Finite Group Databasebeta

← #29576849

Subgroups — #29576849

Order 15616.

480 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455628C211yesmaximal, characteristic
2#21454927C211yesmaximal, characteristic
3#21446768C211yesmaximal, characteristic, complemented
4#21445836C211yesmaximal, characteristic
5#21443721C211yesmaximal, characteristic, complemented
6#21443693C211yesmaximal, characteristic, complemented
7C61×#1548C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16840054—21no—
10#16840049—21no—
11#16840044C412yescomplemented
12#16840039C412yescomplemented
13C8×Dic122—21no—
14C8×D244—21no—
15#16839825—22no—
16#16839814—21no—
17#16839802—21no—
18#16839786C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C4⋊C8×D61—21no—
21C2×#14519703—21no—
22#16839761—21no—
23C4×C4⋊Dic61C2211yescharacteristic
24#16839524—22no—
25#16839523—21no—
26C2×C4⋊Q8×C61C2211yescharacteristic
27C61×#431C2211yescharacteristic
28C61×#423C2211yescharacteristic
29C61×#333—21no—
30C61×#333—21no—
31C2×#11758222D411yescharacteristic
32C2×#11758194—21no—
33C22×#92418D412yes—
34C2×C8×D61—22no—
35C4×Dic122C2×C411yescharacteristic
36C4×Dic122D411yescharacteristic
37C4×D244C2×C411yescharacteristic
38C4×D244D411yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41#14519736D411yescharacteristic
42#14519734—21no—
43C2×C4⋊Dic61—21no—
44C2×C4×Dic61—21no—
45C42×D61—21no—
46#14519710—22no—
47#14519708—22no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418C2×C412yes—
52#14519706—22no—
53#14519703—42no—
54#14519700—22no—
55#14519697—22no—
56#14519689—22no—
57C8×Dic61—22no—
58#14519684—21no—
59C22×Q8×C61—21no—
60C2×M16×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61C2×C412yes—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61D411yescharacteristic
71C4⋊C8×C61D411yescharacteristic
72C22⋊C8×C61—21no—
73C4×C8×C61—21no—
74C2×Q8×C61—22no—
75C2×Q8×C61—41no—
76C2×Q8×C61—82no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C2×C22⋊D61—21no—
82C22×Dic61—41no—
83#11758222—21no—
84#11758222—21no—
85#11758222SD1612yes—
86#11758222Q1612yes—
87C2×D244C22⋊C411yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×Dic122C22⋊C411yescharacteristic
92M16×C61—41no—
93M16×C61—41no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—41no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C22⋊Dic61—21no—
106#11758198—21no—
107#11758198—21no—
108C4⋊Dic61—22no—
109C4⋊Dic61—41no—
110C4⋊Dic61C22⋊C411yescharacteristic
111C4⋊Dic61C22⋊C411yescharacteristic
112#11758196—21no—
113#11758196—21no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C4×Dic61—41no—
118C4×Dic61—41no—
119#11758194—41no—
120#11758194—41no—
121C2×#92418—22no—
122C2×#92418—22no—
123C2×#92418—42no—
124C8×D61—82no—
125C23×C61#12111yescharacteristic
126C22×D61—21no—
127Q8×C61—82no—
128Q8×C61—82no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—82no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12311yescharacteristic
140C2×C4×C61C2×SD1611yescharacteristic
141C2×C4×C61C2×Q1611yescharacteristic
142C2×C4×C61#13511yescharacteristic
143C2×C4×C61#13511yescharacteristic
144C22⋊D61—22no—
145C22⋊D61—22no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—42no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152D244—21no—
153D244#10312yes—
154C4×D61—22no—
155C4×D61—22no—
156C4×D61—41no—
157C4×D61—41no—
158C4×D61—81no—
159Dic122—21no—
160Dic122#10312yes—
161C8×C61—41no—
162C8×C61—41no—
163C8×C61—81no—
164#92418—42no—
165#92418—42no—
166#9315—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#38611yescharacteristic
170C22×C61#46511yescharacteristic
171C22×C61#46711yescharacteristic
172C2×D61—22no—
173C2×D61—41no—
174C2×D61—41no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—82no—
179C4×C61C2×#10311yescharacteristic
180C4×C61#41611yescharacteristic
181C4×C61#45511yescharacteristic
182C4×C61#45611yescharacteristic
183C4×C61#46511yescharacteristic
184C4×C61#46711yescharacteristic
185Dic61—22no—
186Dic61—41no—
187Dic61—41no—
188Dic61—82no—
189#3079—611no—
190#2988—611no—
191#1987—611no—
192#1806—611no—
193#1548D6111yescharacteristic, complemented
194#1303—611no—
195#1292—611no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61#188211yescharacteristic
