Finite Group Databasebeta

← #29576897

Subgroups — #29576897

Order 15616.

474 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455628C211yesmaximal, characteristic
2#21454937C211yesmaximal, characteristic
3#21445840C211yesmaximal, characteristic
4#21444504C211yesmaximal, characteristic, complemented
5#21443722C211yesmaximal, characteristic, complemented
6#21443694C211yesmaximal, characteristic, complemented
7C61×#1981C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16840054C412yescomplemented
10#16840049C412yescomplemented
11#16840044—21no—
12#16840039—21no—
13#16839889—21no—
14#16839839—21no—
15#16839833—22no—
16#16839818—21no—
17#16839815C2211yescharacteristic
18#16839802—21no—
19#16839786C2211yescharacteristic
20#16839786C2211yescharacteristic
21#16839784—21no—
22C2×#14519705—21no—
23#16839761—21no—
24#16839522—21no—
25#16839508—21no—
26#16839508—21no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×#103×C61—22no—
30C4×C4⋊C4×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194—21no—
34C2×#11758189—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—
58#14519687—22no—
59C4×#92418—21no—
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#103×C61—44no—
74#95×C61—21no—
75C2×Q8×C61—22no—
76C2×Q8×C61—42no—
77C2×Q8×C61—42no—
78C2×Q8×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C2×C22⋊D61—21no—
85#11758222—21no—
86#11758222—21no—
87#11758222—21no—
88#11758222—21no—
89C2×D244C22⋊C411yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×Dic122C22⋊C411yescharacteristic
94C2×C8×C61—22no—
95C2×C8×C61—42no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C42×C61—41no—
103C42×C61—41no—
104C42×C61C22×C411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61#4111yescharacteristic
108C22⋊Dic61—21no—
109#11758198—21no—
110#11758198—21no—
111C4⋊Dic61C22⋊C411yescharacteristic
112C4⋊Dic61C22⋊C411yescharacteristic
113#11758196—21no—
114#11758196—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C4×Dic61—21no—
118#11758194—41no—
119#11758194—41no—
120#11758194—41no—
121#11758194—41no—
122C2×#92418—22no—
123C2×#92418—21no—
124C2×#92418—21no—
125C2×#92418—41no—
126#11758189—82no—
127C23×C61#12111yescharacteristic
128C22×D61—21no—
129Q8×C61—44no—
130Q8×C61—81no—
131Q8×C61—81no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—81no—
138C2×C4×C61—82no—
139C2×C4×C61—81no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C61#13711yescharacteristic
148C2×C4×C61#13711yescharacteristic
149C2×C4×C61#13711yescharacteristic
150C22⋊D61—41no—
151C22⋊D61—41no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155D244—21no—
156D244—21no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—81no—
162Dic122—21no—
163Dic122—21no—
164C8×C61—42no—
165#92418—42no—
166#92418—41no—
167#92418—41no—
168#92418—81no—
169#9321—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61#38611yescharacteristic
173C22×C61#46811yescharacteristic
174C22×C61#47011yescharacteristic
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—82no—
182C4×C61—82no—
183C4×C61#41711yescharacteristic
184C4×C61#41911yescharacteristic
185C4×C61#45311yescharacteristic
186C4×C61#45411yescharacteristic
187C4×C61#46811yescharacteristic
188C4×C61#47011yescharacteristic
189Dic61—41no—
190Dic61—41no—
191Dic61—41no—
192#3079—611no—
193#2989—611no—
194#1981D6111yescharacteristic, complemented
195#1806—611no—
196#1549—611no—
197#1303—611no—
198#1292—611no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61#188311yescharacteristic
202C2×C61#189411yescharacteristic
203C2×C61#190211yescharacteristic
204D61—81no—
205C2×C4⋊Q8C2×D6111yescharacteristic
206C4×#41—611no—
207#477—612no—
208#476—612no—
209#475—1221no—
210#474—1221no—
211#446—1221no—
212#436—1221no—
213#435—1222no—
214#432—1221no—
215#431—611no—
216#428—1221no—
217#423—611no—
