Finite Group Databasebeta

← #25134235

Subgroups — #25134235

Order 11008.

1508 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
2C2×#14583126C211yesmaximal, characteristic, complemented
3C2×#14583036C211yesmaximal, characteristic, complemented
4C22×#13063249C211yesmaximal, characteristic, complemented
5#19138036C211yesmaximal, characteristic
6#19135839C211yesmaximal, characteristic, complemented
7#19135789C211yesmaximal, characteristic, complemented
8#19135676C211yesmaximal, characteristic, complemented
9#19135595C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic, complemented
11#19134900C211yesmaximal, characteristic, complemented
12#19134885C211yesmaximal, characteristic, complemented
13#19134861C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C2×C43×#448C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19Q8×C22⋊D43—24no—
20Q8×C22⋊D43—24no—
21C2×#13063323—21no—
22C2×#13063323C2211yescharacteristic
23C2×#13063304—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063301—21no—
26C2×#13063301C2211yescharacteristic
27C2×#13063297—21no—
28C2×#13063296C2211yescharacteristic
29C2×Q8×Dic43C2211yescharacteristic
30C2×C4×C22⋊D43—21no—
31C2×C4×C22⋊D43C2211yescharacteristic
32C22×C4⋊Dic43C2211yescharacteristic
33#14583126—24no—
34#14583036—24no—
35C2×#13063256C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249—24no—
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063246C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47#14582822—21no—
48#14582815—21no—
49#14582802C2211yescharacteristic
50#14582795C2211yescharacteristic
51#14582779—21no—
52#14582756C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C23×Q8×C43C2211yescharacteristic
58C22×SD16×C43C2211yescharacteristic
59C22×SD16×C43C2211yescharacteristic
60C2×#121×C43C2211yescharacteristic
61C43×#448—24no—
62C2×#103×C43C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×C22⋊C8×C43C2211yescharacteristic
65C22×Dic86—21no—
66C22×Dic86C2311yescharacteristic
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—41no—
72C2×Q8×D43—41no—
73C22×C22⋊D43—21no—
74C22×C22⋊D43D411yescharacteristic
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C2×#10621883—22no—
79C2×#10621883—22no—
80C2×#10621883—41no—
81C22×C43⋊C8—22no—
82C22×C43⋊C8—22no—
83C22×C43⋊C8—41no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86#13063323—28no—
87#13063323—22no—
88#13063323—22no—
89#13063304—28no—
90#13063304—22no—
91#13063304D414yescomplemented
92#13063301—28no—
93#13063301—22no—
94#13063301—22no—
95#13063297—44no—
96#13063296—22no—
97#13063296—41no—
98Q8×Dic43—22no—
99Q8×Dic43—22no—
100C4×C22⋊D43—28no—
101C4×C22⋊D43—22no—
102C4×C22⋊D43—22no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43—22no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43—41no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4—21no—
115C2×Dic43⋊C4D411yescharacteristic
116C2×C22⋊Dic43—21no—
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43—21no—
119C2×C22⋊Dic43—21no—
120C2×C22⋊Dic43D411yescharacteristic
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4D411yescharacteristic
124C2×C4×Dic43—21no—
125C2×C4×Dic43C2311yescharacteristic
126#13063256—22no—
127#13063250—22no—
128#13063250—41no—
129#13063249—22no—
130#13063249—22no—
131#13063249—22no—
132#13063249D414yescomplemented
133#13063248—22no—
134#13063246—22no—
135(C2×D43)⋊C8—22no—
136(C2×D43)⋊C8—41no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C22×Q8×C43—22no—
140C22×Q8×C43—21no—
141C22×Q8×C43—22no—
142C22×Q8×C43—22no—
143C22×Q8×C43—41no—
144C22×Q8×C43—41no—
145C22×Q8×C43D414yescomplemented
146C22×Q8×C43C2311yescharacteristic
147C22×Q8×C43C2311yescharacteristic
148C22×D4×C43—21no—
149C22×D4×C43C2311yescharacteristic
150C23×C4×C43—21no—
151C23×C4×C43C2311yescharacteristic
152C2×SD16×C43—22no—
153C2×SD16×C43—22no—
154C2×SD16×C43—22no—
155C2×SD16×C43—22no—
156C2×SD16×C43—41no—
157C2×SD16×C43—41no—
158C22×C8×C43C2311yescharacteristic
159C22×C8×C43C2311yescharacteristic
160#121×C43—22no—
161#121×C43—22no—
162C2×C4⋊C4×C43C2311yescharacteristic
163C2×C22⋊C4×C43—21no—
