Finite Group Databasebeta

← #29577866

Subgroups — #29577866

Order 15616.

542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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#21454899C211yesmaximal, characteristic, complemented
2#21450729C211yesmaximal, characteristic
3#21445812C211yesmaximal, characteristic, complemented
4#21444245C211yesmaximal, characteristic
5#21444243C211yesmaximal, characteristic
6#21443677C211yesmaximal, characteristic, complemented
7C61×#1286C211yesmaximal, characteristic, complemented
8C2×#14519757—21no—
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11C8×Dic122—22no—
12#16839886—22no—
13#16839815C2211yescharacteristic
14#16839812—22no—
15#16839786C2211yescharacteristic
16C2×#14519695—21no—
17#16839694C412yes—
18#16839680C412yes—
19#16839654—22no—
20#16839619—21no—
21#16839530—21no—
22#16839491—22no—
23#16839489—22no—
24C61×#431C2211yescharacteristic
25C61×#423C2211yescharacteristic
26C61×#382C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758194—21no—
31#14519757—42no—
32#14519757—42no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—22no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196C2×C412yes—
45C2×#11758198—21no—
46C2×#11758198—22no—
47C2×#11758198—22no—
48C2×C4×Dic61D412yes—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52#14519706—24no—
53#14519695—42no—
54C22⋊#92418—21no—
55C4×#92418D412yes—
56C8×Dic61—24no—
57#14519684—22no—
58C2×M16×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65C4×C8×C61D412yes—
66#95×C61—21no—
67#95×C61C2×C412yes—
68C23×D61—21no—
69C22×C4×C61—22no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61C22⋊C412yes—
75C22×Dic61C22⋊C412yes—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—42no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×Dic122—21no—
86C2×Dic122—21no—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×Dic122D812yes—
90C2×Dic122SD1612yes—
91M16×C61—41no—
92M16×C61—41no—
93C2×C8×C61—22no—
94C2×C8×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C42×C61C2×D411yescharacteristic
98C42×C61C2×D411yescharacteristic
99C42×C61#4111yescharacteristic
100C42×C61#4111yescharacteristic
101#11758198—44no—
102#11758198—41no—
103#11758198—41no—
104#11758198—44no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—44no—
110#11758196—22no—
111#11758196—22no—
112C4×Dic61—22no—
113C4×Dic61—22no—
114#11758194—41no—
115#11758194—41no—
116C2×#92418—22no—
117C2×#92418—41no—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—22no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12311yescharacteristic
137C2×C4×C61C2×D811yescharacteristic
138C2×C4×C61C2×SD1611yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61#10214yes—
149D244—22no—
150D244—22no—
151D244—41no—
152D244—41no—
153C4×D61—81no—
154C4×D61—81no—
155C4×D61—81no—
156C4×D61—81no—
157Dic122—22no—
158Dic122—22no—
159Dic122—22no—
160Dic122—22no—
161C8×C61—42no—
162C8×C61—81no—
163#92418—42no—
164#92418—81no—
165#9486—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61#38611yescharacteristic
169C22×C61C2×#10211yescharacteristic
170C22×C61#41611yescharacteristic
171C2×D61—42no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—82no—
183C4×C61#46511yescharacteristic
184C4×C61#46511yescharacteristic
185C4×C61#46611yescharacteristic
186C4×C61#46611yescharacteristic
187Dic61—24no—
188Dic61—42no—
189Dic61—81no—
190#2982—611no—
191#2536—611no—
192#1801—611no—
193#1486—611no—
194#1486—611no—
195#1286—611no—
196#1286D6111yescharacteristic, complemented
197C2×C61—21no—
198C2×C61—21no—
199C2×C61#189111yescharacteristic
200C2×C61#189311yescharacteristic
201C2×C61#191211yescharacteristic
202D61—82no—
203C2×C22⋊Q8—1221no—
204C2×C4×Q8—611no—
205C2×C4×D4—611no—
206C8×Q8—1222no—
