Finite Group Databasebeta

← #25062597

Subgroups — #25062597

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583426C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3C2×#14582949C211yesmaximal, characteristic, complemented
4#19132963C212yesmaximal, complemented
5#19132961C212yesmaximal, complemented
6#19132944C211yesmaximal, characteristic, complemented
7#19132943C211yesmaximal, characteristic, complemented
8#19132941C211yesmaximal, characteristic, complemented
9#19132917C212yesmaximal, complemented
10#19132914C212yesmaximal, complemented
11C43×#1468C211yesmaximal, characteristic, complemented
12#14583426—21no—
13#14583426—21no—
14#14583426—21no—
15#14583426—21no—
16#14583426—21no—
17#14583426—21no—
18#14583426—21no—
19#14583426—21no—
20C2×#13063320C2211yescharacteristic
21C2×#13063318C2211yescharacteristic
22C2×#13063315C411yescharacteristic
23C2×#13063311C411yescharacteristic
24C2×#13063308C2211yescharacteristic
25C2×#13063302C411yescharacteristic
26C2×#13063297C411yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×D4×Dic43C411yescharacteristic
29C2×(C22⋊D43)⋊C4C411yescharacteristic
30C2×(C22⋊D43)⋊C4C2211yescharacteristic
31C2×#13063283C411yescharacteristic
32C2×#13063281C411yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34#14582953—21no—
35#14582953C2212yes—
36#14582949—21no—
37#14582949—21no—
38#14582949—21no—
39#14582949C2212yes—
40#14582949C2212yes—
41#14582949C2212yes—
42#14582922—21no—
43C2×Dic43⋊C8—21no—
44#14582863C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46M16×Dic43—21no—
47C2×C8×Dic43—21no—
48#14582625C2212yes—
49#14582624C2212yes—
50#14582624C2212yes—
51#14582623C2212yes—
52#14582622C2212yes—
53#14582622C2212yes—
54C2×#123×C43C2211yescharacteristic
55C43×#407C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#324C2212yes—
58C43×#323C2212yes—
59C22×Dic86C2×C411yescharacteristic
60C22×C22⋊D43C2×C411yescharacteristic
61C22×C22⋊D43C2×C411yescharacteristic
62C23×Dic43C2×C411yescharacteristic
63C23×Dic43C2×C411yescharacteristic
64C23×Dic43C2×C411yescharacteristic
65C22×C4×D43C2×C411yescharacteristic
66C2×#10621877—21no—
67C22×C43⋊C8—21no—
68#13063320—21no—
69#13063320—21no—
70#13063320—21no—
71#13063320—21no—
72#13063318—21no—
73#13063318—21no—
74#13063318—21no—
75#13063318—21no—
76#13063315—21no—
77#13063315—21no—
78#13063315—21no—
79#13063315—21no—
80#13063311—21no—
81#13063311—21no—
82#13063311—21no—
83#13063311—21no—
84#13063308—21no—
85#13063308—21no—
86#13063308—21no—
87#13063308—21no—
88#13063302—21no—
89#13063302—21no—
90#13063302—21no—
91#13063302—21no—
92#13063297—21no—
93#13063297—21no—
94#13063297—21no—
95#13063297—21no—
96#13063290—21no—
97#13063290—21no—
98#13063290—21no—
99#13063290—21no—
100D4×Dic43—21no—
101D4×Dic43—21no—
102D4×Dic43—21no—
103D4×Dic43—21no—
104(C22⋊D43)⋊C4—21no—
105(C22⋊D43)⋊C4—21no—
106(C22⋊D43)⋊C4—21no—
107(C22⋊D43)⋊C4—21no—
108(C22⋊D43)⋊C4—21no—
109(C22⋊D43)⋊C4—21no—
110(C22⋊D43)⋊C4—21no—
111(C22⋊D43)⋊C4—21no—
112#13063283—21no—
113#13063283—21no—
114#13063283—21no—
115#13063283—21no—
116#13063281—21no—
117#13063281—21no—
118#13063281—21no—
119#13063281—21no—
120C2×C4⋊Dic43C2×C411yescharacteristic
121C2×C4⋊Dic43C2×C411yescharacteristic
122C2×Dic43⋊C4C2×C411yescharacteristic
123C2×Dic43⋊C4C2×C411yescharacteristic
124C2×Dic43⋊C4C2×C411yescharacteristic
125C2×Dic43⋊C4C2×C411yescharacteristic
126C2×Dic43⋊C4C2×C411yescharacteristic
127C2×Dic43⋊C4C2311yescharacteristic
128C2×C22⋊Dic43C2×C411yescharacteristic
129C2×C22⋊Dic43C2×C411yescharacteristic
130C2×C22⋊Dic43C2×C411yescharacteristic
131C2×(C2×D43)⋊C4C2×C411yescharacteristic
132C2×(C2×D43)⋊C4C2×C411yescharacteristic
133C2×(C2×D43)⋊C4C2×C411yescharacteristic
