Finite Group Databasebeta

← #29576851

Subgroups — #29576851

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#21455635C211yesmaximal, characteristic
2#21454928C211yesmaximal, characteristic
3#21446766C211yesmaximal, characteristic, complemented
4#21445836C211yesmaximal, characteristic
5#21444501C211yesmaximal, characteristic, complemented
6#21443720C211yesmaximal, characteristic, complemented
7C61×#1292C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C4×#11758222C2211yescharacteristic
10#16840058—21no—
11#16840053—21no—
12#16840048C412yescomplemented
13#16840043C412yescomplemented
14#16839886—21no—
15#16839827—21no—
16C8×C22⋊D61—22no—
17#16839815C2211yescharacteristic
18#16839814—21no—
19#16839804—21no—
20C4⋊C8×D61—21no—
21C2×#14519703—21no—
22#16839764—21no—
23C4×C4⋊Dic61C2211yescharacteristic
24#16839525—22no—
25#16839523—21no—
26#16839510—21no—
27#16839510—21no—
28C61×#423C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C22×Dic122—21no—
33C2×C8×D61—22no—
34#14519777—21no—
35#14519777—21no—
36#14519777—21no—
37#14519777C2×C412yes—
38C4×Dic122C2×C411yescharacteristic
39C4×Dic122D411yescharacteristic
40C4×D244C2×C411yescharacteristic
41C4×D244D411yescharacteristic
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44#14519736D411yescharacteristic
45#14519734—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—21no—
49C2×C4×Dic61—21no—
50C42×D61—21no—
51#14519711—22no—
52#14519709—22no—
53C4⋊#92418D411yescharacteristic
54C4⋊#92418D411yescharacteristic
55#14519706—22no—
56#14519703—42no—
57#14519702—22no—
58#14519699—22no—
59C22⋊#92418—21no—
60#14519689—22no—
61C4×#92418—21no—
62C8×Dic61—22no—
63#14519684—21no—
64C2×M16×C61—21no—
65C2×M16×C61—21no—
66C22×C8×C61D412yes—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61C2×C412yes—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C2×C22⋊D61—21no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80#11758222—21no—
81#11758222—21no—
82#11758222SD1612yes—
83#11758222Q1612yes—
84C2×D244C22⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×Dic122—22no—
89C2×Dic122—41no—
90C2×Dic122—82no—
91C2×Dic122C22⋊C411yescharacteristic
92M16×C61—41no—
93M16×C61—41no—
94M16×C61—41no—
95M16×C61—41no—
96C2×C8×C61—22no—
97C2×C8×C61—22no—
98C2×C8×C61—42no—
99C2×C8×C61—41no—
100C42×C61C22×C411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61#4111yescharacteristic
104C22⋊Dic61—21no—
105#11758198—21no—
106#11758198—21no—
107C4⋊Dic61—22no—
108C4⋊Dic61—22no—
109C4⋊Dic61—22no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61C22⋊C411yescharacteristic
114C4⋊Dic61C22⋊C411yescharacteristic
115#11758196—21no—
116#11758196—21no—
117C4×Dic61—21no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120C4×Dic61—41no—
121C4×Dic61—41no—
122C2×#92418—21no—
123C2×#92418—21no—
124C8×D61—82no—
125C23×C61#12111yescharacteristic
126C22×D61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C2×C4×C61C2×Q1611yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C22⋊D61—22no—
141C22⋊D61—22no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—82no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150D244—21no—
151D244#10312yes—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—81no—
157Dic122—21no—
158Dic122—82no—
159Dic122—82no—
160Dic122#10312yes—
161C8×C61—42no—
162C8×C61—42no—
163C8×C61—81no—
164#92418—41no—
165#92418—41no—
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×C61C2×#10311yescharacteristic
179C4×C61#41611yescharacteristic
180C4×C61#45511yescharacteristic
181C4×C61#45611yescharacteristic
182C4×C61#46511yescharacteristic
183C4×C61#46711yescharacteristic
184Dic61—22no—
185Dic61—41no—
186Dic61—41no—
187Dic61—82no—
188Dic61—82no—
189#3079—611no—
190#2988—611no—
191#1987—611no—
192#1806—611no—
193#1548—611no—
194#1303—611no—
195#1292D6111yescharacteristic, complemented
196C2×C61—21no—
