Finite Group Databasebeta

← #49093838

Subgroups — #49093838

Order 35968.

222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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#31823994C211yesmaximal, characteristic
2#31823517C211yesmaximal, characteristic, complemented
3#31823327C211yesmaximal, characteristic, complemented
4#31823201C211yesmaximal, characteristic, complemented
5#31823199C211yesmaximal, characteristic, complemented
6#31823197C211yesmaximal, characteristic
7#327×C281C211yesmaximal, characteristic
8#22582872—21no—
9#22582870C411yescharacteristic, complemented
10#22582866C411yescharacteristic, complemented
11#22582860—21no—
12#22582858C2211yescharacteristic
13#22582844C411yescharacteristic, complemented
14D4×Dic281—21no—
15D4×Dic281C411yescharacteristic, complemented
16#22582835—21no—
17C2×#17985117—21no—
18C2×C4×Dic281C2211yescharacteristic
19#22582808—21no—
20C22⋊#14555886C2211yescharacteristic
21#22582789—21no—
22#22582786—21no—
23#22582786C2211yescharacteristic
24#121×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C2×Dic562C2×C411yescharacteristic
28C22×Dic281—21no—
29C22×Dic281—21no—
30C22×Dic281D411yescharacteristic
31C22×Dic281D411yescharacteristic
32C2×#14555886—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281C2×C411yescharacteristic
35#17985117—21no—
36#17985117—21no—
37#17985117—21no—
38#17985117—42no—
39C22⋊Dic281—21no—
40C22⋊Dic281—21no—
41C22⋊Dic281—21no—
42C22⋊Dic281—21no—
43C4×Dic281—21no—
44C4×Dic281C2×C411yescharacteristic
45C4×Dic281C2×C411yescharacteristic
46C4×Dic281D411yescharacteristic
47C4×Dic281D411yescharacteristic
48C2×D4×C281—21no—
49C2×D4×C281C2×C411yescharacteristic
50C22×C4×C281—21no—
51C22×C4×C281C2311yescharacteristic
52C2×C8×C281—21no—
53C4⋊C4×C281C2×C411yescharacteristic
54C22⋊C4×C281—21no—
55Dic562—41no—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—41no—
61C2×Dic281—42no—
62C2×Dic281—41no—
63C2×Dic281—41no—
64C2×Dic281—41no—
65C2×Dic281C22⋊C411yescharacteristic
66C2×Dic281C22⋊C411yescharacteristic
67C2×Dic281C22⋊C411yescharacteristic
68C2×Dic281C22⋊C411yescharacteristic
69#14555886—41no—
70C23×C281—21no—
71C23×C281C2×D411yescharacteristic
72D4×C281—41no—
73D4×C281—41no—
74D4×C281—41no—
75C2×C4×C281—21no—
76C2×C4×C281—41no—
77C2×C4×C281—41no—
78C2×C4×C281—41no—
79C2×C4×C281—41no—
80C2×C4×C281C22×C411yescharacteristic
81C2×C4×C281C2×D411yescharacteristic
82C8×C281—41no—
83C22×C281—21no—
84C22×C281—21no—
85C22×C281—41no—
86C22×C281—41no—
87C22×C281—41no—
88C22×C281C2×C22⋊C411yescharacteristic
89C22×C281AGL(1,ℤ/8)11yescharacteristic
90C22×C281#13711yescharacteristic
91C4×C281—21no—
92C4×C281—21no—
93C4×C281—41no—
94C4×C281—81no—
95Dic281—21no—
96Dic281—21no—
97Dic281—21no—
98Dic281—21no—
99Dic281—41no—
100Dic281—41no—
101Dic281—81no—
102C2×C281—21no—
103C2×C281—21no—
104C2×C281—81no—
105C2×C281#41011yescharacteristic
106C2×C281#41711yescharacteristic
107C2×C281#42111yescharacteristic
108C281#151211yescharacteristic, complemented, Sylow
109#1512—2811nomaximal, Sylow
110#529—2811no—
111#432—2811no—
112#382—2811no—
113#328—2811no—
114#328—2811no—
115#327—2811no—
116#327D28111yescharacteristic
117#126—5621no—
118#125—2811no—
119#124—2811no—
120#123—5621no—
121C22⋊Q8—2811no—
122#121C2×D28111yescharacteristic
123C4×Q8—2811no—
124C4×D4—2811no—
125C4×D4—5621no—
126#117—5621no—
127C2×C4⋊C4—5621no—
128C2×C42—2811no—
129C4⋊C8—5621no—
130C22⋊C8—2811no—
131C22⋊C8C2×D28111yescharacteristic
132#97—5621no—
133#95—2811no—
134#95—5621no—
135#95C2×D28111yescharacteristic
136C2×Q8—2811no—
137C2×D4—21no—
138C2×D4C4×D28111yescharacteristic
139C22×C4—21no—
140C22×C4—2811no—
141C22×C4—2811no—
142C22×C4—5621no—
143C22×C4—5621no—
144C22×C4C22×D28111yescharacteristic
145C2×C8—21no—
146C2×C8—5621no—
147C4⋊C4—2811no—
148C4⋊C4—5621no—
149C4⋊C4—5621no—
150C4⋊C4—5621no—
151C4⋊C4—5621no—
152C4⋊C4—11242no—
153C4⋊C4C4×D28111yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—5621no—
156C22⋊C4—5621no—
157C22⋊C4—5621no—
158C22⋊C4—5621no—
159C42—2811no—
160C42—2811no—
161C42—2811no—
162C42—2811no—
163C42—5621no—
164C23—21no—
165C23D4×D28111yescharacteristic
166Q8—11241no—
167D4—41no—
168D4—41no—
169D4—41no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—2811no—
176C2×C4—2811no—
177C2×C4—2811no—
178C2×C4—2811no—
179C2×C4—5621no—
180C2×C4—5621no—
181C2×C4—5621no—
182C2×C4—5621no—
183C2×C4—11241no—
184C2×C4—11242no—
185C2×C4—11241no—
186C2×C4—11241no—
187C2×C4—11241no—
188C2×C4C2×C4×D28111yescharacteristic
189C2×C4D4×D28111yescharacteristic
190C8—41no—
191C8—11241no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22C22⋊C4×D28111yescharacteristic
198C22#2258290311yescharacteristic
199C22#2258290811yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—81no—
204C4—5621no—
205C4—5621no—
206C4—5621no—
207C4—5621no—
208C4—11241no—
209C4—11241no—
210C4—22481no—
211C2—21no—
212C2—21no—
213C2—81no—
214C2#3182343511yescharacteristic
215C2#3182346111yescharacteristic
216C2#3182347811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D281
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#327×C281C2
socleC22×C281C2×C22⋊C4
prime radical#121×C281C22
cosocleC22×C4×C281C23
hypercenter#327D281
hypocenterC281#1512
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31823517C2semidirect
3. #31823327C2semidirect
4. #31823201C2semidirect
5. #31823199C2semidirect
9. #22582870C4semidirect
10. #22582866C4semidirect
13. #22582844C4semidirect
15. D4×Dic281C4semidirect
108. C281#1512semidirect

Maximal subgroups

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

subgroupindex
#318239942
#318235172
#318233272
#318232012
#318231992
#318231972
#327×C2812
#1512281