Finite Group Databasebeta

← #25063041

Subgroups — #25063041

Order 11008.

1214 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×C4×Q8×D43C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic
3#19143223C211yesmaximal, characteristic
4#19133040C214yesmaximal, complemented
5#19133022C214yesmaximal, complemented
6#19132991C211yesmaximal, characteristic, complemented
7#19132990C211yesmaximal, characteristic, complemented
8#19132989C211yesmaximal, characteristic, complemented
9C43×#1479C211yesmaximal, characteristic, complemented
10C22×Q8×D43C411yescharacteristic
11C2×Q8×Dic43C411yescharacteristic
12C2×C4×Dic86—21no—
13C2×C4×Dic86C2211yescharacteristic
14C2×#13063290—21no—
15C2×#13063290C411yescharacteristic
16C4×Q8×D43—21no—
17C4×Q8×D43—21no—
18C4×Q8×D43—21no—
19C4×Q8×D43—21no—
20C4×Q8×D43C412yes—
21C4×Q8×D43C412yes—
22C4×Q8×D43C2212yes—
23C4×Q8×D43C2212yes—
24C2×C4⋊C4×D43—21no—
25C2×C4⋊C4×D43C411yescharacteristic
26C2×C42×D43—21no—
27C2×C42×D43C2211yescharacteristic
28#14582955—21no—
29#14582955C2212yes—
30#14582953—21no—
31#14582953—21no—
32#14582952C2211yescharacteristic
33#14582952C2211yescharacteristic
34#14582950—21no—
35#14582950C2212yes—
36#14582921—21no—
37#14582921C2212yes—
38#14582861—21no—
39#14582861—21no—
40C4×#10621872—21no—
41C4×#10621872C2212yes—
42#14582631C2214yescomplemented
43Q8⋊(C43⋊C8)C2214yescomplemented
44#14582629C2214yescomplemented
45C2×C4×Q8×C43C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#431C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C22×Dic86—21no—
50C22×Dic86C2×C411yescharacteristic
51C2×Q8×D43—24no—
52C2×Q8×D43—21no—
53C2×Q8×D43—21no—
54C2×Q8×D43—24no—
55C2×Q8×D43C2×C412yes—
56C2×Q8×D43C2×C412yes—
57C22×C4×D43—21no—
58C22×C4×D43—21no—
59C22×C4×D43C2×C411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C2×#10621872—22no—
63C2×#10621872—22no—
64Q8×Dic43—21no—
65Q8×Dic43—21no—
66Q8×Dic43C2×C412yes—
67Q8×Dic43C2×C412yes—
68C4×Dic86—21no—
69C4×Dic86—21no—
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×Dic86—22no—
73C4×Dic86—22no—
74C4×Dic86C2×C412yes—
75C4×Dic86C2312yes—
76#13063290—21no—
77#13063290—21no—
78#13063290—22no—
79#13063290—22no—
80#13063290—22no—
81#13063290—22no—
82#13063290C2×C412yes—
83#13063290C2×C412yes—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2×C411yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43—22no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43—22no—
95C4⋊C4×D43C2×C412yes—
96C4⋊C4×D43C2×C412yes—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2×C411yescharacteristic
101C2×C4×Dic43D411yescharacteristic
102C2×C4×Dic43D411yescharacteristic
103C42×D43—22no—
104C42×D43—22no—
105C42×D43—22no—
106C42×D43—22no—
107C42×D43C2×C411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43C2311yescharacteristic
114C42×D43C2311yescharacteristic
115C4⋊(C43⋊C8)—21no—
116C4⋊(C43⋊C8)C2312yes—
117Dic43⋊C8—22no—
118Dic43⋊C8—22no—
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123#13063235—22no—
124#13063235—22no—
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2312yes—
127C22×Q8×C43C2×C411yescharacteristic
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2×C412yes—
