Finite Group Databasebeta

← C2×#19147522 #25977105

Subgroups — C2×#19147522 #25977105

Order 11008.

1778 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583629C211yesmaximal, characteristic
2C2×#14583625C211yesmaximal, characteristic
3#19147522C2116yesmaximal, direct product factor
4C2×#14583306C211yesmaximal, characteristic
5C2×#14583305C211yesmaximal, characteristic
6C2×#14583296C211yesmaximal, characteristic
7C2×#14583209C211yesmaximal, characteristic
8C2×#14583207C211yesmaximal, characteristic
9C2×#14583192C211yesmaximal, characteristic
10C2×#14583183C211yesmaximal, characteristic
11C2×#14583182C211yesmaximal, characteristic
12C2×#14583028C211yesmaximal, characteristic
13C2×#14583004C211yesmaximal, characteristic
14C2×#14583003C211yesmaximal, characteristic
15C2×#14582991C211yesmaximal, characteristic
16C2×C43×#475C211yesmaximal, characteristic
17C22×#10621885C2211yescharacteristic
18#14583629—24no—
19#14583629C2218yes—
20#14583625—24no—
21#14583625C2218yes—
22C2×#13063324—21no—
23C2×#13063324—21no—
24C2×#13063324C2211yescharacteristic
25C2×#13063324C2211yescharacteristic
26C2×#13063324C2211yescharacteristic
27C2×#13063323—21no—
28C2×#13063323—21no—
29C2×#13063317—21no—
30C2×#13063317C2211yescharacteristic
31C2×#13063316—21no—
32C2×#13063316C2211yescharacteristic
33C2×Q8×Dic43C2211yescharacteristic
34C2×Q8×Dic43C2211yescharacteristic
35C2×C4×Dic86—21no—
36C2×C4×Dic86C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38C2×#13063290—21no—
39C2×#13063290C2211yescharacteristic
40C2×#13063290C2211yescharacteristic
41#14583306C2218yes—
42#14583305C2218yes—
43#14583296C2218yes—
44#14583209C2218yes—
45#14583207C2218yes—
46#14583192C2218yes—
47#14583183C2218yes—
48#14583182C2218yes—
49#14583028C2218yes—
50#14583004C2218yes—
51#14583003C2218yes—
52#14582991C2218yes—
53C2×#13063259C2211yescharacteristic
54C2×#13063258C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#475C2218yes—
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×Dic86—21no—
80C22×Dic86D411yescharacteristic
81C22×Dic86C2311yescharacteristic
82C2×#10621885Q818yescomplemented
83C2×#10621885C2314yes—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86#13063324—28no—
87#13063324—28no—
88#13063324—22no—
89#13063324—22no—
90#13063324—22no—
91#13063324C2314yes—
92#13063324C2314yes—
93#13063324C2314yes—
94#13063323—28no—
95#13063323—28no—
96#13063317—22no—
97#13063317—28no—
98#13063317C2314yes—
99#13063316—28no—
100#13063316—22no—
101#13063316C2314yes—
102Q8×Dic43—22no—
103Q8×Dic43—22no—
104Q8×Dic43C2314yes—
105Q8×Dic43C2314yes—
106C4×Dic86—22no—
107C4×Dic86—28no—
108C4×Dic86D414yes—
109C4×Dic86C2314yes—
110C4×Dic86C2314yes—
111#13063290—28no—
112#13063290—22no—
113#13063290—22no—
114#13063290C2314yes—
115#13063290C2314yes—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43D411yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4D411yescharacteristic
133C2×Dic43⋊C4D411yescharacteristic
134C2×C4×Dic43—21no—
135C2×C4×Dic43—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43C2311yescharacteristic
140C2×C4×Dic43C2311yescharacteristic
141#13063259C2314yes—
142#13063258C2314yes—
143#13063258C2314yes—
