Finite Group Databasebeta

← #25111963

Subgroups — #25111963

Order 11008.

1378 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583562C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic
3#19143327C211yesmaximal, characteristic
4C22×#13063243C211yesmaximal, characteristic, complemented
5C2×#101×D43C211yesmaximal, characteristic, complemented
6#19135437C211yesmaximal, characteristic, complemented
7#19135437C211yesmaximal, characteristic, complemented
8#19135064C211yesmaximal, characteristic, complemented
9#19135062C211yesmaximal, characteristic, complemented
10#19135062C211yesmaximal, characteristic, complemented
11#19134590C211yesmaximal, characteristic, complemented
12#19134518C211yesmaximal, characteristic, complemented
13#19134517C211yesmaximal, characteristic, complemented
14#19134390C211yesmaximal, characteristic, complemented
15C43×#1901C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×M16×D43C2211yescharacteristic
21#14583562—21no—
22#14583562—21no—
23#14583562—21no—
24#14583562—21no—
25#14583562—21no—
26#14583562—21no—
27#14583562—21no—
28#14583562—21no—
29C2×#13063324C412yes—
30C2×#13063323C2211yescharacteristic
31C2×#13063305C2211yescharacteristic
32C2×#13063303C412yes—
33C2×#13063302C412yes—
34C2×#13063290C2211yescharacteristic
35C2×C4×C22⋊D43C2211yescharacteristic
36C2×(C22⋊D43)⋊C4C412yes—
37#14582975—21no—
38#14582974—21no—
39#14582973—21no—
40#14582970—21no—
41#14582968—21no—
42#14582967—21no—
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582922C2211yescharacteristic
46#14582922C2211yescharacteristic
47C2×#13063244C2211yescharacteristic
48C2×#13063244C2211yescharacteristic
49C2×#13063243—24no—
50C2×#13063243C2211yescharacteristic
51C2×#13063243C2211yescharacteristic
52C2×#13063243C2211yescharacteristic
53C2×#13063243C2211yescharacteristic
54C2×#13063243C2211yescharacteristic
55C2×#13063243C2211yescharacteristic
56C2×#13063243C2211yescharacteristic
57C2×#13063243C2211yescharacteristic
58#101×D43—24no—
59#14582863C2211yescharacteristic
60#14582862C2211yescharacteristic
61#14582862C2211yescharacteristic
62M16×Dic43C2211yescharacteristic
63M16×Dic43C2211yescharacteristic
64#14582668C2211yescharacteristic
65#14582668C2211yescharacteristic
66C22×M16×C43C2211yescharacteristic
67C2×C22⋊Q8×C43C2211yescharacteristic
68C2×#101×C43C2211yescharacteristic
69C2×#101×C43C2211yescharacteristic
70C43×#407C2211yescharacteristic
71C43×#343C2211yescharacteristic
72C43×#343C2211yescharacteristic
73C22×Dic86—21no—
74C22×Dic86—21no—
75C22×Dic86—21no—
76C22×Dic86—21no—
77C22×Dic86—22no—
78C22×Dic86—22no—
79C22×Dic86—41no—
80C22×Dic86—41no—
81C22×Dic86C2×C412yes—
82C22×Dic86C2×C412yes—
83C22×Dic86C2311yescharacteristic
84C22×Dic86C2311yescharacteristic
85C2×Q8×D43—21no—
86C2×Q8×D43—21no—
87C2×Q8×D43—21no—
88C2×Q8×D43—21no—
89C2×Q8×D43—22no—
90C2×Q8×D43—22no—
91C2×Q8×D43—41no—
92C2×Q8×D43—41no—
93C22×C22⋊D43C2×C411yescharacteristic
94C23×Dic43C2×C412yes—
95C22×C4×D43C2×C412yes—
96C22×C4×D43C2311yescharacteristic
