Finite Group Databasebeta

← #19135723

Subgroups — #19135723

Order 5504.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#14583458C211yesmaximal, characteristic
2C2×#13063308C211yesmaximal, characteristic, complemented
3C2×#13063240C211yesmaximal, characteristic, complemented
4C2×#13063239C211yesmaximal, characteristic, complemented
5#14582762C211yesmaximal, characteristic, complemented
6#14582665C211yesmaximal, characteristic, complemented
7C2×#123×C43C211yesmaximal, characteristic, complemented
8C22×C22⋊D43C2211yescharacteristic
9#13063308—21no—
10#13063308—22no—
11#13063308—22no—
12#13063306—21no—
13#13063297—22no—
14#13063294—21no—
15#13063293—21no—
16C2×Dic43⋊C4—21no—
17C2×C22⋊Dic43C2211yescharacteristic
18C2×C22⋊Dic43C2211yescharacteristic
19C2×C22⋊Dic43C2211yescharacteristic
20C2×(C2×D43)⋊C4—21no—
21#13063240—22no—
22#13063239—22no—
23C43⋊#95—22no—
24C22×D4×C43C2211yescharacteristic
25C23×C4×C43C2211yescharacteristic
26#123×C43—22no—
27#123×C43—22no—
28C2×C4⋊C4×C43—21no—
29C2×C22⋊C4×C43—21no—
30C2×C22⋊C4×C43C2211yescharacteristic
31C24×C43D411yescharacteristic
32C24×C43C2311yescharacteristic
33C23×D43D411yescharacteristic
34C2×D4×C43—21no—
35C2×D4×C43—21no—
36C2×D4×C43—21no—
37C2×D4×C43—21no—
38C2×D4×C43—21no—
39C2×D4×C43—21no—
40C22×C4×C43—21no—
41C22×C4×C43—21no—
42C22×C4×C43—21no—
43C22×C4×C43—21no—
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43D411yescharacteristic
48C22×C4×C43D412yescomplemented
49C2×C22⋊D43—22no—
50C2×C22⋊D43—21no—
51C2×C22⋊D43—21no—
52C2×C22⋊D43—21no—
53C2×C22⋊D43—21no—
54C2×C22⋊D43—21no—
55C2×C22⋊D43—21no—
56C22×Dic43—21no—
57C22×Dic43—21no—
58C22×Dic43D411yescharacteristic
59C22×Dic43D412yes—
60C4⋊C4×C43—24no—
61C22⋊C4×C43—24no—
62C22⋊C4×C43—21no—
63C22⋊C4×C43D412yescomplemented
64C22⋊Dic43—22no—
65C22⋊Dic43—21no—
66C22⋊Dic43—21no—
67C22⋊Dic43—21no—
68C22⋊Dic43—21no—
69C22⋊Dic43—21no—
70C22⋊Dic43D412yescomplemented
71(C2×D43)⋊C4—24no—
72(C2×D43)⋊C4—22no—
73Dic43⋊C4—24no—
74Dic43⋊C4—22no—
75C23×C43—21no—
76C23×C43—21no—
77C23×C43—21no—
78C23×C43—42no—
79C23×C43—42no—
80C23×C43C2×D411yescharacteristic
81C23×C43C2×D411yescharacteristic
82C23×C43C2×D411yescharacteristic
83C23×C43C2×D411yescharacteristic
84C23×C43C2×D411yescharacteristic
85C23×C43C2×D411yescharacteristic
86C23×C43#4111yescharacteristic
87C22×D43—21no—
88C22×D43—21no—
89C22×D43—21no—
90C22×D43—42no—
91D4×C43—41no—
92D4×C43—41no—
93D4×C43—41no—
94D4×C43—41no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C22⋊D43—41no—
108C22⋊D43—41no—
109C22⋊D43—41no—
110C22⋊D43—41no—
111C22⋊D43—82no—
112C2×Dic43—21no—
113C2×Dic43—22no—
114C2×Dic43—21no—
115C2×Dic43—22no—
116C2×Dic43—21no—
117C2×Dic43—42no—
118C2×Dic43—42no—
119C2×Dic43—42no—
120C2×Dic43—41no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—22no—
124C22×C43—41no—
125C22×C43—41no—
126C22×C43—41no—
127C22×C43—41no—
128C22×C43—42no—
129C22×C43—41no—
130C22×C43—42no—
131C22×C43—81no—
132C22×C43#12011yescharacteristic
133C22×C43#12011yescharacteristic
134C22×C43#12011yescharacteristic
135C22×C43#12111yescharacteristic
136C22×C43#12111yescharacteristic
137C22×C43#12111yescharacteristic
138C22×C43#12711yescharacteristic
139C2×D43—42no—
140C2×D43—41no—
141C2×D43—42no—
142C2×D43—81no—
143C4×C43—42no—
144C4×C43—42no—
145C4×C43—41no—
146Dic43—42no—
147Dic43—41no—
148Dic43—42no—
149Dic43—81no—
150#2022—431nomaximal, Sylow
