Finite Group Databasebeta

← #30604878

Subgroups — #30604878

Order 15616.

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

normal subgroups only

This group has 632 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×#14519837C211yesmaximal, characteristic, complemented
2#21461054C211yesmaximal, characteristic, complemented
3#21460820C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21449032C211yesmaximal, characteristic
6C2×#14519837—21no—
7D61⋊(C22⋊C8)—21no—
8C4×#11758217—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840605—21no—
12C2×C4×C22⋊D61—21no—
13C2×C4×C22⋊D61C2211yescharacteristic
14#16839681C2211yescharacteristic
15#16839676—21no—
16#16839676C2211yescharacteristic
17#16839673C411yescharacteristic
18#16839670—21no—
19#16839670C411yescharacteristic
20C4×C22⋊Dic61—21no—
21C4×C22⋊Dic61C411yescharacteristic
22C22×#41×C61C411yescharacteristic
23C2×#11758217—22no—
24C2×D61⋊C8—41no—
25#14519837—24no—
26#14519834—41no—
27C22⋊#92420—22no—
28#14519832—41no—
29C4×#92420—41no—
30C22×C22⋊D61—21no—
31C22×C22⋊D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C4×C22⋊D61—41no—
34C4×C22⋊D61—41no—
35C4×C22⋊D61—44no—
36C2×#11758196—21no—
37C2×#11758196C2311yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61D411yescharacteristic
43C2×#11758198—21no—
44C2×#11758198C2×C411yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684C2×C411yescharacteristic
50#14519684C2×C411yescharacteristic
51C2×#41×C61—44no—
52C2×#41×C61—41no—
53C2×#41×C61—41no—
54C22×Q8×C61C2×C411yescharacteristic
55C22×D4×C61—21no—
56C22×D4×C61C2×C411yescharacteristic
57C23×C4×C61—21no—
58C23×C4×C61C2×C411yescharacteristic
59C24×C61—21no—
60C24×C61C22⋊C411yescharacteristic
61C23×D61C22⋊C411yescharacteristic
62#41×C61—44no—
63#41×C61—44no—
64#41×C61—44no—
65#41×C61—44no—
66C2×Q8×C61—42no—
67C2×Q8×C61—41no—
68C2×D4×C61—42no—
69C2×D4×C61—41no—
70C2×D4×C61—42no—
71C2×D4×C61—42no—
72C2×D4×C61—42no—
73C22×C4×C61—24no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—42no—
78C22×C4×C61—42no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22×C411yescharacteristic
83C2×C22⋊D61—22no—
84C2×C22⋊D61—22no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—42no—
87C2×C22⋊D61—42no—
88C2×C22⋊D61—42no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—42no—
97#11758217—24no—
98#11758217—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101D61⋊C8—82no—
102C22⋊Dic61—41no—
103C22⋊Dic61—42no—
104C22⋊Dic61—42no—
105C22⋊Dic61—42no—
106C22⋊Dic61—42no—
107#11758198—41no—
108#11758198—42no—
109#11758196—41no—
110#11758196—42no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—42no—
114C23×C61—22no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61C2×C22⋊C411yescharacteristic
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61#10412yes—
132Q8×C61—42no—
133Q8×C61—42no—
134D4×C61—42no—
135D4×C61—48no—
136D4×C61—42no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—21no—
140C2×C4×C61—44no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—44no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61#9911yescharacteristic
148C2×C4×C61#9911yescharacteristic
149C22⋊D61—44no—
150C22⋊D61—48no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—22no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61#13512yes—
164C4×D61—42no—
165C4×D61—81no—
166#92420—44no—
167#92420—82no—
168#11733—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—42no—
172C22×C61—42no—
173C22×C61—41no—
174C22×C61—42no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61C2×#9911yescharacteristic
184C22×C61#41611yescharacteristic
185C22×C61C2×#10411yescharacteristic
186C2×D61—22no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—42no—
190C2×D61—81no—
191C4×C61—21no—
192C4×C61—42no—
193C4×C61—41no—
194C4×C61AΣL(1,𝔽16)12yes—
195Dic61—22no—
196Dic61—42no—
197Dic61—41no—
198Dic61—41no—
