Finite Group Databasebeta

← #30604850

Subgroups — #30604850

Order 15616.

606 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#14519836C211yesmaximal, characteristic, complemented
2#21461056C211yesmaximal, characteristic, complemented
3#21460816C212yesmaximal, complemented
4#21460797C212yesmaximal, complemented
5#21449098C211yesmaximal, characteristic
6C2×#14519836—21no—
7D61⋊(C22⋊C8)—21no—
8C4×C22⋊#6923—21no—
9#16840640C2212yes—
10#16840607—21no—
11#16840606C2212yes—
12C2×C4×D244C2211yescharacteristic
13C2×C4×C22⋊D61—21no—
14C2×C4×C22⋊D61—21no—
15#16839698—21no—
16#16839697C411yescharacteristic, complemented
17#16839697C2211yescharacteristic
18#16839671—21no—
19#16839670C411yescharacteristic, complemented
20#16839670C2211yescharacteristic
21#16839608C411yescharacteristic, complemented
22C2×C4×D4×C61C411yescharacteristic, complemented
23C2×D61⋊C8—41no—
24C2×C22⋊#6923—22no—
25C2×C4×#6923—41no—
26#14519836—24no—
27#14519834—41no—
28C22⋊#92420—22no—
29(C2×#6923)⋊C4—41no—
30C22×D244D411yescharacteristic
31C22×C22⋊D61—21no—
32C22×C22⋊D61—21no—
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C4×D244—41no—
36C4×D244—41no—
37C4×C22⋊D61—44no—
38C4×C22⋊D61—44no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×#11758198C2311yescharacteristic
48C2×C4×Dic61—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51#14519684C2×C411yescharacteristic
52C22×D4×C61C2×C411yescharacteristic
53C23×C4×C61—21no—
54C4×D4×C61—41no—
55C4×D4×C61—41no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C42×C61C2×C411yescharacteristic
59C24×C61—21no—
60C23×D61C22⋊C411yescharacteristic
61C23×D61C2×D411yescharacteristic
62C22×#6923—42no—
63C2×D4×C61—41no—
64C2×D4×C61—42no—
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C2×D244—22no—
84C2×D244—22no—
85C2×D244—41no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C22⋊#6923—24no—
93C22⋊#6923—42no—
94C2×#92420—42no—
95C4×#6923—82no—
96D61⋊C8—82no—
97C4⋊C4×C61—41no—
98C22⋊C4×C61—42no—
99C42×C61—21no—
100C42×C61—21no—
101C22⋊Dic61—42no—
102C22⋊Dic61—42no—
103#11758198—41no—
104#11758198—41no—
105#11758198—42no—
106#11758198—42no—
107C4⋊Dic61—41no—
108#11758196—42no—
109#11758196—42no—
110C4×Dic61—24no—
111C23×C61—22no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61#10412yes—
128C22×D61#13512yes—
129C2×#6923—44no—
130C2×#6923—82no—
131C2×#6923—82no—
132D4×C61—42no—
133D4×C61—42no—
134C2×C4×C61—22no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
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—82no—
144C2×C4×C61—82no—
145C2×C4×C61#9911yescharacteristic
146C2×C4×C61#9911yescharacteristic
147C22⋊D61—48no—
148C22⋊D61—48no—
149C2×Dic61—22no—
150C2×Dic61—22no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159D244—44no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—81no—
163C4×D61—81no—
164#92420—82no—
165#11726—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—42no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61C2×#9911yescharacteristic
176C22×C61#41611yescharacteristic
177C22×C61C2×#10411yescharacteristic
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—81no—
187C2×D61—81no—
188#6923—84no—
189C4×C61—21no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61—81no—
193C4×C61#35312yes—
194Dic61—42no—
195Dic61—42no—
196Dic61—41no—
197Dic61—41no—
198#2397—611no—
199C4×#99—611no—
200#1459—611no—
201#1352—612no—
202#1343—612no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—82no—
206C2×C61#150111yescharacteristic
207C2×C61#212011yescharacteristic
208C2×C61C2×#35311yescharacteristic
209D61—42no—
210D61—42no—
211C2×C4×D4—611no—
