Finite Group Databasebeta

← #25113144

Subgroups — #25113144

Order 11008.

1354 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583562C211yesmaximal, characteristic
2C22⋊C4×Dic86C211yesmaximal, characteristic, complemented
3#19137427C211yesmaximal, characteristic, complemented
4#19135581C211yesmaximal, characteristic, complemented
5#19135578C212yesmaximal, complemented
6#19135578C212yesmaximal, complemented
7#19134582C212yesmaximal
8#19134580C211yesmaximal, characteristic
9C4×#13063239C211yesmaximal, characteristic
10#19134382C212yesmaximal
11C43×#1996C211yesmaximal, characteristic, complemented
12C23×Dic86C2211yescharacteristic
13C22×Q8×D43C411yescharacteristic, complemented
14#14583562—21no—
15#14583562—21no—
16#14583562—22no—
17#14583562—22no—
18#14583562—21no—
19#14583562—21no—
20C2×#13063324C412yescomplemented
21C2×#13063323C411yescharacteristic, complemented
22C2×#13063305C411yescharacteristic, complemented
23C2×#13063303C412yescomplemented
24C2×#13063302C2212yes—
25C2×C4×Dic86—21no—
26C2×#13063290—21no—
27C2×#13063290C411yescharacteristic, complemented
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×(C22⋊D43)⋊C4C2212yes—
30C2×#13063239C2212yes—
31C2×#13063239C2211yescharacteristic
32C2×#13063239C2211yescharacteristic
33#14582805—21no—
34#14582804—21no—
35#14582803—22no—
36#14582803—22no—
37#14582759C2211yescharacteristic
38#14582757C2212yes—
39#14582757C2212yes—
40C22⋊C4×Dic43C2212yes—
41C22⋊C4×Dic43C2212yes—
42C4×C22⋊Dic43C2211yescharacteristic
43#14582666C2212yes—
44#14582666C2212yes—
45#14582665C2212yes—
46#14582665C2211yescharacteristic
47#14582665C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C43×#380C2211yescharacteristic
50C4×C22⋊C4×C43C2211yescharacteristic
51C43×#342C2212yes—
52C43×#342C2212yes—
53C22×Dic86—44no—
54C22×Dic86C2×C411yescharacteristic
55C22×Dic86C2×C412yes—
56C22×Dic86C2×C412yes—
57C22×Dic86C2×C411yescharacteristic
58C22×Dic86D411yescharacteristic
59C22×Dic86D411yescharacteristic
60C22×Dic86D412yes—
61C22×Dic86D412yes—
62C22×Dic86D411yescharacteristic
63C22×Dic86D411yescharacteristic
64C2×Q8×D43—21no—
65C2×Q8×D43—22no—
66C2×Q8×D43—21no—
67C2×Q8×D43—44no—
68C22×C22⋊D43C2311yescharacteristic
69C23×Dic43C2312yes—
70C22×C4×D43C2×C412yes—
71C22×C4×D43C2×C411yescharacteristic
72#13063324—22no—
73#13063324—22no—
74#13063324—22no—
75#13063324—22no—
76#13063323—21no—
77#13063323—21no—
78#13063323—22no—
79#13063305—21no—
80#13063305—21no—
81#13063305—22no—
82#13063303—22no—
83#13063303—22no—
84#13063303—22no—
85#13063303—22no—
86#13063302—22no—
87#13063302—22no—
88#13063302—22no—
89#13063302—22no—
90C4×Dic86—44no—
91#13063290—22no—
92#13063290—21no—
93#13063290—21no—
94#13063290—44no—
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97C4×C22⋊D43—21no—
98C4×C22⋊D43—21no—
99(C22⋊D43)⋊C4—22no—
100(C22⋊D43)⋊C4—22no—
101(C22⋊D43)⋊C4—22no—
102(C22⋊D43)⋊C4—22no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43C2×C412yes—
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4C2×C412yes—
108C2×Dic43⋊C4C2×C411yescharacteristic
109C2×Dic43⋊C4C2×C412yes—
110C2×Dic43⋊C4C2×C412yes—
111C2×C22⋊Dic43C2311yescharacteristic
112C2×C22⋊Dic43C2312yes—
113C2×C22⋊Dic43C2311yescharacteristic
114C2×C22⋊Dic43C2311yescharacteristic
115C2×(C2×D43)⋊C4C2×C412yes—