97C2×#10621877—21no—
98C2×#10621877—22no—
99C2×#10621877—41no—
100C2×#10621877C2311yescharacteristic
101C2×#10621877C2311yescharacteristic
102C2×#10621877C2311yescharacteristic
103C2×#10621877C2311yescharacteristic
104C2×#10621872—21no—
105C2×#10621872—21no—
106M16×D43—22no—
107M16×D43—22no—
108M16×D43—41no—
109M16×D43—41no—
110C22×C43⋊C8—21no—
111C2×C8×D43—21no—
112C2×C8×D43—21no—
113#13063324—22no—
114#13063324—22no—
115#13063324—22no—
116#13063324—22no—
117#13063323—21no—
118#13063323—21no—
119#13063323—21no—
120#13063323—21no—
121#13063305—21no—
122#13063305—21no—
123#13063305—21no—
124#13063305—21no—
125#13063303—22no—
126#13063303—22no—
127#13063303—22no—
128#13063303—22no—
129#13063302—22no—
130#13063302—22no—
131#13063302—22no—
132#13063302—22no—
133#13063290—21no—
134#13063290—21no—
135#13063290—21no—
136#13063290—21no—
137C4×C22⋊D43D411yescharacteristic
138C4×C22⋊D43D411yescharacteristic
139C4×C22⋊D43D411yescharacteristic
140C4×C22⋊D43D411yescharacteristic
141C4×C22⋊D43D411yescharacteristic
142C4×C22⋊D43D411yescharacteristic
143C4×C22⋊D43D411yescharacteristic
144C4×C22⋊D43D411yescharacteristic
145(C22⋊D43)⋊C4—22no—
146(C22⋊D43)⋊C4—22no—
147(C22⋊D43)⋊C4—22no—
148(C22⋊D43)⋊C4—22no—
149C2×C4⋊Dic43C2×C412yes—
150C2×Dic43⋊C4C2×C412yes—
151C2×Dic43⋊C4C2×C412yes—
152C2×Dic43⋊C4C2×C412yes—
153C2×Dic43⋊C4C2×C411yescharacteristic
154C2×C22⋊Dic43C2×C411yescharacteristic
155C2×(C2×D43)⋊C4C2×C412yes—
156C2×(C2×D43)⋊C4C2×C411yescharacteristic
157C2×C4×Dic43C2×C412yes—
158C2×C4×Dic43C2311yescharacteristic
159Dic43⋊C8—21no—
160Dic43⋊C8—21no—
161Dic43⋊C8—21no—
162Dic43⋊C8—21no—
163#13063244—22no—
164#13063244—41no—
165#13063243—22no—
166#13063243—22no—
167#13063243—22no—
168#13063243—22no—
169#13063243—22no—
170#13063243—41no—
171#13063243—41no—
172#13063243D414yescomplemented
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)—21no—
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179#13063235—21no—
180#13063235—21no—
181C8×Dic43—21no—
182C8×Dic43—21no—
183C22×Q8×C43C2311yescharacteristic
184C23×C4×C43C2311yescharacteristic
185C2×M16×C43—21no—
186C2×M16×C43—22no—
187C2×M16×C43—41no—
188C2×M16×C43C2311yescharacteristic
189C2×M16×C43C2311yescharacteristic
190C2×M16×C43C2311yescharacteristic
191C2×M16×C43C2311yescharacteristic
192C22×C8×C43—21no—
193C22⋊Q8×C43—21no—
194C22⋊Q8×C43—21no—
195C22⋊Q8×C43—21no—
196C22⋊Q8×C43—21no—
197C2×C4⋊C4×C43C2×C412yes—
198C2×C4⋊C4×C43C2311yescharacteristic
199C2×C22⋊C4×C43C2×C412yes—
200#101×C43—22no—
201#101×C43—41no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43—21no—
204C24×C43C22×C411yescharacteristic
205C23×D43C22×C411yescharacteristic
206C2×Q8×C43—21no—
207C2×Q8×C43—21no—
208C2×Q8×C43—21no—
209C2×Q8×C43—21no—
210C2×Q8×C43—21no—
211C2×Q8×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C22×C412yes—
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C22×C412yes—
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2411yescharacteristic
