Finite Group Databasebeta

← C2×#19133627 #25068746

Subgroups — C2×#19133627 #25068746

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×#14583494C211yesmaximal, characteristic
2C2×#14583235C211yesmaximal, characteristic, complemented
3C2×#14583215C211yesmaximal, characteristic
4C2×#14582839C211yesmaximal, characteristic, complemented
5#19133627C218yesmaximal, direct product factor
6C2×#14582635C211yesmaximal, characteristic, complemented
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#327C211yesmaximal, characteristic
9#14583494—22no—
10#14583494—22no—
11#14583494—22no—
12#14583494C2214yes—
13C2×#13063318—21no—
14C2×#13063315—21no—
15C2×#13063306—21no—
16C2×#13063306—21no—
17C2×#13063304C2211yescharacteristic
18C2×#13063302—21no—
19C2×D4×Dic43—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22#14583235—22no—
23#14583235C2214yescomplemented
24#14583215—22no—
25#14583215C2214yes—
26C2×#13063259—21no—
27C2×#13063256—21no—
28C2×#13063250—21no—
29C2×#13063246—21no—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582839—22no—
32#14582839C2214yescomplemented
33C2×C43⋊#95—21no—
34C2×C43⋊#95—21no—
35#14582635C2214yescomplemented
36#14582624C2214yescomplemented
37C2×#121×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C43×#327C2214yes—
41C22×Dic86D411yescharacteristic
42C23×Dic43—21no—
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C23×Dic43D411yescharacteristic
46C22×C43⋊C8—21no—
47#13063318—24no—
48#13063318—24no—
49#13063315—24no—
50#13063315—24no—
51#13063306—24no—
52#13063306—24no—
53#13063306—24no—
54#13063306—24no—
55#13063304—21no—
56#13063304—21no—
57#13063304D412yes—
58#13063304C2312yes—
59#13063302—24no—
60#13063302—24no—
61D4×Dic43—24no—
62D4×Dic43—24no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2312yes—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4D412yes—
79C2×Dic43⋊C4C2312yes—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85#13063259—24no—
86#13063256—24no—
87#13063250—24no—
88#13063246—24no—
89C22⋊(C43⋊C8)—21no—
90C22⋊(C43⋊C8)C2312yes—
91C43⋊#95—24no—
92C43⋊#95—24no—
93C22×D4×C43—21no—
94C22×D4×C43D411yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43C2311yescharacteristic
97C22×C8×C43—21no—
98#121×C43—21no—
99#121×C43—21no—
100#121×C43D412yes—
101#121×C43C2312yes—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C22⋊C4×C43—21no—
104C22⋊C8×C43—21no—
105C22⋊C8×C43C2312yes—
106#95×C43—21no—
107#95×C43C2312yes—
108C24×C43—21no—
109C24×C43C2×D411yescharacteristic
110C2×D4×C43—21no—
111C2×D4×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—42no—
114C2×D4×C43—42no—
115C2×D4×C43—42no—
116C2×D4×C43C2×D412yes—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—24no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—42no—
140C22×Dic43—44no—
141C22×Dic43—41no—
142C22×Dic43—41no—
143C22×Dic43—82no—
144C22×Dic43C2×D412yes—
145C22×Dic43C2×D412yes—
146C2×Dic86—21no—
147C2×Dic86—42no—
148C2×Dic86C2×D412yes—
149C2×C8×C43—22no—
150C2×C8×C43—42no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43C2×D412yes—
153C22⋊C4×C43—22no—
154C22⋊C4×C43—22no—
155C22⋊Dic43—24no—
156C22⋊Dic43—24no—
157C22⋊Dic43—24no—
158C22⋊Dic43—22no—
159C22⋊Dic43—22no—
160C4⋊Dic43—24no—
