Finite Group Databasebeta

← #19141349

Subgroups — #19141349

Order 5504.

540 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063316C211yesmaximal, characteristic, complemented
2C2×#13063298C211yesmaximal, characteristic
3#14582835C211yesmaximal, characteristic, complemented
4#14582823C211yesmaximal, characteristic, complemented
5#14582816C211yesmaximal, characteristic, complemented
6#14582815C211yesmaximal, characteristic, complemented
7#14582815C211yesmaximal, characteristic, complemented
8#14582814C211yesmaximal, characteristic, complemented
9#14582801C211yesmaximal, characteristic, complemented
10#14582799C211yesmaximal, characteristic, complemented
11#14582788C211yesmaximal, characteristic, complemented
12#14582783C211yesmaximal, characteristic, complemented
13#14582773C211yesmaximal, characteristic, complemented
14#14582773C211yesmaximal, characteristic, complemented
15C43×#388C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20#13063316—24no—
21#13063298—24no—
22C2×C4⋊Dic43C2211yescharacteristic
23C2×C4⋊Dic43C2211yescharacteristic
24C2×C4⋊Dic43C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×Dic43⋊C4C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
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
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×C4×Dic43C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C22⋊C4×C43C2211yescharacteristic
48C2×C22⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C42×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53C24×C43C2311yescharacteristic
54C23×D43C2311yescharacteristic
55C23×D43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—22no—
63C2×C22⋊D43—22no—
64C2×C22⋊D43—22no—
65C2×C22⋊D43—41no—
66C2×C22⋊D43—41no—
67C2×C22⋊D43—41no—
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C2×D172—22no—
75C2×D172—22no—
76C2×D172—41no—
77C2×C4×D43—22no—
78C2×C4×D43—41no—
79C2×C4×D43—41no—
80C4⋊C4×C43—22no—
81C22⋊C4×C43—22no—
82C22⋊C4×C43—22no—
83C22⋊C4×C43—41no—
84C42×C43—41no—
85C22⋊Dic43—41no—
86C22⋊Dic43—41no—
87(C2×D43)⋊C4—22no—
88(C2×D43)⋊C4—22no—
89(C2×D43)⋊C4—22no—
90(C2×D43)⋊C4—22no—
91(C2×D43)⋊C4—41no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96C4⋊Dic43—22no—
97C4⋊Dic43—22no—
98C4⋊Dic43—22no—
99Dic43⋊C4—22no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4D414yes—
104C4×Dic43—22no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43C2411yescharacteristic
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×D43—21no—
126C22×D43#4112yes—
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×C43C2×D412yes—
144C2×C4×C43#4112yes—
145C22⋊D43—44no—
146C22⋊D43—44no—
147C2×Dic43—21no—
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—21no—
163C2×Dic43C2×D412yes—
164C2×Dic43C2×D412yes—
165D172—44no—
166C4×D43—44no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43C22×D411yescharacteristic
175C22×C43C2×#4111yescharacteristic
176C22×C43C2×#4111yescharacteristic
177C22×C43H(5,𝔽2)11yescharacteristic
178C22×C43H(5,𝔽2)11yescharacteristic
179C22×C43H(5,𝔽2)11yescharacteristic
180C22×C432−1+411yescharacteristic
181C2×D43—22no—
182C2×D43—22no—
183C2×D43—22no—
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—
195C4×C43—22no—
196C4×C43—22no—
197C4×C43—41no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43—41no—
201Dic43—22no—
202Dic43—22no—
203Dic43—41no—
204Dic43—41no—
205Dic43—41no—
206Dic43—41no—
207#2711—431nomaximal, Sylow
208C2×C43—81no—
209C2×C43#53511yescharacteristic
210C2×C43#53911yescharacteristic
211C2×C43#54011yescharacteristic
212C2×C43#54611yescharacteristic
213C2×C43#54811yescharacteristic
214C2×C43#55311yescharacteristic
215C2×C43#56211yescharacteristic
