Finite Group Databasebeta

← #29596938

Subgroups — #29596938

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458921C211yesmaximal, characteristic, complemented
2#21454522C211yesmaximal, characteristic
3#21447439C211yesmaximal, characteristic, complemented
4C2×#16839544C211yesmaximal, characteristic, complemented
5#21443906C211yesmaximal, characteristic, complemented
6#21443904C211yesmaximal, characteristic, complemented
7C2×C61×#349C211yesmaximal, characteristic, complemented
8C2×#14519783C2211yescharacteristic
9#16840273C411yescharacteristic
10#16840180—22no—
11#16840178—22no—
12C2×#14519717C2211yescharacteristic
13C2×#14519717C2211yescharacteristic
14M32×D61—22no—
15#16839838—22no—
16#16839831—22no—
17#16839788C411yescharacteristic
18#16839728C411yescharacteristic
19#16839726C411yescharacteristic
20#16839717C2211yescharacteristic
21#16839544—22no—
22#16839543—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×#11758189D412yes—
35C2×C8×D61D412yes—
36#14519760C812yes—
37#14519756—21no—
38#14519751—21no—
39#14519746C812yes—
40C4×C22⋊D61—22no—
41#14519736C2×C411yescharacteristic
42#14519717—21no—
43#14519717—21no—
44#14519717—21no—
45#14519717D412yescomplemented
46#14519716—24no—
47C2×#11758185—21no—
48C2×#11758185—21no—
49C16×D61—24no—
50#14519706—22no—
51C22⋊#92418—22no—
52#14519689—22no—
53#14519687—21no—
54C8×Dic61—21no—
55C23×C4×C61C2×C411yescharacteristic
56C2×M16×C61—21no—
57C2×M16×C61—21no—
58C2×M16×C61—21no—
59C2×M16×C61—21no—
60C2×M16×C61—21no—
61C2×M16×C61—21no—
62C22×C8×C61C2×C411yescharacteristic
63C22×C8×C61C2311yescharacteristic
64M32×C61—21no—
65M32×C61—21no—
66M32×C61—21no—
67M32×C61D412yescomplemented
68C2×C16×C61—21no—
69C2×C16×C61—21no—
70C24×C61C2×C811yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C2×C811yescharacteristic
78C22×C4×C61C22×C411yescharacteristic
79C2×C22⋊D61—22no—
80C2×C22⋊D61C2×C812yes—
81#11758222—21no—
82#11758222—21no—
83#11758222—21no—
84#11758222—21no—
85C2×D244M1611yescharacteristic
86C2×C4×D61C22⋊C412yes—
87C2×Dic122M1611yescharacteristic
88M16×C61—41no—
89M16×C61—41no—
90M16×C61—41no—
91M16×C61—41no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61#4111yescharacteristic
100C2×C8×C61#4111yescharacteristic
101C22⋊Dic61—22no—
102C22⋊Dic61C2×C812yes—
103#11758198—22no—
104C4⋊Dic61—21no—
105#11758196—22no—
106C4×Dic61—21no—
107#11758194—21no—
108#11758194—21no—
109#11758194—21no—
110#11758194—21no—
111C2×#92418—21no—
112C2×#92418C22⋊C412yes—
113#11758189—22no—
114#11758189—22no—
115C8×D61—22no—
116C8×D61—22no—
117C16×C61—22no—
118C16×C61—41no—
119#11758185—22no—
120#11758185—41no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—81no—
125C23×C61C22×C811yescharacteristic
126C22×D61C22⋊C812yes—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C2×C4×C61#13111yescharacteristic
140C22⋊D61—22no—
141C22⋊D61—22no—
142C22⋊D61—82no—
143C2×Dic61—22no—
144C2×Dic61C22⋊C812yes—
145D244—21no—
146D244—21no—
147C4×D61—22no—
148C4×D61—22no—
149Dic122—21no—
150Dic122—21no—
151C8×C61—41no—
152C8×C61#12011yescharacteristic
153C8×C61#12111yescharacteristic
154C8×C61#12111yescharacteristic
155C8×C61#12311yescharacteristic
156#92418—22no—
157#92418—41no—
158#12989—611nomaximal, Sylow
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61C2×C22⋊C811yescharacteristic
166C22×C61C8×D411yescharacteristic
167C22×C61C8×D411yescharacteristic
168C2×D61—22no—
169C2×D61—42no—
170C4×C61—41no—
171C4×C61#38611yescharacteristic
172C4×C61#40811yescharacteristic
173C4×C61#43511yescharacteristic
174C4×C61#43511yescharacteristic
175Dic61—22no—
176Dic61—42no—
177#3407—611no—
178#2930—611no—
179#2115—611no—
180C2×#349—611no—
181C2×#349D6111yescharacteristic, complemented
182#1378—611no—
183#1378—611no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—81no—
188C2×C61#186911yescharacteristic
189D61—42no—
190C2×#131—611no—
191C22×M16C2×D6111yescharacteristic
