Finite Group Databasebeta

← #19148212

Subgroups — #19148212

Order 5504.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583625C211yesmaximal, characteristic, complemented
2#14583621C213yesmaximal, complemented
3#14583590C213yesmaximal, complemented
4#14583584C213yesmaximal, complemented
5Q8×C22⋊D43C211yesmaximal, characteristic, complemented
6#14583561C211yesmaximal, characteristic, complemented
7#14583560C211yesmaximal, characteristic, complemented
8#14583550C213yesmaximal, complemented
9#14583453C213yesmaximal, complemented
10#14583436C213yesmaximal, complemented
11#14583433C213yesmaximal, complemented
12C4×#10621902C211yesmaximal, characteristic, complemented
13C4×#10621898C213yesmaximal, complemented
14C4×Q8×D43C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C43C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621898C2213yes—
18C2×Q8×D43C2211yescharacteristic
19#13063324C2213yes—
20#13063323C2213yes—
21#13063320C2216yes—
22#13063319C2216yes—
23#13063317C2213yes—
24#13063316C2213yes—
25#13063315C2216yes—
26#13063314C2213yes—
27#13063313C2213yes—
28#13063310C2216yes—
29#13063308C2216yes—
30#13063305C2213yes—
31#13063304C2213yes—
32#13063303C2216yes—
33#13063301C2213yes—
34#13063301C2213yes—
35#13063300C2213yes—
36#13063299C2213yes—
37Q8×Dic43C2211yescharacteristic
38Q8×Dic43C2211yescharacteristic
39C4×Dic86C2213yes—
40C4×Dic86C2213yes—
41C4×Dic86C2213yes—
42#13063290C2213yes—
43C4×D172C2213yes—
44C4×D172C2213yes—
45C4×D172C2213yes—
46#13063287C2213yes—
47C4×C22⋊D43C2213yes—
48C4×C22⋊D43C2213yes—
49C4×C22⋊D43C2211yescharacteristic
50C4×C22⋊D43C2213yes—
51#13063284C2213yes—
52#13063283C2213yes—
53#13063282C2213yes—
54#13063282C2213yes—
55#13063282C2216yes—
56C4⋊C4×D43C2213yes—
57C42×D43C2213yes—
58C42×D43C2213yes—
59C22×Q8×C43C2211yescharacteristic
60C4×Q8×C43C2211yescharacteristic
61C4×Q8×C43C2213yes—
62C4×Q8×C43C2211yescharacteristic
63C4×Q8×C43C2213yes—
64C2×C4⋊C4×C43C2213yes—
65C2×C42×C43C2213yes—
66C2×Q8×C43—24no—
67C2×Q8×C43C2313yes—
68C2×Q8×C43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C22×C4×C43C2313yes—
71C22×C4×C43C2313yes—
72C2×C22⋊D43C2313yes—
73C2×C22⋊D43C2311yescharacteristic
74#10621902—24no—
75Q8×D43—24no—
76#10621898—212no—
77C2×D172C2313yes—
78C2×D172C2313yes—
79C2×C4×D43C2311yescharacteristic
80C2×C4×D43C2313yes—
81C2×C4×D43C2313yes—
82C2×C4×D43C2313yes—
83C2×C4×D43C2313yes—
84C2×C4×D43C2313yes—
85C2×Dic86C2313yes—
86C2×Dic86C2313yes—
87C4⋊C4×C43C2313yes—
88C4⋊C4×C43C2313yes—
89C4⋊C4×C43C2316yes—
90C42×C43C2313yes—
91C42×C43C2313yes—
92C42×C43C2313yes—
93C42×C43C2313yes—
94C22⋊Dic43C2311yescharacteristic
95C22⋊Dic43C2313yes—
96(C2×D43)⋊C4C2311yescharacteristic
97(C2×D43)⋊C4C2313yes—
98(C2×D43)⋊C4C2313yes—
99(C2×D43)⋊C4C2313yes—
100(C2×D43)⋊C4C2316yes—
101(C2×D43)⋊C4C2316yes—
102(C2×D43)⋊C4C2316yes—
103C4⋊Dic43C2313yes—
