Finite Group Databasebeta

← #19149004

Subgroups — #19149004

Order 5504.

1002 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583652C212yesmaximal, complemented
2#14583648C212yesmaximal, complemented
3#14583633C212yesmaximal, complemented
4#14583629C212yesmaximal, complemented
5#14583620C212yesmaximal, complemented
6#14583617C212yesmaximal, complemented
7Q8×C22⋊D43C212yesmaximal, complemented
8#14583562C212yesmaximal, complemented
9#14583517C214yesmaximal, complemented
10#14583513C214yesmaximal, complemented
11#14583472C212yesmaximal, complemented
12#14583470C211yesmaximal, characteristic, complemented
13#14583451C212yesmaximal, complemented
14#14583445C211yesmaximal, characteristic
15C43×#536C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×Q8×D43C2212yes—
19#13063324C2214yes—
20#13063324C2212yes—
21#13063324C2214yes—
22#13063323C2212yes—
23#13063323C2214yes—
24#13063323C2211yescharacteristic
25#13063323C2212yes—
26#13063321C2211yescharacteristic
27#13063320C2214yes—
28#13063319C2214yes—
29#13063318C2214yes—
30#13063318C2214yes—
31#13063315C2214yes—
32#13063314C2211yescharacteristic
33#13063312C2211yescharacteristic
34#13063312C2212yes—
35#13063311C2214yes—
36#13063311C2214yes—
37#13063311C2214yes—
38#13063310C2214yes—
39#13063307C2214yes—
40#13063306C2212yes—
41#13063306C2212yes—
42#13063305C2212yes—
43#13063304C2212yes—
44#13063304C2214yes—
45#13063304C2212yes—
46#13063303C2214yes—
47#13063302C2214yes—
48#13063302C2214yes—
49#13063301C2212yes—
50#13063301C2214yes—
51#13063297C2212yes—
52#13063297C2212yes—
53Q8×Dic43C2212yes—
54C4×Dic86C2214yes—
55#13063290C2212yes—
56#13063290C2214yes—
57#13063290C2214yes—
58C4×C22⋊D43C2212yes—
59C4×C22⋊D43C2212yes—
60C4×C22⋊D43C2214yes—
61(C22⋊D43)⋊C4C2214yes—
62#13063284C2211yescharacteristic
63#13063283C2212yes—
64#13063281C2214yes—
65C2×C4×Dic43C2211yescharacteristic
66C2×#41×C43C2211yescharacteristic
67C22×Q8×C43C2211yescharacteristic
68C4⋊Q8×C43C2212yes—
69#124×C43C2212yes—
70#123×C43C2212yes—
71#123×C43C2212yes—
72C22⋊Q8×C43C2212yes—
73C22⋊Q8×C43C2212yes—
74#117×C43C2211yescharacteristic
75#41×C43—42no—
76C2×Q8×C43—42no—
77C2×Q8×C43C2312yes—
78C2×Q8×C43C2312yes—
79C2×Q8×C43C2311yescharacteristic
80C2×D4×C43C2311yescharacteristic
81C2×D4×C43C2311yescharacteristic
82C2×D4×C43C2311yescharacteristic
83C22×C4×C43C2311yescharacteristic
84C22×C4×C43C2311yescharacteristic
85C22×C4×C43C2311yescharacteristic
86C22×C4×C43C2312yes—
87C2×C22⋊D43C2312yes—
88C2×C22⋊D43C2312yes—
89C2×C22⋊D43C2312yes—
90C22×Dic43C2312yes—
91C22×Dic43C2312yes—
92Q8×D43—44no—
93#10621898—42no—
94C2×D172C2311yescharacteristic
95C2×C4×D43C2312yes—
96C2×C4×D43C2314yes—
97C2×Dic86—42no—
98C2×Dic86C2314yes—
99C2×Dic86C2312yes—
100C2×Dic86C2314yes—
101C2×Dic86C2312yes—
102C2×Dic86C2311yescharacteristic
103C4⋊C4×C43C2312yes—
104C4⋊C4×C43C2314yes—
105C4⋊C4×C43C2314yes—
106C22⋊C4×C43C2312yes—
107C22⋊C4×C43C2314yes—
108C22⋊C4×C43C2314yes—
109C42×C43C2312yes—
110C22⋊Dic43C2314yes—
111C22⋊Dic43C2312yes—
112C22⋊Dic43C2312yes—
113C22⋊Dic43C2312yes—
114C22⋊Dic43C2314yes—
