Finite Group Databasebeta

← #29571853

Subgroups — #29571853

Order 15616.

692 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459224C211yesmaximal, characteristic
2#21445803C211yesmaximal, characteristic
3#21444474C212yesmaximal, complemented
4#21444223C212yesmaximal, complemented
5C61×#1458C211yesmaximal, characteristic
6#16840393—21no—
7#16840393C412yes—
8#16840390—22no—
9#16840390—22no—
10#16840388—21no—
11#16840388C412yes—
12#16840319—21no—
13#16840319C2212yes—
14#16840315—24no—
15C2×#14519736—21no—
16C2×C4⋊#92418C2211yescharacteristic
17C2×C4⋊#92418C2211yescharacteristic
18C2×C22⋊#92418—21no—
19#16839517—21no—
20#16839510—22no—
21#16839509—22no—
22#16839494—24no—
23C2×#117×C61C2211yescharacteristic
24C61×#431C2212yes—
25C61×#324—21no—
26C61×#323—21no—
27C22×#92418—21no—
28C22×#92418—21no—
29#14519777—21no—
30#14519777—21no—
31#14519777D412yes—
32#14519777D412yes—
33#14519776—24no—
34#14519776—24no—
35#14519769—22no—
36#14519769—22no—
37#14519768—24no—
38#14519768—24no—
39#14519756—22no—
40#14519756—22no—
41#14519756—22no—
42#14519756C2×C414yes—
43#14519754—24no—
44#14519754—24no—
45#14519754—24no—
46#14519754—24no—
47C4×Dic122—22no—
48C4×Dic122—22no—
49C4×Dic122—22no—
50C4×Dic122D414yes—
51#14519736—22no—
52#14519736—22no—
53#14519736—22no—
54#14519736—22no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—21no—
57C2×C22⋊Dic61—22no—
58C2×C4×Dic61—22no—
59C4⋊#92418—22no—
60C4⋊#92418—22no—
61C22⋊#92418—42no—
62C23×C4×C61D411yescharacteristic
63#117×C61—22no—
64#117×C61—22no—
65C2×C4⋊C4×C61C2×C411yescharacteristic
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C22⋊C4×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61D411yescharacteristic
69C2×C42×C61D411yescharacteristic
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—22no—
72C22⋊C8×C61—22no—
73C4×C8×C61—22no—
74C24×C61C22⋊C411yescharacteristic
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61C22⋊C411yescharacteristic
80C22×C4×C61C22⋊C411yescharacteristic
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61SD1612yes—
83C22×C4×C61Q1612yes—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×Dic61—22no—
88C22×Dic61—22no—
89C2×Dic122—22no—
90C2×Dic122—22no—
91C2×Dic122—22no—
92C2×Dic122C22⋊C414yes—
93C2×C8×C61—42no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—22no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61—22no—
98C42×C61—21no—
99C42×C61—21no—
100C42×C61C2×D412yes—
101C42×C61C2×D412yes—
102C22⋊Dic61—24no—
103C22⋊Dic61—24no—
104C4⋊Dic61—22no—
105C4⋊Dic61—22no—
106C4⋊Dic61—22no—
107C4⋊Dic61—22no—
108C4⋊Dic61—22no—
109C4⋊Dic61—22no—
110C4⋊Dic61—22no—
111C4⋊Dic61C22⋊C414yes—
112#11758196—24no—
113#11758196—24no—
114#11758196—24no—
115#11758196—24no—
116C4×Dic61—24no—
117C4×Dic61—24no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61#10312yes—
129C23×C61C2×C22⋊C411yescharacteristic
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61#10312yes—
143C2×C4×C61C2×C22⋊C412yes—
144C2×C4×C61#12012yes—
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12011yescharacteristic
147C2×C4×C61C2×SD1611yescharacteristic
148C2×C4×C61C2×Q1611yescharacteristic
149C2×C4×C61#13711yescharacteristic
150C2×C4×C61#13711yescharacteristic
151C2×Dic61—24no—
152C2×Dic61—24no—
153C2×Dic61—82no—
154C2×Dic61—82no—
155Dic122—44no—
156Dic122—82no—
157Dic122—82no—
158Dic122—82no—
159C8×C61—82no—
160#92418—81no—
161#92418—81no—
162#8410—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—22no—
166C22×C61—42no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—81no—
170C22×C61#37911yescharacteristic
171C22×C61C2×#10311yescharacteristic
172C22×C61#41911yescharacteristic
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—22no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61#44811yescharacteristic
179C4×C61#44811yescharacteristic
180C4×C61#45111yescharacteristic
181C4×C61#45111yescharacteristic
182Dic61—44no—
183Dic61—44no—
184#3458—611no—
185#1798—611no—
186#1542—612no—
187#1481—612no—
188#1458D6111yescharacteristic
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—42no—
