Finite Group Databasebeta

← #29583220

Subgroups — #29583220

Order 15616.

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

normal subgroups only

This group has 446 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#21451989C211yesmaximal, characteristic, complemented
2#21446655C211yesmaximal, characteristic
3#21444349C211yesmaximal, characteristic
4#21444334C211yesmaximal, characteristic
5#21443726C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1297C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519691—21no—
10C2×#14519691—21no—
11#16839726C2211yescharacteristic
12#16839704—21no—
13#16839685—21no—
14#16839683—21no—
15#16839674—21no—
16#16839668—21no—
17#16839646—21no—
18#16839625C2211yescharacteristic
19#16839622C2211yescharacteristic
20#16839497—21no—
21#16839497—21no—
22#16839495—21no—
23#16839495—21no—
24C61×#407C2211yescharacteristic
25C4×C22⋊C4×C61C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244Q811yescharacteristic, complemented
29C22×C22⋊D61—21no—
30C2×#11758194—21no—
31#14519751—21no—
32#14519751—21no—
33#14519751—21no—
34#14519751—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61Q811yescharacteristic, complemented
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61D411yescharacteristic
42C2×C22⋊Dic61D411yescharacteristic
43C2×#11758198—21no—
44#14519691—42no—
45#14519691—42no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684D411yescharacteristic
55#14519684D411yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C2×M16×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C42×C61—21no—
61C2×C42×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61—21no—
65#95×C61D411yescharacteristic
66#95×C61D411yescharacteristic
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—81no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×Q811yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—81no—
93C2×Dic122—42no—
94C2×Dic122—81no—
95C2×Dic122—81no—
96M16×C61—81no—
97C2×C8×C61—41no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—42no—
100C22⋊C4×C61—41no—
101C42×C61—81no—
102C42×C61—81no—
103C22⋊Dic61—41no—
104C22⋊Dic61—41no—
105C22⋊Dic61—81no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—81no—
111C4⋊Dic61—81no—
112#11758196—42no—
113#11758196—81no—
114#11758194—81no—
115C2×#92418—41no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61#12011yescharacteristic
121C23×C61C22⋊Q811yescharacteristic
122C23×C61#12411yescharacteristic
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—81no—
127C22×D61—81no—
128C2×C4×C61—22no—
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—41no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—81no—
142C2×C4×C61—81no—
143C2×C4×C61C22⋊Q811yescharacteristic
144C2×C4×C61C22⋊Q811yescharacteristic
145C2×C4×C61#12411yescharacteristic
146C2×C4×C61#12411yescharacteristic
147C22⋊D61—81no—
148C22⋊D61—81no—
149C22⋊D61—81no—
150C22⋊D61—81no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166D244—81no—
167D244—81no—
168Dic122—84no—
169C8×C61—81no—
170#92418—81no—
171#10382—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61#39311yescharacteristic
183C22×C61#45311yescharacteristic
184C22×C61#45411yescharacteristic
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—161no—
189C2×D61—161no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—42no—
195C4×C61—81no—
196C4×C61—82no—
197Dic61—81no—
198Dic61—81no—
199Dic61—81no—
200Dic61—81no—
201Dic61—81no—
202#2665—611no—
203#1964—611no—
204#1510—611no—
205#1507—611no—
206#1305—611no—
207#1297D6111yescharacteristic, complemented
208#1284—611no—
209C2×C61—21no—
210C2×C61—21no—
211C2×C61—41no—
212C2×C61—41no—
213C2×C61#202711yescharacteristic
214C2×C61#203111yescharacteristic
215C2×C61#203211yescharacteristic
216D61—161no—
217C2×#121—611no—
218C2×#99—1221no—
219C2×#99—1221no—
220#407—611no—
221#407C2×D6111yescharacteristic
222#400—1221no—
223#396—1221no—
224#395—1221no—
225#393—1221no—
226#391—1221no—
227#387—1221no—
228#381—611no—
229#380—611no—
230C4×C22⋊C4C2×D6111yescharacteristic
231C4×C22⋊C4C2×D6111yescharacteristic
232#327—1221no—
233#327—1221no—
234#327—1221no—
235#327—1221no—
236C61#1038211yescharacteristic, complemented, Sylow
237C22×Q8—1221no—
238C22×D4—611no—
239C22×D4—1221no—
240C23×C4C22×D6111yescharacteristic
241C2×M16—21no—
242C2×M16—1221no—
243#121—1221no—
244#121—1221no—
245#121—1221no—
246#121—1221no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C42—21no—
259C2×C42—21no—
260#99—2442no—
261#99—2442no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—1221no—
265C22⋊C8—1221no—
266#95—21no—
267#95—611no—
268#95—611no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272#95—1221no—
273#95—1221no—
274#95—1221no—
275#95D24411yescharacteristic
276#95D24411yescharacteristic
277C24—1221no—
278C24D4×D6111yescharacteristic
279C2×Q8—4881no—
280C2×Q8—4881no—
281C2×Q8—2442no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—4881no—
285C2×D4—2441no—
286C2×D4—2441no—
287C2×D4—2441no—
288C2×D4—2441no—
289C2×D4—2441no—
290C2×D4—2441no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4—81no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4C2×D24411yescharacteristic
301C22×C4#1175822211yescharacteristic
302C22×C4#1175822211yescharacteristic
303C22×C4D4×D6111yescharacteristic
304C22×C4#1175822411yescharacteristic
305C22×C4Q8×D6111yescharacteristic
306M16—81no—
307M16—4881no—
308C2×C8—41no—
309C2×C8—2441no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—4881no—
313C4⋊C4—4881no—
314C4⋊C4—4881no—
315C4⋊C4—2442no—
316C22⋊C4—22no—
317C22⋊C4—42no—
318C22⋊C4—41no—
319C22⋊C4—4881no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C42—81no—
325C42—81no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—4881no—
331C23—4881no—
332C23—2441no—
333C23—2441no—
334C23—2441no—
335C23#1451974711yescharacteristic
336C23#1451975511yescharacteristic
337C23#1451976311yescharacteristic
338Q8—4884no—
339D4—4881no—
340D4—4881no—
341D4—4881no—
342D4—4881no—
343D4—4881no—
344D4—4881no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4#1451975511yescharacteristic
376C2×C4#1451975711yescharacteristic
377C2×C4#1451976311yescharacteristic
378C2×C4#1451976511yescharacteristic
379C8—81no—
380C8—4881no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—81no—
390C22—81no—
391C22—9761no—
392C22—9761no—
393C22—4881no—
394C22—4881no—
395C22—4881no—
396C22#1683967511yescharacteristic
397C22#1683993111yescharacteristic
398C22#1683993611yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—81no—
405C4—82no—
406C4—4881no—
407C4—4881no—
408C4—4881no—
409C4—4881no—
410C4—4881no—
411C2—21no—
412C2—21no—
413C2—41no—
414C2—41no—
415C2—9761no—
416C2#2144697411yescharacteristic
417C2#2144699211yescharacteristic
418C2#2144699711yescharacteristic
subgroupG/H
centerC22#16839675
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61#393
prime radicalC2×#14519751C22
hypercenter#1297D61
hypocenterC61#10382
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
1. #21451989C2semidirect
5. #21443726C2semidirect
6. #21443672C2semidirect
7. C61×#1297C2semidirect
28. C22×D244Q8semidirect
37. C2×C4⋊Dic61Q8semidirect
207. #1297D61semidirect
236. C61#10382semidirect

Maximal subgroups

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

subgroupindex
#214519892
#214466552
#214443492
#214443342
#214437262
#214436722
C61×#12972
#1038261