199Dic61—81no—
200#2388—611no—
201C4×#100—611no—
202#1459—611no—
203#1354—612no—
204#1345—612no—
205C2×C61—21no—
206C2×C61—21no—
207C2×C61—81no—
208C2×C61—82no—
209C2×C61#150111yescharacteristic
210C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
211C2×C61#213211yescharacteristic
212D61—42no—
213C22×#41#692311yescharacteristic
214C2×C4×D4—611no—
215C2×C4×D4—1221no—
216C2×#100—1221no—
217C2×C22⋊C8—1221no—
218C4×M16—1221no—
219#395—611no—
220#394—611no—
221#394—1221no—
222#393—611no—
223#392—611no—
224#392—1221no—
225C4×C22⋊C4—611no—
226C4×C22⋊C4—1221no—
227#343—612no—
228#324—612no—
229#323—1221no—
230C61#1173311yescharacteristic, complemented, Sylow
231C2×#41—44no—
232C2×#41—41no—
233C2×#41—41no—
234C22×Q8C2×#692311yescharacteristic
235C22×D4—21no—
236C22×D4—611no—
237C22×D4—1221no—
238C22×D4C2×#692311yescharacteristic
239C23×C4—21no—
240C23×C4—611no—
241C23×C4C2×#692311yescharacteristic
242C2×M16—1222no—
243C22×C8—2441no—
244C4×D4—2441no—
245C4×D4—2441no—
246C4×D4—2444no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—1221no—
249C2×C22⋊C4—611no—
250C2×C22⋊C4—611no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C42—611no—
257C2×C42—1221no—
258#100—1224no—
259C22⋊C8—1222no—
260C22⋊C8—2441no—
261#97—2441no—
262C4×C8—2441no—
263#95—611no—
264#95—611no—
265#95—1221no—
266#95—1221no—
267C24—21no—
268C24—611no—
269C24C22⋊#692311yescharacteristic
270#41—44no—
271#41—44no—
272#41—44no—
273#41—44no—
274C2×Q8—42no—
275C2×Q8—41no—
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—1222no—
282C2×D4—1222no—
283C2×D4—2441no—
284C2×D4—2442no—
285C2×D4—2442no—
286C2×D4—2442no—
287C22×C4—24no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—2442no—
303C22×C4C22⋊#692311yescharacteristic
304C22×C4C22×#692311yescharacteristic
305M16—1224no—
306M16—2442no—
307C2×C8—4882no—
308C2×C8—2442no—
309C2×C8—2442no—
310C4⋊C4—2441no—
311C4⋊C4—2442no—
312C22⋊C4—2441no—
313C22⋊C4—2442no—
314C22⋊C4—2442no—
315C22⋊C4—2441no—
316C22⋊C4—2442no—
317C22⋊C4—2442no—
318C22⋊C4—2442no—
319C42—1221no—
320C42—1221no—
321C42—2442no—
322C23—22no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—612no—
335C23—1221no—
336C23—1221no—
337C23—2441no—
338C23—2441no—
339C23C2×C22⋊#692311yescharacteristic
340Q8—42no—
341Q8—42no—
342D4—42no—
343D4—48no—
344D4—42no—
345D4—2444no—
346D4—2448no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—612no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1222no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—4881no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2442no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4#1451983511yescharacteristic
373C2×C4#1451983511yescharacteristic
374C8—4882no—
375C8—2444no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—42no—
380C22—41no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—1222no—
391C22—4881no—
392C22—2442no—
393C22—2441no—
394C22—2441no—
395C22C2×#1451983511yescharacteristic
396C22#1684075211yescharacteristic
397C22D61⋊#10411yescharacteristic
398C4—21no—
399C4—42no—
400C4—41no—
401C4—1222no—
402C4—4881no—
403C4—2442no—
404C4—2441no—
405C4—2441no—
406C4#1684066212yes—
407C2—21no—
408C2—21no—
409C2—82no—
410C2—81no—
411C2—2442no—
412C2#2146119411yescharacteristic
413C2C2×#1684066211yescharacteristic
414C2#2146211011yescharacteristic
subgroupG/H
centerC2×C4#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×#41×C61C4
socleC22×C61C2×#99
prime radical#21449032C2
cosocleC2×#11758196C23
hypercenterC22×#41#6923
hypocenterC61#11733
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C4×#14519837C2semidirect
2. #21461054C2semidirect
3. #21460820C2semidirect
4. #21460801C2semidirect
230. C61#11733semidirect

Maximal subgroups

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

subgroupindex
C4×#145198372
#214610542
#214608202
#214608012
#214490322
#1173361