Finite Group Databasebeta

← #28363551

Subgroups — #28363551

Order 13952.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#20295792C211yesmaximal, characteristic
2#20295600C211yesmaximal, characteristic
3#20295035C211yesmaximal, characteristic, complemented
4#20294999C211yesmaximal, characteristic
5#20294783C211yesmaximal, characteristic, complemented
6#20294782C211yesmaximal, characteristic, complemented
7#419×C109C211yesmaximal, characteristic, complemented
8C2×#13182029C2211yescharacteristic
9#16812707—22no—
10#16812705—22no—
11C2×#13182013C2211yescharacteristic
12M16×D109—22no—
13#16812697C412yescomplemented
14#16812688C412yescomplemented
15#16812682—22no—
16#16812675—22no—
17#16812658C2211yescharacteristic
18#16812658C2211yescharacteristic
19#16812623—22no—
20#16812613—22no—
21C22×Q8×C109C2211yescharacteristic
22C2×M16×C109C2211yescharacteristic
23#117×C109C2211yescharacteristic
24#103×C109—22no—
25#13182029—21no—
26#13182029—21no—
27#13182029—21no—
28#13182029—21no—
29C2×Dic218C2×C411yescharacteristic
30C2×D436C2×C411yescharacteristic
31C2×C22⋊D109D412yes—
32C2×C4×D109D412yes—
33#13182013—21no—
34#13182013—21no—
35#13182012—24no—
36C2×#11724784D412yes—
37C8×D109—24no—
38C4⋊Dic109—21no—
39C4⋊Dic109—21no—
40#13182008—24no—
41C22⋊Dic109—21no—
42C22⋊Dic109—21no—
43#13182006—24no—
44C4×Dic109—21no—
45C4×Dic109C2×C412yes—
46C2×Q8×C109—21no—
47C2×Q8×C109—21no—
48C2×Q8×C109—21no—
49C2×Q8×C109—21no—
50C2×Q8×C109—21no—
51C2×Q8×C109C2×C412yes—
52C22×C4×C109—21no—
53C22×C4×C109C2311yescharacteristic
54M16×C109—21no—
55M16×C109—21no—
56C2×C8×C109D412yes—
57C4⋊C4×C109—21no—
58C22⋊C4×C109—21no—
59C42×C109—21no—
60C23×C109C2×D411yescharacteristic
61C22×D109C22⋊C412yes—
62Q8×C109—22no—
63Q8×C109—22no—
64Q8×C109—41no—
65Q8×C109—41no—
66C2×C4×C109—22no—
67C2×C4×C109—41no—
68C2×C4×C109—41no—
69C2×C4×C109—41no—
70C2×C4×C109C22×C411yescharacteristic
71C2×C4×C109C2×D411yescharacteristic
72C2×C4×C109C2×D411yescharacteristic
73C2×C4×C109C2×D411yescharacteristic
74C2×C4×C109#4111yescharacteristic
75C2×C4×C109#4111yescharacteristic
76C22⋊D109—22no—
77C22⋊D109—22no—
78C2×Dic109—22no—
79C2×Dic109—41no—
80C2×Dic109C22⋊C412yes—
81D436—21no—
82D436—21no—
83C4×D109—22no—
84C4×D109—22no—
85Dic218—21no—
86Dic218—21no—
87C8×C109—22no—
88#11724784—22no—
89C22×C109—41no—
90C22×C109C2×C22⋊C411yescharacteristic
91C22×C109#12111yescharacteristic
92C22×C109#12111yescharacteristic
93C2×D109—22no—
94C2×D109—42no—
95C4×C109—42no—
96C4×C109—81no—
97C4×C109C4×D411yescharacteristic
98C4×C109C4×D411yescharacteristic
99C4×C109#12011yescharacteristic
100C4×C109#12311yescharacteristic
101Dic109—22no—
102Dic109—42no—
103Dic109—81no—
104C2×C109—21no—
105C2×C109—21no—
106C2×C109—21no—
107C2×C109#38611yescharacteristic
108D109—42no—
109#1909—1091nomaximal, Sylow
110C109#190911yescharacteristic, complemented, Sylow
111#568—1091no—
112#536—1091no—
113#419—1091no—
114#419D10911yescharacteristic, complemented
115#410—1091no—
116H(3,ℤ/4)—1091no—
117H(3,ℤ/4)—1091no—
118C2×#41—1091no—
119C22×Q8C2×D10911yescharacteristic
120#131—2182no—
121#131—2182no—
122C2×M16—1091no—
123C2×M16—2182no—
124C2×M16C2×D10911yescharacteristic
125C4⋊Q8—1092no—
126#124—1092no—
127#123—2182no—
128C22⋊Q8—2182no—
129#117—1091no—
130#117—1091no—
131#117C2×D10911yescharacteristic
132#103—22no—
133#103—2182no—
134#99—2182no—
135#41—2181no—
136#41—2181no—
137#41—2181no—
138#41—2181no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—1091no—
145C2×Q8C4×D10912yes—
146C2×D4—1092no—
147C2×D4—1091no—
148C22×C4—21no—
149C22×C4—1092no—
150C22×C4C22×D10911yescharacteristic
151M16—21no—
152M16—21no—
153M16—2184no—
154M16—2181no—
155M16—2181no—
156C2×C8—1092no—
157C2×C8—2184no—
158C2×C8C22⋊D10912yes—
159C4⋊C4—21no—
160C4⋊C4—2184no—
161C4⋊C4—2181no—
162C4⋊C4—2181no—
163C22⋊C4—21no—
164C22⋊C4—2184no—
165C22⋊C4—2181no—
166C22⋊C4—2181no—
167C42—21no—
168C42—1092no—
169C42—2181no—
170C23—1092no—
171C23D4×D10911yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—2181no—
177Q8—2181no—
178D4—2182no—
179D4—2182no—
180D4—2181no—
181D4—2181no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1092no—
187C2×C4—4361no—
188C2×C4—2182no—
189C2×C4—2182no—
190C2×C4—2182no—
191C2×C4C2×C4×D10911yescharacteristic
192C2×C4D4×D10911yescharacteristic
193C2×C4D4×D10911yescharacteristic
194C2×C4C2×C22⋊D10911yescharacteristic
195C2×C4#1318202811yescharacteristic
196C2×C4#1318202911yescharacteristic
197C8—22no—
198C8—2182no—
199C22—41no—
200C22—4362no—
201C22—2182no—
202C22C22⋊C4×D10911yescharacteristic
203C22#1681267011yescharacteristic
204C22#1681267211yescharacteristic
205C4—42no—
206C4—81no—
207C4—8721no—
208C4—4362no—
209C4—2182no—
210C4#1681265911yescharacteristic
211C4C4×C22⋊D10911yescharacteristic
212C4#1681266711yescharacteristic
213C4#1681268111yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—4362no—
218C2#2029490211yescharacteristic
subgroupG/H
centerC2#20294902
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#419×C109C2
socleC2×C109#386
prime radicalC2×#13182029C22
cosocleC22×C4×C109C23
hypercenter#419D109
hypocenterC109#1909
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #20295035C2semidirect
5. #20294783C2semidirect
6. #20294782C2semidirect
7. #419×C109C2semidirect
13. #16812697C4semidirect
14. #16812688C4semidirect
110. C109#1909semidirect
114. #419D109semidirect

Maximal subgroups

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

subgroupindex
#202957922
#202956002
#202950352
#202949992
#202947832
#202947822
#419×C1092
#1909109