199C2×C61#189211yescharacteristic
200C2×C61#190311yescharacteristic
201D61—42no—
202C2×C4⋊Q8C2×D6111yescharacteristic
203C4×#41—611no—
204#477—1221no—
205#476—1221no—
206#475—612no—
207#474—612no—
208C8×Q8—1221no—
209C8×D4—1221no—
210C8×D4—1222no—
211#431—1221no—
212#431C2×D6111yescharacteristic
213#428—1221no—
214#423—611no—
215#423C2×D6111yescharacteristic
216C2×C4⋊C8—611no—
217C2×C4⋊C8—1221no—
218C2×#104—1221no—
219#417—1221no—
220C4×C4⋊C4—611no—
221#340—1222no—
222#339—1221no—
223#333—21no—
224#333—21no—
225C61#931511yescharacteristic, complemented, Sylow
226C2×#41—611no—
227C22×Q8—21no—
228C2×M16—21no—
229C2×M16—1221no—
230C22×C8—612no—
231C22×C8—1222no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8C4×D6112yes—
236C4×Q8—611no—
237C4×Q8—611no—
238C4×D4—611no—
239C4×D4—611no—
240C4×D4—1221no—
241C4×D4—1221no—
242#117—611no—
243#117—1221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—1221no—
247C2×C42—1221no—
248C2×C42—1221no—
249C2×C42C22×D6111yescharacteristic
250#107—1222no—
251#106—1222no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—612no—
255C4⋊C8—1222no—
256C4⋊C8—1221no—
257C4⋊C8—1221no—
258C4⋊C8—1221no—
259C4⋊C8C22⋊D6111yescharacteristic
260C4⋊C8C22⋊D6111yescharacteristic
261#104—2442no—
262#103—1222no—
263#102—1222no—
264C22⋊C8—21no—
265C22⋊C8—1222no—
266C4×C8—21no—
267C4×C8—1222no—
268#95—1221no—
269#41—612no—
270#41—612no—
271#41—1221no—
272#41—1221no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×Q8—611no—
277C2×D4—611no—
278C2×D4—1221no—
279C22×C4—41no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—2441no—
284C22×C4#1175822211yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287M16—41no—
288M16—41no—
289M16—2441no—
290M16—2441no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—41no—
294C2×C8—1222no—
295C2×C8—1222no—
296C2×C8—4882no—
297C2×C8—2442no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—611no—
303C4⋊C4—611no—
304C4⋊C4—1222no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—2441no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C42—1221no—
312C42—1221no—
313C42—1221no—
314C42—2441no—
315C42—2441no—
316C42C2×C4×D6111yescharacteristic
317C42D4×D6111yescharacteristic
318C42#1175822411yescharacteristic
319C42C2×C22⋊D6111yescharacteristic
320C23—1221no—
321C23#1451975011yescharacteristic
322Q8—82no—
323Q8—82no—
324Q8—612no—
325Q8—1221no—
326D4—612no—
327D4—1222no—
328D4—1222no—
329D4—1221no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—1221no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—2442no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4C22⋊C4×D6111yescharacteristic
347C2×C4#1451973711yescharacteristic
348C2×C4C4×C22⋊D6111yescharacteristic
349C2×C4#1451974511yescharacteristic
350C2×C4#1451974811yescharacteristic
351C2×C4#1451975911yescharacteristic
352C2×C4SD16×D6111yescharacteristic
353C2×C4Q16×D6111yescharacteristic
354C2×C4#1451979811yescharacteristic
355C2×C4#1451980011yescharacteristic
356C8—41no—
357C8—41no—
358C8—81no—
359C8—2442no—
360C8—2442no—
361C22—21no—
362C22—21no—
363C22—1222no—
364C22—2441no—
365C22—2441no—
366C22#1683963811yescharacteristic
367C22#1683999411yescharacteristic
368C22#1684000211yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—1222no—
374C4—4882no—
375C4—2441no—
376C4—2441no—
377C4#103×D6111yescharacteristic
378C4#1683975711yescharacteristic
379C4#1683993811yescharacteristic
380C4#1683994311yescharacteristic
381C4#1683998811yescharacteristic
382C4#1684000011yescharacteristic
383C2—21no—
384C2—21no—
385C2—2442no—
386C2#2144618511yescharacteristic
387C2#2144623911yescharacteristic
388C2#2144630211yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1548C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1548D61
hypocenterC61#9315
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
3. #21446768C2semidirect
5. #21443721C2semidirect
6. #21443693C2semidirect
7. C61×#1548C2semidirect
11. #16840044C4semidirect
12. #16840039C4semidirect
193. #1548D61semidirect
225. C61#9315semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214549272
#214467682
#214458362
#214437212
#214436932
C61×#15482
#931561