Finite Group Databasebeta

← #30602629

Subgroups — #30602629

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840642C212yesmaximal
2C2×#16840642C212yesmaximal
3#21461482C212yesmaximal
4C2×C4×#11758196C211yesmaximal, characteristic
5C22×#11758217C2214yes—
6#16840642—24no—
7#16840642C418yescomplemented
8#16840628—22no—
9#16840628—22no—
10C22×#11758196C2211yescharacteristic
11C22×#11758196C2211yescharacteristic
12C22×C4×Dic61C411yescharacteristic
13C22×C4×Dic61C2211yescharacteristic
14C4×#11758196—22no—
15C4×#11758196—22no—
16C2×#14519684C411yescharacteristic
17C2×#14519684C411yescharacteristic
18C22×C42×C61C411yescharacteristic
19C2×#11758217—24no—
20C2×#11758217—24no—
21C2×#11758217—24no—
22C2×#11758217—24no—
23C2×#11758217—24no—
24C2×#11758217C2×C418yes—
25C22×#92420—24no—
26C23×Dic61C2×C411yescharacteristic
27C23×Dic61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29C23×Dic61C2311yescharacteristic
30C2×#11758196—22no—
31C2×#11758196—22no—
32C2×#11758196—22no—
33C2×#11758196—22no—
34C2×#11758196C2×C414yes—
35C2×#11758196D412yes—
36C2×#11758196Q812yes—
37C2×C4×Dic61—22no—
38C2×C4×Dic61—22no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61D412yes—
43C2×C4×Dic61D412yes—
44#14519684—22no—
45#14519684—22no—
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61C2×C411yescharacteristic
49C2×C42×C61—21no—
50C2×C42×C61—21no—
51C2×C42×C61—42no—
52C24×C61C22×C411yescharacteristic
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61C4212yes—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C4⋊C412yes—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61C4212yes—
82C22×Dic61C22⋊C412yes—
83C22×Dic61C4⋊C412yes—
84C22×Dic61C22×C412yes—
85C22×Dic61C2×D411yescharacteristic
86C22×Dic61C2×D412yes—
87C22×Dic61C2×Q811yescharacteristic
88C22×Dic61#4112yes—
89C22×Dic61#4112yes—
90C22×Dic61#4112yes—
91C22×Dic61#4112yes—
92#11758217—28no—
93#11758217—28no—
94#11758217—44no—
95#11758217—44no—
96C2×#92420—28no—
97C2×#92420—44no—
98C2×#92420—44no—
99C42×C61—42no—
100C42×C61—42no—
101#11758196—28no—
102#11758196—24no—
103#11758196—24no—
104C4×Dic61—24no—
105C4×Dic61—24no—
106C4×Dic61—42no—
107C4×Dic61—42no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61C2×C4211yescharacteristic
113C23×C61C2×C22⋊C411yescharacteristic
114C23×C61C2×C4⋊C411yescharacteristic
115C23×C61#11711yescharacteristic
116C23×C61#11711yescharacteristic
117C23×C61#11711yescharacteristic
118C23×C61#11711yescharacteristic
119C2×C4×C61—24no—
120C2×C4×C61—24no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61#10012yes—
136C2×C4×C61#10112yes—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61—22no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61#11714yes—
153C2×Dic61C4×D414yes—
154C2×Dic61C4×D412yes—
155C2×Dic61C4×Q812yes—
156C2×Dic61#12112yes—
157C2×Dic61C22⋊Q812yes—
158C2×Dic61#12314yes—
159C2×Dic61#12412yes—
160C2×Dic61#12512yes—
161C2×Dic61#12614yes—
162#92420—48no—
163#10802—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61#37611yescharacteristic
177C22×C61C4×C22⋊C411yescharacteristic
178C22×C61C4×C4⋊C411yescharacteristic
179C22×C61#38011yescharacteristic
180C22×C61#38111yescharacteristic
181C22×C61#38211yescharacteristic
182C22×C61#38311yescharacteristic
183C22×C61C2×#10011yescharacteristic
184C22×C61C2×#10111yescharacteristic
185C22×C61#41311yescharacteristic
186C22×C61#41311yescharacteristic
187C4×C61—22no—
188C4×C61—22no—
189C4×C61—42no—
190C4×C61—42no—
191Dic61—42no—
192Dic61—42no—
193Dic61—42no—
194Dic61#38714yes—
195Dic61#38814yes—
196C2×C4×C4⋊C4—611no—
197C2×#343—612no—
198C2×#343—612no—
199#1728—612no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61#143411yescharacteristic
