Finite Group Databasebeta

← #29583721

Subgroups — #29583721

Order 15616.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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#21455618C211yesmaximal, characteristic
2#21445808C211yesmaximal, characteristic
3#21444510C211yesmaximal, characteristic, complemented
4#21444275C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic
6#21443693C211yesmaximal, characteristic, complemented
7C61×#1566C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9C2×C4×D244C2211yescharacteristic
10#16840063—22no—
11#16840053—21no—
12#16840043—21no—
13#16839804—21no—
14#16839786C2211yescharacteristic
15C2×C4⋊#92418C2211yescharacteristic
16#16839768—21no—
17C2×#14519693—21no—
18#16839530—21no—
19#16839510—21no—
20#16839507—21no—
21#16839494—21no—
22#16839494—21no—
23#16839491—21no—
24#16839491—21no—
25C61×#423C2211yescharacteristic
26C61×#423C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C61×#334—22no—
29C22×D244D411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758194—21no—
32C22×#92418—21no—
33#14519777D411yescharacteristic
34#14519777D411yescharacteristic
35#14519769—21no—
36#14519756—21no—
37#14519756—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244—21no—
44#14519736—21no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758198—21no—
47#14519711—22no—
48#14519709—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53#14519699—22no—
54#14519699—22no—
55#14519693—42no—
56C2×M16×C61—21no—
57C2×M16×C61—21no—
58C22×C8×C61—21no—
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61D412yes—
64C4×C8×C61—21no—
65C4×C8×C61D411yescharacteristic
66C4×C8×C61D411yescharacteristic
67C23×D61—21no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C22×Dic61—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244SD1612yes—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—81no—
81C2×C4×D61—81no—
82C2×Dic122—21no—
83C2×Dic122—21no—
84M16×C61—41no—
85M16×C61—41no—
86M16×C61—41no—
87M16×C61—41no—
88C2×C8×C61—21no—
89C2×C8×C61—22no—
90C2×C8×C61—21no—
91C2×C8×C61—42no—
92C2×C8×C61—41no—
93C42×C61C2×D411yescharacteristic
94C42×C61C2×D411yescharacteristic
95C42×C61C2×D411yescharacteristic
96C42×C61#4111yescharacteristic
97C22⋊Dic61—41no—
98#11758198—41no—
99#11758198—41no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—41no—
109#11758194—41no—
110#11758194—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—81no—
114C23×C61#12311yescharacteristic
115C22×D61—22no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—81no—
119C22×D61—81no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61#12011yescharacteristic
124C2×C4×C61#12111yescharacteristic
125C2×C4×C61#12111yescharacteristic
126C2×C4×C61#12111yescharacteristic
127C2×C4×C61#12311yescharacteristic
128C2×C4×C61#12411yescharacteristic
129C2×C4×C61C2×SD1611yescharacteristic
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×C4×C61#13711yescharacteristic
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—81no—
137D244—22no—
138D244—22no—
139D244—41no—
140D244—41no—
141C4×D61—82no—
142C4×D61—81no—
143C4×D61—81no—
144Dic122—41no—
145Dic122—41no—
146Dic122—81no—
147C8×C61—22no—
148C8×C61—41no—
149C8×C61—42no—
150C8×C61—81no—
151#92418—81no—
152#92418—81no—
153#10460—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61#39411yescharacteristic
157C22×C61#48311yescharacteristic
158C22×C61#48511yescharacteristic
159C2×D61—42no—
160C2×D61—82no—
161C2×D61—81no—
162C2×D61—81no—
163C2×D61—82no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61#44811yescharacteristic
168C4×C61#45211yescharacteristic
169C4×C61#46511yescharacteristic
170C4×C61#47011yescharacteristic
171C4×C61#47111yescharacteristic
172C4×C61#47211yescharacteristic
173Dic61—81no—
174Dic61—81no—
175Dic61—81no—
176#3077—611no—
177#1800—611no—
178#1566D6111yescharacteristic, complemented
179#1550—611no—
180#1493—611no—
181C2×D4⋊C8—611no—
182#1292—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61#203511yescharacteristic
