Finite Group Databasebeta

← #29663513

Subgroups — #29663513

Order 15616.

652 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457131C211yesmaximal, characteristic
2#21456744C211yesmaximal, characteristic
3#21454565C211yesmaximal, characteristic
4#21445329C212yesmaximal, complemented
5#21445315C212yesmaximal, complemented
6#21445205C212yesmaximal, complemented
7#21445191C212yesmaximal, complemented
8#21444571C211yesmaximal, characteristic, complemented
9#21444476C211yesmaximal, characteristic, complemented
10C2×#16839508C211yesmaximal, characteristic, complemented
11C61×#3165C211yesmaximal, characteristic, complemented
12C2×#14519785—21no—
13#16840312C2211yescharacteristic
14#16840136—21no—
15#16840112—21no—
16#16840049C2212yes—
17#16840047—21no—
18#16839993—22no—
19#16839964C2212yes—
20#16839964C2212yes—
21#16839964C2212yes—
22#16839962—21no—
23#16839901—22no—
24#16839841C2212yes—
25#16839835—22no—
26C8×D244C2212yes—
27#16839815C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30#16839730—21no—
31#16839515C2212yes—
32#16839513C2212yes—
33#16839511C2211yescharacteristic
34#16839511C2211yescharacteristic
35#16839508C2212yes—
36#16839508C2211yescharacteristic
37#16839508C2212yes—
38#16839508C2211yescharacteristic
39C61×#533C2211yescharacteristic
40C2×C4⋊Q8×C61C2211yescharacteristic
41C61×#501—22no—
42C61×#500C2212yes—
43C61×#498C2212yes—
44C61×#428—21no—
45C61×#428—21no—
46C4×M16×C61C2211yescharacteristic
47C2×#11758222—21no—
48C2×#11758201—22no—
49C2×#11758201—22no—
50C2×#11758201—22no—
51#14519785—44no—
52C2×#11758189—22no—
53C22×#92418—21no—
54C22×#92418—21no—
55C2×C8×D61—22no—
56#14519777D411yescharacteristic
57#14519774D411yescharacteristic
58#14519765—21no—
59#14519751—21no—
60#14519751D412yes—
61C4×D244—21no—
62C4×D244C2312yes—
63#14519708—22no—
64C4⋊#92418—21no—
65C4⋊#92418—21no—
66C4⋊#92418C2311yescharacteristic
67C4⋊#92418C2311yescharacteristic
68C4⋊#92418C2312yes—
69C4⋊#92418C2311yescharacteristic
70C4⋊#92418C2311yescharacteristic
71#14519701—22no—
72#14519701—22no—
73#14519701—22no—
74#14519697—22no—
75C22⋊#92418—21no—
76#14519689—22no—
77#14519689—22no—
78C4×#92418—21no—
79C22×Q8×C61—21no—
80C2×M16×C61D411yescharacteristic
81C2×M16×C61D411yescharacteristic
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61C2312yes—
86C4⋊Q8×C61C2311yescharacteristic
87C4⋊Q8×C61C2311yescharacteristic
88#125×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61—21no—
91C4×Q8×C61—21no—
92C4×Q8×C61—21no—
93#117×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C42×C61C2311yescharacteristic
97#107×C61—22no—
98#107×C61—22no—
99#106×C61—22no—
100#106×C61—22no—
101#97×C61D412yes—
102C4×C8×C61C2312yes—
103C2×Q8×C61—21no—
104C2×Q8×C61—22no—
105C2×Q8×C61—21no—
106C2×Q8×C61—41no—
107C2×Q8×C61—81no—
108C2×Q8×C61—81no—
109C22×C4×C61—41no—
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C2×C22⋊D61—22no—
114#11758222—42no—
115#11758222—42no—
116C2×D244—21no—
117C2×D244—21no—
118C2×D244C2×D412yes—
119C2×C4×D61—22no—
120C2×Dic122—21no—
121M16×C61—22no—
122M16×C61SD1614yescomplemented
123C2×C8×C61C2×D412yes—
124C2×C8×C61C2×D412yes—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—22no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C42×C61—41no—