116C2×(C2×D43)⋊C4C2×C411yescharacteristic
117C2×C4×Dic43—21no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43C2×C412yes—
121C2×C4×Dic43C2×C411yescharacteristic
122#13063239—24no—
123#13063239—22no—
124#13063239Q814yescomplemented
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C22×Q8×C43C2×C411yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2×C411yescharacteristic
139C2×C4⋊C4×C43C2×C412yes—
140C2×C22⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43C2312yes—
142C2×C22⋊C4×C43C2312yes—
143C2×C22⋊C4×C43C2311yescharacteristic
144C2×C42×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147C24×C43C2411yescharacteristic
148C23×D43C22×C411yescharacteristic
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—42no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—22no—
155C22×C4×C43—42no—
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C22×C412yes—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C2×C22⋊D43—21no—
165C2×C22⋊D43—21no—
166C2×C22⋊D43—21no—
167C2×C22⋊D43—21no—
168C2×C22⋊D43C2×Q812yes—
169C2×C22⋊D43#4112yes—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—22no—
173C22×Dic43—44no—
174C22×Dic43C22×C412yes—
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C412yes—
179C22×Dic43C2×D412yes—
180C22×Dic43C2×D412yes—
181C22×Dic43C2×D412yes—
182C22×Dic43C2×D412yes—
183Q8×D43—44no—
184Q8×D43—48no—
185Q8×D43—44no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—22no—
189C2×C4×D43—22no—
190C2×C4×D43—44no—
191C2×C4×D43—42no—
192C2×Dic86—24no—
193C2×Dic86—24no—
194C2×Dic86—24no—
195C2×Dic86—22no—
196C2×Dic86—22no—
197C2×Dic86—44no—
198C2×Dic86—44no—
199C2×Dic86—44no—
200C2×Dic86—42no—
201C2×Dic86—42no—
202C2×Dic86—42no—
203C2×Dic86—44no—
204C2×Dic86C22⋊C411yescharacteristic
205C2×Dic86C22⋊C412yes—
206C2×Dic86C22⋊C412yes—
207C2×Dic86C22⋊C412yes—
208C2×Dic86C22⋊C411yescharacteristic
209C2×Dic86C22⋊C411yescharacteristic
210C2×Dic86C22⋊C412yes—
211C2×Dic86C22⋊C412yes—
212C2×Dic86C22⋊C412yes—
213C2×Dic86C22⋊C411yescharacteristic
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—42no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—21no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—21no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—21no—
226C22⋊C4×C43C2×Q812yescomplemented
227C42×C43—42no—
228C22⋊Dic43—21no—
229C22⋊Dic43—21no—
230C22⋊Dic43—21no—
231C22⋊Dic43—22no—
232C22⋊Dic43—21no—
233C22⋊Dic43—21no—
234C22⋊Dic43—22no—
235C22⋊Dic43C2×Q812yescomplemented
236(C2×D43)⋊C4—21no—
237(C2×D43)⋊C4—21no—
238(C2×D43)⋊C4—22no—
239(C2×D43)⋊C4—22no—
240C4⋊Dic43—22no—
241C4⋊Dic43—22no—
242C4⋊Dic43—42no—
243Dic43⋊C4—21no—
244Dic43⋊C4—21no—
245Dic43⋊C4—22no—
246Dic43⋊C4—22no—
247Dic43⋊C4—22no—
248Dic43⋊C4—22no—
249Dic43⋊C4—22no—
250Dic43⋊C4—22no—
251Dic43⋊C4—44no—
252Dic43⋊C4—44no—
253C4×Dic43—21no—
254C4×Dic43—21no—
255C4×Dic43—22no—
256C4×Dic43—22no—
257C4×Dic43—44no—
258C4×Dic43—44no—
259C4×Dic43—42no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43C23×C411yescharacteristic
263C23×C43C22×D411yescharacteristic
264C23×C43C22×D411yescharacteristic
265C23×C43C22×Q811yescharacteristic
266C23×C43C2×#4111yescharacteristic
267C23×C432−1+411yescharacteristic
268C23×C432−1+411yescharacteristic
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43C4×Q812yescomplemented
