Finite Group Databasebeta

← #19146185

Subgroups — #19146185

Order 5504.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063358C211yesmaximal, characteristic, complemented
2C2×#13063347C211yesmaximal, characteristic, complemented
3#14583570C211yesmaximal, characteristic, complemented
4#14583558C211yesmaximal, characteristic, complemented
5#14583288C211yesmaximal, characteristic, complemented
6#14583152C211yesmaximal, characteristic, complemented
7#14583128C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583100C211yesmaximal, characteristic, complemented
10#14583063C211yesmaximal, characteristic, complemented
11#14583046C211yesmaximal, characteristic, complemented
12#14583046C211yesmaximal, characteristic, complemented
13#14583040C211yesmaximal, characteristic, complemented
14#14583007C211yesmaximal, characteristic, complemented
15C43×#435C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×#10621898C2211yescharacteristic
19C22×Dic86C2211yescharacteristic
20#13063358—24no—
21#13063347—24no—
22C2×Dic172C2211yescharacteristic
23C2×Dic172C2211yescharacteristic
24C2×#10621873C2211yescharacteristic
25C2×#10621873C2211yescharacteristic
26C2×#10621873C2211yescharacteristic
27C2×#10621873C2211yescharacteristic
28C2×#10621873C2211yescharacteristic
29C2×D344C2211yescharacteristic
30C2×D344C2211yescharacteristic
31#13063322C2211yescharacteristic
32#13063321—21no—
33#13063313C2211yescharacteristic
34#13063311—21no—
35#13063304C2211yescharacteristic
36#13063303—21no—
37#13063299C2211yescharacteristic
38#13063299C2211yescharacteristic
39#13063299C2211yescharacteristic
40#13063298—21no—
41#13063298—21no—
42#13063297—21no—
43C4×Dic86C2211yescharacteristic
44C4×Dic86C2211yescharacteristic
45#13063287—21no—
46(C22⋊D43)⋊C4—21no—
47#13063257C2211yescharacteristic
48#13063250C2211yescharacteristic
49#13063250C2211yescharacteristic
50#13063250C2211yescharacteristic
51#13063247C2211yescharacteristic
52#13063247C2211yescharacteristic
53#13063247C2211yescharacteristic
54C2×M16×C43C2211yescharacteristic
55C22×C8×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic
57C4⋊C8×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C22⋊C8×C43C2211yescharacteristic
60#97×C43C2211yescharacteristic
61C2×D4×C43D411yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C22×Dic43—21no—
71#10621898—22no—
72#10621898—22no—
73#10621898—22no—
74#10621898—41no—
75#10621898—41no—
76#10621898—41no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172C2311yescharacteristic
80C2×D172C2311yescharacteristic
81C2×D172C2311yescharacteristic
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×Dic86—22no—
86C2×Dic86—21no—
87C2×Dic86—41no—
88C2×Dic86C2311yescharacteristic
89C2×Dic86C2311yescharacteristic
90C2×Dic86C2311yescharacteristic
91M16×C43—22no—
92C2×C8×C43—22no—
93C2×C8×C43C2311yescharacteristic
94C2×C8×C43C2311yescharacteristic
95C2×C8×C43C2311yescharacteristic
96C2×C8×C43C2311yescharacteristic
97C4⋊C4×C43D411yescharacteristic
98C22⋊C4×C43D411yescharacteristic
99C22⋊C4×C43D411yescharacteristic
100C42×C43C2311yescharacteristic
101C22⋊Dic43—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107C4⋊Dic43C2311yescharacteristic
108C4⋊Dic43C2311yescharacteristic
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112C4×Dic43—21no—
113C4×Dic43—21no—
114Dic172—22no—
115Dic172D414yescomplemented
116D344—22no—
117D344—41no—
118#10621873—22no—
119#10621873—22no—
120#10621873—22no—
121#10621873—22no—
122#10621873—41no—
123C23×C43C2×D411yescharacteristic
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—21no—
128D4×C43—41no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2411yescharacteristic
138C22⋊D43—42no—
139C22⋊D43—42no—
140C22⋊D43—42no—
141C22⋊D43—42no—
142C22⋊D43—81no—
143C22⋊D43—81no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—42no—
150D172—21no—
151D172—21no—
152D172—21no—
153D172—21no—
154D172—21no—
155D172—21no—
156D172—42no—
157D172—81no—
158C4×D43—42no—
159C4×D43—42no—
160C4×D43—42no—
161Dic86—21no—
162Dic86—21no—
163Dic86—21no—
164Dic86—21no—
165Dic86—42no—
166Dic86C2×D412yes—
167Dic86C2×D412yes—
168C8×C43—21no—
169C8×C43—21no—
170C8×C43—21no—
171C8×C43C2×D412yes—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43C22×D411yescharacteristic
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43C22×D411yescharacteristic