144#13063257C2314yes—
145#13063256C2314yes—
146#13063256C2314yes—
147#13063256C2314yes—
148Dic43⋊C8C2314yes—
149Dic43⋊C8C2314yes—
150#13063250C2314yes—
151#13063250C2314yes—
152#13063249C2314yes—
153#13063248C2314yes—
154#13063236C2314yes—
155#13063235C2314yes—
156C8×Dic43C2314yes—
157C22×Q8×C43—21no—
158C22×Q8×C43C2311yescharacteristic
159C22×C8×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161C4⋊Q8×C43—22no—
162C4⋊Q8×C43C2314yes—
163C4×Q8×C43—22no—
164C4×Q8×C43C2314yes—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43C2311yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C42×C43—21no—
171C2×C42×C43C2311yescharacteristic
172#106×C43C2314yes—
173#106×C43C2314yes—
174C4⋊C8×C43C2314yes—
175#103×C43C2314yes—
176#103×C43C2314yes—
177C2×Q8×C43—21no—
178C2×Q8×C43—24no—
179C2×Q8×C43—22no—
180C2×Q8×C43—82no—
181C2×Q8×C43C2×Q814yes—
182C2×Q8×C43C2412yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C2×Dic86—21no—
199C2×Dic86—22no—
200C2×Dic86—24no—
201C2×Dic86—24no—
202C2×Dic86—24no—
203C2×Dic86—24no—
204C2×Dic86—44no—
205C2×Dic86—82no—
206C2×Dic86—82no—
207C2×Dic86C2×D414yes—
208C2×Dic86C2×Q814yes—
209C2×Dic86C2412yes—
210C2×C8×C43—22no—
211C2×C8×C43—22no—
212C2×C8×C43C2412yes—
213C2×C8×C43C2412yes—
214C4⋊C4×C43—24no—
215C4⋊C4×C43—24no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43C2412yes—
220C4⋊C4×C43C2412yes—
221C4⋊C4×C43C2412yes—
222C42×C43—24no—
223C42×C43C2×D412yes—
224C42×C43C2412yes—
225#10621885C2×Q8116yescomplemented
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—24no—
230C4⋊Dic43—24no—
231C4⋊Dic43—24no—
232C4⋊Dic43C2×D414yes—
233C4⋊Dic43C2412yes—
234C4⋊Dic43C2412yes—
235C4⋊Dic43C2412yes—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—24no—
242Dic43⋊C4—24no—
243Dic43⋊C4—24no—
244Dic43⋊C4—24no—
245Dic43⋊C4C2×D414yes—
246Dic43⋊C4C2×D414yes—
247C4×Dic43—24no—
248C4×Dic43—24no—
249C4×Dic43—24no—
250C4×Dic43—24no—
251C4×Dic43—24no—
252C4×Dic43C2×D412yes—
253C4×Dic43C2×D412yes—
254C4×Dic43C2412yes—
255C4×Dic43C2412yes—
256C2×C43⋊C8—22no—
257C2×C43⋊C8C2×Q814yes—
258C2×C43⋊C8C2412yes—
259C2×C43⋊C8C2412yes—
260C23×C43C22×D411yescharacteristic
261Q8×C43—24no—
262Q8×C43—22no—
263Q8×C43—84no—
264Q8×C43C22×Q814yes—
265C2×C4×C43—24no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43C22×D412yes—
276C2×C4×C43C22×D412yes—
277C2×C4×C43C22×D411yescharacteristic
278C2×C4×C43C22×Q812yes—
279C2×C4×C432−1+412yes—
280C2×C4×C43C2511yescharacteristic
281C2×Dic43—24no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—42no—
290C2×Dic43—42no—
291C2×Dic43—42no—
292C2×Dic43#13714yes—
293C2×Dic43C22×D412yes—
294C2×Dic43C22×D412yes—
295C2×Dic43C22×D412yes—
296C2×Dic43C22×D412yes—
297Dic86—24no—
298Dic86—22no—
299Dic86—28no—
300Dic86—48no—
301Dic86—84no—
302Dic86—84no—
303Dic86C22×Q814yes—
304C8×C43—22no—
305C8×C43—22no—
306C43⋊C8—22no—
307C43⋊C8C22×Q814yes—
308C2×#3387—431nomaximal, Sylow
309C22×C43D4×Q812yes—
310C22×C43C2×#13712yes—
311C22×C43#57712yes—
312C22×C43C23×D411yescharacteristic
313C4×C43—24no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—42no—
317C4×C43—42no—
318C4×C43—42no—
319C4×C43D4×Q812yes—
320C4×C43C23×Q811yescharacteristic
321C4×C43C2×2−1+411yescharacteristic
