Finite Group Databasebeta

← #29593856

Subgroups — #29593856

Order 15616.

344 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 71 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#21448055C211yesmaximal, characteristic, complemented
2#21447961C211yesmaximal, characteristic, complemented
3#21445342C211yesmaximal, characteristic, complemented
4#21443862C211yesmaximal, characteristic, complemented
5#21443789C211yesmaximal, characteristic, complemented
6#21443777C211yesmaximal, characteristic, complemented
7C61×#3277C211yesmaximal, characteristic
8#16840167C2211yescharacteristic
9#16840052—21no—
10#16839589—21no—
11C4⋊#11758185C2211yescharacteristic
12#16839566—21no—
13#16839566—21no—
14#16839563—21no—
15#16839538C2211yescharacteristic
16#16839513C2211yescharacteristic
17#16839510—21no—
18C2×#137×C61—21no—
19C61×#548—21no—
20C61×#495C2211yescharacteristic
21C61×#468—21no—
22C61×#464—21no—
23C61×#451—21no—
24C61×#449—21no—
25C4×Q16×C61C2211yescharacteristic
26C61×#436C2211yescharacteristic
27#14519777—21no—
28C2×#11758185—21no—
29C2×#11758185—21no—
30#14519711—21no—
31#14519711—21no—
32#14519708—41no—
33C4⋊#92418—21no—
34#14519698—41no—
35C2×#41×C61—21no—
36C22×Q8×C61—21no—
37#137×C61—42no—
38#137×C61—42no—
39C2×Q16×C61—21no—
40C2×Q16×C61D411yescharacteristic
41C2×Q16×C61D411yescharacteristic
42C2×SD16×C61—21no—
43C2×SD16×C61—21no—
44C2×D8×C61D411yescharacteristic
45C2×M16×C61—21no—
46#124×C61—21no—
47#124×C61—41no—
48C22⋊Q8×C61—21no—
49C22⋊Q8×C61—41no—
50#121×C61—21no—
51#121×C61—41no—
52C4×Q8×C61—21no—
53C4×D4×C61—41no—
54C4×D4×C61D411yescharacteristic
55#107×C61D411yescharacteristic
56C4⋊C8×C61D411yescharacteristic
57#103×C61—21no—
58#103×C61—21no—
59#102×C61—21no—
60C22⋊C8×C61—21no—
61C4×C8×C61C2311yescharacteristic
62#41×C61—42no—
63#41×C61—81no—
64C2×Q8×C61—21no—
65C2×Q8×C61—21no—
66C2×Q8×C61—41no—
67C2×Q8×C61—42no—
68C2×Q8×C61—81no—
69C2×D4×C61—21no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61D811yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C2×Dic122—41no—
77Q16×C61—21no—
78Q16×C61—41no—
79Q16×C61—42no—
80Q16×C61SD1612yes—
81SD16×C61—42no—
82SD16×C61—41no—
83SD16×C61—41no—
84D8×C61—41no—
85M16×C61—41no—
86M16×C61—41no—
87C2×C8×C61—21no—
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C4⋊C4×C61—21no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61D811yescharacteristic
94C22⋊C4×C61—21no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C42×C61—41no—
100C42×C61C2×D411yescharacteristic
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C2×#92418—41no—
104#11758185—41no—
105#11758185—41no—
106C23×C61—21no—
107C23×C61—41no—
108Q8×C61—22no—
109Q8×C61—41no—
110Q8×C61—41no—
111Q8×C61—41no—
112Q8×C61—82no—
113D4×C61—41no—
114D4×C61—41no—
115D4×C61—41no—
116D4×C61—82no—
117D4×C61—82no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—82no—
125C2×C4×C61—82no—
126C2×C4×C61#12011yescharacteristic
127C2×C4×C61C2×D811yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×Dic61—81no—
130Dic122—161no—
131C8×C61—21no—
132C8×C61—41no—
133C8×C61C2×SD1611yescharacteristic
134C8×C61AGL(1,ℤ/8)11yescharacteristic
135#92418—81no—
136#12377—611nomaximal, Sylow
137C22×C61—41no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61—81no—
141C22×C61—81no—
142C22×C61—81no—
143C22×C61#44711yescharacteristic
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61—42no—
148C4×C61—81no—
149C4×C61—81no—
150C4×C61#45011yescharacteristic
151C4×C61#45511yescharacteristic
152Dic61—161no—
153#3277D6111yescharacteristic
