Finite Group Databasebeta

← #25245424

Subgroups — #25245424

Order 11008.

1436 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D43C211yesmaximal, characteristic
2C2×#14583108C211yesmaximal, characteristic, complemented
3C2×#14583107C211yesmaximal, characteristic, complemented
4C2×#14583056C211yesmaximal, characteristic
5C2×#14583053C211yesmaximal, characteristic
6#19142944C211yesmaximal, characteristic
7#19134939C211yesmaximal, characteristic, complemented
8#19134936C211yesmaximal, characteristic, complemented
9#19134935C211yesmaximal, characteristic, complemented
10#19134901C211yesmaximal, characteristic
11#19134899C211yesmaximal, characteristic
12#19134599C211yesmaximal, characteristic, complemented
13#19134598C211yesmaximal, characteristic, complemented
14#19134574C211yesmaximal, characteristic
15C43×#1878C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C2×#13063323C2211yescharacteristic
21C2×#13063305C2211yescharacteristic
22C2×#13063301C2211yescharacteristic
23C2×Q8×Dic43C2211yescharacteristic
24C2×C4×Dic86—21no—
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063290—21no—
27C2×#13063290C2211yescharacteristic
28C4×Q8×D43—24no—
29C4×Q8×D43—24no—
30C2×C4⋊C4×D43—21no—
31C2×C4⋊C4×D43C2211yescharacteristic
32C2×C42×D43—21no—
33C2×C42×D43C2211yescharacteristic
34#14583108—24no—
35#14583107—24no—
36#14583056—24no—
37#14583053—24no—
38C2×Dic43⋊C8C2211yescharacteristic
39C2×Dic43⋊C8C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063249C2211yescharacteristic
44C2×#13063248C2211yescharacteristic
45C2×#13063248C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48#14582805C2211yescharacteristic
49#14582796—21no—
50#14582796—21no—
51#14582768C2211yescharacteristic
52#14582758—21no—
53#14582758—21no—
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57#14582654C2211yescharacteristic
58C22×Q16×C43C2211yescharacteristic
59C2×C4×Q8×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C43×#391C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C43×#336C2211yescharacteristic
65C22×Dic86—21no—
66C22×Dic86C2311yescharacteristic
67C22×Dic86C2311yescharacteristic
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—22no—
72C2×Q8×D43—22no—
73C2×Q8×D43D414yes—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43D411yescharacteristic
77C22×C4×D43D411yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C2×Dic172—22no—
80C2×Dic172—22no—
81C2×Dic172—22no—
82C2×#10621885—22no—
83C2×#10621885—22no—
84C2×#10621885—22no—
85C2×#10621885—22no—
86C2×#10621885—22no—
87C2×#10621885—22no—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90#13063323—22no—
91#13063323—22no—
92#13063305—22no—
93#13063305—22no—
94#13063301—22no—
95#13063301—22no—
96Q8×Dic43—22no—
97Q8×Dic43D414yes—
98C4×Dic86—28no—
99C4×Dic86—22no—
100C4×Dic86—22no—
101#13063290—28no—
102#13063290—22no—
103#13063290D414yes—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4—21no—
115C2×Dic43⋊C4—21no—
116C4⋊C4×D43—28no—
117C4⋊C4×D43—22no—
118C4⋊C4×D43—22no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43—21no—
124C2×C4×Dic43D411yescharacteristic
125C2×C4×Dic43D411yescharacteristic
126C2×C4×Dic43C2311yescharacteristic
127C42×D43—28no—
128C42×D43—22no—
129C42×D43—22no—
130Dic43⋊C8—22no—
131Dic43⋊C8—22no—
132#13063250—22no—
133#13063250—22no—
134#13063249—22no—
135#13063249—22no—
136#13063248—22no—
137#13063248—22no—
138(C2×D43)⋊C8—22no—
139(C2×D43)⋊C8—22no—
140C43⋊#95—21no—
141C43⋊#95—21no—
142C22×Q8×C43C2311yescharacteristic
143C22×Q8×C43C2311yescharacteristic
144C2×Q16×C43—22no—
