Finite Group Databasebeta

← #37510944

Subgroups — #37510944

Order 22912.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#26039236C211yesmaximal, characteristic, complemented
2#26038875C211yesmaximal, characteristic, complemented
3#26038689C211yesmaximal, characteristic, complemented
4#26038250C211yesmaximal, characteristic, complemented
5#26038249C211yesmaximal, characteristic, complemented
6#26038220C211yesmaximal, characteristic, complemented
7#509×C179C211yesmaximal, characteristic, complemented
8#41×D179—21no—
9#19153145—21no—
10#19153142—21no—
11#19153140—21no—
12#19153137—21no—
13#19153135C2211yescharacteristic
14#19153133—21no—
15C2×#15668242C2211yescharacteristic
16#19153084—21no—
17#19153057—21no—
18#19153054—21no—
19#19153053C2211yescharacteristic, complemented
20#19153045C2211yescharacteristic, complemented
21#19153034—21no—
22#135×C179C2211yescharacteristic
23C2×D8×C179C2211yescharacteristic, complemented
24SD32×C179—21no—
25D16×C179—21no—
26M32×C179C2211yescharacteristic, complemented
27#15668260—21no—
28#15668259—21no—
29#15668259—41no—
30#15668258—21no—
31#15668258—41no—
32Q8×D179—21no—
33C2×C22⋊D179—41no—
34D4×D179—21no—
35D4×D179—41no—
36C2×C4×D179—41no—
37C2×C4×D179D411yescharacteristic
38Dic716D411yescharacteristic, complemented
39#15668249—21no—
40#15668248—21no—
41#15668247—21no—
42#15668246—21no—
43D1432D411yescharacteristic, complemented
44#15668244—21no—
45#15668242—21no—
46#15668242—21no—
47C2×C179⋊C8D411yescharacteristic
48C4⋊Dic179—21no—
49C22⋊Dic179—41no—
50C179⋊C16—21no—
51#41×C179—21no—
52C2×D4×C179—21no—
53Q16×C179D411yescharacteristic, complemented
54SD16×C179—21no—
55D8×C179—21no—
56D8×C179—21no—
57D8×C179D411yescharacteristic, complemented
58C2×C8×C179C2311yescharacteristic
59C16×C179—21no—
60C22×D179—41no—
61C22×D179D811yescharacteristic
62Dic358—21no—
63Dic358—41no—
64D716—21no—
65D716—41no—
66C22⋊D179—41no—
67C22⋊D179—41no—
68C22⋊D179—41no—
69C22⋊D179—82no—
70C2×Dic179—41no—
71C2×Dic179—41no—
72C2×Dic179D811yescharacteristic
73C4×D179—21no—
74C4×D179—21no—
75C4×D179—41no—
76C4×D179—41no—
77C4×D179—41no—
78C179⋊C8—21no—
79C23×C179—41no—
80Q8×C179—21no—
81D4×C179—21no—
82D4×C179—41no—
83D4×C179—41no—
84D4×C179—41no—
85C2×C4×C179—41no—
86C2×C4×C179C2×D411yescharacteristic
87C8×C179C2×D411yescharacteristic
88C8×C179C2×D411yescharacteristic
89C22×C179—41no—
90C22×C179—81no—
91C22×C179—81no—
92C22×C179—81no—
93C22×C179C2×D811yescharacteristic
94C2×D179—21no—
95C2×D179—41no—
96C2×D179—41no—
97C2×D179—82no—
98C4×C179—41no—
99C4×C179#12011yescharacteristic
100C4×C179AGL(1,ℤ/8)11yescharacteristic
101Dic179—21no—
102Dic179—41no—
103Dic179—81no—
104C2×C179—21no—
105C2×C179—81no—
106C2×C179—161no—
107C2×C179#44711yescharacteristic
108D179—41no—
109D179—81no—
110C179#219011yescharacteristic, complemented, Sylow
111#2190—1791nomaximal, Sylow
112#575—1791no—
113#509—1791no—
