Finite Group Databasebeta

← #29575841

Subgroups — #29575841

Order 15616.

458 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455941C211yesmaximal, characteristic
2#21454908C211yesmaximal, characteristic, complemented
3#21444429C211yesmaximal, characteristic
4#21444313C211yesmaximal, characteristic
5#21443718C211yesmaximal, characteristic, complemented
6#21443675C211yesmaximal, characteristic, complemented
7C61×#1763C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840075—21no—
10#16840057C411yescharacteristic, complemented
11#16840057C411yescharacteristic, complemented
12#16839962C411yescharacteristic, complemented
13#16839962C411yescharacteristic, complemented
14#16839901—21no—
15#16839893—22no—
16#16839893—21no—
17Q8×#92418—21no—
18#16839860—21no—
19#16839860—21no—
20#16839819—21no—
21#16839819C2211yescharacteristic
22#16839819C2211yescharacteristic
23#16839815—21no—
24#16839815C2211yescharacteristic
25#16839501—22no—
26#16839495—21no—
27#16839495—21no—
28C2×C4×Q8×C61C2211yescharacteristic
29C2×#103×C61—21no—
30C2×#97×C61C2211yescharacteristic
31C4×C4⋊C4×C61C2211yescharacteristic
32C61×#340—21no—
33C2×#11758222—21no—
34C2×#11758201—21no—
35C2×#11758201—21no—
36#14519777C2×C411yescharacteristic
37#14519774C2×C411yescharacteristic
38#14519765—21no—
39#14519751—21no—
40#14519751—21no—
41C4×D244—21no—
42C4×D244—21no—
43#14519710—21no—
44#14519710—21no—
45C4⋊#92418—22no—
46C4⋊#92418—22no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418C2×C411yescharacteristic
50C4⋊#92418C2×C411yescharacteristic
51#14519701—21no—
52#14519701—21no—
53#14519697—21no—
54#14519697—21no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57C22⋊#92418D411yescharacteristic
58C22⋊#92418D411yescharacteristic
59#14519688—22no—
60#14519688—21no—
61#14519688D412yes—
62C4×#92418—22no—
63C4×#92418—21no—
64C22×Q8×C61D411yescharacteristic
65C22×C8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61C2×C411yescharacteristic
69C4×Q8×C61C2×C411yescharacteristic
70C4×Q8×C61D411yescharacteristic
71C4×Q8×C61D411yescharacteristic
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C42×C61—21no—
76C2×C42×C61—21no—
77C2×C42×C61C2311yescharacteristic
78#103×C61—24no—
79#97×C61—21no—
80#97×C61—21no—
81#95×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—22no—
84C2×Q8×C61—41no—
85C2×Q8×C61C22⋊C411yescharacteristic
86C2×Q8×C61C22⋊C411yescharacteristic
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—41no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C2×C22⋊D61—41no—
94#11758222—81no—
95#11758222—81no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244—21no—
99C2×C4×D61—41no—
100C2×Dic122—21no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61C22⋊C411yescharacteristic
112C4⋊C4×C61C22⋊C411yescharacteristic
113C42×C61—21no—
114C42×C61—21no—
115C42×C61—21no—
116C42×C61—21no—
117C42×C61—81no—
118C42×C61C22×C411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122#11758201—42no—
123#11758201—42no—
124#11758198—41no—
125#11758198—41no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C2×#92418—21no—
129C2×#92418—21no—
130C2×#92418—21no—
131C2×#92418—21no—
132C2×#92418—22no—
133C23×C61#12111yescharacteristic
134C22×D61—41no—
135Q8×C61—21no—
136Q8×C61—21no—
137Q8×C61—21no—
138Q8×C61—42no—
139Q8×C61#10412yes—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—81no—
154C2×C4×C61—81no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C22⋊D61—81no—
162C22⋊D61—81no—
163C2×Dic61—41no—
164D244—41no—
165D244—41no—
166D244—81no—
167D244—81no—
168C4×D61—82no—
169Dic122—81no—
170C8×C61—42no—
171#92418—41no—
172#92418—41no—
173#92418—42no—
174#92418—41no—
175#92418—41no—
176#9164—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61#38611yescharacteristic
180C22×C61#47111yescharacteristic
181C22×C61#47211yescharacteristic
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C4×C61—21no—
186C4×C61—22no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61—82no—
195C4×C61C2×#10411yescharacteristic
196C4×C61#42111yescharacteristic
197Dic61—81no—
198#3112—611no—
199#2984—611no—
200#1763D6111yescharacteristic, complemented
201#1530—611no—
202#1502—611no—
203#1302—611no—
204#1285—611no—
205C2×C61—21no—
