Finite Group Databasebeta

← #29569006

Subgroups — #29569006

Order 15616.

480 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 81 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#21453763C211yesmaximal, characteristic
2#21446957C211yesmaximal, characteristic, complemented
3#21446952C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic, complemented
5#21443644C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2016C211yesmaximal, characteristic, complemented
8C2×#14519700—21no—
9C2×#14519697—21no—
10#16839704—21no—
11#16839675—21no—
12#16839673—21no—
13#16839668C2211yescharacteristic
14#16839664C2211yescharacteristic
15#16839640—21no—
16#16839636—21no—
17#16839633—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C22×Q16×C61—21no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×#103×C61—21no—
25C61×#391C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31C22×#92418—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40#14519700—42no—
41#14519697—42no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C22×Q8×C61—21no—
48C22×Q8×C61D411yescharacteristic
49C2×Q16×C61—42no—
50C2×Q16×C61—42no—
51C2×Q16×C61—42no—
52C22×C8×C61—21no—
53C4⋊Q8×C61—42no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58#103×C61—42no—
59#95×C61—21no—
60#95×C61—21no—
61C23×D61—21no—
62C2×Q8×C61—22no—
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—41no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C2×D244—21no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244Q1612yescomplemented
85C2×C4×D61—81no—
86C2×C4×D61—81no—
87C2×C4×D61—81no—
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92Q16×C61—48no—
93C2×C8×C61—22no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61—41no—
102#11758198—41no—
103#11758198—41no—
104#11758198—41no—
105#11758198—41no—
106#11758198—81no—
107#11758198—81no—
108#11758198—81no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111#11758196—81no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C23×C61#12011yescharacteristic
119C22×D61—22no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126Q8×C61—42no—
127Q8×C61—42no—
128Q8×C61—42no—
129Q8×C61—81no—
130Q8×C61—81no—
131Q8×C61—81no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
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—42no—
145C2×C4×C61—81no—
146C2×C4×C61—81no—
147C2×C4×C61C2×Q1611yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61#13711yescharacteristic
152C2×C4×C61#13711yescharacteristic
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—
162D244—42no—
163D244—81no—
164C4×D61—84no—
165Dic122—42no—
166Dic122—81no—
167C8×C61—42no—
168#92418—81no—
169#92418—81no—
170#7782—611nomaximal, Sylow
171C22×C61#44911yescharacteristic
172C22×C61#45111yescharacteristic
173C22×C61#45211yescharacteristic
174C22×C61#45311yescharacteristic
175C22×C61#45511yescharacteristic
176C22×C61#45511yescharacteristic
177C22×C61B(4,𝔽2)11yescharacteristic
178C2×D61—42no—
179C2×D61—42no—
180C2×D61—42no—
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—81no—
192C4×C61—82no—
193C4×C61—81no—
194Dic61—81no—
195Dic61—81no—
196Dic61—81no—
197#2804—611no—
198#2024—611no—
199#2023—611no—
200#2016D6111yescharacteristic, complemented
201#1272—611no—
202#1272—611no—
203#1270—611no—
204C2×C61#160011yescharacteristic
205C2×C61#160211yescharacteristic
206C2×C61#160611yescharacteristic
207C2×C61#163211yescharacteristic
208C2×C61#164011yescharacteristic
209C2×C61#164411yescharacteristic
210C2×C61#165911yescharacteristic
211D61—82no—
212C22×Q16—21no—
213C2×C4⋊Q8C2×D6111yescharacteristic
214C2×#103—21no—
215C2×#103—1221no—
216C2×#102—1221no—
217#400—1221no—
218#393—1221no—
219#393—1221no—
220#391—611no—
221#391C2×D6111yescharacteristic
222#390—611no—
223#386—1221no—
224#385—1221no—
225#385—1221no—
226#340—1221no—
227#340—1221no—
228#336—611no—
229#336—611no—
230#336C2×D6111yescharacteristic
231C61#778211yescharacteristic, complemented, Sylow
232C22×Q8—21no—
233C22×Q8—611no—
234C22×Q8C22⋊D6111yescharacteristic
235C22×D4—611no—
236C23×C4—1221no—
237C2×Q16—42no—
238C2×Q16—42no—
239C2×Q16—42no—
240C22×C8—21no—
241C22×C8—1221no—
242C22×C8—1221no—
243C4⋊Q8—42no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4C22⋊D6111yescharacteristic
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C42C22×D6111yescharacteristic
256#103—42no—
257#103—2442no—
258#102—2442no—
259#95—21no—
260#95—21no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266C24—1221no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—1221no—
278C2×Q8—1221no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×D4—612no—
282C2×D4—1221no—
283C2×D4—2441no—
284C2×D4—2441no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—4881no—
292C22×C4—4881no—
293C22×C4—4881no—
294C22×C4D4×D6111yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C22×C4C2×C22⋊D6111yescharacteristic
297Q16—48no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—2441no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8—2441no—
305C2×C8—2441no—
306C2×C8—2441no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—4881no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C22⋊C4—4881no—
316C22⋊C4—4881no—
317C22⋊C4—4881no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C42—41no—
323C23—1222no—
324C23—2441no—
325C23—2441no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23—2441no—
330C23#1451974511yescharacteristic
331Q8—42no—
332Q8—42no—
333Q8—42no—
334Q8—81no—
335Q8—81no—
336Q8—81no—
337Q8—4881no—
338Q8—2442no—
339D4—4881no—
340D4—2442no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—4884no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4Q16×D6111yescharacteristic
367C2×C4#1451979711yescharacteristic
368C2×C4#1451980011yescharacteristic
369C2×C4#1451980311yescharacteristic
370C2×C4#1451980911yescharacteristic
371C2×C4#1451980911yescharacteristic
372C8—42no—
373C8—4881no—
374C8—4881no—
375C22—4881no—
376C22—4881no—
377C22—4881no—
378C22—4881no—
379C22—2442no—
380C22—2442no—
381C22—2442no—
382C22#1683990511yescharacteristic
383C22#1683991611yescharacteristic
384C22#1683992311yescharacteristic
385C22#1683992911yescharacteristic
386C22#1683993811yescharacteristic
387C22#1683993811yescharacteristic
388C22#1683994811yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—81no—
396C4—81no—
397C4—82no—
398C4—4881no—
399C4—4881no—
400C4—4881no—
401C2—4882no—
402C2#2144476311yescharacteristic
403C2#2144477411yescharacteristic
404C2#2144479811yescharacteristic
405C2#2144495011yescharacteristic
406C2#2144500311yescharacteristic
407C2#2144503111yescharacteristic
408C2#2144512311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2016C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2016D61
hypocenterC61#7782
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2016

Complements

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

NH ≅ G/Ntype
2. #21446957C2semidirect
4. #21443645C2semidirect
5. #21443644C2semidirect
7. C61×#2016C2semidirect
84. C2×D244Q16semidirect
200. #2016D61semidirect
231. C61#7782semidirect

Maximal subgroups

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

subgroupindex
#214537632
#214469572
#214469522
#214436452
#214436442
#214436392
C61×#20162
#778261