Finite Group Databasebeta

← #30604851

Subgroups — #30604851

Order 15616.

606 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461566C211yesmaximal, characteristic, complemented
2#21461057C211yesmaximal, characteristic, complemented
3#21460815C212yesmaximal, complemented
4#21460797C212yesmaximal, complemented
5#21449097C211yesmaximal, characteristic
6C2×#14519835—21no—
7C2×C22⋊#92420—21no—
8C4×C22⋊#6923—21no—
9#16840640C2212yes—
10#16840608—21no—
11#16840606C2212yes—
12C2×D4×Dic61—21no—
13C2×D4×Dic61C411yescharacteristic, complemented
14C2×#14519737—21no—
15C2×#14519737C2211yescharacteristic
16#16839699C2211yescharacteristic
17#16839698—21no—
18#16839698C411yescharacteristic, complemented
19#16839670—21no—
20#16839670C2211yescharacteristic
21#16839607C411yescharacteristic, complemented
22C61×#392C411yescharacteristic, complemented
23C22×#92420—41no—
24C2×C22⋊#6923—22no—
25C2×C4×#6923—41no—
26#14519835—24no—
27C22⋊#92420—22no—
28C22⋊#92420—41no—
29(C2×#6923)⋊C4—41no—
30C22×C22⋊D61—21no—
31C22×C22⋊D61D411yescharacteristic
32C23×Dic61—21no—
33C23×Dic61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35D4×Dic61—44no—
36D4×Dic61—41no—
37D4×Dic61—41no—
38#14519737—41no—
39#14519737—41no—
40#14519737—44no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196D411yescharacteristic
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49C2×#11758198C2311yescharacteristic
50C2×C4×Dic61—21no—
51C2×C4×Dic61C2×C411yescharacteristic
52#14519684—21no—
53#14519684C2×C411yescharacteristic
54C22×D4×C61—21no—
55C22×D4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61C2×C411yescharacteristic
58#95×C61C2×C411yescharacteristic
59C24×C61—21no—
60C24×C61C22⋊C411yescharacteristic
61C23×D61C2×D411yescharacteristic
62C22×#6923—42no—
63C2×D4×C61—42no—
64C2×D4×C61—41no—
65C2×D4×C61—42no—
66C2×D4×C61—42no—
67C2×D4×C61—42no—
68C22×C4×C61—21no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C2×C22⋊D61—22no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61—42no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—42no—
92C22⋊#6923—24no—
93C22⋊#6923—42no—
94C2×#92420—42no—
95C2×#92420—82no—
96C4×#6923—82no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—42no—
99C22⋊Dic61—42no—
100C22⋊Dic61—42no—
101C22⋊Dic61—42no—
102#11758198—41no—
103#11758198—42no—
104C4⋊Dic61—42no—
105C4⋊Dic61—41no—
106#11758196—41no—
107#11758196—42no—
108C4×Dic61—24no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—22no—
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#10412yes—
123C23×C61C2×C22⋊C411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61#13512yes—
129C2×#6923—44no—
130C2×#6923—82no—
131C2×#6923—82no—
132D4×C61—42no—
133D4×C61—48no—
134D4×C61—42no—
135C2×C4×C61—22no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C22⋊D61—44no—
143C22⋊D61—48no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—81no—
158C2×Dic61—82no—
159C2×Dic61—82no—
160C2×Dic61#9911yescharacteristic
161C2×Dic61#9911yescharacteristic
162C4×D61—42no—
163C4×D61—81no—
164#92420—82no—
165#11726—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—22no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—42no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61C2×#9911yescharacteristic
181C22×C61#41611yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C2×D61—22no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—42no—
187C2×D61—81no—
188#6923—84no—
189C4×C61—42no—
190C4×C61—41no—
191C4×C61—41no—
192Dic61—21no—
193Dic61—42no—
194Dic61—41no—
195Dic61—41no—
196Dic61—81no—
197Dic61#35312yes—
198#2397—611no—
199C4×#99—611no—
200#1459—611no—
201#1352—612no—
202#1343—612no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—42no—
206C2×C61—82no—
