Finite Group Databasebeta

← #30600511

Subgroups — #30600511

Order 15616.

582 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462672C211yesmaximal, characteristic, complemented
2#21461566C211yesmaximal, characteristic, complemented
3#21461215C212yesmaximal, complemented
4#21460666C212yesmaximal, complemented
5#21451708C211yesmaximal, characteristic
6#16840791—24no—
7#16840783—21no—
8C2×#14519835—21no—
9#16840733C2212yes—
10C2×C22⋊#92420—21no—
11C4×C22⋊#6923C2212yes—
12#16840640—21no—
13#16840613—24no—
14C2×#14519748C2211yescharacteristic
15C2×#14519737C2211yescharacteristic
16#16839702C411yescharacteristic, complemented
17#16839698C411yescharacteristic, complemented
18#16839677—21no—
19#16839676C411yescharacteristic, complemented
20#16839670—21no—
21#16839656—21no—
22#16839642—21no—
23#16839624C2211yescharacteristic
24C61×#392C411yescharacteristic, complemented
25C2×#11758213—22no—
26C22×#92420—22no—
27C2×C22⋊#6923—22no—
28C2×C4×#6923—22no—
29C4⋊#92420—22no—
30#14519835—24no—
31#14519834D414yescomplemented
32C22⋊#92420—22no—
33C22⋊#92420—22no—
34#14519832—22no—
35(C2×#6923)⋊C4—22no—
36C22×C22⋊D61—21no—
37C22×C22⋊D61D411yescharacteristic
38C23×Dic61D411yescharacteristic
39C22×C4×D61C2311yescharacteristic
40#14519748—22no—
41#14519748—22no—
42#14519737—22no—
43#14519737—22no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196C2×C411yescharacteristic
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×#11758198—21no—
52C2×#11758198D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C22×D4×C61—21no—
59C22×D4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61C2×C411yescharacteristic
62#95×C61C2×C411yescharacteristic
63C24×C61—21no—
64C24×C61C22⋊C411yescharacteristic
65C23×D61C2×D411yescharacteristic
66C22×#6923—42no—
67C2×D4×C61—22no—
68C2×D4×C61—42no—
69C2×D4×C61—81no—
70C2×D4×C61—81no—
71C2×D4×C61—81no—
72C22×C4×C61—21no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—81no—
80C2×C22⋊D61—81no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—81no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C2×C4×D61—81no—
90C2×C4×D61C2×D412yes—
91C2×C4×D61#4112yes—
92C22⋊#6923—24no—
93C22⋊#6923—42no—
94C2×#92420—24no—
95C2×#92420—82no—
96C4×#6923—82no—
97#11758213—82no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—81no—
100C22⋊Dic61—42no—
101C22⋊Dic61—41no—
102C22⋊Dic61—41no—
103C22⋊Dic61—81no—
104C22⋊Dic61—81no—
105#11758198—22no—
106#11758198—81no—
107C4⋊Dic61—22no—
108#11758196—22no—
109#11758196—81no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61#10412yes—
124C23×C61C2×C22⋊C411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61#12112yes—
130C2×#6923—44no—
131C2×#6923—82no—
132C2×#6923—82no—
133D4×C61—82no—
134D4×C61—84no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61C4×D412yes—
142C22⋊D61—44no—
143C22⋊D61—84no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—81no—
158C2×Dic61#12011yescharacteristic
159C2×Dic61#12311yescharacteristic
160C4×D61—42no—
161C4×D61—42no—
162#92420—44no—
163#9185—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—22no—
167C22×C61—42no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61#38611yescharacteristic
179C22×C61C2×#10411yescharacteristic
180C22×C61#42111yescharacteristic
181C2×D61—22no—
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—81no—
185C2×D61—81no—
186#6923—84no—
187C4×C61—22no—
188C4×C61—41no—
189C4×C61—81no—
190Dic61—21no—
191Dic61—21no—
192Dic61—41no—
193Dic61—41no—
194Dic61—81no—
195Dic61—81no—
196#2973—611no—
197#2635—611no—
198C4×#99—611no—
199#1507—612no—
200#1284—612no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—42no—
204C2×C61—161no—
205C2×C61#187111yescharacteristic