164#103×C43—22no—
165#103×C43—22no—
166C22⋊C8×C43—22no—
167C24×C43—21no—
168C24×C43C2×D411yescharacteristic
169C23×D43C2×D411yescharacteristic
170C2×Q8×C43—24no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—28no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—42no—
181C2×Q8×C43—42no—
182C2×Q8×C43—44no—
183C2×Q8×C43—44no—
184C2×Q8×C43—44no—
185C2×Q8×C43C2×D412yes—
186C2×Q8×C43C2×D412yes—
187C2×Q8×C43C2×D412yes—
188C2×Q8×C43#4112yes—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—24no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—42no—
207C22×C4×C43—42no—
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2411yescharacteristic
212C2×C22⋊D43—22no—
213C2×C22⋊D43—22no—
214C2×C22⋊D43—42no—
215C2×C22⋊D43—42no—
216C2×C22⋊D43—81no—
217C2×C22⋊D43SD1614yescomplemented
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—42no—
223C22×Dic43—42no—
224C22×Dic43—81no—
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228Q8×D43—44no—
229Q8×D43—44no—
230Q8×D43—44no—
231Q8×D43—44no—
232C2×C4×D43—24no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—42no—
240C2×C4×D43—42no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—24no—
246C2×Dic86—21no—
247C2×Dic86—42no—
248C2×Dic86—42no—
249C2×Dic86C2×D412yes—
250SD16×C43—44no—
251SD16×C43—44no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C22⋊C4×C43—42no—
261C22⋊Dic43—24no—
262C22⋊Dic43—22no—
263C22⋊Dic43—42no—
264C22⋊Dic43—42no—
265C22⋊Dic43—81no—
266#10621883—44no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—22no—
269(C2×D43)⋊C4—42no—
270C4⋊Dic43—24no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—42no—
276C4⋊Dic43C2×D412yes—
277C4⋊Dic43C2×D412yes—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—22no—
283Dic43⋊C4—42no—
284C4×Dic43—24no—
285C4×Dic43—21no—
286C4×Dic43—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—44no—
293C2×C43⋊C8C2×D412yes—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43#12012yes—
306C23×C43C2×SD1612yes—
307C23×C43#13712yes—
308C23×C43C22×D411yescharacteristic
309C22×D43—21no—
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—21no—
315C22×D43C2×SD1612yes—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—22no—
320Q8×C43—22no—
321Q8×C43—48no—
322Q8×C43—41no—
323Q8×C43—41no—
324Q8×C43#12114yescomplemented
325D4×C43—41no—
326D4×C43—41no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—84no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—48no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43#12012yes—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C2×#4111yescharacteristic
351C2×C4×C43H(5,𝔽2)11yescharacteristic
352C2×C4×C43H(5,𝔽2)11yescharacteristic
353C22⋊D43—28no—
354C22⋊D43—84no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—22no—
359C2×Dic43—21no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—84no—
376C2×Dic43C2×SD1612yes—
377C4×D43—48no—
378C4×D43—41no—
379C4×D43—41no—
380C4×D43—41no—
381C4×D43—41no—
382Dic86—22no—
383Dic86—22no—
384Dic86—48no—
385Dic86—41no—
386Dic86—41no—
387C8×C43—41no—
388C8×C43—41no—
389C43⋊C8—22no—
390C43⋊C8—41no—
391#24429—431nomaximal, Sylow
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—81no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43#44814yescomplemented
406C22×C43C2×#12011yescharacteristic
407C22×C43D4211yescharacteristic
408C22×C43#54611yescharacteristic
409C22×C43C22×SD1611yescharacteristic
410C22×C43C2×#13711yescharacteristic
411C22×C43#57711yescharacteristic
412C22×C43#57811yescharacteristic
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—41no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C4×C43—24no—
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—81no—
424C4×C43C2×#12111yescharacteristic
425C4×C43#53411yescharacteristic
426C4×C43D4211yescharacteristic
427C4×C43#54611yescharacteristic
428Dic43—22no—
429Dic43—42no—
430Dic43—41no—
431Dic43—41no—
432Dic43—42no—
433Dic43—42no—
434Dic43—81no—
435C2×D4×Q8—431no—
436C2×#465—431no—
437C2×#448—431no—
438C2×#448D4311yescharacteristic, complemented
439C22×#103—431no—
440#2416—431no—
441#2043—431no—