274Q8×C43—42no—
275Q8×C43—42no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—41no—
295C2×C4×C43C2×C22⋊C411yescharacteristic
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C2×C22⋊C411yescharacteristic
299C22⋊D43—22no—
300C22⋊D43—22no—
301C22⋊D43—22no—
302C22⋊D43—22no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—24no—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—22no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—42no—
320C2×Dic43—41no—
321C2×Dic43—42no—
322C2×Dic43—41no—
323C2×Dic43—42no—
324C2×Dic43C2×C22⋊C412yes—
325C2×Dic43C2×C22⋊C412yes—
326C2×Dic43C2×C22⋊C412yes—
327C2×Dic43C2×C22⋊C412yes—
328C2×Dic43C4×Q812yescomplemented
329C4×D43—44no—
330C4×D43—42no—
331C4×D43—42no—
332C4×D43—44no—
333Dic86—22no—
334Dic86—22no—
335Dic86—22no—
336Dic86—24no—
337Dic86—24no—
338Dic86—24no—
339Dic86—42no—
340Dic86—42no—
341Dic86—42no—
342Dic86—44no—
343Dic86—44no—
344Dic86#9914yescomplemented
345Q8×#99—431nomaximal, Sylow
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—21no—
351C22×C43—21no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43C22×C22⋊C411yescharacteristic
357C22×C43C2×C4×Q811yescharacteristic
358C22×C43#51911yescharacteristic
359C22×C43#54811yescharacteristic
360C22×C43#54811yescharacteristic
361C22×C43D4×Q811yescharacteristic
362C22×C43D4×Q811yescharacteristic
363C2×D43—22no—
364C2×D43—42no—
365C2×D43—41no—
366C2×D43—41no—
367C2×D43—42no—
368C4×C43—21no—
369C4×C43—21no—
370C4×C43—21no—
371C4×C43—42no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43—81no—
375C4×C43—82no—
376C4×C43C2×#9912yes—
377Dic43—22no—
378Dic43—22no—
379Dic43—22no—
380Dic43—22no—
381Dic43—42no—
382Dic43—41no—
383Dic43—41no—
384Dic43—82no—
385Dic43—81no—
386Dic43C2×#9914yes—
387C2×D4×Q8—431no—
388Q8×C22⋊C4—431no—
389Q8×C22⋊C4—431no—
390#1996—432no—
391#1996—432no—
392#1996—431no—
393#1996D4311yescharacteristic, complemented
394#1799—431no—
395#1799—432no—
396C4×#99—431no—
397C4×#99—432no—
398C2×C43—21no—
399C2×C43—21no—
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43Q8×C22⋊C411yescharacteristic
405C2×C43C22×#9911yescharacteristic
406C2×C43#288411yescharacteristic
407D43—42no—
408C23×Q8—431no—
409C23×Q8—431no—
410D4×Q8—861no—
411D4×Q8—861no—
412D4×Q8—862no—
413D4×Q8—862no—
414D4×Q8—861no—
415D4×Q8—861no—
416C2×C4⋊Q8—431no—
417C2×C4⋊Q8—432no—
418C2×C22⋊Q8—432no—
419C2×C22⋊Q8—431no—
420C2×C22⋊Q8—432no—
421C2×C22⋊Q8C2×D4311yescharacteristic
422C2×C4×Q8—431no—
423C2×C4×Q8—861no—
424C2×C4×Q8—861no—
425C2×C4×D4—431no—
426C2×C4×D4—432no—
427C2×#99—431no—
428C2×#99—432no—
429C2×#99—431no—
430#391—862no—
431#391—862no—
432#391—861no—
433#391—861no—
434#380—431no—
435#380—432no—
436#380—432no—
437#380C2×D4311yescharacteristic
438C4×C22⋊C4—431no—
439C4×C22⋊C4—432no—
440C4×C22⋊C4—432no—
441C4×C22⋊C4C2×D4311yescharacteristic
442#342—432no—
443#342—432no—
444#342—431no—
445#342—431no—
446#342—432no—
447#342C2×D4312yes—
448#342C2×D4312yes—
449C43Q8×#9911yescharacteristic, complemented, Sylow
450C22×Q8—431no—
451C22×Q8—432no—
452C22×Q8—431no—
453C22×Q8—432no—
454C22×Q8—431no—
455C22×Q8—431no—
456C22×Q8—432no—
457C22×Q8—432no—
458C22×Q8—431no—
459C22×Q8—431no—
460C22×Q8—861no—
461C22×Q8—862no—
462C22×Q8—861no—
463C22×Q8—1724no—
464C22×Q8—1724no—
