Finite Group Databasebeta

← #29596894

Subgroups — #29596894

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458921C211yesmaximal, characteristic, complemented
2#21454513C211yesmaximal, characteristic
3#21447439C211yesmaximal, characteristic, complemented
4#21447430C211yesmaximal, characteristic, complemented
5#21443906C211yesmaximal, characteristic, complemented
6#21443904C211yesmaximal, characteristic, complemented
7C61×#2112C211yesmaximal, characteristic, complemented
8C2×#14519783C2211yescharacteristic
9#16840273C411yescharacteristic
10#16840180—22no—
11#16840178—22no—
12C2×#14519717C2211yescharacteristic
13C2×#14519717C2211yescharacteristic
14M32×D61—22no—
15#16839833—22no—
16C8×C22⋊D61—22no—
17#16839788C411yescharacteristic
18#16839728C411yescharacteristic
19#16839726C411yescharacteristic
20#16839717C2211yescharacteristic
21#16839543—22no—
22C22⋊#11758185—22no—
23C23×C8×C61C2211yescharacteristic
24C2×M32×C61C2211yescharacteristic
25C2×M32×C61C2211yescharacteristic
26C61×C22⋊C16—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#14519717—21no—
46#14519716—24no—
47C2×#11758185—21no—
48C2×#11758185D412yescomplemented
49C16×D61—24no—
50#14519706—22no—
51C22⋊#92418—22no—
52#14519689—22no—
53#14519687—21no—
54C8×Dic61—21no—
55C23×C4×C61C2×C411yescharacteristic
56C22×C8×C61—21no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62C22×C8×C61C2×C411yescharacteristic
63C22×C8×C61C2311yescharacteristic
64M32×C61—21no—
65M32×C61—21no—
66M32×C61—21no—
67M32×C61—21no—
68C2×C16×C61—21no—
69C2×C16×C61D412yescomplemented
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
88C2×C8×C61—21no—
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
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—42no—
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—44no—
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#12981—611nomaximal, Sylow
159C22×C61—22no—
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C2×C22⋊C811yescharacteristic
168C22×C61C8×D411yescharacteristic
169C22×C61C8×D411yescharacteristic
170C2×D61—22no—
171C2×D61—42no—
172C4×C61—41no—
173C4×C61#38611yescharacteristic
174C4×C61#40811yescharacteristic
175C4×C61#43511yescharacteristic
176C4×C61#43511yescharacteristic
177Dic61—22no—
178Dic61—42no—
179#3407—611no—
180#2929—611no—
181#2115—611no—
182#2112—611no—
183#2112D6111yescharacteristic, complemented
184#1378—611no—
185#1378—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—42no—
190C2×C61#186911yescharacteristic
191D61—42no—
192C2×#131—611no—
193C23×C8C2×D6111yescharacteristic
194#525—611no—
195#504—1222no—
196#504—1222no—
197C2×M32—611no—
198C2×M32—611no—
199C2×M32—1222no—
200C2×M32C2×D6111yescharacteristic
201C2×M32C2×D6111yescharacteristic
202#435—1222no—
203C8×D4—1222no—
204#424—611no—
205#408—611no—
206#407—611no—
207#405—611no—
208#349—1222no—
209C22⋊C16—22no—
210C22⋊C16—1222no—
211C61#1298111yescharacteristic, complemented, Sylow
212C2×#41—611no—
213C23×C4C4×D6111yescharacteristic
214#131—1221no—
215#131—1221no—
216#131—1221no—
217#131—1221no—
218C2×M16—611no—
219C2×M16—612no—
220C2×M16—611no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—612no—
228C22×C8C4×D6111yescharacteristic
229C22×C8C22×D6111yescharacteristic
230#123—612no—
231C22⋊Q8—1221no—
232#121—1221no—
233#120—612no—
234C4×D4—1222no—
235#117—611no—
236M32—21no—
237M32—21no—
238M32—21no—
239M32—21no—
240M32—1224no—
241M32—1221no—
242M32—1221no—
243M32—1221no—
244M32—1221no—
245C2×C16—21no—
246C2×C16—612no—
247C2×C16—1224no—
248C2×C16—1221no—
249C2×C16C22⋊D6112yescomplemented
250C4⋊C8—1222no—
251C22⋊C8—1222no—
252C22⋊C8—1222no—
253#97—1221no—
254C4×C8—1221no—
255C24C8×D6111yescharacteristic
256#41—1221no—
257#41—1221no—
258#41—1221no—
259#41—1221no—
260C2×Q8—611no—
261C2×D4—612no—
262C2×D4—611no—
263C2×D4—1222no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—612no—
271C22×C4C8×D6111yescharacteristic
272C22×C4C2×C4×D6111yescharacteristic
273M16—1221no—
274M16—1221no—
275M16—1222no—
276M16—1222no—
277M16—1221no—
278M16—1221no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—612no—
287C2×C8—1222no—
288C2×C8—1222no—
289C2×C8—1221no—
290C2×C8#1175822211yescharacteristic
291C2×C8D4×D6111yescharacteristic
292C2×C8D4×D6111yescharacteristic
293C2×C8D4×D6111yescharacteristic
294C2×C8#1175822411yescharacteristic
295C2×C8C2×C22⋊D6111yescharacteristic
296C4⋊C4—1222no—
297C4⋊C4—1221no—
298C22⋊C4—612no—
299C22⋊C4—1222no—
300C22⋊C4—1222no—
301C42—1221no—
302C16—22no—
303C16—41no—
304C16—1222no—
305C16—2441no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—42no—
310C23—612no—
311C23C2×C8×D6111yescharacteristic
312Q8—1221no—
313Q8—1221no—
314D4—1222no—
315D4—1222no—
316D4—1221no—
317D4—1221no—
318D4—2444no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—612no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4C22⋊C4×D6111yescharacteristic
331C2×C4#1451973711yescharacteristic
332C2×C4C4×C22⋊D6111yescharacteristic
333C2×C4M16×D6111yescharacteristic
334C2×C4#1451978311yescharacteristic
335C2×C4#1451978511yescharacteristic
336C8—41no—
337C8—1222no—
338C8—2441no—
339C8#1451974511yescharacteristic
340C8#1451974811yescharacteristic
341C8#1451975011yescharacteristic
342C8#1451975911yescharacteristic
343C22—22no—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1222no—
352C22—2442no—
353C22C22⋊C8×D6111yescharacteristic
354C22#1683982511yescharacteristic
355C22C8×C22⋊D6111yescharacteristic
356C4—41no—
357C4—1222no—
358C4—2442no—
359C4#1683963811yescharacteristic
360C4#1683972711yescharacteristic
361C4#1683983111yescharacteristic
362C4#1683983611yescharacteristic
363C2—21no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—2442no—
368C2#2144610811yescharacteristic
subgroupG/H
centerC8#14519745
commutatorC23×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#2112C2
socleC2×C61#1869
prime radical#16840273C4
cosocleC22×C8×C61C23
hypercenter#2112D61
hypocenterC61#12981
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
1. #21458921C2semidirect
3. #21447439C2semidirect
4. #21447430C2semidirect
5. #21443906C2semidirect
6. #21443904C2semidirect
7. C61×#2112C2semidirect
48. C2×#11758185D4semidirect
69. C2×C16×C61D4semidirect
183. #2112D61semidirect
211. C61#12981semidirect
249. C2×C16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214589212
#214545132
#214474392
#214474302
#214439062
#214439042
C61×#21122
#1298161