Finite Group Databasebeta

← #29578186

Subgroups — #29578186

Order 15616.

460 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446613C211yesmaximal, characteristic
2C4×#14519697C211yesmaximal, characteristic
3C2×#16839514C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic
5#21443660C211yesmaximal, characteristic, complemented
6#21443646C211yesmaximal, characteristic, complemented
7C8×C4⋊C4×C61C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×C4⋊#92418C2211yescharacteristic
10C2×#14519697C411yescharacteristic
11C2×#14519697C411yescharacteristic
12C2×#14519689—21no—
13C2×#14519689—21no—
14C2×C4×#92418C2211yescharacteristic
15C2×C4×#92418C2211yescharacteristic
16#16839524C411yescharacteristic
17#16839524C411yescharacteristic
18#16839514—22no—
19#16839489—22no—
20C2×C4⋊C8×C61C2211yescharacteristic
21C2×C4×C8×C61—21no—
22C2×C4×C8×C61C2211yescharacteristic
23C4×C4⋊C4×C61C2211yescharacteristic
24C61×#336—21no—
25C22×D244C2×C411yescharacteristic
26C22×C4×D61—21no—
27C22×#92418—21no—
28C22×#92418—21no—
29C22×#92418C2×C411yescharacteristic
30C22×#92418C2×C411yescharacteristic
31C4×D244—21no—
32C4×D244—21no—
33C4×D244—21no—
34C4×D244—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758198—21no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39#14519697—22no—
40#14519697C814yescomplemented
41#14519689—42no—
42#14519689—42no—
43C4×#92418—21no—
44C4×#92418—21no—
45C4×#92418—21no—
46C4×#92418—21no—
47C22×C8×C61—21no—
48C22×C8×C61D411yescharacteristic
49C22×C8×C61D411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—21no—
55C4⋊C8×C61D412yes—
56C4×C8×C61—21no—
57C4×C8×C61—21no—
58C4×C8×C61—42no—
59#95×C61—21no—
60C23×D61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61#4111yescharacteristic
66C22×Dic61—21no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244C2×C812yes—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C8×C61—21no—
80C2×C8×C61—21no—
81C2×C8×C61—22no—
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—21no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61D812yes—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61C2×C812yes—
91C4⋊C4×C61M1612yes—
92C42×C61—41no—
93C42×C61—41no—
94C42×C61C2×D411yescharacteristic
95C42×C61#4111yescharacteristic
96C42×C61#4111yescharacteristic
97C42×C61#4111yescharacteristic
98#11758198—41no—
99#11758198—41no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C2×#92418—21no—
103C2×#92418—21no—
104C2×#92418—22no—
105C2×#92418—21no—
106C2×#92418—21no—
107C2×#92418—21no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418C2×C812yes—
114C23×C61C4×D411yescharacteristic
115C22×D61—22no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61#11711yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12311yescharacteristic
134C2×C4×C61#12411yescharacteristic
135C2×C4×C61#12611yescharacteristic
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C2×C4×C61#13111yescharacteristic
140C2×C4×C61C2×D811yescharacteristic
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147D244—22no—
148D244—22no—
149D244—41no—
150D244—41no—
151C4×D61—81no—
152C4×D61—81no—
153C4×D61—81no—
154C4×D61—81no—
155C8×C61—22no—
156C8×C61—42no—
157C8×C61—41no—
158#92418—22no—
159#92418—42no—
160#92418—41no—
161#92418—81no—
162#9541—611nomaximal, Sylow
163C22×C61#38811yescharacteristic
164C22×C61C8×D411yescharacteristic
165C22×C61#43511yescharacteristic
166C22×C61C4×D811yescharacteristic
167C22×C61#44011yescharacteristic
168C22×C61#44311yescharacteristic
169C22×C61#44411yescharacteristic
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—42no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—42no—
180C4×C61—42no—
181C4×C61#43111yescharacteristic
182C4×C61#43311yescharacteristic
183C4×C61C8×D411yescharacteristic
184C4×C61#43611yescharacteristic
185C4×C61#45911yescharacteristic
186C4×C61#46411yescharacteristic
187C4×C61#48011yescharacteristic
188C4×C61#48211yescharacteristic
189Dic61—81no—
190#1954—611no—
191C8×C4⋊C4D6111yescharacteristic, complemented
192C4×#102—611no—
193C2×#335—611no—
194C2×D4⋊C8—611no—
195#1279—611no—
196#1273—611no—
197C2×C61C8×D811yescharacteristic
198C2×C61SD16⋊C811yescharacteristic
199C2×C61#158111yescharacteristic
200C2×C61#158811yescharacteristic
201C2×C61#192311yescharacteristic
202C2×C61#192511yescharacteristic
203C2×C61#192911yescharacteristic
