Finite Group Databasebeta

← #25062690

Subgroups — #25062690

Order 11008.

1034 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D43C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic, complemented
3#19143223C211yesmaximal, characteristic, complemented
4#19132965C211yesmaximal, characteristic, complemented
5#19132964C211yesmaximal, characteristic, complemented
6#19132963C212yesmaximal, complemented
7#19132962C211yesmaximal, characteristic, complemented
8#19132961C212yesmaximal, complemented
9#19132923C212yesmaximal, complemented
10#19132920C212yesmaximal
11C43×#1473C211yesmaximal, characteristic, complemented
12C2×#13063320C411yescharacteristic
13C2×#13063320C411yescharacteristic
14C2×#13063320C2211yescharacteristic
15C2×#13063319C2211yescharacteristic
16C2×#13063318C411yescharacteristic
17C2×#13063318C411yescharacteristic
18C2×#13063318C2211yescharacteristic
19#126×D43—21no—
20#126×D43—21no—
21#126×D43—21no—
22#126×D43—21no—
23#126×D43—21no—
24#126×D43—21no—
25#126×D43—21no—
26#126×D43—21no—
27C2×C4⋊C4×D43C411yescharacteristic
28C2×C4⋊C4×D43C411yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C22⋊C4×D43C411yescharacteristic
31C2×C22⋊C4×D43C411yescharacteristic
32C2×C22⋊C4×D43C2211yescharacteristic
33C2×C42×D43C2211yescharacteristic
34#14582956C2211yescharacteristic, complemented
35#14582955—21no—
36#14582954—21no—
37#14582953C2212yescomplemented
38#14582952C2211yescharacteristic, complemented
39#14582951—21no—
40#14582950—21no—
41#14582949C2212yescomplemented
42#14582921—21no—
43#14582921—21no—
44#14582861C2212yes—
45#14582861C2212yes—
46#14582851—21no—
47C4×#10621872—21no—
48#14582625C2212yescomplemented
49#14582624C2212yescomplemented
50#14582624C2212yescomplemented
51#14582623C2212yes—
52#14582622C2212yes—
53#14582622C2212yes—
54C2×#126×C43C2211yescharacteristic
55C43×#432C2211yescharacteristic, complemented
56C43×#431C2211yescharacteristic, complemented
57C43×#324C2212yescomplemented
58C43×#323C2212yes—
59C24×D43C2×C411yescharacteristic
60C22×C4×D43C2×C411yescharacteristic
61C22×C4×D43C2×C411yescharacteristic
62C22×C4×D43C2×C411yescharacteristic
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43C2×C411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621872—22no—
67C2×#10621872—22no—
68#13063320—21no—
69#13063320—21no—
70#13063320—21no—
71#13063320—21no—
72#13063320—21no—
73#13063320—21no—
74#13063320—21no—
75#13063320—21no—
76#13063320—21no—
77#13063320—21no—
78#13063320—21no—
79#13063320—21no—
80#13063319—21no—
81#13063319—21no—
82#13063319—21no—
83#13063319—21no—
84#13063318—21no—
85#13063318—21no—
86#13063318—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063318—21no—
93#13063318—21no—
94#13063318—21no—
95#13063318—21no—
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2311yescharacteristic
105C4⋊C4×D43—21no—
106C4⋊C4×D43—21no—
107C4⋊C4×D43—21no—
108C4⋊C4×D43—21no—
109C4⋊C4×D43—21no—
110C4⋊C4×D43—21no—
111C4⋊C4×D43—21no—
112C4⋊C4×D43—21no—
113C4⋊C4×D43—21no—
114C4⋊C4×D43—21no—
115C4⋊C4×D43—21no—
116C4⋊C4×D43—21no—
117C2×C22⋊Dic43C2×C411yescharacteristic
118C2×C22⋊Dic43C2×C411yescharacteristic
119C2×C22⋊Dic43C2×C411yescharacteristic
120C2×(C2×D43)⋊C4C2×C411yescharacteristic
121C2×(C2×D43)⋊C4C2×C411yescharacteristic
122C2×(C2×D43)⋊C4C2×C411yescharacteristic
123C2×(C2×D43)⋊C4C2×C411yescharacteristic
124C2×(C2×D43)⋊C4C2×C411yescharacteristic
125C2×(C2×D43)⋊C4C2311yescharacteristic
126C22⋊C4×D43—21no—
127C22⋊C4×D43—21no—
128C22⋊C4×D43—21no—
129C22⋊C4×D43—21no—
