Finite Group Databasebeta

← #19135718

Subgroups — #19135718

Order 5504.

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

normal subgroups only

This group has 638 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, complemented
2C2×#13063294C211yesmaximal, characteristic, complemented
3C2×#13063240C211yesmaximal, characteristic, complemented
4C2×#13063239C211yesmaximal, characteristic, complemented
5#14582755C211yesmaximal, characteristic, complemented
6#14582665C211yesmaximal, characteristic, complemented
7C2×#120×C43C211yesmaximal, characteristic, complemented
8C22×C22⋊D43—21no—
9C22×C22⋊D43C2211yescharacteristic
10#13063308—21no—
11#13063306—21no—
12#13063297—22no—
13#13063294—22no—
14#13063294—21no—
15#13063294—22no—
16#13063293—21no—
17C2×C22⋊Dic43—21no—
18C2×C22⋊Dic43—22no—
19C2×C22⋊Dic43C2211yescharacteristic
20C2×C22⋊Dic43C2211yescharacteristic
21C2×C22⋊Dic43C2211yescharacteristic
22#13063240—22no—
23#13063239—22no—
24C25×C43C2211yescharacteristic
25C22×D4×C43—21no—
26C22×D4×C43C2211yescharacteristic
27#120×C43—22no—
28#120×C43—22no—
29C2×C22⋊C4×C43—21no—
30C2×C22⋊C4×C43C2211yescharacteristic
31C24×C43—21no—
32C24×C43—21no—
33C24×C43—21no—
34C24×C43—21no—
35C24×C43—21no—
36C24×C43—21no—
37C24×C43—44no—
38C24×C43D412yescomplemented
39C24×C43D411yescharacteristic, complemented
40C24×C43C2311yescharacteristic
41C23×D43D411yescharacteristic, complemented
42C2×D4×C43—24no—
43C2×D4×C43—21no—
44C2×D4×C43—21no—
45C2×D4×C43—21no—
46C2×D4×C43—21no—
47C2×D4×C43—21no—
48C2×D4×C43—21no—
49C2×D4×C43—44no—
50C22×C4×C43—21no—
51C22×C4×C43D411yescharacteristic, complemented
52C2×C22⋊D43—24no—
53C2×C22⋊D43—22no—
54C2×C22⋊D43—21no—
55C2×C22⋊D43—21no—
56C2×C22⋊D43—21no—
57C2×C22⋊D43—21no—
58C2×C22⋊D43—21no—
59C2×C22⋊D43—21no—
60C2×C22⋊D43—44no—
61C22×Dic43—21no—
62C22×Dic43—21no—
63C22×Dic43D411yescharacteristic, complemented
64C22×Dic43D412yescomplemented
65C22⋊C4×C43—24no—
66C22⋊C4×C43—21no—
67C22⋊C4×C43D412yescomplemented
68C22⋊Dic43—24no—
69C22⋊Dic43—22no—
70C22⋊Dic43—21no—
71C22⋊Dic43—21no—
72C22⋊Dic43—21no—
73C22⋊Dic43—21no—
74C22⋊Dic43—21no—
75C22⋊Dic43—44no—
76C22⋊Dic43D412yescomplemented
77(C2×D43)⋊C4—22no—
78Dic43⋊C4—22no—
79C23×C43—24no—
80C23×C43—24no—
81C23×C43—24no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43—21no—
86C23×C43—21no—
87C23×C43—21no—
88C23×C43—44no—
89C23×C43—42no—
90C23×C43—42no—
91C23×C43—42no—
92C23×C43—42no—
93C23×C43—44no—
94C23×C43—44no—
95C23×C43—44no—
96C23×C43—42no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43—41no—
101C23×C43C2×D411yescharacteristic
102C23×C43C2×D411yescharacteristic
103C23×C43C2×D411yescharacteristic
104C23×C43C2×D411yescharacteristic
105C23×C43C2×D411yescharacteristic
106C23×C43C2×D411yescharacteristic
107C23×C43#4111yescharacteristic
108C22×D43—21no—
109C22×D43—21no—
110C22×D43—21no—
111C22×D43—42no—
112D4×C43—48no—
113D4×C43—41no—
114D4×C43—41no—
115D4×C43—41no—
116D4×C43—41no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—22no—
120C2×C4×C43—21no—
121C2×C4×C43—42no—
122C22⋊D43—48no—
123C22⋊D43—41no—
124C22⋊D43—41no—
125C22⋊D43—41no—
126C22⋊D43—41no—
127C22⋊D43—82no—
128C2×Dic43—21no—
129C2×Dic43—22no—
130C2×Dic43—21no—
131C2×Dic43—22no—
132C2×Dic43—21no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—41no—
137C22×C43—22no—
138C22×C43—22no—
139C22×C43—22no—
140C22×C43—24no—
141C22×C43—24no—
142C22×C43—24no—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—42no—
148C22×C43—44no—
149C22×C43—42no—
150C22×C43—44no—
151C22×C43—42no—
152C22×C43—44no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43—44no—
156C22×C43—41no—
157C22×C43—42no—
158C22×C43—81no—
159C22×C43#12011yescharacteristic
160C22×C43#12011yescharacteristic
161C22×C43#12011yescharacteristic
162C22×C43#12111yescharacteristic
163C22×C43#12111yescharacteristic
164C22×C43#12111yescharacteristic
165C22×C43#12711yescharacteristic
166C2×D43—42no—
167C2×D43—41no—
168C2×D43—42no—
169C2×D43—81no—
170C4×C43—42no—
171C4×C43—41no—
172Dic43—42no—
173Dic43—41no—
174Dic43—42no—
175Dic43—81no—
176#2021—431nomaximal, Sylow
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—44no—