151C2×C43—21no—
152C2×C43—21no—
153C2×C43—21no—
154C2×C43—21no—
155C2×C43—21no—
156C2×C43—21no—
157C2×C43—81no—
158C2×C43#39211yescharacteristic
159C2×C43#45812yes—
160D43—81no—
161#534—431no—
162C2×#123—431no—
163C2×#123D4311yescharacteristic, complemented
164C2×#99—431no—
165C2×#99—431no—
166#381—431no—
167#342—431no—
168C43#202211yescharacteristic, complemented, Sylow
169C22×D4—431no—
170C22×D4C2×D4311yescharacteristic
171C23×C4C2×D4311yescharacteristic
172#123—22no—
173#123—22no—
174#123—862no—
175#123—861no—
176#123—861no—
177#123—862no—
178#121—862no—
179#120—861no—
180#120—861no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—861no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—431no—
185C2×C22⋊C4—431no—
186C2×C22⋊C4—431no—
187C2×C22⋊C4—861no—
188C2×C22⋊C4C2×D4311yescharacteristic
189#99—862no—
190#99—862no—
191#95—862no—
192C24—431no—
193C24C22⋊D4311yescharacteristic
194C24C22×D4311yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—862no—
202C2×D4—861no—
203C2×D4—861no—
204C2×D4—861no—
205C2×D4—861no—
206C2×D4—861no—
207C2×D4—861no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—431no—
216C22×C4—432no—
217C22×C4—861no—
218C22×C4—861no—
219C22×C4C22⋊D4311yescharacteristic
220C22×C4C22⋊D4312yescomplemented
221C4⋊C4—24no—
222C4⋊C4—864no—
223C4⋊C4—862no—
224C22⋊C4—24no—
225C22⋊C4—21no—
226C22⋊C4—432no—
227C22⋊C4—864no—
228C22⋊C4—862no—
229C22⋊C4—862no—
230C22⋊C4—861no—
231C22⋊C4—861no—
232C22⋊C4—861no—
233C22⋊C4—861no—
234C22⋊C4—861no—
235C22⋊C4C22⋊D4312yescomplemented
236C23—21no—
237C23—21no—
238C23—21no—
239C23—42no—
240C23—42no—
241C23—861no—
242C23—861no—
243C23—861no—
244C23—1722no—
245C23D4×D4311yescharacteristic
246C23D4×D4311yescharacteristic
247C23D4×D4311yescharacteristic
248C23#1062190011yescharacteristic
249C23C2×C22⋊D4311yescharacteristic
250C23C2×C22⋊D4311yescharacteristic
251C23C2×C22⋊D4311yescharacteristic
252D4—41no—
253D4—41no—
254D4—41no—
255D4—41no—
256D4—3442no—
257D4—1721no—
258D4—1721no—
259D4—1721no—
260D4—1721no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—862no—
274C2×C4—861no—
275C2×C4—862no—
276C2×C4—861no—
277C2×C4—861no—
278C2×C4—1722no—
279C2×C4—1721no—
280C2×C4—1722no—
281C2×C4—1722no—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—41no—
291C22—42no—
292C22—81no—
293C22—3441no—
294C22—1722no—
295C22—1721no—
296C22—1722no—
297C22#1306329311yescharacteristic
298C22#1306329311yescharacteristic
299C22#1306329411yescharacteristic
300C22#1306329611yescharacteristic
301C22#1306329711yescharacteristic
302C22#1306329711yescharacteristic
303C22#1306332111yescharacteristic
304C4—42no—
305C4—42no—
306C4—41no—
307C4—3441no—
308C4—1722no—
309C4—1721no—
310C4—1722no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—81no—
318C2—3441no—
319C2#1458280711yescharacteristic
320C2#1458308812yes—
subgroupG/H
centerC22#13063293
commutatorC24×C43C23
FrattiniC24C22×D43
FittingC2×#123×C43C2
socleC22×C43#120
hypercenterC2×#123D43
hypocenterC43#2022
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#13063308C2semidirect
3. C2×#13063240C2semidirect
4. C2×#13063239C2semidirect
5. #14582762C2semidirect
6. #14582665C2semidirect
7. C2×#123×C43C2semidirect
48. C22×C4×C43D4semidirect
63. C22⋊C4×C43D4semidirect
70. C22⋊Dic43D4semidirect
163. C2×#123D43semidirect
168. C43#2022semidirect
220. C22×C4C22⋊D43semidirect
235. C22⋊C4C22⋊D43semidirect