Finite Group Databasebeta

← #29589277

Subgroups — #29589277

Order 15616.

460 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 87 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#21448487C211yesmaximal, characteristic
2#21444138C211yesmaximal, characteristic
3#21444134C211yesmaximal, characteristic
4#21443767C211yesmaximal, characteristic, complemented
5#21443748C211yesmaximal, characteristic, complemented
6#21443748C211yesmaximal, characteristic, complemented
7C61×#1326C211yesmaximal, characteristic, complemented
8C2×#14519761C411yescharacteristic
9C2×#14519737C2211yescharacteristic
10C22×#11758196C411yescharacteristic
11#16839812—21no—
12C22⋊C8×D61—21no—
13#16839658—21no—
14#16839651—21no—
15#16839645—21no—
16#16839641C411yescharacteristic
17#16839633—21no—
18#16839623C2211yescharacteristic
19C22⋊C4×Dic61C411yescharacteristic
20#16839487—21no—
21#16839486C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#385C2211yescharacteristic
25C61×#323C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29C23×Dic61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×C8×D61—41no—
32#14519761—22no—
33#14519761C814yescomplemented
34#14519737—41no—
35#14519737—41no—
36C2×C4⋊Dic61—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—41no—
40C2×#11758196—41no—
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61C2×C411yescharacteristic
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61—21no—
47C2×C4×Dic61D411yescharacteristic
48#14519706—41no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519689—41no—
52C8×Dic61—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C23×C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61—21no—
59C2×C22⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63#95×C61—21no—
64C24×C61C22×C411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61—81no—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61C2×C812yes—
75C2×C22⋊D61M1612yes—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—81no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C2×C812yescomplemented
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—81no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C4⋊C4×C61—81no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61C2×C812yescomplemented
97C22⋊Dic61—41no—
98#11758198—24no—
99#11758198—41no—
100#11758198—81no—
101C4⋊Dic61—24no—
102#11758196—41no—
103#11758196—42no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—81no—
109C2×#92418—41no—
110C2×#92418—41no—
111C8×D61—82no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61C2×C22⋊C411yescharacteristic
117C23×C61C22×C811yescharacteristic
118C23×C61C2×M1611yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61C22⋊C812yes—
124C2×C4×C61—22no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—82no—
135C22⋊D61—42no—
136C22⋊D61—42no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152C2×Dic61C22⋊C812yes—
153C2×Dic61#9911yescharacteristic
154C2×Dic61#9911yescharacteristic
155C4×D61—42no—
156C4×D61—81no—
157C8×C61—81no—
158C8×C61—81no—
159#92418—81no—
160#92418—81no—
161#11474—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—42no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61C2×C22⋊C811yescharacteristic
172C22×C61C2×#9911yescharacteristic
173C22×C61#41311yescharacteristic
174C2×D61—22no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—42no—
178C2×D61—81no—
179C4×C61—42no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—81no—
183Dic61—21no—
184Dic61—21no—
185Dic61—22no—
186Dic61—41no—
187Dic61—42no—
188Dic61—81no—
189#2322—611no—
190#1460—611no—
191#1459—611no—
192#1326—611no—
193#1326D6111yescharacteristic, complemented
194#1317—611no—
195#1317—611no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—41no—
199C2×C61—41no—
200C2×C61#145911yescharacteristic
201C2×C61#212111yescharacteristic
202C2×C61#212311yescharacteristic
203D61—42no—
204C2×#123—611no—
205C2×C4×D4—611no—
206C22×C4⋊C4—611no—
207#431—1221no—
208C2×C22⋊C8—1221no—
209#389—1221no—
210#388—1221no—
211#387—1221no—
212#386—611no—
213#385—1221no—
214#385C2×D6111yescharacteristic
215#381—611no—
216C4×C22⋊C4—611no—
217#324—1221no—
218#323—611no—
219#323—611no—
220#323—1221no—
221#323C2×D6111yescharacteristic
222#323C2×D6111yescharacteristic
223C61#1147411yescharacteristic, complemented, Sylow
224C22×D4—611no—
225C23×C4—611no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4C4×D6111yescharacteristic
229C22×C8—2441no—
230#123—614no—
231#123—1222no—
232C4×D4—2441no—
233C4×D4—2441no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—2441no—
240C2×C4⋊C4—2441no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4—611no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4C4×D6111yescharacteristic
246C2×C22⋊C4C22×D6111yescharacteristic
247C2×C42—611no—
248C2×C42—1221no—
249C4⋊C8—2441no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—1221no—
253C22⋊C8—1221no—
254C22⋊C8—2441no—
255C4×C8—2441no—
256#95—21no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261C24—611no—
262C24C2×C4×D6111yescharacteristic
263C2×D4—612no—
264C2×D4—612no—
265C2×D4—2441no—
266C2×D4—2441no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—81no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—612no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—4881no—
283C22×C4—4881no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4D4×D6111yescharacteristic
287C22×C4D4×D6111yescharacteristic
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—4882no—
291C2×C8—2441no—
292C2×C8—2441no—
293C4⋊C4—81no—
294C4⋊C4—1224no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2442no—
299C22⋊C4—21no—
300C22⋊C4—41no—
301C22⋊C4—1224no—
302C22⋊C4—4881no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4C8×D6112yescomplemented
306C42—1221no—
307C42—1221no—
308C42—4881no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—612no—
314C23—1221no—
315C23—1221no—
316C23—2441no—
317C23—2441no—
318C23C22⋊C4×D6111yescharacteristic
319C23C2×C8×D6111yescharacteristic
320C23M16×D6111yescharacteristic
321D4—2442no—
322D4—2442no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—82no—
334C2×C4—612no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1222no—
340C2×C4—1221no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—2442no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2442no—
354C8—81no—
355C8—81no—
356C8—4881no—
357C8—4881no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—1222no—
368C22—4881no—
369C22—2442no—
370C22—2441no—
371C22—2441no—
372C22C22⋊C8×D6111yescharacteristic
373C22#99×D6111yescharacteristic
374C22#1683974511yescharacteristic
375C4—42no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—1221no—
380C4—1221no—
381C4—1222no—
382C4—4881no—
383C4—2441no—
384C4—2442no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—2442no—
390C2#2144413611yescharacteristic
391C2#2144746211yescharacteristic
392C2#2144747111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC23×C61C22×C8
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1326C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1326D61
hypocenterC61#11474
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1326

Complements

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

NH ≅ G/Ntype
4. #21443767C2semidirect
5. #21443748C2semidirect
6. #21443748C2semidirect
7. C61×#1326C2semidirect
33. #14519761C8semidirect
87. C22×Dic61C2×C8semidirect
96. C22⋊C4×C61C2×C8semidirect
193. #1326D61semidirect
223. C61#11474semidirect
305. C22⋊C4C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214484872
#214441382
#214441342
#214437672
#214437482
C61×#13262
#1147461