Finite Group Databasebeta

← #29582279

Subgroups — #29582279

Order 15616.

484 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 95 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#21456947C211yesmaximal, characteristic
2#21456767C211yesmaximal, characteristic, complemented
3#21456165C211yesmaximal, characteristic
4#21444382C211yesmaximal, characteristic, complemented
5#21444378C211yesmaximal, characteristic
6#21443664C211yesmaximal, characteristic, complemented
7C61×#1993C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9#16840312C2211yescharacteristic
10#16840158—21no—
11#16840141—21no—
12#16840131—21no—
13#16840127—21no—
14#16840122—21no—
15#16840122—21no—
16#16840112—21no—
17#16840110—21no—
18#16840080—22no—
19#16840049—22no—
20#16839969—22no—
21#16839918—22no—
22#16839815C2211yescharacteristic
23#16839815C2211yescharacteristic
24#16839759—22no—
25#16839498—22no—
26#16839495—22no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C2×#97×C61C2211yescharacteristic
29C61×#382C2211yescharacteristic
30C61×#340—22no—
31C2×#11758222—21no—
32C2×#11758202—24no—
33#14519777D411yescharacteristic
34#14519777D411yescharacteristic
35#14519777D411yescharacteristic
36#14519774D411yescharacteristic
37#14519769—21no—
38#14519765—21no—
39#14519756—21no—
40#14519756—21no—
41#14519751—21no—
42#14519751—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×D244—21no—
46C4×D244—21no—
47#14519736—21no—
48#14519708—24no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51#14519702—22no—
52#14519702—22no—
53#14519701—24no—
54#14519699—22no—
55#14519699—22no—
56#14519697—24no—
57C22⋊#92418D412yes—
58C22⋊#92418D412yes—
59C4×#92418—21no—
60C4×#92418—21no—
61C22×Q8×C61—21no—
62C22×C8×C61D412yes—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61D412yes—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61C2311yescharacteristic
71#97×C61—21no—
72#97×C61—21no—
73#95×C61—21no—
74#95×C61—21no—
75C2×Q8×C61—22no—
76C2×Q8×C61—41no—
77C2×Q8×C61—82no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C2×C22⋊D61—41no—
84#11758222—42no—
85#11758222—42no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×C4×D61—41no—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×C8×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—42no—
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C22⋊Dic61—41no—
106#11758202—84no—
107#11758198—41no—
108#11758198—41no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115#11758196—41no—
116#11758196—41no—
117C4×Dic61—41no—
118C2×#92418—22no—
119C2×#92418—22no—
120C23×C61#12711yescharacteristic
121C22×D61—41no—
122Q8×C61—44no—
123Q8×C61—82no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—82no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#13512yes—
138C2×C4×C61#13712yes—
139C22⋊D61—81no—
140C22⋊D61—81no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144D244—42no—
145D244—42no—
146D244—81no—
147C4×D61—82no—
148Dic122—42no—
149Dic122—42no—
150Dic122—81no—
151C8×C61—42no—
152#92418—42no—
153#92418—42no—
154#10223—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61#39211yescharacteristic
158C22×C61#49511yescharacteristic
159C22×C61#49711yescharacteristic
160C2×D61—81no—
161C2×D61—81no—
162C2×D61—81no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—82no—
168C4×C61—161no—
169C4×C61#45212yes—
170C4×C61#46412yes—
171Dic61—81no—
172Dic61—81no—
173Dic61—81no—
174#3227—611no—
175#3209—611no—
176#3135—611no—
177#1993D6111yescharacteristic, complemented
178#1518—611no—
179#1517—611no—
180#1281—611no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61#200811yescharacteristic
