Finite Group Databasebeta

← #29598222

Subgroups — #29598222

Order 15616.

420 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454522C211yesmaximal, characteristic
2#21447584C211yesmaximal, characteristic, complemented
3#21447448C211yesmaximal, characteristic, complemented
4#21447446C211yesmaximal, characteristic, complemented
5C2×#16839544C211yesmaximal, characteristic, complemented
6#21447423C211yesmaximal, characteristic, complemented
7C2×C61×#349C211yesmaximal, characteristic, complemented
8C2×#14519783C2211yescharacteristic
9#16840273C411yescharacteristic
10C2×#14519717C2211yescharacteristic
11C2×#14519717C2211yescharacteristic
12#16839838—22no—
13#16839831—22no—
14#16839788C411yescharacteristic
15#16839728C411yescharacteristic
16#16839726C411yescharacteristic
17#16839717C2211yescharacteristic
18#16839582—22no—
19#16839547—22no—
20#16839545—22no—
21#16839544—22no—
22#16839539—22no—
23C22×M16×C61C2211yescharacteristic
24C2×M32×C61C2211yescharacteristic
25C2×M32×C61C2211yescharacteristic
26C61×#349—22no—
27C2×#11758222C2×C411yescharacteristic
28#14519783—21no—
29#14519783—21no—
30#14519783—21no—
31#14519783—21no—
32C2×#11758194C2×C411yescharacteristic
33C2×#11758194C2×C411yescharacteristic
34C2×#11758189—21no—
35C2×C8×D61—21no—
36#14519760—21no—
37#14519756—21no—
38#14519751—21no—
39#14519746—21no—
40C4×C22⋊D61—22no—
41#14519736C2×C411yescharacteristic
42#14519717—21no—
43#14519717—21no—
44#14519717—21no—
45#14519717D412yescomplemented
46C2×#11758185—21no—
47C2×#11758185—21no—
48#14519706—22no—
49C22⋊#92418—22no—
50#14519689—22no—
51#14519687D412yes—
52C8×Dic61D412yes—
53C23×C4×C61C2×C411yescharacteristic
54C2×M16×C61—21no—
55C2×M16×C61—21no—
56C2×M16×C61—21no—
57C2×M16×C61—21no—
58C2×M16×C61—21no—
59C2×M16×C61—21no—
60C22×C8×C61C2×C411yescharacteristic
61C22×C8×C61C2311yescharacteristic
62M32×C61—21no—
63M32×C61—21no—
64M32×C61—21no—
65M32×C61D412yescomplemented
66C2×C16×C61—21no—
67C2×C16×C61—21no—
68C24×C61M1611yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61M1611yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C2×C22⋊D61—21no—
78C2×C22⋊D61—22no—
79#11758222—21no—
80#11758222—21no—
81#11758222—21no—
82#11758222—21no—
83C2×D244M1611yescharacteristic
84C2×C4×D61—21no—
85C2×Dic122M1611yescharacteristic
86M16×C61—41no—
87M16×C61—41no—
88M16×C61—41no—
89M16×C61—41no—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61#4111yescharacteristic
98C2×C8×C61#4111yescharacteristic
99C22⋊Dic61—22no—
100C22⋊Dic61—21no—
101#11758198—22no—
102C4⋊Dic61—21no—
103#11758196—22no—
104C4×Dic61C22⋊C412yes—
105#11758194—21no—
106#11758194—21no—
107#11758194—21no—
108#11758194—21no—
109C2×#92418—21no—
110C2×#92418C22⋊C412yes—
111#11758189—41no—
112#11758189—41no—
113C8×D61—41no—
114C8×D61—41no—
115C16×C61—22no—
116C16×C61—41no—
117#11758185—22no—
118#11758185—41no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—81no—
123C23×C61C2×M1611yescharacteristic
124C22×D61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61C2×C22⋊C411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61C2×M1611yescharacteristic
136C2×C4×C61#13111yescharacteristic
137C2×C4×C61#13111yescharacteristic
138C22⋊D61—41no—
139C22⋊D61—41no—
140C22⋊D61—82no—
141C2×Dic61—22no—
142C2×Dic61—21no—
143D244—21no—
144D244—21no—
145C4×D61—41no—
146C4×D61—41no—
147Dic122—21no—
148Dic122—21no—
149C8×C61—41no—
150C8×C61#12111yescharacteristic
151C8×C61#12111yescharacteristic
152C8×C61#12411yescharacteristic
153C8×C61#12711yescharacteristic
154#92418—22no—
155#92418—41no—
156#13201—611nomaximal, Sylow
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61#40711yescharacteristic
164C22×C61#43511yescharacteristic
165C22×C61#43511yescharacteristic
166C2×D61—42no—
167C2×D61—41no—
168C4×C61—41no—
169C4×C61#39011yescharacteristic
170C4×C61#40811yescharacteristic
171C4×C61#43511yescharacteristic
172C4×C61#43511yescharacteristic
173Dic61—42no—
174Dic61—41no—
175#2930—611no—
176#2153—611no—
177#2117—611no—
178#2117—611no—
179C2×#349—611no—
180C2×#349D6111yescharacteristic, complemented