207C2×C61#150111yescharacteristic
208C2×C61#212011yescharacteristic
209C2×C61C2×#35311yescharacteristic
210D61—42no—
211C2×C4×D4—611no—
212C2×C4×D4—611no—
213C2×C4×D4—1221no—
214C2×C4×D4—1221no—
215C2×#99—1221no—
216C2×C22⋊C8—1221no—
217#399—611no—
218#399—611no—
219#399—1221no—
220#392—611no—
221#392—1221no—
222#392#692311yescharacteristic, complemented
223C4×C22⋊C4—1221no—
224#376—611no—
225#342—612no—
226#324—1221no—
227#323—612no—
228C61#1172611yescharacteristic, complemented, Sylow
229C22×D4—21no—
230C22×D4—611no—
231C22×D4—1221no—
232C22×D4C2×#692311yescharacteristic
233C23×C4—611no—
234C23×C4—611no—
235C23×C4—1221no—
236C22×C8—2441no—
237C4×D4—2441no—
238C4×D4—2441no—
239C4×D4—2444no—
240C4×D4—2444no—
241C4×D4—2441no—
242C4×D4—2441no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—611no—
249C2×C22⋊C4—1222no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4C2×#692311yescharacteristic
255C2×C42—611no—
256C2×C42—1221no—
257C2×C42—2441no—
258#99—1224no—
259C22⋊C8—1222no—
260C22⋊C8—2441no—
261#95—611no—
262#95—1221no—
263#95—2441no—
264#95C2×#692311yescharacteristic
265C24—21no—
266C24—611no—
267C24C22⋊#692311yescharacteristic
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—1222no—
274C2×D4—1222no—
275C2×D4—2441no—
276C2×D4—2442no—
277C2×D4—2442no—
278C2×D4—2442no—
279C22×C4—21no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2442no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4—2442no—
295C22×C4—2442no—
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298C2×C8—4882no—
299C2×C8—2442no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C4⋊C4—2442no—
303C4⋊C4—2442no—
304C22⋊C4—41no—
305C22⋊C4—42no—
306C22⋊C4—1224no—
307C22⋊C4—2441no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C22⋊C4—2442no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C42—1221no—
314C42—1221no—
315C42—1224no—
316C42—4882no—
317C23—21no—
318C23—21no—
319C23—22no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—612no—
329C23—1221no—
330C23—1221no—
331C23—2441no—
332C23—2441no—
333C23#1451984112yes—
334C23C2×C22⋊#692311yescharacteristic
335D4—42no—
336D4—48no—
337D4—42no—
338D4—2444no—
339D4—2448no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—4881no—
356C2×C4—4882no—
357C2×C4—4882no—
358C2×C4—4881no—
359C2×C4—4882no—
360C2×C4—4882no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2444no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C8—4882no—
371C22—21no—
372C22—21no—
373C22—22no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—41no—
378C22—41no—
379C22—42no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—1222no—
386C22—4881no—
387C22—2442no—
388C22—2441no—
389C22—2441no—
390C22D61⋊#9911yescharacteristic
391C22#1684075211yescharacteristic
392C22C2×#1451984111yescharacteristic
393C4—42no—
394C4—41no—
395C4—41no—
396C4—612no—
397C4—1221no—
398C4—4884no—
399C4—4881no—
400C4—2442no—
401C4—2441no—
402C4—2441no—
403C2—21no—
404C2—21no—
405C2—42no—
406C2—82no—
407C2—2442no—
408C2#2146119511yescharacteristic
409C2#2146207111yescharacteristic
410C2D61⋊#35311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#392C4
socleC22×C61C2×#99
prime radical#21449097C2
cosocleC2×#11758198C23
hypercenter#392#6923
hypocenterC61#11726
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #21461566C2semidirect
2. #21461057C2semidirect
3. #21460815C2semidirect
4. #21460797C2semidirect
13. C2×D4×Dic61C4semidirect
18. #16839698C4semidirect
21. #16839607C4semidirect
22. C61×#392C4semidirect
222. #392#6923semidirect
228. C61#11726semidirect

Maximal subgroups

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

subgroupindex
#214615662
#214610572
#214608152
#214607972
#214490972
#1172661