Finite Group Databasebeta

← #29590360

Subgroups — #29590360

Order 15616.

500 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451671C211yesmaximal, characteristic
2#21444137C211yesmaximal, characteristic, complemented
3#21443839C212yesmaximal, complemented
4#21443815C212yesmaximal, complemented
5C4×#99×C61C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic, complemented
7C2×C22⋊#92418—21no—
8#16839688—21no—
9#16839674C411yescharacteristic, complemented
10#16839674C2211yescharacteristic
11#16839671C411yescharacteristic, complemented
12#16839671C2211yescharacteristic
13#16839670—21no—
14#16839641—21no—
15#16839641—21no—
16#16839630C411yescharacteristic, complemented
17#16839488—21no—
18#16839486C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C4×C22⋊C4×C61—21no—
22C61×#342C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×D244C2×C411yescharacteristic
25C22×C22⋊D61—21no—
26C22×C22⋊D61—21no—
27C22×#92418—41no—
28#14519765—41no—
29#14519765—41no—
30C2×C22⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C22⋊#92418—22no—
37C22⋊#92418—41no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C22×D4×C61D411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C4×D4×C61—41no—
48C4×D4×C61—41no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C22⋊C4×C61—22no—
51C2×C22⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61C2311yescharacteristic
53C2×C42×C61—41no—
54C2×C42×C61C2×C411yescharacteristic
55#99×C61—24no—
56#95×C61—41no—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C2×D411yescharacteristic
59C23×D61—21no—
60C2×D4×C61—22no—
61C2×D4×C61—22no—
62C2×D4×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—42no—
68C22×C4×C61—81no—
69C22×C4×C61—81no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—81no—
78C2×C22⋊D61—81no—
79C2×C22⋊D61—81no—
80C2×C22⋊D61—81no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C2×D244—41no—
85C2×D244—81no—
86C2×Dic122—41no—
87C2×Dic122—81no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—24no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—42no—
93C42×C61—21no—
94C42×C61—21no—
95C42×C61—82no—
96C22⋊Dic61—81no—
97C22⋊Dic61—81no—
98#11758198—42no—
99#11758198—41no—
100#11758198—41no—
101#11758198—81no—
102#11758198—81no—
103C2×#92418—42no—
104C2×#92418—82no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61#10412yes—
114C23×C61C2×C22⋊C411yescharacteristic
115C23×C61#13512yes—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123D4×C61—44no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—44no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—82no—
140C2×C4×C61—82no—
141C2×C4×C61#9911yescharacteristic
142C2×C4×C61#9911yescharacteristic
143C22⋊D61—84no—
144C22⋊D61—84no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154D244—82no—
155Dic122—82no—
156#92418—82no—
157#11730—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—42no—
163C22×C61—42no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61C2×#9911yescharacteristic
171C22×C61#41611yescharacteristic
172C22×C61C2×#10411yescharacteristic
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—81no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—84no—
187Dic61—81no—
188Dic61—81no—
189Dic61—81no—
190#2631—611no—
191C4×#99D6111yescharacteristic, complemented
192#1459—611no—
193#1351—612no—
194#1343—612no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—42no—
198C2×C61—42no—
199C2×C61#150111yescharacteristic
200C2×C61#212211yescharacteristic
201C2×C61#212711yescharacteristic
202D61—161no—
203C2×#124—611no—
204C2×C4×D4C2×D6111yescharacteristic
205C2×#99—21no—
206C2×C22⋊C8—1221no—
207#397—1221no—
208#393—611no—
209#393—611no—
210#392—611no—
211#392—611no—
212#392—1221no—
213#386—1221no—
214#386—1221no—
215#383—611no—
216C4×C22⋊C4—21no—
217#342C2×D6112yes—
218#324—1221no—
219#323—612no—
220C61#1173011yescharacteristic, complemented, Sylow
221C22×Q8—611no—
222C22×D4—611no—
223C22×D4—1221no—
224C22×D4—1221no—
225C22×D4C22⋊D6111yescharacteristic
226C23×C4D24411yescharacteristic
227C23×C4C22⋊D6111yescharacteristic
228C22×C8—2441no—
229#124—2441no—
230#124—2441no—
231C4×D4—41no—
232C4×D4—41no—
233C2×C4⋊C4D24411yescharacteristic
234C2×C22⋊C4—22no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4C4×D6111yescharacteristic
242C2×C22⋊C4C22×D6111yescharacteristic
243C2×C42—41no—
244C2×C42C4×D6111yescharacteristic
245#99—24no—
246C22⋊C8—1222no—
247C22⋊C8—2441no—
248#95—41no—
249#95—611no—
250#95—611no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255C24—1221no—
256C24#1175819811yescharacteristic
257C24C2×C22⋊D6111yescharacteristic
258C2×Q8—4881no—
259C2×Q8—2441no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—4881no—
264C2×D4—4881no—
265C2×D4—4881no—
266C2×D4—4881no—
267C2×D4—4881no—
268C2×D4—2441no—
269C2×D4—2442no—
270C2×D4—2442no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4#1175819811yescharacteristic
282C22×C4#1175819811yescharacteristic
283C22×C4#1175819811yescharacteristic
284C22×C4C2×C4×D6111yescharacteristic
285C22×C4C2×D24411yescharacteristic
286C2×C8—4882no—
287C2×C8—2442no—
288C4⋊C4—41no—
289C22⋊C4—24no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—4881no—
294C22⋊C4—4881no—
295C22⋊C4—4881no—
296C22⋊C4—4881no—
297C22⋊C4—2442no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C42—21no—
301C42—21no—
302C42—82no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23#1451970512yes—
319C23C2×#1175819811yescharacteristic
320C23#1451979712yes—
321Q8—4882no—
322D4—44no—
323D4—4882no—
324D4—4884no—
325D4—4884no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—44no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4#1451969111yescharacteristic
353C2×C4#1451969111yescharacteristic
354C8—4882no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22—42no—
360C22—42no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22—81no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22C2×#1451969111yescharacteristic
375C22#1683975611yescharacteristic
376C22C2×#1451970511yescharacteristic
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—84no—
384C4—4881no—
385C4—4881no—
386C4—4881no—
387C2—21no—
388C2—21no—
389C2—42no—
390C2—42no—
391C2—9761no—
392C2#2144430811yescharacteristic
393C2#2144746811yescharacteristic
394C2#2144748611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC4×#99×C61C2
socleC22×C61C2×#99
prime radical#21451671C2
cosocleC2×C22⋊C4×C61C23
hypercenterC4×#99D61
hypocenterC61#11730
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21444137C2semidirect
3. #21443839C2semidirect
4. #21443815C2semidirect
5. C4×#99×C61C2semidirect
6. C2×#14519765C4semidirect
9. #16839674C4semidirect
11. #16839671C4semidirect
16. #16839630C4semidirect
191. C4×#99D61semidirect
220. C61#11730semidirect

Maximal subgroups

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

subgroupindex
#214516712
#214441372
#214438392
#214438152
C4×#99×C612
#1173061