Finite Group Databasebeta

← #30595664

Subgroups — #30595664

Order 15616.

580 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 102 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#21461711C211yesmaximal, characteristic, complemented
2#21461480C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21454152C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519834—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519762—21no—
13C2×#14519752C411yescharacteristic
14C2×C42×D61C2211yescharacteristic
15#16839664C411yescharacteristic
16#16839663C2211yescharacteristic
17#16839658C2211yescharacteristic
18#16839652—21no—
19#16839651—21no—
20#16839640—21no—
21#16839619C411yescharacteristic
22C61×#389C411yescharacteristic
23C2×D61⋊C8—24no—
24C2×D61⋊C8—42no—
25C2×D61⋊C8—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519834—42no—
29C22×D244—21no—
30C22×D244C2×C411yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519762—42no—
35#14519762—42no—
36#14519752—42no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48C42×D61—42no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55#95×C61—21no—
56C23×D61—21no—
57C23×D61C22⋊C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×D244—22no—
68C2×D244—41no—
69C2×D244—41no—
70C2×D244—42no—
71C2×D244—42no—
72C2×D244—42no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61D812yes—
82C2×C4×D61SD1612yes—
83C2×#92420—24no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89D61⋊C8—48no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—42no—
93C42×C61—41no—
94#11758198—42no—
95#11758198—42no—
96#11758198—42no—
97#11758198—42no—
98#11758198—41no—
99#11758198—41no—
100#11758198—42no—
101C4⋊Dic61—22no—
102#11758196—41no—
103#11758196—41no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C23×C61C2×C22⋊C411yescharacteristic
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61#9912yes—
120C22×D61#10212yes—
121C22×D61#10412yes—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#10212yes—
136C2×C4×C61#13112yes—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61C2×D811yescharacteristic
148C2×Dic61C2×SD1611yescharacteristic
149C2×Dic61#13512yes—
150D244—82no—
151D244—84no—
152C4×D61—24no—
153C4×D61—24no—
154C4×D61—44no—
155C4×D61—44no—
156#92420—44no—
157#92420—82no—
158#7654—611nomaximal, Sylow
159C22×C61#40811yescharacteristic
160C22×C61C2×#9911yescharacteristic
161C22×C61#41311yescharacteristic
162C22×C61C2×#10211yescharacteristic
163C22×C61#41611yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C22×C61#42111yescharacteristic
166C2×D61—22no—
167C2×D61—22no—
168C2×D61—22no—
169C2×D61—22no—
170C2×D61—22no—
171C2×D61—22no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61#32714yes—
180C4×C61—22no—
181C4×C61—22no—
182C4×C61—41no—
183C4×C61—81no—
184C4×C61—81no—
185Dic61—21no—
186Dic61—21no—
187Dic61—22no—
188Dic61—41no—
189Dic61—81no—
190#2854—611no—
191#1817—611no—
192C2×#336—611no—
193#1271—612no—
194#1270—612no—
195C2×C61#146811yescharacteristic
196C2×C61#148011yescharacteristic
197C2×C61#149411yescharacteristic
198C2×C61C2×#32711yescharacteristic
199C2×C61#151611yescharacteristic
200C2×C61#153211yescharacteristic
201C2×C61#154011yescharacteristic
202D61—24no—
203D61—161no—
204C23×C8—1221no—
205C2×#123—1221no—
206C2×#121—611no—
207C22×C42—611no—
208C2×C22⋊C8—1221no—
209#390—611no—
210#390—611no—
211#389—611no—
212#389#692311yescharacteristic
213#388—1221no—
214#388—1221no—
215#386—1221no—
216#380—611no—
217#336—612no—
218#336—612no—
219#336—1221no—
220#336—1221no—
221C61#765411yescharacteristic, complemented, Sylow
222C22×D4—611no—
223C22×D4—1221no—
224C23×C4—611no—
225C23×C4—611no—
226C23×C4—611no—
227C22×C8—1222no—
228C22×C8—1224no—
229C22×C8—1222no—
230C22×C8—2442no—
231C22×C8—2442no—
232#123—2442no—
233#123—2442no—
234#121—2442no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4C2×#692311yescharacteristic
239C2×C4⋊C4C2×#692311yescharacteristic
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—2442no—
250C2×C42C2×#692311yescharacteristic
251C22⋊C8—2442no—
252#95—21no—
253#95—1221no—
254#95—1221no—
255C24—611no—
256C24—1221no—
257C2×D4—1222no—
258C2×D4—2441no—
259C2×D4—2441no—
260C2×D4—2442no—
261C2×D4—2442no—
262C2×D4—2442no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—612no—
268C22×C4—612no—
269C22×C4—611no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4—1222no—
273C22×C4—1222no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1221no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4C22⋊#692311yescharacteristic
280C22×C4C22⋊#692311yescharacteristic
281C22×C4C22×#692311yescharacteristic
282C2×C8—1224no—
283C2×C8—2442no—
284C2×C8—2442no—
285C2×C8—2442no—
286C2×C8—2442no—
287C2×C8—2448no—
288C2×C8—2442no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—42no—
292C4⋊C4—1222no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C22⋊C4—2442no—
296C22⋊C4—2442no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2442no—
300C22⋊C4—2442no—
301C22⋊C4—2442no—
302C42—41no—
303C42—2441no—
304C42—2441no—
305C42—2441no—
306C23—612no—
307C23—612no—
308C23—612no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23—1221no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23C2×C22⋊#692311yescharacteristic
321D4—4882no—
322D4—4884no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—612no—
339C2×C4—1224no—
340C2×C4—1224no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—2444no—
349C2×C4—2444no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4#1451983912yes—
354C2×C4#1451986512yes—
355C8—4882no—
356C8—2444no—
357C22—614no—
358C22—1222no—
359C22—1222no—
360C22—1222no—
361C22—1222no—
362C22—1222no—
363C22—1222no—
364C22—4881no—
365C22—4881no—
366C22—4881no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22#1684073711yescharacteristic
372C22D61⋊#9911yescharacteristic
373C22#1684074811yescharacteristic
374C22C2×#1451983911yescharacteristic
375C22#1684075211yescharacteristic
376C22D61⋊#10411yescharacteristic
377C22#1684076111yescharacteristic
378C4—22no—
379C4—22no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—1221no—
384C4—1221no—
385C4—1222no—
386C4—4881no—
387C4—2441no—
388C2—1224no—
389C2—9761no—
390C2#2146108711yescharacteristic
391C2#2146112611yescharacteristic
392C2#2146117311yescharacteristic
393C2D61⋊#32711yescharacteristic
394C2#2146124611yescharacteristic
395C2#2146129611yescharacteristic
396C2#2146131611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7654
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #21461711C2semidirect
2. #21461480C2semidirect
3. #21460638C2semidirect
4. #21460636C2semidirect
221. C61#7654semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214614802
#214606382
#214606362
#214541522
#765461