Finite Group Databasebeta

← #49096462

Subgroups — #49096462

Order 35968.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#31824091C211yesmaximal, characteristic
2#31823472C211yesmaximal, characteristic
3#31823370C211yesmaximal, characteristic
4#31823231C211yesmaximal, characteristic
5#31823224C211yesmaximal, characteristic
6#31823222C211yesmaximal, characteristic
7#419×C281C211yesmaximal, characteristic
8C2×#17985122C2211yescharacteristic
9#22582879—21no—
10#22582878—21no—
11#22582871—21no—
12#22582870—21no—
13#22582856—22no—
14#22582838C2211yescharacteristic
15C2×C4⋊Dic281C2211yescharacteristic
16C2×C4×Dic281C2211yescharacteristic
17#22582803—21no—
18#22582803—21no—
19#22582786—22no—
20C22×Q8×C281C2211yescharacteristic
21C2×M16×C281C2211yescharacteristic
22#117×C281C2211yescharacteristic
23#103×C281—21no—
24#103×C281—21no—
25C2×Dic562—22no—
26C22×Dic281—21no—
27C22×Dic281D412yes—
28#17985122—21no—
29#17985122—21no—
30C2×#14555886—21no—
31C4⋊Dic281—22no—
32C4⋊Dic281—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281D411yescharacteristic
35C4⋊Dic281D411yescharacteristic
36#17985117—22no—
37#17985117—22no—
38C22⋊Dic281—21no—
39C4×Dic281—21no—
40C4×Dic281—21no—
41C4×Dic281—21no—
42C2×Q8×C281—21no—
43C2×Q8×C281—21no—
44C2×Q8×C281—21no—
45C2×Q8×C281—21no—
46C2×Q8×C281—21no—
47C2×Q8×C281Q812yescomplemented
48C22×C4×C281—21no—
49C22×C4×C281C2311yescharacteristic
50M16×C281—21no—
51M16×C281—21no—
52C2×C8×C281—21no—
53C4⋊C4×C281D411yescharacteristic
54C4⋊C4×C281D411yescharacteristic
55C22⋊C4×C281—21no—
56C42×C281—21no—
57Dic562—82no—
58C2×Dic281—22no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—22no—
62C2×Dic281—41no—
63C2×Dic281—41no—
64C2×Dic281—42no—
65#14555886—41no—
66C23×C281C2×D411yescharacteristic
67Q8×C281—22no—
68Q8×C281—22no—
69Q8×C281—41no—
70Q8×C281—41no—
71C2×C4×C281—21no—
72C2×C4×C281—21no—
73C2×C4×C281—22no—
74C2×C4×C281—41no—
75C2×C4×C281—41no—
76C2×C4×C281C2×D411yescharacteristic
77C2×C4×C281C2×D411yescharacteristic
78C2×C4×C281C2×Q811yescharacteristic
79C2×C4×C281#4111yescharacteristic
80C2×C4×C281#4111yescharacteristic
81C2×C4×C281#4111yescharacteristic
82C8×C281—41no—
83C22×C281—21no—
84C22×C281—21no—
85C22×C281#12011yescharacteristic
86C22×C281C22⋊Q811yescharacteristic
87C22×C281#12411yescharacteristic
88C4×C281—42no—
89C4×C281—41no—
90C4×C281—41no—
91C4×C281C22⋊Q811yescharacteristic
92C4×C281C22⋊Q811yescharacteristic
93C4×C281#12411yescharacteristic
94C4×C281#12411yescharacteristic
95Dic281—42no—
96Dic281—42no—
97Dic281—41no—
98Dic281—41no—
99C2×C281—21no—
100C2×C281—21no—
101C2×C281#39311yescharacteristic
102C2×C281#45511yescharacteristic
103C2×C281#45611yescharacteristic
104C281#202811yescharacteristic, complemented, Sylow
105#2028—2811nomaximal, Sylow
106#544—2811no—
107#419—2811no—
108#419D28111yescharacteristic
109#391—2811no—
110#343—2811no—
111#339—2811no—
112#339—2811no—
113C22×Q8C2×D28111yescharacteristic
114C2×M16—2811no—
115C2×M16C2×D28111yescharacteristic
116C4⋊Q8—5621no—
117C4⋊Q8—5621no—
118#125—5621no—
119#125—5621no—
120C22⋊Q8—5622no—
121#117—2811no—
122#117C2×D28111yescharacteristic
123C2×C4⋊C4—2811no—
124C2×C42—2811no—
125#103—21no—
126#103—21no—
127#103—5621no—
128#103—5621no—
129#95—5622no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—5622no—
136C2×Q8Dic56212yescomplemented
137C22×C4—21no—
138C22×C4—2812no—
139C22×C4—5621no—
140C22×C4C22×D28111yescharacteristic
141M16—21no—
142M16—21no—
143M16—5621no—
144M16—5621no—
145C2×C8—21no—
146C2×C8—5621no—
147C4⋊C4—2811no—
148C4⋊C4—2811no—
149C4⋊C4—5622no—
150C4⋊C4—5622no—
151C4⋊C4—5622no—
152C4⋊C4—5621no—
153C4⋊C4—5621no—
154C4⋊C4C22⋊D28111yescharacteristic
155C4⋊C4C22⋊D28111yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—5621no—
158C42—21no—
159C42—5621no—
160C42—5621no—
161C42—5621no—
162C23D4×D28111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—22482no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—5622no—
174C2×C4—5621no—
175C2×C4—5621no—
176C2×C4—5622no—
177C2×C4—11241no—
178C2×C4—11241no—
179C2×C4—11242no—
180C2×C4D4×D28111yescharacteristic
181C2×C4C2×C22⋊D28111yescharacteristic
182C2×C4C2×Dic56211yescharacteristic
183C2×C4#1798513711yescharacteristic
184C2×C4#1798513711yescharacteristic
185C2×C4#1798513811yescharacteristic
186C8—41no—
187C8—11241no—
188C22—21no—
189C22—21no—
190C22#2258284711yescharacteristic
191C22#2258285611yescharacteristic
192C22#2258286511yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—11242no—
197C4—11242no—
198C4—11241no—
199C4—11241no—
200C4#2258285611yescharacteristic
201C4#2258285811yescharacteristic
202C4#2258286511yescharacteristic
203C4#2258286611yescharacteristic
204C2—21no—
205C2—21no—
206C2#3182337511yescharacteristic
207C2#3182363911yescharacteristic
208C2#3182364411yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#419×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
hypercenter#419D281
hypocenterC281#2028
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C281Q8semidirect
104. C281#2028semidirect
136. C2×Q8Dic562semidirect

Maximal subgroups

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

subgroupindex
#318240912
#318234722
#318233702
#318232312
#318232242
#318232222
#419×C2812
#2028281