104C4⋊Dic43C2313yes—
105C4⋊Dic43C2313yes—
106C4⋊Dic43C2313yes—
107Dic43⋊C4C2316yes—
108Dic43⋊C4C2311yescharacteristic
109Dic43⋊C4C2313yes—
110Dic43⋊C4C2313yes—
111Dic43⋊C4C2313yes—
112Dic43⋊C4C2316yes—
113Dic43⋊C4C2316yes—
114C4×Dic43C2311yescharacteristic
115C4×Dic43C2313yes—
116C4×Dic43C2313yes—
117C4×Dic43C2313yes—
118C4×Dic43C2313yes—
119C4×Dic43C2313yes—
120C23×C43C2411yescharacteristic
121C22×D43C2413yes—
122C22×D43C2411yescharacteristic
123Q8×C43—26no—
124Q8×C43#4114yescomplemented
125C2×C4×C43—26no—
126C2×C4×C43—26no—
127C2×C4×C43—22no—
128C2×C4×C43C2413yes—
129C2×C4×C43C2411yescharacteristic
130C2×C4×C43C2413yes—
131C2×C4×C43C2413yes—
132C2×C4×C43C2413yes—
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—26no—
135C22⋊D43#4114yescomplemented
136C2×Dic43C2411yescharacteristic
137C2×Dic43C2411yescharacteristic
138C2×Dic43C2413yes—
139C2×Dic43C2413yes—
140C2×Dic43C2413yes—
141C2×Dic43C2411yescharacteristic
142D172—26no—
143D172—26no—
144C4×D43—26no—
145C4×D43—26no—
146C4×D43—26no—
147C4×D43—22no—
148C4×D43—26no—
149C4×D43—26no—
150Dic86—26no—
151Dic86—26no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43C2×#4112yes—
155C22×C43C2511yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—23no—
159C2×D43—23no—
160C2×D43—23no—
161C2×D43C2×#4112yes—
162C4×C43—23no—
163C4×C43—23no—
164C4×C43—23no—
165C4×C43—21no—
166C4×C43C2×#4116yes—
167C4×C432−1+412yes—
168Dic43—23no—
169Dic43—23no—
170Dic43—21no—
171Dic43—21no—
172Dic43—23no—
173Dic43C2×#4112yes—
174#3482—431nomaximal, Sylow
175C2×C43—22no—
176C2×C43C22×#4111yescharacteristic
177C2×C43C22×#4111yescharacteristic
178C2×C43C2×2−1+411yescharacteristic
179D43—22no—
180D43—43no—
181#557—431no—
182#556—433no—
183#552—433no—
184#552—433no—
185D4×Q8—431no—
186#548—431no—
187#548—431no—
188#547—433no—
189#533—433no—
190#529—433no—
191#529—433no—
192C4×#41—431no—
193C4×#41—433no—
194C2×C4×Q8—431no—
195C2×C4×Q8D4311yescharacteristic, complemented
196C43#348211yescharacteristic, complemented, Sylow
197C2×#41—431no—
198C2×#41—433no—
199C22×Q8—431no—
200C22×Q8C2×D4311yescharacteristic
201C4⋊Q8—433no—
202C4⋊Q8—433no—
203#126—436no—
204#126—436no—
205#125—433no—
206#125—436no—
207#125—433no—
208#124—433no—
209#124—433no—
210#123—436no—
211#123—436no—
212C22⋊Q8—433no—
213C22⋊Q8—433no—
214C22⋊Q8—433no—
215C22⋊Q8—436no—
216C22⋊Q8—433no—
217#121—433no—
218#121—433no—
219C4×Q8—431no—
220C4×Q8—431no—
221C4×Q8—433no—
222C4×Q8—433no—
223C4×Q8—433no—
224C4×Q8—433no—
225C4×Q8C2×D4311yescharacteristic
226C4×Q8C2×D4313yes—
227C4×Q8C2×D4311yescharacteristic
228C4×Q8C2×D4313yes—
229C4×D4—431no—
230C4×D4—433no—
231C4×D4—433no—
232C4×D4—433no—
233C4×D4—433no—
234C4×D4—433no—
235C4×D4—433no—
236C4×D4—433no—
237#117—433no—
238#117—433no—
239#117—433no—
240#117—433no—
241#117—436no—
242C2×C4⋊C4—433no—
243C2×C4⋊C4C2×D4313yes—
