Finite Group Databasebeta

← #30604894

Subgroups — #30604894

Order 15616.

470 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C4×#14519837C211yesmaximal, characteristic, complemented
2#21461054C211yesmaximal, characteristic, complemented
3#21460818C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21451704C211yesmaximal, characteristic
6C2×#14519837—21no—
7D61⋊(C22⋊C8)—21no—
8C4×#11758217—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840605—21no—
12C2×C4×C22⋊D61C2211yescharacteristic
13#16839700C2211yescharacteristic
14#16839697C411yescharacteristic
15#16839676—21no—
16#16839676C2211yescharacteristic
17#16839670—21no—
18#16839670C411yescharacteristic
19#16839650—21no—
20#16839638—21no—
21#16839625C411yescharacteristic
22C2×#121×C61C411yescharacteristic
23C2×#11758217—22no—
24C2×D61⋊C8—41no—
25#14519837—24no—
26#14519834—41no—
27C22⋊#92420—22no—
28#14519832—41no—
29C4×#92420—41no—
30C22×C22⋊D61—21no—
31C22×C22⋊D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C4×C22⋊D61—41no—
34C4×C22⋊D61—41no—
35C2×#11758196—21no—
36C2×#11758196C2311yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61D411yescharacteristic
42C2×#11758198—21no—
43C2×#11758198C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C22×D4×C61—21no—
51C22×D4×C61C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53#121×C61—41no—
54#121×C61—41no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C24×C61—21no—
58C24×C61C22⋊C411yescharacteristic
59C23×D61C22⋊C411yescharacteristic
60C2×D4×C61—41no—
61C2×D4×C61—42no—
62C2×D4×C61—81no—
63C2×D4×C61—81no—
64C2×D4×C61—81no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—81no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C2×C22⋊D61—22no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—81no—
76C2×C22⋊D61—81no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—81no—
85#11758217—24no—
86#11758217—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89D61⋊C8—82no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—42no—
95C22⋊Dic61—81no—
96C22⋊Dic61—81no—
97C22⋊Dic61—81no—
98#11758198—41no—
99#11758198—81no—
100#11758196—41no—
101#11758196—81no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61#10412yes—
122D4×C61—82no—
123D4×C61—84no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61#9911yescharacteristic
133C2×C4×C61#9911yescharacteristic
134C22⋊D61—44no—
135C22⋊D61—84no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61#13512yes—
149C4×D61—42no—
150C4×D61—81no—
151#92420—44no—
152#92420—82no—
153#11737—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61C2×#9911yescharacteristic
169C22×C61#41611yescharacteristic
170C22×C61C2×#10411yescharacteristic
171C2×D61—22no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—42no—
175C2×D61—81no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—41no—
179C4×C61—81no—
180Dic61—22no—
181Dic61—41no—
182Dic61—41no—
183Dic61—81no—
184Dic61—81no—
185#2635—611no—
186C4×#100—611no—
187#1459—611no—
188#1353—612no—
189#1345—612no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—81no—
193C2×C61—161no—
194C2×C61#150111yescharacteristic
195C2×C61#212111yescharacteristic
196C2×C61#213411yescharacteristic
197D61—42no—
198C2×#121#692311yescharacteristic
199C2×C4×D4—611no—
200C2×#100—1221no—
201C2×C22⋊C8—1221no—
202C4×M16—1221no—
203#400—611no—
204#399—611no—
205#394—611no—
206#394—1221no—
207#392—611no—
208#392—1221no—
209#388—1221no—
210#386—1221no—
211#381—611no—
212#343—612no—
213#324—612no—
214#323—1221no—
215C61#1173711yescharacteristic, complemented, Sylow
216C22×D4—21no—
217C22×D4—611no—
218C22×D4—1221no—
219C22×D4C2×#692311yescharacteristic
220C23×C4—611no—
221C23×C4C2×#692311yescharacteristic
222C2×M16—1222no—
223C22×C8—2441no—
224#121—41no—
225#121—41no—
226C4×D4—2441no—
227C4×D4—2441no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4C2×#692311yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C42—611no—
240#100—1224no—
241C22⋊C8—1222no—
242C22⋊C8—2441no—
243#97—2441no—
244C4×C8—2441no—
245#95—611no—
246#95—611no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250C24—21no—
251C24—611no—
252C24C22⋊#692311yescharacteristic
253C2×D4—41no—
254C2×D4—42no—
255C2×D4—81no—
256C2×D4—81no—
257C2×D4—81no—
258C2×D4—1222no—
259C2×D4—1222no—
260C2×D4—4881no—
261C2×D4—4881no—
262C2×D4—2441no—
263C2×D4—2442no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—81no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—4881no—
276C22×C4C22⋊#692311yescharacteristic
277C22×C4C22×#692311yescharacteristic
278M16—1224no—
279M16—2442no—
280C2×C8—4882no—
281C2×C8—2442no—
282C2×C8—2442no—
283C4⋊C4—41no—
284C4⋊C4—4881no—
285C4⋊C4—2441no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—4881no—
289C22⋊C4—4881no—
290C22⋊C4—4881no—
291C22⋊C4—4881no—
292C22⋊C4—2441no—
293C22⋊C4—2442no—
294C22⋊C4—2441no—
295C42—1221no—
296C42—1221no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—612no—
310C23—1221no—
311C23—1221no—
312C23—2441no—
313C23—2441no—
314C23C2×C22⋊#692311yescharacteristic
315D4—82no—
316D4—84no—
317D4—4884no—
318D4—2444no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—612no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—4881no—
333C2×C4—2442no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4#1451983511yescharacteristic
343C2×C4#1451983511yescharacteristic
344C8—4882no—
345C8—2444no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—1222no—
361C22—4881no—
362C22—2442no—
363C22—2441no—
364C22—2441no—
365C22C2×#1451983511yescharacteristic
366C22#1684075211yescharacteristic
367C22D61⋊#10411yescharacteristic
368C4—21no—
369C4—21no—
370C4—41no—
371C4—81no—
372C4—1222no—
373C4—4881no—
374C4—4881no—
375C4—2441no—
376C4—2441no—
377C2—21no—
378C2—21no—
379C2—81no—
380C2—161no—
381C2—2442no—
382C2#2146119411yescharacteristic
383C2#2146207411yescharacteristic
384C2#2146211811yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#121×C61C4
socleC22×C61C2×#99
prime radical#21451704C2
cosocleC2×#11758196C23
hypercenterC2×#121#6923
hypocenterC61#11737
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C4×#14519837C2semidirect
2. #21461054C2semidirect
3. #21460818C2semidirect
4. #21460801C2semidirect
215. C61#11737semidirect

Maximal subgroups

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

subgroupindex
C4×#145198372
#214610542
#214608182
#214608012
#214517042
#1173761