114#509D17911yescharacteristic, complemented
115#469—1791no—
116#360—1791no—
117#360—1791no—
118#349—1791no—
119C2×#41—3581no—
120#137—3581no—
121#137—3581no—
122AGL(1,ℤ/8)—3581no—
123AGL(1,ℤ/8)—3581no—
124#135—3581no—
125#135—1791no—
126#135C2×D17911yescharacteristic
127C2×D8C2×D17911yescharacteristic, complemented
128C2×M16—1791no—
129#121—3581no—
130SD32—21no—
131SD32—3581no—
132D16—21no—
133D16—3581no—
134M32—1791no—
135M32C2×D17911yescharacteristic, complemented
136#106—1791no—
137#102—3581no—
138#41—21no—
139#41—3581no—
140#41—3581no—
141#41—3581no—
142#41—7161no—
143#41—7161no—
144C2×Q8—3581no—
145C2×D4—21no—
146C2×D4—3581no—
147C2×D4—7161no—
148C2×D4—7161no—
149C22×C4—1791no—
150C22×C4—7161no—
151Q16—3581no—
152Q16—1791no—
153Q16C22⋊D17911yescharacteristic, complemented
154SD16—21no—
155SD16—3581no—
156SD16—3581no—
157SD16—3581no—
158D8—21no—
159D8—21no—
160D8—3581no—
161D8—1791no—
162D8C22⋊D17911yescharacteristic, complemented
163M16—3581no—
164M16—3581no—
165C2×C8—1791no—
166C2×C8C22×D17911yescharacteristic
167C4⋊C4—3581no—
168C22⋊C4—7161no—
169C16—21no—
170C16—3581no—
171C23—41no—
172C23—1791no—
173C23—7161no—
174Q8—21no—
175Q8—3581no—
176Q8—7161no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—3581no—
182D4—14322no—
183D4—7161no—
184D4—7161no—
185D4—7161no—
186D4—7161no—
187C2×C4—41no—
188C2×C4—3581no—
189C2×C4—3581no—
190C2×C4—1791no—
191C2×C4—7161no—
192C2×C4—7161no—
193C2×C4—7161no—
194C2×C4—7161no—
195C2×C4—7161no—
196C2×C4D4×D17911yescharacteristic
197C8—3581no—
198C8D4×D17911yescharacteristic
199C8C2×C22⋊D17911yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—3581no—
205C22—14322no—
206C22—7161no—
207C22—7161no—
208C22D8×D17911yescharacteristic
209C4—41no—
210C4—3581no—
211C4—14321no—
212C4—7161no—
213C4#1915308111yescharacteristic
214C4#1915313711yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—14321no—
219C2—7161no—
220C2#2603857111yescharacteristic
subgroupG/H
centerC2#26038571
commutator, cosocleC2×C8×C179C23
FrattiniC2×C8C22×D179
Fitting#509×C179C2
socleC2×C179#447
hypercenter#509D179
hypocenterC179#2190
LCSG ▷ C2×C8×C179 ▷ C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #26039236C2semidirect
2. #26038875C2semidirect
3. #26038689C2semidirect
4. #26038250C2semidirect
5. #26038249C2semidirect
6. #26038220C2semidirect
7. #509×C179C2semidirect
19. #19153053C22semidirect
20. #19153045C22semidirect
23. C2×D8×C179C22semidirect
26. M32×C179C22semidirect
38. Dic716D4semidirect
43. D1432D4semidirect
53. Q16×C179D4semidirect
57. D8×C179D4semidirect
110. C179#2190semidirect
114. #509D179semidirect
127. C2×D8C2×D179semidirect
135. M32C2×D179semidirect
153. Q16C22⋊D179semidirect
162. D8C22⋊D179semidirect

Maximal subgroups

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

subgroupindex
#260392362
#260388752
#260386892
#260382502
#260382492
#260382202
#509×C1792
#2190179