Finite Group Databasebeta

← #29572992

Subgroups — #29572992

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454513C211yesmaximal, characteristic
2#21445857C211yesmaximal, characteristic, complemented
3#21444360C212yesmaximal
4#21443725C212yesmaximal, complemented
5C61×#1808C211yesmaximal, characteristic, complemented
6C2×#14519783C411yescharacteristic, complemented
7#16840273C2211yescharacteristic
8#16839833—21no—
9#16839833—21no—
10C8×C22⋊D61—21no—
11C8×C22⋊D61—21no—
12C2×#14519713—21no—
13#16839788C411yescharacteristic, complemented
14#16839728C411yescharacteristic, complemented
15#16839726C2212yes—
16#16839726C2211yescharacteristic
17#16839717C411yescharacteristic, complemented
18#16839527—21no—
19#16839498—22no—
20#16839495—22no—
21C23×C8×C61C2211yescharacteristic
22C2×#107×C61—21no—
23C61×#380C2212yes—
24C61×#340—21no—
25C2×#11758222C2×C411yescharacteristic
26#14519783—42no—
27C2×#11758194—22no—
28C2×#11758194C2×C411yescharacteristic
29C2×#11758194C2×C411yescharacteristic
30C2×#11758189—21no—
31C2×C8×D61—21no—
32#14519760—21no—
33#14519756D411yescharacteristic
34#14519756Q811yescharacteristic
35#14519751D411yescharacteristic
36#14519751Q811yescharacteristic
37#14519746—21no—
38C4×C22⋊D61—21no—
39C4×C22⋊D61—21no—
40#14519736C2×C411yescharacteristic
41#14519713—42no—
42#14519706—21no—
43#14519706—21no—
44C22⋊#92418—21no—
45C22⋊#92418—21no—
46C22⋊#92418—22no—
47C22⋊#92418—22no—
48#14519689—21no—
49#14519689—21no—
50#14519687—21no—
51C8×Dic61—21no—
52C23×C4×C61C2311yescharacteristic
53C22×C8×C61—42no—
54C22×C8×C61C2×C411yescharacteristic
55C22×C8×C61C2×C411yescharacteristic
56C22×C8×C61D411yescharacteristic
57C22×C8×C61D411yescharacteristic
58C22×C8×C61D411yescharacteristic
59C22×C8×C61D411yescharacteristic
60C2×C4⋊C4×C61—22no—
61C2×C22⋊C4×C61—22no—
62#107×C61—42no—
63#95×C61—22no—
64C24×C61#4111yescharacteristic
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—42no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×Q811yescharacteristic
73C22×C4×C61#4111yescharacteristic
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61—21no—
77#11758222—41no—
78#11758222—41no—
79C2×D244C4⋊C411yescharacteristic
80C2×C4×D61—21no—
81C2×Dic122C4⋊C411yescharacteristic
82C2×C8×C61—22no—
83C2×C8×C61—22no—
84C2×C8×C61—22no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61C22⋊C411yescharacteristic
89C2×C8×C61C22⋊C411yescharacteristic
90C2×C8×C61C22⋊C411yescharacteristic
91C2×C8×C61C22⋊C411yescharacteristic
92C4⋊C4×C61—42no—
93C4⋊C4×C61—42no—
94C22⋊C4×C61—82no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61C4⋊C411yescharacteristic
101C4⋊Dic61C4⋊C411yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105#11758194—41no—
106#11758194—41no—
107#11758194—42no—
108#11758194—42no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—42no—
112#11758189—42no—
113C8×D61—42no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61#11711yescharacteristic
119C23×C61#12111yescharacteristic
120C23×C61C22⋊Q811yescharacteristic
121C22×D61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—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—82no—
132C2×C4×C61—82no—
133C2×C4×C61—82no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C2×C4⋊C411yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61C22⋊Q811yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—41no—
141C22⋊D61—41no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145D244—41no—
146C4×D61—41no—
147C4×D61—41no—
148Dic122—41no—
149C8×C61—21no—
150C8×C61—21no—
151C8×C61—21no—
152C8×C61#9912yes—
153#92418—41no—
154#92418—41no—
155#92418—82no—
156#8628—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61#38011yescharacteristic
168C22×C61#47211yescharacteristic
169C22×C61#47311yescharacteristic
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—162no—
177C4×C61C2×#9911yescharacteristic
178C4×C61#41011yescharacteristic
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182#2929—611no—
183#1810—611no—
184#1808D6111yescharacteristic, complemented