137C42×C61C2×D411yescharacteristic
138C42×C61C2×D411yescharacteristic
139C42×C61#4111yescharacteristic
140C42×C61C2411yescharacteristic
141#11758201—82no—
142#11758201—82no—
143#11758201—82no—
144#11758198—22no—
145#11758198—22no—
146C4⋊Dic61—21no—
147C4⋊Dic61C2×D412yes—
148C2×#92418—21no—
149C2×#92418—21no—
150C2×#92418—21no—
151C2×#92418—21no—
152C2×#92418—22no—
153C2×#92418—42no—
154C2×#92418—81no—
155#11758189—44no—
156C8×D61—44no—
157C23×C61#12111yescharacteristic
158C22×D61—22no—
159Q8×C61—41no—
160Q8×C61—42no—
161Q8×C61—42no—
162Q8×C61—41no—
163Q8×C61—82no—
164Q8×C61—81no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—42no—
171C2×C4×C61—82no—
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61C2×SD1612yes—
176C2×C4×C61#13712yes—
177C2×C4×C61C22×D411yescharacteristic
178C2×C4×C61C22×D411yescharacteristic
179C2×C4×C61C2×#4111yescharacteristic
180C22⋊D61—44no—
181C2×Dic61—22no—
182D244—22no—
183D244—22no—
184D244—42no—
185D244—81no—
186C4×D61—42no—
187C4×D61—42no—
188Dic122—42no—
189C8×C61—22no—
190C8×C61C2×SD1614yes—
191#92418—41no—
192#92418—41no—
193#92418—42no—
194#92418—41no—
195#92418—41no—
196#19232—611nomaximal, Sylow
197C22×C61—21no—
198C22×C61—21no—
199C22×C61#46112yes—
200C22×C61C2×#12111yescharacteristic
201C2×D61—42no—
202C2×D61—42no—
203C2×D61—42no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—82no—
208C4×C61—81no—
209C4×C61—81no—
210C4×C61#46112yes—
211C4×C61C22×SD1611yescharacteristic
212C4×C61C2×#13711yescharacteristic
213C4×C61#57611yescharacteristic
214C4×C61#57711yescharacteristic
215Dic61—42no—
216#3246—611no—
217#3206—611no—
218#3165D6111yescharacteristic, complemented
219#2935—611no—
220#1693—612no—
221#1691—612no—
222#1673—612no—
223#1671—612no—
224#1565—611no—
225#1542—611no—
226C2×#332—611no—
227C2×C61—22no—
228C2×C61C2×#46111yescharacteristic
229C2×C61#306211yescharacteristic
230C2×C61#306911yescharacteristic
231D61—82no—
232C2×#131—1221no—
233#533C2×D6111yescharacteristic
234#532—611no—
235C2×C4⋊Q8C2×D6111yescharacteristic
236#501—22no—
237#500C2×D6112yes—
238#498C2×D6112yes—
239#492—1221no—
240#487—1221no—
241#476—612no—
242#475—1221no—
243#465—1222no—
244#461—612no—
245#461—612no—
246#461—612no—
247#460—1221no—
248#448—1222no—
249#436—612no—
250#435—1222no—
251C8×D4—612no—
252#431—611no—
253#428—21no—
254#428—21no—
255C2×C4⋊C8—611no—
256C2×C4⋊C8—611no—
257#408—1221no—
258C4×M16C2×D6111yescharacteristic
259#335—612no—
260#334—612no—
261#333—611no—
262#333—611no—
263#332—612no—
264#332—612no—
265#332—611no—
266#332—611no—
267C61#1923211yescharacteristic, complemented, Sylow
268C2×#41—1221no—
269C22×Q8—21no—
270C2×SD16—1222no—
271C2×SD16—1222no—
272C2×SD16—1222no—
273#131—2444no—
274C2×M16—1222no—
275C2×M16C22⋊D6111yescharacteristic
276C2×M16C22⋊D6111yescharacteristic
277C22×C8—1221no—
278C22×C8—1221no—
279C22×C8—1222no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—611no—
284C4⋊Q8C22×D6112yes—
285C4⋊Q8C22×D6111yescharacteristic
286C4⋊Q8C22×D6111yescharacteristic
287#127—611no—
288#125—21no—
289#124—1221no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292#121—612no—
293#121—1221no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×D4—612no—
297C4×D4—1221no—
298#117—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C42C22×D6111yescharacteristic