206C2×C61#191011yescharacteristic
207C2×C61#191311yescharacteristic
208D61—42no—
209C2×#121—611no—
210C2×C4×D4—611no—
211#435—1224no—
212#432—1221no—
213C2×#99—1221no—
214#407—612no—
215C2×C22⋊C8—1221no—
216#400—611no—
217#399—611no—
218#394—611no—
219#394—1221no—
220#392—1221no—
221#392#692311yescharacteristic, complemented
222#388—1221no—
223#386—1221no—
224#381—611no—
225C4×C22⋊C4—612no—
226#342—1221no—
227#327—1224no—
228C61#918511yescharacteristic, complemented, Sylow
229C22×D4—21no—
230C22×D4—611no—
231C22×D4—1221no—
232C22×D4C2×#692311yescharacteristic
233C23×C4—611no—
234C23×C4—611no—
235C2×M16—1222no—
236C22×C8—1222no—
237#121—1222no—
238#121—1222no—
239C4×D4—1222no—
240C4×D4—1222no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—611no—
246C2×C22⋊C4—1222no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4C2×#692311yescharacteristic
253C2×C42—611no—
254C2×C42—1222no—
255C4⋊C8—1222no—
256#99—1224no—
257C22⋊C8—614no—
258C22⋊C8—1222no—
259C22⋊C8—1222no—
260#97—1222no—
261#95—611no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1222no—
266#95C2×#692311yescharacteristic
267C24—21no—
268C24—611no—
269C24C22⋊#692311yescharacteristic
270C2×D4—22no—
271C2×D4—42no—
272C2×D4—81no—
273C2×D4—81no—
274C2×D4—81no—
275C2×D4—1222no—
276C2×D4—1222no—
277C2×D4—4881no—
278C2×D4—4881no—
279C2×D4—2441no—
280C2×D4—2442no—
281C22×C4—21no—
282C22×C4—611no—
283C22×C4—612no—
284C22×C4—612no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—4881no—
292C22×C4—4881no—
293C22×C4—2442no—
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22×#692311yescharacteristic
296M16—4882no—
297C2×C8—1224no—
298C2×C8—4882no—
299C4⋊C4—1222no—
300C4⋊C4—1222no—
301C4⋊C4—4881no—
302C22⋊C4—22no—
303C22⋊C4—81no—
304C22⋊C4—1222no—
305C22⋊C4—1224no—
306C22⋊C4—4881no—
307C22⋊C4—4881no—
308C22⋊C4—4881no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C42—1221no—
314C42—1221no—
315C42—4882no—
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—612no—
328C23—1221no—
329C23—1221no—
330C23—2441no—
331C23—2441no—
332C23#1451984112yes—
333C23C2×C22⋊#692311yescharacteristic
334D4—82no—
335D4—84no—
336D4—4884no—
337D4—2444no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—4881no—
351C2×C4—4882no—
352C2×C4—4882no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2441no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2444no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4D4×#692312yes—
366C8—2444no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—42no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—1222no—
382C22—1222no—
383C22—1222no—
384C22—4881no—
385C22—4881no—
386C22#1684071011yescharacteristic
387C22C2×#1451984111yescharacteristic
388C22#1684075911yescharacteristic
389C4—22no—
390C4—41no—
391C4—81no—
392C4—1221no—
393C4—1221no—
394C4—4881no—
395C4—4884no—
396C4—4881no—
397C4—2441no—
398C4—2441no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—161no—
403C2—2442no—
404C2#2146180211yescharacteristic
405C2#2146186211yescharacteristic
406C2#2146186811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#392C4
socleC22×C61#386
prime radical#21451708C2
cosocleC22×C4×D61C23
hypercenter#392#6923
hypocenterC61#9185
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #21462672C2semidirect
2. #21461566C2semidirect
3. #21461215C2semidirect
4. #21460666C2semidirect
16. #16839702C4semidirect
17. #16839698C4semidirect
19. #16839676C4semidirect
24. C61×#392C4semidirect
31. #14519834D4semidirect
221. #392#6923semidirect
228. C61#9185semidirect

Maximal subgroups

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

subgroupindex
#214626722
#214615662
#214612152
#214606662
#214517082
#918561