131C4×Q8×C43C2312yes—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2312yes—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2312yes—
142C23×D43C22⋊C411yescharacteristic
143C2×Q8×C43—21no—
144C2×Q8×C43—22no—
145C2×Q8×C43M1614yescomplemented
146C2×Q8×C43C22×C412yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C22⋊C411yescharacteristic
155C22×Dic43C22⋊C411yescharacteristic
156C22×Dic43C22⋊C411yescharacteristic
157Q8×D43—28no—
158Q8×D43—28no—
159Q8×D43—24no—
160Q8×D43—24no—
161Q8×D43—24no—
162Q8×D43—24no—
163C2×C4×D43—28no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—24no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—42no—
172C2×C4×D43—44no—
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22⋊C411yescharacteristic
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22⋊C411yescharacteristic
179C2×C4×D43C22×C411yescharacteristic
180C2×C4×D43C22×C411yescharacteristic
181C2×C4×D43C2×D411yescharacteristic
182C2×C4×D43C2×D411yescharacteristic
183C2×C4×D43C2×D411yescharacteristic
184C2×C4×D43C2×D411yescharacteristic
185C2×Dic86—28no—
186C2×Dic86—21no—
187C2×Dic86—22no—
188C2×Dic86—22no—
189C2×Dic86—22no—
190C2×Dic86M1614yescomplemented
191C2×Dic86C22×C412yes—
192C2×C8×C43—22no—
193C2×C8×C43—22no—
194C4⋊C4×C43—22no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—22no—
197C4⋊C4×C43C22×C412yes—
198C42×C43—22no—
199C42×C43—22no—
200C42×C43C22×C411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C42×C43C2×D411yescharacteristic
203C42×C43C2411yescharacteristic
204C4⋊Dic43—21no—
205C4⋊Dic43—22no—
206C4⋊Dic43—22no—
207C4⋊Dic43C22×C412yes—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C22×C411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229C4×Dic43C2×D411yescharacteristic
230C4×Dic43C2×D411yescharacteristic
231C4×Dic43C2×D411yescharacteristic
232C2×C43⋊C8—22no—
233C2×C43⋊C8—22no—
234#10621872—44no—
235#10621872—44no—
236C23×C43C2×C22⋊C411yescharacteristic
237C22×D43—22no—
238C22×D43—22no—
239C22×D43—22no—
240C22×D43C2×C22⋊C411yescharacteristic
241C22×D43C2×C22⋊C411yescharacteristic
242Q8×C43—22no—
243Q8×C43—24no—
244Q8×C43C2×M1614yes—
245C2×C4×C43—22no—
246C2×C4×C43—24no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C2×M1612yes—
255C2×C4×C43C2×M1612yes—
256C2×C4×C43C23×C411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—24no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—42no—
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C4×D43—28no—
273C4×D43—28no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—21no—
278C4×D43—21no—
279C4×D43—21no—
280C4×D43—21no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—41no—
286C4×D43—41no—
287C4×D43—44no—
288C4×D43—44no—
289C4×D43#13714yes—
290Dic86—28no—
291Dic86—28no—
292Dic86—22no—
293Dic86—24no—
294Dic86C2×M1614yes—
295C8×C43—42no—
296C8×C43—42no—
297C43⋊C8—42no—
298C43⋊C8—42no—
299#17449—431nomaximal, Sylow
300C22×C43—21no—
301C22×C43—21no—
302C22×C43#40712yes—
303C22×C43C22×C22⋊C411yescharacteristic
304C2×D43—28no—
305C2×D43—21no—
306C2×D43—21no—
307C2×D43—21no—
308C2×D43—21no—
309C2×D43#41912yes—
310C2×D43#42112yes—
311C4×C43—24no—
312C4×C43—21no—
313C4×C43—21no—
314C4×C43—21no—
315C4×C43—42no—
316C4×C43#40712yes—
317C4×C43C22×M1611yescharacteristic
