Finite Group Databasebeta

← #29592189

Subgroups — #29592189

Order 15616.

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

normal subgroups only

This group has 426 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#21447769C211yesmaximal, characteristic, complemented
2#21447764C211yesmaximal, characteristic, complemented
3#21446886C211yesmaximal, characteristic, complemented
4#21443807C211yesmaximal, characteristic, complemented
5#21443804C211yesmaximal, characteristic, complemented
6#21443755C211yesmaximal, characteristic, complemented
7C61×#3197C211yesmaximal, characteristic, complemented
8#16840562C2211yescharacteristic
9#16840273—21no—
10#16840203—21no—
11#16840198—21no—
12#16839778—21no—
13#16839571—21no—
14#16839571—21no—
15#16839544C2211yescharacteristic
16#16839544C2211yescharacteristic
17#16839519C2211yescharacteristic
18C61×#525—21no—
19C61×#485—21no—
20C61×#482—21no—
21C61×#470C2211yescharacteristic
22C61×#469C2211yescharacteristic
23C61×#468—21no—
24C61×#452—21no—
25C61×#449—21no—
26C61×#407C2211yescharacteristic
27C2×#11758222—21no—
28#14519810—41no—
29#14519805—41no—
30#14519799—21no—
31#14519799—21no—
32#14519760—41no—
33#14519756—41no—
34#14519751—41no—
35#14519746—41no—
36C4×C22⋊D61—42no—
37#14519736—21no—
38#14519723—41no—
39#14519721—41no—
40#14519720—41no—
41#14519718—41no—
42#14519717—21no—
43#14519717—21no—
44#14519703—42no—
45C2×#41×C61—21no—
46C23×C4×C61D411yescharacteristic
47C2×Q16×C61D411yescharacteristic, complemented
48C2×SD16×C61—21no—
49C2×D8×C61D411yescharacteristic, complemented
50C2×M16×C61D411yescharacteristic
51C2×M16×C61C2311yescharacteristic
52#123×C61—41no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—21no—
55#121×C61—21no—
56#121×C61—21no—
57#120×C61—41no—
58C4×D4×C61—41no—
59C4×D4×C61—41no—
60#117×C61—21no—
61#107×C61—21no—
62#106×C61D411yescharacteristic, complemented
63#106×C61D411yescharacteristic, complemented
64#103×C61—21no—
65#103×C61—21no—
66#102×C61—21no—
67#102×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70C24×C61D811yescharacteristic
71#41×C61—81no—
72#41×C61—81no—
73C2×Q8×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61D811yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C2×C22⋊D61—42no—
86C2×C22⋊D61—41no—
87#11758222—41no—
88#11758222—41no—
89#11758222—41no—
90#11758222—41no—
91C2×D244—21no—
92C2×C4×D61—41no—
93C2×Dic122—21no—
94Q16×C61—41no—
95SD16×C61—81no—
96D8×C61—41no—
97M16×C61—41no—
98M16×C61—41no—
99C2×C8×C61—21no—
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C42×C61—41no—
112C22⋊Dic61—42no—
113C22⋊Dic61—41no—
114#11758198—42no—
115C4⋊Dic61—41no—
116#11758196—42no—
117C4×Dic61—22no—
118Dic244—21no—
119Dic244—21no—
120D488—21no—
121D488—21no—
122#11758190—41no—
123#11758190—41no—
124#11758185—41no—
125#11758185—41no—
126C23×C61—21no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—81no—
130C23×C61C2×D811yescharacteristic
131C22×D61—41no—
132Q8×C61—41no—
133Q8×C61—41no—
134D4×C61—41no—
135D4×C61—41no—
136D4×C61—82no—
137D4×C61—82no—
138D4×C61—82no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
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—81no—
149C2×C4×C61—82no—
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C22⋊D61—81no—
153C22⋊D61—84no—
154C22⋊D61—81no—
155C2×Dic61—42no—
156C2×Dic61—41no—
157D244—41no—
158D244—41no—
159C4×D61—81no—
160C4×D61—81no—
161Dic122—41no—
162Dic122—41no—
163C8×C61—21no—
164C8×C61—21no—
165C8×C61—41no—
166#12116—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—42no—
172C22×C61—41no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61#44711yescharacteristic
178C2×D61—82no—
179C2×D61—81no—
180C4×C61—21no—
181C4×C61—41no—
182C4×C61—81no—
183C4×C61—81no—
184C4×C61—81no—
185C4×C61#45311yescharacteristic
186C4×C61B(4,𝔽2)11yescharacteristic
187Dic61—82no—
188Dic61—81no—
189#3197D6111yescharacteristic, complemented
190#2191—611no—
191#2190—611no—
192#2010—611no—
193#1340—611no—
194#1339—611no—
195#1320—611no—
196C2×C61—21no—
197C2×C61—41no—
198C2×C61—81no—
199C2×C61—161no—
200C2×C61#159511yescharacteristic