302#107—22no—
303#107—22no—
304#106—22no—
305#106—22no—
306#106—1222no—
307C4⋊C8—611no—
308C4⋊C8—611no—
309C4⋊C8—612no—
310C4⋊C8—611no—
311C4⋊C8—611no—
312C4⋊C8—1221no—
313C4⋊C8—1221no—
314#103—1222no—
315#103—1222no—
316#103—1222no—
317#102—1222no—
318C22⋊C8—1221no—
319C22⋊C8—1222no—
320C22⋊C8—1222no—
321#97C22⋊D6112yes—
322C4×C8—1221no—
323C4×C8C22×D6112yes—
324#41—2442no—
325#41—2442no—
326C2×Q8—21no—
327C2×Q8—22no—
328C2×Q8—21no—
329C2×Q8—41no—
330C2×Q8—81no—
331C2×Q8—81no—
332C2×Q8—1221no—
333C2×D4—612no—
334C2×D4—1222no—
335C2×D4—1221no—
336C2×D4—1221no—
337C22×C4—41no—
338C22×C4—1222no—
339C22×C4D4×D6111yescharacteristic
340C22×C4#1175822411yescharacteristic
341C22×C4C2×C22⋊D6111yescharacteristic
342SD16—4882no—
343SD16—4882no—
344SD16—4882no—
345M16—22no—
346M16—2444no—
347M16#1175820114yescomplemented
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—1222no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—4881no—
354C2×C8—2442no—
355C2×C8—2444no—
356C2×C8C2×C22⋊D6112yes—
357C2×C8C2×C22⋊D6112yes—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—612no—
369C4⋊C4—1221no—
370C22⋊C4—41no—
371C22⋊C4—1222no—
372C22⋊C4—1222no—
373C42—41no—
374C42D4×D6111yescharacteristic
375C42#1175822411yescharacteristic
376C42C2×C22⋊D6111yescharacteristic
377C42C23×D6111yescharacteristic
378C23—1222no—
379C23#1451974811yescharacteristic
380Q8—41no—
381Q8—42no—
382Q8—42no—
383Q8—41no—
384Q8—81no—
385Q8—82no—
386Q8—2442no—
387D4—1222no—
388D4—1222no—
389D4—4881no—
390D4—2444no—
391D4—2442no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—82no—
399C2×C4—1222no—
400C2×C4—2442no—
401C2×C4—2442no—
402C2×C4#1451974811yescharacteristic
403C2×C4#1451974811yescharacteristic
404C2×C4#1451974811yescharacteristic
405C2×C4C2×#1175820112yes—
406C2×C4#1451980812yes—
407C2×C4C2×D4×D6111yescharacteristic
408C2×C4C22×C22⋊D6111yescharacteristic
409C2×C4C2×#1175822411yescharacteristic
410C8—22no—
411C8—2441no—
412C8—2441no—
413C8—2442no—
414C8—2441no—
415C8—2441no—
416C8C2×#1175820114yes—
417C22—21no—
418C22—21no—
419C22—2442no—
420C22—2442no—
421C22—2442no—
422C22#1683996412yes—
423C22C2×#1451974811yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—82no—
428C4—81no—
429C4—81no—
430C4—2442no—
431C4#1683996412yes—
432C4C22×#1175820111yescharacteristic
433C4C2×#1451980811yescharacteristic
434C4#1684056611yescharacteristic
435C4#1684057211yescharacteristic
436C2—22no—
437C2—4882no—
438C2C2×#1683996411yescharacteristic
439C2#2145549311yescharacteristic
440C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3165C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#3165D61
hypocenterC61#19232
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
4. #21445329C2semidirect
5. #21445315C2semidirect
6. #21445205C2semidirect
7. #21445191C2semidirect
8. #21444571C2semidirect
9. #21444476C2semidirect
10. C2×#16839508C2semidirect
11. C61×#3165C2semidirect
122. M16×C61SD16semidirect
218. #3165D61semidirect
267. C61#19232semidirect
347. M16#11758201semidirect

Maximal subgroups

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

subgroupindex
#214571312
#214567442
#214545652
#214453292
#214453152
#214452052
#214451912
#214445712
#214444762
C2×#168395082
C61×#31652
#1923261