Finite Group Databasebeta

← #30602979

Subgroups — #30602979

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462383C211yesmaximal, characteristic
2C2×#16840643C212yesmaximal
3#21461525C211yesmaximal, characteristic
4#21461482C212yesmaximal
5#21448298C211yesmaximal, characteristic
6C22×#11758217C2212yes—
7C22×#11758217C2212yes—
8#16840726—24no—
9C4×#11758217—21no—
10C4×#11758217—21no—
11#16840643C418yescomplemented
12#16840642—21no—
13#16840642—21no—
14#16840628—24no—
15C2×#14519733C2211yescharacteristic
16C2×#14519733C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18#16839659—21no—
19#16839657—21no—
20#16839637C411yescharacteristic
21#16839635C411yescharacteristic
22#16839634C411yescharacteristic
23C4⋊C4×Dic61—21no—
24#16839613—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×#11758217—22no—
35C2×#11758217C2×C414yes—
36C2×#11758217C2×C414yes—
37C2×#11758217Q814yes—
38C22×#92420—22no—
39C22×#92420D414yes—
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—21no—
53C2×#11758196—21no—
54C2×#11758196D411yescharacteristic
55C2×#11758196D411yescharacteristic
56C2×C22⋊Dic61C2×C411yescharacteristic
57C2×C22⋊Dic61C2×C411yescharacteristic
58C2×C4×Dic61—21no—
59C2×C4×Dic61—22no—
60C2×C4×Dic61—21no—
61C2×C4×Dic61—21no—
62C2×C4×Dic61—22no—
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—42no—
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—42no—
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—24no—
100#11758217—42no—
101#11758217—42no—
102C2×#92420—24no—
103C2×#92420—24no—
104C2×#92420—24no—
105C2×#92420—42no—
106C2×#92420—42no—
107C2×#92420C4⋊C418yescomplemented
108C4⋊C4×C61—42no—
109C22⋊C4×C61—21no—
110C22⋊C4×C61—22no—
111C22⋊C4×C61C4212yes—
112C22⋊Dic61—21no—
113C22⋊Dic61—22no—
114C22⋊Dic61C4212yes—
115C4⋊Dic61—42no—
116#11758196—24no—
117#11758196—22no—
118#11758196—22no—
119#11758196—42no—
120#11758196—42no—
121C4×Dic61—24no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—41no—
127C4×Dic61—42no—
128C4×Dic61—41no—
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—24no—
138C2×C4×C61—22no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×Dic61—22no—
149C2×Dic61—24no—
150C2×Dic61—22no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61C2×C4⋊C412yes—
161C2×Dic61#11712yes—
162C2×Dic61C4×D412yes—
163C2×Dic61C4×D412yes—
164C2×Dic61C4×D412yes—
165C2×Dic61C4×Q812yes—
166C2×Dic61#12011yescharacteristic
167C2×Dic61#12112yes—
168C2×Dic61C22⋊Q812yes—
169C2×Dic61C22⋊Q812yes—
170C2×Dic61#12312yes—
171C2×Dic61#12311yescharacteristic
172C2×Dic61#12411yescharacteristic
173C2×Dic61#12512yes—
174C2×Dic61#12612yes—
175C2×Dic61C4⋊Q811yescharacteristic
176#92420—28no—
177#92420—44no—
178#10919—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—22no—
181C22×C61—21no—
182C22×C61—22no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—42no—
186C22×C61C4×C22⋊C411yescharacteristic
187C22×C61C4×C4⋊C412yes—
188C22×C61#38611yescharacteristic
189C22×C61#38712yes—
190C22×C61#39111yescharacteristic
191C4×C61—42no—
192C4×C61—42no—
193C4×C61—41no—
194C4×C61—41no—
195Dic61—42no—
196Dic61—42no—
197Dic61—41no—
198Dic61—41no—
199Dic61#38512yes—
200Dic61#38712yes—
201Dic61#38812yes—
202Dic61#38912yes—
203#2873—611no—
204#2296—611no—
205C2×#344—612no—
206#1742—611no—
207#1728—612no—
208C2×C61—21no—
209C2×C61—22no—
210C2×C61—22no—
211C2×C61—21no—
212C2×C61#143611yescharacteristic
213C2×C61#189111yescharacteristic
214C2×C61#189111yescharacteristic
215C22×M16—612no—
216C22×M16—612no—
217C2×#117—611no—
218C2×#117—611no—
219C22×C42—611no—
220#405—1224no—
221C4×M16—1221no—
222C4×M16—1221no—
223#389—1221no—
224#389—1221no—