192C2×C61#178711yescharacteristic
193C2×C61#179111yescharacteristic
194C2×C61#179411yescharacteristic
195#544—612no—
196#544—1222no—
197#544—1222no—
198#544—1221no—
199#543—612no—
200#543—1221no—
201#533—612no—
202#533—1224no—
203#533—1221no—
204C2×#117—1221no—
205C2×#117C2×D6111yescharacteristic
206#431C2×D6112yes—
207C2×C4⋊C8—611no—
208C2×C4⋊C8—611no—
209C2×C22⋊C8—1221no—
210#336—1221no—
211#333—1222no—
212#332—1222no—
213Q8⋊C8—1224no—
214#324—21no—
215#323—21no—
216C61#841011yescharacteristic, complemented, Sylow
217C23×C4D24411yescharacteristic
218C22×C8—1221no—
219C22×C8—1221no—
220C4⋊Q8—612no—
221C4⋊Q8—612no—
222C4⋊Q8—1221no—
223C4⋊Q8—1221no—
224C4⋊Q8—1224no—
225C4⋊Q8—1224no—
226#125—1222no—
227#125—1224no—
228#125—1224no—
229#125—1222no—
230C22⋊Q8—614no—
231C22⋊Q8—1224no—
232C22⋊Q8—1224no—
233C22⋊Q8—1224no—
234C22⋊Q8—1224no—
235C22⋊Q8—1222no—
236C22⋊Q8—1222no—
237C22⋊Q8—1222no—
238C4×Q8—614no—
239C4×Q8—1222no—
240C4×Q8—1222no—
241C4×Q8—1222no—
242#117—22no—
243#117—22no—
244#117—1222no—
245#117—1222no—
246#117—1222no—
247#117—1222no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4C4×D6111yescharacteristic
251C2×C4⋊C4C22⋊D6111yescharacteristic
252C2×C22⋊C4—1222no—
253C2×C22⋊C4C4×D6111yescharacteristic
254C2×C22⋊C4C22⋊D6111yescharacteristic
255C2×C42—1222no—
256C2×C42D24411yescharacteristic
257C2×C42C22×D6111yescharacteristic
258C4⋊C8—22no—
259C4⋊C8—1222no—
260C4⋊C8—1222no—
261C22⋊C8—22no—
262C22⋊C8—2442no—
263C4×C8—22no—
264C24#1175819811yescharacteristic
265C2×Q8—614no—
266C2×Q8—1222no—
267C2×Q8—1222no—
268C2×Q8—1222no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—1222no—
274C22×C4—1222no—
275C22×C4#1175819012yes—
276C22×C4Dic24412yes—
277C22×C4#1175819811yescharacteristic
278C22×C4#1175819811yescharacteristic
279C22×C4#1175819811yescharacteristic
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4C2×D24411yescharacteristic
282C22×C4C2×C22⋊D6111yescharacteristic
283C2×C8—42no—
284C2×C8—2441no—
285C2×C8—2441no—
286C2×C8—2441no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8—2441no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—614no—
293C4⋊C4—1222no—
294C4⋊C4—1222no—
295C4⋊C4—1224no—
296C4⋊C4—1224no—
297C4⋊C4—1222no—
298C4⋊C4—1222no—
299C4⋊C4—1224no—
300C4⋊C4—1224no—
301C4⋊C4—1222no—
302C4⋊C4—1222no—
303C4⋊C4—1222no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—1224no—
307C22⋊C4—1224no—
308C42—21no—
309C42—21no—
310C42—1224no—
311C42—1224no—
312C42D4×D6112yes—
313C42D4×D6112yes—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23#1451970212yes—
319C23C2×#1175819811yescharacteristic
320Q8—4882no—
321Q8—4882no—
322Q8—4882no—
323Q8—2444no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—1224no—
337C2×C4—1224no—
338C2×C4—4882no—
339C2×C4—4882no—
340C2×C4#1451970212yes—
341C2×C4C22⋊C4×D6112yes—
342C2×C4#1451974512yes—
343C2×C4#1451974711yescharacteristic
344C2×C4#1451974711yescharacteristic
345C2×C4C2×#1175819011yescharacteristic
346C2×C4C2×Dic24411yescharacteristic
347C2×C4#1451981011yescharacteristic
348C2×C4#1451981011yescharacteristic
349C8—82no—
350C8—4881no—
351C8—4881no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22#1683961711yescharacteristic
360C22C2×#1451970211yescharacteristic
361C22#1683977211yescharacteristic
362C4—22no—
363C4—22no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—2444no—
368C4—2444no—
369C4#1683990311yescharacteristic
370C4#1683990311yescharacteristic
371C4#1683992011yescharacteristic
372C4#1683992011yescharacteristic
373C2—21no—
374C2—21no—
375C2—42no—
376C2#2144575511yescharacteristic
377C2#2144576811yescharacteristic
378C2#2144578511yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#379
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#8410
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #21444474C2semidirect
4. #21444223C2semidirect
216. C61#8410semidirect

Maximal subgroups

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

subgroupindex
#214592242
#214458032
#214444742
#214442232
C61×#14582
#841061