Finite Group Databasebeta

← #29576136

Subgroups — #29576136

Order 15616.

450 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455879C211yesmaximal, characteristic
2#21454463C211yesmaximal, characteristic, complemented
3#21444410C211yesmaximal, characteristic, complemented
4#21444269C211yesmaximal, characteristic, complemented
5#21443708C211yesmaximal, characteristic, complemented
6#21443657C211yesmaximal, characteristic, complemented
7C61×#1489C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840086—21no—
10#16840057C411yescharacteristic
11#16840052C411yescharacteristic
12#16839962C411yescharacteristic
13#16839957C411yescharacteristic
14#16839907—21no—
15C4×#11758201—21no—
16C4×#11758199—21no—
17#16839823—22no—
18#16839815—22no—
19#16839815C2211yescharacteristic
20#16839789—21no—
21#16839729—21no—
22C4×#11758194C2211yescharacteristic
23C2×C4×#92418C2211yescharacteristic
24#16839501—22no—
25#16839489—22no—
26C4×#41×C61C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C4×M16×C61C2211yescharacteristic
29C61×Q8⋊C8—21no—
30C61×D4⋊C8—21no—
31C2×#11758222—21no—
32C2×#11758201—21no—
33C2×#11758199—21no—
34C2×#11758194—21no—
35C22×#92418—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#14519708—21no—
45C4⋊#92418—24no—
46C4⋊#92418C2×C411yescharacteristic
47C4⋊#92418C2×C411yescharacteristic
48#14519701—21no—
49#14519698—21no—
50#14519697—21no—
51#14519697—21no—
52C22⋊#92418—24no—
53C22⋊#92418—21no—
54#14519688D412yes—
55C4×#92418—21no—
56C4×#92418—21no—
57C4×#92418—21no—
58C4×#92418D412yes—
59C2×#41×C61D411yescharacteristic
60C2×M16×C61—21no—
61C2×M16×C61—21no—
62C4×Q8×C61C2×C411yescharacteristic
63C4×Q8×C61D411yescharacteristic
64C4×D4×C61—21no—
65C4×D4×C61—21no—
66C4×D4×C61C2×C411yescharacteristic
67C4×D4×C61D411yescharacteristic
68#117×C61—21no—
69#117×C61D411yescharacteristic
70C2×C42×C61—21no—
71C2×C42×C61C2311yescharacteristic
72C4⋊C8×C61—21no—
73C4⋊C8×C61—21no—
74#97×C61—21no—
75C4×C8×C61—21no—
76#41×C61—41no—
77#41×C61—41no—
78C2×Q8×C61C22⋊C411yescharacteristic
79C2×D4×C61—21no—
80C2×D4×C61C22⋊C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—41no—
88#11758222—81no—
89#11758222—81no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—21no—
93C2×C4×D61—41no—
94C2×Dic122—21no—
95M16×C61—22no—
96M16×C61—41no—
97M16×C61—81no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61C22⋊C411yescharacteristic
103C4⋊C4×C61C22⋊C411yescharacteristic
104C22⋊C4×C61—21no—
105C22⋊C4×C61—21no—
106C22⋊C4×C61—21no—
107C42×C61—21no—
108C42×C61—21no—
109C42×C61—21no—
110C42×C61C22×C411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114#11758201—42no—
115#11758199—42no—
116#11758198—41no—
117#11758198—41no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120#11758194—41no—
121#11758194—41no—
122C2×#92418—21no—
123C2×#92418—21no—
124C2×#92418—22no—
125C2×#92418—22no—
126C2×#92418—41no—
127C2×#92418—41no—
128C23×C61—21no—
129C23×C61#12311yescharacteristic
130C22×D61—41no—
131Q8×C61—21no—
132Q8×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—42no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61#12011yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C22⋊D61—82no—
157C2×Dic61—41no—
158D244—41no—
159D244—41no—
160D244—41no—
161D244—41no—
162D244—81no—
163C4×D61—81no—
164C4×D61—81no—
165Dic122—81no—
166C8×C61—42no—
167C8×C61—81no—
168#92418—42no—
169#92418—42no—
170#92418—41no—
171#92418—41no—
172#9213—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61#38611yescharacteristic
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61#42111yescharacteristic
190C4×C61#42111yescharacteristic
191C4×C61#44311yescharacteristic
192C4×C61#44411yescharacteristic
193C4×C61#47111yescharacteristic
194C4×C61#47211yescharacteristic
195Dic61—81no—
196#3106—611no—
197#2922—611no—
198#1525—611no—
199#1492—611no—
200#1489D6111yescharacteristic, complemented
201#1299—611no—
202#1278—611no—
203C2×C61—41no—
204C2×C61—81no—
205C2×C61#187611yescharacteristic
206C2×C61#189711yescharacteristic
207C2×C61#190711yescharacteristic
