Finite Group Databasebeta

← #29575817

Subgroups — #29575817

Order 15616.

450 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454839C211yesmaximal, characteristic
2#21445629C211yesmaximal, characteristic
3#21444414C211yesmaximal, characteristic, complemented
4#21444331C211yesmaximal, characteristic, complemented
5#21443711C211yesmaximal, characteristic, complemented
6#21443690C211yesmaximal, characteristic, complemented
7C61×#3116C211yesmaximal, characteristic
8Q8×#92418—21no—
9#16839840—22no—
10#16839840—21no—
11#16839819—21no—
12#16839819C2211yescharacteristic
13C2×#14519704—21no—
14C4×#11758194—21no—
15C4×#11758194C2211yescharacteristic
16C4×#11758194C2211yescharacteristic
17#16839608C2211yescharacteristic
18#16839521—21no—
19#16839504—21no—
20#16839504—21no—
21#16839499—22no—
22C61×#533C2211yescharacteristic
23C4×#41×C61C2211yescharacteristic
24C61×#485—21no—
25C61×#477C411yescharacteristic, complemented
26C61×#476C411yescharacteristic, complemented
27C61×#462C411yescharacteristic, complemented
28C61×#461C411yescharacteristic, complemented
29C61×#452—21no—
30C61×#441—21no—
31C61×#440—21no—
32C61×#432C2211yescharacteristic
33C2×#11758194—22no—
34C2×#11758194—21no—
35C2×#11758194—21no—
36C2×C4×Dic61—21no—
37C4⋊#92418—22no—
38C4⋊#92418—21no—
39#14519704—24no—
40C22⋊#92418—22no—
41C22⋊#92418D412yes—
42#14519688—21no—
43#14519688—21no—
44#14519688D411yescharacteristic
45#14519688D411yescharacteristic
46C4×#92418—22no—
47C4×#92418—21no—
48C4×#92418—21no—
49#14519684—21no—
50#14519684—21no—
51C2×#41×C61D411yescharacteristic
52C2×Q16×C61—21no—
53C2×SD16×C61—21no—
54C4⋊Q8×C61C2×C411yescharacteristic
55C4⋊Q8×C61C2×C411yescharacteristic
56#125×C61—21no—
57C22⋊Q8×C61—21no—
58C22⋊Q8×C61—21no—
59C4×Q8×C61—21no—
60C4×Q8×C61—21no—
61C4×Q8×C61C2×C411yescharacteristic
62C4×Q8×C61D411yescharacteristic
63C4×D4×C61—21no—
64C4×D4×C61—21no—
65C4×D4×C61C2×C411yescharacteristic
66C4×D4×C61D411yescharacteristic
67#117×C61—21no—
68#117×C61—21no—
69#117×C61D411yescharacteristic
70C2×C42×C61—21no—
71C2×C42×C61C2311yescharacteristic
72#107×C61—21no—
73#106×C61—21no—
74C4⋊C8×C61C2×C411yescharacteristic
75C4⋊C8×C61C2×C411yescharacteristic
76#103×C61—21no—
77#103×C61—21no—
78#103×C61—21no—
79#102×C61—21no—
80C22⋊C8×C61—21no—
81#97×C61—21no—
82#41×C61—22no—
83#41×C61—41no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61C22⋊C411yescharacteristic
87C2×D4×C61—21no—
88C2×D4×C61C22⋊C411yescharacteristic
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×Dic61—41no—
96Q16×C61—42no—
97SD16×C61—42no—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61C22⋊C411yescharacteristic
109C4⋊C4×C61C22⋊C411yescharacteristic
110C22⋊C4×C61—21no—
111C22⋊C4×C61—21no—
112C22⋊C4×C61—21no—
113C22⋊C4×C61—41no—
114C42×C61—21no—
115C42×C61—21no—
116C42×C61—21no—
117C42×C61—41no—
118C42×C61C22×C411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122C4×Dic61—22no—
123C4×Dic61—41no—
124#11758194—22no—
125#11758194—42no—
126#11758194—44no—
127#11758194—41no—
128C2×#92418—21no—
129C2×#92418—22no—
130C2×#92418—21no—
131C2×#92418—41no—
132C23×C61—21no—
133C23×C61#12111yescharacteristic
134Q8×C61—21no—
135Q8×C61—41no—
136Q8×C61—41no—
137Q8×C61—81no—
138Q8×C61#10412yes—
139D4×C61—21no—
140D4×C61—21no—
141D4×C61—42no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—81no—
154C2×C4×C61C2×C22⋊C411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12311yescharacteristic
160C2×Dic61—42no—
161C2×Dic61—81no—
162C2×Dic61—81no—
163C8×C61—41no—
164C8×C61—41no—
165#92418—22no—
166#92418—42no—
167#92418—41no—
168#92418—42no—
169#9160—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61#38611yescharacteristic
177C4×C61—21no—
178C4×C61—22no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—81no—
186C4×C61—81no—
187C4×C61C2×#10411yescharacteristic
188C4×C61#42111yescharacteristic
189Dic61—82no—
190#3116D6111yescharacteristic
191#2971—611no—
192#1759—611no—
193#1526—611no—
194#1506—611no—
195#1300—611no—
196#1291—611no—
197C2×C61—41no—
198C2×C61—81no—
199C2×C61#187111yescharacteristic
200C2×C61#190211yescharacteristic