225#385—611no—
226#385—611no—
227#385—611no—
228#385#692311yescharacteristic
229C4×C4⋊C4—1221no—
230C4×C4⋊C4—1221no—
231#344—618no—
232#343—1221no—
233#343—1221no—
234#336—1224no—
235C61#1091911yescharacteristic, complemented, Sylow
236C23×C4—611no—
237C23×C4—611no—
238C23×C4C2×#692311yescharacteristic
239C2×M16—614no—
240C2×M16—614no—
241C2×M16—614no—
242C2×M16—1222no—
243C2×M16—1222no—
244C2×M16—1222no—
245C2×M16—1222no—
246C2×M16—1222no—
247C2×M16—1222no—
248C2×M16—1222no—
249C2×M16—1222no—
250C2×M16—1222no—
251C22×C8—614no—
252C22×C8—1222no—
253#117—614no—
254#117—1222no—
255#117—1222no—
256#117—1222no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—611no—
266C2×C22⋊C4C2×#692311yescharacteristic
267C2×C22⋊C4C2×#692311yescharacteristic
268C2×C42—611no—
269C2×C42—611no—
270C2×C42—1221no—
271C2×C42—1222no—
272C2×C42—1221no—
273C2×C42—1221no—
274C2×C42—1222no—
275#97—1222no—
276#97—1222no—
277C4×C8—1222no—
278C4×C8—1222no—
279#95—21no—
280#95—1221no—
281#95—1221no—
282#95—1221no—
283C24C22×#692311yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—42no—
288C22×C4—612no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—612no—
295C22×C4—612no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1222no—
301C22×C4—2442no—
302C22×C4C22⋊#692311yescharacteristic
303C22×C4C22⋊#692311yescharacteristic
304M16—1224no—
305M16—1224no—
306M16—1224no—
307M16—1224no—
308M16—1224no—
309M16—1224no—
310M16—2442no—
311M16—2442no—
312C2×C8—618no—
313C2×C8—1224no—
314C2×C8—1224no—
315C2×C8—1224no—
316C2×C8—2442no—
317C2×C8—2442no—
318C4⋊C4—42no—
319C4⋊C4—1222no—
320C4⋊C4—1222no—
321C4⋊C4—1224no—
322C4⋊C4—2442no—
323C4⋊C4—2442no—
324C4⋊C4—2442no—
325C22⋊C4—21no—
326C22⋊C4—22no—
327C22⋊C4—612no—
328C22⋊C4—1221no—
329C22⋊C4—1222no—
330C22⋊C4C4×#692312yes—
331C42—1221no—
332C42—1221no—
333C42—1221no—
334C42—1221no—
335C42—1224no—
336C42—2441no—
337C42—2442no—
338C42—2441no—
339C23—41no—
340C23—41no—
341C23C2×C4×#692311yescharacteristic
342C23C2×C22⋊#692311yescharacteristic
343C23#1451985611yescharacteristic
344C23D4×#692312yes—
345C23Q8×#692312yes—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—611no—
359C2×C4—612no—
360C2×C4—611no—
361C2×C4—612no—
362C2×C4—612no—
363C2×C4—612no—
364C2×C4—612no—
365C2×C4—612no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—612no—
369C2×C4—612no—
370C2×C4—612no—
371C2×C4—612no—
372C2×C4—612no—
373C2×C4—612no—
374C2×C4—1222no—
375C2×C4—1224no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1222no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2442no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C8—1228no—
387C8—2444no—
388C22—21no—
389C22—22no—
390C22—21no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—42no—
395C22C4×C22⋊#692311yescharacteristic
396C22C4⋊C4×#692312yes—
397C22#1684071011yescharacteristic
398C22#1684071112yes—
399C22(C2×#6923)⋊Q811yescharacteristic
400C4—42no—
401C4—42no—
402C4—41no—
403C4—41no—
404C4—612no—
405C4—612no—
406C4—612no—
407C4—612no—
408C4—2442no—
409C4—2441no—
410C4—2442no—
411C4—2441no—
412C2—21no—
413C2—22no—
414C2—21no—
415C2—22no—
416C2#2146099811yescharacteristic
417C2#2146183011yescharacteristic
418C2#2146183111yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#385C4
socleC22×C61#386
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenter#385#6923
hypocenterC61#10919
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
107. C2×#92420C4⋊C4semidirect
235. C61#10919semidirect

Maximal subgroups

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

subgroupindex
#214623832
C2×#168406432
#214615252
#214614822
#214482982
#1091961