145C2×Q16×C43—22no—
146C2×Q16×C43—22no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C4×Q8×C43—22no—
150C4×Q8×C43—22no—
151C2×C4⋊C4×C43—21no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C42×C43—21no—
155C2×C42×C43C2311yescharacteristic
156#103×C43—22no—
157#103×C43—22no—
158#95×C43—21no—
159#95×C43—21no—
160C23×D43C2×D411yescharacteristic
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43C2×D412yes—
171C2×Q8×C43C2×D412yes—
172C2×Q8×C43#4112yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187Q8×D43—28no—
188Q8×D43—28no—
189Q8×D43—28no—
190Q8×D43—28no—
191C2×C4×D43—24no—
192C2×C4×D43—24no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—22no—
198C2×C4×D43—22no—
199C2×C4×D43—24no—
200C2×C4×D43—22no—
201C2×C4×D43—24no—
202C2×C4×D43—22no—
203C2×C4×D43—41no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43Q1614yescomplemented
207C2×C4×D43C2×D412yes—
208C2×C4×D43#4112yes—
209C2×Dic86—24no—
210C2×Dic86—24no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—24no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86C2×D412yes—
222C2×Dic86C2×D412yes—
223C2×Dic86#4112yes—
224Q16×C43—44no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C2×D412yes—
236C42×C43—24no—
237C42×C43—21no—
238C42×C43—21no—
239#10621885—44no—
240#10621885—44no—
241(C2×D43)⋊C4—42no—
242(C2×D43)⋊C4—42no—
243C4⋊Dic43—21no—
244C4⋊Dic43—24no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—42no—
248C4⋊Dic43C2×D412yes—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251Dic43⋊C4—24no—
252Dic43⋊C4—42no—
253Dic43⋊C4—42no—
254Dic43⋊C4—42no—
255Dic43⋊C4—42no—
256Dic43⋊C4—42no—
257C4×Dic43—24no—
258C4×Dic43—24no—
259C4×Dic43—24no—
260C4×Dic43—22no—
261C4×Dic43—22no—
262C4×Dic43C2×D412yes—
263C4×Dic43C2×D412yes—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270Dic172—44no—
271C23×C43C22×D411yescharacteristic
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43#12112yes—
277C22×D43C2×Q1612yes—
278C22×D43#13712yes—
279Q8×C43—22no—
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43—41no—
283Q8×C43—41no—
284Q8×C43—41no—
285Q8×C43—41no—
286Q8×C43#12114yes—
287C2×C4×C43—21no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—22no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43C2×Q1612yes—
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×Dic43—21no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—22no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43#12012yes—
328C2×Dic43#12012yes—
329C2×Dic43#12112yes—
330C2×Dic43C2×Q1612yes—
331C2×Dic43#13712yes—
332C4×D43—216no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—28no—
338C4×D43—44no—
339C4×D43—48no—
340Dic86—216no—
341Dic86—22no—
342Dic86—22no—
343Dic86—22no—
344Dic86—41no—
345Dic86—41no—
346Dic86—41no—
347Dic86—41no—
348Dic86#12114yes—
349C8×C43—41no—
350C8×C43—41no—
351C43⋊C8—41no—
352C43⋊C8—41no—
353#32906—431nomaximal, Sylow
354C22×C43C2×#12011yescharacteristic
355C22×C43C2×#12111yescharacteristic
356C22×C43#52511yescharacteristic
357C22×C43C22×Q1611yescharacteristic
358C22×C43C2×#13711yescharacteristic
359C22×C43C2×#13711yescharacteristic
360C22×C43#57511yescharacteristic
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—22no—
367C2×D43#46214yescomplemented
368C4×C43—24no—
369C4×C43—22no—
370C4×C43—41no—
371C4×C43—42no—
372C4×C43—81no—
373C4×C43—81no—
374C4×C43C2×#12111yescharacteristic
375C4×C43C2×#12111yescharacteristic
376C4×C43#52511yescharacteristic
377C4×C43#52511yescharacteristic
378Dic43—22no—
379Dic43—24no—
380Dic43—22no—
381Dic43—42no—
382Dic43—81no—
383Dic43—81no—