201D61—161no—
202#575—611no—
203#525—21no—
204#525—1221no—
205#510—1221no—
206#509—1221no—
207#485—21no—
208#482—21no—
209#470C2×D6111yescharacteristic
210#469C2×D6111yescharacteristic
211#468—21no—
212#452—21no—
213#449—21no—
214#421—1221no—
215#407C2×D6111yescharacteristic
216#360—1221no—
217#360—1221no—
218#349—611no—
219#349—611no—
220H(3,ℤ/4)—611no—
221C61#1211611yescharacteristic, complemented, Sylow
222C2×#41—21no—
223C2×#41—1221no—
224C23×C4C22⋊D6111yescharacteristic
225#137—2441no—
226AGL(1,ℤ/8)—2441no—
227#135—1221no—
228#135—1221no—
229C2×Q16C22⋊D6111yescharacteristic, complemented
230C2×SD16—21no—
231C2×D8C22⋊D6111yescharacteristic, complemented
232C2×M16C22⋊D6111yescharacteristic
233C2×M16C22×D6111yescharacteristic
234#123—41no—
235#123—2441no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—2441no—
239#121—21no—
240#121—21no—
241#121—2441no—
242#120—41no—
243#120—2441no—
244C4×D4—41no—
245C4×D4—41no—
246C4×D4—2442no—
247#117—21no—
248#117—1221no—
249Q32—2441no—
250SD32—2441no—
251SD32—2441no—
252D16—2441no—
253M32—1221no—
254M32—1221no—
255#107—21no—
256#106C22⋊D6111yescharacteristic, complemented
257#106C22⋊D6111yescharacteristic, complemented
258#104—2442no—
259#103—21no—
260#103—21no—
261#102—21no—
262#102—21no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C24#1175819911yescharacteristic
266#41—81no—
267#41—81no—
268#41—2441no—
269#41—2441no—
270#41—2441no—
271#41—2441no—
272C2×Q8—21no—
273C2×Q8—1221no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—1221no—
279C2×D4—2442no—
280C2×D4—2441no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—2441no—
287C22×C4#1175819911yescharacteristic
288C22×C4C2×C22⋊D6111yescharacteristic
289Q16—41no—
290Q16—1221no—
291Q16—1221no—
292SD16—81no—
293SD16—2441no—
294SD16—2441no—
295D8—41no—
296D8—1221no—
297D8—1221no—
298M16—41no—
299M16—41no—
300C2×C8—21no—
301C2×C8C2×C22⋊D6111yescharacteristic
302C2×C8C2×C22⋊D6111yescharacteristic
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—2441no—
308C4⋊C4—2442no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—2442no—
315C22⋊C4—2442no—
316C22⋊C4—2441no—
317C42—41no—
318C42—1222no—
319C16—2441no—
320C16—2441no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23—81no—
325C23—2441no—
326C23C2×#1175819911yescharacteristic
327Q8—41no—
328Q8—41no—
329Q8—2441no—
330Q8—2441no—
331D4—41no—
332D4—41no—
333D4—82no—
334D4—82no—
335D4—82no—
336D4—4881no—
337D4—4884no—
338D4—4881no—
339D4—2441no—
340D4—2441no—
341C2×C4—21no—
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—81no—
351C2×C4—82no—
352C2×C4—4881no—
353C2×C4—4881no—
354C2×C4—2442no—
355C2×C4—2441no—
356C2×C4#1451974611yescharacteristic
357C2×C4#1451980311yescharacteristic
358C8—21no—
359C8—21no—
360C8—41no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—42no—
366C22—41no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—4882no—
372C22—4881no—
373C22#1683989611yescharacteristic
374C4—21no—
375C4—41no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—4882no—
380C4—4881no—
381C4#1683993011yescharacteristic
382C4#1683994911yescharacteristic
383C2—21no—
384C2—41no—
385C2—81no—
386C2—161no—
387C2—9761no—
388C2#2144473711yescharacteristic
subgroupG/H
centerC2#21444737
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#3197C2
socleC2×C61#1595
hypercenter#3197D61
hypocenterC61#12116
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3197

Complements

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

NH ≅ G/Ntype
1. #21447769C2semidirect
2. #21447764C2semidirect
3. #21446886C2semidirect
4. #21443807C2semidirect
5. #21443804C2semidirect
6. #21443755C2semidirect
7. C61×#3197C2semidirect
47. C2×Q16×C61D4semidirect
49. C2×D8×C61D4semidirect
62. #106×C61D4semidirect
63. #106×C61D4semidirect
189. #3197D61semidirect
221. C61#12116semidirect
229. C2×Q16C22⋊D61semidirect
231. C2×D8C22⋊D61semidirect
256. #106C22⋊D61semidirect
257. #106C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214477692
#214477642
#214468862
#214438072
#214438042
#214437552
C61×#31972
#1211661