Finite Group Databasebeta

← #30602972

Subgroups — #30602972

Order 15616.

718 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462383C211yesmaximal, characteristic
2C2×#16840643C212yesmaximal
3#21461525C211yesmaximal, characteristic
4C2×#16840642C212yesmaximal
5#21448438C211yesmaximal, characteristic
6C22×#11758217C2212yes—
7C22×#11758217C2212yes—
8#16840726—24no—
9C4×#11758217—21no—
10C4×#11758217—21no—
11#16840643C418yescomplemented
12#16840642—21no—
13#16840642—21no—
14#16840642—24no—
15C2×#14519733C2211yescharacteristic
16C2×#14519733C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18#16839659—21no—
19#16839657—21no—
20#16839637C411yescharacteristic
21#16839635C411yescharacteristic
22#16839634C411yescharacteristic
23#16839631—21no—
24#16839626—21no—
25C61×#385C411yescharacteristic
26C2×#11758217—22no—
27C2×#11758217—22no—
28C2×#11758217—22no—
29C2×#11758217—22no—
30C2×#11758217—22no—
31C2×#11758217—22no—
32C2×#11758217—22no—
33C2×#11758217—22no—
34C2×#11758217C2×C414yes—
35C2×#11758217C2×C414yes—
36C2×#11758217D414yes—
37C2×#11758217Q814yes—
38C22×#92420—22no—
39C22×#92420—22no—
40#14519832—22no—
41#14519832—22no—
42C4×#92420—22no—
43C4×#92420—22no—
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2311yescharacteristic
46#14519733—22no—
47#14519733—22no—
48#14519733—22no—
49#14519733C2×C414yes—
50C2×C4⋊Dic61—21no—
51C2×#11758196—21no—
52C2×#11758196—22no—
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×#11758196—22no—
56C2×#11758196—21no—
57C2×#11758196—21no—
58C2×#11758196D411yescharacteristic
59C2×#11758196D411yescharacteristic
60C2×C22⋊Dic61C2×C411yescharacteristic
61C2×C22⋊Dic61C2×C411yescharacteristic
62C2×C4×Dic61—21no—
63C2×C4×Dic61D411yescharacteristic
64C2×C4×Dic61D411yescharacteristic
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C23×C4×C61C2×C411yescharacteristic
69C2×C4⋊C4×C61—21no—
70C2×C22⋊C4×C61C2×C411yescharacteristic
71C2×C22⋊C4×C61C2×C411yescharacteristic
72#95×C61—21no—
73C24×C61C22×C411yescharacteristic
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—22no—
77C22×C4×C61—81no—
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—81no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22×C412yes—
87C22×Dic61C2×D412yes—
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90C22×Dic61C2×Q812yes—
91C22×Dic61#4112yes—
92C22×Dic61#4112yes—
93C22×Dic61#4112yes—
94#11758217—24no—
95#11758217—24no—
96#11758217—24no—
97#11758217—24no—
98#11758217—24no—
99#11758217—42no—
100#11758217—42no—
101#11758217C4⋊C418yescomplemented
102C2×#92420—24no—
103C2×#92420—24no—
104C2×#92420—24no—
105C2×#92420—24no—
106C2×#92420—42no—
107C2×#92420—42no—
108C4⋊C4×C61—81no—
109C22⋊C4×C61—21no—
110C22⋊C4×C61—22no—
111C22⋊C4×C61C4212yes—
112C22⋊Dic61—21no—
113C22⋊Dic61—22no—
114C22⋊Dic61C4212yes—
115C4⋊Dic61—81no—
116#11758196—24no—
117#11758196—22no—
118#11758196—22no—
119#11758196—41no—
120#11758196—42no—
121#11758196—41no—
122#11758196—81no—
123#11758196—81no—
124C4×Dic61—24no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61C2×C4211yescharacteristic
132C23×C61C2×C22⋊C411yescharacteristic
133C23×C61#11711yescharacteristic
134C23×C61C4×D412yes—
135C23×C61C4×Q812yes—
136C2×C4×C61—22no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—82no—
147C2×Dic61—22no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—82no—
158C2×Dic61C2×C4⋊C412yes—
159C2×Dic61#11712yes—
160C2×Dic61C4×D412yes—
161C2×Dic61C4×D412yes—
162C2×Dic61C4×D412yes—
163C2×Dic61C4×Q812yes—
164C2×Dic61#12011yescharacteristic
165C2×Dic61#12112yes—
166C2×Dic61C22⋊Q812yes—
167C2×Dic61C22⋊Q812yes—
168C2×Dic61#12312yes—
169C2×Dic61#12311yescharacteristic
170C2×Dic61#12411yescharacteristic
171C2×Dic61#12512yes—
172C2×Dic61#12612yes—
173C2×Dic61C4⋊Q811yescharacteristic
174#92420—28no—
175#92420—44no—
176#10916—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—22no—
179C22×C61—21no—
180C22×C61—22no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—42no—
184C22×C61C4×C22⋊C411yescharacteristic
185C22×C61C4×C4⋊C412yes—
186C22×C61#38611yescharacteristic
187C22×C61#38712yes—
188C22×C61#39111yescharacteristic
189C4×C61—42no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61—81no—
193Dic61—42no—