186C2×C61#205011yescharacteristic
187C2×C61#205111yescharacteristic
188D61—82no—
189#533—611no—
190C2×C4×D4—611no—
191#478—1222no—
192#476—1221no—
193#474—1221no—
194#428—1221no—
195#423—611no—
196#423C2×D6111yescharacteristic
197#423C2×D6111yescharacteristic
198C2×C4⋊C8—611no—
199#418—1221no—
200C2×#100—1221no—
201C2×C4×C8C2×D6111yescharacteristic
202#343—1221no—
203#334—22no—
204#333—1221no—
205#332—1221no—
206Q8⋊C8—1221no—
207Q8⋊C8—1221no—
208D4⋊C8—1221no—
209D4⋊C8—1221no—
210C61#1046011yescharacteristic, complemented, Sylow
211C22×D4—611no—
212C23×C4—1221no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16—1221no—
216C22×C8—21no—
217C22×C8—1221no—
218C4⋊Q8—611no—
219C4⋊Q8—611no—
220#125—1221no—
221C22⋊Q8—1221no—
222C22⋊Q8—1221no—
223C4×Q8—1221no—
224C4×Q8—1221no—
225C4×D4—1221no—
226C4×D4—1221no—
227C4×D4—1221no—
228C4×D4—1221no—
229#117—1221no—
230C2×C4⋊C4—611no—
231C2×C22⋊C4—1221no—
232C2×C42C22×D6111yescharacteristic
233#107—1222no—
234#106—1222no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—1221no—
239C4⋊C8—1221no—
240C4⋊C8—1221no—
241C4⋊C8—1221no—
242C4⋊C8C22⋊D6112yes—
243#102—1222no—
244#102—1222no—
245#100—2442no—
246C4×C8—21no—
247C4×C8D24411yescharacteristic
248C4×C8D24411yescharacteristic
249C24—1221no—
250C2×Q8—1221no—
251C2×Q8—1221no—
252C2×D4—612no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C22×C4—1221no—
259C22×C4—4881no—
260C22×C4—4881no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4#1175822211yescharacteristic
264C22×C4D4×D6111yescharacteristic
265C22×C4#1175822611yescharacteristic
266M16—41no—
267M16—41no—
268M16—41no—
269M16—41no—
270M16—2441no—
271M16—2441no—
272C2×C8—21no—
273C2×C8—22no—
274C2×C8—21no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—4881no—
278C2×C8—2441no—
279C2×C8—2441no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C22⋊C4—2441no—
289C22⋊C4—2441no—
290C22⋊C4—2441no—
291C42—2441no—
292C42C2×D24411yescharacteristic
293C42D4×D6111yescharacteristic
294C42#1175822611yescharacteristic
295C42C2×C22⋊D6111yescharacteristic
296C23—1222no—
297C23—4881no—
298C23—4881no—
299C23—2441no—
300C23—2441no—
301C23#1451976211yescharacteristic
302Q8—4881no—
303Q8—2441no—
304Q8—2441no—
305D4—1222no—
306D4—1222no—
307D4—2441no—
308D4—2441no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—4882no—
313C2×C4—4881no—
314C2×C4—4881no—
315C2×C4—4881no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451974511yescharacteristic
320C2×C4#1451975111yescharacteristic
321C2×C4#1451975211yescharacteristic
322C2×C4#1451975211yescharacteristic
323C2×C4#1451976211yescharacteristic
324C2×C4#1451976611yescharacteristic
325C2×C4SD16×D6111yescharacteristic
326C2×C4#1451979811yescharacteristic
327C2×C4#1451980611yescharacteristic
328C2×C4#1451980611yescharacteristic
329C8—22no—
330C8—41no—
331C8—42no—
332C8—81no—
333C8—4881no—
334C8—4881no—
335C22—21no—
336C22—21no—
337C22—4882no—
338C22—4882no—
339C22—4881no—
340C22—4881no—
341C22—2442no—
342C22#1683967911yescharacteristic
343C22#1684009411yescharacteristic
344C22#1684010611yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—4881no—
349C4—4881no—
350C4—4881no—
351C4#1683989911yescharacteristic
352C4#1683992111yescharacteristic
353C4#1683999211yescharacteristic
354C4#1684002111yescharacteristic
355C4#1684002611yescharacteristic
356C4#1684003311yescharacteristic
357C2—21no—
358C2—21no—
359C2—4882no—
360C2#2144701711yescharacteristic
361C2#2144710611yescharacteristic
362C2#2144711311yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1566C2
socleC22×C61#394
prime radicalC22×D244D4
hypercenter#1566D61
hypocenterC61#10460
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
3. #21444510C2semidirect
4. #21444275C2semidirect
6. #21443693C2semidirect
7. C61×#1566C2semidirect
178. #1566D61semidirect
210. C61#10460semidirect

Maximal subgroups

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

subgroupindex
#214556182
#214458082
#214445102
#214442752
C2×#168394912
#214436932
C61×#15662
#1046061