Finite Group Databasebeta

← #29583214

Subgroups — #29583214

Order 15616.

446 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 77 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#21446654C211yesmaximal, characteristic
2#21444347C211yesmaximal, characteristic
3#21444334C211yesmaximal, characteristic
4#21443725C211yesmaximal, characteristic, complemented
5#21443705C211yesmaximal, characteristic, complemented
6#21443671C211yesmaximal, characteristic, complemented
7C61×#2665C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519691—21no—
10C2×#14519691—21no—
11#16839726C2211yescharacteristic
12#16839726C2211yescharacteristic
13C4×C22⋊Dic61C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839495—21no—
17#16839495—21no—
18C61×#400—21no—
19C61×#396—21no—
20C61×#395—21no—
21C61×#393—21no—
22C61×#391—21no—
23C61×#387—21no—
24C61×#381C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×D244Q811yescharacteristic, complemented
28C22×C22⋊D61—21no—
29C2×#11758194—21no—
30C2×#11758194—21no—
31#14519751—21no—
32#14519751—21no—
33#14519751—21no—
34#14519751—21no—
35C2×C4⋊Dic61Q811yescharacteristic, complemented
36C2×C22⋊Dic61—21no—
37C2×#11758198—21no—
38C2×C4×Dic61—21no—
39#14519691—42no—
40#14519691—42no—
41C22⋊#92418—21no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22⋊#92418—21no—
45#14519684—21no—
46C22×Q8×C61—21no—
47C23×C4×C61C2311yescharacteristic
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61D411yescharacteristic
56C2×C42×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65#95×C61D411yescharacteristic
66#95×C61D411yescharacteristic
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C2×Q8×C61—42no—
70C2×Q8×C61—81no—
71C2×Q8×C61—81no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—81no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×Q811yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C22×Dic61—21no—
92C22×Dic61—41no—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—81no—
96C4⋊C4×C61—42no—
97C4⋊C4×C61—81no—
98C4⋊C4×C61—81no—
99C4⋊C4×C61—81no—
100C22⋊C4×C61—42no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—81no—
104C42×C61—81no—
105C22⋊Dic61—22no—
106C22⋊Dic61—41no—
107#11758198—41no—
108#11758198—41no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4×Dic61—81no—
112#11758194—81no—
113#11758194—81no—
114C2×#92418—41no—
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—
128Q8×C61—84no—
129C2×C4×C61—22no—
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—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61C22⋊Q811yescharacteristic
154C2×C4×C61C22⋊Q811yescharacteristic
155C2×C4×C61#12411yescharacteristic
156C2×C4×C61#12411yescharacteristic
157C22⋊D61—81no—
158C22⋊D61—81no—
159C22⋊D61—81no—
160C22⋊D61—81no—
161C2×Dic61—42no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167D244—81no—
168D244—81no—
169#92418—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—81no—
197C4×C61—81no—
198C4×C61—81no—
199C4×C61—81no—
200Dic61—82no—
201Dic61—81no—
202#2665D6111yescharacteristic, complemented
203#1964—611no—
204#1510—611no—
205#1507—611no—
206#1305—611no—
207#1297—611no—
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#407—611no—
222#400—21no—
223#396—21no—
224#395—21no—
225#393—21no—
226#391—21no—
227#387—21no—
228#381C2×D6111yescharacteristic
229#380C2×D6111yescharacteristic
230C4×C22⋊C4—611no—
231C4×C22⋊C4C2×D6111yescharacteristic
232#327—1221no—
233#327—1221no—
234#327—1221no—
235#327—1221no—
236C61#1038211yescharacteristic, complemented, Sylow
237C22×Q8—21no—
238C22×D4—611no—
239C22×D4—1221no—
240C23×C4C22×D6111yescharacteristic
241C2×M16—1221no—
242C2×M16—1221no—
243#121—1221no—
244#121—1221no—
245#121—1221no—
246#121—1221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—611no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4C22⋊D6111yescharacteristic
257C2×C22⋊C4C22⋊D6111yescharacteristic
258C2×C42—21no—
259C2×C42—1221no—
260#99—2442no—
261#99—2442no—
262C22⋊C8—1221no—
263C22⋊C8—1221no—
264C22⋊C8—1221no—
265C22⋊C8—1221no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—1221no—
273#95C22⋊D6111yescharacteristic
274#95C22⋊D6111yescharacteristic
275#95C22⋊D6111yescharacteristic
276#95C22⋊D6111yescharacteristic
277C24—1221no—
278C24C2×C22⋊D6111yescharacteristic
279C2×Q8—42no—
280C2×Q8—81no—
281C2×Q8—81no—
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—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—81no—
298C22×C4—1221no—
299C22×C4—2441no—
300C22×C4Q8×D6111yescharacteristic
301C22×C4#1175822611yescharacteristic
302C22×C4#1175822611yescharacteristic
303C22×C4#1175822611yescharacteristic
304C22×C4C2×C22⋊D6111yescharacteristic
305C22×C4C2×C22⋊D6111yescharacteristic
306M16—4881no—
307M16—4881no—
308C2×C8—2441no—
309C2×C8—2441no—
310C4⋊C4—42no—
311C4⋊C4—81no—
312C4⋊C4—81no—
313C4⋊C4—81no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C22⋊C4—42no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—81no—
320C22⋊C4—1222no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C42—81no—
325C42—4881no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—4881no—
331C23—4881no—
332C23—2441no—
333C23—2441no—
334C23—2441no—
335C23#1451974611yescharacteristic
336C23#1451975311yescharacteristic
337C23#1451976611yescharacteristic
338Q8—84no—
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—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—4881no—
370C2×C4—4881no—
371C2×C4—2442no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4#1451975311yescharacteristic
376C2×C4#1451975311yescharacteristic
377C2×C4#1451976611yescharacteristic
378C2×C4#1451976611yescharacteristic
379C8—4881no—
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#1683967311yescharacteristic
397C22#1683993011yescharacteristic
398C22#1683993511yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—4882no—
410C4—4881no—
411C2—21no—
412C2—21no—
413C2—41no—
414C2—41no—
415C2—9761no—
416C2#2144697211yescharacteristic
417C2#2144698811yescharacteristic
418C2#2144699511yescharacteristic
subgroupG/H
centerC22#16839673
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2665C2
socleC22×C61#393
prime radicalC2×#14519751C22
hypercenter#2665D61
hypocenterC61#10382
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2665

Complements

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

NH ≅ G/Ntype
4. #21443725C2semidirect
5. #21443705C2semidirect
6. #21443671C2semidirect
7. C61×#2665C2semidirect
27. C22×D244Q8semidirect
35. C2×C4⋊Dic61Q8semidirect
202. #2665D61semidirect
236. C61#10382semidirect

Maximal subgroups

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

subgroupindex
#214466542
#214443472
#214443342
#214437252
#214437052
#214436712
C61×#26652
#1038261