192#525—611no—
193#504—1222no—
194#504—1222no—
195C2×M32—611no—
196C2×M32—611no—
197C2×M32—1222no—
198C2×M32C2×D6111yescharacteristic
199C2×M32C2×D6111yescharacteristic
200#436—1222no—
201#435—1222no—
202#424—611no—
203#408—611no—
204#407—611no—
205#405—611no—
206#349—22no—
207#349—1222no—
208#349—1222no—
209C61#1298911yescharacteristic, complemented, Sylow
210C2×#41—611no—
211C23×C4C4×D6111yescharacteristic
212#131—1221no—
213#131—1221no—
214#131—1221no—
215#131—1221no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—611no—
223C2×M16—612no—
224C2×M16—611no—
225C22×C8—612no—
226C22×C8C4×D6111yescharacteristic
227C22×C8C22×D6111yescharacteristic
228#123—612no—
229C22⋊Q8—1221no—
230#121—1221no—
231#120—612no—
232C4×D4—1222no—
233#117—611no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32—612no—
238M32—1224no—
239M32—1221no—
240M32—1221no—
241M32—1221no—
242M32C22⋊D6112yescomplemented
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—1224no—
246C2×C16—1221no—
247C2×C16—1221no—
248C4⋊C8—1222no—
249C22⋊C8—1222no—
250C22⋊C8—1222no—
251#97—1221no—
252C4×C8—1221no—
253C24C8×D6111yescharacteristic
254#41—1221no—
255#41—1221no—
256#41—1221no—
257#41—1221no—
258C2×Q8—611no—
259C2×D4—612no—
260C2×D4—611no—
261C2×D4—1222no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—612no—
269C22×C4C8×D6111yescharacteristic
270C22×C4C2×C4×D6111yescharacteristic
271M16—41no—
272M16—41no—
273M16—41no—
274M16—41no—
275M16—1221no—
276M16—1221no—
277M16—1222no—
278M16—1222no—
279M16—1221no—
280M16—1221no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—612no—
285C2×C8—1222no—
286C2×C8—1222no—
287C2×C8—1221no—
288C2×C8#1175822211yescharacteristic
289C2×C8D4×D6111yescharacteristic
290C2×C8D4×D6111yescharacteristic
291C2×C8D4×D6111yescharacteristic
292C2×C8#1175822411yescharacteristic
293C2×C8C2×C22⋊D6111yescharacteristic
294C4⋊C4—1222no—
295C4⋊C4—1221no—
296C22⋊C4—612no—
297C22⋊C4—1222no—
298C22⋊C4—1222no—
299C42—1221no—
300C16—22no—
301C16—41no—
302C16—1222no—
303C16—2441no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—81no—
308C23—612no—
309C23C2×C8×D6111yescharacteristic
310Q8—1221no—
311Q8—1221no—
312D4—1222no—
313D4—1222no—
314D4—1221no—
315D4—1221no—
316D4—4882no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—612no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4—1222no—
328C2×C4C22⋊C4×D6111yescharacteristic
329C2×C4#1451973711yescharacteristic
330C2×C4C4×C22⋊D6111yescharacteristic
331C2×C4M16×D6111yescharacteristic
332C2×C4#1451978311yescharacteristic
333C2×C4#1451978511yescharacteristic
334C8—41no—
335C8—1222no—
336C8—2441no—
337C8#1451974511yescharacteristic
338C8#1451974811yescharacteristic
339C8#1451975011yescharacteristic
340C8#1451975911yescharacteristic
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—1222no—
348C22—2442no—
349C22C22⋊C8×D6111yescharacteristic
350C22#1683982511yescharacteristic
351C22C8×C22⋊D6111yescharacteristic
352C4—41no—
353C4—1222no—
354C4—2442no—
355C4#1683963811yescharacteristic
356C4#1683972711yescharacteristic
357C4#1683983111yescharacteristic
358C4#1683983611yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—81no—
363C2—2442no—
364C2#2144610811yescharacteristic
subgroupG/H
centerC4#16839638
commutatorC23×C61C22×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#349C2
socleC2×C61#1869
prime radical#16840273C4
cosocleC22×C8×C61C23
hypercenterC2×#349D61
hypocenterC61#12989
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
1. #21458921C2semidirect
3. #21447439C2semidirect
4. C2×#16839544C2semidirect
5. #21443906C2semidirect
6. #21443904C2semidirect
7. C2×C61×#349C2semidirect
45. #14519717D4semidirect
67. M32×C61D4semidirect
181. C2×#349D61semidirect
209. C61#12989semidirect
242. M32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214589212
#214545222
#214474392
C2×#168395442
#214439062
#214439042
C2×C61×#3492
#1298961