224C2×C22⋊D43—24no—
225C2×C22⋊D43C22⋊C411yescharacteristic
226C2×C22⋊D43C22⋊C411yescharacteristic
227C2×C22⋊D43C22⋊C411yescharacteristic
228C2×C22⋊D43C22⋊C411yescharacteristic
229C22×Dic43—24no—
230C22×Dic43—22no—
231C22×Dic43—22no—
232C22×Dic43—42no—
233C22×Dic43C22×C412yes—
234C22×Dic43C22×C411yescharacteristic
235C22×Dic43C22×C411yescharacteristic
236C22×Dic43C22×C412yes—
237C22×Dic43C22×C411yescharacteristic
238Q8×D43—42no—
239Q8×D43—42no—
240Q8×D43—42no—
241Q8×D43—42no—
242Q8×D43—42no—
243Q8×D43—42no—
244Q8×D43—42no—
245Q8×D43—42no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—24no—
251C2×C4×D43—22no—
252C2×C4×D43—22no—
253C2×C4×D43—42no—
254C2×C4×D43C2×D411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×Dic86—21no—
259C2×Dic86—21no—
260C2×Dic86—21no—
261C2×Dic86—21no—
262C2×Dic86—22no—
263C2×Dic86—22no—
264C2×Dic86—21no—
265C2×Dic86—21no—
266C2×Dic86—21no—
267C2×Dic86—21no—
268C2×Dic86—21no—
269C2×Dic86—21no—
270C2×Dic86—22no—
271C2×Dic86—22no—
272C2×Dic86—24no—
273C2×Dic86—24no—
274C2×Dic86—42no—
275C2×Dic86—42no—
276C2×Dic86—42no—
277C2×Dic86—42no—
278C2×Dic86—42no—
279C2×Dic86—42no—
280C2×Dic86—42no—
281C2×Dic86—42no—
282C2×Dic86—42no—
283C2×Dic86—42no—
284C2×Dic86C2×D412yes—
285C2×Dic86#4112yes—
286M16×C43—21no—
287M16×C43—21no—
288M16×C43—21no—
289M16×C43—21no—
290M16×C43—21no—
291M16×C43—21no—
292M16×C43—21no—
293M16×C43—42no—
294M16×C43C2×D412yes—
295C2×C8×C43—21no—
296C2×C8×C43—21no—
297C2×C8×C43—21no—
298C2×C8×C43—21no—
299C2×C8×C43—42no—
300C4⋊C4×C43—22no—
301C4⋊C4×C43—22no—
302C4⋊C4×C43—21no—
303C4⋊C4×C43—21no—
304C22⋊C4×C43—22no—
305C22⋊C4×C43—22no—
306C22⋊Dic43C22⋊C411yescharacteristic
307C22⋊Dic43C22⋊C411yescharacteristic
308C22⋊Dic43C22⋊C411yescharacteristic
309C22⋊Dic43C22⋊C411yescharacteristic
310(C2×D43)⋊C4—22no—
311(C2×D43)⋊C4—22no—
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314(C2×D43)⋊C4C22⋊C411yescharacteristic
315(C2×D43)⋊C4C22⋊C411yescharacteristic
316C4⋊Dic43—22no—
317C4⋊Dic43—22no—
318Dic43⋊C4—22no—
319Dic43⋊C4—22no—
320Dic43⋊C4—22no—
321Dic43⋊C4—22no—
322Dic43⋊C4—22no—
323Dic43⋊C4—22no—
324Dic43⋊C4C22⋊C411yescharacteristic
325Dic43⋊C4C22⋊C411yescharacteristic
326Dic43⋊C4C22⋊C411yescharacteristic
327Dic43⋊C4C22⋊C411yescharacteristic
328C4×Dic43—22no—
329C4×Dic43—22no—
330C4×Dic43C2×D411yescharacteristic
331C4×Dic43C2×D411yescharacteristic
332C4×Dic43C2×D411yescharacteristic
333C4×Dic43C2×D411yescharacteristic
334#10621877—21no—
335#10621877—21no—
336#10621877—21no—
337#10621877—21no—
338#10621877—21no—
339#10621877—21no—
340#10621877—21no—
341#10621877—42no—
342#10621877C2×D412yes—
343C2×C43⋊C8—21no—
344C2×C43⋊C8—21no—
345C2×C43⋊C8—21no—
346C2×C43⋊C8—21no—
347C2×C43⋊C8—42no—
348#10621872—42no—
349#10621872—42no—
350C8×D43—42no—
351C8×D43—42no—
352C23×C43—21no—
353C23×C43—21no—
354C23×C43—22no—
355C23×C43—41no—
356C23×C43C2×C22⋊C411yescharacteristic
357C23×C43C2×C22⋊C411yescharacteristic
358C23×C43C23×C411yescharacteristic
359C22×D43—21no—
360C22×D43—21no—