181#2110—611no—
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—81no—
186C2×C61#195511yescharacteristic
187D61—81no—
188C2×#131—611no—
189C22×M16C2×D6111yescharacteristic
190#525—611no—
191C2×M32—611no—
192C2×M32—611no—
193C2×M32C2×D6111yescharacteristic
194C2×M32C2×D6111yescharacteristic
195#436—1222no—
196#435—1222no—
197#424—611no—
198#408—611no—
199#407—611no—
200#405—611no—
201#364—1222no—
202#350—1222no—
203#350—1222no—
204#349—22no—
205#349—1222no—
206#347—1222no—
207C61#1320111yescharacteristic, complemented, Sylow
208C2×#41—611no—
209C23×C4C4×D6111yescharacteristic
210#131—1221no—
211#131—1221no—
212#131—1221no—
213#131—1221no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—611no—
221C2×M16—611no—
222C2×M16—1221no—
223C22×C8—1221no—
224C22×C8C4×D6111yescharacteristic
225C22×C8C22×D6111yescharacteristic
226#123—1221no—
227C22⋊Q8—1221no—
228#121—1221no—
229#120—1221no—
230C4×D4—1222no—
231#117—611no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32—612no—
236M32—1221no—
237M32—1221no—
238M32—1221no—
239M32C22⋊D6112yescomplemented
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—1221no—
243C2×C16—1221no—
244C4⋊C8—1222no—
245C22⋊C8—1222no—
246C22⋊C8—1222no—
247#97—612no—
248C4×C8—612no—
249C24#1175818911yescharacteristic
250#41—1221no—
251#41—1221no—
252#41—1221no—
253#41—1221no—
254C2×Q8—611no—
255C2×D4—611no—
256C2×D4—1222no—
257C2×D4—1221no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—1221no—
265C22×C4#1175818911yescharacteristic
266C22×C4C2×C4×D6111yescharacteristic
267M16—41no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—1221no—
272M16—1221no—
273M16—1221no—
274M16—1221no—
275M16—2441no—
276M16—2441no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—612no—
281C2×C8—1221no—
282C2×C8—2441no—
283C2×C8—2441no—
284C2×C8#1175822211yescharacteristic
285C2×C8D4×D6111yescharacteristic
286C2×C8D4×D6111yescharacteristic
287C2×C8D4×D6111yescharacteristic
288C2×C8#1175822411yescharacteristic
289C2×C8C2×C22⋊D6111yescharacteristic
290C4⋊C4—1222no—
291C4⋊C4—1221no—
292C22⋊C4—1222no—
293C22⋊C4—1222no—
294C22⋊C4—1221no—
295C42—612no—
296C16—22no—
297C16—41no—
298C16—1222no—
299C16—2441no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—81no—
304C23—1221no—
305C23C2×#1175818911yescharacteristic
306Q8—1221no—
307Q8—1221no—
308D4—1221no—
309D4—1221no—
310D4—4882no—
311D4—2441no—
312D4—2441no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—1222no—
321C2×C4—1221no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4C22⋊C4×D6111yescharacteristic
325C2×C4#1451973711yescharacteristic
326C2×C4C4×C22⋊D6111yescharacteristic
327C2×C4M16×D6111yescharacteristic
328C2×C4#1451978311yescharacteristic
329C2×C4#1451978511yescharacteristic
330C8—41no—
331C8—1222no—
332C8—2441no—
333C8#1451974911yescharacteristic
334C8#1451975011yescharacteristic
335C8#1451976311yescharacteristic
336C8#1451977311yescharacteristic
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22—2442no—
344C22—2441no—
345C22#1683972411yescharacteristic
346C22#1683983011yescharacteristic
347C22#1683983311yescharacteristic
348C4—41no—
349C4—2442no—
350C4—2441no—
351C4#1683966211yescharacteristic
352C4#1683972711yescharacteristic
353C4#1683983111yescharacteristic
354C4#1683983611yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—81no—
359C2—4881no—
360C2#2144661511yescharacteristic
subgroupG/H
centerC4#16839662
commutatorC22×C4×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#349C2
socleC2×C61#1955
prime radical#16840273C4
cosocleC22×C8×C61C23
hypercenterC2×#349D61
hypocenterC61#13201
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. #21447584C2semidirect
3. #21447448C2semidirect
4. #21447446C2semidirect
5. C2×#16839544C2semidirect
6. #21447423C2semidirect
7. C2×C61×#349C2semidirect
45. #14519717D4semidirect
65. M32×C61D4semidirect
180. C2×#349D61semidirect
207. C61#13201semidirect
239. M32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214545222
#214475842
#214474482
#214474462
C2×#168395442
#214474232
C2×C61×#3492
#1320161