Finite Group Databasebeta

← #19138565

Subgroups — #19138565

Order 5504.

646 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063314C211yesmaximal, characteristic, complemented
2C2×#13063310C211yesmaximal, characteristic, complemented
3C2×#13063301C211yesmaximal, characteristic, complemented
4C2×#13063287C211yesmaximal, characteristic, complemented
5#14582821C211yesmaximal, characteristic, complemented
6#14582817C211yesmaximal, characteristic, complemented
7#14582809C211yesmaximal, characteristic
8#14582800C211yesmaximal, characteristic, complemented
9#14582791C211yesmaximal, characteristic, complemented
10#14582789C211yesmaximal, characteristic, complemented
11#14582788C211yesmaximal, characteristic, complemented
12#14582777C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582750C211yesmaximal, characteristic, complemented
15C43×#395C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic
21#13063314—24no—
22#13063310—24no—
23#13063301—24no—
24#13063287—24no—
25C2×C4⋊Dic43C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊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
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×C4×Dic43C2211yescharacteristic
43C2×C4×Dic43C2211yescharacteristic
44C2×C4×Dic43C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C43⋊#95C2211yescharacteristic
48C22×Q8×C43C2211yescharacteristic
49C2×C4⋊C4×C43C2211yescharacteristic
50C2×C4⋊C4×C43C2211yescharacteristic
51C2×C4⋊C4×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53#95×C43C2211yescharacteristic
54#95×C43C2211yescharacteristic
55C23×D43C2311yescharacteristic
56C23×D43C2311yescharacteristic
57C23×D43C2311yescharacteristic
58C2×Q8×C43—22no—
59C2×Q8×C43—22no—
60C2×Q8×C43—41no—
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C2×D172—22no—
74C2×D172—22no—
75C2×D172—22no—
76C2×D172—22no—
77C2×D172—22no—
78C2×D172—22no—
79C2×D172—22no—
80C2×D172—41no—
81C2×D172—41no—
82C2×C4×D43—22no—
83C2×C4×D43—22no—
84C2×C4×D43—22no—
85C2×C4×D43—22no—
86C2×C4×D43—41no—
87C2×C4×D43—41no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—41no—
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—22no—
98(C2×D43)⋊C4—22no—
99(C2×D43)⋊C4—22no—
100(C2×D43)⋊C4—22no—
101(C2×D43)⋊C4—22no—
102(C2×D43)⋊C4—22no—
103(C2×D43)⋊C4D414yescomplemented
104C4⋊Dic43—22no—
105Dic43⋊C4—22no—
106Dic43⋊C4—22no—
107Dic43⋊C4D414yescomplemented
108C4×Dic43—22no—
109C4×Dic43—22no—
110C4×Dic43—22no—
111C23×C43C2411yescharacteristic
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×D43—21no—
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—21no—
130C22×D43—21no—
131C22×D43C2×D412yes—
132C22×D43#4112yes—
133Q8×C43—44no—
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×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43C2×D412yes—
152C2×C4×C43C2×D412yes—
153C2×C4×C43#4112yes—
154C2×C4×C43#4112yes—
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×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43C2×D412yes—
168C2×Dic43C2×D412yes—
169C2×Dic43C2×D412yes—
170D172—28no—
171D172—44no—
172D172—44no—
173C4×D43—44no—
174C4×D43—44no—
175C22×C43C22×D411yescharacteristic
176C22×C43C22×D411yescharacteristic
177C22×C43C2×#4111yescharacteristic
178C22×C43C2×#4111yescharacteristic
179C22×C43C2×#4111yescharacteristic
180C22×C43H(5,𝔽2)11yescharacteristic
181C22×C432−1+411yescharacteristic
182C2×D43—22no—
183C2×D43—22no—
184C2×D43—22no—
185C2×D43—22no—
186C2×D43—22no—
187C2×D43—22no—
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—
197C2×D43—41no—
198C2×D43—41no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—41no—
202C2×D43—41no—
203C4×C43—22no—
204C4×C43—22no—
205C4×C43—22no—
206C4×C43—22no—
207C4×C43—41no—
208C4×C43—41no—
209C4×C43—41no—
210Dic43—22no—
211Dic43—22no—
212Dic43—22no—
213Dic43—41no—
214Dic43—41no—
215#2461—431nomaximal, Sylow
216C2×C43#52511yescharacteristic
217C2×C43#53211yescharacteristic
218C2×C43#54211yescharacteristic
219C2×C43D4211yescharacteristic
220C2×C43#54711yescharacteristic
221C2×C43#54811yescharacteristic
222C2×C43#55111yescharacteristic
223D43—42no—
224D43—42no—
225D43—81no—
226C2×#124—431no—
227C2×#123—431no—
228C2×C22⋊Q8—431no—
229C2×C4×D4—431no—
230#396—431no—
231#395D4311yescharacteristic, complemented
232#394—431no—
233#392—431no—
234#390—431no—