244C2×C42—433no—
245C2×C42—433no—
246C2×C42C2×D4313yes—
247#41—8612no—
248#41—864no—
249C2×Q8—24no—
250C2×Q8—433no—
251C2×Q8—433no—
252C2×Q8—864no—
253C2×Q8C22×D4313yes—
254C2×Q8C22×D4311yescharacteristic
255C2×D4—431no—
256C2×D4—433no—
257C2×D4—433no—
258C2×D4—433no—
259C22×C4—433no—
260C22×C4—433no—
261C22×C4—433no—
262C22×C4—433no—
263C22×C4—431no—
264C22×C4—433no—
265C22×C4C22×D4313yes—
266C22×C4C22×D4313yes—
267C22×C4C22×D4311yescharacteristic
268C4⋊C4—433no—
269C4⋊C4—436no—
270C4⋊C4—431no—
271C4⋊C4—433no—
272C4⋊C4—433no—
273C4⋊C4—433no—
274C4⋊C4—433no—
275C4⋊C4—433no—
276C4⋊C4—433no—
277C4⋊C4—436no—
278C4⋊C4—436no—
279C4⋊C4C22×D4313yes—
280C4⋊C4C22×D4313yes—
281C4⋊C4C22×D4316yes—
282C22⋊C4—431no—
283C22⋊C4—433no—
284C22⋊C4—431no—
285C22⋊C4—433no—
286C22⋊C4—436no—
287C22⋊C4—433no—
288C22⋊C4—433no—
289C22⋊C4—436no—
290C22⋊C4—436no—
291C42—433no—
292C42—433no—
293C42—433no—
294C42—433no—
295C42—431no—
296C42—433no—
297C42C22×D4313yes—
298C42C22×D4313yes—
299C42C22×D4313yes—
300C42C22×D4313yes—
301C23—431no—
302C23—433no—
303C23C23×D4311yescharacteristic
304Q8—26no—
305Q8—866no—
306Q8—866no—
307Q8#1062189814yescomplemented
308D4—434no—
309D4—866no—
310D4—866no—
311D4—866no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—22no—
315C2×C4—431no—
316C2×C4—431no—
317C2×C4—431no—
318C2×C4—433no—
319C2×C4—433no—
320C2×C4—433no—
321C2×C4—866no—
322C2×C4—866no—
323C2×C4—866no—
324C2×C4—866no—
325C2×C4—862no—
326C2×C4—866no—
327C2×C4C23×D4313yes—
328C2×C4C23×D4311yescharacteristic
329C2×C4C23×D4313yes—
330C2×C4C23×D4313yes—
331C2×C4C23×D4313yes—
332C2×C4C23×D4311yescharacteristic
333C22—21no—
334C22—21no—
335C22—432no—
336C22—861no—
337C22—861no—
338C22—863no—
339C22—863no—
340C22—863no—
341C22#41×D4312yes—
342C22C24×D4311yescharacteristic
343C4—23no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—432no—
348C4—863no—
349C4—861no—
350C4—863no—
351C4—861no—
352C4—863no—
353C4C2×#1062189816yes—
354C4#1306337312yes—
355C2—22no—
356C2—862no—
357C2—1723no—
358C2C2×#41×D4311yescharacteristic
359C2C22×#1062189811yescharacteristic
360C2C2×#1306337311yescharacteristic
subgroupG/H
centerC2×C4C23×D43
commutator, socleC22×C43C25
FrattiniC22C24×D43
FittingC2×C4×Q8×C43C2
hypercenterC2×C4×Q8D43
hypocenterC43#3482
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14583625C2semidirect
2. #14583621C2semidirect
3. #14583590C2semidirect
4. #14583584C2semidirect
5. Q8×C22⋊D43C2semidirect
6. #14583561C2semidirect
7. #14583560C2semidirect
8. #14583550C2semidirect
9. #14583453C2semidirect
10. #14583436C2semidirect
11. #14583433C2semidirect
12. C4×#10621902C2semidirect
13. C4×#10621898C2semidirect
14. C4×Q8×D43C2semidirect
15. C2×C4×Q8×C43C2semidirect
124. Q8×C43#41semidirect
135. C22⋊D43#41semidirect
195. C2×C4×Q8D43semidirect
196. C43#3482semidirect
307. Q8#10621898semidirect