197C2×C61—21no—
198C2×C61#188211yescharacteristic
199C2×C61#189211yescharacteristic
200C2×C61#190311yescharacteristic
201D61—42no—
202C2×C4⋊Q8—611no—
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—611no—
212#431—1221no—
213#428—1221no—
214#423C2×D6111yescharacteristic
215#423C2×D6111yescharacteristic
216C2×C4⋊C8—1221no—
217C2×C4⋊C8C2×D6111yescharacteristic
218C2×#104—1221no—
219#417—1221no—
220C4×C4⋊C4—611no—
221#340—1222no—
222#339—1221no—
223#333—1221no—
224#333—1221no—
225C61#931511yescharacteristic, complemented, Sylow
226C2×#41—611no—
227C22×Q8—1221no—
228C2×M16—21no—
229C2×M16—21no—
230C22×C8—1222no—
231C22×C8D24412yes—
232C4⋊Q8—612no—
233C4⋊Q8—1221no—
234C4⋊Q8—1221no—
235C4⋊Q8—1221no—
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—1221no—
245C2×C4⋊C4—1221no—
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—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—611no—
258C4⋊C8—611no—
259C4⋊C8—1222no—
260C4⋊C8C4×D6112yes—
261#104—2442no—
262#103—1222no—
263#102—1222no—
264C22⋊C8—1222no—
265C22⋊C8—1221no—
266C4×C8—1222no—
267C4×C8—1221no—
268#95—1221no—
269#41—612no—
270#41—612no—
271#41—1221no—
272#41—1221no—
273C2×Q8—611no—
274C2×Q8—1222no—
275C2×Q8—4882no—
276C2×Q8—2441no—
277C2×D4—611no—
278C2×D4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4C2×D24411yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4#1175822611yescharacteristic
287M16—41no—
288M16—41no—
289M16—41no—
290M16—41no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—42no—
294C2×C8—41no—
295C2×C8—1221no—
296C2×C8—1221no—
297C2×C8—4882no—
298C4⋊C4—611no—
299C4⋊C4—611no—
300C4⋊C4—1222no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—1222no—
304C4⋊C4—1222no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
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
317C42#1175822211yescharacteristic
318C42D4×D6111yescharacteristic
319C42D4×D6111yescharacteristic
320C23—1221no—
321C23#1451975211yescharacteristic
322Q8—612no—
323Q8—1221no—
324Q8—4882no—
325Q8—4882no—
326D4—612no—
327D4—1222no—
328D4—1222no—
329D4—1221no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—1221no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—4882no—
341C2×C4—4881no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4C22⋊C4×D6111yescharacteristic
347C2×C4#1451973911yescharacteristic
348C2×C4C4×D24411yescharacteristic
349C2×C4#1451974711yescharacteristic
350C2×C4#1451975011yescharacteristic
351C2×C4#1451976211yescharacteristic
352C2×C4SD16×D6111yescharacteristic
353C2×C4Q16×D6111yescharacteristic
354C2×C4#1451979611yescharacteristic
355C2×C4#1451979811yescharacteristic
356C8—42no—
357C8—42no—
358C8—81no—
359C8—2441no—
360C8—2441no—
361C22—21no—
362C22—21no—
363C22—1222no—
364C22—2441no—
365C22—2441no—
366C22#1683964011yescharacteristic
367C22#1683999211yescharacteristic
368C22#1684000411yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—1222no—
373C4—4882no—
374C4—4882no—
375C4—2441no—
376C4—2441no—
377C4#103×D6111yescharacteristic
378C4#1683975511yescharacteristic
379C4#1683994211yescharacteristic
380C4#1683994711yescharacteristic
381C4#1683999011yescharacteristic
382C4#1684000211yescharacteristic
383C2—21no—
384C2—21no—
385C2—2442no—
386C2#2144618711yescharacteristic
387C2#2144624111yescharacteristic
388C2#2144630011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1292C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1292D61
hypocenterC61#9315
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #21446766C2semidirect
5. #21444501C2semidirect
6. #21443720C2semidirect
7. C61×#1292C2semidirect
12. #16840048C4semidirect
13. #16840043C4semidirect
195. #1292D61semidirect
225. C61#9315semidirect

Maximal subgroups

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

subgroupindex
#214556352
#214549282
#214467662
#214458362
#214445012
#214437202
C61×#12922
#931561