322Dic43—24no—
323Dic43—22no—
324Dic43—22no—
325Dic43—22no—
326Dic43—42no—
327Dic43—42no—
328Dic43—42no—
329Dic43C2×#13714yes—
330C2×Q82—431no—
331C2×#557—431no—
332#3387—4316no—
333C2×#501—431no—
334C2×#501—431no—
335C2×#498—431no—
336C2×#479—431no—
337C2×#479—431no—
338C2×#477—431no—
339C2×#475—431no—
340C2×#475—431no—
341C2×#475D4311yescharacteristic
342C2×#446—431no—
343C2×#441—431no—
344C2×#441—431no—
345C2×C4×Q16—431no—
346C2×C43#338714yescomplemented
347C2×C43C2×D4×Q811yescharacteristic
348C2×C43C22×#13711yescharacteristic
349C2×C43C2×#57711yescharacteristic
350C22×Q16—431no—
351Q82—438no—
352Q82—864no—
353#557—438no—
354#557—864no—
355C2×C4⋊Q8—431no—
356C2×C4⋊Q8—431no—
357C2×C4⋊Q8—431no—
358C2×C4⋊Q8—861no—
359C2×C4⋊Q8—861no—
360C2×C4⋊Q8—861no—
361C2×C4⋊Q8—861no—
362C2×C4⋊Q8C2×D4311yescharacteristic
363C2×#125—431no—
364C2×#125—431no—
365C2×#125—861no—
366C2×#125—861no—
367C2×C4×Q8—431no—
368C2×C4×Q8—431no—
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×C4×Q8—431no—
372C2×C4×Q8—431no—
373C2×C4×Q8—861no—
374C2×C4×Q8—861no—
375C2×C4×Q8C2×D4311yescharacteristic
376#501—438no—
377#501—438no—
378#498—438no—
379#479—438no—
380#479—438no—
381#477—438no—
382#475—438no—
383#475—438no—
384#475C2×D4318yes—
385#446—438no—
386#441—438no—
387#441—438no—
388C4×Q16—438no—
389C2×#107—431no—
390C2×#107—431no—
391C2×#107—431no—
392C2×#106—431no—
393C2×#106—431no—
394C2×#106—431no—
395C2×#106—431no—
396C2×#106C2×D4311yescharacteristic
397C2×#106C2×D4311yescharacteristic
398C2×C4⋊C8—431no—
399C2×C4⋊C8—431no—
400C2×C4⋊C8C2×D4311yescharacteristic
401C2×#103—431no—
402C2×#103—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#103C2×D4311yescharacteristic
406C2×#103C2×D4311yescharacteristic
407C2×#97—431no—
408C2×#97—431no—
409C2×C4×C8—431no—
410C43C2×#338711yescharacteristic, complemented, Sylow
411C22×Q8—21no—
412C22×Q8—431no—
413C22×Q8—431no—
414C22×Q8—861no—
415C22×Q8—861no—
416C22×Q8—861no—
417C22×Q8C22×D4311yescharacteristic
418C2×Q16—438no—
419C2×Q16—434no—
420C22×C8—431no—
421C22×C8—431no—
422C22×C8C22×D4311yescharacteristic
423C22×C8C22×D4311yescharacteristic
424C4⋊Q8—22no—
425C4⋊Q8—434no—
426C4⋊Q8—434no—
427C4⋊Q8—434no—
428C4⋊Q8—862no—
429C4⋊Q8—862no—
430C4⋊Q8—862no—
431C4⋊Q8—868no—
432C4⋊Q8—868no—
433C4⋊Q8—868no—
434C4⋊Q8—868no—
435C4⋊Q8C22×D4314yes—
436#125—434no—
437#125—434no—
438#125—868no—
439#125—862no—
440#125—868no—
441#125—862no—
442C4×Q8—22no—
443C4×Q8—434no—
444C4×Q8—434no—
445C4×Q8—434no—
446C4×Q8—434no—
447C4×Q8—434no—
448C4×Q8—434no—
449C4×Q8—434no—
450C4×Q8—868no—
451C4×Q8—862no—
452C4×Q8—862no—
453C4×Q8—862no—
454C4×Q8—862no—
455C4×Q8—868no—
456C4×Q8—862no—
457C4×Q8C22×D4314yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C42—21no—
482C2×C42—431no—
483C2×C42—431no—
484C2×C42—861no—
485C2×C42—861no—
486C2×C42—861no—
487C2×C42—861no—
488C2×C42—861no—
489C2×C42C22×D4311yescharacteristic
490#107—434no—
491#107—434no—
492#107—434no—
493#106—434no—
494#106—434no—
495#106—434no—
496#106—434no—
497#106C22×D4314yes—
498#106C22×D4314yes—
499C4⋊C8—434no—
500C4⋊C8—434no—
501C4⋊C8C22×D4314yes—
502#103—434no—
503#103—434no—
504#103—434no—
505#103—434no—
506#103C22×D4314yes—