361C22×D43—22no—
362C22×D43—41no—
363C22×D43C2×C22⋊C411yescharacteristic
364C22×D43C2×C22⋊C411yescharacteristic
365Q8×C43—41no—
366Q8×C43—41no—
367Q8×C43—41no—
368Q8×C43—41no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—21no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—42no—
384C2×C4×C43C2×C22⋊C411yescharacteristic
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C22×D411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C2×#4111yescharacteristic
390C2×C4×C43H(5,𝔽2)11yescharacteristic
391C2×C4×C43H(5,𝔽2)11yescharacteristic
392C22⋊D43—22no—
393C22⋊D43—22no—
394C22⋊D43—22no—
395C22⋊D43#10114yescomplemented
396C2×Dic43—22no—
397C2×Dic43—21no—
398C2×Dic43—22no—
399C2×Dic43—21no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—41no—
405C2×Dic43—44no—
406C2×Dic43—44no—
407C2×Dic43C2×C22⋊C411yescharacteristic
408C2×Dic43C2×C22⋊C411yescharacteristic
409C2×Dic43C2×C22⋊C411yescharacteristic
410C2×Dic43C2×C22⋊C411yescharacteristic
411C2×Dic43C2×C22⋊C411yescharacteristic
412C2×Dic43C2×C22⋊C411yescharacteristic
413C2×Dic43C4×D414yes—
414C4×D43—21no—
415C4×D43—21no—
416C4×D43—21no—
417C4×D43—21no—
418C4×D43—21no—
419C4×D43—21no—
420C4×D43—21no—
421C4×D43—21no—
422C4×D43—44no—
423C4×D43—44no—
424Dic86—22no—
425Dic86—22no—
426Dic86—22no—
427Dic86—22no—
428Dic86—44no—
429Dic86—44no—
430Dic86—44no—
431Dic86—44no—
432Dic86—41no—
433Dic86—41no—
434Dic86—41no—
435Dic86—41no—
436C8×C43—22no—
437C8×C43—41no—
438C8×C43—41no—
439C8×C43—41no—
440C43⋊C8—22no—
441C43⋊C8—41no—
442C43⋊C8—41no—
443C43⋊C8—41no—
444D4×#101—431nomaximal, Sylow
445C22×C43—21no—
446C22×C43—21no—
447C22×C43—21no—
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—42no—
453C22×C43—42no—
454C22×C43C2×#10112yescomplemented
455C22×C43C22×C22⋊C411yescharacteristic
456C22×C43C2×C4×D411yescharacteristic
457C22×C43#51811yescharacteristic
458C2×D43—21no—
459C2×D43—21no—
460C2×D43—21no—
461C2×D43—21no—
462C2×D43—21no—
463C2×D43—42no—
464C2×D43—42no—
465C2×D43C2×#10112yescomplemented
466C4×C43—21no—
467C4×C43—21no—
468C4×C43—42no—
469C4×C43—42no—
470C4×C43D4211yescharacteristic
471C4×C43D4211yescharacteristic
472C4×C43#54611yescharacteristic
473C4×C43#54611yescharacteristic
474Dic43—24no—
475Dic43—21no—
476Dic43—21no—
477Dic43—21no—
478Dic43—21no—
479Dic43—21no—
480Dic43—42no—
481Dic43C2×#10112yescomplemented
482C2×D4×Q8—431no—
483D4×M16—431no—
484D4×M16—431no—
485C22×#101—431no—
486C22×#101—431no—
487#1966—431no—
488#1966—431no—
489#1901—431no—
490#1901—431no—
491#1901—431no—
492#1901D4311yescharacteristic, complemented
493#1801—431no—
494#1784—431no—
495#1784—431no—
496C4×#101—431no—
497C2×C43—21no—
498C2×C43—21no—
499C2×C43—22no—
500C2×C43—41no—
501C2×C43D4×C22⋊C411yescharacteristic
502C2×C43C22×#10111yescharacteristic
503C2×C43#288911yescharacteristic
504D43—22no—
505D43—41no—
506C23×Q8—431no—
507C23×Q8—431no—
508C22×M16—431no—
509C22×M16—431no—
510C22×M16—431no—
511C22×M16C2×D4311yescharacteristic
512D4×Q8—861no—
513D4×Q8—861no—
514D4×Q8—861no—