206C2×C61—21no—
207C2×C61#187111yescharacteristic
208C2×C61#190511yescharacteristic
209C2×C61#190711yescharacteristic
210D61—161no—
211#532—611no—
212C2×C4×Q8C2×D6111yescharacteristic
213#480—1221no—
214#477—611no—
215#477—611no—
216#460—611no—
217#460—611no—
218#448—1221no—
219#446—1222no—
220#446—1221no—
221C8×Q8—1221no—
222#440—1221no—
223#440—1221no—
224#432—611no—
225#432—611no—
226#432—1221no—
227#431—611no—
228#431—1221no—
229C2×#103—21no—
230C2×#97C2×D6111yescharacteristic
231C4×C4⋊C4C2×D6111yescharacteristic
232#340—21no—
233#329—1222no—
234#327—1221no—
235#327—1221no—
236C61#916411yescharacteristic, complemented, Sylow
237C2×#41—1221no—
238C22×Q8C22⋊D6111yescharacteristic
239C2×SD16—1221no—
240C2×SD16—1221no—
241C22×C8—21no—
242C4⋊Q8—611no—
243#127—611no—
244#124—1221no—
245#121—1221no—
246#121—1221no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8C4×D6111yescharacteristic
250C4×Q8C4×D6111yescharacteristic
251C4×Q8D24411yescharacteristic
252C4×Q8D24411yescharacteristic
253C4×D4—1221no—
254C4×D4—1221no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C22⋊D6111yescharacteristic
258C2×C42—21no—
259C2×C42—21no—
260C2×C42C22×D6111yescharacteristic
261#107—1221no—
262#107—1221no—
263C4⋊C8—611no—
264C4⋊C8—611no—
265C4⋊C8—1222no—
266C4⋊C8—1222no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269#103—24no—
270#103—1221no—
271#103—1221no—
272#102—1221no—
273#102—1221no—
274C22⋊C8—611no—
275C22⋊C8—611no—
276C22⋊C8—1221no—
277C22⋊C8—1221no—
278#97—21no—
279#97—21no—
280#97—612no—
281#97—1222no—
282#97—1221no—
283C4×C8—1222no—
284C4×C8—1221no—
285#95—21no—
286#41—4881no—
287#41—4881no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—41no—
291C2×Q8—1221no—
292C2×Q8#1175819811yescharacteristic
293C2×Q8#1175819811yescharacteristic
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—2441no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—2441no—
302C22×C4D4×D6111yescharacteristic
303C22×C4#1175822411yescharacteristic
304C22×C4C2×C22⋊D6111yescharacteristic
305SD16—2442no—
306SD16—2442no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—1221no—
311C2×C8—1221no—
312C2×C8—1221no—
313C2×C8—1222no—
314C2×C8—1221no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4#1175819811yescharacteristic
325C4⋊C4#1175819811yescharacteristic
326C22⋊C4—2441no—
327C22⋊C4—2441no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—21no—
332C42—81no—
333C42C2×C4×D6111yescharacteristic
334C42C2×D24411yescharacteristic
335C42D4×D6111yescharacteristic
336C42#1175822411yescharacteristic
337C23—2441no—
338C23#1451974911yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—21no—
342Q8—42no—
343Q8—4881no—
344Q8#1451970512yes—
345D4—4881no—
346D4—4881no—
347D4—4881no—
348D4—4881no—
349D4—2441no—
350D4—2441no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—4882no—
367C2×C4—2441no—
368C2×C4C2×#1175819811yescharacteristic
369C2×C4#1451973711yescharacteristic
370C2×C4#1451973711yescharacteristic
371C2×C4#1451974711yescharacteristic
372C2×C4#1451974911yescharacteristic
373C2×C4#1451976111yescharacteristic
374C8—42no—
375C8—2441no—
376C8—2442no—
377C8—2441no—
378C8—2441no—
379C8—2441no—
380C22—21no—
381C22—21no—
382C22—4881no—
383C22—4881no—
384C22—4881no—
385C22#1683963911yescharacteristic
386C22#1684002711yescharacteristic
387C22#1684003011yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—82no—
398C4—4881no—
399C4C2×#1451970511yescharacteristic
400C4#1683978011yescharacteristic
401C2—21no—
402C2—21no—
403C2—9761no—
404C2#2144611911yescharacteristic
405C2#2144631111yescharacteristic
406C2#2144632511yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1763C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1763D61
hypocenterC61#9164
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. #21454908C2semidirect
5. #21443718C2semidirect
6. #21443675C2semidirect
7. C61×#1763C2semidirect
10. #16840057C4semidirect
11. #16840057C4semidirect
12. #16839962C4semidirect
13. #16839962C4semidirect
200. #1763D61semidirect
236. C61#9164semidirect

Maximal subgroups

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

subgroupindex
#214559412
#214549082
#214444292
#214443132
#214437182
#214436752
C61×#17632
#916461