Finite Group Databasebeta

← #19138142

Subgroups — #19138142

Order 5504.

666 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063308C211yesmaximal, characteristic, complemented
2C2×#13063297C211yesmaximal, characteristic
3C2×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
4#14582830C211yesmaximal, characteristic, complemented
5#14582825C211yesmaximal, characteristic, complemented
6#14582822C211yesmaximal, characteristic, complemented
7#14582815C211yesmaximal, characteristic, complemented
8#14582795C211yesmaximal, characteristic, complemented
9#14582787C211yesmaximal, characteristic, complemented
10#14582779C211yesmaximal, characteristic, complemented
11#14582775C211yesmaximal, characteristic, complemented
12#14582774C211yesmaximal, characteristic, complemented
13#14582756C211yesmaximal, characteristic, complemented
14C2×C43⋊#95C211yesmaximal, characteristic, complemented
15C2×#123×C43C211yesmaximal, characteristic, complemented
16C22×C22⋊D43C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C23×Dic43C2211yescharacteristic
19C23×Dic43C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic
21#13063308—24no—
22#13063297—24no—
23(C22⋊D43)⋊C4—24no—
24C2×C4⋊Dic43C2211yescharacteristic
25C2×C4⋊Dic43C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×Dic43⋊C4C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×C4×Dic43C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C22×D4×C43C2211yescharacteristic
48C23×C4×C43C2211yescharacteristic
49#123×C43—24no—
50C2×C4⋊C4×C43C2211yescharacteristic
51C2×C4⋊C4×C43C2211yescharacteristic
52C2×C22⋊C4×C43C2211yescharacteristic
53C2×C22⋊C4×C43C2211yescharacteristic
54C2×C22⋊C4×C43C2211yescharacteristic
55C24×C43C2311yescharacteristic
56C24×C43C2311yescharacteristic
57C23×D43C2311yescharacteristic
58C2×D4×C43—22no—
59C2×D4×C43—22no—
60C2×D4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C2×C22⋊D43—22no—
70C2×C22⋊D43—22no—
71C2×C22⋊D43—22no—
72C2×C22⋊D43—22no—
73C2×C22⋊D43—41no—
74C2×C22⋊D43D414yes—
75C22×Dic43—22no—
76C22×Dic43—22no—
77C22×Dic43—22no—
78C22×Dic43—22no—
79C22×Dic43—41no—
80C22×Dic43—41no—
81C22×Dic43C2311yescharacteristic
82C22×Dic43C2311yescharacteristic
83C22×Dic43C2311yescharacteristic
84C22×Dic43C2311yescharacteristic
85C22×Dic43C2311yescharacteristic
86C22×Dic43C2311yescharacteristic
87C22×Dic43C2311yescharacteristic
88C2×C4×D43—22no—
89C2×C4×D43—22no—
90C2×C4×D43—41no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—22no—
93C22⋊C4×C43—22no—
94C22⋊C4×C43—22no—
95C22⋊C4×C43D414yescomplemented
96C22⋊Dic43—22no—
97C22⋊Dic43—22no—
98C22⋊Dic43—22no—
99C22⋊Dic43—41no—
100(C2×D43)⋊C4—22no—
101(C2×D43)⋊C4—22no—
102(C2×D43)⋊C4—22no—
103(C2×D43)⋊C4—22no—
104C4⋊Dic43—22no—
105C4⋊Dic43—41no—
106Dic43⋊C4—22no—
107Dic43⋊C4—22no—
108Dic43⋊C4—22no—
109Dic43⋊C4—22no—
110C4×Dic43—22no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43C2×D412yes—
123C23×C43C2×D412yes—
124C23×C43#4112yes—
125C23×C43C2411yescharacteristic
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—21no—
130C22×D43—21no—
131C22×D43—21no—
132C22×D43C2×D412yes—
133D4×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—44no—
148C2×C4×C43C2×D412yes—
149C2×C4×C43C2×D412yes—
150C22⋊D43—28no—
151C22⋊D43—44no—
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×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—44no—
171C2×Dic43—44no—
172C2×Dic43C2×D412yes—
173C2×Dic43#4112yes—
174C2×Dic43#4112yes—
175C4×D43—44no—
176C22×C43—22no—
177C22×C43—22no—
178C22×C43—22no—
179C22×C43—22no—
180C22×C43—22no—
181C22×C43—22no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43#12114yes—
190C22×C43C22×D411yescharacteristic
191C22×C43C22×D411yescharacteristic
192C22×C43C2×#4111yescharacteristic
193C22×C43C2×#4111yescharacteristic
194C22×C43C2×#4111yescharacteristic
195C22×C43H(5,𝔽2)11yescharacteristic
196C22×C432−1+411yescharacteristic
197C2×D43—22no—
198C2×D43—22no—
199C2×D43—22no—
200C2×D43—41no—
201C2×D43—41no—
202C2×D43—41no—
203C2×D43—41no—
204C4×C43—22no—
205C4×C43—22no—
206C4×C43—41no—
207C4×C43—41no—
208C4×C43—41no—
209Dic43—22no—
210Dic43—22no—
211Dic43—22no—
212Dic43—41no—
213Dic43—41no—
214Dic43—41no—
215Dic43—41no—
216#2425—431nomaximal, Sylow
217C2×C43—24no—
218C2×C43—81no—
219C2×C43C2×#12111yescharacteristic
220C2×C43#52911yescharacteristic
221C2×C43#53911yescharacteristic