154#2243—611no—
155#2225—611no—
156#1695—611no—
157#1360—611no—
158#1334—611no—
159#1330—611no—
160C2×C61—81no—
161C2×C61—161no—
162C2×C61#163911yescharacteristic
163C2×C61#219111yescharacteristic
164C2×C61#219311yescharacteristic
165C2×#137—21no—
166#548—21no—
167#500—611no—
168#495C2×D6111yescharacteristic
169#476—1221no—
170#468—21no—
171#464—21no—
172#451—21no—
173#449—21no—
174C4×Q16C2×D6111yescharacteristic
175#436C2×D6111yescharacteristic
176#367—1221no—
177C4⋊C16—611no—
178#358—1221no—
179#358—1221no—
180#357—1221no—
181#346—611no—
182#334—611no—
183#333—1221no—
184C61#1237711yescharacteristic, complemented, Sylow
185C2×#41—21no—
186C22×Q8—21no—
187#137—42no—
188#137—42no—
189C2×Q16—21no—
190C2×Q16C22⋊D6111yescharacteristic
191C2×Q16C22⋊D6111yescharacteristic
192C2×SD16—21no—
193C2×SD16—21no—
194C2×D8C22⋊D6111yescharacteristic
195C2×M16—21no—
196C4⋊Q8—1221no—
197#124—21no—
198#124—41no—
199C22⋊Q8—21no—
200C22⋊Q8—41no—
201#121—21no—
202#121—41no—
203C4×Q8—21no—
204C4×D4—41no—
205C4×D4C22⋊D6111yescharacteristic
206C2×C16—1221no—
207C2×C16—1221no—
208#107—1221no—
209#107—1221no—
210#107C22⋊D6111yescharacteristic
211#106—2441no—
212C4⋊C8—1221no—
213C4⋊C8C22⋊D6111yescharacteristic
214#103—21no—
215#103—21no—
216#102—21no—
217#102—2441no—
218C22⋊C8—21no—
219C4×C8C22×D6111yescharacteristic
220#41—42no—
221#41—81no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—41no—
225C2×Q8—42no—
226C2×Q8—81no—
227C2×Q8—2441no—
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4#1175819911yescharacteristic
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—41no—
235Q16—21no—
236Q16—41no—
237Q16—42no—
238Q16#1175820012yes—
239SD16—42no—
240SD16—41no—
241SD16—41no—
242D8—41no—
243M16—41no—
244M16—41no—
245C2×C8—21no—
246C2×C8—2441no—
247C2×C8C2×C22⋊D6111yescharacteristic
248C2×C8C2×C22⋊D6111yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4#1175819911yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C42—41no—
261C42C2×C22⋊D6111yescharacteristic
262C16—2441no—
263C16—2441no—
264C23—21no—
265C23—41no—
266Q8—22no—
267Q8—41no—
268Q8—41no—
269Q8—41no—
270Q8—82no—
271Q8—9761no—
272D4—41no—
273D4—41no—
274D4—41no—
275D4—82no—
276D4—82no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—4881no—
286C2×C4#1451974611yescharacteristic
287C2×C4C2×#1175819911yescharacteristic
288C2×C4#1451980311yescharacteristic
289C8—21no—
290C8—41no—
291C8—4881no—
292C8C2×#1175820011yescharacteristic
293C8#1451980311yescharacteristic
294C22—41no—
295C22—41no—
296C22—41no—
297C22—81no—
298C22—81no—
299C22—81no—
300C22#1683989611yescharacteristic
301C4—21no—
302C4—21no—
303C4—41no—
304C4—42no—
305C4—81no—
306C4—81no—
307C4—9761no—
308C4#1683991311yescharacteristic
309C4#1683994011yescharacteristic
310C2—81no—
311C2—161no—
312C2#2144499811yescharacteristic
313C2#2144777011yescharacteristic
314C2#2144778311yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
Fitting, prime radicalC61×#3277C2
socleC22×C61#447
hypercenter#3277D61
hypocenterC61#12377
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #3277

Complements

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

NH ≅ G/Ntype
1. #21448055C2semidirect
2. #21447961C2semidirect
3. #21445342C2semidirect
4. #21443862C2semidirect
5. #21443789C2semidirect
6. #21443777C2semidirect
184. C61#12377semidirect

Maximal subgroups

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

subgroupindex
#214480552
#214479612
#214453422
#214438622
#214437892
#214437772
C61×#32772
#1237761