115(C2×D43)⋊C4C2314yes—
116(C2×D43)⋊C4C2314yes—
117(C2×D43)⋊C4C2312yes—
118(C2×D43)⋊C4C2312yes—
119(C2×D43)⋊C4C2314yes—
120C4⋊Dic43C2312yes—
121C4⋊Dic43C2314yes—
122C4⋊Dic43C2314yes—
123Dic43⋊C4C2314yes—
124Dic43⋊C4C2314yes—
125Dic43⋊C4C2314yes—
126Dic43⋊C4C2312yes—
127Dic43⋊C4C2312yes—
128Dic43⋊C4C2314yes—
129Dic43⋊C4C2314yes—
130Dic43⋊C4C2314yes—
131Dic43⋊C4C2314yes—
132C4×Dic43C2312yes—
133C4×Dic43C2311yescharacteristic
134C4×Dic43C2311yescharacteristic
135C4×Dic43C2314yes—
136C4×Dic43C2314yes—
137C4×Dic43C2314yes—
138C4×Dic43C2312yes—
139C23×C43C2411yescharacteristic
140C23×C43C2411yescharacteristic
141C23×C43C2411yescharacteristic
142C22×D43C2412yes—
143Q8×C43—24no—
144Q8×C43—42no—
145Q8×C43—41no—
146D4×C43—41no—
147D4×C43—41no—
148D4×C43—41no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—22no—
152C2×C4×C43—42no—
153C2×C4×C43C2411yescharacteristic
154C2×C4×C43C2414yes—
155C2×C4×C43C2411yescharacteristic
156C2×C4×C43C2414yes—
157C2×C4×C43C2411yescharacteristic
158C2×C4×C43C2411yescharacteristic
159C22⋊D43—24no—
160C22⋊D43—24no—
161C22⋊D43—42no—
162C2×Dic43—24no—
163C2×Dic43—42no—
164C2×Dic43C2414yes—
165C2×Dic43C2412yes—
166C2×Dic43C2412yes—
167C2×Dic43C2414yes—
168C2×Dic43C2412yes—
169D172—41no—
170C4×D43—24no—
171C4×D43—44no—
172Dic86—24no—
173Dic86—28no—
174Dic86—42no—
175Dic86—41no—
176Dic86—44no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—22no—
181C22×C43—22no—
182C22×C43—22no—
183C22×C43C2511yescharacteristic
184C2×D43—22no—
185C2×D43—22no—
186C2×D43—22no—
187C4×C43—21no—
188C4×C43—24no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—24no—
192C4×C43H(5,𝔽2)12yes—
193Dic43—24no—
194Dic43—22no—
195Dic43—24no—
196Dic43—22no—
197Dic432−1+414yes—
198#3550—431nomaximal, Sylow
199C2×C43—41no—
200C2×C43—41no—
201C2×C43—41no—
202C2×C43C2×H(5,𝔽2)11yescharacteristic
203C2×C43C2×2−1+412yes—
204D43—42no—
205#563—432no—
206#563—432no—
207#559—432no—
208Q82—432no—
209#556—432no—
210#556—432no—
211D4×Q8—432no—
212D4×Q8—432no—
213#542—434no—
214#542—434no—
215#536—431no—
216#536—432no—
217#536D4311yescharacteristic, complemented
218#533—432no—
219#532—431no—
220C43#355011yescharacteristic, complemented, Sylow
221C2×#41—431no—
222C2×#41C2×D4311yescharacteristic
223C22×Q8—432no—
224C22×Q8—431no—
225C22×Q8C2×D4311yescharacteristic
226C4⋊Q8—431no—
227C4⋊Q8—432no—
228C4⋊Q8—432no—
229C4⋊Q8—434no—
230C4⋊Q8—432no—
231C4⋊Q8—434no—
232C4⋊Q8—434no—
233C4⋊Q8C2×D4312yes—
234#127—431no—
235#126—434no—
236#126—434no—
237#126—434no—
238#126—434no—
239#125—434no—
240#124—431no—
241#124—431no—
242#124—432no—
243#124—434no—
244#124—434no—
245#124—434no—
246#124C2×D4312yes—
247#123—432no—
248#123—432no—
249#123—434no—
250#123—434no—
251#123C2×D4312yes—
252#123C2×D4312yes—
253C22⋊Q8—432no—
254C22⋊Q8—434no—
255C22⋊Q8—432no—
256C22⋊Q8—432no—
257C22⋊Q8—434no—
258C22⋊Q8—432no—
259C22⋊Q8—434no—
260C22⋊Q8—434no—
261C22⋊Q8—434no—
262C22⋊Q8C2×D4312yes—
263C22⋊Q8C2×D4312yes—
264#121—432no—
265#121—432no—
266C4×Q8—432no—
267C4×Q8—432no—
268C4×Q8—434no—
269C4×Q8—434no—
270C4×Q8—434no—
