Finite Group Databasebeta

← #29593229

Subgroups — #29593229

Order 15616.

396 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 63 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#21456566C211yesmaximal, characteristic
2#21448004C211yesmaximal, characteristic, complemented
3#21447248C211yesmaximal, characteristic, complemented
4#21443829C211yesmaximal, characteristic, complemented
5#21443828C211yesmaximal, characteristic, complemented
6#21443742C211yesmaximal, characteristic, complemented
7C61×#2233C211yesmaximal, characteristic, complemented
8#121×D61—21no—
9#16840077—21no—
10#16840074—21no—
11#16839998C2211yescharacteristic
12#16839996—21no—
13#16839897—21no—
14#16839894—21no—
15C2×#14519689C2211yescharacteristic
16#16839619—21no—
17#16839589—21no—
18#16839562—21no—
19C22⋊#11758185C2211yescharacteristic, complemented
20#16839525C2211yescharacteristic, complemented
21#16839524—21no—
22C61×#466C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic, complemented
24C61×#367—21no—
25C61×#357—21no—
26C61×C22⋊C16C2211yescharacteristic, complemented
27C2×D4×D61—21no—
28C2×D4×D61—41no—
29C22×C4×D61D411yescharacteristic
30C2×D488D411yescharacteristic
31C2×#11758199—21no—
32C22×#92418D411yescharacteristic
33#14519752—21no—
34#14519751—21no—
35#14519750—41no—
36#14519749—41no—
37#14519748—21no—
38C2×C4⋊Dic61—21no—
39C4⋊C4×D61—21no—
40C2×#11758198—41no—
41C22⋊C4×D61—41no—
42C2×#11758185—21no—
43#14519711D411yescharacteristic
44#14519710—21no—
45#14519699—21no—
46#14519698—21no—
47#14519697—21no—
48#14519689—21no—
49#14519689—21no—
50#14519684—41no—
51C2×D8×C61D411yescharacteristic
52C22×C8×C61C2311yescharacteristic
53#121×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C16×C61—21no—
56#107×C61—21no—
57#107×C61—21no—
58#107×C61D411yescharacteristic
59#102×C61—21no—
60C23×D61—41no—
61C23×D61D811yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61C2×D411yescharacteristic
66C2×C22⋊D61—41no—
67C2×C22⋊D61—41no—
68C2×C22⋊D61—41no—
69C22×Dic61—41no—
70C22×Dic61D811yescharacteristic
71D4×D61—81no—
72D4×D61—81no—
73D4×D61—82no—
74D4×D61—82no—
75C2×D244—21no—
76C2×D244—41no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82D8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61C2×D411yescharacteristic
85C2×C8×C61C2×D411yescharacteristic
86C4⋊C4×C61—21no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊Dic61—41no—
91#11758199—81no—
92#11758198—41no—
93#11758198—41no—
94#11758198—82no—
95C4⋊Dic61—21no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98#11758196—41no—
99C2×#92418—21no—
100C2×#92418—41no—
101D488—41no—
102C16×C61—41no—
103#11758185—41no—
104C23×C61—41no—
105C23×C61C2×D811yescharacteristic
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—82no—
112C22×D61—82no—
113C22×D61—82no—
114C22×D61SD3212yes—
115D4×C61—41no—
116D4×C61—41no—
117D4×C61—81no—
118D4×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—81no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61#12011yescharacteristic
126C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
127C22⋊D61—82no—
128C22⋊D61—82no—
129C22⋊D61—81no—
130C22⋊D61—81no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137D244—41no—
138D244—41no—
139D244—82no—
140C4×D61—41no—
141C4×D61—41no—
142C4×D61—81no—
143C4×D61—82no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—41no—
147#12281—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—81no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61#44711yescharacteristic
154C22×C61C2×SD3211yescharacteristic
155C22×C61#50911yescharacteristic
156C2×D61—22no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—42no—
160C2×D61—81no—
161C2×D61—81no—
162C2×D61—81no—
163C2×D61—81no—
164C2×D61—164no—
165C4×C61—21no—
166C4×C61—81no—
167C4×C61—161no—
168C4×C61#45511yescharacteristic
169C4×C61#45811yescharacteristic
170Dic61—41no—
171Dic61—81no—
172Dic61—161no—
173#3186—611no—
174#2233—611no—
175#2233D6111yescharacteristic, complemented
176#2076—611no—
177#1347—611no—
