Finite Group Databasebeta

← #30601881

Subgroups — #30601881

Order 15616.

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

normal subgroups only

This group has 442 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#21461998C211yesmaximal, characteristic
2#21461997C211yesmaximal, characteristic
3#21461613C211yesmaximal, characteristic
4D61⋊#334C211yesmaximal, characteristic
5D61⋊#333C211yesmaximal, characteristic
6D61⋊#332C211yesmaximal, characteristic
7#487×D61C211yesmaximal, characteristic
8D61⋊(C4⋊C8)C2211yescharacteristic
9D61⋊(C4⋊C8)C2211yescharacteristic
10D61⋊(C4⋊C8)C2211yescharacteristic
11C2×#14519831—21no—
12C4×C4⋊#6923C2211yescharacteristic
13#16840635—22no—
14#16840635—22no—
15(C2×#6923)⋊C8—21no—
16#16840624—21no—
17#16840623—21no—
18#16840622—22no—
19#16840621—22no—
20C4⋊Q8×D61C2211yescharacteristic
21C4⋊Q8×D61C2211yescharacteristic
22#16840114C411yescharacteristic, complemented
23#16840113C411yescharacteristic, complemented
24#16840112C411yescharacteristic, complemented
25#16840111—21no—
26#16840111—21no—
27#103×D61—21no—
28#103×D61—21no—
29C4×C8×D61C2211yescharacteristic
30C61×#487C411yescharacteristic, complemented
31C2×D61⋊C8—21no—
32C2×D61⋊C8—21no—
33C2×D61⋊C8—21no—
34C2×C4⋊#6923D412yes—
35C2×C4×#6923—21no—
36#14519844—21no—
37#14519844—21no—
38#14519844D412yes—
39C4⋊#92420—21no—
40C4⋊#92420—21no—
41C4⋊#92420—21no—
42#14519831—42no—
43(C2×#6923)⋊C4—21no—
44C2×Q8×D61—21no—
45C2×Q8×D61—21no—
46C2×C8×D61D411yescharacteristic
47C2×C8×D61D411yescharacteristic
48#14519777C2×C411yescharacteristic
49#14519777C2×C411yescharacteristic
50#14519776—21no—
51#14519776—21no—
52#14519776—21no—
53#14519776—21no—
54#14519775—21no—
55#14519775—21no—
56C4⋊C4×D61—21no—
57C4⋊C4×D61—21no—
58C4⋊C4×D61—21no—
59C4⋊C4×D61—21no—
60C42×D61C2311yescharacteristic
61#14519702—21no—
62#14519702—21no—
63#14519701—21no—
64#14519701—21no—
65#14519700—21no—
66#14519700—21no—
67C4×#92418C2×C411yescharacteristic
68C8×Dic61D411yescharacteristic
69C8×Dic61D411yescharacteristic
70C4⋊Q8×C61C2×C411yescharacteristic
71C4⋊Q8×C61C2×C411yescharacteristic
72#103×C61—21no—
73#103×C61—21no—
74C4×C8×C61C2×C411yescharacteristic
75C22×#6923—22no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78Q8×D61—41no—
79Q8×D61—41no—
80Q8×D61—41no—
81Q8×D61—41no—
82Q8×D61—82no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61C2×D411yescharacteristic
86C2×C4×D61C2×D411yescharacteristic
87C2×C4×D61#4111yescharacteristic
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×#92420—22no—
93C2×#92420—41no—
94C2×#92420—41no—
95C4⋊#6923—22no—
96C4⋊#6923—22no—
97C4×#6923—41no—
98C4×#6923—41no—
99D61⋊C8—41no—
100D61⋊C8—41no—
101D61⋊C8—42no—
102D61⋊C8—42no—
103C2×C8×C61C22⋊C411yescharacteristic
104C2×C8×C61C22⋊C411yescharacteristic
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C42×C61C22×C411yescharacteristic
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114#11758196—41no—
115#11758196—41no—
116#11758196—41no—
117#11758196—41no—
118C4×Dic61C2×D411yescharacteristic
119C4×Dic61C2×D411yescharacteristic
120C4×Dic61#4111yescharacteristic
121C2×#92418C22⋊C411yescharacteristic
122C2×#92418C22⋊C411yescharacteristic
123C8×D61—21no—
124C8×D61—21no—
125C8×D61—21no—
126C8×D61—21no—
127C22×D61#12111yescharacteristic
128C2×#6923—42no—
129C2×#6923—42no—
130C2×#6923—42no—
131Q8×C61—41no—
132Q8×C61—41no—
133Q8×C61—81no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61C2×C22⋊C411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#12111yescharacteristic
142C2×Dic61#12411yescharacteristic
143C2×Dic61#12711yescharacteristic
144C4×D61—22no—
145C4×D61—81no—
146C4×D61—81no—
147C4×D61—82no—
148C4×D61#13511yescharacteristic
149C4×D61#13511yescharacteristic
150C4×D61AGL(1,ℤ/8)11yescharacteristic
151C4×D61#13711yescharacteristic
152C4×D61#13712yes—
153C4×D61#13712yes—
154Dic122—41no—
155Dic122—41no—
156Dic122—82no—
157Dic122—81no—
158Dic122—81no—
159Dic122—81no—
160#92420—42no—
161#92420—81no—
162#92420—81no—
163C8×C61—21no—
164C8×C61—21no—
165#92418—21no—
166#92418—21no—
167#9745—611nomaximal, Sylow
168C22×C61#39011yescharacteristic
169C2×D61#46311yescharacteristic
