Finite Group Databasebeta

← #34057366

Subgroups — #34057366

Order 19072.

336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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#23750355C211yesmaximal, characteristic
2#23750350C211yesmaximal, characteristic
3#23749974C212yesmaximal
4#23749918C212yesmaximal
5#23749917C211yesmaximal, characteristic
6#23749834C212yesmaximal
7#23749832C211yesmaximal, characteristic
8C8×Dic298C211yesmaximal, characteristic
9C4×Dic596C211yesmaximal, characteristic
10#23749717C212yesmaximal
11#487×C149C211yesmaximal, characteristic
12C2×Dic596C2211yescharacteristic
13C2×#14558726C2212yes—
14#18011910—21no—
15#18011910C2212yes—
16#18011909—22no—
17#18011909C2212yes—
18#18011902—21no—
19#18011901—22no—
20Q8×Dic149C2212yes—
21C4×Dic298C2211yescharacteristic
22C4×Dic298C2211yescharacteristic
23C4×Dic298C2211yescharacteristic
24#18011876—21no—
25#18011876—21no—
26#18011876C2212yes—
27#18011845C2211yescharacteristic
28#18011844C2212yes—
29C4⋊#11924746C2211yescharacteristic
30#18011840C2212yes—
31#18011836C2211yescharacteristic
32#18011836C2211yescharacteristic
33#18011835C2212yes—
34#18011834C2212yes—
35C8×Dic149C2212yes—
36C4⋊Q8×C149C2211yescharacteristic
37C4⋊Q8×C149C2211yescharacteristic
38#103×C149C2212yes—
39#103×C149C2212yes—
40C4×C8×C149C2211yescharacteristic
41C2×Dic298—22no—
42C2×Dic298D411yescharacteristic
43C2×Dic298C2311yescharacteristic
44C2×Dic298C2311yescharacteristic
45Dic596—22no—
46#14558726—24no—
47C2×#11924746C2312yes—
48C4⋊Dic149—22no—
49C4⋊Dic149D411yescharacteristic
50C4⋊Dic149C2311yescharacteristic
51C4⋊Dic149C2311yescharacteristic
52#14558715—22no—
53#14558715—22no—
54#14558715—22no—
55#14558715—22no—
56#14558715—21no—
57#14558715—21no—
58#14558715D412yes—
59C4×Dic149—22no—
60C4×Dic149—22no—
61C4×Dic149—21no—
62C4×Dic149—21no—
63C4×Dic149C2312yes—
64C2×Q8×C149—21no—
65C2×Q8×C149C2312yes—
66C2×C8×C149C2311yescharacteristic
67C2×C8×C149C2311yescharacteristic
68C4⋊C4×C149—21no—
69C4⋊C4×C149—21no—
70C4⋊C4×C149—21no—
71C4⋊C4×C149C2312yes—
72C42×C149C2311yescharacteristic
73Dic298—21no—
74Dic298—21no—
75Dic298—21no—
76Dic298—82no—
77Dic298Q1614yescomplemented
78Dic298#4112yes—
79C2×Dic149—21no—
80C2×Dic149—21no—
81C2×Dic149—21no—
82C2×Dic149—21no—
83C2×Dic149C2×D412yes—
84C2×Dic149C2×D412yes—
85#11924746—22no—
86Q8×C149—22no—
87Q8×C149—22no—
88Q8×C149—81no—
89C2×C4×C149—22no—
90C2×C4×C149—22no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2411yescharacteristic
94C8×C149—21no—
95C8×C149—21no—
96C22×C149C22×D411yescharacteristic
97C4×C149—21no—
98C4×C149—42no—
99C4×C149—42no—
100C4×C149C2×Q1612yes—
101C4×C149C2×#4111yescharacteristic
102C4×C1492−1+411yescharacteristic
103Dic149—22no—
104Dic149—22no—
105Dic149—41no—
106Dic149—41no—
107Dic149—41no—
108Dic149C2×Q1614yes—
109C2×C149#54811yescharacteristic
110C2×C149C22×Q1611yescharacteristic
111C2×C149#57711yescharacteristic
112C149#336311yescharacteristic, complemented, Sylow
113#3363—1491nomaximal, Sylow
114Q82—1491no—
115#557—1491no—
116#487—1492no—
117#487D14911yescharacteristic
118#477—1491no—
119#477—1492no—
120#462—1491no—
121#462—1492no—
122C8×Q8—1491no—
123C4×Q16—1492no—
124C4×Q16—1491no—
125C2×Q16—1492no—
126C2×Q16—1491no—
127C4⋊Q8—2981no—
128C4⋊Q8—2982no—
129C4⋊Q8—1492no—
130C4⋊Q8—1492no—
131C4⋊Q8C2×D14911yescharacteristic
132C4⋊Q8C2×D14911yescharacteristic
133#125—2982no—
134#125—2981no—
135C4×Q8—2981no—
136C4×Q8—2981no—
137C4×Q8—1492no—
138C4×Q8—1492no—
139C4×Q8—1491no—
140C4×Q8—1491no—
141C4×Q8—1491no—
142#107—1491no—
143#107—1492no—
144C4⋊C8—1492no—
145C4⋊C8—1491no—
146#103—1492no—
147#103—1491no—
148#103—1491no—
149#103—1492no—
150#103C2×D14912yes—
151#103C2×D14912yes—
152C4×C8—1492no—
153C4×C8C2×D14911yescharacteristic
154C2×Q8—21no—
155C2×Q8—2982no—
156C2×Q8—1491no—
157C2×Q8—1491no—
158C2×Q8—1491no—
159C2×Q8C22×D14912yes—
160Q16—2982no—
161Q16—2984no—
162C2×C8—1492no—
163C2×C8C22×D14911yescharacteristic
164C2×C8C22×D14911yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—2982no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—2982no—
172C4⋊C4—2982no—
173C4⋊C4—2981no—
174C4⋊C4—2981no—
175C4⋊C4—1491no—
176C4⋊C4—1491no—
177C4⋊C4—1492no—
178C4⋊C4—1491no—
179C4⋊C4C22×D14912yes—
180C42—2982no—
181C42—2982no—
182C42—2981no—
183C42—2981no—
184C42—1492no—
185C42C22×D14911yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—81no—
189Q8—2981no—
190Q8—2981no—
191Q8—2981no—
192Q8—1492no—
193Q8—1494no—
194Q8—11922no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—2981no—
198C2×C4—2981no—
199C2×C4—2981no—
200C2×C4—2981no—
201C2×C4—1492no—
202C2×C4—1492no—
203C2×C4D4×D14911yescharacteristic
204C2×C4D4×D14911yescharacteristic
205C2×C4C23×D14911yescharacteristic
206C8—21no—
207C8—21no—
208C8—2982no—
209C22C2×D4×D14911yescharacteristic
210C4—21no—
211C4—42no—
212C4—42no—
213C4—2982no—
214C4—2982no—
215C4—5961no—
216C4—5961no—
217C4—5961no—
218C4—1494no—
219C4Q16×D14912yes—
220C4#41×D14911yescharacteristic
221C4#1801195811yescharacteristic
222C2#2375028311yescharacteristic
223C2C2×Q16×D14911yescharacteristic
224C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#487×C149C2
socle, prime radicalC22×C149C22×D4
hypercenter#487D149
hypocenterC149#3363
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
77. Dic298Q16semidirect
112. C149#3363semidirect

Maximal subgroups

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

subgroupindex
#237503552
#237503502
#237499742
#237499182
#237499172
#237498342
#237498322
C8×Dic2982
C4×Dic5962
#237497172
#487×C1492
#3363149