178#1347—611no—
179#1314—611no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—161no—
183C2×C61#160711yescharacteristic
184C2×C61#218711yescharacteristic
185C2×C61#219011yescharacteristic
186D61—42no—
187D61—161no—
188C2×#121—1221no—
189#480—1221no—
190#480—1221no—
191#466—611no—
192#466—1221no—
193#466C2×D6111yescharacteristic
194#447—1221no—
195#447—1221no—
196C2×#107C2×D6111yescharacteristic, complemented
197C2×C22⋊C8—611no—
198#380—1221no—
199#367—21no—
200#367—1221no—
201#357—21no—
202#357—1221no—
203C22⋊C16—611no—
204C22⋊C16C2×D6111yescharacteristic, complemented
205#340—611no—
206#340—1221no—
207C61#1228111yescharacteristic, complemented, Sylow
208C22×D4—1221no—
209C22×D4—2441no—
210C23×C4—611no—
211C2×D8—611no—
212C2×D8—1221no—
213C2×D8C22⋊D6111yescharacteristic
214C22×C8—611no—
215C22×C8C22×D6111yescharacteristic
216#121—21no—
217#121—1221no—
218#121—1221no—
219#121—1221no—
220#121—2441no—
221#121—2441no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C22⋊C4—2441no—
226C2×C22⋊C4—2441no—
227C2×C16—21no—
228C2×C16—1221no—
229#107—21no—
230#107—21no—
231#107—611no—
232#107—1221no—
233#107C22⋊D6111yescharacteristic
234#102—21no—
235#102—1221no—
236#102—1221no—
237#102—1221no—
238C22⋊C8—1221no—
239C22⋊C8—1221no—
240#95—2441no—
241C24—611no—
242C24—2441no—
243C2×D4—21no—
244C2×D4—41no—
245C2×D4—1221no—
246C2×D4—4882no—
247C2×D4—4882no—
248C2×D4—4881no—
249C2×D4—4881no—
250C2×D4—2441no—
251C2×D4—2441no—
252C2×D4—2441no—
253C2×D4—2441no—
254C22×C4—41no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—2441no—
259C22×C4—2441no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4D4×D6111yescharacteristic
263D8—41no—
264D8—4881no—
265D8—2441no—
266C2×C8—41no—
267C2×C8—1221no—
268C2×C8—2441no—
269C2×C8D4×D6111yescharacteristic
270C2×C8C2×C22⋊D6111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—1221no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C22⋊C4—41no—
279C22⋊C4—4882no—
280C22⋊C4—2441no—
281C22⋊C4—2441no—
282C22⋊C4—2441no—
283C16—41no—
284C16—2441no—
285C23—41no—
286C23—612no—
287C23—1221no—
288C23—1221no—
289C23—4882no—
290C23—4882no—
291C23—4882no—
292C23—2441no—
293C23—2441no—
294C23—2441no—
295C23D8×D6111yescharacteristic
296D4—41no—
297D4—41no—
298D4—81no—
299D4—81no—
300D4—4882no—
301D4—4882no—
302D4—4881no—
303D4—4881no—
304D4—4882no—
305D4—2441no—
306D4—2441no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—1221no—
314C2×C4—4881no—
315C2×C4—4882no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4#1451974511yescharacteristic
324C2×C4#1451980111yescharacteristic
325C8—21no—
326C8—21no—
327C8—2441no—
328C22—21no—
329C22—21no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—1222no—
334C22—9764no—
335C22—4881no—
336C22—4881no—
337C22—4881no—
338C22—4881no—
339C22—2442no—
340C22—2441no—
341C22—2441no—
342C22#1683989411yescharacteristic
343C22SD32×D6111yescharacteristic
344C22#1684019911yescharacteristic
345C4—21no—
346C4—81no—
347C4—161no—
348C4—9761no—
349C4—4881no—
350C4—2441no—
351C4#1683993811yescharacteristic
352C4#1683995111yescharacteristic
353C2—21no—
354C2—21no—
355C2—161no—
356C2—9761no—
357C2—2442no—
358C2#2144480311yescharacteristic
359C2#2144774611yescharacteristic
360C2#2144776311yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2233C2
socleC22×C61#447
prime radical#21456566C2
hypercenter#2233D61
hypocenterC61#12281
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
2. #21448004C2semidirect
3. #21447248C2semidirect
4. #21443829C2semidirect
5. #21443828C2semidirect
6. #21443742C2semidirect
7. C61×#2233C2semidirect
19. C22⋊#11758185C22semidirect
20. #16839525C22semidirect
23. C2×#107×C61C22semidirect
26. C61×C22⋊C16C22semidirect
175. #2233D61semidirect
196. C2×#107C2×D61semidirect
204. C22⋊C16C2×D61semidirect
207. C61#12281semidirect

Maximal subgroups

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

subgroupindex
#214565662
#214480042
#214472482
#214438292
#214438282
#214437422
C61×#22332
#1228161