Finite Group Databasebeta

← #29578546

Subgroups — #29578546

Order 15616.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446594C211yesmaximal, characteristic, complemented
2#21444468C211yesmaximal, characteristic
3#21444270C211yesmaximal, characteristic
4#21444106C211yesmaximal, characteristic, complemented
5#21443722C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1980C211yesmaximal, characteristic
8#16839815C2211yescharacteristic
9C2×#14519712—21no—
10#16839786C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4×#92418C2211yescharacteristic
13#16839526—21no—
14#16839508C411yescharacteristic, complemented
15#16839508C411yescharacteristic, complemented
16#16839506C411yescharacteristic, complemented
17#16839506C411yescharacteristic, complemented
18D4⋊#92418—21no—
19D4⋊#92418—21no—
20#16839484—21no—
21#16839484—21no—
22C61×#532C2211yescharacteristic
23C2×#104×C61—21no—
24C2×#104×C61—21no—
25C4×M16×C61C2211yescharacteristic
26C4×C4⋊C4×C61C2211yescharacteristic
27C2×#11758194—21no—
28C22×#92418—21no—
29C22×#92418—21no—
30#14519712—42no—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34C4⋊#92418C2×C411yescharacteristic
35C4⋊#92418C2×C411yescharacteristic
36C4⋊#92418C2×C411yescharacteristic
37C4⋊#92418C2×C411yescharacteristic
38C22⋊#92418—21no—
39C4×#92418—21no—
40C4×#92418—21no—
41C4×#92418D411yescharacteristic
42C4×#92418D411yescharacteristic
43C2×#41×C61—21no—
44C2×M16×C61D411yescharacteristic
45C2×M16×C61D411yescharacteristic
46C4⋊Q8×C61C2×C411yescharacteristic
47#127×C61C2×C411yescharacteristic
48#124×C61—21no—
49#121×C61—21no—
50#121×C61—21no—
51C4×D4×C61—21no—
52C4×D4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C42×C61—21no—
55C2×C42×C61C2311yescharacteristic
56#104×C61—42no—
57#104×C61—42no—
58#97×C61—21no—
59C4×C8×C61—21no—
60#95×C61—21no—
61#41×C61—41no—
62#41×C61—41no—
63#41×C61—41no—
64#41×C61—41no—
65C2×Q8×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4111yescharacteristic
74C22×C4×C61#4111yescharacteristic
75M16×C61—21no—
76M16×C61—21no—
77M16×C61—21no—
78M16×C61—21no—
79C2×C8×C61—21no—
80C2×C8×C61—21no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C42×C61—41no—
88C42×C61—41no—
89C42×C61C22×C411yescharacteristic
90C42×C61C2×D411yescharacteristic
91C42×C61#4111yescharacteristic
92C42×C61#4111yescharacteristic
93#11758194—41no—
94#11758194—41no—
95C2×#92418—21no—
96C2×#92418—21no—
97C2×#92418—21no—
98C2×#92418—21no—
99C2×#92418—21no—
100C2×#92418—21no—
101C2×#92418—42no—
102C2×#92418—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C23×C61—41no—
106C23×C61#12411yescharacteristic
107Q8×C61—41no—
108Q8×C61—41no—
109D4×C61—41no—
110D4×C61—41no—
111D4×C61—41no—
112D4×C61—41no—
113D4×C61—81no—
114D4×C61—81no—
115D4×C61—81no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—81no—
122C2×C4×C61—81no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61#11711yescharacteristic
126C2×C4×C61C4×D411yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12311yescharacteristic
130C2×C4×C61#12611yescharacteristic
131C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C8×C61—41no—
136C8×C61—41no—
137#92418—22no—
138#92418—41no—
139#92418—41no—
140#92418—41no—
141#92418—41no—
142#92418—41no—
143#92418—81no—
144#9592—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—81no—
148C22×C61—81no—
149C22×C61—81no—
150C22×C61#38811yescharacteristic
151C22×C61#48911yescharacteristic
152C22×C61#49011yescharacteristic
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—82no—
157C4×C61—81no—
158C4×C61#44011yescharacteristic
159C4×C61#44211yescharacteristic
160C4×C61#44311yescharacteristic
161C4×C61#44411yescharacteristic
162C4×C61#46811yescharacteristic
163C4×C61#46911yescharacteristic
164#1980D6111yescharacteristic
165#1950—611no—
166#1540—611no—
167#1492—611no—
168#1451—611no—
169#1303—611no—
