Finite Group Databasebeta

← #29575517

Subgroups — #29575517

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454842C211yesmaximal, characteristic, complemented
2#21448544C211yesmaximal, characteristic
3#21444211C211yesmaximal, characteristic, complemented
4#21444209C211yesmaximal, characteristic, complemented
5#21444139C211yesmaximal, characteristic, complemented
6#21443648C211yesmaximal, characteristic, complemented
7C61×#1274C211yesmaximal, characteristic, complemented
8C2×#14519774C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11C8×D244—22no—
12#16839827—22no—
13#16839815C2211yescharacteristic
14#16839815C2211yescharacteristic
15C22⋊C8×D61—22no—
16#16839664C411yescharacteristic
17#16839664C411yescharacteristic
18#16839640—22no—
19#16839640—22no—
20#16839628C411yescharacteristic
21#16839491—22no—
22#16839489—22no—
23#16839485—22no—
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C61×#376C2211yescharacteristic
27C22×D244—22no—
28C22×D244C2×C411yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×C4×D61—21no—
31C22×C4×D61D412yes—
32C2×C8×D61—24no—
33#14519774—22no—
34#14519774C814yescomplemented
35C4×D244—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—22no—
47C2×#11758198—22no—
48C2×#11758198D412yes—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53#14519689—24no—
54C4×#92418—21no—
55C4×#92418D412yescomplemented
56#14519684—22no—
57C2×C42×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C4×C8×C61—21no—
65C4×C8×C61D412yescomplemented
66#95×C61—21no—
67#95×C61—21no—
68C23×D61—21no—
69C23×D61C22⋊C412yes—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61C22⋊C412yes—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—28no—
87C2×D244—82no—
88C2×D244—82no—
89C2×D244C2×C812yes—
90C2×D244C2×C812yescomplemented
91C2×D244M1612yes—
92C2×C4×D61—22no—
93C2×C4×D61—22no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—82no—
97C2×C4×D61—82no—
98C2×C8×C61—22no—
99C2×C8×C61—41no—
100C42×C61—21no—
101C42×C61—21no—
102C42×C61—21no—
103C42×C61C2×C812yescomplemented
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107C42×C61#4111yescharacteristic
108#11758198—22no—
109#11758198—22no—
110#11758198—41no—
111#11758198—41no—
112#11758198—82no—
113#11758198—82no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C2×#92418—22no—
119C2×#92418—41no—
120C8×D61—84no—
121C23×C61C2×C22⋊C411yescharacteristic
122C22×D61—22no—
123C22×D61—22no—
124C22×D61—22no—
125C22×D61—42no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61C22⋊C814yes—
132C2×C4×C61—22no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61C22×C811yescharacteristic
147C2×C4×C61C2×M1611yescharacteristic
148C2×C4×C61#13111yescharacteristic
149C2×C4×C61#13111yescharacteristic
150C2×Dic61—22no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—41no—
154D244—22no—
155D244—22no—
156D244—22no—
157D244—22no—
158D244—22no—
159D244—22no—
160D244—41no—
161D244—41no—
162D244—88no—
163C4×D61—44no—
164C4×D61—82no—
165C4×D61—82no—
166C4×D61—82no—
167C8×C61—42no—
168C8×C61—81no—
169#92418—42no—
170#92418—81no—
171#9101—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#38611yescharacteristic
175C22×C61C2×C22⋊C811yescharacteristic
176C22×C61#40811yescharacteristic
177C2×D61—24no—
178C2×D61—42no—
179C2×D61—42no—
180C2×D61—44no—
181C2×D61—44no—
182C2×D61—42no—
183C2×D61—82no—
184C2×D61—82no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—42no—
192C4×C61—81no—
193C4×C61C8×D411yescharacteristic
194C4×C61C8×D411yescharacteristic
195C4×C61#43511yescharacteristic
196C4×C61#43511yescharacteristic
197Dic61—42no—
198Dic61—81no—
199#2972—611no—
200#2328—611no—
201#1478—611no—
202#1478—611no—
203#1460—611no—
204#1274—611no—
205#1274D6111yescharacteristic, complemented
206C2×C61—21no—
207C2×C61—21no—
208C2×C61#186911yescharacteristic
209C2×C61#191011yescharacteristic
210C2×C61#191111yescharacteristic
211D61—44no—
212D61—82no—
213C2×#127—611no—
214C2×C4×D4—611no—
215C2×C4×D4—611no—
216C8×D4—1222no—
217C8×D4—1222no—
218#431—611no—
219#431—611no—
220#431C2×D6111yescharacteristic
221#431C2×D6111yescharacteristic
222C2×C22⋊C8—1222no—
