Finite Group Databasebeta

← C2×#19133926 #25077766

Subgroups — C2×#19133926 #25077766

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583653C211yesmaximal, characteristic
2C2×#14583305C211yesmaximal, characteristic, complemented
3C2×#14583261C211yesmaximal, characteristic
4#19133926C218yesmaximal, direct product factor
5C2×#14582641C211yesmaximal, characteristic, complemented
6C2×#14582640C211yesmaximal, characteristic, complemented
7C2×#14582638C211yesmaximal, characteristic
8C2×C43×#491C211yesmaximal, characteristic, complemented
9#14583653—22no—
10#14583653—22no—
11#14583653—22no—
12#14583653C2214yes—
13C2×#13063324—21no—
14C2×#13063320—21no—
15C2×#13063320—21no—
16C2×#13063317C2211yescharacteristic
17C2×#13063313C2211yescharacteristic
18C2×#13063310—21no—
19C2×#13063305—21no—
20C2×#13063303—21no—
21#14583305—22no—
22#14583305C2214yescomplemented
23#14583261—22no—
24#14583261C2214yes—
25C2×#13063258—21no—
26C2×#13063256—21no—
27C2×#13063248—21no—
28C2×#13063245—21no—
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31#14582641C2214yescomplemented
32#14582640C2214yescomplemented
33#14582638C2214yes—
34C2×C4⋊Q8×C43C2211yescharacteristic
35C2×#125×C43C2211yescharacteristic
36C43×#491—22no—
37C43×#491C2214yescomplemented
38C2×#103×C43—21no—
39C2×#103×C43—21no—
40C2×#97×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D411yescharacteristic
43C22×D172D411yescharacteristic
44C22×C4×D43—21no—
45C22×C43⋊C8—21no—
46C22×C43⋊C8—21no—
47#13063324—24no—
48#13063324—24no—
49#13063320—24no—
50#13063320—24no—
51#13063320—24no—
52#13063320—24no—
53#13063317—21no—
54#13063317—21no—
55#13063317D412yes—
56#13063317C2312yes—
57#13063313—21no—
58#13063313—21no—
59#13063313D412yes—
60#13063313C2312yes—
61#13063310—24no—
62#13063310—24no—
63#13063305—24no—
64#13063305—24no—
65#13063303—24no—
66#13063303—24no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D411yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×C4×Dic43—21no—
79#13063258—24no—
80#13063256—24no—
81#13063248—24no—
82#13063245—24no—
83#13063236—21no—
84#13063236—21no—
85#13063236C2312yes—
86#13063236C2312yes—
87C22×Q8×C43—21no—
88C22×C8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43C2312yes—
93#125×C43—21no—
94#125×C43—21no—
95#125×C43D412yes—
96#125×C43C2312yes—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C42×C43C2311yescharacteristic
104#103×C43—24no—
105#103×C43—24no—
106#97×C43—21no—
107#97×C43C2312yes—
108C23×D43—21no—
109C2×Q8×C43—22no—
110C2×Q8×C43—44no—
111C2×Q8×C43—41no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—41no—
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—21no—
121C2×D172—21no—
122C2×D172—42no—
123C2×D172C2×D412yes—
124C2×C4×D43—24no—
125C2×C4×D43—82no—
126C2×Dic86—24no—
127C2×Dic86—21no—
128C2×Dic86—42no—
129C2×Dic86—82no—
130C2×Dic86C2×D412yes—
131C2×C8×C43—22no—
132C2×C8×C43—42no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—41no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43C2×D412yes—
144C4⋊C4×C43C2×D412yes—
145C42×C43C2×D411yescharacteristic
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2411yescharacteristic
149(C2×D43)⋊C4—24no—
150(C2×D43)⋊C4—24no—
151(C2×D43)⋊C4—24no—
152(C2×D43)⋊C4—22no—
