Finite Group Databasebeta

← #30617890

Subgroups — #30617890

Order 15616.

978 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C212yesmaximal
2#21462013C218yesmaximal, complemented
3#21461718C212yesmaximal
4#21461718C212yesmaximal
5C22×#14519767C211yesmaximal, characteristic
6#16840783—22no—
7#16840782—22no—
8#16840779—22no—
9#16840778—22no—
10#16840765C2214yes—
11#16840732C2214yes—
12C4×#11758217C2214yes—
13#16840642C2218yes—
14#16840642C2218yes—
15C2×#14519767—22no—
16C2×#14519767—22no—
17C2×#14519767—22no—
18C2×#14519767—22no—
19C2×#14519767C414yes—
20C2×#14519767C2214yes—
21C22×C4⋊Dic61C411yescharacteristic
22C22×#11758196C411yescharacteristic
23C22×#11758196C411yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C4⋊C4×C61C411yescharacteristic
28C2×#11758217C2318yes—
29#14519844—24no—
30C4⋊#92420—24no—
31C22⋊#92420—24no—
32C22⋊#92420—24no—
33#14519832—24no—
34C4×#92420—24no—
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61C2×C411yescharacteristic
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61C2311yescharacteristic
39#14519767—24no—
40#14519767—24no—
41#14519767—24no—
42#14519767—24no—
43#14519767—24no—
44#14519767—24no—
45#14519767—24no—
46#14519767—24no—
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61C2×C414yes—
51C2×#11758196—22no—
52C2×#11758196—21no—
53C2×#11758196—21no—
54C2×#11758196—22no—
55C2×#11758196—21no—
56C2×#11758196—21no—
57C2×#11758196—22no—
58C2×#11758196—22no—
59C2×#11758196—22no—
60C2×#11758196—22no—
61C2×#11758196C2×C414yes—
62C2×#11758196C2×C414yes—
63C2×#11758196C2×C412yes—
64C2×#11758196C2×C412yes—
65C2×#11758196C2312yes—
66C2×#11758196C2312yes—
67C2×C4×Dic61C2×C412yes—
68C2×C4×Dic61D412yes—
69C2×C4×Dic61D412yes—
70C2×C4×Dic61D412yes—
71C2×C4×Dic61D412yes—
72C2×C4×Dic61C2312yes—
73C23×C4×C61C2×C411yescharacteristic
74C23×C4×C61C2×C411yescharacteristic
75C23×C4×C61C2×C411yescharacteristic
76C2×C4⋊C4×C61—22no—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61C2×C414yes—
80C24×C61C22×C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—42no—
86C22×C4×C61—42no—
87C22×C4×C61—42no—
88C22×C4×C61C22⋊C412yes—
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C22×C412yes—
92C22×C4×C61C22×C412yes—
93C22×C4×C61C22×C412yes—
94C22×Dic61—24no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—42no—
100C22×Dic61—42no—
101C22×Dic61—42no—
102C22×Dic61C22⋊C412yes—
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22×C411yescharacteristic
106C22×Dic61C22×C412yes—
107C22×Dic61C22×C412yes—
108C22×Dic61C22×C412yes—
109C22×Dic61C2×D412yes—
110C22×Dic61C2×D412yes—
111C22×Dic61C2411yescharacteristic
112#11758217—216no—
113C2×#92420—28no—
114C4⋊C4×C61—24no—
115C4⋊C4×C61—24no—
116C4⋊Dic61—24no—
117C4⋊Dic61—24no—
118#11758196—24no—
119#11758196—24no—
120#11758196—24no—
121#11758196—24no—
122#11758196—24no—
123#11758196—24no—
124#11758196—24no—
125#11758196—24no—
126C4×Dic61C22⋊C412yes—
127C4×Dic61C22⋊C412yes—
128C4×Dic61C22⋊C412yes—
129C4×Dic61C22⋊C412yes—
130C4×Dic61C2×D412yes—
131C4×Dic61C2×D412yes—
132C4×Dic61C2×D412yes—
133C4×Dic61C2×D412yes—
134C23×C61—22no—
135C23×C61—22no—
136C23×C61—22no—
137C23×C61C2×C22⋊C411yescharacteristic
138C23×C61C2×C22⋊C411yescharacteristic
139C23×C61C23×C411yescharacteristic
140C2×C4×C61—24no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61—42no—
152C2×C4×C61C2×C22⋊C412yes—
153C2×C4×C61C2×C22⋊C412yes—
154C2×Dic61—22no—
155C2×Dic61—24no—
156C2×Dic61—24no—
157C2×Dic61—24no—
158C2×Dic61—22no—
159C2×Dic61—22no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165C2×Dic61—42no—
166C2×Dic61—42no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61C2×C22⋊C412yes—
170C2×Dic61C2×C22⋊C412yes—
171C2×Dic61C2×C22⋊C412yes—
172C2×Dic61C22×D412yes—
173C2×Dic612−1+414yes—
174#92420—48no—
175#21830—611nomaximal, Sylow
176C22×C61—28no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61#41312yes—
184C22×C61#41312yes—
185C22×C61C22×C22⋊C411yescharacteristic
