Finite Group Databasebeta

← #29591005

Subgroups — #29591005

Order 15616.

396 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455465C211yesmaximal, characteristic
2#21447438C211yesmaximal, characteristic, complemented
3#21445864C211yesmaximal, characteristic, complemented
4#21443805C211yesmaximal, characteristic, complemented
5#21443804C211yesmaximal, characteristic, complemented
6#21443803C211yesmaximal, characteristic, complemented
7C61×#1339C211yesmaximal, characteristic, complemented
8C2×D8×D61C411yescharacteristic, complemented
9C2×#14519785C2211yescharacteristic
10#16840328—21no—
11M32×D61—21no—
12#16840016C411yescharacteristic, complemented
13#16840015C2211yescharacteristic
14#16840012C411yescharacteristic, complemented
15#16839997—21no—
16#16839996—21no—
17#16839798—21no—
18#16839797C411yescharacteristic, complemented
19#16839765—21no—
20#16839735—21no—
21#16839544C2211yescharacteristic, complemented
22#16839543—21no—
23#16839519C2211yescharacteristic, complemented
24C61×#469C2211yescharacteristic
25C61×#349C2211yescharacteristic, complemented
26C61×H(3,ℤ/4)C2211yescharacteristic, complemented
27C2×#11758222D411yescharacteristic
28C2×D4×D61—21no—
29C2×D488C2×C411yescharacteristic
30C2×#11758199—21no—
31D8×D61—41no—
32D8×D61—41no—
33#14519785—41no—
34#14519785—41no—
35C2×#11758189C2×C411yescharacteristic
36C2×#11758189D411yescharacteristic
37C22×#92418D411yescharacteristic
38C2×C8×D61C2×C411yescharacteristic
39C2×C8×D61D411yescharacteristic
40#14519773—41no—
41#14519763—41no—
42#14519752—21no—
43#14519751—21no—
44#14519748—21no—
45#14519747—41no—
46#14519745—41no—
47#14519736—21no—
48#14519735—21no—
49#14519717—21no—
50#14519716—41no—
51C16×D61—41no—
52#14519710—21no—
53#14519710—41no—
54#14519709C2×C411yescharacteristic
55#14519708—41no—
56#14519699—21no—
57#14519698—21no—
58#14519697—21no—
59#14519691—41no—
60#14519691—41no—
61C2×D8×C61C2×C411yescharacteristic
62C2×M16×C61C2311yescharacteristic
63#121×C61—21no—
64#117×C61—21no—
65M32×C61—21no—
66#106×C61C2×C411yescharacteristic
67#102×C61—21no—
68C23×D61—41no—
69C2×D4×C61—21no—
70C2×D4×C61—41no—
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61D811yescharacteristic
76C2×C22⋊D61D811yescharacteristic
77D4×D61—42no—
78D4×D61—42no—
79#11758222—41no—
80#11758222—41no—
81C2×D244—21no—
82C2×D244—41no—
83C2×D244SD1611yescharacteristic
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61C22⋊C411yescharacteristic
86C2×Dic122SD1611yescharacteristic
87D8×C61—41no—
88M16×C61—41no—
89C2×C8×C61C22×C411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C42×C61—41no—
96C22⋊Dic61—41no—
97C22⋊Dic61—41no—
98#11758199—41no—
99#11758199—41no—
100#11758198—41no—
101#11758198—41no—
102#11758198—41no—
103C4⋊Dic61—21no—
104C4⋊Dic61—41no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C2×#92418—21no—
108C2×#92418—21no—
109C2×#92418C22⋊C411yescharacteristic
110C2×#92418C22⋊C411yescharacteristic
111D488—41no—
112#11758189—41no—
113#11758189—41no—
114C8×D61—21no—
115C8×D61—21no—
116C8×D61—21no—
117C8×D61—21no—
118C16×C61—41no—
119#11758185—41no—
120C23×C61—41no—
121C23×C61C2×D811yescharacteristic
122C22×D61—41no—
123C22×D61—82no—
124C22×D61—161no—
125C22×D61—161no—
126C22×D61#10211yescharacteristic
127C22×D61#10211yescharacteristic
128D4×C61—41no—
129D4×C61—41no—
130D4×C61—161no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—81no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C22⋊D61—41no—
138C22⋊D61—41no—
139C22⋊D61—82no—
140C22⋊D61—161no—
141C22⋊D61—161no—
142C2×Dic61—41no—
143C2×Dic61—81no—
144C2×Dic61#10211yescharacteristic
145C2×Dic61#10211yescharacteristic
146D244—41no—
147D244—41no—
148D244—41no—
149D244—161no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154Dic122—41no—
155C8×C61—21no—
156C8×C61—21no—
157#92418—21no—
158#92418#9911yescharacteristic
159#92418#9911yescharacteristic
160#11868—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—41no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61C2×#10211yescharacteristic
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—164no—
175C4×C61—21no—
176C4×C61—81no—
177C4×C61—161no—
178C4×C61C2×#9911yescharacteristic
179C4×C61#42111yescharacteristic
180Dic61—21no—
181Dic61—21no—
182Dic61—81no—