223#390—611no—
224#390—611no—
225#386—1222no—
226#386—1222no—
227#382—611no—
228#376C2×D6111yescharacteristic
229D4⋊C8—1222no—
230D4⋊C8—1222no—
231#323—1222no—
232C61#910111yescharacteristic, complemented, Sylow
233C22×D4—611no—
234C22×D4—611no—
235C22×D4—1222no—
236C23×C4—612no—
237C23×C4—1221no—
238C22×C8—1224no—
239#127—614no—
240#127—1222no—
241C4×D4—1221no—
242C4×D4—1221no—
243C4×D4—1221no—
244C4×D4—1221no—
245C4×D4—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248C4×D4—1221no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C22⋊C4—612no—
252C2×C22⋊C4—1222no—
253C2×C22⋊C4—1222no—
254C2×C22⋊C4—1221no—
255C2×C42C4×D6111yescharacteristic
256C2×C42C4×D6111yescharacteristic
257C2×C42C22×D6111yescharacteristic
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—1224no—
265C22⋊C8—1221no—
266C22⋊C8—1221no—
267C4×C8—21no—
268C4×C8—612no—
269C4×C8—1221no—
270C4×C8D24412yescomplemented
271#95—21no—
272#95—21no—
273#95—1222no—
274C24—612no—
275C24—1221no—
276C2×D4—612no—
277C2×D4—612no—
278C2×D4—612no—
279C2×D4—1228no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—4882no—
290C2×D4—4882no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—612no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—1221no—
297C22×C4—4882no—
298C22×C4—4882no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4C2×C4×D6111yescharacteristic
302C22×C4D4×D6111yescharacteristic
303C22×C4D4×D6111yescharacteristic
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—1222no—
307C2×C8—4884no—
308C2×C8—2441no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C22⋊C4—1222no—
314C22⋊C4—1222no—
315C22⋊C4—4882no—
316C22⋊C4—4882no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42C8×D6112yescomplemented
323C42C2×D24411yescharacteristic
324C42#1175822211yescharacteristic
325C42D4×D6111yescharacteristic
326C42#1175822611yescharacteristic
327C23—614no—
328C23—1222no—
329C23—1222no—
330C23—1222no—
331C23—2442no—
332C23—2442no—
333C23—2442no—
334C23—2442no—
335C23—2441no—
336C23—2441no—
337C23C22⋊C4×D6111yescharacteristic
338D4—1222no—
339D4—1222no—
340D4—1222no—
341D4—1222no—
342D4—1222no—
343D4—1222no—
344D4—4888no—
345D4—2441no—
346D4—2441no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—1222no—
356C2×C4—4882no—
357C2×C4—4882no—
358C2×C4—4882no—
359C2×C4—2444no—
360C2×C4—2442no—
361C2×C4—2441no—
362C2×C4—2442no—
363C2×C4#1451973911yescharacteristic
364C2×C4C4×D24411yescharacteristic
365C2×C4#1451974711yescharacteristic
366C2×C4#1451975011yescharacteristic
367C2×C4#1451975211yescharacteristic
368C2×C4#1451976211yescharacteristic
369C2×C4C2×C8×D6111yescharacteristic
370C2×C4M16×D6111yescharacteristic
371C2×C4#1451978311yescharacteristic
372C2×C4#1451978511yescharacteristic
373C8—42no—
374C8—81no—
375C8—4881no—
376C8—2442no—
377C22—21no—
378C22—21no—
379C22—1224no—
380C22—4882no—
381C22—4882no—
382C22—4881no—
383C22—4881no—
384C22—2444no—
385C22—2444no—
386C22—2442no—
387C22—2442no—
388C22—2442no—
389C22#1683964011yescharacteristic
390C22C22⋊C8×D6111yescharacteristic
391C22#1683972711yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—4881no—
399C4—2442no—
400C4#1683982711yescharacteristic
401C4C8×D24411yescharacteristic
402C4#1683983211yescharacteristic
403C4#1683983511yescharacteristic
404C2—21no—
405C2—21no—
406C2—4882no—
407C2—2444no—
408C2#2144611011yescharacteristic
409C2#2144634511yescharacteristic
410C2#2144635011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#386
prime radicalC2×#14519774C4
cosocleC2×C42×C61C23
hypercenter#1274D61
hypocenterC61#9101
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
1. #21454842C2semidirect
3. #21444211C2semidirect
4. #21444209C2semidirect
5. #21444139C2semidirect
6. #21443648C2semidirect
7. C61×#1274C2semidirect
34. #14519774C8semidirect
55. C4×#92418D4semidirect
65. C4×C8×C61D4semidirect
90. C2×D244C2×C8semidirect
103. C42×C61C2×C8semidirect
205. #1274D61semidirect
232. C61#9101semidirect
270. C4×C8D244semidirect
322. C42C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214548422
#214485442
#214442112
#214442092
#214441392
#214436482
C61×#12742
#910161