507#103C22×D4314yes—
508#97—434no—
509#97—434no—
510C4×C8—434no—
511C2×Q8—21no—
512C2×Q8—24no—
513C2×Q8—22no—
514C2×Q8—82no—
515C2×Q8—434no—
516C2×Q8—434no—
517C2×Q8—432no—
518C2×Q8—864no—
519C2×Q8—864no—
520C2×Q8—864no—
521C2×Q8—864no—
522C2×Q8—861no—
523C2×Q8—862no—
524C2×Q8—3442no—
525C2×Q8—3442no—
526C2×Q8—1724no—
527C2×Q8Q8×D4314yes—
528C2×Q8C23×D4312yes—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—431no—
534C22×C4—431no—
535C22×C4—431no—
536C22×C4—431no—
537C22×C4—861no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4D4×D4311yescharacteristic
542C22×C4D4×D4311yescharacteristic
543C22×C4C23×D4311yescharacteristic
544Q16—4316no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—434no—
548C2×C8—432no—
549C2×C8—432no—
550C2×C8—862no—
551C2×C8C23×D4312yes—
552C2×C8C23×D4312yes—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—434no—
559C4⋊C4—434no—
560C4⋊C4—434no—
561C4⋊C4—432no—
562C4⋊C4—432no—
563C4⋊C4—432no—
564C4⋊C4—864no—
565C4⋊C4—864no—
566C4⋊C4—864no—
567C4⋊C4—864no—
568C4⋊C4—864no—
569C4⋊C4—864no—
570C4⋊C4—864no—
571C4⋊C4—864no—
572C4⋊C4—864no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—864no—
577C4⋊C4—864no—
578C4⋊C4—864no—
579C4⋊C4C23×D4312yes—
580C4⋊C4C23×D4312yes—
581C4⋊C4C23×D4312yes—
582C42—24no—
583C42—432no—
584C42—432no—
585C42—432no—
586C42—432no—
587C42—864no—
588C42—864no—
589C42—864no—
590C42—864no—
591C42—864no—
592C42D4×D4312yes—
593C42C23×D4312yes—
594C23C2×D4×D4311yescharacteristic
595Q8—24no—
596Q8—22no—
597Q8—84no—
598Q8—434no—
599Q8—868no—
600Q8—864no—
601Q8—862no—
602Q8—3444no—
603Q8—3444no—
604Q8—1728no—
605Q8C2×Q8×D4314yes—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—434no—
617C2×C4—432no—
618C2×C4—432no—
619C2×C4—432no—
620C2×C4—432no—
621C2×C4—864no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1722no—
632C2×C4C2×D4×D4312yes—
633C2×C4C2×D4×D4312yes—
634C2×C4C2×D4×D4311yescharacteristic
635C2×C4C2×Q8×D4312yes—
636C2×C4#1306337212yes—
637C2×C4C24×D4311yescharacteristic
638C8—22no—
639C8—22no—
640C8—434no—
641C8—862no—
642C22#1458356212yes—
643C22#137×D4312yes—
644C22#1458370512yes—
645C22C22×D4×D4311yescharacteristic
646C4—22no—
647C4—24no—
648C4—22no—
649C4—42no—
650C4—42no—
651C4—42no—
652C4—434no—
653C4—862no—
654C4—864no—
655C4—862no—
656C4—862no—
657C4—1722no—
658C4—1722no—
659C4—1722no—
660C4#1458356212yes—
661C4C22×Q8×D4311yescharacteristic
662C4C2×#1306337211yescharacteristic
663C2#1914752214yesdirect product factor
664C2C2×#1458356211yescharacteristic
665C2C2×#137×D4311yescharacteristic
666C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#475C2
socle, prime radicalC23×C43C22×D4
hypercenterC2×#475D43
hypocenterC43C2×#3387
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #19147522C2direct (N × H)
82. C2×#10621885Q8semidirect
225. #10621885C2×Q8semidirect
346. C2×C43#3387semidirect
410. C43C2×#3387semidirect
663. C2#19147522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836292
C2×#145836252
#191475222
C2×#145833062
C2×#145833052
C2×#145832962
C2×#145832092
C2×#145832072
C2×#145831922
C2×#145831832
C2×#145831822
C2×#145830282
C2×#145830042
C2×#145830032
C2×#145829912
C2×C43×#4752
C2×#338743