384Dic43#45114yescomplemented
385C22×C4×Q8—431no—
386C2×#462—431no—
387C2×#462—431no—
388C2×#451—431no—
389C2×#451—431no—
390#2857—431no—
391#1878—431no—
392#1878—431no—
393#1878—431no—
394#1878D4311yescharacteristic, complemented
395#1872—431no—
396#1872—431no—
397#1803—431no—
398#1803—431no—
399#1797—431no—
400C2×C43#284711yescharacteristic
401C2×C43C2×#45111yescharacteristic
402C2×C43#300711yescharacteristic
403C2×C43C2×#46211yescharacteristic
404C2×C43#303711yescharacteristic
405C2×C43#310411yescharacteristic
406C2×C43#311311yescharacteristic
407D43—24no—
408C23×Q8—431no—
409C22×Q16—431no—
410C22×Q16—431no—
411C22×Q16—431no—
412C22×Q16C2×D4311yescharacteristic
413C2×C4⋊Q8—431no—
414C2×C22⋊Q8—431no—
415C2×C22⋊Q8—431no—
416C2×C4×Q8—431no—
417C2×C4×Q8—431no—
418C2×C4×Q8—431no—
419C2×C4×Q8—861no—
420C2×C4×Q8—861no—
421C2×C4×Q8—864no—
422C2×C4×Q8—864no—
423C2×C4×Q8C2×D4311yescharacteristic
424C22×C4⋊C4—431no—
425C22×C4⋊C4—861no—
426C22×C42—431no—
427C22×C42—861no—
428#462—864no—
429#462—864no—
430#451—864no—
431#451—864no—
432C2×C4⋊C8—431no—
433C2×C4⋊C8—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103C2×D4311yescharacteristic
441C2×#103C2×D4311yescharacteristic
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444#391—431no—
445#391C2×D4311yescharacteristic
446#389—861no—
447#389—861no—
448#384—431no—
449#380—861no—
450#380—861no—
451#340—431no—
452#340—431no—
453#340—431no—
454#340C2×D4311yescharacteristic
455#336—431no—
456#336C2×D4311yescharacteristic
457C43#3290611yescharacteristic, complemented, Sylow
458C22×Q8—434no—
459C22×Q8—431no—
460C22×Q8—431no—
461C22×Q8—861no—
462C22×Q8—862no—
463C22×Q8—862no—
464C22×Q8—862no—
465C22×Q8—862no—
466C22×Q8—862no—
467C22×Q8C22×D4311yescharacteristic
468C22×Q8C22×D4311yescharacteristic
469C23×C4—431no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—861no—
473C23×C4—861no—
474C2×Q16—22no—
475C2×Q16—22no—
476C2×Q16—22no—
477C2×Q16—862no—
478C2×Q16—862no—
479C2×Q16—862no—
480C2×Q16—862no—
481C2×Q16—862no—
482C2×Q16—862no—
483C2×Q16—862no—
484C2×Q16—862no—
485C2×Q16—862no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C4⋊Q8—862no—
491C4⋊Q8—862no—
492C22⋊Q8—862no—
493C22⋊Q8—862no—
494C22⋊Q8—862no—
495C22⋊Q8—862no—
496C4×Q8—22no—
497C4×Q8—22no—
498C4×Q8—434no—
499C4×Q8—434no—
500C4×Q8—862no—
501C4×Q8—862no—
502C4×Q8—868no—
503C4×Q8—862no—
504C4×Q8—862no—
505C4×Q8—868no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—862no—
510C2×C4⋊C4—868no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—862no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4C22×D4311yescharacteristic
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C42—21no—
527C2×C42—431no—
528C2×C42—431no—
529C2×C42—431no—
530C2×C42—862no—
531C2×C42—862no—
532C2×C42—868no—
533C2×C42—861no—
534C2×C42—861no—
535C2×C42—861no—
536C2×C42C22×D4311yescharacteristic
537C4⋊C8—862no—
538C4⋊C8—862no—
539#103—22no—
540#103—22no—
541#103—862no—
542#103—862no—
543#103—862no—
544#103—862no—
545#103—862no—
546#103—862no—
547C22⋊C8—862no—
548C22⋊C8—862no—
549#95—21no—
550#95—21no—
551#95—861no—
552#95—861no—
553C24—431no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—432no—
564C2×Q8—432no—
565C2×Q8—432no—
566C2×Q8—864no—
567C2×Q8—864no—
568C2×Q8—864no—
569C2×Q8—868no—
570C2×Q8—868no—
571C2×Q8—868no—
572C2×Q8—868no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8—861no—
576C2×Q8—861no—
577C2×Q8—861no—
578C2×Q8—861no—
579C2×Q8—861no—
580C2×Q8—861no—
581C2×Q8—861no—
582C2×Q8#1062189812yes—
583C2×Q8D4×D4312yes—