134C2×(C2×D43)⋊C4C2311yescharacteristic
135C2×C4×Dic43C2×C411yescharacteristic
136C2×C4×Dic43C2×C411yescharacteristic
137C2×C4×Dic43C2×C411yescharacteristic
138C2×C4×Dic43C2×C411yescharacteristic
139C2×C4×Dic43D411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43C2311yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149Dic43⋊C8—22no—
150Dic43⋊C8—22no—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)—21no—
154C22⋊(C43⋊C8)—21no—
155C22⋊(C43⋊C8)C2312yes—
156C22⋊(C43⋊C8)C2312yes—
157#13063235—22no—
158C8×Dic43—22no—
159C8×Dic43—22no—
160C8×Dic43—22no—
161C22×D4×C43C2×C411yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C2×M16×C43—21no—
164C22×C8×C43—21no—
165#123×C43—21no—
166#123×C43—21no—
167#123×C43—21no—
168#123×C43—21no—
169C2×C4⋊C4×C43C2×C411yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C22⋊C4×C43C2×C411yescharacteristic
172C2×C22⋊C4×C43C2×C411yescharacteristic
173C2×C22⋊C4×C43C2311yescharacteristic
174C22⋊C8×C43—21no—
175C22⋊C8×C43—21no—
176C22⋊C8×C43C2312yes—
177C22⋊C8×C43C2312yes—
178C24×C43C22×C411yescharacteristic
179C24×C43C22×C411yescharacteristic
180C23×D43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—42no—
184C22×C4×C43—42no—
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—42no—
200C22×Dic43—24no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—42no—
204C22×Dic43—42no—
205C22×Dic43C22⋊C411yescharacteristic
206C22×Dic43C22⋊C411yescharacteristic
207C22×Dic43C22⋊C411yescharacteristic
208C22×Dic43C22⋊C411yescharacteristic
209C22×Dic43C22⋊C411yescharacteristic
210C22×Dic43C22⋊C411yescharacteristic
211C22×Dic43C22⋊C411yescharacteristic
212C22×Dic43C22⋊C411yescharacteristic
213C22×Dic43C22×C411yescharacteristic
214C22×Dic43C22×C411yescharacteristic
215C22×Dic43C22×C411yescharacteristic
216C22×Dic43C22×C411yescharacteristic
217C22×Dic43C22×C411yescharacteristic
218C22×Dic43C22×C411yescharacteristic
219C22×Dic43C22×C411yescharacteristic
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—42no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—24no—
226M16×C43—42no—
227C2×C8×C43—22no—
228C2×C8×C43—22no—
229C2×C8×C43—42no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊Dic43—21no—
241C22⋊Dic43—21no—
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246(C2×D43)⋊C4—21no—
247(C2×D43)⋊C4—21no—
248(C2×D43)⋊C4—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258Dic43⋊C4—21no—
259Dic43⋊C4—21no—
260Dic43⋊C4—21no—
261Dic43⋊C4—21no—
262Dic43⋊C4—21no—
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270C4×Dic43—21no—
271C4×Dic43—21no—
272C4×Dic43—21no—
273C4×Dic43—21no—
274C4×Dic43C22⋊C411yescharacteristic
275C4×Dic43C22⋊C411yescharacteristic
276C4×Dic43C22⋊C411yescharacteristic
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C2×D411yescharacteristic
283C4×Dic43C2×D411yescharacteristic
284C4×Dic43C2×D411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290#10621877—42no—
291C2×C43⋊C8—22no—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—42no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—21no—
297C23×C43—22no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43C2×C22⋊C411yescharacteristic
302C23×C43C2×C22⋊C411yescharacteristic
303C23×C43C23×C411yescharacteristic
304C22×D43—21no—
305C22×D43—22no—
306C22×D43—41no—
307C22×D43—41no—
308D4×C43—42no—
309D4×C43—42no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C22⋊D43—42no—
327C22⋊D43—42no—
328C22⋊D43—42no—
329C22⋊D43—42no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—22no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43C2×C22⋊C411yescharacteristic
350C2×Dic43C2×C22⋊C411yescharacteristic
351C2×Dic43C2×C22⋊C411yescharacteristic
352C2×Dic43C2×C22⋊C411yescharacteristic
