Finite Group Databasebeta

← #29569011

Subgroups — #29569011

Order 15616.

480 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21453765C211yesmaximal, characteristic
2#21446961C211yesmaximal, characteristic, complemented
3#21446955C211yesmaximal, characteristic
4#21446921C211yesmaximal, characteristic, complemented
5#21443644C211yesmaximal, characteristic, complemented
6#21443644C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic
8C22×Dic244—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519702—21no—
11C2×#14519702—21no—
12C2×#14519698—21no—
13#16839701—21no—
14#16839674—21no—
15#16839674—21no—
16#16839668C2211yescharacteristic
17#16839668C2211yescharacteristic
18#16839642—21no—
19#16839637—21no—
20#16839637—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122D411yescharacteristic
29C22×Dic122D411yescharacteristic
30C23×Dic61—21no—
31C2×Dic244—42no—
32C2×Dic244—42no—
33C2×Dic244—42no—
34C22×#92418—21no—
35#14519777—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44#14519702—42no—
45#14519702—42no—
46#14519698—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C22×D4×C61D411yescharacteristic
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C24×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C2×D4×C61Q1612yescomplemented
66C22×C4×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—41no—
75C22×Dic61—81no—
76C22×Dic61—81no—
77C22×Dic61—81no—
78C2×Dic122—22no—
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×Dic122—21no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×Dic122—41no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×C8×C61—22no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C42×C61—41no—
104C22⋊Dic61—81no—
105C22⋊Dic61—81no—
106C22⋊Dic61—81no—
107C4⋊Dic61—22no—
108C4⋊Dic61—22no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61—81no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117Dic244—48no—
118C23×C61—22no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61#12011yescharacteristic
126D4×C61—42no—
127D4×C61—81no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61C2×Q1611yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61#13711yescharacteristic
142C2×C4×C61#13711yescharacteristic
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—84no—
157C2×Dic61—81no—
158C2×Dic61—81no—
159Dic122—42no—
160Dic122—42no—
161Dic122—42no—
162Dic122—42no—
163Dic122—81no—
164Dic122—81no—
165Dic122—81no—
166Dic122—81no—
167C8×C61—42no—
168C8×C61—81no—
169#92418—81no—
170#7782—611nomaximal, Sylow
171C22×C61—42no—
172C22×C61—42no—
173C22×C61—42no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61#44911yescharacteristic
179C22×C61#45111yescharacteristic
180C22×C61#45211yescharacteristic
181C22×C61#45311yescharacteristic
182C22×C61#45511yescharacteristic
183C22×C61#45511yescharacteristic
184C22×C61B(4,𝔽2)11yescharacteristic
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—81no—
192Dic61—82no—
193Dic61—81no—
194Dic61—81no—
195Dic61—81no—
196Dic61—81no—
197#2804—611no—
198#2024—611no—
199#2023—611no—
200#2016—611no—
201#1272—611no—
202#1272—611no—
203#1270D6111yescharacteristic
204C2×C61—82no—
205C2×C61#160011yescharacteristic
206C2×C61#160211yescharacteristic
207C2×C61#160611yescharacteristic
208C2×C61#163211yescharacteristic
209C2×C61#164011yescharacteristic
210C2×C61#164411yescharacteristic
211C2×C61#165911yescharacteristic
212C22×Q16—1221no—
213C2×C4⋊Q8—611no—
214C2×#103—1221no—
215C2×#103—1221no—
216C2×#102—1221no—
217#400—1221no—
218#393—1221no—
219#393—1221no—
220#391—611no—
221#391—611no—
222#390C2×D6111yescharacteristic
223#386—1221no—
224#385—1221no—
225#385—1221no—
226#340—1221no—
227#340—1221no—
228#336—611no—
229#336C2×D6111yescharacteristic
230#336C2×D6111yescharacteristic
231C61#778211yescharacteristic, complemented, Sylow
232C22×Q8—611no—
233C22×Q8—611no—
234C22×Q8—1221no—
235C22×D4D24411yescharacteristic
236C23×C4—1221no—
237C2×Q16—2442no—
238C2×Q16—2442no—
239C2×Q16—2442no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—1221no—
243C4⋊Q8—2442no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4D24411yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C42C22×D6111yescharacteristic
256#103—2442no—
257#103—2442no—
258#102—2442no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266C24—21no—
267C2×Q8—1222no—
268C2×Q8—1221no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×Q8—1221no—
272C2×Q8—2441no—
273C2×Q8—2441no—
274C2×Q8—2441no—
275C2×Q8—2441no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4Dic24412yescomplemented
285C22×C4—21no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—4881no—
291C22×C4—4881no—
292C22×C4—4881no—
293C22×C4—2441no—
294C22×C4C2×D24411yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C22×C4D4×D6111yescharacteristic
297Q16—2448no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—2441no—
305C2×C8—2441no—
306C2×C8—2441no—
307C4⋊C4—41no—
308C4⋊C4—1222no—
309C4⋊C4—1222no—
310C4⋊C4—4881no—
311C4⋊C4—2441no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—4881no—
320C22⋊C4—4881no—
321C22⋊C4—4881no—
322C42—41no—
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23#1451974711yescharacteristic
331Q8—4881no—
332Q8—4881no—
333Q8—4881no—
334Q8—4881no—
335Q8—2442no—
336Q8—2442no—
337Q8—2442no—
338Q8—2442no—
339D4—42no—
340D4—81no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—4884no—
351C2×C4—4881no—
352C2×C4—4881no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2442no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4C2×Dic24411yescharacteristic
367C2×C4#1451979611yescharacteristic
368C2×C4#1451979811yescharacteristic
369C2×C4#1451980111yescharacteristic
370C2×C4#1451980611yescharacteristic
371C2×C4#1451981011yescharacteristic
372C8—42no—
373C8—81no—
374C8—4881no—
375C22—42no—
376C22—42no—
377C22—42no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22#1683990811yescharacteristic
383C22#1683992011yescharacteristic
384C22#1683992511yescharacteristic
385C22#1683993111yescharacteristic
386C22#1683994111yescharacteristic
387C22#1683994211yescharacteristic
388C22#1683995011yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—81no—
396C4—4881no—
397C4—4881no—
398C4—4882no—
399C4—4881no—
400C4—4881no—
401C2—82no—
402C2#2144476611yescharacteristic
403C2#2144477811yescharacteristic
404C2#2144480011yescharacteristic
405C2#2144495511yescharacteristic
406C2#2144500611yescharacteristic
407C2#2144503611yescharacteristic
408C2#2144512711yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7782
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21446961C2semidirect
4. #21446921C2semidirect
5. #21443644C2semidirect
6. #21443644C2semidirect
65. C2×D4×C61Q16semidirect
231. C61#7782semidirect
284. C2×D4Dic244semidirect

Maximal subgroups

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

subgroupindex
#214537652
#214469612
#214469552
#214469212
#214436442
C61×#12702
#778261