Finite Group Databasebeta

← #29592121

Subgroups — #29592121

Order 15616.

480 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 67 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#21447747C211yesmaximal, characteristic, complemented
2#21447730C211yesmaximal, characteristic, complemented
3#21446817C211yesmaximal, characteristic, complemented
4#21443831C211yesmaximal, characteristic, complemented
5#21443828C211yesmaximal, characteristic, complemented
6#21443743C211yesmaximal, characteristic, complemented
7C61×#3191C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C2×#14519751—21no—
10C2×#14519720—21no—
11C2×#14519718—21no—
12C2×#14519699—21no—
13#16839562—21no—
14#16839562—21no—
15C22⋊#11758185C2211yescharacteristic
16C22⋊#11758185C2211yescharacteristic
17#16839525C2211yescharacteristic
18C61×#525—21no—
19C61×#485—21no—
20C61×#482—21no—
21C61×#467C2211yescharacteristic
22C61×#466C2211yescharacteristic
23C61×#465—21no—
24C61×#452—21no—
25C61×#449—21no—
26C2×C22⋊C8×C61C2211yescharacteristic
27C22×D244—21no—
28C22×C22⋊D61—41no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—42no—
32#14519751—42no—
33#14519751—42no—
34C2×C4⋊Dic61—21no—
35C2×#11758198—41no—
36#14519720—42no—
37#14519718—42no—
38C2×#11758185—21no—
39C2×#11758185—21no—
40#14519699—42no—
41C2×#41×C61—21no—
42C23×C4×C61D411yescharacteristic
43C2×Q16×C61D411yescharacteristic, complemented
44C2×SD16×C61—21no—
45C2×D8×C61D411yescharacteristic, complemented
46C22×C8×C61D411yescharacteristic
47C22×C8×C61C2311yescharacteristic
48#123×C61—41no—
49C22⋊Q8×C61—21no—
50C22⋊Q8×C61—21no—
51#121×C61—21no—
52#121×C61—21no—
53#120×C61—41no—
54C4×D4×C61—41no—
55C4×D4×C61—41no—
56#117×C61—21no—
57#107×C61D411yescharacteristic, complemented
58#107×C61D411yescharacteristic, complemented
59#106×C61—21no—
60#103×C61—21no—
61#103×C61—21no—
62#102×C61—21no—
63#102×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C24×C61D811yescharacteristic
67C23×D61—41no—
68#41×C61—81no—
69#41×C61—81no—
70C2×Q8×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61D811yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C2×C22⋊D61—44no—
83C2×C22⋊D61—82no—
84C2×C22⋊D61—82no—
85C22×Dic61—41no—
86C2×D244—22no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92Q16×C61—41no—
93SD16×C61—81no—
94D8×C61—41no—
95C2×C8×C61—21no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C42×C61—41no—
110#11758198—44no—
111C4⋊Dic61—22no—
112C4⋊Dic61—41no—
113D488—22no—
114D488—22no—
115D488—41no—
116D488—41no—
117#11758185—41no—
118#11758185—41no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61C2×D811yescharacteristic
126C22×D61—42no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61—81no—
132C22×D61—81no—
133Q8×C61—41no—
134Q8×C61—41no—
135D4×C61—41no—
136D4×C61—41no—
137D4×C61—82no—
138D4×C61—82no—
139D4×C61—81no—
140D4×C61—81no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
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—81no—
151C2×C4×C61—82no—
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C22⋊D61—88no—
155C2×Dic61—42no—
156C2×Dic61—81no—
157C2×Dic61—81no—
158D244—42no—
159D244—42no—
160D244—81no—
161D244—81no—
162C8×C61—21no—
163C8×C61—21no—
164C8×C61—41no—
165#12104—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—42no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61#44711yescharacteristic
177C22×C61#50811yescharacteristic
178C22×C61#50911yescharacteristic
179C2×D61—82no—
180C2×D61—82no—
181C2×D61—82no—
182C2×D61—161no—
183C2×D61—161no—
184C2×D61—161no—
185C2×D61—161no—
186C4×C61—21no—
187C4×C61—41no—
188C4×C61—81no—
189C4×C61—81no—
190C4×C61—81no—
191C4×C61#45311yescharacteristic
192C4×C61B(4,𝔽2)11yescharacteristic
193Dic61—82no—
194#3191D6111yescharacteristic, complemented
195#2187—611no—
196#2184—611no—
197#1999—611no—
198#1348—611no—
199#1347—611no—
200#1314—611no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—81no—
204C2×C61—161no—
205C2×C61#159511yescharacteristic
206C2×C61#218611yescharacteristic
207C2×C61#219011yescharacteristic
208D61—162no—
209C22×D8—611no—