218#423—611no—
219#423—1221no—
220C2×C4⋊C8C2×D6111yescharacteristic
221C2×#104—1221no—
222#417—1221no—
223C2×#103—22no—
224C4×C4⋊C4C2×D6111yescharacteristic
225#339—1221no—
226#332—1221no—
227#332—1221no—
228C61#932111yescharacteristic, complemented, Sylow
229C2×#41—611no—
230C22×Q8—21no—
231C2×M16—1222no—
232C2×M16—1221no—
233C2×M16—1221no—
234C22×C8C22⋊D6112yes—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8C4×D6112yes—
239C4×Q8—611no—
240C4×Q8—611no—
241C4×D4—611no—
242C4×D4—611no—
243C4×D4—1221no—
244C4×D4—1221no—
245#117—611no—
246#117—1221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C42—21no—
251C2×C42—1221no—
252C2×C42C22×D6111yescharacteristic
253#107—1222no—
254#106—1222no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—612no—
258C4⋊C8—611no—
259C4⋊C8—611no—
260C4⋊C8—1222no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8—1221no—
264#104—2442no—
265#103—44no—
266#103—1222no—
267#102—1222no—
268C22⋊C8—1222no—
269C22⋊C8—1221no—
270#97—1222no—
271C4×C8—1221no—
272#95—21no—
273#41—1221no—
274#41—1221no—
275#41—1221no—
276#41—1221no—
277C2×Q8—22no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—41no—
281C2×Q8—611no—
282C2×D4—611no—
283C2×D4—1221no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4D4×D6111yescharacteristic
290C22×C4#1175822411yescharacteristic
291C22×C4C2×C22⋊D6111yescharacteristic
292M16—4882no—
293M16—2441no—
294M16—2441no—
295M16—2441no—
296M16—2441no—
297C2×C8—22no—
298C2×C8—42no—
299C2×C8—1222no—
300C2×C8—1221no—
301C2×C8—1221no—
302C2×C8—2441no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—611no—
310C4⋊C4—611no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C42—41no—
317C42—41no—
318C42—1221no—
319C42—1221no—
320C42—1221no—
321C42C2×C4×D6111yescharacteristic
322C42#1175822211yescharacteristic
323C42D4×D6111yescharacteristic
324C42D4×D6111yescharacteristic
325C23—1221no—
326C23#1451974811yescharacteristic
327Q8—44no—
328Q8—81no—
329Q8—81no—
330Q8—1221no—
331Q8—1221no—
332D4—1221no—
333D4—1221no—
334D4—2441no—
335D4—2441no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—82no—
343C2×C4—81no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—4881no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4C22⋊C4×D6111yescharacteristic
353C2×C4#1451973711yescharacteristic
354C2×C4C4×C22⋊D6111yescharacteristic
355C2×C4#1451974511yescharacteristic
356C2×C4#1451975011yescharacteristic
357C2×C4#1451975911yescharacteristic
358C2×C4#1451980411yescharacteristic
359C2×C4#1451980611yescharacteristic
360C2×C4#1451980911yescharacteristic
361C2×C4#1451980911yescharacteristic
362C8—42no—
363C8—4881no—
364C8—2442no—
365C8—2441no—
366C8—2441no—
367C22—21no—
368C22—21no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22#1683963811yescharacteristic
373C22#1684000511yescharacteristic
374C22#1684001711yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—82no—
379C4—82no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4#1683976211yescharacteristic
384C4#1683976911yescharacteristic
385C4#1683992911yescharacteristic
386C4#1683993411yescharacteristic
387C4#1684001111yescharacteristic
388C4#1684001911yescharacteristic
389C2—21no—
390C2—21no—
391C2—4881no—
392C2#2144619811yescharacteristic
393C2#2144624911yescharacteristic
394C2#2144628911yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1981C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1981D61
hypocenterC61#9321
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
4. #21444504C2semidirect
5. #21443722C2semidirect
6. #21443694C2semidirect
7. C61×#1981C2semidirect
9. #16840054C4semidirect
10. #16840049C4semidirect
194. #1981D61semidirect
228. C61#9321semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214549372
#214458402
#214445042
#214437222
#214436942
C61×#19812
#932161