Finite Group Databasebeta

← #19146259

Subgroups — #19146259

Order 5504.

482 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063356C211yesmaximal, characteristic, complemented
2C2×#13063354C211yesmaximal, characteristic, complemented
3#14583567C211yesmaximal, characteristic
4Q8×C22⋊D43C211yesmaximal, characteristic, complemented
5#14583270C211yesmaximal, characteristic, complemented
6#14583148C211yesmaximal, characteristic, complemented
7#14583143C211yesmaximal, characteristic, complemented
8#14583108C211yesmaximal, characteristic, complemented
9#14583097C211yesmaximal, characteristic, complemented
10#14583063C211yesmaximal, characteristic, complemented
11#14583058C211yesmaximal, characteristic, complemented
12#14583039C211yesmaximal, characteristic, complemented
13#14582991C211yesmaximal, characteristic, complemented
14#14582974C211yesmaximal, characteristic, complemented
15C43×#448C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19#13063356—24no—
20#13063354—24no—
21C2×Dic172C2211yescharacteristic
22C2×#10621885C2211yescharacteristic
23C2×#10621885C2211yescharacteristic
24C2×#10621873C2211yescharacteristic
25C2×#10621883C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27C2×#10621884C2211yescharacteristic
28C2×#10621877C2211yescharacteristic
29C2×#10621872C2211yescharacteristic
30#13063323—21no—
31#13063323C2211yescharacteristic
32#13063321—21no—
33#13063321C2211yescharacteristic
34#13063304—21no—
35#13063304C2211yescharacteristic
36#13063301—21no—
37#13063301C2211yescharacteristic
38#13063300C2211yescharacteristic
39#13063298—21no—
40#13063297—21no—
41Q8×Dic43C2211yescharacteristic
42#13063290C2211yescharacteristic
43C4×C22⋊D43—21no—
44C4×C22⋊D43C2211yescharacteristic
45(C22⋊D43)⋊C4—21no—
46#13063258C2211yescharacteristic
47Dic43⋊C8C2211yescharacteristic
48#13063250C2211yescharacteristic
49#13063248C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063246C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53C8×Dic43C2211yescharacteristic
54C22×Q8×C43C2211yescharacteristic
55C2×SD16×C43C2211yescharacteristic
56C2×SD16×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59#103×C43C2211yescharacteristic
60C22⋊C8×C43C2211yescharacteristic
61C2×Q8×C43—21no—
62C2×Q8×C43—22no—
63C2×Q8×C43—41no—
64C2×Q8×C43C2311yescharacteristic
65C2×Q8×C43C2311yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43C2311yescharacteristic
68C22×C4×C43—21no—
69C22×C4×C43C2311yescharacteristic
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43D411yescharacteristic
75C22×Dic43—21no—
76Q8×D43—22no—
77Q8×D43—41no—
78#10621900—22no—
79#10621900—41no—
80#10621898—22no—
81#10621898—41no—
82C2×D172—21no—
83C2×D172C2311yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43C2311yescharacteristic
87C2×Dic86—21no—
88C2×Dic86C2311yescharacteristic
89C2×Dic86C2311yescharacteristic
90SD16×C43—22no—
91SD16×C43—41no—
92C2×C8×C43C2311yescharacteristic
93C2×C8×C43C2311yescharacteristic
94C4⋊C4×C43C2311yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43D411yescharacteristic
98#10621885—22no—
99#10621885D414yescomplemented
100#10621884—22no—
101#10621884—22no—
102#10621883—22no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4D411yescharacteristic
106C4⋊Dic43—21no—
107C4⋊Dic43C2311yescharacteristic
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113Dic43⋊C4D411yescharacteristic
114C4×Dic43—21no—
115C4×Dic43—21no—
116C4×Dic43C2311yescharacteristic
117#10621877—22no—
118C2×C43⋊C8C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120Dic172—22no—
121#10621873—41no—
122#10621872—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43C2×D411yescharacteristic
127Q8×C43—21no—
128Q8×C43—21no—
129Q8×C43—21no—
130Q8×C43—42no—
131Q8×C43C2×D412yes—
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—81no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—42no—
141C2×C4×C43C2×D411yescharacteristic
142C2×C4×C43C2411yescharacteristic
143C22⋊D43—22no—
144C22⋊D43—42no—
145C22⋊D43—42no—
146C22⋊D43—42no—
147C22⋊D43—81no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—42no—
152C2×Dic43C2×D411yescharacteristic
153C2×Dic43C2×D411yescharacteristic
154C2×Dic43C2×D411yescharacteristic
155D172—21no—
156D172—21no—
157D172—81no—
158C4×D43—21no—
159C4×D43—21no—
160C4×D43—42no—
161C4×D43—42no—
162Dic86—21no—
163Dic86—21no—
164Dic86—21no—
165Dic86—42no—
166Dic86C2×D412yes—
167C8×C43—21no—
168C8×C43—21no—
169C43⋊C8—21no—
170C43⋊C8C2×D412yes—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43C22×D411yescharacteristic
