Finite Group Databasebeta

← #29576044

Subgroups — #29576044

Order 15616.

624 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 127 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#21454383C211yesmaximal, characteristic, complemented
2#21451569C211yesmaximal, characteristic
3#21444486C212yesmaximal, complemented
4#21443678C212yesmaximal, complemented
5C61×#1458C211yesmaximal, characteristic, complemented
6C22×#11758194—21no—
7C2×#14519774C2211yescharacteristic
8C2×#14519751—21no—
9#16839789—24no—
10#16839786—21no—
11#16839786C2212yes—
12#16839679—21no—
13#16839679C412yes—
14#16839671—21no—
15#16839671C412yes—
16#16839664—21no—
17#16839628C2211yescharacteristic
18#16839505—24no—
19C2×#117×C61C2211yescharacteristic
20C61×#431C2212yes—
21C61×#324—21no—
22C61×#323—21no—
23C22×D244—21no—
24C22×D244—21no—
25C22×D244C2×C412yes—
26C22×C22⋊D61—22no—
27C2×#11758194—22no—
28C2×#11758194—22no—
29C2×#11758194—42no—
30C2×#11758194—42no—
31C22×#92418—22no—
32#14519774—22no—
33#14519774—22no—
34#14519751—42no—
35#14519751—42no—
36C2×C4⋊Dic61—21no—
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198—22no—
40C4⋊#92418—24no—
41C4⋊#92418—22no—
42C4⋊#92418D414yescomplemented
43#14519684—21no—
44#14519684C2×C412yes—
45C23×C4×C61D411yescharacteristic
46#117×C61—22no—
47#117×C61—22no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C22⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—22no—
55C22⋊C8×C61—22no—
56C4×C8×C61—22no—
57C24×C61C22⋊C411yescharacteristic
58C23×D61—22no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61D812yes—
67C22×C4×C61SD1612yes—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C2×C22⋊D61—44no—
72C2×C22⋊D61—82no—
73C2×C22⋊D61—82no—
74C22×Dic61—22no—
75C2×D244—24no—
76C2×D244—41no—
77C2×D244—42no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—82no—
84C2×D244—82no—
85C2×C8×C61—42no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—22no—
88C22⋊C4×C61—22no—
89C22⋊C4×C61—22no—
90C42×C61—21no—
91C42×C61—21no—
92C42×C61C2×D412yes—
93C42×C61#4112yes—
94#11758198—44no—
95#11758198—82no—
96#11758198—82no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99#11758194—44no—
100#11758194—42no—
101#11758194—42no—
102C2×#92418—24no—
103C2×#92418—44no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61#10212yes—
109C23×C61C2×C22⋊C411yescharacteristic
110C22×D61—42no—
111C22×D61—42no—
112C22×D61—42no—
113C22×D61—42no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—42no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61#10212yes—
130C2×C4×C61C4×D412yes—
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61#12112yes—
133C2×C4×C61#12311yescharacteristic
134C2×C4×C61C2×D811yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C22⋊D61—88no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142D244—84no—
143D244—84no—
144D244—81no—
145D244—81no—
146D244—81no—
147D244—81no—
148C8×C61—82no—
149#92418—44no—
150#9197—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—22no—
154C22×C61—42no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—81no—
158C22×C61#38611yescharacteristic
159C22×C61C2×#10211yescharacteristic
160C22×C61#41711yescharacteristic
161C2×D61—82no—
162C2×D61—82no—
163C2×D61—82no—
164C2×D61—82no—
165C2×D61—82no—
166C2×D61—82no—
167C2×D61—82no—
168C4×C61—22no—
169C4×C61—22no—
170C4×C61—22no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61#44711yescharacteristic
174C4×C61#44811yescharacteristic
175C4×C61#48011yescharacteristic
176C4×C61#48111yescharacteristic
177Dic61—82no—
178#2905—611no—
179#2619—611no—
180#1545—612no—
181#1458D6111yescharacteristic, complemented
182#1286—612no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—42no—
186C2×C61#187411yescharacteristic
187C2×C61#191011yescharacteristic
188C2×C61#191411yescharacteristic
189D61—162no—
