Finite Group Databasebeta

← #19141004

Subgroups — #19141004

Order 5504.

562 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063313C211yesmaximal, characteristic, complemented
2C2×#13063300C211yesmaximal, characteristic
3#14582828C211yesmaximal, characteristic, complemented
4#14582819C211yesmaximal, characteristic, complemented
5#14582817C211yesmaximal, characteristic, complemented
6#14582817C211yesmaximal, characteristic, complemented
7#14582816C211yesmaximal, characteristic, complemented
8#14582812C211yesmaximal, characteristic, complemented
9#14582790C211yesmaximal, characteristic, complemented
10#14582777C211yesmaximal, characteristic, complemented
11#14582777C211yesmaximal, characteristic, complemented
12#14582770C211yesmaximal, characteristic, complemented
13#14582761C211yesmaximal, characteristic, complemented
14#14582758C211yesmaximal, characteristic, complemented
15C43×#387C211yesmaximal, characteristic, complemented
16C22×Dic86C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×D172C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic
21C22×C4×D43C2211yescharacteristic
22#13063313—24no—
23#13063300—24no—
24C2×Dic43⋊C4C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×(C2×D43)⋊C4C2211yescharacteristic
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×(C2×D43)⋊C4C2211yescharacteristic
32C2×(C2×D43)⋊C4C2211yescharacteristic
33C2×(C2×D43)⋊C4C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C4⋊C4×C43C2211yescharacteristic
48C2×C42×C43C2211yescharacteristic
49#95×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53C23×D43C2311yescharacteristic
54C23×D43C2311yescharacteristic
55C23×D43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×Dic43C2311yescharacteristic
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C22×Dic43C2311yescharacteristic
68C2×D172—22no—
69C2×D172—22no—
70C2×D172—22no—
71C2×D172—41no—
72C2×D172—41no—
73C2×D172—41no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172D414yes—
77C2×C4×D43—22no—
78C2×C4×D43—22no—
79C2×C4×D43—22no—
80C2×C4×D43—41no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×Dic86—22no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—22no—
88C42×C43—22no—
89(C2×D43)⋊C4—22no—
90(C2×D43)⋊C4—22no—
91(C2×D43)⋊C4—22no—
92(C2×D43)⋊C4—22no—
93(C2×D43)⋊C4—22no—
94(C2×D43)⋊C4—22no—
95(C2×D43)⋊C4—22no—
96(C2×D43)⋊C4—22no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105C23×C43C2411yescharacteristic
106C22×D43—21no—
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—21no—
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43C2×D412yes—
126C22×D43C2×D412yes—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43C2×D412yes—
147C2×C4×C43#4112yes—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43#4112yes—
163D172—44no—
164D172—44no—
165D172—44no—
166C4×D43—44no—
167C4×D43—44no—
168Dic86—44no—
169C22×C43C22×D411yescharacteristic
170C22×C43C2×#4111yescharacteristic
171C22×C43C2×#4111yescharacteristic
172C22×C43H(5,𝔽2)11yescharacteristic
173C22×C43H(5,𝔽2)11yescharacteristic
174C22×C43H(5,𝔽2)11yescharacteristic
175C22×C432−1+411yescharacteristic
176C2×D43—22no—
177C2×D43—22no—
178C2×D43—22no—
179C2×D43—22no—
180C2×D43—22no—
181C2×D43—22no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—41no—
190C2×D43—41no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—41no—
195C2×D43—41no—
196C2×D43—41no—
197C4×C43—22no—
198C4×C43—22no—
199C4×C43—41no—
200C4×C43—41no—
201C4×C43—41no—
202C4×C43—41no—
203C4×C43—41no—
204Dic43—22no—
205Dic43—41no—
206Dic43—41no—
207Dic43—41no—
208Dic43—41no—
209#2686—431nomaximal, Sylow
210C2×C43#53411yescharacteristic
211C2×C43#53811yescharacteristic
212C2×C43#54211yescharacteristic
213C2×C43#54611yescharacteristic
214C2×C43#54711yescharacteristic
215C2×C43#55511yescharacteristic
216C2×C43#56211yescharacteristic
217D43—42no—
218D43—42no—
219D43—81no—
220C2×#124—431no—
221C2×#121—431no—
222#397—431no—
223#395—431no—
224#394—431no—
225#394—431no—
226#394—431no—
227#393—431no—
228#388—431no—