161C4⋊Dic43—21no—
162C4⋊Dic43—22no—
163C4⋊Dic43—22no—
164C4⋊Dic43—41no—
165C4⋊Dic43—41no—
166C4⋊Dic43C2×D412yes—
167Dic43⋊C4—24no—
168Dic43⋊C4—24no—
169Dic43⋊C4—22no—
170Dic43⋊C4—22no—
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—22no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43#12011yescharacteristic
185C23×C43#12011yescharacteristic
186C23×C43#13512yes—
187C23×C43#13712yes—
188C23×C43C22×D411yescharacteristic
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—42no—
192D4×C43—44no—
193D4×C43—81no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—84no—
206C2×C4×C43#12011yescharacteristic
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C22×D411yescharacteristic
210C2×Dic43—22no—
211C2×Dic43—22no—
212C2×Dic43—22no—
213C2×Dic43—22no—
214C2×Dic43—22no—
215C2×Dic43—22no—
216C2×Dic43—42no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—42no—
220C2×Dic43—42no—
221C2×Dic43—42no—
222C2×Dic43—44no—
223C2×Dic43—42no—
224C2×Dic43—81no—
225C2×Dic43—84no—
226C2×Dic43—82no—
227C2×Dic43—82no—
228Dic86—42no—
229Dic86—81no—
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—42no—
240C22×C43—42no—
241C22×C43—42no—
242C22×C43—84no—
243C22×C43#45212yes—
244C22×C43#45212yes—
245C22×C43#45412yes—
246C22×C43#45812yes—
247C22×C43C2×#12011yescharacteristic
248C22×C43C2×#13511yescharacteristic
249C22×C43C2×#13711yescharacteristic
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—42no—
255C4×C43—82no—
256Dic43—42no—
257Dic43—42no—
258Dic43—42no—
259Dic43—42no—
260Dic43—82no—
261C2×#539—431no—
262C2×#484—431no—
263C2×#481—431no—
264C2×#400—431no—
265#1615—438no—
266C2×#328—431no—
267C2×#327D4311yescharacteristic
268C2×#324—431no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43—22no—
272C2×C43—82no—
273C2×C43#161514yescomplemented
274C2×C43C2×#45211yescharacteristic
275C2×C43C2×#45411yescharacteristic
276C2×C43C2×#45811yescharacteristic
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—431no—
286C2×C22⋊Q8—861no—
287C2×#121C2×D4311yescharacteristic
288C2×C4×D4—861no—
289C22×C4⋊C4—431no—
290C22×C4⋊C4—431no—
291#484—434no—
292#484—862no—
293#481—434no—
294#481—862no—
295C2×#107—861no—
296C2×#106—861no—
297C2×#103—861no—
298C2×#102—861no—
299C2×C22⋊C8—431no—
300C2×C22⋊C8C2×D4311yescharacteristic
301#400—434no—
302#400—862no—
303C2×#95—861no—
304C2×#95—861no—
305C2×#95C2×D4311yescharacteristic
306#328—434no—
307#327C2×D4314yes—
308#324—434no—
309C43C2×#161511yescharacteristic, complemented, Sylow
310C22×Q8—431no—
311C22×D4—21no—
312C22×D4D17211yescharacteristic
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—432no—
330C22⋊Q8—432no—
331C22⋊Q8—864no—
332C22⋊Q8—864no—
333C22⋊Q8—861no—
334C22⋊Q8—861no—
335#121—21no—
336#121—21no—
337#121D17212yes—
338#121C22×D4312yes—
339C4×D4—864no—
340C4×D4—864no—
341C2×C4⋊C4—431no—
342C2×C4⋊C4—432no—
343C2×C4⋊C4—432no—
344C2×C4⋊C4—432no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4—861no—
348C2×C4⋊C4—861no—
349C2×C4⋊C4—861no—
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⋊C4—861no—
358C2×C4⋊C4D17211yescharacteristic
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—864no—
366#106—864no—
367#103—864no—
368#102—864no—
369C22⋊C8—21no—
370C22⋊C8—432no—