318C4×C43C22×M1611yescharacteristic
319C4×C43C2×#13712yes—
320Dic43—21no—
321Dic43—21no—
322Dic43—24no—
323Dic43—21no—
324Dic43—21no—
325Dic43—21no—
326Dic43—42no—
327Dic43#41912yes—
328C22×C4×Q8—431no—
329#2920—431no—
330#2920—431no—
331#1491—434no—
332#1487—434no—
333#1479—431no—
334#1479—431no—
335#1479—431no—
336#1479D4311yescharacteristic, complemented
337C2×C43—22no—
338C2×C43C2×#40711yescharacteristic
339C2×C43C2×#41911yescharacteristic
340C2×C43C2×#42111yescharacteristic
341D43—22no—
342D43—22no—
343C23×Q8—431no—
344C2×C4×Q8—431no—
345C2×C4×Q8—432no—
346C2×C4×Q8—432no—
347C2×C4×Q8—432no—
348C2×C4×Q8—432no—
349C2×C4×Q8—431no—
350C2×C4×Q8—431no—
351C2×C4×Q8—861no—
352C2×C4×Q8—861no—
353C2×C4×Q8—861no—
354C2×C4×Q8—861no—
355C2×C4×Q8—861no—
356C2×C4×Q8—861no—
357C2×C4×Q8C2×D4311yescharacteristic
358C22×C4⋊C4—431no—
359C22×C4⋊C4—861no—
360C22×C42—431no—
361C22×C42—861no—
362#432—432no—
363#432—861no—
364#432—861no—
365#432—861no—
366#431—431no—
367#431—432no—
368#431—431no—
369#431—861no—
370#431C2×D4311yescharacteristic
371#431C2×D4311yescharacteristic
372#423—432no—
373#423—861no—
374#407—861no—
375#407—861no—
376C4×M16—432no—
377C4×M16—861no—
378Q8⋊C8—434no—
379Q8⋊C8—434no—
380Q8⋊C8—434no—
381Q8⋊C8C2×D4314yescomplemented
382C43#1744911yescharacteristic, complemented, Sylow
383C22×Q8—432no—
384C22×Q8—432no—
385C22×Q8—431no—
386C22×Q8—861no—
387C22×Q8—861no—
388C22×Q8—861no—
389C22×Q8—864no—
390C22×Q8—864no—
391C22×Q8C4×D4311yescharacteristic
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—861no—
396C23×C4—861no—
397C2×M16—862no—
398C2×M16—862no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—432no—
402C4×Q8—432no—
403C4×Q8—432no—
404C4×Q8—432no—
405C4×Q8—432no—
406C4×Q8—432no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×Q8—861no—
418C4×Q8—861no—
419C4×Q8—861no—
420C4×Q8—861no—
421C4×Q8C4×D4312yes—
422C4×Q8C22×D4312yes—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—432no—
426C2×C4⋊C4—432no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—862no—
431C2×C4⋊C4—862no—
432C2×C4⋊C4—862no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4C4×D4311yescharacteristic
438C2×C42—21no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—862no—
451C2×C42—862no—
452C2×C42—862no—
453C2×C42—862no—
454C2×C42—861no—
455C2×C42—861no—
456C2×C42—861no—
457C2×C42C22×D4311yescharacteristic
458C4⋊C8—21no—
459C4⋊C8—432no—
460C4⋊C8—862no—
461C4⋊C8—862no—
462C4⋊C8—861no—
463C4⋊C8C22×D4312yes—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8—862no—
467C22⋊C8—862no—
468C22⋊C8—861no—
469C22⋊C8—861no—
470#97—862no—
471#97—862no—
472C4×C8—21no—
473C4×C8—432no—
474C4×C8—861no—
475C4×C8C22×D4312yes—
476C24—431no—
477C2×Q8—21no—
478C2×Q8—22no—
479C2×Q8—434no—
480C2×Q8—432no—
481C2×Q8—862no—
482C2×Q8—862no—
483C2×Q8—868no—
484C2×Q8—864no—
485C2×Q8—864no—
486C2×Q8—868no—
487C2×Q8—868no—
488C2×Q8—864no—
489C2×Q8—864no—
490C2×Q8—861no—
491C2×Q8—862no—
492C2×Q8#1062187214yescomplemented
493C2×Q8C2×C4×D4312yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—864no—
512C22×C4—862no—
513C22×C4—862no—
514C22×C4—868no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—861no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—861no—