185#1513—612no—
186#1305—612no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—41no—
190C2×C61—41no—
191C2×C61#179911yescharacteristic
192C2×C61#181411yescharacteristic
193C2×C61#181611yescharacteristic
194D61—81no—
195C2×#131—611no—
196C23×C8C2×D6111yescharacteristic
197#525—611no—
198#435—1221no—
199#435—1221no—
200C8×D4—1221no—
201C8×D4—1221no—
202C2×#108—1221no—
203C2×#107—21no—
204#424—611no—
205#408—611no—
206#407—611no—
207#407—612no—
208#405—611no—
209#380C2×D6112yes—
210#341—1221no—
211#340—21no—
212#328—1222no—
213#327—1222no—
214C61#862811yescharacteristic, complemented, Sylow
215C2×#41—611no—
216C23×C4C22×D6111yescharacteristic
217#131—2442no—
218C2×M16—611no—
219C2×M16—611no—
220C2×M16—1221no—
221C2×M16—1222no—
222C22×C8—42no—
223C22×C8—1221no—
224C22×C8C4×D6111yescharacteristic
225C22×C8C4×D6111yescharacteristic
226C22×C8D24411yescharacteristic
227C22×C8D24411yescharacteristic
228C22×C8C22⋊D6111yescharacteristic
229C22×C8C22⋊D6111yescharacteristic
230#123—1221no—
231C22⋊Q8—611no—
232C22⋊Q8—611no—
233#121—611no—
234#121—611no—
235#120—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238#117—611no—
239C2×C4⋊C4—22no—
240C2×C22⋊C4—22no—
241#108—2442no—
242#107—42no—
243C4⋊C8—1221no—
244C4⋊C8—1221no—
245C22⋊C8—1221no—
246C22⋊C8—1221no—
247C22⋊C8—1221no—
248C22⋊C8—1221no—
249C22⋊C8—1222no—
250C22⋊C8—1222no—
251#97—1221no—
252C4×C8—1221no—
253#95—22no—
254C24#1175822411yescharacteristic
255#41—2441no—
256#41—2441no—
257C2×Q8—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4—1221no—
266C22×C4C2×C4×D6111yescharacteristic
267C22×C4C2×D24411yescharacteristic
268C22×C4D4×D6111yescharacteristic
269C22×C4Q8×D6111yescharacteristic
270C22×C4#1175822611yescharacteristic
271C22×C4C2×C22⋊D6111yescharacteristic
272M16—2442no—
273M16—2442no—
274M16—2442no—
275M16—2441no—
276M16—2441no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—1221no—
284C2×C8—1221no—
285C2×C8—2442no—
286C2×C8—2442no—
287C2×C8#1175819811yescharacteristic
288C2×C8#1175819811yescharacteristic
289C2×C8#1175819811yescharacteristic
290C2×C8#1175819811yescharacteristic
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—611no—
294C4⋊C4—611no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C22⋊C4—82no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C42—1221no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—1221no—
309C23#1451973511yescharacteristic
310C23#1451974811yescharacteristic
311C23#1451975711yescharacteristic
312Q8—2441no—
313D4—2441no—
314D4—2442no—
315D4—2442no—
316D4—2441no—
317D4—2441no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4C2×#1175819811yescharacteristic
336C2×C4C4⋊C4×D6111yescharacteristic
337C2×C4#1451975211yescharacteristic
338C2×C4#1451975311yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—4882no—
343C8—2441no—
344C8—2441no—
345C8#1451969112yes—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—42no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22#1683961911yescharacteristic
360C22#1684002911yescharacteristic
361C22#1684003411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—162no—
366C4—2441no—
367C4—2441no—
368C4—2441no—
369C4C2×#1451969111yescharacteristic
370C4#1683973511yescharacteristic
371C2—21no—
372C2—21no—
373C2—41no—
374C2—41no—
375C2—4881no—
376C2#2144580411yescharacteristic
377C2#2144587011yescharacteristic
378C2#2144588411yescharacteristic
subgroupG/H
centerC22#16839619
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1808C2
socleC22×C61#380
prime radical#16840273C22
cosocleC23×C4×C61C23
hypercenter#1808D61
hypocenterC61#8628
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. #21445857C2semidirect
4. #21443725C2semidirect
5. C61×#1808C2semidirect
6. C2×#14519783C4semidirect
13. #16839788C4semidirect
14. #16839728C4semidirect
17. #16839717C4semidirect
184. #1808D61semidirect
214. C61#8628semidirect

Maximal subgroups

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

subgroupindex
#214545132
#214458572
#214443602
#214437252
C61×#18082
#862861