178C2×D43—21no—
179C2×D43—21no—
180C2×D43—21no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C4×C43—22no—
185C4×C43—21no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43C22×D411yescharacteristic
189C4×C43H(5,𝔽2)11yescharacteristic
190Dic43—22no—
191Dic43—21no—
192Dic43—21no—
193Dic43—41no—
194Dic43—41no—
195Dic43#13712yescomplemented
196#3278—431nomaximal, Sylow
197C2×C43—41no—
198C2×C43—81no—
199C2×C43D4211yescharacteristic
200C2×C43C2×#13711yescharacteristic
201C2×C43#57711yescharacteristic
202D43—41no—
203D43—81no—
204C2×#137—431no—
205C2×#137—431no—
206#550—431no—
207D4×Q8—431no—
208#492—431no—
209#468—431no—
210#468—431no—
211#462—431no—
212#460—431no—
213#452—431no—
214#452—431no—
215#448—431no—
216#448D4311yescharacteristic, complemented
217C4×Q16—431no—
218#436—431no—
219C43#327811yescharacteristic, complemented, Sylow
220C2×#41—431no—
221C2×#41—431no—
222C22×Q8—431no—
223C22×Q8C2×D4311yescharacteristic
224#137—864no—
225#137—864no—
226C2×Q16—431no—
227C2×Q16—431no—
228C2×Q16—431no—
229C2×SD16—431no—
230C2×SD16—431no—
231C2×SD16—431no—
232C2×SD16—431no—
233C2×SD16C2×D4311yescharacteristic
234C2×SD16C2×D4311yescharacteristic
235C2×M16—431no—
236C2×M16—431no—
237C4⋊Q8—431no—
238C4⋊Q8—861no—
239#127—431no—
240#127—861no—
241C22⋊Q8—431no—
242C22⋊Q8—431no—
243C22⋊Q8—861no—
244C22⋊Q8—861no—
245#121—431no—
246#121—861no—
247#121—861no—
248#121C2×D4311yescharacteristic
249C4×Q8—431no—
250C4×Q8—431no—
251C4×D4—431no—
252C4×D4—861no—
253C4×D4—861no—
254#107—431no—
255C4⋊C8—431no—
256#103—431no—
257#103—431no—
258#103C2×D4311yescharacteristic
259#103C2×D4311yescharacteristic
260#102—431no—
261#102—431no—
262C22⋊C8—431no—
263C22⋊C8C2×D4311yescharacteristic
264C4×C8—431no—
265#41—862no—
266#41—862no—
267#41—1721no—
268#41—1721no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—431no—
273C2×Q8—431no—
274C2×Q8—861no—
275C2×Q8—862no—
276C2×Q8—1721no—
277C2×Q8C22×D4311yescharacteristic
278C2×Q8C22×D4311yescharacteristic
279C2×D4—21no—
280C2×D4—431no—
281C2×D4—431no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4C22×D4311yescharacteristic
288C22×C4—21no—
289C22×C4—431no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4C22×D4311yescharacteristic
294Q16—434no—
295Q16—862no—
296Q16—862no—
297SD16—22no—
298SD16—41no—
299SD16—862no—
300SD16—862no—
301SD16—862no—
302SD16—1721no—
303M16—862no—
304M16—862no—
305C2×C8—431no—
306C2×C8—431no—
307C2×C8C22×D4311yescharacteristic
308C2×C8C22×D4311yescharacteristic
309C4⋊C4—431no—
310C4⋊C4—431no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4—861no—
317C4⋊C4C22×D4311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—431no—
320C22⋊C4—431no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C42—431no—
325C42—861no—
326C42—861no—
327C23—21no—
328C23—431no—
329C23—861no—
330C23D4×D4311yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—432no—
336Q8—861no—
337Q8—861no—
338Q8—861no—
339Q8—1722no—
340Q8D4×D4312yes—
341D4—21no—
342D4—21no—
343D4—81no—
344D4—862no—
345D4—861no—
346D4—861no—
347D4—3441no—
348D4—3441no—
349D4—1722no—
350D4—1722no—
351D4—1722no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—431no—
359C2×C4—431no—
360C2×C4—431no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—1722no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4D4×D4311yescharacteristic
370C2×C4C23×D4311yescharacteristic
371C8—21no—
372C8—21no—
373C8—432no—
374C8—861no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—861no—
382C22—861no—
383C22—861no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22C2×D4×D4311yescharacteristic
388C4—21no—
389C4—22no—
390C4—41no—
391C4—41no—
392C4—432no—
393C4—861no—
394C4—861no—
395C4—862no—
396C4—1721no—
397C4—1721no—
398C4C2×D4×D4311yescharacteristic
399C4#1306337011yescharacteristic
400C2—41no—
401C2—81no—
402C2—3441no—
403C2—1721no—
404C2#1458353111yescharacteristic
405C2#137×D4311yescharacteristic
406C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#448C2
socleC22×C43C22×D4
hypercenter#448D43
hypocenterC43#3278
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#13063356C2semidirect
2. C2×#13063354C2semidirect
4. Q8×C22⋊D43C2semidirect
5. #14583270C2semidirect
6. #14583148C2semidirect
7. #14583143C2semidirect
8. #14583108C2semidirect
9. #14583097C2semidirect
10. #14583063C2semidirect
11. #14583058C2semidirect
12. #14583039C2semidirect
13. #14582991C2semidirect
14. #14582974C2semidirect
15. C43×#448C2semidirect
99. #10621885D4semidirect
195. Dic43#137semidirect
216. #448D43semidirect
219. C43#3278semidirect