130C22⋊C4×D43—21no—
131C22⋊C4×D43—21no—
132C22⋊C4×D43—21no—
133C22⋊C4×D43—21no—
134C22⋊C4×D43—21no—
135C22⋊C4×D43—21no—
136C22⋊C4×D43—21no—
137C22⋊C4×D43—21no—
138C2×C4×Dic43C2×C411yescharacteristic
139C2×C4×Dic43C2×C411yescharacteristic
140C2×C4×Dic43C2311yescharacteristic
141C42×D43D411yescharacteristic
142C42×D43D411yescharacteristic
143C42×D43D411yescharacteristic
144C42×D43D411yescharacteristic
145C42×D43D411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C4⋊(C43⋊C8)—21no—
150C4⋊(C43⋊C8)—21no—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)C2312yes—
154C22⋊(C43⋊C8)C2312yes—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157#13063236—21no—
158#13063235—22no—
159C4×C43⋊C8—21no—
160C8×Dic43—22no—
161#126×C43—21no—
162#126×C43—21no—
163#126×C43—21no—
164#126×C43—21no—
165C2×C4⋊C4×C43C2×C411yescharacteristic
166C2×C4⋊C4×C43C2×C411yescharacteristic
167C2×C4⋊C4×C43C2311yescharacteristic
168C2×C22⋊C4×C43C2×C411yescharacteristic
169C2×C22⋊C4×C43C2×C411yescharacteristic
170C2×C22⋊C4×C43C2311yescharacteristic
171C2×C42×C43C2311yescharacteristic
172C4⋊C8×C43—21no—
173C4⋊C8×C43—21no—
174C22⋊C8×C43C2312yes—
175C22⋊C8×C43C2312yes—
176#97×C43—21no—
177C4×C8×C43—21no—
178C24×C43C22×C411yescharacteristic
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—42no—
182C23×D43—42no—
183C23×D43—42no—
184C23×D43C22×C411yescharacteristic
185C23×D43C22×C411yescharacteristic
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C22×C411yescharacteristic
190C22×C4×C43C22×C411yescharacteristic
191C22×C4×C43C2411yescharacteristic
192C22×Dic43C22×C411yescharacteristic
193C22×Dic43C22×C411yescharacteristic
194C22×Dic43C22×C411yescharacteristic
195C22×Dic43C22×C411yescharacteristic
196C22×Dic43C22×C411yescharacteristic
197C22×Dic43C22×C411yescharacteristic
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43C22⋊C411yescharacteristic
211C2×C4×D43C22⋊C411yescharacteristic
212C2×C4×D43C22⋊C411yescharacteristic
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22⋊C411yescharacteristic
217C2×C4×D43C22⋊C411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C8×C43—22no—
223C2×C8×C43—22no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C22⋊C4×C43—21no—
231C22⋊C4×C43—21no—
232C22⋊C4×C43—21no—
233C22⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C42×C43C2×D411yescharacteristic
237C42×C43C2×D411yescharacteristic
238C42×C43C2×D411yescharacteristic
239C42×C43C2×D411yescharacteristic
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—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276C4×Dic43C22⋊C411yescharacteristic
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C2×D411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C2×C43⋊C8—22no—
289C2×C43⋊C8—22no—
290#10621872—44no—
291#10621872—44no—
292C23×C43—21no—
293C23×C43—22no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43C23×C411yescharacteristic
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—21no—
301C22×D43—22no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—88no—
311C22×D43C2×C22⋊C411yescharacteristic
312C22×D43C2×C22⋊C411yescharacteristic
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
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×C43C2×C22⋊C411yescharacteristic
325C2×C4×C43C2×C22⋊C411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×Dic43—22no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—22no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342C2×Dic43C2×C22⋊C411yescharacteristic
