Finite Group Databasebeta

← C2×#19133625 #25068744

Subgroups — C2×#19133625 #25068744

Order 11008.

1016 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583498C211yesmaximal, characteristic
2C2×#14583217C211yesmaximal, characteristic
3C2×#14582837C211yesmaximal, characteristic, complemented
4#19133625C218yesmaximal, direct product factor
5C2×#14582636C211yesmaximal, characteristic, complemented
6C2×#14582634C211yesmaximal, characteristic
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#484C211yesmaximal, characteristic, complemented
9#14583498—22no—
10#14583498—22no—
11#14583498—22no—
12#14583498C2214yes—
13C2×#13063320—21no—
14C2×#13063316—21no—
15C2×#13063310—21no—
16C2×#13063309—21no—
17C2×#13063301—21no—
18C2×#13063299C2211yescharacteristic
19C2×(C22⋊D43)⋊C4—21no—
20C22×Dic43⋊C4C2211yescharacteristic
21#14583217—22no—
22#14583217C2214yes—
23C2×#13063256—21no—
24C2×#13063245—21no—
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26#14582837—22no—
27#14582837C2214yescomplemented
28C2×C43⋊#95—21no—
29C2×C43⋊#95—21no—
30C2×C43⋊#95C2211yescharacteristic
31#14582636C2214yescomplemented
32#14582634C2214yes—
33#14582624C2214yescomplemented
34C2×C22⋊Q8×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#484—22no—
37C43×#484C2214yescomplemented
38C2×#107×C43—21no—
39C2×#103×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
41C22×D172D411yescharacteristic
42C22×C22⋊D43—21no—
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C23×Dic43D411yescharacteristic
46C22×C4×D43—21no—
47C22×C43⋊C8—21no—
48#13063320—24no—
49#13063320—24no—
50#13063316—24no—
51#13063316—24no—
52#13063310—24no—
53#13063310—24no—
54#13063309—24no—
55#13063309—24no—
56#13063301—24no—
57#13063301—24no—
58#13063299—21no—
59#13063299—21no—
60#13063299D412yes—
61#13063299C2312yes—
62(C22⋊D43)⋊C4—24no—
63(C22⋊D43)⋊C4—24no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4D412yes—
73C2×Dic43⋊C4C2312yes—
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#13063256—24no—
80#13063245—24no—
81C22⋊(C43⋊C8)—21no—
82C22⋊(C43⋊C8)C2312yes—
83C43⋊#95—21no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C43⋊#95C2312yes—
87C22×Q8×C43D411yescharacteristic
88C23×C4×C43—21no—
89C23×C4×C43C2311yescharacteristic
90C22×C8×C43—21no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43D412yes—
94C22⋊Q8×C43C2312yes—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
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×C43C2312yes—
103C2×C22⋊C4×C43—21no—
104#107×C43—24no—
105#103×C43—24no—
106C22⋊C8×C43—21no—
107C22⋊C8×C43C2312yes—
108C24×C43C2×D411yescharacteristic
109C23×D43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—42no—
112C2×Q8×C43C2×D412yes—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—42no—
117C22×C4×C43—44no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C2×C22⋊D43—22no—
127C2×C22⋊D43—22no—
128C2×C22⋊D43—42no—
129C2×C22⋊D43—42no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—42no—
139C22×Dic43—42no—
140C22×Dic43—42no—
141C22×Dic43—42no—
142C22×Dic43C2×D412yes—
143C22×Dic43C2×D412yes—
144C2×D172—21no—
145C2×D172—42no—
146C2×D172C2×D412yes—
147C2×C4×D43—24no—
148C2×C4×D43—82no—
149C2×C8×C43—22no—
150C2×C8×C43—42no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—41no—
157C4⋊C4×C43—41no—
158C4⋊C4×C43C2×D412yes—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161(C2×D43)⋊C4—24no—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—22no—
165(C2×D43)⋊C4—22no—
166C4⋊Dic43—24no—
167C4⋊Dic43—24no—
168C4⋊Dic43—21no—
169C4⋊Dic43C2×D412yes—
170Dic43⋊C4—24no—
171Dic43⋊C4—22no—