442#2035—431no—
443#2013—431no—
444#2000—431no—
445#1880—431no—
446#1872—431no—
447#1869—431no—
448#1865—431no—
449#1787—431no—
450C2×C43—24no—
451C2×C43—161no—
452C2×C43#241011yescharacteristic
453C2×C43C2×#44811yescharacteristic
454C2×C43#301311yescharacteristic
455C2×C43#327011yescharacteristic
456C2×C43D4×SD1611yescharacteristic
457C2×C43#329811yescharacteristic
458C2×C43#332011yescharacteristic
459D43—42no—
460C23×Q8—431no—
461C23×Q8C2×D4311yescharacteristic
462C22×SD16—431no—
463C22×SD16C2×D4311yescharacteristic
464C22×SD16C2×D4311yescharacteristic
465C23×C8—431no—
466D4×Q8—864no—
467D4×Q8—864no—
468C2×C4⋊Q8—431no—
469C2×C4⋊Q8—861no—
470C2×C22⋊Q8—431no—
471C2×C22⋊Q8—431no—
472C2×C22⋊Q8—861no—
473C2×C22⋊Q8—861no—
474C2×#121—431no—
475C2×#121—861no—
476C2×#121C2×D4311yescharacteristic
477C2×C4×Q8—431no—
478C2×C4×D4—431no—
479C2×C4×D4—861no—
480C22×C4⋊C4—431no—
481#465—864no—
482#448—24no—
483#448—864no—
484C2×#106—431no—
485C2×#103—431no—
486C2×#103—431no—
487C2×#103—431no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103—431no—
491C2×#103—431no—
492C2×#103—864no—
493C2×#103C2×D4311yescharacteristic
494C2×#103C2×D4311yescharacteristic
495C2×#102—431no—
496C2×C22⋊C8—431no—
497C2×C22⋊C8—431no—
498C2×C22⋊C8C2×D4311yescharacteristic
499#396—861no—
500#394—861no—
501#390—431no—
502#389—431no—
503#386—861no—
504#380—431no—
505#340—431no—
506#340—431no—
507#336—431no—
508#336—431no—
509C43#2442911yescharacteristic, complemented, Sylow
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—431no—
517C22×Q8—861no—
518C22×Q8—862no—
519C22×Q8—862no—
520C22×Q8—862no—
521C22×Q8—862no—
522C22×Q8—1721no—
523C22×Q8—1721no—
524C22×Q8C22⋊D4314yescomplemented
525C22×Q8C22×D4311yescharacteristic
526C22×Q8C22×D4311yescharacteristic
527C22×D4—21no—
528C22×D4—431no—
529C22×D4—861no—
530C22×D4C22×D4311yescharacteristic
531C23×C4—21no—
532C23×C4—431no—
533C23×C4—861no—
534C23×C4—861no—
535C23×C4C22×D4311yescharacteristic
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—862no—
543C2×SD16—862no—
544C2×SD16—1721no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—862no—
548C22×C8—862no—
549C22×C8—1721no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552C4⋊Q8—862no—
553C4⋊Q8—868no—
554C4⋊Q8—862no—
555C22⋊Q8—434no—
556C22⋊Q8—862no—
557C22⋊Q8—868no—
558C22⋊Q8—868no—
559C22⋊Q8—862no—
560C22⋊Q8—862no—
561#121—22no—
562#121—22no—
563#121—862no—
564#121—1721no—
565#121—1724no—
566C4×Q8—862no—
567C4×Q8—862no—
568C4×D4—868no—
569C4×D4—862no—
570C4×D4—862no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—431no—
573C2×C4⋊C4—431no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—862no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4—861no—
582C2×C4⋊C4—861no—
583C2×C4⋊C4—1721no—
584C2×C4⋊C4C22×D4311yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—431no—
587C2×C22⋊C4—431no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4—861no—
593C2×C22⋊C4—861no—
594C2×C42—431no—
595C2×C42—861no—
596#106—862no—
597#103—22no—
598#103—22no—
599#103—434no—
600#103—862no—
601#103—862no—
602#103—862no—
603#103—862no—
604#103—862no—
605#103—1721no—
606#102—862no—
607C22⋊C8—22no—
608C22⋊C8—862no—
609C22⋊C8—1721no—
610#95—861no—
611#95—861no—
612C24—21no—
613C24—431no—
614C24D4×D4311yescharacteristic
615C2×Q8—24no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—28no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—42no—
626C2×Q8—42no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—432no—
631C2×Q8—864no—
632C2×Q8—861no—
633C2×Q8—861no—
634C2×Q8—861no—
635C2×Q8—861no—
636C2×Q8—861no—
637C2×Q8—1722no—
638C2×Q8—1722no—
639C2×Q8—1724no—
640C2×Q8—1724no—
641C2×Q8—1724no—
642C2×Q8—1724no—
643C2×Q8D4×D4312yes—
644C2×Q8#1062190012yes—
645C2×Q8C2×C22⋊D4312yes—
646C2×Q8C2×C22⋊D4312yes—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—434no—
657C2×D4—862no—
658C2×D4—862no—
659C2×D4—3441no—
660C2×D4—1722no—
661C2×D4—1722no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—24no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—431no—
675C22×C4—864no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—3441no—