229#387D4311yescharacteristic, complemented
230#386—431no—
231#386—431no—
232#385—431no—
233#381—431no—
234#380—431no—
235C43#268611yescharacteristic, complemented, Sylow
236C22×Q8—431no—
237C22×D4—431no—
238C22×D4—431no—
239C22×D4—431no—
240C23×C4—431no—
241C23×C4—431no—
242#124—864no—
243#121—864no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4C2×D4311yescharacteristic
248C2×C4⋊C4C2×D4311yescharacteristic
249C2×C22⋊C4—431no—
250C2×C22⋊C4—431no—
251C2×C22⋊C4—431no—
252C2×C22⋊C4—431no—
253C2×C22⋊C4—431no—
254C2×C22⋊C4—431no—
255C2×C22⋊C4—431no—
256C2×C22⋊C4—431no—
257C2×C22⋊C4—431no—
258C2×C22⋊C4—431no—
259C2×C22⋊C4—431no—
260C2×C22⋊C4—431no—
261C2×C22⋊C4—431no—
262C2×C42C2×D4311yescharacteristic
263#95—431no—
264#95—431no—
265#95—431no—
266#95—431no—
267#95—431no—
268#95—431no—
269#95C2×D4311yescharacteristic
270#95C2×D4311yescharacteristic
271#95C2×D4311yescharacteristic
272#95C2×D4311yescharacteristic
273C24—431no—
274C24—431no—
275C24—431no—
276C2×Q8—862no—
277C2×Q8—1721no—
278C2×Q8—1721no—
279C2×D4—434no—
280C2×D4—862no—
281C2×D4—862no—
282C2×D4—862no—
283C2×D4—1721no—
284C2×D4—1721no—
285C2×D4—1721no—
286C2×D4—1721no—
287C2×D4—1721no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—431no—
291C22×C4—431no—
292C22×C4—431no—
293C22×C4—862no—
294C22×C4—862no—
295C22×C4—862no—
296C22×C4—1721no—
297C22×C4—1721no—
298C22×C4—1721no—
299C22×C4C22×D4311yescharacteristic
300C22×C4C22×D4311yescharacteristic
301C22×C4C22×D4311yescharacteristic
302C22×C4C22×D4311yescharacteristic
303C22×C4C22×D4311yescharacteristic
304C22×C4C22×D4311yescharacteristic
305C22×C4C22×D4311yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C22⋊C4—862no—
312C22⋊C4—862no—
313C22⋊C4—862no—
314C22⋊C4—862no—
315C22⋊C4—862no—
316C22⋊C4—862no—
317C22⋊C4—862no—
318C22⋊C4—862no—
319C22⋊C4—1721no—
320C22⋊C4—1721no—
321C22⋊C4—1721no—
322C22⋊C4—1721no—
323C22⋊C4—1721no—
324C42—22no—
325C23—432no—
326C23—432no—
327C23—861no—
328C23—861no—
329C23—861no—
330C23—861no—
331C23—861no—
332C23—861no—
333C23—861no—
334C23—861no—
335C23—861no—
336C23—861no—
337C23—861no—
338C23—861no—
339C23—861no—
340C23—861no—
341C23—861no—
342C23—861no—
343C23—861no—
344C23—861no—
345C23—861no—
346C23C23×D4311yescharacteristic
347Q8—1724no—
348D4—1724no—
349D4—1724no—
350D4—1724no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—432no—
371C2×C4—861no—
372C2×C4—861no—
373C2×C4—861no—
374C2×C4—861no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—1724no—
386C2×C4—1724no—
387C2×C4#1062189812yes—
388C2×C4D4×D4312yes—
389C22—862no—
390C22—862no—
391C22—862no—
392C22—862no—
393C22—862no—
394C22—862no—
395C22—1721no—
396C22—1721no—
397C22—1721no—
398C22—1721no—
399C22—1721no—
400C22—1721no—
401C22—1721no—
402C22—1721no—
403C22—1721no—
404C22—1721no—
405C22—1721no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22—1721no—
410C22C2×D4×D4311yescharacteristic
411C22#41×D4311yescharacteristic
412C22C2×#1062189811yescharacteristic
413C22#1306337111yescharacteristic
414C22#1306337111yescharacteristic
415C22#1306337111yescharacteristic
416C22#1306337311yescharacteristic
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—862no—
425C4—1721no—
426C4—1721no—
427C4—1721no—
428C4—1721no—
429C2—3441no—
430C2—1722no—
431C2—1722no—
432C2#1458346011yescharacteristic
433C2#1458348811yescharacteristic
434C2#1458352111yescharacteristic
435C2#1458354511yescharacteristic
436C2#1458355111yescharacteristic
437C2#1458361211yescharacteristic
438C2#1458364711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#387C2
hypercenter#387D43
hypocenterC43#2686
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#13063313C2semidirect
3. #14582828C2semidirect
4. #14582819C2semidirect
5. #14582817C2semidirect
6. #14582817C2semidirect
7. #14582816C2semidirect
8. #14582812C2semidirect
9. #14582790C2semidirect
10. #14582777C2semidirect
11. #14582777C2semidirect
12. #14582770C2semidirect
13. #14582761C2semidirect
14. #14582758C2semidirect
15. C43×#387C2semidirect
229. #387D43semidirect
235. C43#2686semidirect