Finite Group Databasebeta

← #30605232

Subgroups — #30605232

Order 15616.

450 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 66 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, complemented
2#21461074C211yesmaximal, characteristic, complemented
3#21460818C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21451704C211yesmaximal, characteristic
6#16840765—21no—
7C2×#14519837—21no—
8#16840733—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×#11758213—41no—
24C2×#11758217—22no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519837—42no—
28#14519834—41no—
29C22⋊#92420—22no—
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—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—81no—
77C2×C22⋊D61—81no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—81no—
86#11758217—42no—
87#11758217—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90#11758213—82no—
91C4⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97C22⋊Dic61—81no—
98C22⋊Dic61—81no—
99C22⋊Dic61—81no—
100#11758198—41no—
101#11758198—81no—
102#11758196—41no—
103#11758196—81no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61—41no—
124D4×C61—82no—
125D4×C61—84no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
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#9911yescharacteristic
135C2×C4×C61#9911yescharacteristic
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—84no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61AGL(1,ℤ/8)11yescharacteristic
152C2×Dic61#13711yescharacteristic
153C4×D61—42no—
154C4×D61—81no—
155#92420—82no—
156#92420—82no—
157#11832—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61C2×#9911yescharacteristic
173C22×C61#41711yescharacteristic
174C22×C61#42111yescharacteristic
175C2×D61—42no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—81no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—41no—
183C4×C61—81no—
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—81no—
189Dic61—81no—
190#2635—611no—
191#1800—611no—
192#1465—611no—
193#1353—612no—
194#1345—612no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—81no—
198C2×C61—161no—
199C2×C61#151311yescharacteristic
200C2×C61#212111yescharacteristic
201C2×C61#213411yescharacteristic
202D61—81no—
203C2×#121#692311yescharacteristic
204C2×C4×D4—611no—
205#423—1221no—
206C2×#100—1221no—
207#407—1221no—
208#400—611no—
209#399—611no—
210#394—611no—
211#394—1221no—
212#392—611no—
213#392—1221no—
214#388—1221no—
215#386—1221no—
216#381—611no—
217#343—612no—
218#324—612no—
219#323—1221no—
220C61#1183211yescharacteristic, complemented, Sylow
221C22×D4—21no—
222C22×D4—611no—
223C22×D4—1221no—
224C22×D4C2×#692311yescharacteristic
225C23×C4—611no—
226C23×C4C2×#692311yescharacteristic
227C2×M16—1222no—
228C2×M16—2441no—
229#121—41no—
230#121—41no—
231C4×D4—2441no—
232C4×D4—2441no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4C2×#692311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—611no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C4⋊C8—2441no—
246C4⋊C8—2441no—
247#100—2442no—
248C22⋊C8—1222no—
249C22⋊C8—2441no—
250#95—611no—
251#95—611no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255C24—21no—
256C24—611no—
257C24C22⋊#692311yescharacteristic
258C2×D4—41no—
259C2×D4—42no—
260C2×D4—81no—
261C2×D4—81no—
262C2×D4—81no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—4881no—
266C2×D4—4881no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2442no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—81no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—4881no—
282C22×C4C22⋊#692311yescharacteristic
283C22×C4C22×#692311yescharacteristic
284M16—4882no—
285M16—2442no—
286M16—2442no—
287C2×C8—2442no—
288C2×C8—2442no—
289C4⋊C4—41no—
290C4⋊C4—4881no—
291C4⋊C4—2441no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—4881no—
295C22⋊C4—4881no—
296C22⋊C4—4881no—
297C22⋊C4—4881no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C42—1221no—
303C42—1221no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23—2441no—
320C23—2441no—
321C23C2×C22⋊#692311yescharacteristic
322D4—82no—
323D4—84no—
324D4—4884no—
325D4—2442no—
326D4—2442no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—4881no—
342C2×C4—2442no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4#1451983511yescharacteristic
352C2×C4#1451983511yescharacteristic
353C8—4882no—
354C8—4882no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—4881no—
370C22—2442no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22C2×#1451983511yescharacteristic
375C22#1684075311yescharacteristic
376C22#1684075911yescharacteristic
377C4—21no—
378C4—21no—
379C4—41no—
380C4—81no—
381C4—1221no—
382C4—1221no—
383C4—4881no—
384C4—4881no—
385C4—2441no—
386C4—2441no—
387C2—21no—
388C2—21no—
389C2—81no—
390C2—161no—
391C2—4881no—
392C2#2146123411yescharacteristic
393C2#2146207411yescharacteristic
394C2#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#11832
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. #21461683C2semidirect
2. #21461074C2semidirect
3. #21460818C2semidirect
4. #21460801C2semidirect
220. C61#11832semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214610742
#214608182
#214608012
#214517042
#1183261