210#525—21no—
211C2×#121—1221no—
212C2×SD32—1221no—
213C2×D16—1221no—
214#485—21no—
215#482—21no—
216#467C2×D6111yescharacteristic
217#466C2×D6111yescharacteristic
218#465—21no—
219#452—21no—
220#449—21no—
221C2×#102—1221no—
222C2×C22⋊C8C2×D6111yescharacteristic
223#357—1221no—
224#357—1221no—
225C22⋊C16—611no—
226C22⋊C16—611no—
227#340—611no—
228C61#1210411yescharacteristic, complemented, Sylow
229C2×#41—21no—
230C22×D4—1221no—
231C22×D4—2441no—
232C23×C4C22⋊D6111yescharacteristic
233C2×Q16C22⋊D6111yescharacteristic, complemented
234C2×SD16—21no—
235C2×D8—1221no—
236C2×D8—1221no—
237C2×D8—2442no—
238C2×D8C22⋊D6111yescharacteristic, complemented
239C22×C8C22⋊D6111yescharacteristic
240C22×C8C22×D6111yescharacteristic
241#123—41no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244#121—21no—
245#121—21no—
246#121—2442no—
247#121—2442no—
248#120—41no—
249C4×D4—41no—
250C4×D4—41no—
251#117—21no—
252C2×C4⋊C4—1221no—
253C2×C22⋊C4—2441no—
254SD32—2442no—
255D16—2442no—
256C2×C16—1221no—
257C2×C16—1221no—
258#107C22⋊D6111yescharacteristic, complemented
259#107C22⋊D6111yescharacteristic, complemented
260#106—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264#102—21no—
265#102—2442no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C24—2441no—
269C24#1175819911yescharacteristic
270#41—81no—
271#41—81no—
272C2×Q8—21no—
273C2×D4—21no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—1222no—
278C2×D4—4882no—
279C2×D4—4882no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2444no—
284C2×D4—2441no—
285C2×D4—2441no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—2441no—
292C22×C4#1175819911yescharacteristic
293C22×C4C2×C22⋊D6111yescharacteristic
294Q16—41no—
295SD16—81no—
296D8—41no—
297D8—1222no—
298D8—1222no—
299D8—2441no—
300D8—2441no—
301C2×C8—21no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8C2×C22⋊D6111yescharacteristic
305C2×C8C2×C22⋊D6111yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—1222no—
311C4⋊C4—2441no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—2444no—
318C42—41no—
319C16—2441no—
320C16—2441no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—4881no—
328C23—4881no—
329C23—4881no—
330C23—4881no—
331C23—4881no—
332C23—4881no—
333C23—2442no—
334C23C2×#1175819911yescharacteristic
335Q8—41no—
336Q8—41no—
337D4—41no—
338D4—41no—
339D4—82no—
340D4—82no—
341D4—81no—
342D4—81no—
343D4—4881no—
344D4—4888no—
345D4—4881no—
346D4—2442no—
347D4—2442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—82no—
359C2×C4—4881no—
360C2×C4—4881no—
361C2×C4—2442no—
362C2×C4#1451974611yescharacteristic
363C2×C4#1451980311yescharacteristic
364C8—21no—
365C8—21no—
366C8—41no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—9761no—
378C22—9761no—
379C22—9761no—
380C22—9761no—
381C22—4882no—
382C22—4882no—
383C22—4882no—
384C22#1683989611yescharacteristic
385C22#1684019211yescharacteristic
386C22#1684019711yescharacteristic
387C4—21no—
388C4—41no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—4882no—
393C4#1683993011yescharacteristic
394C4#1683994911yescharacteristic
395C2—21no—
396C2—21no—
397C2—81no—
398C2—161no—
399C2—9762no—
400C2#2144473711yescharacteristic
401C2#2144774211yescharacteristic
402C2#2144776511yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#3191C2
socleC22×C61#447
hypercenter#3191D61
hypocenterC61#12104
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #3191

Complements

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

NH ≅ G/Ntype
1. #21447747C2semidirect
2. #21447730C2semidirect
3. #21446817C2semidirect
4. #21443831C2semidirect
5. #21443828C2semidirect
6. #21443743C2semidirect
7. C61×#3191C2semidirect
43. C2×Q16×C61D4semidirect
45. C2×D8×C61D4semidirect
57. #107×C61D4semidirect
58. #107×C61D4semidirect
194. #3191D61semidirect
228. C61#12104semidirect
233. C2×Q16C22⋊D61semidirect
238. C2×D8C22⋊D61semidirect
258. #107C22⋊D61semidirect
259. #107C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214477472
#214477302
#214468172
#214438312
#214438282
#214437432
C61×#31912
#1210461