515D4×Q8—861no—
516D4×Q8—861no—
517D4×Q8—861no—
518D4×Q8—861no—
519D4×Q8—861no—
520C2×C4⋊Q8—431no—
521C2×C4⋊Q8—432no—
522C2×C22⋊Q8—431no—
523C2×C22⋊Q8—432no—
524C2×C22⋊Q8—432no—
525C2×C22⋊Q8C2×D4311yescharacteristic
526C2×C4×Q8—431no—
527C2×C4×D4—431no—
528C2×C4×D4—432no—
529#436—861no—
530#436—861no—
531#435—861no—
532#435—861no—
533#435—861no—
534#435—861no—
535C8×D4—861no—
536C8×D4—861no—
537#423—431no—
538#423—431no—
539C2×#101—431no—
540C2×#101—431no—
541C2×#101—431no—
542C2×#101—431no—
543C2×#101—431no—
544C2×#101—431no—
545C2×#101—431no—
546C2×#101—431no—
547C2×#101—431no—
548C2×#101—431no—
549C2×#101—864no—
550C2×#101—864no—
551C2×#101C2×D4311yescharacteristic
552C2×#101C2×D4311yescharacteristic
553#407—431no—
554#407—431no—
555#407—431no—
556#407C2×D4311yescharacteristic
557C4×M16—431no—
558C4×M16—431no—
559#343—431no—
560#343—431no—
561#343C2×D4311yescharacteristic
562#343C2×D4311yescharacteristic
563C43D4×#10111yescharacteristic, complemented, Sylow
564C22×Q8—432no—
565C22×Q8—432no—
566C22×Q8—431no—
567C22×Q8—431no—
568C22×Q8—862no—
569C22×Q8—862no—
570C22×Q8—861no—
571C22×Q8—861no—
572C22×Q8—861no—
573C22×Q8—861no—
574C22×Q8—862no—
575C22×Q8—862no—
576C22×Q8—861no—
577C22×Q8—861no—
578C22×Q8—861no—
579C22×Q8—861no—
580C22×Q8—1721no—
581C22×Q8—1721no—
582C22×Q8—1721no—
583C22×Q8—1721no—
584C22×Q8C22×D4311yescharacteristic
585C22×D4—431no—
586C23×C4—431no—
587C23×C4—432no—
588C23×C4—432no—
589C23×C4C22×D4311yescharacteristic
590C2×M16—21no—
591C2×M16—22no—
592C2×M16—41no—
593C2×M16—431no—
594C2×M16—431no—
595C2×M16—431no—
596C2×M16—431no—
597C2×M16—861no—
598C2×M16—861no—
599C2×M16—861no—
600C2×M16—862no—
601C2×M16—862no—
602C2×M16—862no—
603C2×M16—1721no—
604C2×M16—1721no—
605C2×M16—1721no—
606C2×M16C22×D4311yescharacteristic
607C2×M16C22×D4311yescharacteristic
608C2×M16C22×D4311yescharacteristic
609C2×M16C22×D4311yescharacteristic
610C22×C8—21no—
611C22×C8—861no—
612C22×C8—861no—
613C22×C8—861no—
614C4⋊Q8—861no—
615C4⋊Q8—861no—
616C4⋊Q8—861no—
617C4⋊Q8—861no—
618C4⋊Q8—862no—
619C4⋊Q8—862no—
620C4⋊Q8—862no—
621C4⋊Q8—862no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8—862no—
627C22⋊Q8—862no—
628C22⋊Q8—862no—
629C22⋊Q8—862no—
630C22⋊Q8—862no—
631C22⋊Q8—862no—
632C22⋊Q8—862no—
633C22⋊Q8—862no—
634C22⋊Q8—861no—
635C22⋊Q8—861no—
636C22⋊Q8—861no—
637C22⋊Q8—861no—
638C4×Q8—861no—
639C4×Q8—861no—
640C4×Q8—861no—
641C4×Q8—861no—
642C4×D4—431no—
643C4×D4—431no—
644C4×D4—431no—
645C4×D4—431no—
646C4×D4—431no—
647C4×D4—431no—
648C4×D4—431no—
649C4×D4—431no—
650C4×D4—862no—
651C4×D4—862no—
652C4×D4—862no—
653C4×D4—862no—
654C2×C4⋊C4—431no—
655C2×C4⋊C4—432no—
656C2×C4⋊C4—432no—
657C2×C4⋊C4—432no—
658C2×C4⋊C4—432no—
659C2×C4⋊C4C4×D4312yes—
660C2×C4⋊C4C22×D4311yescharacteristic
661C2×C22⋊C4—431no—
662C2×C22⋊C4—431no—
663C2×C22⋊C4—432no—
664C2×C22⋊C4C4×D4312yes—
665C2×C42—431no—
666C2×C42—432no—
667C4⋊C8—861no—
668C4⋊C8—861no—
669C4⋊C8—861no—
670C4⋊C8—861no—
671#101—22no—
672#101—41no—
673#101—434no—