208D61—161no—
209#532—611no—
210C4×#41C2×D6111yescharacteristic
211#482—1221no—
212#477—611no—
213#476—611no—
214#460—611no—
215#459—611no—
216#449—1221no—
217C4×SD16—1221no—
218C4×D8—1221no—
219#433—1222no—
220#431—611no—
221#431—1222no—
222#424—1221no—
223#423C2×D6111yescharacteristic
224#408—1221no—
225C4×M16—611no—
226C4×M16C2×D6111yescharacteristic
227C2×C4×C8—611no—
228#329—1222no—
229Q8⋊C8—21no—
230D4⋊C8—21no—
231D4⋊C8—1222no—
232C61#921311yescharacteristic, complemented, Sylow
233C2×#41—1221no—
234C2×#41D24411yescharacteristic
235C2×SD16—1221no—
236C2×D8—1221no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—1221no—
240C22×C8—1221no—
241C4⋊Q8—611no—
242#127—611no—
243#124—1221no—
244#121—1221no—
245#121—1221no—
246C4×Q8C4×D6111yescharacteristic
247C4×Q8C22⋊D6111yescharacteristic
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—1221no—
251C4×D4—1221no—
252C4×D4C4×D6111yescharacteristic
253C4×D4C22⋊D6111yescharacteristic
254#117—21no—
255#117D24411yescharacteristic
256C2×C42—21no—
257C2×C42C22×D6111yescharacteristic
258#107—1221no—
259#106—1221no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—611no—
263C4⋊C8—611no—
264C4⋊C8—1224no—
265#103—1221no—
266#102—1221no—
267#102—1221no—
268#102—1221no—
269C22⋊C8—1224no—
270C22⋊C8—1221no—
271#97—21no—
272#97—612no—
273C4×C8—21no—
274C4×C8—612no—
275C4×C8—1221no—
276C4×C8—1221no—
277C4×C8—1221no—
278#41—41no—
279#41—41no—
280#41—4881no—
281#41—4881no—
282C2×Q8—1221no—
283C2×Q8#1175819811yescharacteristic
284C2×D4—21no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—2441no—
289C2×D4#1175819811yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—2441no—
294C22×C4C2×D24411yescharacteristic
295C22×C4#1175822411yescharacteristic
296C22×C4#1175822411yescharacteristic
297SD16—2442no—
298D8—2442no—
299M16—22no—
300M16—41no—
301M16—81no—
302M16—2441no—
303M16—2441no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—1221no—
307C2×C8—1221no—
308C2×C8—1222no—
309C2×C8—1222no—
310C2×C8—2441no—
311C2×C8—2441no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4#1175819811yescharacteristic
317C4⋊C4#1175819811yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C2×C4×D6111yescharacteristic
327C42D4×D6111yescharacteristic
328C42D4×D6111yescharacteristic
329C42C2×C22⋊D6111yescharacteristic
330C23—21no—
331C23—2441no—
332C23#1451976111yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—4881no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—4881no—
340D4—4882no—
341D4—2441no—
342D4—2441no—
343D4—2441no—
344D4—2441no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—4881no—
360C2×C4—4881no—
361C2×C4—2441no—
362C2×C4C2×#1175819811yescharacteristic
363C2×C4#1451973711yescharacteristic
364C2×C4#1451973711yescharacteristic
365C2×C4#1451974711yescharacteristic
366C2×C4#1451974911yescharacteristic
367C2×C4#1451974911yescharacteristic
368C8—42no—
369C8—81no—
370C8—2442no—
371C8—2442no—
372C8—2441no—
373C8—2441no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—4881no—
381C22—4881no—
382C22—4881no—
383C22#1683963911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—4881no—
391C4#1683977811yescharacteristic
392C4#1683977811yescharacteristic
393C4#1683987611yescharacteristic
394C4#1683988111yescharacteristic
395C4#1684002711yescharacteristic
396C4#1684003011yescharacteristic
397C2—41no—
398C2—81no—
399C2—9761no—
400C2#2144614411yescharacteristic
401C2#2144626511yescharacteristic
402C2#2144632511yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1489C2
socleC22×C61#386
prime radical#21455879C2
cosocleC2×C42×C61C23
hypercenter#1489D61
hypocenterC61#9213
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #21454463C2semidirect
3. #21444410C2semidirect
4. #21444269C2semidirect
5. #21443708C2semidirect
6. #21443657C2semidirect
7. C61×#1489C2semidirect
200. #1489D61semidirect
232. C61#9213semidirect

Maximal subgroups

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

subgroupindex
#214558792
#214544632
#214444102
#214442692
#214437082
#214436572
C61×#14892
#921361