190C22×M16—1221no—
191C2×#127—611no—
192C2×#121—1221no—
193C2×#117C2×D6111yescharacteristic
194#431C2×D6112yes—
195#424—1224no—
196#423—612no—
197#423—1221no—
198#394—612no—
199#394—1221no—
200#392—612no—
201#392—1221no—
202#390—1221no—
203#382—611no—
204#331—1224no—
205#324—21no—
206#323—21no—
207C61#919711yescharacteristic, complemented, Sylow
208C22×D4—612no—
209C22×D4—1222no—
210C22×D4—1221no—
211C22×D4—1221no—
212C23×C4D24411yescharacteristic
213C2×M16—1222no—
214C2×M16—1222no—
215C2×M16—2442no—
216C2×M16—2442no—
217C22×C8—1222no—
218#127—1222no—
219#127—1222no—
220#121—2442no—
221#121—2442no—
222#117—22no—
223#117—22no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4C4×D6111yescharacteristic
226C2×C4⋊C4C22⋊D6111yescharacteristic
227C2×C22⋊C4—1222no—
228C2×C22⋊C4—1222no—
229C2×C22⋊C4—1222no—
230C2×C22⋊C4C4×D6111yescharacteristic
231C2×C22⋊C4C22⋊D6111yescharacteristic
232C2×C42D24411yescharacteristic
233C2×C42C22×D6111yescharacteristic
234C4⋊C8—22no—
235C4⋊C8—614no—
236C4⋊C8—1224no—
237C4⋊C8—1222no—
238C22⋊C8—22no—
239C4×C8—22no—
240#95—612no—
241#95—1221no—
242C24—1222no—
243C24#1175819811yescharacteristic
244C2×D4—1224no—
245C2×D4—4882no—
246C2×D4—4882no—
247C2×D4—4882no—
248C2×D4—4882no—
249C2×D4—2444no—
250C2×D4—2441no—
251C2×D4—2441no—
252C2×D4—2442no—
253C2×D4—2441no—
254C2×D4—2441no—
255C2×D4—2441no—
256C2×D4—2441no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1222no—
262C22×C4#1175819012yes—
263C22×C4D48812yes—
264C22×C4#1175819811yescharacteristic
265C22×C4#1175819811yescharacteristic
266C22×C4#1175819811yescharacteristic
267C22×C4C2×C4×D6111yescharacteristic
268C22×C4C2×D24411yescharacteristic
269C22×C4C2×C22⋊D6111yescharacteristic
270M16—2444no—
271M16—2442no—
272M16—2442no—
273C2×C8—42no—
274C2×C8—1224no—
275C2×C8—2444no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—4882no—
283C22⋊C4—4882no—
284C22⋊C4—2444no—
285C42—21no—
286C42—21no—
287C42D4×D6112yes—
288C42#1175822412yes—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—2442no—
294C23—2442no—
295C23—2442no—
296C23—2442no—
297C23—2442no—
298C23—2442no—
299C23—2442no—
300C23#1451969912yes—
301C23C2×#1175819811yescharacteristic
302D4—4884no—
303D4—4884no—
304D4—4888no—
305D4—4881no—
306D4—4881no—
307D4—4881no—
308D4—4881no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4#1451969912yes—
325C2×C4#1451973712yes—
326C2×C4#1451974711yescharacteristic
327C2×C4#1451974912yes—
328C2×C4#1451976111yescharacteristic
329C2×C4C2×D48811yescharacteristic
330C2×C4C2×#1175819011yescharacteristic
331C2×C4#1451980511yescharacteristic
332C2×C4#1451981011yescharacteristic
333C8—82no—
334C8—2444no—
335C22—21no—
336C22—21no—
337C22—22no—
338C22—42no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—4882no—
343C22—4882no—
344C22—4882no—
345C22—4882no—
346C22—4882no—
347C22—4882no—
348C22—4882no—
349C22#1683963911yescharacteristic
350C22C2×#1451969911yescharacteristic
351C22#1683976411yescharacteristic
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—4882no—
358C4#1683989811yescharacteristic
359C4#1683990311yescharacteristic
360C4#1684007611yescharacteristic
361C4#1684008111yescharacteristic
362C2—21no—
363C2—21no—
364C2—42no—
365C2—9762no—
366C2#2144613411yescharacteristic
367C2#2144634411yescharacteristic
368C2#2144636411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#386
prime radical#21451569C2
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#9197
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
1. #21454383C2semidirect
3. #21444486C2semidirect
4. #21443678C2semidirect
5. C61×#1458C2semidirect
42. C4⋊#92418D4semidirect
181. #1458D61semidirect
207. C61#9197semidirect

Maximal subgroups

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

subgroupindex
#214543832
#214515692
#214444862
#214436782
C61×#14582
#919761