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—41no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351C4×D43—41no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—41no—
355C4×D43—42no—
356C4×D43—42no—
357C4×D43—42no—
358C4×D43—42no—
359C4×D43—42no—
360C4×D43—42no—
361C8×C43—42no—
362C8×C43—42no—
363C43⋊C8—42no—
364C43⋊C8—42no—
365#17398—431nomaximal, Sylow
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—82no—
372C22×C43C22×C22⋊C411yescharacteristic
373C22×C43#56812yes—
374C2×D43—28no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—84no—
383C2×D43—84no—
384C2×D43—82no—
385C2×D43#41012yes—
386C2×D43#41312yes—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—21no—
393C4×C43—41no—
394C4×C43—41no—
395C4×C43—41no—
396Dic43—21no—
397Dic43—21no—
398Dic43—21no—
399Dic43—21no—
400Dic43—21no—
401Dic43—21no—
402Dic43—41no—
403Dic43—41no—
404Dic43—41no—
405C22×#126—431no—
406#2920—431no—
407#2920—431no—
408#1473—431no—
409#1473—431no—
410#1473—432no—
411#1473—432no—
412#1473—431no—
413#1473D4311yescharacteristic, complemented
414#1463—432no—
415#1462—432no—
416C2×C43—22no—
417C2×C43—81no—
418C2×C43#287911yescharacteristic
419C2×C43C2×#41011yescharacteristic
420C2×C43C2×#41311yescharacteristic
421D43—22no—
422D43—22no—
423D43—81no—
424C2×#126—431no—
425C2×#126—431no—
426C2×#126—431no—
427C2×#126—431no—
428C2×#126—431no—
429C2×#126—431no—
430C2×#126—431no—
431C2×#126—861no—
432C2×#126—861no—
433C2×#126—861no—
434C2×#126—861no—
435C2×#126—861no—
436C2×#126—861no—
437C2×#126—861no—
438C2×#126—861no—
439C2×#126C2×D4311yescharacteristic
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C22⋊C4—431no—
444C22×C22⋊C4—431no—
445C22×C22⋊C4—431no—
446C22×C42—431no—
447#432—431no—
448#432—432no—
449#432—861no—
450#432—861no—
451#432C2×D4311yescharacteristic, complemented
452#431—431no—
453#431—432no—
454#431—861no—
455#431—861no—
456#431C2×D4311yescharacteristic, complemented
457#423—861no—
458#423—861no—
459#407—432no—
460#407—432no—
461C4×M16—861no—
462C4×M16—861no—
463#324—432no—
464#324—432no—
465#324—432no—
466#324C2×D4312yescomplemented
467#323—432no—
468#323—432no—
469#323—432no—
470#323C2×D4312yes—
471C43#1739811yescharacteristic, complemented, Sylow
472C25—431no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C2×M16—862no—
480C2×M16—862no—
481#126—21no—
482#126—21no—
483#126—21no—
484#126—21no—
485#126—861no—
486#126—861no—
487#126—861no—
488#126—861no—
489#126—861no—
490#126—861no—
491#126—861no—
492#126—861no—
493#126—861no—
494#126—861no—
495#126—861no—
496#126—861no—
497#126—861no—
498#126—861no—
499#126—861no—
500#126—861no—
501#126—861no—
502#126—861no—
503#126—861no—
504#126—861no—
505#126—861no—
506#126—861no—
507#126—861no—
508#126—861no—
509#126—861no—
510#126—861no—
511#126—861no—
512#126—861no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4C4×D4311yescharacteristic
535C2×C4⋊C4C4×D4311yescharacteristic
536C2×C4⋊C4C22×D4311yescharacteristic
537C2×C22⋊C4—431no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—431no—
540C2×C22⋊C4—431no—
541C2×C22⋊C4—431no—
542C2×C22⋊C4—431no—
543C2×C22⋊C4—431no—
544C2×C22⋊C4—431no—
545C2×C22⋊C4—431no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4C4×D4311yescharacteristic
559C2×C22⋊C4C4×D4311yescharacteristic
560C2×C22⋊C4C22×D4311yescharacteristic
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×C42C22×D4311yescharacteristic
573C4⋊C8—21no—
574C4⋊C8—21no—
575C4⋊C8—862no—
576C4⋊C8—862no—
577C4⋊C8—861no—