235#388—431no—
236#388—431no—
237#388—431no—
238#386—431no—
239#385—431no—
240C4×C4⋊C4—431no—
241C43#246111yescharacteristic, complemented, Sylow
242C22×Q8C2×D4311yescharacteristic
243C22×D4—431no—
244C22×D4—431no—
245C22×D4—431no—
246C23×C4—431no—
247C23×C4—431no—
248#124—864no—
249#123—864no—
250C22⋊Q8—864no—
251C4×D4—864no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—431no—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4C2×D4311yescharacteristic
257C2×C4⋊C4C2×D4311yescharacteristic
258C2×C4⋊C4C2×D4311yescharacteristic
259C2×C22⋊C4—431no—
260C2×C22⋊C4—431no—
261C2×C22⋊C4—431no—
262C2×C22⋊C4—431no—
263C2×C22⋊C4—431no—
264C2×C22⋊C4—431no—
265C2×C22⋊C4—431no—
266C2×C22⋊C4—431no—
267C2×C22⋊C4—431no—
268C2×C22⋊C4—431no—
269C2×C22⋊C4—431no—
270C2×C22⋊C4—431no—
271C2×C22⋊C4—431no—
272C2×C42—431no—
273C2×C42—431no—
274C2×C42—431no—
275#95—431no—
276#95—431no—
277#95—431no—
278#95C2×D4311yescharacteristic
279#95C2×D4311yescharacteristic
280#95C2×D4311yescharacteristic
281C24—431no—
282C24—431no—
283C24—431no—
284C2×Q8—22no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×D4—862no—
288C2×D4—862no—
289C2×D4—862no—
290C2×D4—862no—
291C2×D4—862no—
292C2×D4—862no—
293C2×D4—862no—
294C2×D4—1721no—
295C2×D4—1721no—
296C22×C4—431no—
297C22×C4—431no—
298C22×C4—431no—
299C22×C4—431no—
300C22×C4—431no—
301C22×C4—862no—
302C22×C4—862no—
303C22×C4—862no—
304C22×C4—862no—
305C22×C4—1721no—
306C22×C4—1721no—
307C22×C4C22×D4311yescharacteristic
308C22×C4C22×D4311yescharacteristic
309C22×C4C22×D4311yescharacteristic
310C22×C4C22×D4311yescharacteristic
311C22×C4C22×D4311yescharacteristic
312C22×C4C22×D4311yescharacteristic
313C22×C4C22×D4311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—434no—
318C4⋊C4—862no—
319C4⋊C4—862no—
320C4⋊C4—862no—
321C22⋊C4—434no—
322C22⋊C4—862no—
323C22⋊C4—862no—
324C22⋊C4—862no—
325C22⋊C4—862no—
326C22⋊C4—862no—
327C22⋊C4—862no—
328C22⋊C4—862no—
329C22⋊C4—862no—
330C22⋊C4—862no—
331C22⋊C4—862no—
332C22⋊C4—862no—
333C22⋊C4—862no—
334C42—862no—
335C42—862no—
336C42—862no—
337C23—432no—
338C23—432no—
339C23—861no—
340C23—861no—
341C23—861no—
342C23—861no—
343C23—861no—
344C23—861no—
345C23—861no—
346C23—861no—
347C23—861no—
348C23—861no—
349C23—861no—
350C23—861no—
351C23—861no—
352C23—861no—
353C23—861no—
354C23—861no—
355C23—861no—
356C23—861no—
357C23—861no—
358C23C23×D4311yescharacteristic
359Q8—44no—
360D4—868no—
361D4—1724no—
362D4—1724no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—432no—
381C2×C4—432no—
382C2×C4—432no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—861no—
390C2×C4—861no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—861no—
395C2×C4—1724no—
396C2×C4—1724no—
397C2×C4D4×D4312yes—
398C2×C4D4×D4312yes—
399C2×C4#1062190212yes—
400C2×C4#1062190212yes—
401C22—862no—
402C22—862no—
403C22—862no—
404C22—862no—
405C22—862no—
406C22—862no—
407C22—1721no—
408C22—1721no—
409C22—1721no—
410C22—1721no—
411C22—1721no—
412C22—1721no—
413C22—1721no—
414C22—1721no—
415C22—1721no—
416C22—1721no—
417C22—1721no—
418C22—1721no—
419C22—1721no—
420C22—1721no—
421C22—1721no—
422C22C2×D4×D4311yescharacteristic
423C22C2×D4×D4311yescharacteristic
424C22#41×D4311yescharacteristic
425C22C2×#1062190211yescharacteristic
426C22C2×#1062190211yescharacteristic
427C22#1306337011yescharacteristic
428C22#1306337311yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—862no—
437C4—862no—
438C4—862no—
439C4—1721no—
440C4—1721no—
441C2—3441no—
442C2—1722no—
443C2—1722no—
444C2#1458341211yescharacteristic
445C2#1458345011yescharacteristic
446C2#1458352311yescharacteristic
447C2#1458353111yescharacteristic
448C2#1458355211yescharacteristic
449C2#1458355911yescharacteristic
450C2#1458357611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2461
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#13063314C2semidirect
2. C2×#13063310C2semidirect
3. C2×#13063301C2semidirect
4. C2×#13063287C2semidirect
5. #14582821C2semidirect
6. #14582817C2semidirect
8. #14582800C2semidirect
9. #14582791C2semidirect
10. #14582789C2semidirect
11. #14582788C2semidirect
12. #14582777C2semidirect
13. #14582770C2semidirect
14. #14582750C2semidirect
15. C43×#395C2semidirect
103. (C2×D43)⋊C4D4semidirect
107. Dic43⋊C4D4semidirect
231. #395D43semidirect
241. C43#2461semidirect