194Dic61—41no—
195Dic61—41no—
196Dic61—81no—
197Dic61#38512yes—
198Dic61#38712yes—
199Dic61#38812yes—
200Dic61#38912yes—
201#2873—611no—
202#2317—611no—
203C2×#344—612no—
204#1742—611no—
205C2×#343—612no—
206C2×C61—21no—
207C2×C61—22no—
208C2×C61—22no—
209C2×C61—21no—
210C2×C61#143611yescharacteristic
211C2×C61#191411yescharacteristic
212C2×C61#191511yescharacteristic
213C22×M16—612no—
214C22×M16—612no—
215C2×#117—611no—
216C2×#117—611no—
217C22×C4⋊C4—611no—
218#405—1224no—
219C4×M16—1221no—
220C4×M16—1221no—
221#389—1221no—
222#389—1221no—
223#385—611no—
224#385—611no—
225#385—611no—
226#385#692311yescharacteristic
227#384—1221no—
228#382—1221no—
229#344—618no—
230#343—1221no—
231#343—1221no—
232#343—1224no—
233C61#1091611yescharacteristic, complemented, Sylow
234C23×C4—611no—
235C23×C4—611no—
236C23×C4C2×#692311yescharacteristic
237C2×M16—614no—
238C2×M16—614no—
239C2×M16—614no—
240C2×M16—614no—
241C2×M16—1222no—
242C2×M16—1222no—
243C2×M16—1222no—
244C2×M16—1222no—
245C2×M16—1222no—
246C2×M16—1222no—
247C2×M16—1222no—
248C2×M16—1222no—
249C22×C8—1222no—
250C22×C8—1222no—
251#117—614no—
252#117—1222no—
253#117—1222no—
254#117—1222no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—1222no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1222no—
266C2×C22⋊C4—611no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4C2×#692311yescharacteristic
269C2×C22⋊C4C2×#692311yescharacteristic
270C2×C42—611no—
271C2×C42—611no—
272C2×C42—1221no—
273#97—1222no—
274#97—1222no—
275C4×C8—1222no—
276C4×C8—1222no—
277#95—21no—
278#95—1221no—
279#95—1221no—
280#95—1221no—
281C24C22×#692311yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—81no—
286C22×C4—612no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—612no—
290C22×C4—612no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1221no—
297C22×C4—1222no—
298C22×C4—1221no—
299C22×C4—4881no—
300C22×C4C22⋊#692311yescharacteristic
301C22×C4C22⋊#692311yescharacteristic
302M16—618no—
303M16—1224no—
304M16—1224no—
305M16—1224no—
306M16—1224no—
307M16—1224no—
308M16—2442no—
309M16—2442no—
310C2×C8—1224no—
311C2×C8—1224no—
312C2×C8—1224no—
313C2×C8—1224no—
314C2×C8—2442no—
315C2×C8—2442no—
316C4⋊C4—81no—
317C4⋊C4—1222no—
318C4⋊C4—1222no—
319C4⋊C4—1224no—
320C4⋊C4—4881no—
321C4⋊C4—4881no—
322C4⋊C4—4881no—
323C4⋊C4—2441no—
324C4⋊C4—2442no—
325C4⋊C4—2441no—
326C22⋊C4—21no—
327C22⋊C4—22no—
328C22⋊C4—612no—
329C22⋊C4—1221no—
330C22⋊C4—1222no—
331C22⋊C4C4×#692312yes—
332C42—1221no—
333C42—1221no—
334C42—1221no—
335C42—1221no—
336C42—1224no—
337C23—41no—
338C23—41no—
339C23C2×C4×#692311yescharacteristic
340C23C2×C22⋊#692311yescharacteristic
341C23#1451985611yescharacteristic
342C23D4×#692312yes—
343C23Q8×#692312yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—82no—
355C2×C4—611no—
356C2×C4—612no—
357C2×C4—611no—
358C2×C4—612no—
359C2×C4—612no—
360C2×C4—612no—
361C2×C4—612no—
362C2×C4—612no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—612no—
366C2×C4—612no—
367C2×C4—612no—
368C2×C4—612no—
369C2×C4—612no—
370C2×C4—612no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1222no—
374C2×C4—4882no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C8—1228no—
383C8—2444no—
384C22—21no—
385C22—22no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22C4×C22⋊#692311yescharacteristic
392C22C4⋊C4×#692312yes—
393C22#1684071011yescharacteristic
394C22#1684071112yes—
395C22(C2×#6923)⋊Q811yescharacteristic
396C4—42no—
397C4—41no—
398C4—41no—
399C4—81no—
400C4—612no—
401C4—612no—
402C4—612no—
403C4—612no—
404C4—4881no—
405C4—2442no—
406C4—2441no—
407C4—2441no—
408C2—21no—
409C2—22no—
410C2—21no—
411C2—22no—
412C2#2146099811yescharacteristic
413C2#2146187011yescharacteristic
414C2#2146187111yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#385C4
socleC22×C61#386
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenter#385#6923
hypocenterC61#10916
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
11. #16840643C4semidirect
101. #11758217C4⋊C4semidirect
233. C61#10916semidirect

Maximal subgroups

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

subgroupindex
#214623832
C2×#168406432
#214615252
C2×#168406422
#214484382
#1091661