Finite Group Databasebeta

← #34057625

Subgroups — #34057625

Order 19072.

326 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 133 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
1Q8×Dic298C211yesmaximal, characteristic
2#23750353C211yesmaximal, characteristic
3#23750034C212yesmaximal
4#23750023C211yesmaximal, characteristic
5#23749933C212yesmaximal
6#23749921C211yesmaximal, characteristic
7#23749911C211yesmaximal, characteristic
8#23749911C212yesmaximal
9#23749733C212yesmaximal
10C4×Dic596C211yesmaximal, characteristic
11#446×C149C211yesmaximal, characteristic
12C2×Dic596C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011911C2212yes—
15#18011911C2211yescharacteristic
16#18011910—21no—
17#18011910—22no—
18#18011909—21no—
19#18011903C2212yes—
20#18011901—22no—
21Q8×Dic149—21no—
22C4×Dic298C2211yescharacteristic
23C4×Dic298C2212yes—
24C4×Dic298C2211yescharacteristic
25C4×Dic298C2212yes—
26#18011876—21no—
27#18011845C2212yes—
28#18011845C2211yescharacteristic
29#18011843C2212yes—
30#18011843C2212yes—
31#18011843C2212yes—
32#18011836C2211yescharacteristic
33#18011836C2212yes—
34#18011836C2212yes—
35#18011836C2211yescharacteristic
36C4×Q8×C149C2211yescharacteristic
37C4⋊C8×C149C2211yescharacteristic
38C4⋊C8×C149C2212yes—
39#97×C149C2212yes—
40C4×C8×C149C2211yescharacteristic
41C2×Dic298—21no—
42C2×Dic298—22no—
43C2×Dic298—21no—
44C2×Dic298C2311yescharacteristic
45C2×Dic298C2311yescharacteristic
46Dic596Q814yescomplemented
47C4⋊Dic149—22no—
48C4⋊Dic149—21no—
49C4⋊Dic149—21no—
50C4⋊Dic149C2311yescharacteristic
51C4⋊Dic149C2312yes—
52C4⋊Dic149C2312yes—
53C4⋊Dic149C2311yescharacteristic
54#14558715—22no—
55#14558715—22no—
56#14558715—22no—
57#14558715—21no—
58#14558715—22no—
59#14558715—21no—
60C4×Dic149—21no—
61C4×Dic149—22no—
62C4×Dic149—21no—
63C4×Dic149—22no—
64C2×Q8×C149D411yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C2×C8×C149C2312yes—
67C2×C8×C149C2311yescharacteristic
68C4⋊C4×C149D411yescharacteristic
69C4⋊C4×C149D412yes—
70C42×C149C2311yescharacteristic
71C42×C149C2312yes—
72Dic298—21no—
73Dic298—21no—
74Dic298—42no—
75Dic298—82no—
76Dic298—81no—
77Dic298C2×Q812yes—
78Dic298C2×Q812yes—
79C2×Dic149—21no—
80C2×Dic149—21no—
81C2×Dic149—21no—
82C2×Dic149—22no—
83C2×Dic149—22no—
84C2×Dic149—21no—
85Q8×C149—22no—
86C2×C4×C149C2×D412yes—
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D412yes—
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2411yescharacteristic
91C8×C149—21no—
92C8×C149—22no—
93C8×C149C2×Q812yes—
94C22×C149C22×D411yescharacteristic
95C4×C149—22no—
96C4×C149—22no—
97C4×C149—21no—
98C4×C149#13712yes—
99C4×C149C22×Q811yescharacteristic
100C4×C1492−1+411yescharacteristic
101Dic149—22no—
102Dic149—22no—
103Dic149—42no—
104Dic149—41no—
105Dic149—41no—
106Dic149—42no—
107C2×C149D4×Q811yescharacteristic
108C2×C149C2×#13711yescharacteristic
109C2×C149#57711yescharacteristic
110C149#338711yescharacteristic, complemented, Sylow
111#3387—1491nomaximal, Sylow
112Q82—1491no—
113#557—1491no—
114#501—1492no—
115#498—1491no—
116#479—1492no—
117#477—1491no—
118#475—1492no—
119#475—1491no—
120#446D14911yescharacteristic
121#441—1492no—
122C4×Q16—1491no—
123C2×Q16—1491no—
124C4⋊Q8—2981no—
125C4⋊Q8—2981no—
126C4⋊Q8—2982no—
127C4⋊Q8—1491no—
128C4⋊Q8—1492no—
129C4⋊Q8—1491no—
130#125—2982no—
131#125—1492no—
132C4×Q8—2981no—
133C4×Q8—2981no—
134C4×Q8—1491no—
135C4×Q8—1492no—
136C4×Q8—1491no—
137C4×Q8—1492no—
138C4×Q8C2×D14911yescharacteristic
139#107—1491no—
140#107—1492no—
141#106—1492no—
142#106—1492no—
143#106—1492no—
144C4⋊C8C2×D14911yescharacteristic
145C4⋊C8C2×D14912yes—
146#103—1491no—
147#103—1491no—
148#103—1492no—
149#103—1492no—
150#97C2×D14912yes—
151C4×C8C2×D14911yescharacteristic
152C2×Q8—2981no—
153C2×Q8—2982no—
154C2×Q8—2981no—
155C2×Q8—1491no—
156C2×Q8—1491no—
157C2×Q8D59611yescharacteristic
158Q16—1494no—
159C2×C8C22×D14911yescharacteristic
160C2×C8C22×D14912yes—
161C2×C8C22×D14911yescharacteristic
162C4⋊C4—2982no—
163C4⋊C4—2982no—
164C4⋊C4—2981no—
165C4⋊C4—2981no—
166C4⋊C4—2982no—
167C4⋊C4—2982no—
168C4⋊C4—2981no—
169C4⋊C4—2981no—
170C4⋊C4—2982no—
171C4⋊C4—1492no—
172C4⋊C4—1491no—
173C4⋊C4—1492no—
174C4⋊C4—1491no—
175C4⋊C4D59611yescharacteristic
176C4⋊C4D59612yes—
177C42—2982no—
178C42—2981no—
179C42—2982no—
180C42—2981no—
181C42C22×D14911yescharacteristic
182C42C22×D14912yes—
183Q8—22no—
184Q8—2981no—
185Q8—2981no—
186Q8—5962no—
187Q8—1492no—
188Q8—1492no—
189Q8—11922no—
190Q8—11921no—
191C2×C4—2981no—
192C2×C4—2981no—
193C2×C4—2981no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4—2981no—
197C2×C4C2×D59612yes—
198C2×C4C2×D59612yes—
199C2×C4C2×D59611yescharacteristic
200C2×C4C2×D59611yescharacteristic
201C2×C4C23×D14911yescharacteristic
202C8—21no—
203C8—22no—
204C8Q8×D14912yes—
205C22C22×D59611yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—2982no—
210C4—2982no—
211C4—5962no—
212C4—5962no—
213C4—5961no—
214C4—5961no—
215C4#1801194412yes—
216C4C2×Q8×D14911yescharacteristic
217C4#1801195811yescharacteristic
218C2Q8×D59611yescharacteristic
219C2C2×#1801194411yescharacteristic
220C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#446×C149C2
socle, prime radicalC22×C149C22×D4
hypercenter#446D149
hypocenterC149#3387
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
46. Dic596Q8semidirect
110. C149#3387semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic2982
#237503532
#237500342
#237500232
#237499332
#237499212
#237499112
#237497332
C4×Dic5962
#446×C1492
#3387149