Finite Group Databasebeta

← #29590585

Subgroups — #29590585

Order 15616.

480 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 73 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#21450810C211yesmaximal, characteristic
2#21445606C211yesmaximal, characteristic
3#21444154C211yesmaximal, characteristic
4#21443820C211yesmaximal, characteristic, complemented
5#21443819C211yesmaximal, characteristic, complemented
6#21443818C211yesmaximal, characteristic, complemented
7C61×#1344C211yesmaximal, characteristic, complemented
8C2×#14519776C411yescharacteristic, complemented
9C2×#14519763—21no—
10C2×#14519737C2211yescharacteristic
11C2×#14519691—21no—
12#16839724—21no—
13#16839689C411yescharacteristic, complemented
14#16839688C411yescharacteristic, complemented
15#16839687C2211yescharacteristic
16#16839666—21no—
17#16839621—21no—
18#16839620—21no—
19#16839613C411yescharacteristic, complemented
20C22⋊C4×Dic61—21no—
21#16839529C2211yescharacteristic
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×Dic122—21no—
28C22×C22⋊D61D411yescharacteristic
29C23×Dic61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—41no—
32#14519776—41no—
33#14519776—41no—
34#14519763—42no—
35#14519763—42no—
36#14519737—41no—
37#14519737—41no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×C4×Dic61—21no—
48C2×C4×Dic61—41no—
49C2×C4×Dic61C2×C411yescharacteristic
50#14519691—24no—
51C22⋊#92418—21no—
52#14519689—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—41no—
57#14519684C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63#95×C61—21no—
64#95×C61C2×C411yescharacteristic
65C24×C61C2×D411yescharacteristic
66C23×D61C22⋊C411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—22no—
75C2×C22⋊D61—41no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—42no—
81C22×Dic61—41no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—42no—
88C2×Dic122—42no—
89C2×Dic122—42no—
90C2×Dic122—42no—
91C2×C8×C61—41no—
92C4⋊C4×C61—41no—
93C22⋊C4×C61—22no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊Dic61—22no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102#11758198—41no—
103#11758198—42no—
104#11758198—42no—
105C4⋊Dic61—41no—
106#11758196—41no—
107#11758196—42no—
108#11758196—41no—
109#11758196—41no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—42no—
113C4×Dic61—82no—
114C2×#92418—41no—
115#11758189—82no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61C2×C22⋊C411yescharacteristic
121C23×C61AGL(1,ℤ/8)11yescharacteristic
122C23×C61AGL(1,ℤ/8)11yescharacteristic
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—41no—
127C22×D61—41no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C22⋊D61—42no—
142C22⋊D61—42no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61—21no—
147C2×Dic61—42no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—42no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—81no—
157C2×Dic61—81no—
158C2×Dic61—81no—
159C2×Dic61#9911yescharacteristic
160C2×Dic61#9911yescharacteristic
161C2×Dic61#10412yes—
162C4×D61—42no—
163C4×D61—81no—
164Dic122—84no—
165C8×C61—81no—
166#92418—81no—
167#11777—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—81no—
177C22×C61C2×#9911yescharacteristic
178C22×C61#41811yescharacteristic
179C22×C61C2×#10411yescharacteristic
180C2×D61—42no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—81no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—81no—
188C4×C61—82no—
189C4×C61—81no—
190Dic61—21no—
191Dic61—22no—
192Dic61—41no—
193Dic61—81no—
194Dic61—82no—
195Dic61—81no—
196Dic61#35412yes—
197#2547—611no—
198C4×#99—611no—
199#1465—611no—
200#1344—611no—
201#1344—611no—
202#1344—611no—
203#1344D6111yescharacteristic, complemented
204C2×C61—21no—
205C2×C61—21no—
206C2×C61—41no—
207C2×C61—41no—
208C2×C61#150711yescharacteristic
209C2×C61#212311yescharacteristic
210C2×C61C2×#35411yescharacteristic
211D61—81no—
212C2×C4⋊Q8—611no—
213C2×#124—1221no—
214C2×C4×D4—611no—
215C2×#99—1221no—
216#407—1221no—
217#397—611no—
218#397—611no—
219#397—611no—
220#397C2×D6111yescharacteristic
221#391—1221no—
222#380—1221no—
223#380—1221no—
224C4×C4⋊C4—611no—
225C4×C22⋊C4—1221no—
226#342—611no—
227#342C2×D6111yescharacteristic
228#324—1221no—
229#323—611no—
230#323C2×D6111yescharacteristic
231C61#1177711yescharacteristic, complemented, Sylow
232C22×Q8—1221no—
233C22×D4—611no—
234C23×C4—611no—
235C23×C4—611no—
236C2×M16—2441no—
237C4⋊Q8—2441no—
238C4⋊Q8—2441no—
239#124—2442no—
240#124—2442no—
241C4×D4—2441no—
242C4×D4—2441no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4C4×D6111yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—611no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4C22×D6111yescharacteristic
256C2×C42—611no—
257C2×C42—1221no—
258C2×C42—2441no—
259#99—1224no—
260C22⋊C8—21no—
261C22⋊C8—1221no—
262C22⋊C8—2441no—
263#95—21no—
264#95—611no—
265#95—1221no—
266#95—1221no—
267#95—1221no—
268#95—2441no—
269#95C4×D6111yescharacteristic
270C24—611no—
271C24D4×D6111yescharacteristic
272C2×Q8—2442no—
273C2×Q8—2442no—
274C2×Q8—2442no—
275C2×D4—1222no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—2441no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—2442no—
292C22×C4—2442no—
293C22×C4—2441no—
294C22×C4C2×C4×D6111yescharacteristic
295C22×C4D4×D6111yescharacteristic
296M16—4882no—
297C2×C8—41no—
298C2×C8—2441no—
299C4⋊C4—41no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2442no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—1222no—
311C22⋊C4—2441no—
312C22⋊C4—2442no—
313C22⋊C4—2442no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C42—1221no—
318C42—1221no—
319C42—4882no—
320C42—2442no—
321C23—21no—
322C23—21no—
323C23—41no—
324C23—41no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23—2441no—
329C23—2441no—
330C23C22⋊C4×D6111yescharacteristic
331C23#1451980111yescharacteristic
332C23#1451980411yescharacteristic
333Q8—4884no—
334D4—2442no—
335D4—2442no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—612no—
352C2×C4—1222no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—4881no—
357C2×C4—4881no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C8—81no—
371C8—4881no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—4881no—
382C22—2442no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22#99×D6111yescharacteristic
387C22#1683976511yescharacteristic
388C22#104×D6111yescharacteristic
389C4—41no—
390C4—41no—
391C4—81no—
392C4—82no—
393C4—81no—
394C4—612no—
395C4—1221no—
396C4—1222no—
397C4—4881no—
398C4—4882no—
399C4—4881no—
400C4—2441no—
401C2—21no—
402C2—21no—
403C2—41no—
404C2—41no—
405C2—4881no—
406C2#2144433311yescharacteristic
407C2#2144747111yescharacteristic
408C2#354×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11777
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #21443820C2semidirect
5. #21443819C2semidirect
6. #21443818C2semidirect
7. C61×#1344C2semidirect
8. C2×#14519776C4semidirect
13. #16839689C4semidirect
14. #16839688C4semidirect
19. #16839613C4semidirect
203. #1344D61semidirect
231. C61#11777semidirect

Maximal subgroups

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

subgroupindex
#214508102
#214456062
#214441542
#214438202
#214438192
#214438182
C61×#13442
#1177761