Finite Group Databasebeta

← #30604272

Subgroups — #30604272

Order 15616.

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

normal subgroups only

This group has 440 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#21461067C211yesmaximal, characteristic, complemented
2C2×#16840607C211yesmaximal, characteristic, complemented
3#21460760C212yesmaximal, complemented
4#21460747C212yesmaximal, complemented
5#21450312C211yesmaximal, characteristic
6#16840732—21no—
7C2×C22⋊#92420—21no—
8#16840607—21no—
9#16840607—21no—
10#16840607C2212yes—
11#16840607C2212yes—
12C22×C4⋊Dic61C2211yescharacteristic
13#16839687—21no—
14#16839687—21no—
15#16839665C411yescharacteristic
16#16839665C2211yescharacteristic
17#16839642—21no—
18#16839642—21no—
19#16839627C411yescharacteristic
20#16839627C2211yescharacteristic
21C4×C22⋊Dic61C411yescharacteristic
22C2×#121×C61C411yescharacteristic
23C2×#11758217—41no—
24C22×#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C22⋊#92420—41no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C2×C4⋊Dic61—41no—
32C2×C4⋊Dic61—41no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61C2311yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61C2×C411yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×D4×C61—21no—
50C22×D4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52#121×C61—41no—
53#121×C61—41no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C24×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C2×D4×C61—22no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C2×D4×C61—42no—
62C2×D4×C61—42no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—81no—
79C22×Dic61—81no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84#11758217—82no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—82no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—42no—
90C22⋊Dic61—42no—
91C22⋊Dic61—81no—
92C22⋊Dic61—81no—
93C22⋊Dic61—81no—
94C22⋊Dic61—81no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4×Dic61—22no—
100C4×Dic61—41no—
101C23×C61—22no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61#9911yescharacteristic
113C23×C61#9911yescharacteristic
114C23×C61C2×C22⋊C411yescharacteristic
115D4×C61—82no—
116D4×C61—82no—
117D4×C61—82no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61#13112yes—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
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—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147#92420—82no—
148#92420—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—81no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61#35512yes—
167C22×C61#40811yescharacteristic
168C22×C61C2×#9911yescharacteristic
169C22×C61#41311yescharacteristic
170C4×C61—22no—
171C4×C61—41no—
172C4×C61—81no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—81no—
178Dic61—81no—
179#2504—611no—
180#1463—611no—
181C2×#324—611no—
182#1324—612no—
183#1318—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—22no—
187C2×C61—41no—
188C2×C61—161no—
189C2×C61#146811yescharacteristic
190C2×C61#212711yescharacteristic
191C2×C61C2×#35511yescharacteristic
192C2×#121#692311yescharacteristic
193C22×C4⋊C4—611no—
194#407—1221no—
195C2×C22⋊C8—1221no—
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—612no—
206#324—612no—
207#324—1221no—
208#324—1221no—
209C61#1155311yescharacteristic, complemented, Sylow
210C22×D4—21no—
211C22×D4C2×#692311yescharacteristic
212C23×C4—611no—
213C23×C4—611no—
214C23×C4C2×#692311yescharacteristic
215C2×M16—2441no—
216C22×C8—2441no—
217#121—41no—
218#121—41no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—2441no—
224C2×C4⋊C4—2441no—
225C2×C4⋊C4C2×#692311yescharacteristic
226C2×C22⋊C4—21no—
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—1222no—
235C22⋊C8—1222no—
236C22⋊C8—2441no—
237C22⋊C8—2441no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243C24—21no—
244C24C22⋊#692311yescharacteristic
245C2×D4—22no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—41no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—4881no—
268C22×C4—4881no—
269C22×C4C22⋊#692311yescharacteristic
270C22×C4C22×#692311yescharacteristic
271M16—4882no—
272C2×C8—4882no—
273C2×C8—2442no—
274C2×C8—2442no—
275C4⋊C4—41no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C22⋊C4—42no—
281C22⋊C4—4881no—
282C22⋊C4—4881no—
283C22⋊C4—4881no—
284C22⋊C4—4881no—
285C22⋊C4—2442no—
286C42—1222no—
287C42—2441no—
288C23—21no—
289C23—21no—
290C23—22no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23#1451983511yescharacteristic
300C23#1451983511yescharacteristic
301C23C2×C22⋊#692311yescharacteristic
302D4—82no—
303D4—82no—
304D4—82no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4#1451986412yes—
334C8—4882no—
335C8—4882no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#1684067012yes—
353C22#1684073511yescharacteristic
354C22C2×#1451983511yescharacteristic
355C22#1684074911yescharacteristic
356C4—22no—
357C4—41no—
358C4—81no—
359C4—4881no—
360C4—4881no—
361C4—2441no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C2—21no—
366C2—21no—
367C2—22no—
368C2—41no—
369C2—161no—
370C2#2146108411yescharacteristic
371C2#2146209411yescharacteristic
372C2C2×#1684067011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#121×C61C4
socleC22×C61C2×#99
cosocleC2×C4⋊Dic61C23
hypercenterC2×#121#6923
hypocenterC61#11553
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21461067C2semidirect
2. C2×#16840607C2semidirect
3. #21460760C2semidirect
4. #21460747C2semidirect
209. C61#11553semidirect

Maximal subgroups

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

subgroupindex
#214610672
C2×#168406072
#214607602
#214607472
#214503122
#1155361