Finite Group Databasebeta

← #29576855

Subgroups — #29576855

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#21454928C211yesmaximal, characteristic
3#21445840C211yesmaximal, characteristic
4#21444500C211yesmaximal, characteristic, complemented
5#21443722C211yesmaximal, characteristic, complemented
6#21443694C211yesmaximal, characteristic, complemented
7C61×#1987C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16840054—21no—
10#16840049—21no—
11#16840044C412yescomplemented
12#16840039C412yescomplemented
13#16839886—21no—
14#16839827—21no—
15C8×C22⋊D61—22no—
16#16839815C2211yescharacteristic
17#16839814—21no—
18#16839802—21no—
19#16839786C2211yescharacteristic
20#16839786C2211yescharacteristic
21C4⋊C8×D61—21no—
22C2×#14519705—21no—
23#16839761—21no—
24#16839522—21no—
25#16839511—21no—
26#16839511—21no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#340—22no—
31C2×#11758222D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194—21no—
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—
43C42×D61—21no—
44#14519710—22no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418C2×C412yes—
50C4⋊#92418D411yescharacteristic
51C4⋊#92418D411yescharacteristic
52#14519706—22no—
53#14519705—42no—
54#14519700—22no—
55#14519697—22no—
56C22⋊#92418—21no—
57#14519689—22no—
58C4×#92418—21no—
59C8×Dic61—22no—
60C22×Q8×C61—21no—
61C22×C8×C61D412yes—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61C2×C412yes—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C42×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73#95×C61—21no—
74C2×Q8×C61—22no—
75C2×Q8×C61—41no—
76C2×Q8×C61—82no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C2×C22⋊D61—21no—
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
92C2×C8×C61—22no—
93C2×C8×C61—42no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C42×C61—41no—
101C42×C61—41no—
102C42×C61C22×C411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106C22⋊Dic61—21no—
107#11758198—21no—
108#11758198—21no—
109C4⋊Dic61C22⋊C411yescharacteristic
110C4⋊Dic61C22⋊C411yescharacteristic
111#11758196—21no—
112#11758196—21no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116#11758194—41no—
117#11758194—41no—
118#11758194—41no—
119#11758194—41no—
120C2×#92418—22no—
121C2×#92418—21no—
122C2×#92418—21no—
123C2×#92418—41no—
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—42no—
134C2×C4×C61—81no—
135C2×C4×C61—82no—
136C2×C4×C61—81no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×C4×C61C2×SD1611yescharacteristic
144C2×C4×C61C2×Q1611yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61#13511yescharacteristic
147C22⋊D61—22no—
148C22⋊D61—22no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
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—42no—
162#92418—42no—
163#92418—41no—
164#92418—41no—
165#92418—81no—
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×C61—82no—
180C4×C61C2×#10311yescharacteristic
181C4×C61#41611yescharacteristic
182C4×C61#45511yescharacteristic
183C4×C61#45611yescharacteristic
184C4×C61#46511yescharacteristic
185C4×C61#46711yescharacteristic
186Dic61—22no—
187Dic61—41no—
188Dic61—41no—
189#3079—611no—
190#2988—611no—
191#1987D6111yescharacteristic, complemented
192#1806—611no—
193#1548—611no—
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—611no—
212#431—1221no—
213#428—1221no—
214#423—611no—
215#423—611no—
216C2×C4⋊C8—1221no—
217C2×C4⋊C8C2×D6111yescharacteristic
218C2×#104—1221no—
219#417—1221no—
220C4×C4⋊C4C2×D6111yescharacteristic
221#340—22no—
222#339—1221no—
223#333—1221no—
224#333—1221no—
225C61#931511yescharacteristic, complemented, Sylow
226C2×#41—611no—
227C22×Q8—21no—
228C2×M16—1221no—
229C2×M16—1221no—
230C22×C8—1222no—
231C22×C8C22⋊D6112yes—
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—21no—
247C2×C42—21no—
248C2×C42—1221no—
249C2×C42C22×D6111yescharacteristic
250#107—1222no—
251#106—1222no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—612no—
255C4⋊C8—611no—
256C4⋊C8—611no—
257C4⋊C8—1222no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261#104—2442no—
262#103—1222no—
263#102—1222no—
264C22⋊C8—1222no—
265C22⋊C8—1221no—
266C4×C8—1222no—
267C4×C8—1221no—
268#95—21no—
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—41no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4D4×D6111yescharacteristic
285C22×C4#1175822411yescharacteristic
286C22×C4C2×C22⋊D6111yescharacteristic
287M16—2441no—
288M16—2441no—
289M16—2441no—
290M16—2441no—
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—1222no—
294C2×C8—1221no—
295C2×C8—1221no—
296C2×C8—4882no—
297C2×C8—2441no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—611no—
305C4⋊C4—611no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C42—41no—
312C42—41no—
313C42—1221no—
314C42—1221no—
315C42—1221no—
316C42C2×C4×D6111yescharacteristic
317C42#1175822211yescharacteristic
318C42D4×D6111yescharacteristic
319C42D4×D6111yescharacteristic
320C23—1221no—
321C23#1451974811yescharacteristic
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—42no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—1221no—
339C2×C4—1222no—
340C2×C4—1222no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—4881no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4C22⋊C4×D6111yescharacteristic
347C2×C4#1451973711yescharacteristic
348C2×C4C4×C22⋊D6111yescharacteristic
349C2×C4#1451974511yescharacteristic
350C2×C4#1451975011yescharacteristic
351C2×C4#1451975911yescharacteristic
352C2×C4SD16×D6111yescharacteristic
353C2×C4Q16×D6111yescharacteristic
354C2×C4#1451979811yescharacteristic
355C2×C4#1451980011yescharacteristic
356C8—42no—
357C8—4881no—
358C8—2441no—
359C8—2441no—
360C8—2442no—
361C22—21no—
362C22—21no—
363C22—1222no—
364C22—2441no—
365C22—2441no—
366C22#1683963811yescharacteristic
367C22#1683998811yescharacteristic
368C22#1684000011yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—1222no—
375C4—2441no—
376C4—2441no—
377C4#103×D6111yescharacteristic
378C4#1683975711yescharacteristic
379C4#1683993911yescharacteristic
380C4#1683994411yescharacteristic
381C4#1683999411yescharacteristic
382C4#1684000211yescharacteristic
383C2—21no—
384C2—21no—
385C2—2442no—
386C2#2144619111yescharacteristic
387C2#2144623911yescharacteristic
388C2#2144629611yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1987C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1987D61
hypocenterC61#9315
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
4. #21444500C2semidirect
5. #21443722C2semidirect
6. #21443694C2semidirect
7. C61×#1987C2semidirect
11. #16840044C4semidirect
12. #16840039C4semidirect
191. #1987D61semidirect
225. C61#9315semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214549282
#214458402
#214445002
#214437222
#214436942
C61×#19872
#931561