521C22×C4—1722no—
522C22×C4—1724no—
523C22×C4C2×C4×D4311yescharacteristic
524C22×C4D4×D4311yescharacteristic
525C22×C4D4×D4311yescharacteristic
526M16—1724no—
527M16—1724no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—862no—
531C2×C8—862no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—22no—
535C4⋊C4—432no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—862no—
539C4⋊C4—862no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—861no—
543C4⋊C4—862no—
544C4⋊C4—862no—
545C4⋊C4C2×C4×D4312yes—
546C42—22no—
547C42—22no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—431no—
556C42—431no—
557C42—431no—
558C42—431no—
559C42—431no—
560C42—862no—
561C42—862no—
562C42—862no—
563C42—862no—
564C42—862no—
565C42—862no—
566C42C2×C4×D4311yescharacteristic
567C42D4×D4311yescharacteristic
568C42D4×D4311yescharacteristic
569C42C23×D4311yescharacteristic
570C23—431no—
571C23—431no—
572C23—862no—
573C23—862no—
574C23—862no—
575C23C22⋊C4×D4311yescharacteristic
576Q8—24no—
577Q8—22no—
578Q8—434no—
579Q8—868no—
580Q8—868no—
581Q8—864no—
582Q8—862no—
583Q8C2×#1062187214yes—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—431no—
591C2×C4—434no—
592C2×C4—431no—
593C2×C4—431no—
594C2×C4—431no—
595C2×C4—431no—
596C2×C4—431no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—868no—
602C2×C4—868no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—864no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1724no—
618C2×C4—1724no—
619C2×C4—1721no—
620C2×C4—1722no—
621C2×C4C22⋊C4×D4311yescharacteristic
622C2×C4C22⋊C4×D4311yescharacteristic
623C2×C4C22⋊C4×D4311yescharacteristic
624C2×C4M16×D4312yes—
625C2×C4C2×#1062187212yes—
626C2×C4C22×C4×D4311yescharacteristic
627C2×C4C2×D4×D4311yescharacteristic
628C2×C4C2×D4×D4311yescharacteristic
629C8—42no—
630C8—42no—
631C8—1722no—
632C8—1722no—
633C22—21no—
634C22—21no—
635C22—432no—
636C22—432no—
637C22—868no—
638C22—861no—
639C22—861no—
640C22—861no—
641C22—861no—
642C22#1458286112yes—
643C22C2×C22⋊C4×D4311yescharacteristic
644C4—24no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—432no—
650C4—861no—
651C4—861no—
652C4—864no—
653C4—861no—
654C4—861no—
655C4—861no—
656C4—1722no—
657C4#1458286112yes—
658C4C2×M16×D4311yescharacteristic
659C4C22×#1062187211yescharacteristic
660C4#137×D4312yes—
661C2—22no—
662C2—862no—
663C2—862no—
664C2C2×#1458286111yescharacteristic
665C2#419×D4311yescharacteristic
666C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1479C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1479D43
hypocenterC43#17449
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. #19133040C2semidirect
5. #19133022C2semidirect
6. #19132991C2semidirect
7. #19132990C2semidirect
8. #19132989C2semidirect
9. C43×#1479C2semidirect
42. #14582631C22semidirect
43. Q8⋊(C43⋊C8)C22semidirect
44. #14582629C22semidirect
48. C43×Q8⋊C8C22semidirect
145. C2×Q8×C43M16semidirect
190. C2×Dic86M16semidirect
336. #1479D43semidirect
381. Q8⋊C8C2×D43semidirect
382. C43#17449semidirect
492. C2×Q8#10621872semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D432
#191432232
#191330402
#191330222
#191329912
#191329902
#191329892
C43×#14792
#1744943