353C2×Dic43C2×C22⋊C411yescharacteristic
354C2×Dic43C2×C22⋊C411yescharacteristic
355C2×Dic43C2×C22⋊C411yescharacteristic
356C2×Dic43C2×C22⋊C411yescharacteristic
357C2×Dic43#13114yes—
358C4×D43—42no—
359C4×D43—42no—
360Dic86—42no—
361Dic86—42no—
362C8×C43—42no—
363C8×C43—42no—
364C43⋊C8—42no—
365C43⋊C8—42no—
366#17383—431nomaximal, Sylow
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—44no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—82no—
379C22×C43#41012yes—
380C22×C43C22×C22⋊C411yescharacteristic
381C22×C43C2×#13112yes—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43—82no—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43—41no—
393Dic43—21no—
394Dic43—21no—
395Dic43—21no—
396Dic43—21no—
397Dic43—21no—
398Dic43—41no—
399Dic43—41no—
400Dic43—41no—
401Dic43#40812yes—
402Dic43#40812yes—
403Dic43#41312yes—
404C2×#529—431no—
405#2920—431no—
406C2×#431—431no—
407#1473—432no—
408#1473—432no—
409#1468—431no—
410#1468—431no—
411#1468—431no—
412#1468D4311yescharacteristic, complemented
413#1461—432no—
414#1460—432no—
415C2×C43—22no—
416C2×C43—22no—
417C2×C43—41no—
418C2×C43—81no—
419C2×C43C2×#40811yescharacteristic
420C2×C43C2×#41011yescharacteristic
421C2×C43C2×#41311yescharacteristic
422D43—81no—
423#529—861no—
424#529—861no—
425#529—861no—
426#529—861no—
427#529—861no—
428#529—861no—
429#529—861no—
430#529—861no—
431C2×#126—431no—
432C2×#126—431no—
433C2×#125—431no—
434C2×#124—431no—
435C2×#123—431no—
436C2×#123C2×D4311yescharacteristic
437C2×C22⋊Q8—431no—
438C2×#121—431no—
439C2×C4×Q8—431no—
440C2×C4×D4—431no—
441C2×C4×D4—431no—
442C2×C4×D4—431no—
443C2×#117—431no—
444C2×#117—431no—
445C22×C42—431no—
446#432—432no—
447#432—861no—
448#431—432no—
449#431—432no—
450#431—432no—
451#431—861no—
452#431—861no—
453#431—861no—
454#423—861no—
455C2×C4⋊C8—861no—
456#407—431no—
457#407C2×D4311yescharacteristic
458C2×C22⋊C8—431no—
459C2×C22⋊C8C2×D4311yescharacteristic
460C4×M16—861no—
461C2×C4×C8—861no—
462#324—432no—
463#324—432no—
464#324—432no—
465#324C2×D4312yes—
466#323—432no—
467#323—432no—
468#323—432no—
469#323C2×D4312yes—
470C43#1738311yescharacteristic, complemented, Sylow
471C22×Q8—431no—
472C22×D4—431no—
473C22×D4—431no—
474C22×D4C4×D4311yescharacteristic
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4C22×D4311yescharacteristic
480C2×M16—21no—
481C2×M16—861no—
482C22×C8—21no—
483C22×C8—861no—
484#126—861no—
485#126—861no—
486#126—861no—
487#126—861no—
488#126—861no—
489#126—861no—
490#126—861no—
491#126—861no—
492#125—861no—
493#125—861no—
494#125—861no—
495#125—861no—
496#124—861no—
497#124—861no—
498#124—861no—
499#124—861no—
500#123—21no—
501#123—21no—
502#123—21no—
503#123—21no—
504#123—861no—
505#123—861no—
506#123—861no—
507#123—861no—
508C22⋊Q8—861no—
509C22⋊Q8—861no—
510C22⋊Q8—861no—
511C22⋊Q8—861no—
512#121—861no—
513#121—861no—
514#121—861no—
515#121—861no—
516C4×Q8—861no—
517C4×Q8—861no—
518C4×Q8—861no—
519C4×Q8—861no—
520C4×D4—861no—
521C4×D4—861no—
522C4×D4—861no—
523C4×D4—861no—
524C4×D4—861no—
525C4×D4—861no—
526C4×D4—861no—
527C4×D4—861no—
528C4×D4—861no—
529C4×D4—861no—
530C4×D4—861no—
531C4×D4—861no—
532#117—861no—
533#117—861no—
534#117—861no—
535#117—861no—
536#117—861no—
537#117—861no—
538#117—861no—
539#117—861no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4C4×D4311yescharacteristic
549C2×C4⋊C4C22×D4311yescharacteristic
550C2×C22⋊C4—431no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—431no—
553C2×C22⋊C4—431no—
554C2×C22⋊C4—431no—
555C2×C22⋊C4—431no—
556C2×C22⋊C4—431no—
557C2×C22⋊C4C4×D4311yescharacteristic
558C2×C22⋊C4C4×D4311yescharacteristic
559C2×C22⋊C4C22×D4311yescharacteristic
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—431no—