212C2×C4×D4—1221no—
213C2×C4×D4—1221no—
214C2×C4×D4#692311yescharacteristic, complemented
215C2×#99—1221no—
216C2×C22⋊C8—1221no—
217#399—611no—
218#399—611no—
219#399—1221no—
220#392—611no—
221#392—611no—
222#392—1221no—
223C4×C22⋊C4—1221no—
224#376—611no—
225#342—612no—
226#324—1221no—
227#323—612no—
228C61#1172611yescharacteristic, complemented, Sylow
229C22×D4—611no—
230C22×D4—1221no—
231C22×D4—1221no—
232C22×D4C2×#692311yescharacteristic
233C23×C4—21no—
234C23×C4—611no—
235C23×C4—611no—
236C22×C8—2441no—
237C4×D4—41no—
238C4×D4—41no—
239C4×D4—2441no—
240C4×D4—2441no—
241C4×D4—2444no—
242C4×D4—2444no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4C2×#692311yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—611no—
249C2×C22⋊C4—611no—
250C2×C22⋊C4—1222no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C42—1221no—
256C2×C42—2441no—
257C2×C42C2×#692311yescharacteristic
258#99—1224no—
259C22⋊C8—1222no—
260C22⋊C8—2441no—
261#95—611no—
262#95—611no—
263#95—1221no—
264#95—2441no—
265C24—21no—
266C24—611no—
267C24—611no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—1222no—
271C2×D4—1222no—
272C2×D4—2441no—
273C2×D4—2442no—
274C2×D4—2442no—
275C2×D4—2442no—
276C2×D4—2442no—
277C2×D4—2442no—
278C2×D4—2442no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4—2442no—
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298C2×C8—4882no—
299C2×C8—2442no—
300C4⋊C4—41no—
301C4⋊C4—2441no—
302C4⋊C4—2442no—
303C4⋊C4—2442no—
304C22⋊C4—42no—
305C22⋊C4—1224no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C22⋊C4—2442no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C42—21no—
314C42—21no—
315C42—1224no—
316C42—4882no—
317C23—22no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—612no—
325C23—612no—
326C23—1221no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23—2441no—
331C23—2441no—
332C23—2441no—
333C23—2441no—
334C23C2×C22⋊#692311yescharacteristic
335D4—42no—
336D4—42no—
337D4—2444no—
338D4—2448no—
339D4—2448no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—4882no—
358C2×C4—4882no—
359C2×C4—2444no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2442no—
365C2×C4—2442no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4#1451983511yescharacteristic
369C2×C4#1451983511yescharacteristic
370C8—4882no—
371C22—21no—
372C22—21no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—1222no—
381C22—1222no—
382C22—4881no—
383C22—4881no—
384C22—2442no—
385C22—2442no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22—2441no—
390C22C2×#1451983511yescharacteristic
391C22#1684075211yescharacteristic
392C22D61⋊#10411yescharacteristic
393C4—21no—
394C4—41no—
395C4—41no—
396C4—81no—
397C4—4884no—
398C4—2442no—
399C4—2442no—
400C4—2441no—
401C4—2441no—
402C4#1684066612yes—
403C2—21no—
404C2—21no—
405C2—82no—
406C2—2442no—
407C2—2442no—
408C2#2146119411yescharacteristic
409C2#2146207011yescharacteristic
410C2C2×#1684066611yescharacteristic
subgroupG/H
centerC2×C4#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C2×#99
prime radical#21449098C2
cosocleC2×#11758198C23
hypercenterC2×C4×D4#6923
hypocenterC61#11726
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#14519836C2semidirect
2. #21461056C2semidirect
3. #21460816C2semidirect
4. #21460797C2semidirect
16. #16839697C4semidirect
19. #16839670C4semidirect
21. #16839608C4semidirect
22. C2×C4×D4×C61C4semidirect
214. C2×C4×D4#6923semidirect
228. C61#11726semidirect

Maximal subgroups

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

subgroupindex
C4×#145198362
#214610562
#214608162
#214607972
#214490982
#1172661