Finite Group Databasebeta

← #29590526

Subgroups — #29590526

Order 15616.

470 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451509C211yesmaximal, characteristic
2#21445556C211yesmaximal, characteristic, complemented
3#21444152C211yesmaximal, characteristic, complemented
4#21443850C211yesmaximal, characteristic, complemented
5#21443848C211yesmaximal, characteristic, complemented
6#21443822C211yesmaximal, characteristic, complemented
7C61×#1345C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519764C411yescharacteristic
10C2×#14519735C2211yescharacteristic
11#16839816—21no—
12#16839682C2211yescharacteristic
13#16839675C411yescharacteristic
14#16839670C411yescharacteristic
15#16839662—21no—
16#16839656—21no—
17#16839655—21no—
18#16839638—21no—
19#16839607C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C4×D61D411yescharacteristic
30C2×#11758194—21no—
31C2×#11758189—41no—
32M16×D61—24no—
33M16×D61—42no—
34C2×C8×D61—41no—
35#14519764—41no—
36#14519764—41no—
37#14519735—41no—
38#14519735—41no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198C2×C411yescharacteristic
46C2×#11758198D411yescharacteristic
47C2×C4×Dic61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519706—41no—
51C22⋊#92418—21no—
52#14519687—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C22×D4×C61C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61C2311yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C22⋊C8×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61—21no—
65C23×D61C22⋊C411yescharacteristic
66C2×D4×C61—41no—
67C2×D4×C61—81no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—81no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C2×C4×D61—22no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×Dic122—41no—
86C2×Dic122—81no—
87M16×C61—22no—
88M16×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C4⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—81no—
95C22⋊Dic61—42no—
96C22⋊Dic61—42no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99#11758198—41no—
100#11758198—41no—
101#11758198—81no—
102C4⋊Dic61—41no—
103#11758196—81no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—42no—
109#11758194—22no—
110#11758194—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113#11758189—44no—
114C8×D61—44no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61#10412yes—
128D4×C61—82no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C22⋊D61—84no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—22no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61#9911yescharacteristic
154C2×Dic61#9911yescharacteristic
155C4×D61—22no—
156C4×D61—22no—
157C4×D61—22no—
158C4×D61—22no—
159Dic122—82no—
160C8×C61—42no—
161C8×C61—81no—
162#92418—42no—
163#92418—81no—
164#11765—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61C2×#9911yescharacteristic
175C22×C61#41711yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C2×D61—22no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—42no—
181C2×D61—81no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—81no—
187Dic61—21no—
188Dic61—21no—
189Dic61—42no—
190Dic61—41no—
191Dic61—41no—
192Dic61—81no—
193#2610—611no—
194#1742—611no—
195#1464—611no—
196#1354—611no—
197#1354—611no—
198#1345—611no—
199#1345D6111yescharacteristic, complemented
200C2×C61—21no—
201C2×C61—21no—
202C2×C61—161no—
203C2×C61#150411yescharacteristic
204C2×C61#212211yescharacteristic
205C2×C61#213211yescharacteristic
206D61—42no—
207C22×M16—1221no—
208C2×#124—611no—
209C2×#117—611no—
210#432—1221no—
211#395—611no—
212#394C2×D6111yescharacteristic
213#393—611no—
214#392—611no—
215#390—1221no—
216#388—1221no—
217#388—1221no—
218#386—1221no—
219#376—611no—
220#343—611no—
221#343—1221no—
222#343C2×D6111yescharacteristic
223#324—611no—
224#324C2×D6111yescharacteristic
225#323—1221no—
226C61#1176511yescharacteristic, complemented, Sylow
227C22×Q8—611no—
228C22×D4—1221no—
229C22×D4C4×D6111yescharacteristic
230C23×C4—611no—
231C2×M16—21no—
232C2×M16—1224no—
233C2×M16—1221no—
234C2×M16—2441no—
235C2×M16—2442no—
236C22×C8—2441no—
237#124—2441no—
238#124—2441no—
239#117—2441no—
240#117—2441no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4C22×D6111yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—611no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—1221no—
255C4⋊C8—2441no—
256C22⋊C8—21no—
257C22⋊C8—1221no—
258#97—2441no—
259#95—611no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95C4×D6111yescharacteristic
264C24—21no—
265C24—611no—
266C2×Q8—4881no—
267C2×Q8—2441no—
268C2×D4—41no—
269C2×D4—81no—
270C2×D4—4881no—
271C2×D4—2442no—
272C2×D4—2442no—
273C22×C4—21no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1222no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C2×C4×D6111yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287M16—22no—
288M16—41no—
289M16—1222no—
290M16—2444no—
291M16—2441no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—2444no—
295C2×C8—2441no—
296C2×C8—2441no—
297C4⋊C4—41no—
298C4⋊C4—4881no—
299C4⋊C4—2441no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—81no—
303C22⋊C4—4881no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C42—1221no—
311C42—1221no—
312C42—1221no—
313C42—1221no—
314C42—2442no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—612no—
323C23—1221no—
324C23—1221no—
325C23—2441no—
326C23—2441no—
327C23C22⋊C4×D6111yescharacteristic
328Q8—4882no—
329D4—82no—
330D4—4884no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—1222no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1222no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4#1451980111yescharacteristic
359C2×C4#1451980611yescharacteristic
360C8—42no—
361C8—81no—
362C8—4881no—
363C8—2442no—
364C22—21no—
365C22—21no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—1222no—
374C22—4881no—
375C22—2442no—
376C22—2441no—
377C22—2441no—
378C22#99×D6111yescharacteristic
379C22#1683976011yescharacteristic
380C22#104×D6111yescharacteristic
381C4—21no—
382C4—21no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—1221no—
387C4—1221no—
388C4—4881no—
389C4—2442no—
390C4—2441no—
391C4—2441no—
392C2—21no—
393C2—21no—
394C2—161no—
395C2—2442no—
396C2#2144432011yescharacteristic
397C2#2144746711yescharacteristic
398C2#2144750111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radical#16839670C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61#11765
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #21445556C2semidirect
3. #21444152C2semidirect
4. #21443850C2semidirect
5. #21443848C2semidirect
6. #21443822C2semidirect
7. C61×#1345C2semidirect
199. #1345D61semidirect
226. C61#11765semidirect

Maximal subgroups

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

subgroupindex
#214515092
#214455562
#214441522
#214438502
#214438482
#214438222
C61×#13452
#1176561