207C8×Q8—1222no—
208#431—611no—
209#431—1222no—
210#431C2×D6111yescharacteristic
211#423—611no—
212#423C2×D6111yescharacteristic
213C2×#101—1221no—
214#398—612no—
215#394—612no—
216#388—1222no—
217#382C2×D6111yescharacteristic
218#380—1221no—
219#343—1221no—
220D4⋊C8—1222no—
221D4⋊C8—1222no—
222C61#948611yescharacteristic, complemented, Sylow
223C22×Q8—611no—
224C22×D4—611no—
225C23×C4—1221no—
226C2×M16—21no—
227C2×M16—1221no—
228C22⋊Q8—2442no—
229C22⋊Q8—2442no—
230C4×Q8—1221no—
231C4×Q8—1221no—
232C4×Q8—1221no—
233C4×Q8—1221no—
234C4×D4—1221no—
235C4×D4—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—612no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—1222no—
243C2×C22⋊C4—1222no—
244C2×C22⋊C4—1222no—
245C2×C22⋊C4—1221no—
246C2×C42—612no—
247C2×C42C22×D6111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—1224no—
252C4⋊C8—1221no—
253C4⋊C8—1221no—
254C4⋊C8—1221no—
255#101—2442no—
256C22⋊C8—21no—
257C22⋊C8—1221no—
258C4×C8—612no—
259C4×C8—1224no—
260C4×C8D24412yes—
261#95—21no—
262#95—1222no—
263#95C4×D6112yes—
264C24—1221no—
265C2×Q8—612no—
266C2×Q8—612no—
267C2×Q8—1221no—
268C2×Q8—1221no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—2442no—
274C22×C4—22no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—1221no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4C2×C4×D6111yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287M16—41no—
288M16—41no—
289M16—2441no—
290M16—2441no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—1222no—
294C2×C8—2441no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—1222no—
298C4⋊C4—1222no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—2444no—
304C22⋊C4—2444no—
305C22⋊C4—2444no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42—1222no—
309C42—1222no—
310C42C2×D24411yescharacteristic
311C42#1175822211yescharacteristic
312C42D4×D6111yescharacteristic
313C42#1175822611yescharacteristic
314C23—1222no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23C22⋊C4×D6111yescharacteristic
322Q8—1222no—
323Q8—1222no—
324Q8—1222no—
325Q8—1222no—
326D4—1222no—
327D4—1222no—
328D4—2441no—
329D4—2441no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—614no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2442no—
347C2×C4#1451973911yescharacteristic
348C2×C4C4×D24411yescharacteristic
349C2×C4#1451974711yescharacteristic
350C2×C4#1451975011yescharacteristic
351C2×C4#1451975211yescharacteristic
352C2×C4#1451976211yescharacteristic
353C2×C4D8×D6111yescharacteristic
354C2×C4SD16×D6111yescharacteristic
355C2×C4#1451979811yescharacteristic
356C2×C4#1451980011yescharacteristic
357C8—42no—
358C8—81no—
359C8—4881no—
360C8—2442no—
361C22—21no—
362C22—21no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22—4881no—
367C22—2442no—
368C22—2442no—
369C22—2442no—
370C22#1683964011yescharacteristic
371C22#102×D6111yescharacteristic
372C22#1683975711yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—1224no—
379C4—4881no—
380C4—2442no—
381C4#1683999211yescharacteristic
382C4#1683999411yescharacteristic
383C4#1683999711yescharacteristic
384C4#1683999911yescharacteristic
385C2—21no—
386C2—21no—
387C2—4882no—
388C2#2144623611yescharacteristic
389C2#2144624611yescharacteristic
390C2#2144635511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1286C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1286D61
hypocenterC61#9486
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
1. #21454899C2semidirect
3. #21445812C2semidirect
6. #21443677C2semidirect
7. C61×#1286C2semidirect
196. #1286D61semidirect
222. C61#9486semidirect

Maximal subgroups

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

subgroupindex
#214548992
#214507292
#214458122
#214442452
#214442432
#214436772
C61×#12862
#948661