153(C2×D43)⋊C4—22no—
154(C2×D43)⋊C4—22no—
155(C2×D43)⋊C4—22no—
156C4⋊Dic43—24no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43C2×D412yes—
160C4⋊Dic43C2×D412yes—
161Dic43⋊C4—24no—
162Dic43⋊C4—22no—
163Dic43⋊C4—22no—
164Dic43⋊C4—22no—
165Dic43⋊C4—22no—
166C4×Dic43—24no—
167C2×C43⋊C8—24no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—42no—
171C23×C43#12011yescharacteristic
172C22×D43—22no—
173C22×D43—42no—
174C22×D43—42no—
175C22×D43—42no—
176Q8×C43—44no—
177Q8×C43—82no—
178C2×C4×C43—22no—
179C2×C4×C43—22no—
180C2×C4×C43—22no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—42no—
186C2×C4×C43—82no—
187C2×C4×C43#12011yescharacteristic
188C2×C4×C43#12011yescharacteristic
189C2×C4×C43#12011yescharacteristic
190C2×C4×C43C22×D411yescharacteristic
191C2×C4×C43C22×D411yescharacteristic
192C2×C4×C43C22×D411yescharacteristic
193C2×Dic43—22no—
194C2×Dic43—22no—
195C2×Dic43—22no—
196C2×Dic43—42no—
197C2×Dic43—42no—
198C2×Dic43—42no—
199D172—42no—
200D172—81no—
201C4×D43—84no—
202Dic86—42no—
203Dic86—81no—
204Dic86—84no—
205C8×C43—42no—
206C43⋊C8—24no—
207C43⋊C8—42no—
208C2×#1664—431nomaximal, Sylow
209C22×C43#45412yes—
210C22×C43#45512yes—
211C22×C43#45612yes—
212C22×C43C2×#12011yescharacteristic
213C2×D43—42no—
214C2×D43—42no—
215C2×D43—42no—
216C2×D43—84no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—42no—
224C4×C43—42no—
225C4×C43—82no—
226Dic43—42no—
227Dic43—42no—
228Dic43—42no—
229C2×#563—431no—
230C2×#501—431no—
231C2×#491D4311yescharacteristic, complemented
232C2×#489—431no—
233#1664—438no—
234C2×#330—431no—
235C2×#330—431no—
236C2×#329—431no—
237C2×C43#166414yescomplemented
238C2×C43C2×#45511yescharacteristic
239C2×C43C2×#45411yescharacteristic
240C2×C43C2×#45611yescharacteristic
241D43—82no—
242#563—434no—
243#563—862no—
244#563—862no—
245#563—862no—
246C2×C4⋊Q8—861no—
247C2×C4⋊Q8C2×D4311yescharacteristic
248C2×#126—861no—
249C2×#126—861no—
250C2×#125—431no—
251C2×#125C2×D4311yescharacteristic
252C2×#124—431no—
253C2×#123—861no—
254C2×C22⋊Q8—861no—
255C2×C22⋊Q8—861no—
256#501—434no—
257#501—862no—
258#491—22no—
259#491C2×D4314yescomplemented
260#489—434no—
261#489—862no—
262C2×#107—861no—
263C2×#106—861no—
264C2×#103—21no—
265C2×#103—21no—
266C2×#103—861no—
267C2×#102—861no—
268C2×#97—431no—
269C2×#97—431no—
270C2×#97C2×D4311yescharacteristic
271#330—434no—
272#330—434no—
273#329—434no—
274C43C2×#166411yescharacteristic, complemented, Sylow
275C22×Q8—21no—
276C22×Q8—431no—
277C22×Q8—861no—
278C22×D4—431no—
279C23×C4—861no—
280C22×C8—21no—
281C22×C8—861no—
282C22×C8—861no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—864no—
287C4⋊Q8—864no—
288C4⋊Q8C22×D4312yes—
289#126—864no—
290#126—864no—
291#126—864no—
292#126—864no—
293#125—21no—
294#125—21no—
295#125—432no—
296#125—432no—
297#125—861no—
298#125—861no—
299#125C22⋊D4312yes—
300#125C22×D4312yes—
301#124—432no—
302#124—432no—
303#124—861no—
304#124—861no—
305#123—864no—
306#123—864no—
307C22⋊Q8—864no—
308C22⋊Q8—864no—
309C22⋊Q8—864no—
310C22⋊Q8—864no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—431no—
316C2×C4⋊C4—431no—
317C2×C4⋊C4—861no—
318C2×C4⋊C4—861no—
319C2×C4⋊C4—861no—
320C2×C4⋊C4—861no—
321C2×C4⋊C4C22⋊D4311yescharacteristic