465C22×Q8C4×D4311yescharacteristic
466C22×D4—431no—
467C23×C4—432no—
468C23×C4—432no—
469C23×C4—431no—
470C23×C4C22×D4311yescharacteristic
471C4⋊Q8—862no—
472C4⋊Q8—862no—
473C4⋊Q8—862no—
474C4⋊Q8—862no—
475C4⋊Q8—861no—
476C4⋊Q8—861no—
477C4⋊Q8—862no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—862no—
483C22⋊Q8—862no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8—862no—
490C22⋊Q8—861no—
491C22⋊Q8—861no—
492C22⋊Q8—862no—
493C4×Q8—861no—
494C4×Q8—862no—
495C4×Q8—861no—
496C4×Q8—1724no—
497C4×Q8—1724no—
498C4×D4—862no—
499C4×D4—862no—
500C4×D4—862no—
501C4×D4—862no—
502C4×D4—861no—
503C4×D4—861no—
504C4×D4—861no—
505C4×D4—861no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—432no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—432no—
510C2×C4⋊C4—432no—
511C2×C4⋊C4—432no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—862no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4C4×D4311yescharacteristic
516C2×C4⋊C4C4×D4312yes—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—431no—
519C2×C22⋊C4—432no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—432no—
523C2×C22⋊C4C22×D4312yes—
524C2×C22⋊C4C22×D4311yescharacteristic
525C2×C22⋊C4C22×D4312yes—
526C2×C22⋊C4C22×D4311yescharacteristic
527C2×C42—21no—
528C2×C42—432no—
529C2×C42—431no—
530C2×C42—862no—
531C2×C42—862no—
532C2×C42—861no—
533#99—434no—
534#99—864no—
535#99—862no—
536#95—21no—
537#95—21no—
538#95—862no—
539#95—862no—
540#95—862no—
541#95—862no—
542#95—861no—
543#95—861no—
544C24—431no—
545C24C23×D4311yescharacteristic
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—42no—
549C2×Q8—431no—
550C2×Q8—432no—
551C2×Q8—431no—
552C2×Q8—432no—
553C2×Q8—432no—
554C2×Q8—431no—
555C2×Q8—431no—
556C2×Q8—432no—
557C2×Q8—432no—
558C2×Q8—432no—
559C2×Q8—862no—
560C2×Q8—862no—
561C2×Q8—864no—
562C2×Q8—864no—
563C2×Q8—864no—
564C2×Q8—1722no—
565C2×Q8—1722no—
566C2×Q8—1722no—
567C2×Q8—1724no—
568C2×Q8—1724no—
569C2×Q8—1724no—
570C2×Q8—1724no—
571C2×Q8—1724no—
572C2×Q8—1728no—
573C2×Q8—1724no—
574C2×D4—432no—
575C2×D4—432no—
576C2×D4—861no—
577C2×D4—861no—
578C2×D4—861no—
579C2×D4—861no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—42no—
584C22×C4—431no—
585C22×C4—432no—
586C22×C4—432no—
587C22×C4—432no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—431no—
592C22×C4—431no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—862no—
600C22×C4—1722no—
601C22×C4—1724no—
602C22×C4—1724no—
603C22×C4C2×C4×D4311yescharacteristic
604C22×C4C2×C4×D4312yes—
605C22×C4C2×C4×D4312yes—
606C22×C4C2×C4×D4311yescharacteristic
607C22×C4D4×D4311yescharacteristic
608C22×C4D4×D4311yescharacteristic
609C22×C4D4×D4311yescharacteristic
610C22×C4D4×D4311yescharacteristic
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—42no—
616C4⋊C4—862no—
617C4⋊C4—862no—
618C4⋊C4—862no—
619C4⋊C4—862no—
620C4⋊C4—862no—
621C4⋊C4—862no—
622C4⋊C4—862no—
623C4⋊C4—862no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—1722no—
627C4⋊C4—1724no—
628C4⋊C4—1724no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—21no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—22no—
635C22⋊C4—21no—
636C22⋊C4—432no—
637C22⋊C4—862no—
638C22⋊C4—862no—
639C22⋊C4—861no—
640C22⋊C4—861no—
641C22⋊C4—861no—
642C22⋊C4—861no—
643C22⋊C4—861no—
644C22⋊C4—861no—