687C22×C4—1722no—
688C22×C4—1722no—
689C22×C4—1722no—
690C22×C4—1722no—
691C22×C4D4×D4311yescharacteristic
692C22×C4D4×D4312yes—
693C22×C4C2×C22⋊D4312yes—
694C22×C4C23×D4311yescharacteristic
695SD16—44no—
696SD16—44no—
697SD16—1724no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—432no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—1724no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—432no—
714C4⋊C4—432no—
715C4⋊C4—864no—
716C4⋊C4—864no—
717C4⋊C4—864no—
718C4⋊C4—864no—
719C4⋊C4—862no—
720C4⋊C4—864no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—1722no—
726C4⋊C4—1722no—
727C22⋊C4—42no—
728C22⋊C4—864no—
729C22⋊C4—862no—
730C22⋊C4—864no—
731C22⋊C4—862no—
732C22⋊C4—3441no—
733C22⋊C4—1722no—
734C22⋊C4—1722no—
735C22⋊C4—1722no—
736C42—864no—
737C42—861no—
738C42—861no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—432no—
751C23—861no—
752C23—861no—
753C23—861no—
754C23—861no—
755C23—861no—
756C23—861no—
757C23#1306329312yes—
758C23SD16×D4312yes—
759C23#1306335412yes—
760C23C2×D4×D4311yescharacteristic
761Q8—22no—
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—48no—
767Q8—41no—
768Q8—41no—
769Q8—862no—
770Q8—862no—
771Q8—1728no—
772Q8—1721no—
773Q8—1721no—
774Q8#1306329714yescomplemented
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—84no—
780D4—868no—
781D4—3444no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—432no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—862no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—862no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—862no—
809C2×C4—861no—
810C2×C4—3444no—
811C2×C4—1728no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4#1306329312yes—
826C2×C4C2×D4×D4311yescharacteristic
827C2×C4C2×D4×D4311yescharacteristic
828C2×C4C22×C22⋊D4311yescharacteristic
829C2×C4C2×#1062190011yescharacteristic
830C2×C4#1306337011yescharacteristic
831C2×C4#1306337011yescharacteristic
832C8—41no—
833C8—41no—
834C8—862no—
835C8—1721no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—862no—
850C22—862no—
851C22—862no—
852C22—1721no—
853C22—1721no—
854C22—1721no—
855C22—1721no—
856C22#1458303614yescomplemented
857C22C2×#1306329311yescharacteristic
858C22#1458353111yescharacteristic
859C22#1458353611yescharacteristic
860C22C2×SD16×D4311yescharacteristic
861C22C2×#1306335411yescharacteristic
862C22#1458370811yescharacteristic
863C22#1458371511yescharacteristic
864C4—22no—
865C4—24no—
866C4—42no—
867C4—81no—
868C4—862no—
869C4—3441no—
870C4—1722no—
871C4—1721no—
872C4—1722no—
873C4—1721no—
874C4—1722no—
875C4C2×#1306329711yescharacteristic
876C4#1458345811yescharacteristic
877C4#1458353111yescharacteristic
878C4#1458353611yescharacteristic
879C2—24no—
880C2—161no—
881C2—1722no—
882C2#1913797011yescharacteristic
883C2C2×#1458303611yescharacteristic
884C2#1914390911yescharacteristic
885C2#1914615811yescharacteristic
886C2#1914628411yescharacteristic
887C2#1914645311yescharacteristic
888C2#1914677011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#448C2
socleC23×C43C22×D4
prime radical#19138036C2
hypercenterC2×#448D43
hypocenterC43#24429
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D43C2semidirect
2. C2×#14583126C2semidirect
3. C2×#14583036C2semidirect
4. C22×#13063249C2semidirect
6. #19135839C2semidirect
7. #19135789C2semidirect
8. #19135676C2semidirect
9. #19135595C2semidirect
10. #19134952C2semidirect
11. #19134900C2semidirect
12. #19134885C2semidirect
13. #19134861C2semidirect
14. #19134528C2semidirect
15. C2×C43×#448C2semidirect
91. #13063304D4semidirect
132. #13063249D4semidirect
145. C22×Q8×C43D4semidirect
217. C2×C22⋊D43SD16semidirect
324. Q8×C43#121semidirect
405. C22×C43#448semidirect
438. C2×#448D43semidirect
509. C43#24429semidirect
524. C22×Q8C22⋊D43semidirect
774. Q8#13063297semidirect
856. C22#14583036semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D432
C2×#145831262
C2×#145830362
C22×#130632492
#191380362
#191358392
#191357892
#191356762
#191355952
#191349522
#191349002
#191348852
#191348612
#191345282
C2×C43×#4482
#2442943