222C2×C43#54611yescharacteristic
223C2×C43#54611yescharacteristic
224C2×C43#54711yescharacteristic
225C2×C43#54711yescharacteristic
226D43—42no—
227C2×#123—431no—
228C2×#123D4311yescharacteristic, complemented
229C2×#121—431no—
230C2×C4×D4—431no—
231#398—431no—
232#397—431no—
233#396—431no—
234#394—431no—
235#389—431no—
236#388—431no—
237#386—431no—
238#386—431no—
239#385—431no—
240#380—431no—
241C2×#95—431no—
242C43#242511yescharacteristic, complemented, Sylow
243C22×D4—431no—
244C22×D4—431no—
245C22×D4C2×D4311yescharacteristic
246C23×C4—431no—
247C23×C4—431no—
248C23×C4—431no—
249C23×C4C2×D4311yescharacteristic
250#123—24no—
251#123—864no—
252#121—864no—
253C4×D4—864no—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—431no—
258C2×C4⋊C4—431no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4C2×D4311yescharacteristic
261C2×C4⋊C4C2×D4311yescharacteristic
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⋊C4C2×D4311yescharacteristic
271C2×C22⋊C4C2×D4311yescharacteristic
272C2×C22⋊C4C2×D4311yescharacteristic
273C2×C42—431no—
274#95—431no—
275#95—431no—
276#95—431no—
277#95—431no—
278#95—431no—
279#95—431no—
280#95—431no—
281#95—431no—
282C24—431no—
283C24C22×D4311yescharacteristic
284C24C22×D4311yescharacteristic
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—434no—
289C2×D4—862no—
290C2×D4—862no—
291C2×D4—862no—
292C2×D4—862no—
293C2×D4—1721no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—431no—
298C22×C4—431no—
299C22×C4—431no—
300C22×C4—431no—
301C22×C4—431no—
302C22×C4—431no—
303C22×C4—431no—
304C22×C4—862no—
305C22×C4—862no—
306C22×C4—862no—
307C22×C4—862no—
308C22×C4—862no—
309C22×C4—862no—
310C22×C4—1721no—
311C22×C4—1721no—
312C22×C4—1721no—
313C22×C4C22×D4311yescharacteristic
314C22×C4C22×D4311yescharacteristic
315C22×C4C22×D4311yescharacteristic
316C22×C4C22×D4311yescharacteristic
317C22×C4C22×D4311yescharacteristic
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—862no—
321C4⋊C4—862no—
322C4⋊C4—862no—
323C4⋊C4—862no—
324C4⋊C4—862no—
325C4⋊C4—1721no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—862no—
329C22⋊C4—862no—
330C22⋊C4—862no—
331C22⋊C4—862no—
332C22⋊C4—862no—
333C22⋊C4—862no—
334C22⋊C4—862no—
335C22⋊C4—1721no—
336C22⋊C4C22⋊D4314yescomplemented
337C42—862no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—432no—
350C23—861no—
351C23—861no—
352C23—861no—
353C23—861no—
354C23—861no—
355C23—861no—
356C23D4×D4312yes—
357C23#1062190012yes—
358C23C2×C22⋊D4312yes—
359C23C23×D4311yescharacteristic
360D4—44no—
361D4—868no—
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—44no—
377C2×C4—432no—
378C2×C4—432no—
379C2×C4—432no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
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—861no—
396C2×C4—861no—
397C2×C4—861no—
398C2×C4—1724no—
399C2×C4—1724no—
400C2×C4—1724no—
401C2×C4C2×C22⋊D4312yes—
402C2×C4C2×C22⋊D4312yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—862no—
417C22—862no—
418C22—862no—
419C22—1721no—
420C22—1721no—
421C22—1721no—
422C22—1721no—
423C22#1306329614yes—
424C22C2×D4×D4311yescharacteristic
425C22C22×C22⋊D4311yescharacteristic
426C22#41×D4311yescharacteristic
427C22#41×D4311yescharacteristic
428C22C2×#1062190011yescharacteristic
429C22#1306337111yescharacteristic
430C22#1306337211yescharacteristic
431C4—22no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—862no—
437C4—862no—
438C4—862no—
439C4—1721no—
440C4—1721no—
441C4—1721no—
442C4—1721no—
443C2—24no—
444C2—81no—
445C2—1722no—
446C2C2×#1306329611yescharacteristic
447C2#1458342611yescharacteristic
448C2#1458349311yescharacteristic
449C2#1458353711yescharacteristic
450C2#1458354111yescharacteristic
451C2#1458354711yescharacteristic
452C2#1458354811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#123×C43C2
hypercenterC2×#123D43
hypocenterC43#2425
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#13063308C2semidirect
3. C2×(C22⋊D43)⋊C4C2semidirect
4. #14582830C2semidirect
5. #14582825C2semidirect
6. #14582822C2semidirect
7. #14582815C2semidirect
8. #14582795C2semidirect
9. #14582787C2semidirect
10. #14582779C2semidirect
11. #14582775C2semidirect
12. #14582774C2semidirect
13. #14582756C2semidirect
14. C2×C43⋊#95C2semidirect
15. C2×#123×C43C2semidirect
95. C22⋊C4×C43D4semidirect
228. C2×#123D43semidirect
242. C43#2425semidirect
336. C22⋊C4C22⋊D43semidirect