201C2×C61#190611yescharacteristic
202#533C2×D6111yescharacteristic
203C4×#41C2×D6111yescharacteristic
204#485—21no—
205#477Dic6111yescharacteristic, complemented
206#476Dic6111yescharacteristic, complemented
207#462Dic6111yescharacteristic, complemented
208#461Dic6111yescharacteristic, complemented
209#452—21no—
210C8×Q8—1221no—
211#441—21no—
212#440—21no—
213#436—1222no—
214#436—1221no—
215#432—611no—
216#432—1221no—
217#432C2×D6111yescharacteristic
218C2×#104—1221no—
219C4×M16—611no—
220C4×M16—611no—
221C4×M16—1221no—
222#376—611no—
223#339—1221no—
224#330—1221no—
225#330—1221no—
226#328—1222no—
227C61#916011yescharacteristic, complemented, Sylow
228C2×#41C22⋊D6111yescharacteristic
229C2×Q16—21no—
230C2×SD16—21no—
231C2×M16—1222no—
232C2×M16—1221no—
233C2×M16—1221no—
234C4⋊Q8C2×Dic6111yescharacteristic
235C4⋊Q8C2×Dic6111yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C2×Dic6111yescharacteristic
242C4×Q8C22⋊D6111yescharacteristic
243C4×D4—21no—
244C4×D4—21no—
245C4×D4C2×Dic6111yescharacteristic
246C4×D4C22⋊D6111yescharacteristic
247#117—21no—
248#117—21no—
249#117C22⋊D6111yescharacteristic
250C2×C42—21no—
251C2×C42—1221no—
252C2×C42C22×D6111yescharacteristic
253#107—21no—
254#106—21no—
255C4⋊C8—1222no—
256C4⋊C8—1221no—
257C4⋊C8C2×Dic6111yescharacteristic
258C4⋊C8C2×Dic6111yescharacteristic
259#104—1224no—
260#103—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264C22⋊C8—21no—
265C22⋊C8—612no—
266C22⋊C8—1222no—
267#97—21no—
268#97—611no—
269#97—611no—
270#97—1221no—
271#97—1221no—
272C4×C8—1222no—
273C4×C8—1221no—
274C4×C8—1221no—
275#95—1221no—
276#95—1221no—
277#41—22no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8C22⋊Dic6111yescharacteristic
282C2×D4—21no—
283C2×D4C22⋊Dic6111yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—2441no—
288C22×C4D4×D6111yescharacteristic
289C22×C4#1175822411yescharacteristic
290C22×C4C2×C22⋊D6111yescharacteristic
291Q16—42no—
292SD16—42no—
293M16—1222no—
294M16—2442no—
295M16—2444no—
296M16—2441no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—1221no—
300C2×C8—1221no—
301C2×C8—1222no—
302C2×C8—2441no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4C22⋊Dic6111yescharacteristic
312C4⋊C4C22⋊Dic6111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—41no—
321C42—1222no—
322C42—2441no—
323C42D4×D6111yescharacteristic
324C42#1175822411yescharacteristic
325C42C22×Dic6111yescharacteristic
326C42C2×C22⋊D6111yescharacteristic
327C23—21no—
328C23#1451974911yescharacteristic
329Q8—21no—
330Q8—41no—
331Q8—41no—
332Q8—81no—
333Q8#1451970412yes—
334D4—21no—
335D4—21no—
336D4—42no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—2442no—
352C2×C4C2×C22⋊Dic6111yescharacteristic
353C2×C4D4×Dic6111yescharacteristic
354C2×C4D4×Dic6111yescharacteristic
355C2×C4#1451974511yescharacteristic
356C2×C4#1451974911yescharacteristic
357C2×C4#1451975811yescharacteristic
358C8—41no—
359C8—41no—
360C8—1222no—
361C8—2441no—
362C8—2442no—
363C8—2442no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22#1683964211yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—4882no—
382C4C2×#1451970411yescharacteristic
383C4#1683977911yescharacteristic
384C2—41no—
385C2—81no—
386C2#2144612211yescharacteristic
387C2#2144629411yescharacteristic
388C2#2144632211yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#3116C2
socleC22×C61#386
prime radicalC2×#41×C61D4
cosocleC2×C42×C61C23
hypercenter#3116D61
hypocenterC61#9160
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3116

Complements

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

NH ≅ G/Ntype
3. #21444414C2semidirect
4. #21444331C2semidirect
5. #21443711C2semidirect
6. #21443690C2semidirect
25. C61×#477C4semidirect
26. C61×#476C4semidirect
27. C61×#462C4semidirect
28. C61×#461C4semidirect
205. #477Dic61semidirect
206. #476Dic61semidirect
207. #462Dic61semidirect
208. #461Dic61semidirect
227. C61#9160semidirect

Maximal subgroups

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

subgroupindex
#214548392
#214456292
#214444142
#214443312
#214437112
#214436902
C61×#31162
#916061