Finite Group Databasebeta

← #29592867

Subgroups — #29592867

Order 15616.

510 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 59 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#21447172C211yesmaximal, characteristic, complemented
2#21444843C211yesmaximal, characteristic, complemented
3#21444741C211yesmaximal, characteristic
4#21443843C211yesmaximal, characteristic, complemented
5#21443816C211yesmaximal, characteristic
6#21443767C211yesmaximal, characteristic, complemented
7C61×#2455C211yesmaximal, characteristic
8#16840388C2211yescharacteristic
9#16840097—21no—
10#16839913—21no—
11#16839635—21no—
12#16839529C2211yescharacteristic
13#16839528—21no—
14#16839498—21no—
15#16839498—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C2×#123×C61—21no—
19C2×C4×D4×C61—21no—
20C61×#399C2211yescharacteristic
21C61×#394—21no—
22C61×#392C2211yescharacteristic
23C61×#389—21no—
24C61×#388—21no—
25C61×#385—21no—
26C61×#385C2211yescharacteristic
27C2×#11758200—41no—
28#14519756—21no—
29#14519756—21no—
30#14519754—41no—
31#14519754—41no—
32C2×#11758196—41no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35#14519710—41no—
36#14519700—41no—
37#14519698—41no—
38C22⋊#92418—21no—
39C22⋊#92418—21no—
40#14519684—41no—
41C22×D4×C61—21no—
42C22×D4×C61D411yescharacteristic
43C23×C4×C61—21no—
44C23×C4×C61D411yescharacteristic
45#123×C61—44no—
46C4×D4×C61—44no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61D411yescharacteristic
58C2×C22⋊C4×C61C2311yescharacteristic
59C2×C42×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61D411yescharacteristic
63#95×C61D411yescharacteristic
64C24×C61—21no—
65C24×C61C2×D411yescharacteristic
66C2×D4×C61—42no—
67C2×D4×C61—41no—
68C2×D4×C61—42no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—42no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—42no—
78C22×C4×C61—42no—
79C22×C4×C61—41no—
80C22×C4×C61—42no—
81C22×C4×C61—81no—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—41no—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—42no—
91C4⋊C4×C61—42no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—24no—
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—42no—
99C22⋊C4×C61—42no—
100C22⋊C4×C61—42no—
101C22⋊C4×C61—42no—
102C42×C61—42no—
103C22⋊Dic61—22no—
104C22⋊Dic61—41no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107#11758200—82no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110#11758196—41no—
111#11758196—41no—
112#11758196—82no—
113C2×#92418—41no—
114C2×#92418—41no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—22no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61#12011yescharacteristic
127C23×C61#13511yescharacteristic
128C23×C61#13711yescharacteristic
129D4×C61—42no—
130D4×C61—44no—
131D4×C61—44no—
132D4×C61—81no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
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—42no—
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×C61—81no—
154C2×C4×C61—84no—
155C2×Dic61—42no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—81no—
159C2×Dic61—81no—
160C2×Dic61—81no—
161C2×Dic61—81no—
162Dic122—81no—
163Dic122—81no—
164#92418—81no—
165#92418—81no—
166#12226—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—42no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61#45211yescharacteristic
184C22×C61#45611yescharacteristic
185C22×C61B(4,𝔽2)11yescharacteristic
186C4×C61—42no—
187C4×C61—42no—
188C4×C61—41no—
189C4×C61—42no—
190C4×C61—41no—
191C4×C61—81no—
192C4×C61—81no—
193Dic61—82no—
194Dic61—81no—
195Dic61—81no—
196#2455D6111yescharacteristic
197#2062—611no—
198#1614—611no—
199#1596—611no—
200#1352—611no—
201#1343—611no—
202#1326—611no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—41no—
206C2×C61—41no—
207C2×C61—82no—
208C2×C61#160311yescharacteristic
209C2×C61#219611yescharacteristic
210C2×C61#219811yescharacteristic
211#543—611no—
212C2×#123—21no—
213C2×C4×D4—21no—
214#484—1221no—
215#450—1221no—
216#399C2×D6111yescharacteristic
217#394—21no—
218#392C2×D6111yescharacteristic
219#389—21no—
220#388—21no—
221#385—21no—
222#385—1221no—
223#385C2×D6111yescharacteristic
224#342—611no—
225#342—1221no—
226#328—1221no—
227#328—1221no—
228#323—611no—
229#323—611no—
230C61#1222611yescharacteristic, complemented, Sylow
231C22×D4—21no—
232C22×D4C22⋊D6111yescharacteristic
233C23×C4—21no—
234C23×C4C22⋊D6111yescharacteristic
235C2×SD16—2441no—
236#123—44no—
237C22⋊Q8—1221no—
238C22⋊Q8—1221no—
239C22⋊Q8—2441no—
240C22⋊Q8—2441no—
241C4×D4—44no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—2441no—
247C2×C4⋊C4C22⋊D6111yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4C22⋊D6111yescharacteristic
256C2×C22⋊C4C22×D6111yescharacteristic
257C2×C42—21no—
258#107—2441no—
259#103—2441no—
260#102—2441no—
261C22⋊C8—1221no—
262C22⋊C8—1221no—
263#95—21no—
264#95—21no—
265#95—2441no—
266#95C22⋊D6111yescharacteristic
267#95C22⋊D6111yescharacteristic
268C24—21no—
269C24C2×C22⋊D6111yescharacteristic
270C2×Q8—1221no—
271C2×Q8—1221no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—42no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—81no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—2441no—
291C22×C4C2×C22⋊D6111yescharacteristic
292C22×C4C2×C22⋊D6111yescharacteristic
293SD16—4882no—
294C2×C8—2441no—
295C2×C8—2441no—
296C4⋊C4—41no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—4882no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—24no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—1222no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C42—42no—
319C23—21no—
320C23—21no—
321C23—22no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23#1451974611yescharacteristic
331C23#1451979711yescharacteristic
332C23#1451980711yescharacteristic
333Q8—4881no—
334Q8—4881no—
335D4—42no—
336D4—44no—
337D4—44no—
338D4—81no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—84no—
361C2×C4—4881no—
362C2×C4—4881no—
363C2×C4—4881no—
364C2×C4—4881no—
365C2×C4—2442no—
366C2×C4—2441no—
367C2×C4—2441no—
368C8—4881no—
369C8—4881no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—42no—
377C22—42no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#1683992411yescharacteristic
387C22#1683994511yescharacteristic
388C22#1683994911yescharacteristic
389C4—42no—
390C4—42no—
391C4—41no—
392C4—42no—
393C4—41no—
394C4—81no—
395C4—81no—
396C4—4882no—
397C4—4881no—
398C4—4881no—
399C2—21no—
400C2—21no—
401C2—41no—
402C2—41no—
403C2—82no—
404C2#2144478211yescharacteristic
405C2#2144780311yescharacteristic
406C2#2144781511yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2455C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#392C22
hypercenter#2455D61
hypocenterC61#12226
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2455

Complements

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

NH ≅ G/Ntype
1. #21447172C2semidirect
2. #21444843C2semidirect
4. #21443843C2semidirect
6. #21443767C2semidirect
230. C61#12226semidirect

Maximal subgroups

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

subgroupindex
#214471722
#214448432
#214447412
#214438432
#214438162
#214437672
C61×#24552
#1222661