322C2×C4⋊C4C22⋊D4311yescharacteristic
323C2×C22⋊C4—861no—
324C2×C22⋊C4—861no—
325C2×C22⋊C4—861no—
326C2×C22⋊C4—861no—
327C2×C22⋊C4—861no—
328C2×C42—861no—
329C2×C42C22×D4311yescharacteristic
330#107—864no—
331#106—864no—
332#103—24no—
333#103—24no—
334#103—864no—
335#102—864no—
336#97—21no—
337#97—432no—
338#97—432no—
339#97—861no—
340#97—861no—
341#97C22×D4312yes—
342C24—861no—
343C2×Q8—22no—
344C2×Q8—44no—
345C2×Q8—41no—
346C2×Q8—432no—
347C2×Q8—864no—
348C2×Q8—861no—
349C2×Q8—3442no—
350C2×Q8—1722no—
351C2×D4—432no—
352C2×D4—861no—
353C2×D4—1722no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4—864no—
358C22×C4—861no—
359C22×C4—861no—
360C22×C4—861no—
361C22×C4—3442no—
362C22×C4D4×D4311yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4C2×C22⋊D4311yescharacteristic
365C2×C8—22no—
366C2×C8—42no—
367C2×C8—864no—
368C2×C8—862no—
369C2×C8—862no—
370C2×C8—1722no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—432no—
382C4⋊C4—432no—
383C4⋊C4—864no—
384C4⋊C4—864no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4—862no—
388C4⋊C4—862no—
389C4⋊C4—862no—
390C4⋊C4—862no—
391C4⋊C4C2×C22⋊D4312yes—
392C4⋊C4C2×C22⋊D4312yes—
393C22⋊C4—864no—
394C22⋊C4—864no—
395C22⋊C4—864no—
396C22⋊C4—862no—
397C22⋊C4—862no—
398C22⋊C4—862no—
399C22⋊C4—862no—
400C42—864no—
401C42D4×D4311yescharacteristic
402C42D4×D4311yescharacteristic
403C42C2×C22⋊D4311yescharacteristic
404C42C23×D4311yescharacteristic
405C23—862no—
406C23—1722no—
407C23—1722no—
408C23—1722no—
409C23#1306329311yescharacteristic
410Q8—44no—
411Q8—82no—
412Q8—3441no—
413Q8—3444no—
414Q8—1722no—
415D4—3441no—
416D4—1722no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—82no—
426C2×C4—862no—
427C2×C4—862no—
428C2×C4—862no—
429C2×C4—3444no—
430C2×C4—1722no—
431C2×C4—1722no—
432C2×C4—1722no—
433C2×C4#1306329311yescharacteristic
434C2×C4#1306329311yescharacteristic
435C2×C4#1306329311yescharacteristic
436C2×C4C2×D4×D4311yescharacteristic
437C2×C4C2×D4×D4311yescharacteristic
438C2×C4C22×C22⋊D4311yescharacteristic
439C8—42no—
440C8—864no—
441C8—1722no—
442C22—3444no—
443C22—1722no—
444C22—1722no—
445C22—1722no—
446C22#1458307112yes—
447C22#1458307512yes—
448C22#1458308012yes—
449C22C2×#1306329311yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—42no—
457C4—42no—
458C4—82no—
459C4—1722no—
460C4—1722no—
461C4—1722no—
462C2—3442no—
463C2#1913392614yesdirect product factor
464C2C2×#1458307511yescharacteristic
465C2C2×#1458307111yescharacteristic
466C2C2×#1458308011yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#491C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenterC2×#491D43
hypocenterC43C2×#1664
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
2. C2×#14583305C2semidirect
4. #19133926C2direct (N × H)
5. C2×#14582641C2semidirect
6. C2×#14582640C2semidirect
8. C2×C43×#491C2semidirect
22. #14583305C22semidirect
31. #14582641C22semidirect
32. #14582640C22semidirect
37. C43×#491C22semidirect
231. C2×#491D43semidirect
237. C2×C43#1664semidirect
259. #491C2×D43semidirect
274. C43C2×#1664semidirect
463. C2#19133926direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145836532
C2×#145833052
C2×#145832612
#191339262
C2×#145826412
C2×#145826402
C2×#145826382
C2×C43×#4912
C2×#166443