—2442no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C22⋊C4—2442no—
282C22⋊C4—2442no—
283C42—22no—
284C42—1221no—
285C42—1221no—
286C42—1222no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#1451983812yes—
297C23C2×C22⋊#692311yescharacteristic
298Q8—4882no—
299Q8—4882no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—1222no—
312C2×C4—1222no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4#1451986412yes—
329C8—4882no—
330C8—4882no—
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#1684073511yescharacteristic
344C22D61⋊#9911yescharacteristic
345C22C2×#1451983811yescharacteristic
346C4—22no—
347C4—42no—
348C4—81no—
349C4—612no—
350C4—1221no—
351C4—4881no—
352C4—2442no—
353C4—2441no—
354C4—2441no—
355C4—2441no—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#2146109811yescharacteristic
361C2D61⋊#35311yescharacteristic
362C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C4⋊Dic61C23
hypercenter#390#6923
hypocenterC61#11570
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #390

Complements

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

NH ≅ G/Ntype
3. #21460762C2semidirect
4. #21460761C2semidirect
204. C61#11570semidirect

Maximal subgroups

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

subgroupindex
#214610752
#214610552
#214607622
#214607612
#214507702
#1157061