Finite Group Databasebeta

← #29573201

Subgroups — #29573201

Order 15616.

408 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454775C211yesmaximal, characteristic
2C4×#14519712C211yesmaximal, characteristic, complemented
3#21444577C211yesmaximal, characteristic, complemented
4#21444259C211yesmaximal, characteristic
5#21444256C211yesmaximal, characteristic
6#21443710C211yesmaximal, characteristic, complemented
7C61×#1299C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16839886C411yescharacteristic
10#16839886C411yescharacteristic
11#16839827C411yescharacteristic
12#16839827C411yescharacteristic
13#16839825—21no—
14#16839825—21no—
15#16839813—21no—
16C2×#14519712—21no—
17#16839786C2211yescharacteristic
18C4×#11758194C2211yescharacteristic
19C2×C4×#92418C2211yescharacteristic
20C4×C8×D61—21no—
21#16839526—21no—
22#16839514—21no—
23#16839514—21no—
24#16839494—21no—
25#16839492—21no—
26#16839491—21no—
27#16839489—21no—
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C4×M16×C61C2211yescharacteristic
31C2×#11758222Q811yescharacteristic
32C2×#11758194—21no—
33C2×#11758194—21no—
34C22×#92418D411yescharacteristic
35C22×#92418D411yescharacteristic
36C2×C8×D61—21no—
37C2×C8×D61—21no—
38C4×Dic122C2×C411yescharacteristic
39C4×Dic122D411yescharacteristic
40C4×D244C2×C411yescharacteristic
41C4×D244D411yescharacteristic
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44#14519736Q811yescharacteristic
45#14519734—21no—
46C42×D61—21no—
47#14519712—24no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519706—21no—
51#14519706—21no—
52#14519689—21no—
53#14519689—21no—
54#14519688—21no—
55C4×#92418—21no—
56C4×#92418C2×C411yescharacteristic
57C4×#92418C2×C411yescharacteristic
58C4×#92418D411yescharacteristic
59C4×#92418D411yescharacteristic
60C8×Dic61—21no—
61C8×Dic61—21no—
62C2×M16×C61—21no—
63C2×M16×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61C2×C411yescharacteristic
68C4⋊C8×C61C2×C411yescharacteristic
69C22⋊C8×C61—21no—
70#97×C61—21no—
71C4×C8×C61—21no—
72C4×C8×C61—21no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×Q811yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C2×C22⋊D61—21no—
77#11758222—22no—
78#11758222—22no—
79C2×D244C4⋊C411yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×Dic122C4⋊C411yescharacteristic
84M16×C61—22no—
85M16×C61—41no—
86M16×C61—81no—
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C42×C61C22×C411yescharacteristic
92C42×C61C2×D411yescharacteristic
93C42×C61C2×D411yescharacteristic
94C42×C61#4111yescharacteristic
95C22⋊Dic61—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61C4⋊C411yescharacteristic
99C4⋊Dic61C4⋊C411yescharacteristic
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105#11758194—22no—
106#11758194—41no—
107#11758194—81no—
108C2×#92418—22no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418C22⋊C411yescharacteristic
113C2×#92418C22⋊C411yescharacteristic
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418C22⋊C411yescharacteristic
116C8×D61—42no—
117C8×D61—42no—
118C23×C61C22⋊Q811yescharacteristic
119C22×D61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61C2×C22⋊C411yescharacteristic
127C2×C4×C61C2×C4⋊C411yescharacteristic
128C2×C4×C61#11711yescharacteristic
129C2×C4×C61#12111yescharacteristic
130C2×C4×C61#12111yescharacteristic
131C2×C4×C61C22⋊Q811yescharacteristic
132C22⋊D61—24no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136D244—21no—
137D244#10812yescomplemented
138C4×D61—24no—
139C4×D61—41no—
140C4×D61—41no—
141C4×D61—41no—
142C4×D61—41no—
143Dic122—21no—
144Dic122#10812yescomplemented
145C8×C61—42no—
146C8×C61—41no—
147C8×C61—41no—
148C8×C61—81no—
149#92418—21no—
150#92418—21no—
151#92418—21no—
152#92418—42no—
153#92418—81no—
154#92418#10412yes—
155#8671—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61#38011yescharacteristic
160C2×D61—22no—
161C2×D61—41no—
162C2×D61—41no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61C2×#10411yescharacteristic
167C4×C61#42111yescharacteristic
168C4×C61C2×#10811yescharacteristic
169C4×C61C2×#10811yescharacteristic
170C4×C61#47211yescharacteristic
171C4×C61#47311yescharacteristic