574C4⋊C8—862no—
575C4⋊C8—862no—
576C4⋊C8—862no—
577C4⋊C8—862no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—432no—
581C22⋊C8—432no—
582C22⋊C8—861no—
583C22⋊C8—861no—
584C22⋊C8C22×D4312yes—
585C22⋊C8C22×D4312yes—
586#97—862no—
587C4×C8—862no—
588C4×C8—862no—
589C4×C8—862no—
590C24—431no—
591C24C2×C4×D4311yescharacteristic
592C24C2×C4×D4311yescharacteristic
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—864no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—42no—
599C2×D4—861no—
600C2×D4—861no—
601C2×D4—864no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—1722no—
605C22×C4—42no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—864no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4—1722no—
629C22×C4C2×C4×D4311yescharacteristic
630C22×C4C2×C4×D4311yescharacteristic
631C22×C4C2×C4×D4311yescharacteristic
632C22×C4C2×C4×D4311yescharacteristic
633C22×C4D4×D4311yescharacteristic
634C22×C4D4×D4311yescharacteristic
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638M16—42no—
639M16—1722no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—42no—
643C2×C8—862no—
644C2×C8—862no—
645C2×C8—1722no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—861no—
673C22⋊C4—861no—
674C22⋊C4—861no—
675C22⋊C4—861no—
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—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—431no—
701C42—431no—
702C42—861no—
703C42—861no—
704C42—861no—
705C42—861no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—862no—
714C23—861no—
715C23—1721no—
716C23—1721no—
717C23C22⋊C4×D4311yescharacteristic
718C23C22⋊C4×D4311yescharacteristic
719C23C22×C4×D4311yescharacteristic
720Q8—1722no—
721Q8—1722no—
722D4—42no—
723D4—42no—
724D4—1722no—
725D4—1722no—
726D4—1722no—
727D4—1722no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—431no—
741C2×C4—431no—
742C2×C4—431no—
743C2×C4—434no—
744C2×C4—431no—
745C2×C4—431no—
746C2×C4—431no—
747C2×C4—431no—
748C2×C4—431no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—861no—
758C2×C4—861no—
759C2×C4—861no—
760C2×C4—862no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1722no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4C22⋊C4×D4311yescharacteristic
771C2×C4C22⋊C4×D4311yescharacteristic
772C2×C4C2×D4×D4311yescharacteristic
773C2×C4C2×D4×D4311yescharacteristic
774C8—42no—
775C8—42no—
776C8—1722no—
777C8—1722no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—44no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—82no—
790C22—3442no—
791C22—1721no—
792C22—1721no—
793C22—1721no—
794C22#1458287112yes—
795C22C2×C22⋊C4×D4311yescharacteristic
796C22#131×D4312yes—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—432no—
805C4—432no—
806C4—432no—
807C4—861no—
808C4—861no—
809C4—861no—
810C4—861no—
811C4—861no—
812C4—1721no—
813C4—1721no—
814C4—1721no—
815C2—22no—
816C2—22no—
817C2—41no—
818C2—81no—
819C2—3441no—
820C2#408×D4311yescharacteristic
821C2C2×#1458287111yescharacteristic
822C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1468C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063297C4
cosocleC22×C4×C43C24
hypercenter#1468D43
hypocenterC43#17383
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. C2×#14582949C2semidirect
4. #19132963C2semidirect
5. #19132961C2semidirect
6. #19132944C2semidirect
7. #19132943C2semidirect
8. #19132941C2semidirect
9. #19132917C2semidirect
10. #19132914C2semidirect
11. C43×#1468C2semidirect
412. #1468D43semidirect
470. C43#17383semidirect

Maximal subgroups

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

subgroupindex
C2×#145834262
#191432242
C2×#145829492
#191329632
#191329612
#191329442
#191329432
#191329412
#191329172
#191329142
C43×#14682
#1738343