170C2×D61#46411yescharacteristic
171C2×D61#47012yes—
172C2×D61#47112yes—
173#6923—82no—
174C4×C61—21no—
175C4×C61—81no—
176C4×C61—81no—
177C4×C61#41611yescharacteristic
178C4×C61#41711yescharacteristic
179C4×C61#44112yes—
180Dic61—21no—
181Dic61—81no—
182Dic61—81no—
183Dic61#46311yescharacteristic
184Dic61#46411yescharacteristic
185Dic61#49711yescharacteristic
186Dic61#49711yescharacteristic
187C2×#487—611no—
188#1988—611no—
189#1987—611no—
190#1770—611no—
191C2×#334—611no—
192C2×#333—611no—
193C2×#332—611no—
194C2×C61#197111yescharacteristic
195C2×C61#197711yescharacteristic
196C2×C61#198311yescharacteristic
197D61#170312yes—
198D61#170412yes—
199C2×C4⋊Q8—611no—
200C2×C4⋊Q8—611no—
201#487—611no—
202#487—611no—
203#487—611no—
204#487—1221no—
205#487—1221no—
206#487#692311yescharacteristic, complemented
207C2×C4⋊C8—611no—
208C2×C4⋊C8—611no—
209C2×C4⋊C8—611no—
210C2×#103—1221no—
211C2×#103—1221no—
212C2×#97—1221no—
213C2×C4×C8—611no—
214C4×C4⋊C4—611no—
215#340—1222no—
216#340—1222no—
217#336—1221no—
218#334—1221no—
219#334—1221no—
220#333—1222no—
221#332—1222no—
222C61#974511yescharacteristic, complemented, Sylow
223C22×Q8—1221no—
224C22×Q8—1221no—
225C22×C8—611no—
226C22×C8—611no—
227C22×C8—1221no—
228C22×C8—1221no—
229C22×C8—1221no—
230C4⋊Q8—611no—
231C4⋊Q8—611no—
232C4⋊Q8—1221no—
233C4⋊Q8—1221no—
234C4⋊Q8—1221no—
235C4⋊Q8—1221no—
236C4⋊Q8—1221no—
237C4⋊Q8—1221no—
238C4⋊Q8C2×#692311yescharacteristic
239C4⋊Q8C2×#692311yescharacteristic
240C2×C4⋊C4—612no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C42—611no—
246C2×C42—1221no—
247C4⋊C8—612no—
248C4⋊C8—1221no—
249C4⋊C8—1221no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253#103—21no—
254#103—21no—
255#103—1221no—
256#103—1221no—
257#103—1221no—
258#103—1221no—
259#103—1221no—
260#103—1221no—
261#97—2442no—
262C4×C8—611no—
263C4×C8—611no—
264C4×C8—611no—
265C4×C8C2×#692311yescharacteristic
266#95—1221no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×Q8—4882no—
272C2×Q8—2441no—
273C2×Q8—2441no—
274C2×Q8—2441no—
275C2×Q8—2441no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1222no—
282C22×C4—2441no—
283C22×C4—2441no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1222no—
291C2×C8—2441no—
292C2×C8—2441no—
293C2×C8—2442no—
294C2×C8—2442no—
295C2×C8—2441no—
296C2×C8—2441no—
297C2×C8C22⋊#692311yescharacteristic
298C2×C8C22⋊#692311yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—1222no—
304C4⋊C4—1222no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C4⋊C4—2441no—
312C4⋊C4—2441no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—2441no—
317C42—2441no—
318C42C22×#692311yescharacteristic
319C23—611no—
320Q8—41no—
321Q8—41no—
322Q8—81no—
323Q8—4881no—
324Q8—4881no—
325Q8—4881no—
326Q8—4882no—
327Q8—2441no—
328Q8—2441no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—612no—
338C2×C4—612no—
339C2×C4—611no—
340C2×C4—1222no—
341C2×C4—4882no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4C2×C22⋊#692311yescharacteristic
350C2×C4D4×#692311yescharacteristic
351C2×C4D4×#692311yescharacteristic
352C8—21no—
353C8—21no—
354C8—1221no—
355C8—1221no—
356C8—4881no—
357C8—4881no—
358C8—2442no—
359C22—612no—
360C22—612no—
361C22—611no—
362C22—611no—
363C22#1684071411yescharacteristic
364C4—21no—
365C4—81no—
366C4—81no—
367C4—611no—
368C4—611no—
369C4—611no—
370C4—611no—
371C4—1221no—
372C4—4882no—
373C4—4881no—
374C4—4881no—
375C4#1684075211yescharacteristic
376C4#1684075311yescharacteristic
377C4#1684080212yes—
378C2—612no—
379C2—612no—
380C2#2146196711yescharacteristic
381C2#2146197911yescharacteristic
382C2#2146198711yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#487C4
socleC22×C61#390
prime radicalC22×D61#121
cosocleC42×D61C23
hypercenter#487#6923
hypocenterC61#9745
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
22. #16840114C4semidirect
23. #16840113C4semidirect
24. #16840112C4semidirect
30. C61×#487C4semidirect
206. #487#6923semidirect
222. C61#9745semidirect

Maximal subgroups

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

subgroupindex
#214619982
#214619972
#214616132
D61⋊#3342
D61⋊#3332
D61⋊#3322
#487×D612
#974561