186C22×C61#51912yes—
187C4×C61—22no—
188C4×C61—22no—
189C4×C61—42no—
190C4×C61—42no—
191Dic61—22no—
192Dic61—22no—
193Dic61—22no—
194Dic61—42no—
195Dic61—42no—
196Dic61#53614yes—
197C22×#125—611no—
198#2920—612no—
199#1998—618no—
200#1821—612no—
201#1821—612no—
202C2×C61—22no—
203C2×C61—22no—
204C2×C61—22no—
205C2×C61#231011yescharacteristic
206C2×C61C2×#41311yescharacteristic
207C2×C61C2×#41311yescharacteristic
208C2×#125—614no—
209C2×#125—614no—
210C2×#125—1222no—
211C2×#125—1222no—
212C2×#125—1222no—
213C2×#125—1222no—
214C22×C4⋊C4—611no—
215C22×C4⋊C4—611no—
216C22×C4⋊C4—611no—
217C22×C4⋊C4—611no—
218C22×C4⋊C4—611no—
219C22×C4⋊C4#692311yescharacteristic
220C22×C42—611no—
221#432—1222no—
222#432—1222no—
223#431—1222no—
224#431—1222no—
225#423—614no—
226#407—614no—
227C4×M16—614no—
228#343—618no—
229#343—618no—
230C61#2183011yescharacteristic, complemented, Sylow
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—611no—
234C23×C4—611no—
235C23×C4C2×#692311yescharacteristic
236C23×C4C2×#692311yescharacteristic
237C23×C4C2×#692311yescharacteristic
238C2×M16—618no—
239#125—1224no—
240#125—1224no—
241#125—1224no—
242#125—1224no—
243#125—1224no—
244#125—1224no—
245#125—1224no—
246#125—1224no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—612no—
251C2×C4⋊C4—612no—
252C2×C4⋊C4—612no—
253C2×C4⋊C4—612no—
254C2×C4⋊C4—614no—
255C2×C4⋊C4—614no—
256C2×C4⋊C4—614no—
257C2×C4⋊C4—1222no—
258C2×C4⋊C4—1222no—
259C2×C4⋊C4—1222no—
260C2×C4⋊C4—1222no—
261C2×C4⋊C4—1222no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1222no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—1222no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4C2×#692314yes—
271C2×C42—612no—
272C2×C42—612no—
273C2×C42—612no—
274C2×C42—612no—
275C2×C42—612no—
276C2×C42—612no—
277C4⋊C8—1224no—
278C4⋊C8—1224no—
279C22⋊C8—1224no—
280C22⋊C8—1224no—
281#97—1224no—
282C4×C8—1224no—
283C24C22×#692311yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—611no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—612no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—612no—
299C22×C4—612no—
300C22×C4—612no—
301C22×C4—1224no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—2442no—
307C22×C4—2442no—
308C22×C4—2442no—
309C22×C4C22⋊#692312yes—
310C22×C4C22⋊#692311yescharacteristic
311C22×C4C22⋊#692311yescharacteristic
312C22×C4C22×#692312yes—
313C22×C4C22×#692312yes—
314C22×C4C22×#692312yes—
315M16—12216no—
316C2×C8—1228no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—1224no—
320C4⋊C4—1224no—
321C4⋊C4—1224no—
322C4⋊C4—1224no—
323C4⋊C4—1224no—
324C4⋊C4—1224no—
325C4⋊C4—1224no—
326C4⋊C4—1224no—
327C4⋊C4—1224no—
328C4⋊C4—1224no—
329C42—612no—
330C42—612no—
331C42—612no—
332C42—612no—
333C42—612no—
334C42—612no—
335C42—612no—
336C42—612no—
337C23—22no—
338C23—22no—
339C23—22no—
340C23C2×C22⋊#692311yescharacteristic
341C23C2×C22⋊#692311yescharacteristic
342C23C23×#692311yescharacteristic
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—612no—
356C2×C4—614no—
357C2×C4—612no—
358C2×C4—612no—
359C2×C4—612no—
360C2×C4—1224no—
361C2×C4—1224no—
362C2×C4—1224no—
363C2×C4—1222no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4—2442no—
374C2×C4—2442no—
375C2×C4C2×C22⋊#692312yes—
376C2×C4C2×C22⋊#692312yes—
377C8—2448no—
378C22—28no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22#1684074812yes—
386C22#1684074912yes—
387C22C22×C22⋊#692311yescharacteristic
388C22#1684083012yes—
389C4—22no—
390C4—22no—
391C4—42no—
392C4—42no—
393C4—614no—
394C4—1222no—
395C4—1222no—
396C4—1222no—
397C4—2442no—
398C4—2442no—
399C2—22no—
400C2—22no—
401C2—22no—
402C2#2146229311yescharacteristic
403C2C2×#1684074811yescharacteristic
404C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61#21830
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21462013C2semidirect
230. C61#21830semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214620132
#214617182
C22×#145197672
#2183061