170#1279—611no—
171C2×C61—21no—
172C2×C61—21no—
173C2×C61—161no—
174C2×C61#192911yescharacteristic
175C2×C61#193211yescharacteristic
176C2×C61#193611yescharacteristic
177#532C2×D6111yescharacteristic
178#431—611no—
179C2×#108—1221no—
180#423—611no—
181C2×C4⋊C8—611no—
182C2×#104—21no—
183C2×#104—21no—
184C4×M16C2×D6111yescharacteristic
185C2×C4×C8—611no—
186C4×C4⋊C4C2×D6111yescharacteristic
187#341—1221no—
188#332—611no—
189#332—611no—
190#331—611no—
191#331—611no—
192D4⋊C8—1221no—
193D4⋊C8—1221no—
194#322—1221no—
195#322—1221no—
196C61#959211yescharacteristic, complemented, Sylow
197C2×#41—21no—
198C2×M16—1221no—
199C2×M16C22⋊D6111yescharacteristic
200C2×M16C22⋊D6111yescharacteristic
201C22×C8—1221no—
202C22×C8—1221no—
203C4⋊Q8C4×D6111yescharacteristic
204#127C4×D6111yescharacteristic
205#124—21no—
206#121—21no—
207#121—21no—
208C4×D4—21no—
209C4×D4—21no—
210C2×C4⋊C4—21no—
211C2×C42—21no—
212C2×C42C22×D6111yescharacteristic
213#108—2442no—
214C4⋊C8—611no—
215C4⋊C8—611no—
216C4⋊C8—611no—
217C4⋊C8—611no—
218C4⋊C8—1221no—
219C4⋊C8—1221no—
220C4⋊C8—1221no—
221#104—42no—
222#104—42no—
223C22⋊C8—1221no—
224#97—21no—
225C4×C8—21no—
226C4×C8—611no—
227C4×C8—611no—
228C4×C8—1221no—
229C4×C8—1221no—
230#95—21no—
231#41—41no—
232#41—41no—
233#41—41no—
234#41—41no—
235C2×Q8—21no—
236C2×D4—21no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4#1175822411yescharacteristic
243C22×C4#1175822411yescharacteristic
244C22×C4C2×C22⋊D6111yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—21no—
249M16—2441no—
250M16—2441no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—1221no—
254C2×C8—1221no—
255C2×C8—1221no—
256C2×C8—1221no—
257C2×C8—1221no—
258C2×C8—1221no—
259C2×C8—2442no—
260C2×C8—2441no—
261C2×C8—2441no—
262C2×C8—2441no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—41no—
270C42—41no—
271C42C2×C4×D6111yescharacteristic
272C42#1175822211yescharacteristic
273C42D4×D6111yescharacteristic
274C42#1175822411yescharacteristic
275C23—41no—
276C23#1451976411yescharacteristic
277Q8—41no—
278Q8—41no—
279D4—41no—
280D4—41no—
281D4—41no—
282D4—41no—
283D4—81no—
284D4—81no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4#1451973311yescharacteristic
296C2×C4#1451973711yescharacteristic
297C2×C4C4×C22⋊D6111yescharacteristic
298C2×C4#1451974911yescharacteristic
299C2×C4#1451975911yescharacteristic
300C2×C4#1451977011yescharacteristic
301C2×C4#1451980211yescharacteristic
302C2×C4#1451980311yescharacteristic
303C2×C4#1451980311yescharacteristic
304C2×C4#1451980711yescharacteristic
305C8—41no—
306C8—41no—
307C8—1222no—
308C8—4881no—
309C8—2441no—
310C8—2441no—
311C8—2441no—
312C8—2441no—
313C8—2441no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1683965611yescharacteristic
320C22#1684012111yescharacteristic
321C22#1684012611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—82no—
326C4—81no—
327C4#1683986211yescharacteristic
328C4#1683987211yescharacteristic
329C4#1683987611yescharacteristic
330C4#1683988111yescharacteristic
331C4#1684000611yescharacteristic
332C4#1684001311yescharacteristic
333C2—21no—
334C2—21no—
335C2—161no—
336C2#2144647011yescharacteristic
337C2#2144649111yescharacteristic
338C2#2144651911yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1980C2
socleC22×C61#388
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#1980D61
hypocenterC61#9592
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
1. #21446594C2semidirect
4. #21444106C2semidirect
5. #21443722C2semidirect
6. #21443660C2semidirect
14. #16839508C4semidirect
15. #16839508C4semidirect
16. #16839506C4semidirect
17. #16839506C4semidirect
196. C61#9592semidirect

Maximal subgroups

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

subgroupindex
#214465942
#214444682
#214442702
#214441062
#214437222
#214436602
C61×#19802
#959261