Finite Group Databasebeta

← #29573617

Subgroups — #29573617

Order 15616.

446 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 85 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#21448752C211yesmaximal, characteristic
2C4×#14519693C211yesmaximal, characteristic
3#21444159C211yesmaximal, characteristic
4#21443713C211yesmaximal, characteristic, complemented
5#21443711C211yesmaximal, characteristic, complemented
6#21443683C211yesmaximal, characteristic, complemented
7C61×#1288C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16839819C2211yescharacteristic
10C2×#14519693—21no—
11C4×#11758194C2211yescharacteristic
12#16839651—21no—
13#16839647—21no—
14#16839640—21no—
15#16839624C411yescharacteristic
16#16839621C411yescharacteristic
17#16839609—21no—
18#16839609C411yescharacteristic
19#16839608C2211yescharacteristic
20#95×D61C411yescharacteristic
21#16839530—21no—
22#16839485—21no—
23#16839485—21no—
24C61×#432C2211yescharacteristic
25C4×M16×C61C2211yescharacteristic
26C61×#383C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61C2×C411yescharacteristic
31C2×#11758194—21no—
32C4×D244—21no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198D411yescharacteristic
42C2×#11758198D411yescharacteristic
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C4⋊#92418—21no—
46#14519693—24no—
47C22⋊#92418—21no—
48#14519688—21no—
49#14519688—21no—
50C4×#92418—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55#14519684C2×C411yescharacteristic
56C2×M16×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60#97×C61—21no—
61#97×C61—21no—
62C4×C8×C61—21no—
63#95×C61—21no—
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66#95×C61C2×C411yescharacteristic
67C23×D61C22⋊C411yescharacteristic
68C23×D61C22⋊C411yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C2×D244—22no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—41no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61—81no—
89C2×C4×D61—81no—
90C2×C4×D61—81no—
91M16×C61—22no—
92M16×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C42×C61#4111yescharacteristic
96C42×C61#4111yescharacteristic
97C42×C61#4111yescharacteristic
98C42×C61#4111yescharacteristic
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—42no—
104#11758198—42no—
105#11758198—81no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108#11758196—81no—
109C4×Dic61—42no—
110C4×Dic61—81no—
111#11758194—22no—
112#11758194—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61#10412yes—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
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—41no—
135C2×C4×C61—41no—
136C2×C4×C61#11711yescharacteristic
137C2×C4×C61#11711yescharacteristic
138C2×C4×C61#12311yescharacteristic
139C2×C4×C61#12311yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×C4×C61#12311yescharacteristic
142C2×Dic61—22no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152D244—42no—
153D244—42no—
154C4×D61—81no—
155C4×D61—81no—
156C4×D61—81no—
157C4×D61—81no—
158C4×D61—84no—
159C8×C61—42no—
160C8×C61—81no—
161#92418—42no—
162#92418—81no—
163#8772—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61#38111yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C22×C61#42111yescharacteristic
169C2×D61—22no—
170C2×D61—42no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—42no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—81no—
186C4×C61—81no—
187Dic61—42no—
188Dic61—41no—
189Dic61—41no—
190Dic61—81no—
191#2353—611no—
192C4×#100—611no—
193#1466—611no—
194#1300—611no—
195#1300—611no—
196#1288—611no—
197#1288D6111yescharacteristic, complemented
198C2×C61—21no—
199C2×C61—21no—
200C2×C61#182611yescharacteristic
201C2×C61#182711yescharacteristic
202C2×C61#182911yescharacteristic
203D61—42no—
204D61—81no—
205C2×C4×D4—611no—
206#432—611no—
207#432C2×D6111yescharacteristic
208C2×#100—1221no—
209C4×M16—611no—
210C4×M16C2×D6111yescharacteristic
211#388—1221no—
212#387—1221no—
213#386—1221no—
214#383C2×D6111yescharacteristic
215#381—611no—
216#380—611no—
217C4×C22⋊C4—611no—
218C4×C22⋊C4—1221no—
219#376—611no—
220C2×#95—611no—
221#343—1221no—
222#323—1221no—
223#323—1221no—
224C61#877211yescharacteristic, complemented, Sylow
225C22×D4—611no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—1221no—
229C2×M16—21no—
230C2×M16—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233C4×D4—1221no—
234C4×D4—1221no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C22⋊C4—611no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C42—1221no—
243C2×C42—1221no—
244C2×C42C22×D6111yescharacteristic
245C4⋊C8—21no—
246C4⋊C8—1221no—
247#100—1224no—
248C22⋊C8—21no—
249C22⋊C8—1221no—
250#97—21no—
251#97—21no—
252#97—1221no—
253#97—1221no—
254C4×C8—21no—
255C4×C8—1221no—
256#95—21no—
257#95—21no—
258#95—611no—
259#95—611no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95C4×D6111yescharacteristic
264#95C4×D6111yescharacteristic
265C24—611no—
266C24—611no—
267C2×D4—1222no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—2441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—4881no—
282C22×C4—4881no—
283C22×C4—4881no—
284C22×C4—2442no—
285C22×C4—2442no—
286C22×C4C2×C4×D6111yescharacteristic
287C22×C4D4×D6111yescharacteristic
288C22×C4D4×D6111yescharacteristic
289M16—22no—
290M16—41no—
291M16—1222no—
292M16—2441no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—2441no—
296C2×C8—2441no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—4881no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—4881no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C42—4881no—
308C42—2442no—
309C42#1175822211yescharacteristic
310C42#1175822211yescharacteristic
311C42#1175822411yescharacteristic
312C42#1175822611yescharacteristic
313C23—612no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23C22⋊C4×D6111yescharacteristic
324D4—2442no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—1222no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—4884no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4#1451973411yescharacteristic
352C2×C4#1451973511yescharacteristic
353C2×C4#1451975911yescharacteristic
354C2×C4#1451975911yescharacteristic
355C2×C4#1451976211yescharacteristic
356C2×C4#1451976211yescharacteristic
357C8—42no—
358C8—81no—
359C8—4881no—
360C8—2442no—
361C22—21no—
362C22—21no—
363C22—1222no—
364C22—4881no—
365C22—4881no—
366C22—2442no—
367C22—2442no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22#1683962411yescharacteristic
374C22#104×D6111yescharacteristic
375C22#1683977711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—81no—
384C4—4881no—
385C4—2442no—
386C4—2441no—
387C4—2441no—
388C2—21no—
389C2—21no—
390C2—4881no—
391C2—2442no—
392C2#2144591711yescharacteristic
393C2#2144592111yescharacteristic
394C2#2144592911yescharacteristic
subgroupG/H
centerC22#16839624
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1288C2
socleC22×C61#381
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1288D61
hypocenterC61#8772
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
4. #21443713C2semidirect
5. #21443711C2semidirect
6. #21443683C2semidirect
7. C61×#1288C2semidirect
197. #1288D61semidirect
224. C61#8772semidirect

Maximal subgroups

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

subgroupindex
#214487522
C4×#145196932
#214441592
#214437132
#214437112
#214436832
C61×#12882
#877261