172Dic61—22no—
173Dic61—41no—
174Dic61—41no—
175C8×#41—611no—
176C4×#108—611no—
177#1567—611no—
178#1489—611no—
179#1489—611no—
180#1299—611no—
181#1299D6111yescharacteristic, complemented
182C2×C61—41no—
183C2×C61#180611yescharacteristic
184C2×C61#181011yescharacteristic
185C2×C61#181611yescharacteristic
186D61—42no—
187C4×#41—611no—
188C8×Q8—611no—
189C8×Q8—611no—
190C8×D4—611no—
191C8×D4—611no—
192C8×D4—1221no—
193C8×D4—1221no—
194#431—1221no—
195#431C2×D6111yescharacteristic
196C2×#108—1221no—
197#423—611no—
198#423C2×D6111yescharacteristic
199C4×M16—611no—
200C4×M16C2×D6111yescharacteristic
201C2×C4×C8—611no—
202C2×C4×C8—1221no—
203#341—1221no—
204#335—1221no—
205#335—1221no—
206Q8⋊C8—1221no—
207Q8⋊C8—1221no—
208D4⋊C8—1221no—
209D4⋊C8—1221no—
210C61#867111yescharacteristic, complemented, Sylow
211C2×#41—611no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16—1221no—
215C2×M16—1221no—
216C22×C8—611no—
217C22×C8—611no—
218C22×C8—1221no—
219C22×C8—1221no—
220C4×Q8—611no—
221C4×Q8—611no—
222C4×D4—611no—
223C4×D4—611no—
224C4×D4—1221no—
225C4×D4—1221no—
226#117—611no—
227#117—1221no—
228C2×C42—1221no—
229C2×C42C22×D6111yescharacteristic
230#108—1224no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—1221no—
234C4⋊C8—1221no—
235C4⋊C8—1221no—
236C4⋊C8—1221no—
237C4⋊C8C4×D6111yescharacteristic
238C4⋊C8C4×D6111yescharacteristic
239C22⋊C8—21no—
240C22⋊C8—1221no—
241C22⋊C8—1221no—
242#97—21no—
243#97—1221no—
244C4×C8—21no—
245C4×C8—21no—
246C4×C8—611no—
247C4×C8—611no—
248C4×C8—611no—
249C4×C8—611no—
250C4×C8—1221no—
251C4×C8—1221no—
252C4×C8—1221no—
253#41—1222no—
254#41—1222no—
255C2×Q8—611no—
256C2×D4—611no—
257C2×D4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4#1175822211yescharacteristic
262C22×C4D4×D6111yescharacteristic
263C22×C4Q8×D6111yescharacteristic
264M16—22no—
265M16—41no—
266M16—81no—
267M16—1222no—
268M16—4881no—
269M16—2441no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—611no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8—611no—
278C2×C8—1222no—
279C2×C8—2442no—
280C2×C8—2442no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—611no—
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C42—1221no—
292C42—1221no—
293C42—1221no—
294C42C2×C4×D6111yescharacteristic
295C42#1175822211yescharacteristic
296C42D4×D6111yescharacteristic
297C42D4×D6111yescharacteristic
298C23—1221no—
299C23#1451975511yescharacteristic
300Q8—612no—
301Q8—1221no—
302D4—612no—
303D4—1224no—
304D4—1221no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—1224no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4C22⋊C4×D6111yescharacteristic
320C2×C4C4⋊C4×D6111yescharacteristic
321C2×C4#1451973411yescharacteristic
322C2×C4#1451975011yescharacteristic
323C2×C4#1451975011yescharacteristic
324C2×C4#1451975511yescharacteristic
325C8—42no—
326C8—41no—
327C8—41no—
328C8—81no—
329C8—612no—
330C8—1221no—
331C8—1221no—
332C8—1221no—
333C8—4881no—
334C8—2442no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—1222no—
339C22—2441no—
340C22—2441no—
341C22#1683962111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—1222no—
346C4—2441no—
347C4—2441no—
348C4#104×D6111yescharacteristic
349C4#1683977711yescharacteristic
350C4#108×D6111yescharacteristic
351C4#108×D6111yescharacteristic
352C4#1684003111yescharacteristic
353C4#1684003611yescharacteristic
354C2—41no—
355C2—2442no—
356C2#2144583811yescharacteristic
357C2#2144585611yescharacteristic
358C2#2144588211yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1299C2
socleC22×C61#380
prime radicalC2×#11758222Q8
cosocleC2×C42×C61C23
hypercenter#1299D61
hypocenterC61#8671
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1299

Complements

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

NH ≅ G/Ntype
2. C4×#14519712C2semidirect
3. #21444577C2semidirect
6. #21443710C2semidirect
7. C61×#1299C2semidirect
137. D244#108semidirect
144. Dic122#108semidirect
181. #1299D61semidirect
210. C61#8671semidirect

Maximal subgroups

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

subgroupindex
#214547752
C4×#145197122
#214445772
#214442592
#214442562
#214437102
C61×#12992
#867161