Finite Group Databasebeta

← #29592923

Subgroups — #29592923

Order 15616.

448 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 59 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#21447164C211yesmaximal, characteristic, complemented
2#21444792C211yesmaximal, characteristic, complemented
3#21444758C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic, complemented
5#21443822C211yesmaximal, characteristic
6#21443765C211yesmaximal, characteristic, complemented
7C61×#2680C211yesmaximal, characteristic
8#16840393C2211yescharacteristic
9#16839918—21no—
10#16839913—21no—
11#16839802—21no—
12#16839531C2211yescharacteristic
13#16839522—21no—
14#16839498—21no—
15#16839498—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C2×#123×C61—21no—
19C2×C22⋊Q8×C61—21no—
20C61×#398—21no—
21C61×#397—21no—
22C61×#395C2211yescharacteristic
23C61×#394C2211yescharacteristic
24C61×#388—21no—
25C61×#385—21no—
26C61×#384C2211yescharacteristic
27C2×#11758202—41no—
28C2×#11758200—41no—
29C2×#11758194—21no—
30#14519776—41no—
31#14519768—41no—
32#14519756—21no—
33#14519756—21no—
34#14519736—21no—
35#14519710—41no—
36#14519708—41no—
37#14519701—41no—
38#14519698—41no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C22×Q8×C61D411yescharacteristic
42C22×D4×C61D411yescharacteristic
43C23×C4×C61—21no—
44#123×C61—44no—
45C22⋊Q8×C61—44no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61C2311yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C42×C61D411yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61D411yescharacteristic
63#95×C61D411yescharacteristic
64C24×C61—21no—
65C2×Q8×C61—42no—
66C2×Q8×C61—41no—
67C2×D4×C61—41no—
68C2×D4×C61—42no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—42no—
75C22×C4×C61—42no—
76C22×C4×C61—81no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C2×Dic122—21no—
81C2×Dic122—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—42no—
85C4⋊C4×C61—42no—
86C4⋊C4×C61—42no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—24no—
90C22⋊C4×C61—42no—
91C22⋊C4×C61—42no—
92C22⋊C4×C61—42no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C42×C61—21no—
96C42×C61—21no—
97C22⋊Dic61—41no—
98#11758202—82no—
99#11758200—82no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—41no—
107#11758194—22no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C23×C61—22no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61#12011yescharacteristic
120Q8×C61—42no—
121Q8×C61—81no—
122D4×C61—42no—
123D4×C61—81no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
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×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—84no—
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61#13711yescharacteristic
148C2×Dic61—41no—
149C2×Dic61—41no—
150Dic122—81no—
151Dic122—81no—
152#92418—42no—
153#92418—81no—
154#92418—81no—
155#12234—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—42no—
159C22×C61—42no—
160C22×C61—42no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61#45211yescharacteristic
166C22×C61#45611yescharacteristic
167C22×C61B(4,𝔽2)11yescharacteristic
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—42no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—42no—
174C4×C61—81no—
175C4×C61—81no—
176C4×C61—81no—
177Dic61—81no—
178Dic61—81no—
179#2680D6111yescharacteristic
180#2060—611no—
181#1605—611no—
182#1599—611no—
183#1354—611no—
184#1345—611no—
185#1325—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—82no—
189C2×C61#160311yescharacteristic
190C2×C61#219611yescharacteristic
191C2×C61#220311yescharacteristic
192#544—611no—
193C2×#123—21no—
194C2×C22⋊Q8—21no—
195#451—1221no—
196#450—1221no—
197#428—1221no—
198#398—21no—
199#397—21no—
200#395C2×D6111yescharacteristic
201#394C2×D6111yescharacteristic
202#388—21no—
203#385—21no—
204#384C2×D6111yescharacteristic
205#343—611no—
206#339—1221no—
207#328—1221no—
208#328—1221no—
209#324—611no—
210#324—611no—
211C61#1223411yescharacteristic, complemented, Sylow
212C22×Q8C22⋊D6111yescharacteristic
213C22×D4C22⋊D6111yescharacteristic
214C23×C4—21no—
215C2×Q16—2441no—
216C2×SD16—2441no—
217C2×M16—1221no—
218C4⋊Q8—2441no—
219#125—2441no—
220#123—44no—
221C22⋊Q8—44no—
222C22⋊Q8—1221no—
223C22⋊Q8—1221no—
224#117—1221no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C22⋊D6111yescharacteristic
231C2×C4⋊C4C22×D6111yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C42C22⋊D6111yescharacteristic
238#107—2441no—
239#106—2441no—
240#103—2441no—
241#102—2441no—
242C22⋊C8—1221no—
243C22⋊C8—1221no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95C22⋊D6111yescharacteristic
248#95C22⋊D6111yescharacteristic
249C24—21no—
250C2×Q8—42no—
251C2×Q8—41no—
252C2×Q8—1221no—
253C2×Q8—1221no—
254C2×D4—41no—
255C2×D4—42no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—81no—
264C22×C4C2×C22⋊D6111yescharacteristic
265C22×C4C2×C22⋊D6111yescharacteristic
266C22×C4C2×C22⋊D6111yescharacteristic
267Q16—4882no—
268SD16—4882no—
269M16—1222no—
270M16—2441no—
271C2×C8—2441no—
272C2×C8—2441no—
273C2×C8—2441no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C22⋊C4—24no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—2441no—
294C42—21no—
295C42—21no—
296C42—2441no—
297C23—22no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23#1451974611yescharacteristic
305Q8—42no—
306Q8—81no—
307Q8—4881no—
308Q8—4881no—
309D4—42no—
310D4—81no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—84no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4#1451979711yescharacteristic
336C2×C4#1451980711yescharacteristic
337C8—4881no—
338C8—4881no—
339C8—2442no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22#1683992411yescharacteristic
350C22#1683994511yescharacteristic
351C22#1683994911yescharacteristic
352C4—21no—
353C4—21no—
354C4—42no—
355C4—41no—
356C4—41no—
357C4—42no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—4881no—
362C4—4881no—
363C2—21no—
364C2—21no—
365C2—82no—
366C2#2144478211yescharacteristic
367C2#2144780311yescharacteristic
368C2#2144784011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2680C2
socleC22×C61B(4,𝔽2)
prime radicalC22×D4×C61D4
hypercenter#2680D61
hypocenterC61#12234
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2680

Complements

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

NH ≅ G/Ntype
1. #21447164C2semidirect
2. #21444792C2semidirect
4. #21443849C2semidirect
6. #21443765C2semidirect
211. C61#12234semidirect

Maximal subgroups

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

subgroupindex
#214471642
#214447922
#214447582
#214438492
#214438222
#214437652
C61×#26802
#1223461