645C22⋊C4—862no—
646C22⋊C4—861no—
647C22⋊C4—862no—
648C22⋊C4Q8×D4312yescomplemented
649C42—42no—
650C42—862no—
651C42—862no—
652C42—861no—
653C42—861no—
654C42—1722no—
655C42—1724no—
656C42—1724no—
657C23—41no—
658C23—41no—
659C23—432no—
660C23—861no—
661C23—861no—
662C23—1721no—
663C23—1721no—
664C23C22×C4×D4311yescharacteristic
665C23C2×D4×D4311yescharacteristic
666C23C2×D4×D4311yescharacteristic
667C23C2×Q8×D4311yescharacteristic
668C23#41×D4311yescharacteristic
669C23#1306337211yescharacteristic
670C23#1306337311yescharacteristic
671Q8—42no—
672Q8—42no—
673Q8—434no—
674Q8—864no—
675Q8—864no—
676Q8—864no—
677Q8—862no—
678Q8—862no—
679Q8—862no—
680Q8—1722no—
681Q8—1722no—
682Q8—1722no—
683Q8—1724no—
684Q8—1724no—
685D4—862no—
686D4—862no—
687D4—862no—
688D4—862no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—432no—
709C2×C4—432no—
710C2×C4—432no—
711C2×C4—432no—
712C2×C4—432no—
713C2×C4—864no—
714C2×C4—864no—
715C2×C4—864no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—862no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—1722no—
722C2×C4—1724no—
723C2×C4—1724no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1721no—
728C2×C4—1722no—
729C2×C4—1721no—
730C2×C4—1722no—
731C2×C4—1721no—
732C2×C4—1722no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1722no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4C22⋊C4×D4311yescharacteristic
739C2×C4C22⋊C4×D4311yescharacteristic
740C2×C4C22⋊C4×D4311yescharacteristic
741C2×C4C22⋊C4×D4311yescharacteristic
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—862no—
753C22—1722no—
754C22—1722no—
755C22—1721no—
756C22—1721no—
757C22C2×C22⋊C4×D4311yescharacteristic
758C22C4×Q8×D4311yescharacteristic
759C22#1458337511yescharacteristic
760C22#1458355711yescharacteristic
761C22#1458355911yescharacteristic
762C22#1458356211yescharacteristic
763C22#1458356411yescharacteristic
764C4—21no—
765C4—21no—
766C4—21no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—82no—
771C4—81no—
772C4—434no—
773C4—862no—
774C4—862no—
775C4—862no—
776C4—862no—
777C4—3441no—
778C4—3442no—
779C4—1722no—
780C4—1721no—
781C4—1721no—
782C4#99×D4312yes—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—21no—
788C2—21no—
789C2—1722no—
790C2#1913742911yescharacteristic
791C2C2×#99×D4311yescharacteristic
792C2#1914305711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1996C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C23
cosocleC24×C43C24
hypercenter#1996D43
hypocenterC43Q8×#99
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×Dic86C2semidirect
3. #19137427C2semidirect
4. #19135581C2semidirect
5. #19135578C2semidirect
6. #19135578C2semidirect
11. C43×#1996C2semidirect
13. C22×Q8×D43C4semidirect
20. C2×#13063324C4semidirect
21. C2×#13063323C4semidirect
22. C2×#13063305C4semidirect
23. C2×#13063303C4semidirect
27. C2×#13063290C4semidirect
124. #13063239Q8semidirect
226. C22⋊C4×C43C2×Q8semidirect
235. C22⋊Dic43C2×Q8semidirect
273. C22×D43C4×Q8semidirect
328. C2×Dic43C4×Q8semidirect
344. Dic86#99semidirect
393. #1996D43semidirect
449. C43Q8×#99semidirect
648. C22⋊C4Q8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835622
C22⋊C4×Dic862
#191374272
#191355812
#191355782
#191345822
#191345802
C4×#130632392
#191343822
C43×#19962
Q8×#9943