Finite Group Databasebeta

← #30595753

Subgroups — #30595753

Order 15616.

572 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461604C211yesmaximal, characteristic, complemented
2#21461533C211yesmaximal, characteristic, complemented
3#21460636C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454173C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519832—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×#14519773C411yescharacteristic
14C2×#14519763—21no—
15C2×#14519763—21no—
16#16839665C2211yescharacteristic
17#16839664C411yescharacteristic
18#16839663C2211yescharacteristic
19#16839662—21no—
20#16839662—21no—
21C42×Dic61C2211yescharacteristic
22C61×#390C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—24no—
26#14519832—42no—
27C4×#92420—24no—
28C22×Dic122—21no—
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61—21no—
31C22×C22⋊D61—21no—
32#14519776—42no—
33#14519773—42no—
34#14519763—44no—
35#14519763—42no—
36#14519763—42no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
51C22×D4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C42×C61C2×C411yescharacteristic
56C24×C61—21no—
57C23×D61—21no—
58C2×D4×C61—22no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C22×C4×C61—21no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C2×C22⋊D61—42no—
66C2×C22⋊D61—42no—
67C2×C22⋊D61—42no—
68C2×C22⋊D61—42no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×D244—22no—
77C2×D244—41no—
78C2×D244—41no—
79C2×Dic122—42no—
80C2×Dic122—42no—
81C2×Dic122—42no—
82C2×#92420—24no—
83C2×#92420—24no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—42no—
90C22⋊C4×C61—42no—
91C42×C61—22no—
92C22⋊Dic61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—42no—
95#11758198—42no—
96#11758198—42no—
97#11758198—41no—
98#11758198—41no—
99#11758198—42no—
100C4⋊Dic61—41no—
101#11758196—42no—
102C4×Dic61—22no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—22no—
106C4×Dic61—41no—
107C4×Dic61D812yes—
108C4×Dic61SD1612yes—
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—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124D4×C61—82no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#10212yes—
136C2×C4×C61#13112yes—
137C22⋊D61—84no—
138C22⋊D61—84no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61#10012yes—
149C2×Dic61#10212yes—
150C2×Dic61#10412yes—
151C2×Dic61#10412yes—
152C2×Dic61C2×D811yescharacteristic
153C2×Dic61C2×SD1611yescharacteristic
154C2×Dic61AGL(1,ℤ/8)12yes—
155D244—82no—
156Dic122—84no—
157#92420—44no—
158#92420—44no—
159#7679—611nomaximal, Sylow
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61#40811yescharacteristic
168C22×C61#41011yescharacteristic
169C22×C61C2×#10011yescharacteristic
170C22×C61C2×#10211yescharacteristic
171C22×C61#41811yescharacteristic
172C22×C61C2×#10411yescharacteristic
173C22×C61C2×#10411yescharacteristic
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C4×C61—22no—
182C4×C61—22no—
183C4×C61—41no—
184C4×C61—81no—
185Dic61—22no—
186Dic61—21no—
187Dic61—21no—
188Dic61—22no—
189Dic61—81no—
190Dic61#32914yes—
191#2858—611no—
192#1767—611no—
193#1744—611no—
194#1270—612no—
195#1270—612no—
196C2×C61—161no—
197C2×C61#146911yescharacteristic
198C2×C61#148411yescharacteristic
199C2×C61#149211yescharacteristic
200C2×C61#150211yescharacteristic
201C2×C61#150511yescharacteristic
202C2×C61C2×#32911yescharacteristic
203C2×C61#154511yescharacteristic
204D61—161no—
205C2×C4⋊Q8—611no—
206C2×#127—611no—
207C2×#124—1221no—
208C2×#124—1221no—
209C2×C4⋊C8—1221no—
210C2×#97—1221no—
211C2×C4×C8—1221no—
212#390—611no—
213#390—611no—
214#390—611no—
215#390—1221no—
216#390—1221no—
217#390#692311yescharacteristic
218C43—611no—
219#336—612no—
220#336—612no—
221#336—1221no—
222C61#767911yescharacteristic, complemented, Sylow
223C22×Q8—1221no—
224C22×D4—611no—
225C22×D4—1221no—
226C22×D4—1221no—
227C22×D4C2×#692311yescharacteristic
228C22×C8—1222no—
229C22×C8—1222no—
230C4⋊Q8—2442no—
231#127—2442no—
232#124—2442no—
233#124—2442no—
234#124—2444no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4C2×#692311yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
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—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42C2×#692311yescharacteristic
253C4⋊C8—1224no—
254#97—2442no—
255C4×C8—1224no—
256C24—21no—
257C24—1221no—
258C2×Q8—2442no—
259C2×Q8—2442no—
260C2×Q8—2442no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—1222no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2442no—
268C2×D4—2442no—
269C2×D4—2442no—
270C2×D4—2442no—
271C2×D4—2442no—
272C2×D4—2442no—
273C22×C4—21no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4C22⋊#692311yescharacteristic
280C22×C4C22⋊#692311yescharacteristic
281C22×C4C22×#692311yescharacteristic
282C2×C8—1224no—
283C2×C8—1224no—
284C2×C8—2442no—
285C2×C8—2442no—
286C2×C8—2442no—
287C2×C8—2442no—
288C4⋊C4—41no—
289C4⋊C4—2441no—
290C4⋊C4—2442no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—2442no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C22⋊C4—2442no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2442no—
300C22⋊C4—2442no—
301C42—22no—
302C42—612no—
303C42—612no—
304C42—1222no—
305C42—1222no—
306C42—1222no—
307C42—1222no—
308C42—2441no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23C2×C22⋊#692311yescharacteristic
324Q8—4884no—
325D4—82no—
326D4—4882no—
327D4—4884no—
328D4—4884no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—612no—
342C2×C4—612no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—612no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4#1451983912yes—
356C2×C4#1451986412yes—
357C8—2444no—
358C8—2444no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—4881no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22—4881no—
372C22—4881no—
373C22#1684073511yescharacteristic
374C22#1684074111yescharacteristic
375C22D61⋊#10011yescharacteristic
376C22C2×#1451983911yescharacteristic
377C22#1684075411yescharacteristic
378C22D61⋊#10411yescharacteristic
379C22D61⋊#10411yescharacteristic
380C4—22no—
381C4—22no—
382C4—41no—
383C4—81no—
384C4—614no—
385C4—1222no—
386C4—1221no—
387C4—1221no—
388C4—1222no—
389C4—4881no—
390C2—161no—
391C2—9761no—
392C2#2146108811yescharacteristic
393C2#2146113811yescharacteristic
394C2#2146116411yescharacteristic
395C2#2146119811yescharacteristic
396C2#2146120911yescharacteristic
397C2D61⋊#32911yescharacteristic
398C2#2146132711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#7679
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21461604C2semidirect
2. #21461533C2semidirect
3. #21460636C2semidirect
4. #21460635C2semidirect
222. C61#7679semidirect

Maximal subgroups

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

subgroupindex
#214616042
#214615332
#214606362
#214606352
#214541732
#767961