578C4⋊C8—861no—
579C22⋊C8—432no—
580C22⋊C8—432no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8C22×D4312yes—
584C22⋊C8C22×D4312yes—
585#97—21no—
586#97—862no—
587#97—861no—
588C4×C8—21no—
589C4×C8—862no—
590C4×C8—861no—
591C24—431no—
592C24—431no—
593C24—861no—
594C24—861no—
595C24—1722no—
596C24—1722no—
597C24—1722no—
598C24C2×C4×D4311yescharacteristic
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
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—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
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×C4C2×C4×D4311yescharacteristic
634C22×C4C23×D4311yescharacteristic
635M16—1724no—
636M16—1724no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—862no—
640C2×C8—862no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—861no—
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—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—861no—
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—
686C22⋊C4—861no—
687C22⋊C4—861no—
688C22⋊C4—861no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—431no—
701C42D4×D4311yescharacteristic
702C42D4×D4311yescharacteristic
703C42D4×D4311yescharacteristic
704C42D4×D4311yescharacteristic
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—431no—
710C23—431no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—861no—
716C23—3448no—
717C23—1721no—
718C23—1721no—
719C23—1722no—
720C23—1722no—
721C23—1722no—
722C23—1722no—
723C23—1722no—
724C23—1722no—
725C23C22×C4×D4311yescharacteristic
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—431no—
736C2×C4—431no—
737C2×C4—431no—
738C2×C4—431no—
739C2×C4—431no—
740C2×C4—431no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—862no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4C22⋊C4×D4311yescharacteristic
769C2×C4C22⋊C4×D4311yescharacteristic
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—41no—
781C22—41no—
782C22—41no—
783C22—82no—
784C22—432no—
785C22—432no—
786C22—868no—
787C22—861no—
788C22—861no—
789C22—861no—
790C22—861no—
791C22—3442no—
792C22—3444no—
793C22—3444no—
794C22—1721no—
795C22—1721no—
796C22—1721no—
797C22C2×C22⋊C4×D4311yescharacteristic
798C22#1458366412yes—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—861no—
809C4—861no—
810C4—861no—
811C4—861no—
812C4—861no—
813C4—861no—
814C4—1721no—
815C4—1721no—
816C4—1721no—
817C2—22no—
818C2—81no—
819C2—862no—
820C2—862no—
821C2—3441no—
822C2#1914303711yescharacteristic
823C2#410×D4311yescharacteristic
824C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1473C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1473D43
hypocenterC43#17398
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. #19143223C2semidirect
4. #19132965C2semidirect
5. #19132964C2semidirect
6. #19132963C2semidirect
7. #19132962C2semidirect
8. #19132961C2semidirect
9. #19132923C2semidirect
11. C43×#1473C2semidirect
34. #14582956C22semidirect
37. #14582953C22semidirect
38. #14582952C22semidirect
41. #14582949C22semidirect
48. #14582625C22semidirect
49. #14582624C22semidirect
50. #14582624C22semidirect
55. C43×#432C22semidirect
56. C43×#431C22semidirect
57. C43×#324C22semidirect
413. #1473D43semidirect
451. #432C2×D43semidirect
456. #431C2×D43semidirect
466. #324C2×D43semidirect
471. C43#17398semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D432
#191432252
#191432232
#191329652
#191329642
#191329632
#191329622
#191329612
#191329232
#191329202
C43×#14732
#1739843