271C4×D4—432no—
272C4×D4—432no—
273C4×D4—434no—
274C4×D4—434no—
275#117—431no—
276#117—432no—
277#117—434no—
278#117C2×D4311yescharacteristic
279C2×C42—431no—
280#41—42no—
281#41—1722no—
282C2×Q8—42no—
283C2×Q8—434no—
284C2×Q8—432no—
285C2×Q8—434no—
286C2×Q8—432no—
287C2×Q8—431no—
288C2×Q8—1722no—
289C2×Q8—1724no—
290C2×Q8C22×D4312yes—
291C2×Q8C22×D4312yes—
292C2×Q8C22×D4311yescharacteristic
293C2×D4—432no—
294C2×D4—432no—
295C2×D4—432no—
296C2×D4—431no—
297C2×D4C22×D4311yescharacteristic
298C2×D4C22×D4311yescharacteristic
299C2×D4C22×D4311yescharacteristic
300C22×C4—432no—
301C22×C4—432no—
302C22×C4—432no—
303C22×C4—434no—
304C22×C4C22×D4311yescharacteristic
305C22×C4C22×D4311yescharacteristic
306C22×C4C22×D4311yescharacteristic
307C22×C4C22×D4312yes—
308C4⋊C4—432no—
309C4⋊C4—434no—
310C4⋊C4—434no—
311C4⋊C4—434no—
312C4⋊C4—432no—
313C4⋊C4—432no—
314C4⋊C4—434no—
315C4⋊C4—434no—
316C4⋊C4—434no—
317C4⋊C4—434no—
318C4⋊C4—434no—
319C4⋊C4—434no—
320C4⋊C4C22×D4312yes—
321C4⋊C4C22×D4314yes—
322C4⋊C4C22×D4314yes—
323C22⋊C4—434no—
324C22⋊C4—432no—
325C22⋊C4—432no—
326C22⋊C4—432no—
327C22⋊C4—434no—
328C22⋊C4—434no—
329C22⋊C4—432no—
330C22⋊C4—432no—
331C22⋊C4—434no—
332C22⋊C4—434no—
333C22⋊C4C22×D4314yes—
334C22⋊C4C22×D4312yes—
335C22⋊C4C22×D4314yes—
336C42—432no—
337C42—431no—
338C42—431no—
339C42—434no—
340C42—434no—
341C42—432no—
342C42—434no—
343C42C22×D4312yes—
344C23—432no—
345C23C23×D4311yescharacteristic
346C23C23×D4311yescharacteristic
347C23C23×D4311yescharacteristic
348Q8—24no—
349Q8—42no—
350Q8—41no—
351Q8—868no—
352Q8—864no—
353Q8—1722no—
354Q8—1724no—
355Q8—1721no—
356D4—41no—
357D4—41no—
358D4—41no—
359D4—864no—
360D4—864no—
361D4—1721no—
362D4—1722no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—432no—
368C2×C4—434no—
369C2×C4—432no—
370C2×C4—432no—
371C2×C4—434no—
372C2×C4—864no—
373C2×C4—864no—
374C2×C4—1724no—
375C2×C4—1722no—
376C2×C4C23×D4314yes—
377C2×C4C23×D4311yescharacteristic
378C2×C4C23×D4311yescharacteristic
379C2×C4C23×D4314yes—
380C2×C4C23×D4311yescharacteristic
381C2×C4C23×D4311yescharacteristic
382C22—21no—
383C22—21no—
384C22—21no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—862no—
389C22—862no—
390C22—862no—
391C22C24×D4311yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—24no—
396C4—24no—
397C4—434no—
398C4—862no—
399C4—864no—
400C4—862no—
401C4—864no—
402C4#1306337012yes—
403C2—41no—
404C2—41no—
405C2—41no—
406C2—1722no—
407C2C2×#1306337011yescharacteristic
408C22−1+4×D4312yes—
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingC43×#536C2
hypercenter#536D43
hypocenterC43#3550
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #14583652C2semidirect
2. #14583648C2semidirect
3. #14583633C2semidirect
4. #14583629C2semidirect
5. #14583620C2semidirect
6. #14583617C2semidirect
7. Q8×C22⋊D43C2semidirect
8. #14583562C2semidirect
9. #14583517C2semidirect
10. #14583513C2semidirect
11. #14583472C2semidirect
12. #14583470C2semidirect
13. #14583451C2semidirect
15. C43×#536C2semidirect
217. #536D43semidirect
220. C43#3550semidirect