216D43—42no—
217D43—81no—
218C2×#125—431no—
219C2×#121—431no—
220#399—431no—
221#396—431no—
222#394—431no—
223#394—431no—
224#394—431no—
225#394—431no—
226#390—431no—
227#390—431no—
228#388—431no—
229#388D4311yescharacteristic, complemented
230#387—431no—
231#385—431no—
232#385—431no—
233C43#271111yescharacteristic, complemented, Sylow
234C22×D4—431no—
235C22×D4—431no—
236C22×D4—431no—
237C23×C4—431no—
238#125—864no—
239#121—864no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—431no—
242C2×C4⋊C4—431no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
261C2×C22⋊C4C2×D4311yescharacteristic
262C2×C22⋊C4C2×D4311yescharacteristic
263C2×C42—431no—
264C2×C42C2×D4311yescharacteristic
265#95—431no—
266#95—431no—
267#95—431no—
268#95—431no—
269#95C2×D4311yescharacteristic
270#95C2×D4311yescharacteristic
271C24—431no—
272C24—431no—
273C24C22×D4311yescharacteristic
274C2×D4—862no—
275C2×D4—862no—
276C2×D4—862no—
277C2×D4—862no—
278C2×D4—862no—
279C2×D4—1721no—
280C2×D4—1721no—
281C2×D4—1721no—
282C2×D4—1721no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—431no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—862no—
290C22×C4—1721no—
291C22×C4—1721no—
292C22×C4C22×D4311yescharacteristic
293C22×C4C22×D4311yescharacteristic
294C22×C4C22×D4311yescharacteristic
295C22×C4C22×D4311yescharacteristic
296C22×C4C22×D4311yescharacteristic
297C22×C4C22×D4311yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—434no—
300C4⋊C4—862no—
301C4⋊C4—862no—
302C4⋊C4—862no—
303C4⋊C4—862no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C4⋊C4—1721no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—41no—
310C22⋊C4—862no—
311C22⋊C4—862no—
312C22⋊C4—862no—
313C22⋊C4—862no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C22⋊C4—1721no—
319C22⋊C4—1721no—
320C22⋊C4—1721no—
321C42—41no—
322C42—862no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—432no—
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—
344C23C23×D4311yescharacteristic
345D4—1724no—
346D4—1724no—
347D4—1724no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
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—432no—
365C2×C4—432no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
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—1724no—
383C2×C4#1062189812yes—
384C2×C4D4×D4312yes—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
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—
406C22C2×D4×D4311yescharacteristic
407C22#41×D4311yescharacteristic
408C22C2×#1062189811yescharacteristic
409C22#1306337011yescharacteristic
410C22#1306337111yescharacteristic
411C22#1306337111yescharacteristic
412C22#1306337211yescharacteristic
413C4—22no—
414C4—22no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—862no—
420C4—862no—
421C4—1721no—
422C4—1721no—
423C4—1721no—
424C4—1721no—
425C2—81no—
426C2—3441no—
427C2—1722no—
428C2#1458346711yescharacteristic
429C2#1458349011yescharacteristic
430C2#1458350011yescharacteristic
431C2#1458353811yescharacteristic
432C2#1458355811yescharacteristic
433C2#1458359311yescharacteristic
434C2#1458364611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#388C2
hypercenter#388D43
hypocenterC43#2711
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#13063316C2semidirect
3. #14582835C2semidirect
4. #14582823C2semidirect
5. #14582816C2semidirect
6. #14582815C2semidirect
7. #14582815C2semidirect
8. #14582814C2semidirect
9. #14582801C2semidirect
10. #14582799C2semidirect
11. #14582788C2semidirect
12. #14582783C2semidirect
13. #14582773C2semidirect
14. #14582773C2semidirect
15. C43×#388C2semidirect
229. #388D43semidirect
233. C43#2711semidirect