204D61—82no—
205C2×C4×D4—611no—
206C2×C4⋊C8—611no—
207C2×C4⋊C8C2×D6111yescharacteristic
208C2×#102—611no—
209C2×#102—611no—
210C2×C22⋊C8—1221no—
211C2×C22⋊C8—1221no—
212C2×C4×C8—21no—
213C2×C4×C8—611no—
214C2×C4×C8—611no—
215C2×C4×C8C2×D6111yescharacteristic
216C4×C4⋊C4C2×D6111yescharacteristic
217#340—611no—
218#340—611no—
219#336—21no—
220#335—1222no—
221D4⋊C8—1222no—
222C61#954111yescharacteristic, complemented, Sylow
223C22×D4—611no—
224C23×C4—1221no—
225C22×C8—21no—
226C22×C8—611no—
227C22×C8—611no—
228C22×C8—1221no—
229C22×C8—1221no—
230C22×C8C22⋊D6111yescharacteristic
231C22×C8C22⋊D6111yescharacteristic
232C4×D4—1221no—
233C4×D4—1221no—
234C4×D4—1221no—
235C4×D4—1221no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4C4×D6111yescharacteristic
238C2×C4⋊C4C4×D6111yescharacteristic
239C2×C22⋊C4—1221no—
240C2×C42—21no—
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—1221no—
244C4⋊C8—1221no—
245C4⋊C8D24412yes—
246#102—614no—
247#102—1222no—
248C22⋊C8—2442no—
249C22⋊C8—2442no—
250C4×C8—21no—
251C4×C8—21no—
252C4×C8—42no—
253C4×C8—1221no—
254C4×C8—1221no—
255C4×C8—1221no—
256C4×C8—1221no—
257#95—21no—
258C24—1221no—
259C2×D4—612no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1221no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—1221no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4C2×C4×D6111yescharacteristic
275C22×C4#1175822211yescharacteristic
276C22×C4C2×C22⋊D6111yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—612no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—1222no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—2441no—
293C2×C8—2441no—
294C2×C8—2441no—
295C2×C8—2441no—
296C2×C8—2441no—
297C2×C8#1175819912yes—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4C8×D6112yes—
303C4⋊C4#1175818912yes—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C42—41no—
307C42—41no—
308C42C2×D24411yescharacteristic
309C42#1175822211yescharacteristic
310C42#1175822211yescharacteristic
311C42#1175822211yescharacteristic
312C23—1222no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23C4×C22⋊D6111yescharacteristic
320D4—1222no—
321D4—1222no—
322D4—2441no—
323D4—2441no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4#1451973411yescharacteristic
340C2×C4C4×D24411yescharacteristic
341C2×C4#1451975111yescharacteristic
342C2×C4#1451976011yescharacteristic
343C2×C4#1451976511yescharacteristic
344C2×C4#1451977111yescharacteristic
345C2×C4C2×C8×D6111yescharacteristic
346C2×C4C2×#1175818911yescharacteristic
347C2×C4#1451978311yescharacteristic
348C2×C4#1451978311yescharacteristic
349C2×C4C2×#1175819911yescharacteristic
350C2×C4#1451979711yescharacteristic
351C2×C4#1451980211yescharacteristic
352C2×C4#1451980811yescharacteristic
353C8—22no—
354C8—42no—
355C8—41no—
356C8—1222no—
357C8—4881no—
358C8—2442no—
359C8—2441no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—2442no—
365C22—2442no—
366C22—2442no—
367C22#1683965311yescharacteristic
368C22C8×C22⋊D6111yescharacteristic
369C22#1683983311yescharacteristic
370C22C4×#1175819911yescharacteristic
371C22#1683986011yescharacteristic
372C22#1683987711yescharacteristic
373C22#1683988211yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—42no—
378C4—4881no—
379C4#1683981311yescharacteristic
380C4#1683982111yescharacteristic
381C4C8×D24411yescharacteristic
382C4#1683984111yescharacteristic
383C4#1683995711yescharacteristic
384C4#1683998411yescharacteristic
385C4#1684007511yescharacteristic
386C4#1684008611yescharacteristic
387C2—4882no—
388C2C8×#1175819911yescharacteristic
389C2#2144462911yescharacteristic
390C2#2144464811yescharacteristic
391C2#2144469711yescharacteristic
392C2#2144642511yescharacteristic
393C2#2144643911yescharacteristic
394C2#2144646711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC8×C4⋊C4×C61C2
socleC23×C61C4×D4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenterC8×C4⋊C4D61
hypocenterC61#9541
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16839514C2semidirect
5. #21443660C2semidirect
6. #21443646C2semidirect
7. C8×C4⋊C4×C61C2semidirect
40. #14519697C8semidirect
191. C8×C4⋊C4D61semidirect
222. C61#9541semidirect

Maximal subgroups

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

subgroupindex
#214466132
C4×#145196972
C2×#168395142
C2×#168394892
#214436602
#214436462
C8×C4⋊C4×C612
#954161