183Dic61—161no—
184#3058—611no—
185#2115—611no—
186#1812—611no—
187#1339—611no—
188#1339—611no—
189#1339—611no—
190#1339D6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—41no—
193C2×C61—161no—
194C2×C61#151911yescharacteristic
195D61—41no—
196D61—41no—
197D61—161no—
198C22×D8—611no—
199C2×#131—611no—
200#535—1221no—
201C2×M32—1221no—
202#469—611no—
203#469—611no—
204#469—611no—
205#469C2×D6111yescharacteristic
206#466—1221no—
207#466—1221no—
208#427—611no—
209#427—1221no—
210#418—1221no—
211#410—1221no—
212#349—611no—
213#349—1221no—
214#349C2×D6111yescharacteristic, complemented
215H(3,ℤ/4)—611no—
216H(3,ℤ/4)C2×D6111yescharacteristic, complemented
217C61#1186811yescharacteristic, complemented, Sylow
218C2×#41—611no—
219C22×D4—1221no—
220C2×D8—611no—
221C2×D8—1221no—
222C2×D8—2441no—
223C2×D8—2441no—
224C2×D8C4×D6111yescharacteristic
225#131—2441no—
226#131—2441no—
227C2×M16—611no—
228C2×M16—611no—
229C2×M16C22×D6111yescharacteristic
230C22×C8—611no—
231C22×C8—611no—
232C22×C8—611no—
233#127—2441no—
234#124—2441no—
235#121—21no—
236#121—1221no—
237#121—1221no—
238#121—1221no—
239#120—2441no—
240#120—2441no—
241#117—21no—
242#117—1221no—
243#117—1221no—
244M32—21no—
245M32—1221no—
246M32—2441no—
247C2×C16—2441no—
248#107—1221no—
249#107—2441no—
250#106—611no—
251#106—2441no—
252#106C4×D6111yescharacteristic
253#102—21no—
254#102—1221no—
255#102—1221no—
256#102—1221no—
257#99—2441no—
258#99—2441no—
259C24—2441no—
260#41—2441no—
261#41—2441no—
262C2×Q8—611no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—1221no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2442no—
272C2×D4—2442no—
273C2×D4—2441no—
274C2×D4—2441no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4D4×D6111yescharacteristic
278D8—41no—
279D8—2441no—
280D8—2441no—
281D8—2441no—
282M16—41no—
283M16—2441no—
284M16—2441no—
285C2×C8—611no—
286C2×C8—611no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—1221no—
293C2×C8C2×C4×D6111yescharacteristic
294C2×C8D4×D6111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—1221no—
298C4⋊C4—2441no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C42—41no—
307C42—2441no—
308C42—2441no—
309C16—41no—
310C16—2441no—
311C23—41no—
312C23—611no—
313C23—611no—
314C23—9761no—
315C23—9761no—
316C23—4882no—
317C23—2441no—
318C23D8×D6111yescharacteristic
319Q8—2441no—
320D4—41no—
321D4—41no—
322D4—161no—
323D4—9761no—
324D4—9761no—
325D4—9761no—
326D4—4882no—
327D4—2441no—
328D4—2441no—
329D4—2441no—
330D4—2441no—
331D4—2441no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—4881no—
343C2×C4—2441no—
344C2×C4C22⋊C4×D6111yescharacteristic
345C2×C4SD16×D6111yescharacteristic
346C8—21no—
347C8—21no—
348C8—611no—
349C8—611no—
350C8—1221no—
351C22—21no—
352C22—41no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—1221no—
357C22—1221no—
358C22—9764no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—2441no—
363C22—2441no—
364C22#102×D6111yescharacteristic
365C4—21no—
366C4—81no—
367C4—161no—
368C4—1221no—
369C4—1221no—
370C4—9761no—
371C4—4881no—
372C4#99×D6111yescharacteristic
373C4#1683977711yescharacteristic
374C2—21no—
375C2—41no—
376C2—161no—
377C2—9761no—
378C2—2441no—
379C2—2441no—
380C2#2144438511yescharacteristic
subgroupG/H
centerC2#21444385
commutatorC2×C8×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1339C2
socleC2×C61#1519
prime radical#21455465C2
cosocleC2×M16×C61C23
hypercenter#1339D61
hypocenterC61#11868
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1339

Complements

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

NH ≅ G/Ntype
2. #21447438C2semidirect
3. #21445864C2semidirect
4. #21443805C2semidirect
5. #21443804C2semidirect
6. #21443803C2semidirect
7. C61×#1339C2semidirect
8. C2×D8×D61C4semidirect
12. #16840016C4semidirect
14. #16840012C4semidirect
18. #16839797C4semidirect
21. #16839544C22semidirect
23. #16839519C22semidirect
25. C61×#349C22semidirect
26. C61×H(3,ℤ/4)C22semidirect
190. #1339D61semidirect
214. #349C2×D61semidirect
216. H(3,ℤ/4)C2×D61semidirect
217. C61#11868semidirect

Maximal subgroups

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

subgroupindex
#214554652
#214474382
#214458642
#214438052
#214438042
#214438032
C61×#13392
#1186861