371C22⋊C8—861no—
372C22⋊C8C22×D4312yes—
373#95—21no—
374#95—864no—
375#95—864no—
376#95C22×D4312yes—
377C24—21no—
378C24D4×D4311yescharacteristic
379C2×Q8—432no—
380C2×Q8—861no—
381C2×Q8—1722no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4C2×D17212yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—432no—
396C22×C4—432no—
397C22×C4—864no—
398C22×C4—861no—
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—1724no—
409C22×C4—1721no—
410C22×C4—1721no—
411C22×C4—1722no—
412C22×C4C2×D17211yescharacteristic
413C22×C4C2×D17211yescharacteristic
414C22×C4D4×D4311yescharacteristic
415C22×C4D4×D4311yescharacteristic
416C22×C4D4×D4311yescharacteristic
417C22×C4C23×D4311yescharacteristic
418C2×C8—22no—
419C2×C8—42no—
420C2×C8—862no—
421C2×C8—1722no—
422C4⋊C4—21no—
423C4⋊C4—432no—
424C4⋊C4—864no—
425C4⋊C4—864no—
426C4⋊C4—864no—
427C4⋊C4—862no—
428C4⋊C4—862no—
429C4⋊C4—861no—
430C4⋊C4—862no—
431C4⋊C4—862no—
432C4⋊C4—862no—
433C4⋊C4—862no—
434C4⋊C4—862no—
435C4⋊C4—862no—
436C4⋊C4—1721no—
437C4⋊C4—1721no—
438C4⋊C4C2×D17212yes—
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—22no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23#1306329511yescharacteristic
454C23#1306329511yescharacteristic
455C23#1306334412yes—
456C23#1306335412yes—
457C23C2×D4×D4311yescharacteristic
458Q8—3441no—
459Q8—1722no—
460D4—42no—
461D4—44no—
462D4—42no—
463D4—42no—
464D4—81no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—84no—
477C2×C4—862no—
478C2×C4—862no—
479C2×C4—862no—
480C2×C4—862no—
481C2×C4—862no—
482C2×C4—862no—
483C2×C4—3442no—
484C2×C4—3442no—
485C2×C4—3441no—
486C2×C4—3444no—
487C2×C4—1724no—
488C2×C4—1722no—
489C2×C4—1722no—
490C2×C4—1722no—
491C2×C4—1722no—
492C2×C4—1722no—
493C2×C4—1722no—
494C2×C4—1722no—
495C2×C4#1306329511yescharacteristic
496C2×C4#1306329511yescharacteristic
497C2×C4C2×D4×D4311yescharacteristic
498C2×C4C22×D17211yescharacteristic
499C8—42no—
500C8—1722no—
501C22—21no—
502C22—21no—
503C22—24no—
504C22—24no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—84no—
511C22#1458306212yes—
512C22#1458306212yes—
513C22#1458307312yes—
514C22#1458309012yes—
515C22C2×#1306329511yescharacteristic
516C22C2×#1306334411yescharacteristic
517C22C2×#1306335411yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—82no—
524C4—3442no—
525C4—1722no—
526C4—1722no—
527C4—1722no—
528C4—1722no—
529C2—21no—
530C2—22no—
531C2—21no—
532C2—82no—
533C2#1913362714yesdirect product factor
534C2C2×#1458306211yescharacteristic
535C2C2×#1458307311yescharacteristic
536C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#327C2
socleC23×C43#120
prime radicalC2×#121×C43C22
hypercenterC2×#327D43
hypocenterC43C2×#1615
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#14583235C2semidirect
4. C2×#14582839C2semidirect
5. #19133627C2direct (N × H)
6. C2×#14582635C2semidirect
7. C2×#14582624C2semidirect
23. #14583235C22semidirect
32. #14582839C22semidirect
35. #14582635C22semidirect
36. #14582624C22semidirect
273. C2×C43#1615semidirect
309. C43C2×#1615semidirect
533. C2#19133627direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834942
C2×#145832352
C2×#145832152
C2×#145828392
#191336272
C2×#145826352
C2×#145826242
C2×C43×#3272
C2×#161543