674#101—862no—
675#101—862no—
676#101—862no—
677#101—862no—
678#101—862no—
679#101—862no—
680#101—1721no—
681#101—1721no—
682#101—1721no—
683C22⋊C8—21no—
684C22⋊C8—21no—
685C22⋊C8—861no—
686C22⋊C8—861no—
687C22⋊C8—861no—
688C22⋊C8—861no—
689C22⋊C8—861no—
690C22⋊C8—861no—
691#97—861no—
692#97—861no—
693C4×C8—861no—
694C4×C8—861no—
695C24—431no—
696C24C2×C4×D4311yescharacteristic
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—432no—
704C2×Q8—432no—
705C2×Q8—862no—
706C2×Q8—862no—
707C2×Q8—864no—
708C2×Q8—864no—
709C2×Q8—862no—
710C2×Q8—862no—
711C2×Q8—861no—
712C2×Q8—861no—
713C2×Q8—861no—
714C2×Q8—861no—
715C2×Q8—861no—
716C2×Q8—861no—
717C2×Q8—861no—
718C2×Q8—861no—
719C2×Q8—861no—
720C2×Q8—861no—
721C2×Q8—1722no—
722C2×Q8—1722no—
723C2×Q8—1722no—
724C2×Q8—1722no—
725C2×Q8—1722no—
726C2×Q8—1722no—
727C2×Q8—1722no—
728C2×Q8—1722no—
729C2×Q8—1722no—
730C2×Q8—1722no—
731C2×Q8—1722no—
732C2×Q8—1722no—
733C2×Q8—1722no—
734C2×Q8—1722no—
735C2×Q8—1722no—
736C2×Q8—1722no—
737C2×Q8—1722no—
738C2×Q8—1722no—
739C2×D4—431no—
740C2×D4—431no—
741C2×D4—431no—
742C2×D4—431no—
743C2×D4—864no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—431no—
749C22×C4—432no—
750C22×C4—431no—
751C22×C4—431no—
752C22×C4—431no—
753C22×C4—431no—
754C22×C4—431no—
755C22×C4—431no—
756C22×C4—432no—
757C22×C4—864no—
758C22×C4—862no—
759C22×C4—862no—
760C22×C4—864no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—862no—
766C22×C4—862no—
767C22×C4—1722no—
768C22×C4—1722no—
769C22×C4C2×C4×D4312yes—
770C22×C4C2×C4×D4311yescharacteristic
771C22×C4C2×C4×D4312yes—
772C22×C4D4×D4311yescharacteristic
773C22×C4D4×D4311yescharacteristic
774C22×C4D4×D4311yescharacteristic
775C22×C4D4×D4311yescharacteristic
776C22×C4C23×D4311yescharacteristic
777M16—21no—
778M16—21no—
779M16—21no—
780M16—21no—
781M16—21no—
782M16—21no—
783M16—21no—
784M16—42no—
785M16—432no—
786M16—861no—
787M16—861no—
788M16—861no—
789M16—861no—
790M16—861no—
791M16—861no—
792M16—861no—
793M16—1722no—
794M16—1722no—
795M16—1722no—
796M16D4×D4312yes—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—42no—
802C2×C8—861no—
803C2×C8—861no—
804C2×C8—861no—
805C2×C8—861no—
806C2×C8—1722no—
807C2×C8—1722no—
808C2×C8—1722no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—431no—
814C4⋊C4—431no—
815C4⋊C4—431no—
816C4⋊C4—431no—
817C4⋊C4—862no—
818C4⋊C4—862no—
819C4⋊C4—862no—
820C4⋊C4—862no—
821C4⋊C4—862no—
822C4⋊C4—862no—
823C4⋊C4—862no—
824C4⋊C4—862no—
825C22⋊C4—22no—
826C22⋊C4—22no—
827C22⋊C4—431no—
828C22⋊C4—431no—
829C22⋊C4—431no—
830C22⋊C4—431no—
831C22⋊C4—431no—
832C22⋊C4—431no—
833C22⋊C4—431no—
834C22⋊C4—431no—
835C22⋊C4—862no—
836C22⋊C4—862no—
837C42—431no—
838C42—431no—
839C42—431no—
840C42—431no—
841C42—862no—
842C42—862no—
843C23—21no—
844C23—21no—
845C23—22no—
846C23—41no—
847C23—431no—
848C23—431no—
849C23—862no—
850C23—861no—
851C23—861no—
852C23—1721no—
853C23C22⋊C4×D4311yescharacteristic
854C23C22⋊C4×D4311yescharacteristic
855C23C22×C4×D4311yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860Q8—862no—