193C4×C43H(5,𝔽2)11yescharacteristic
194Dic43—22no—
195Dic43—22no—
196Dic43—41no—
197Dic43—41no—
198Dic43—41no—
199#3271—431nomaximal, Sylow
200C2×C43—41no—
201C2×C43—41no—
202C2×C43D4211yescharacteristic
203C2×C43#57511yescharacteristic
204C2×C43#57711yescharacteristic
205D43—81no—
206D43—81no—
207D43—81no—
208C2×#137—431no—
209C2×#135—431no—
210#550—431no—
211#548—431no—
212#496—431no—
213#469—431no—
214#465—431no—
215#464—431no—
216#460—431no—
217#452—431no—
218#449—431no—
219#449—431no—
220#448—431no—
221#441—431no—
222#435D4311yescharacteristic, complemented
223C43#327111yescharacteristic, complemented, Sylow
224C2×#41—431no—
225C2×#41—431no—
226C2×#41—431no—
227C22×Q8—431no—
228#137—864no—
229#135—864no—
230C2×Q16—431no—
231C2×Q16—431no—
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—431no—
236C2×SD16—431no—
237C2×D8—431no—
238C2×D8—431no—
239C2×M16C2×D4311yescharacteristic
240C22×C8C2×D4311yescharacteristic
241#127—431no—
242#127—861no—
243#124—431no—
244#124—861no—
245C22⋊Q8—431no—
246C22⋊Q8—861no—
247#121—431no—
248#121—431no—
249#121—431no—
250#121—861no—
251#121—861no—
252#121—861no—
253C4×Q8—431no—
254C4×Q8—431no—
255C4×D4—861no—
256C4×D4—861no—
257C4×D4C2×D4311yescharacteristic
258#106—431no—
259C4⋊C8C2×D4311yescharacteristic
260#103—431no—
261#103—431no—
262#103—431no—
263#102—431no—
264#102—431no—
265#102—431no—
266C22⋊C8C2×D4311yescharacteristic
267C22⋊C8C2×D4311yescharacteristic
268#97C2×D4311yescharacteristic
269#41—862no—
270#41—862no—
271#41—862no—
272#41—1721no—
273#41—1721no—
274#41—1721no—
275C2×Q8—431no—
276C2×Q8—431no—
277C2×Q8—431no—
278C2×Q8—862no—
279C2×Q8—861no—
280C2×Q8—1721no—
281C2×D4—431no—
282C2×D4—431no—
283C2×D4—431no—
284C2×D4—861no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—861no—
292C2×D4D17211yescharacteristic
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4C22×D4311yescharacteristic
298C22×C4C22×D4311yescharacteristic
299Q16—434no—
300Q16—862no—
301SD16—862no—
302SD16—862no—
303SD16—862no—
304SD16—862no—
305SD16—1721no—
306D8—862no—
307D8—1721no—
308M16—22no—
309C2×C8—22no—
310C2×C8C22×D4311yescharacteristic
311C2×C8C22×D4311yescharacteristic
312C2×C8C22×D4311yescharacteristic
313C2×C8C22×D4311yescharacteristic
314C4⋊C4—431no—
315C4⋊C4—431no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4D17211yescharacteristic
320C22⋊C4—861no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4D17211yescharacteristic
327C22⋊C4D17211yescharacteristic
328C42—861no—
329C42—861no—
330C42C22×D4311yescharacteristic
331C23—861no—
332C23—861no—
333C23—861no—
334C23C2×D17211yescharacteristic
335C23C2×D17211yescharacteristic
336Q8—432no—
337Q8—432no—
338Q8—861no—
339Q8—861no—
340Q8—861no—
341Q8—861no—
342Q8—1722no—
343D4—41no—
344D4—861no—
345D4—861no—
346D4—861no—
347D4—861no—
348D4—861no—
349D4—861no—
350D4—3441no—
351D4—3441no—
352D4—3441no—
353D4—1722no—
354D4—1722no—
355D4—1722no—
356D4—1722no—
357D4—1722no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4C2×D17211yescharacteristic
372C2×C4C2×D17211yescharacteristic
373C2×C4C2×D17211yescharacteristic
374C2×C4C2×D17211yescharacteristic
375C2×C4C23×D4311yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8D4×D4312yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—1721no—
387C22—1721no—
388C22—1721no—
389C22—1721no—
390C22—1721no—
391C22—1721no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22C22×D17211yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—862no—
401C4—862no—
402C4—1721no—
403C4—1721no—
404C4—1721no—
405C4C2×D4×D4311yescharacteristic
406C4#1306337111yescharacteristic
407C2—41no—
408C2—41no—
409C2—3441no—
410C2—3441no—
411C2—3441no—
412C2D4×D17211yescharacteristic
413C2#1458369911yescharacteristic
414C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#435C2
socleC22×C43C22×D4
hypercenter#435D43
hypocenterC43#3271
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#13063358C2semidirect
2. C2×#13063347C2semidirect
3. #14583570C2semidirect
4. #14583558C2semidirect
5. #14583288C2semidirect
6. #14583152C2semidirect
7. #14583128C2semidirect
8. #14583122C2semidirect
9. #14583100C2semidirect
10. #14583063C2semidirect
11. #14583046C2semidirect
12. #14583046C2semidirect
13. #14583040C2semidirect
14. #14583007C2semidirect
15. C43×#435C2semidirect
115. Dic172D4semidirect
222. #435D43semidirect
223. C43#3271semidirect