184C2×C61#200911yescharacteristic
185C2×C61#201511yescharacteristic
186D61—161no—
187#533—611no—
188#532—611no—
189C2×C4⋊Q8C2×D6111yescharacteristic
190#498—1221no—
191#494—1221no—
192#491—1221no—
193#490—1221no—
194#489—1221no—
195#489—1221no—
196#487—1221no—
197#486—1221no—
198#481—1222no—
199#476—1222no—
200#462—1222no—
201#451—1222no—
202#431—611no—
203#431—611no—
204#416—1222no—
205C2×#97C2×D6111yescharacteristic
206#382C2×D6111yescharacteristic
207#340—22no—
208#328—1222no—
209#327—1222no—
210C61#1022311yescharacteristic, complemented, Sylow
211C2×#41—1221no—
212C22×Q8—21no—
213C2×Q16—1224no—
214C22×C8C22⋊D6112yes—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—611no—
219C4⋊Q8—611no—
220C4⋊Q8—611no—
221C4⋊Q8D24412yes—
222#127—611no—
223#125—1221no—
224#124—1221no—
225C22⋊Q8—1221no—
226C22⋊Q8—1221no—
227#121—1221no—
228#121—1221no—
229C4×Q8—1221no—
230C4×Q8—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233#117—1221no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C42C22×D6111yescharacteristic
238#106—1224no—
239C4⋊C8—1221no—
240C4⋊C8—1221no—
241#103—1222no—
242#103—1222no—
243#103—1224no—
244#102—1224no—
245#102—1222no—
246#102—1222no—
247C22⋊C8—612no—
248C22⋊C8—612no—
249#97—21no—
250#97—21no—
251C4×C8—1221no—
252C4×C8—1221no—
253#95—21no—
254#95—21no—
255#41—2442no—
256#41—2442no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—82no—
260C2×Q8—1221no—
261C2×Q8—1221no—
262C2×Q8—1221no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—2441no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—2441no—
270C22×C4D4×D6111yescharacteristic
271C22×C4D4×D6111yescharacteristic
272C22×C4C2×C22⋊D6111yescharacteristic
273Q16—4884no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—1222no—
278C2×C8—1222no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C42—2441no—
296C42C2×D24411yescharacteristic
297C42#1175822211yescharacteristic
298C42D4×D6111yescharacteristic
299C42D4×D6111yescharacteristic
300C23—2441no—
301C23#1451977311yescharacteristic
302Q8—44no—
303Q8—82no—
304Q8—4881no—
305Q8—2442no—
306Q8—2442no—
307D4—4881no—
308D4—4881no—
309D4—4881no—
310D4—2442no—
311D4—2442no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—82no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—4882no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4#1451974511yescharacteristic
324C2×C4#1451974711yescharacteristic
325C2×C4#1451974711yescharacteristic
326C2×C4#1451975011yescharacteristic
327C2×C4#1451975011yescharacteristic
328C2×C4#1451975111yescharacteristic
329C2×C4#1451979712yes—
330C2×C4#1451980812yes—
331C8—42no—
332C8—2442no—
333C8—2442no—
334C22—21no—
335C22—21no—
336C22—4881no—
337C22—4881no—
338C22—4881no—
339C22#1683967111yescharacteristic
340C22#1684014411yescharacteristic
341C22#1684015411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—82no—
347C4—161no—
348C4—4881no—
349C4—4881no—
350C4—4881no—
351C4#1683992212yes—
352C4#1683998412yes—
353C2—21no—
354C2—21no—
355C2—9761no—
356C2#2144687411yescharacteristic
357C2#2144688111yescharacteristic
358C2#2144691211yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1993C2
socleC22×C61#392
prime radical#16840312C22
hypercenter#1993D61
hypocenterC61#10223
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
2. #21456767C2semidirect
4. #21444382C2semidirect
6. #21443664C2semidirect
7. C61×#1993C2semidirect
177. #1993D61semidirect
210. C61#10223semidirect

Maximal subgroups

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

subgroupindex
#214569472
#214567672
#214561652
#214443822
#214443782
#214436642
C61×#19932
#1022361