172Dic43⋊C4—22no—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175C4×Dic43—24no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—42no—
178C23×C43—22no—
179C23×C43—22no—
180C23×C43#12011yescharacteristic
181C23×C43#12011yescharacteristic
182C23×C43#13512yes—
183C23×C43#13712yes—
184C23×C43C22×D411yescharacteristic
185C22×D43—22no—
186C22×D43—42no—
187C22×D43—42no—
188C22×D43—42no—
189Q8×C43—42no—
190Q8×C43—81no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—44no—
202C2×C4×C43—42no—
203C2×C4×C43—82no—
204C2×C4×C43—82no—
205C2×C4×C43#12011yescharacteristic
206C2×C4×C43#12011yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C22⋊D43—42no—
210C22⋊D43—42no—
211C22⋊D43—44no—
212C2×Dic43—22no—
213C2×Dic43—22no—
214C2×Dic43—22no—
215C2×Dic43—22no—
216C2×Dic43—22no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—42no—
220C2×Dic43—42no—
221C2×Dic43—42no—
222C2×Dic43—42no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225C2×Dic43—81no—
226C2×Dic43—84no—
227D172—42no—
228D172—81no—
229C4×D43—84no—
230C8×C43—42no—
231C43⋊C8—42no—
232C2×#1615—431nomaximal, Sylow
233C22×C43—24no—
234C22×C43—24no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43#45212yes—
240C22×C43#45212yes—
241C22×C43#45412yes—
242C22×C43#45812yes—
243C22×C43C2×#12011yescharacteristic
244C22×C43C2×#13511yescharacteristic
245C22×C43C2×#13711yescharacteristic
246C2×D43—42no—
247C2×D43—42no—
248C2×D43—42no—
249C2×D43—84no—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—42no—
255C4×C43—42no—
256C4×C43—82no—
257Dic43—42no—
258Dic43—42no—
259Dic43—42no—
260Dic43—82no—
261C2×#539—431no—
262C2×#484D4311yescharacteristic, complemented
263C2×#481—431no—
264C2×#400—431no—
265#1615—438no—
266C2×#328—431no—
267C2×#327—431no—
268C2×#324—431no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43—22no—
272C2×C43#161514yescomplemented
273C2×C43C2×#45211yescharacteristic
274C2×C43C2×#45411yescharacteristic
275C2×C43C2×#45811yescharacteristic
276D43—82no—
277#539—434no—
278#539—862no—
279#539—862no—
280#539—862no—
281C2×#126—861no—
282C2×#125—861no—
283C2×#123—861no—
284C2×#123—861no—
285C2×C22⋊Q8—861no—
286C2×C22⋊Q8C2×D4311yescharacteristic
287C2×#121—431no—
288C2×C4×D4—861no—
289C22×C4⋊C4—431no—
290C22×C4⋊C4C2×D4311yescharacteristic
291#484—22no—
292#484C2×D4314yescomplemented
293#481—434no—
294#481—862no—
295C2×#107—21no—
296C2×#106—861no—
297C2×#103—21no—
298C2×#102—861no—
299C2×C22⋊C8—431no—
300C2×C22⋊C8C2×D4311yescharacteristic
301#400—434no—
302#400—862no—
303C2×#95—431no—
304C2×#95—861no—
305C2×#95—861no—
306#328—434no—
307#327—434no—
308#324—434no—
309C43C2×#161511yescharacteristic, complemented, Sylow
310C22×Q8C22⋊D4311yescharacteristic
311C22×D4—431no—
312C22×D4—861no—
313C23×C4—21no—
314C23×C4—431no—
315C23×C4—431no—
316C23×C4—861no—
317C23×C4—861no—
318C23×C4C22×D4311yescharacteristic
319C22×C8—21no—
320C22×C8—861no—
321#126—864no—
322#126—864no—
323#125—864no—
324#125—864no—
325#123—864no—
326#123—864no—
327#123—864no—
328#123—864no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—864no—
332C22⋊Q8—864no—
333C22⋊Q8C22⋊D4312yes—
334C22⋊Q8C22×D4312yes—
335#121—432no—
336#121—432no—
337#121—861no—
338#121—861no—
339C4×D4—864no—
340C4×D4—864no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—431no—
348C2×C4⋊C4—432no—
349C2×C4⋊C4—432no—
350C2×C4⋊C4—861no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4—861no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4C22⋊D4311yescharacteristic
358C2×C4⋊C4C22×D4312yes—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—861no—
361C2×C22⋊C4—861no—
362C2×C22⋊C4—861no—
363C2×C22⋊C4—861no—
364C2×C42—861no—
365#107—24no—
366#106—864no—