584C2×Q8D4×D4312yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—431no—
592C22×C4—434no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—864no—
599C22×C4—864no—
600C22×C4—864no—
601C22×C4—862no—
602C22×C4—864no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—1721no—
612C22×C4—1722no—
613C22×C4—1722no—
614C22×C4D4×D4311yescharacteristic
615C22×C4D4×D4311yescharacteristic
616C22×C4C23×D4311yescharacteristic
617Q16—44no—
618Q16—1724no—
619Q16—1724no—
620Q16—1724no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—432no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—864no—
641C4⋊C4—864no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—1722no—
646C4⋊C4—1722no—
647C4⋊C4—1722no—
648C4⋊C4—1722no—
649C4⋊C4—1722no—
650C4⋊C4—1722no—
651C4⋊C4D4×D4312yes—
652C22⋊C4—1722no—
653C22⋊C4—1722no—
654C42—24no—
655C42—21no—
656C42—21no—
657C42—432no—
658C42—432no—
659C42—862no—
660C42—862no—
661C42—864no—
662C42—864no—
663C42—864no—
664C23—432no—
665C23—432no—
666C23—432no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23C2×D4×D4311yescharacteristic
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—434no—
680Q8—8616no—
681Q8—862no—
682Q8—862no—
683Q8—862no—
684Q8—1721no—
685Q8—1721no—
686Q8—1721no—
687Q8—1721no—
688Q8#1306329814yes—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—432no—
707C2×C4—432no—
708C2×C4—432no—
709C2×C4—432no—
710C2×C4—432no—
711C2×C4—868no—
712C2×C4—8616no—
713C2×C4—861no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—861no—
717C2×C4—862no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—1724no—
726C2×C4—1728no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4Q16×D4312yes—
736C2×C4C2×D4×D4311yescharacteristic
737C2×C4C2×D4×D4311yescharacteristic
738C2×C4C2×D4×D4311yescharacteristic
739C2×C4#41×D4311yescharacteristic
740C2×C4#41×D4311yescharacteristic
741C2×C4C2×#1062189811yescharacteristic
742C8—41no—
743C8—41no—
744C8—1721no—
745C8—1721no—
746C22—434no—
747C22—862no—
748C22—862no—
749C22—862no—
750C22—862no—
751C22—862no—
752C22—862no—
753C22#120×D4311yescharacteristic
754C22#121×D4311yescharacteristic
755C22#1458340811yescharacteristic
756C22C2×Q16×D4311yescharacteristic
757C22#137×D4311yescharacteristic
758C22#137×D4311yescharacteristic
759C22#1458369611yescharacteristic
760C4—22no—
761C4—24no—
762C4—41no—
763C4—42no—
764C4—81no—
765C4—81no—
766C4—434no—
767C4—862no—
768C4—862no—
769C4—864no—
770C4—3441no—
771C4—3441no—
772C4—1722no—
773C4#121×D4311yescharacteristic
774C4C2×#1306329811yescharacteristic
775C4#1458340711yescharacteristic
776C4#1458340811yescharacteristic
777C2—864no—
778C2#1914287611yescharacteristic
779C2#451×D4311yescharacteristic
780C2#1914385211yescharacteristic
781C2#462×D4311yescharacteristic
782C2#1914406511yescharacteristic
783C2#1914463211yescharacteristic
784C2#1914472311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1878C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1878D43
hypocenterC43#32906
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×#14583108C2semidirect
3. C2×#14583107C2semidirect
7. #19134939C2semidirect
8. #19134936C2semidirect
9. #19134935C2semidirect
12. #19134599C2semidirect
13. #19134598C2semidirect
15. C43×#1878C2semidirect
206. C2×C4×D43Q16semidirect
367. C2×D43#462semidirect
384. Dic43#451semidirect
394. #1878D43semidirect
457. C43#32906semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D432
C2×#145831082
C2×#145831072
C2×#145830562
C2×#145830532
#191429442
#191349392
#191349362
#191349352
#191349012
#191348992
#191345992
#191345982
#191345742
C43×#18782
#3290643