861Q8—862no—
862Q8—862no—
863Q8—862no—
864Q8—1724no—
865Q8—1724no—
866Q8—1724no—
867Q8—1724no—
868Q8—1721no—
869Q8—1721no—
870Q8—1721no—
871Q8—1721no—
872D4—434no—
873D4—862no—
874D4—862no—
875D4—862no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—42no—
891C2×C4—431no—
892C2×C4—431no—
893C2×C4—431no—
894C2×C4—431no—
895C2×C4—431no—
896C2×C4—431no—
897C2×C4—434no—
898C2×C4—862no—
899C2×C4—862no—
900C2×C4—861no—
901C2×C4—861no—
902C2×C4—862no—
903C2×C4—861no—
904C2×C4—861no—
905C2×C4—861no—
906C2×C4—861no—
907C2×C4—861no—
908C2×C4—861no—
909C2×C4—861no—
910C2×C4—861no—
911C2×C4—862no—
912C2×C4—862no—
913C2×C4—862no—
914C2×C4—1724no—
915C2×C4—1724no—
916C2×C4—1721no—
917C2×C4—1724no—
918C2×C4—1724no—
919C2×C4C22⋊C4×D4311yescharacteristic
920C2×C4C22⋊C4×D4311yescharacteristic
921C2×C4C2×D4×D4311yescharacteristic
922C2×C4C2×D4×D4311yescharacteristic
923C2×C4C2×D4×D4311yescharacteristic
924C2×C4#41×D4311yescharacteristic
925C2×C4#1306337011yescharacteristic
926C2×C4#1306337111yescharacteristic
927C8—22no—
928C8—41no—
929C8—41no—
930C8—41no—
931C8—862no—
932C8—1721no—
933C8—1721no—
934C8—1721no—
935C22—21no—
936C22—21no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—21no—
942C22—42no—
943C22—42no—
944C22—432no—
945C22—861no—
946C22—861no—
947C22—861no—
948C22—861no—
949C22—861no—
950C22—1722no—
951C22—1722no—
952C22#101×D4312yescomplemented
953C22C2×C22⋊C4×D4311yescharacteristic
954C22C4×D4×D4311yescharacteristic
955C22#1458337111yescharacteristic
956C4—21no—
957C4—21no—
958C4—42no—
959C4—42no—
960C4—432no—
961C4—861no—
962C4—861no—
963C4—864no—
964C4—861no—
965C4—861no—
966C4—861no—
967C4—1722no—
968C4#1458353111yescharacteristic
969C4#1458353311yescharacteristic
970C4#1458353811yescharacteristic
971C4#1458354111yescharacteristic
972C2—21no—
973C2—21no—
974C2—22no—
975C2—41no—
976C2—862no—
977C2—1721no—
978C2#1913741311yescharacteristic
979C2C2×#101×D4311yescharacteristic
980C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1901C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1901D43
hypocenterC43D4×#101
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1901

Complements

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

NH ≅ G/Ntype
4. C22×#13063243C2semidirect
5. C2×#101×D43C2semidirect
6. #19135437C2semidirect
7. #19135437C2semidirect
8. #19135064C2semidirect
9. #19135062C2semidirect
10. #19135062C2semidirect
11. #19134590C2semidirect
12. #19134518C2semidirect
13. #19134517C2semidirect
14. #19134390C2semidirect
15. C43×#1901C2semidirect
172. #13063243D4semidirect
395. C22⋊D43#101semidirect
454. C22×C43C2×#101semidirect
465. C2×D43C2×#101semidirect
481. Dic43C2×#101semidirect
492. #1901D43semidirect
563. C43D4×#101semidirect
952. C22#101×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835622
M16×C22⋊D432
#191433272
C22×#130632432
C2×#101×D432
#191354372
#191350642
#191350622
#191345902
#191345182
#191345172
#191343902
C43×#19012
D4×#10143