367#103—24no—
368#102—864no—
369C22⋊C8—21no—
370C22⋊C8—432no—
371C22⋊C8—861no—
372C22⋊C8C22×D4312yes—
373#95—432no—
374#95—864no—
375#95—864no—
376#95—861no—
377C24—861no—
378C24D4×D4311yescharacteristic
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8C2×C22⋊D4312yes—
382C2×D4—432no—
383C2×D4—862no—
384C2×D4—862no—
385C2×D4—861no—
386C2×D4—1722no—
387C2×D4—1722no—
388C2×D4—1722no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—42no—
393C22×C4—44no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—432no—
397C22×C4—432no—
398C22×C4—864no—
399C22×C4—861no—
400C22×C4—861no—
401C22×C4—861no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—862no—
405C22×C4—862no—
406C22×C4—862no—
407C22×C4—3442no—
408C22×C4—1722no—
409C22×C4—1722no—
410C22×C4—1722no—
411C22×C4—1722no—
412C22×C4D4×D4311yescharacteristic
413C22×C4D4×D4311yescharacteristic
414C22×C4D4×D4311yescharacteristic
415C22×C4C2×C22⋊D4311yescharacteristic
416C22×C4C2×C22⋊D4311yescharacteristic
417C22×C4C23×D4311yescharacteristic
418C2×C8—22no—
419C2×C8—42no—
420C2×C8—862no—
421C2×C8—1722no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—432no—
430C4⋊C4—864no—
431C4⋊C4—864no—
432C4⋊C4—864no—
433C4⋊C4—862no—
434C4⋊C4—862no—
435C4⋊C4—861no—
436C4⋊C4—862no—
437C4⋊C4—862no—
438C4⋊C4C2×C22⋊D4312yes—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—864no—
442C22⋊C4—864no—
443C22⋊C4—864no—
444C22⋊C4—862no—
445C22⋊C4—862no—
446C42—864no—
447C23—22no—
448C23—22no—
449C23—862no—
450C23—1722no—
451C23—1722no—
452C23—1722no—
453C23#1306329311yescharacteristic
454C23#1306329311yescharacteristic
455C23#1306334812yes—
456C23#1306335712yes—
457C23C2×D4×D4311yescharacteristic
458Q8—42no—
459Q8—81no—
460D4—3441no—
461D4—1722no—
462D4—1724no—
463D4—1722no—
464D4—1722no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—862no—
480C2×C4—862no—
481C2×C4—862no—
482C2×C4—862no—
483C2×C4—862no—
484C2×C4—3444no—
485C2×C4—3444no—
486C2×C4—3441no—
487C2×C4—1722no—
488C2×C4—1722no—
489C2×C4—1722no—
490C2×C4—1722no—
491C2×C4—1722no—
492C2×C4—1722no—
493C2×C4—1722no—
494C2×C4—1722no—
495C2×C4#1306329311yescharacteristic
496C2×C4#1306329311yescharacteristic
497C2×C4C2×D4×D4311yescharacteristic
498C2×C4C22×C22⋊D4311yescharacteristic
499C8—42no—
500C8—1722no—
501C22—21no—
502C22—21no—
503C22—24no—
504C22—24no—
505C22—21no—
506C22—21no—
507C22—3444no—
508C22—1722no—
509C22—1722no—
510C22—1722no—
511C22#1458306012yes—
512C22#1458306012yes—
513C22#1458307012yes—
514C22#1458308812yes—
515C22C2×#1306329311yescharacteristic
516C22C2×#1306334811yescharacteristic
517C22C2×#1306335711yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—82no—
525C4—3442no—
526C4—1722no—
527C4—1722no—
528C4—1722no—
529C2—21no—
530C2—22no—
531C2—21no—
532C2—3442no—
533C2#1913362514yesdirect product factor
534C2C2×#1458306011yescharacteristic
535C2C2×#1458307011yescharacteristic
536C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#484C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenterC2×#484D43
hypocenterC43C2×#1615
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. C2×#14582837C2semidirect
4. #19133625C2direct (N × H)
5. C2×#14582636C2semidirect
7. C2×#14582624C2semidirect
8. C2×C43×#484C2semidirect
27. #14582837C22semidirect
31. #14582636C22semidirect
33. #14582624C22semidirect
37. C43×#484C22semidirect
262. C2×#484D43semidirect
272. C2×C43#1615semidirect
292. #484C2×D43semidirect
309. C43C2×#1615semidirect
533. C2#19133625direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834982
C2×#145832172
C2×#145828372
#191336252
C2×#145826362
C2×#145826342
C2×#145826242
C2×C43×#4842
C2×#161543