184C2×C43—81no—
185C2×C43#39211yescharacteristic
186C2×C43B(4,𝔽2)12yes—
187D43—81no—
188#534—431no—
189C2×#120—431no—
190C2×#120D4311yescharacteristic, complemented
191C2×#99—431no—
192C2×#99—431no—
193#379—431no—
194#342—431no—
195C43#202111yescharacteristic, complemented, Sylow
196C25C2×D4311yescharacteristic
197C22×D4—21no—
198C22×D4—431no—
199C22×D4—861no—
200C22×D4C2×D4311yescharacteristic
201#123—861no—
202#123—861no—
203#121—862no—
204#120—22no—
205#120—22no—
206#120—862no—
207#120—861no—
208#120—862no—
209#120—861no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—431no—
212C2×C22⋊C4—431no—
213C2×C22⋊C4—431no—
214C2×C22⋊C4—861no—
215C2×C22⋊C4—862no—
216C2×C22⋊C4C2×D4311yescharacteristic
217#99—862no—
218#99—862no—
219C24—21no—
220C24—21no—
221C24—21no—
222C24—21no—
223C24—21no—
224C24—21no—
225C24—44no—
226C24—431no—
227C24C22⋊D4312yescomplemented
228C24C22⋊D4311yescharacteristic, complemented
229C24C22×D4311yescharacteristic
230C2×D4—24no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—21no—
237C2×D4—44no—
238C2×D4—862no—
239C2×D4—864no—
240C2×D4—861no—
241C2×D4—861no—
242C2×D4—861no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4—861no—
246C2×D4—1724no—
247C22×C4—21no—
248C22×C4—431no—
249C22×C4—432no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4C22⋊D4311yescharacteristic, complemented
253C4⋊C4—862no—
254C22⋊C4—24no—
255C22⋊C4—21no—
256C22⋊C4—432no—
257C22⋊C4—862no—
258C22⋊C4—864no—
259C22⋊C4—862no—
260C22⋊C4—861no—
261C22⋊C4—861no—
262C22⋊C4—861no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C22⋊C4—1724no—
266C22⋊C4C22⋊D4312yescomplemented
267C23—24no—
268C23—24no—
269C23—24no—
270C23—22no—
271C23—22no—
272C23—22no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—42no—
277C23—44no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—44no—
282C23—44no—
283C23—44no—
284C23—42no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—861no—
290C23—861no—
291C23—861no—
292C23—1722no—
293C23D4×D4311yescharacteristic
294C23D4×D4311yescharacteristic
295C23D4×D4311yescharacteristic
296C23#1062190011yescharacteristic
297C23C2×C22⋊D4311yescharacteristic
298C23C2×C22⋊D4311yescharacteristic
299C23C2×C22⋊D4311yescharacteristic
300D4—48no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—3442no—
306D4—1728no—
307D4—1721no—
308D4—1721no—
309D4—1721no—
310D4—1721no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—862no—
317C2×C4—861no—
318C2×C4—862no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—1722no—
322C2×C4—1721no—
323C2×C4—1722no—
324C2×C4—1722no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—24no—
329C22—24no—
330C22—24no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—42no—
336C22—44no—
337C22—42no—
338C22—42no—
339C22—44no—
340C22—44no—
341C22—42no—
342C22—42no—
343C22—44no—
344C22—41no—
345C22—42no—
346C22—81no—
347C22—3441no—
348C22—1722no—
349C22—1721no—
350C22—1722no—
351C22#1306329311yescharacteristic
352C22#1306329311yescharacteristic
353C22#1306329411yescharacteristic
354C22#1306329611yescharacteristic
355C22#1306329711yescharacteristic
356C22#1306329711yescharacteristic
357C22#1306332111yescharacteristic
358C4—42no—
359C4—41no—
360C4—3441no—
361C4—1722no—
362C4—1721no—
363C4—1722no—
364C2—21no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—44no—
371C2—81no—
372C2—3441no—
373C2#1458280711yescharacteristic
374C2#1458308512yes—
subgroupG/H
centerC22#13063293
commutatorC24×C43C23
FrattiniC24C22×D43
FittingC2×#120×C43C2
socleC22×C43#120
hypercenterC2×#120D43
hypocenterC43#2021
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #14583458C2semidirect
2. C2×#13063294C2semidirect
3. C2×#13063240C2semidirect
4. C2×#13063239C2semidirect
5. #14582755C2semidirect
6. #14582665C2semidirect
7. C2×#120×C43C2semidirect
38. C24×C43D4semidirect
39. C24×C43D4semidirect
41. C23×D43D4semidirect
51. C22×C4×C43D4semidirect
63. C22×Dic43D4semidirect
64. C22×Dic43D4semidirect
67. C22⋊C4×C43D4semidirect
76. C22⋊Dic43D4semidirect
190. C2×#120D43semidirect
195. C43#2021semidirect
227. C24C22⋊D43semidirect
228. C24C22⋊D43semidirect
252. C22×C4C22⋊D43semidirect
266. C22⋊C4C22⋊D43semidirect