205C2×C61C4×#10011yescharacteristic
206C2×C61C4×#10111yescharacteristic
207C2×C61#180011yescharacteristic
208C2×C61#180111yescharacteristic
209C2×C61#182111yescharacteristic
210C2×C61#182211yescharacteristic
211C22×M16—614no—
212C22×C4⋊C4—611no—
213C22×C4⋊C4—611no—
214C22×C42—611no—
215C22×C42—611no—
216C22×C42#692311yescharacteristic
217C4×C4⋊C4—1222no—
218C4×C4⋊C4—1222no—
219C2×#95—611no—
220C2×#95—611no—
221#343—618no—
222#343—1224no—
223#336—1222no—
224#336—1222no—
225C61#1080211yescharacteristic, complemented, Sylow
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C23×C4C2×#692311yescharacteristic
231C23×C4C2×#692311yescharacteristic
232C23×C4C2×#692311yescharacteristic
233C2×M16—618no—
234C2×M16—1224no—
235C2×M16—1224no—
236C2×M16—1224no—
237C2×M16—1224no—
238C2×M16—1224no—
239C22×C8—1224no—
240C2×C4⋊C4—614no—
241C2×C4⋊C4—612no—
242C2×C4⋊C4—612no—
243C2×C4⋊C4—1222no—
244C2×C4⋊C4—1222no—
245C2×C4⋊C4—1222no—
246C2×C4⋊C4—1222no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42—42no—
250C2×C42—612no—
251C2×C42—612no—
252C2×C42—1222no—
253C2×C42—1222no—
254C2×C42—1221no—
255C2×C42—1221no—
256C2×C42—2442no—
257#95—1222no—
258#95—1222no—
259C24C22×#692311yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—612no—
273C22×C4—612no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—612no—
280C22×C4—612no—
281C22×C4—612no—
282C22×C4—612no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4C4×#692312yes—
296C22×C4C4⋊#692312yes—
297C22×C4C22⋊#692311yescharacteristic
298C22×C4C22⋊#692311yescharacteristic
299M16—1228no—
300M16—1228no—
301M16—2444no—
302M16—2444no—
303C2×C8—1228no—
304C2×C8—2444no—
305C2×C8—2444no—
306C4⋊C4—1224no—
307C4⋊C4—1224no—
308C4⋊C4—1228no—
309C42—42no—
310C42—42no—
311C42—1224no—
312C42—1224no—
313C42—2442no—
314C42—2442no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23C2×C4×#692311yescharacteristic
320C23C2×C22⋊#692311yescharacteristic
321C23C2×C4⋊#692311yescharacteristic
322C23#1451985611yescharacteristic
323C23#1451985611yescharacteristic
324C23#1451985611yescharacteristic
325C23#1451985611yescharacteristic
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—612no—
343C2×C4—612no—
344C2×C4—614no—
345C2×C4—612no—
346C2×C4—612no—
347C2×C4—614no—
348C2×C4—614no—
349C2×C4—614no—
350C2×C4—612no—
351C2×C4—612no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2442no—
366C2×C4—2442no—
367C2×C4#1451983712yes—
368C2×C4#1451983812yes—
369C8—2448no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22#1684069811yescharacteristic
383C22C4×C22⋊#692311yescharacteristic
384C22C4×C4⋊#692311yescharacteristic
385C22#1684070411yescharacteristic
386C22#1684070511yescharacteristic
387C22#1684070611yescharacteristic
388C22#1684070711yescharacteristic
389C22C2×#1451983711yescharacteristic
390C22C2×#1451983811yescharacteristic
391C22#1684074811yescharacteristic
392C22#1684074811yescharacteristic
393C4—22no—
394C4—22no—
395C4—42no—
396C4—42no—
397C4—614no—
398C4—614no—
399C4—2442no—
400C4—2442no—
401C4—2442no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#2146099511yescharacteristic
407C2C4×#1451983711yescharacteristic
408C2C4×#1451983811yescharacteristic
409C2#2146168311yescharacteristic
410C2#2146168511yescharacteristic
411C2#2146171811yescharacteristic
412C2#2146172011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C42×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC22×C42#6923
hypocenterC61#10802
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
7. #16840642C4semidirect
225. C61#10802semidirect

Maximal subgroups

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

subgroupindex
C2×#168406422
#214614822
C2×C4×#117581962
#1080261