Finite Group Databasebeta

← #25105718

Subgroups — #25105718

Order 11008.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic
2C2×#14582864C211yesmaximal, characteristic, complemented
3#19137184C211yesmaximal, characteristic, complemented
4#19135030C211yesmaximal, characteristic, complemented
5#19135025C211yesmaximal, characteristic, complemented
6#19135020C211yesmaximal, characteristic, complemented
7#19135015C211yesmaximal, characteristic, complemented
8#19134914C211yesmaximal, characteristic, complemented
9#19134909C211yesmaximal, characteristic, complemented
10#19134904C211yesmaximal, characteristic, complemented
11#19134899C211yesmaximal, characteristic, complemented
12#19134686C211yesmaximal, characteristic, complemented
13#19134679C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583477—24no—
20#14583477C418yescomplemented
21C2×#13063304—21no—
22C2×#13063301C2211yescharacteristic
23C2×#13063301C2211yescharacteristic
24C2×#13063299—21no—
25C2×#13063297—21no—
26C2×#13063297—21no—
27C2×#13063296C2211yescharacteristic
28C2×#13063296C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36#14582864—24no—
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40#14582803—21no—
41#14582799—21no—
42#14582777—21no—
43#14582775—21no—
44#14582759C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×#41×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C2×#10621898—41no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898C2×C414yes—
67C2×#10621898D414yes—
68C22×Dic86D411yescharacteristic
69C22×D172D411yescharacteristic
70C22×C22⋊D43—21no—
71C22×C22⋊D43—21no—
72C22×C22⋊D43D411yescharacteristic
73C22×C22⋊D43D411yescharacteristic
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C22×C4×D43C2311yescharacteristic
78C2×#10621872—22no—
79C2×#10621872—41no—
80C2×#10621872—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C2×C8×D43—22no—
84C2×C8×D43—41no—
85C2×C8×D43—41no—
86#13063304—28no—
87#13063301—22no—
88#13063301—22no—
89#13063301C2×C414yes—
90#13063301C2×C414yescomplemented
91#13063299—28no—
92#13063297—28no—
93#13063297—28no—
94#13063296—22no—
95#13063296—22no—
96#13063296C2×C414yes—
97#13063296C2×C414yescomplemented
98#13063283—41no—
99#13063283—41no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—22no—
102C2×C4⋊Dic43C2×C414yescomplemented
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C4⋊C4×D43—41no—
111C4⋊C4×D43—41no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×C4×Dic43—21no—
121#13063249—41no—
122#13063249—41no—
123#13063246—41no—
124#13063246—41no—
125C22⋊(C43⋊C8)—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C2×#41×C43—22no—
132C2×#41×C43—41no—
133C2×#41×C43—41no—
134C2×#41×C43—41no—
135C2×#41×C43—41no—
136C2×#41×C43C2×C414yescomplemented
137C22×Q8×C43C2311yescharacteristic
138C22×D4×C43—21no—
139C22×D4×C43C2311yescharacteristic
140C23×C4×C43—21no—
141C23×C4×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#103×C43—41no—
148#103×C43—41no—
149#102×C43—41no—
150#102×C43—41no—
151C22⋊C8×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155C23×D43C2×D411yescharacteristic
156C23×D43C2×D411yescharacteristic
157#41×C43—44no—
158#41×C43—44no—
159#41×C43—44no—
160#41×C43—44no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43C22×C412yes—
167C2×D4×C43—21no—
168C2×D4×C43—24no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—42no—
174C2×D4×C43—42no—
175C2×D4×C43C22×C412yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—24no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43C22×C412yes—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—41no—
193C2×C22⋊D43—41no—
194C2×C22⋊D43—41no—
195C2×C22⋊D43—41no—
196C2×C22⋊D43—81no—
197C2×C22⋊D43—81no—
198C2×C22⋊D43—81no—
199C2×C22⋊D43—81no—
200C2×C22⋊D43C22⋊C414yes—
201C2×C22⋊D43C22⋊C414yes—
202C22×Dic43—24no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—81no—
208C22×Dic43—81no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211#10621898—44no—
212#10621898—44no—
213#10621898—44no—
214#10621898—44no—
215C2×D172—41no—
216C2×D172—41no—
217C2×D172C22⋊C414yes—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—42no—
227C2×C4×D43—81no—
228C2×C4×D43—81no—
229C2×C4×D43C22×C412yes—
230C2×C4×D43C22×C412yes—
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2×D412yes—
233C2×Dic86—41no—
234C2×Dic86—41no—
235C2×Dic86C22⋊C414yes—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C22⋊C4×C43—81no—
247C22⋊Dic43—24no—
248C22⋊Dic43—24no—
249C22⋊Dic43—81no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—42no—
253(C2×D43)⋊C4—81no—
254(C2×D43)⋊C4—81no—
255C4⋊Dic43—24no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C22×C412yes—
263C4⋊Dic43C22×C412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—42no—
267C4×Dic43—42no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274#10621872—44no—
275C8×D43—44no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—22no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43C2×C22⋊C412yes—
290C23×C43C22×D411yescharacteristic
291C22×D43—21no—
292C22×D43—21no—
293C22×D43—21no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—21no—
303C22×D43C2×C22⋊C412yes—
304C22×D43C2×C22⋊C412yes—
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—41no—
308Q8×C43—41no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—48no—
312D4×C43—41no—
313D4×C43—41no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—48no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43C2×C22⋊C412yes—
331C2×C4×C43C23×C411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C2×C4×C43H(5,𝔽2)11yescharacteristic
337C22⋊D43—44no—
338C22⋊D43—44no—
339C22⋊D43—84no—
340C22⋊D43—84no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—84no—
358C2×Dic43C2×C22⋊C412yes—
359C2×Dic43C2×C22⋊C412yes—
360D172—44no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—22no—
367C4×D43—22no—
368C4×D43—22no—
369C4×D43—84no—
370Dic86—44no—
371C8×C43—41no—
372C8×C43—41no—
373C43⋊C8—41no—
374C43⋊C8—41no—
375#21772—431nomaximal, Sylow
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43C22×C22⋊C411yescharacteristic
391C22×C43#53411yescharacteristic
392C22×C43#53411yescharacteristic
393C22×C43#57611yescharacteristic
394C22×C43#57711yescharacteristic
395C22×C43#57711yescharacteristic
396C22×C43#57811yescharacteristic
397C2×D43—22no—
398C2×D43—22no—
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—41no—
411C4×C43—22no—
412C4×C43—42no—
413C4×C43—81no—
414C4×C43—81no—
415C4×C43#51811yescharacteristic
416C4×C43#51811yescharacteristic
417C4×C43#53411yescharacteristic
418C4×C43#53411yescharacteristic
419Dic43—22no—
420Dic43—22no—
421Dic43—42no—
422Dic43—42no—
423Dic43—81no—
424Dic43—81no—
425C2×#537—431no—
426C2×#408—431no—
427#2311—431no—
428#1895—431no—
429#1894—431no—
430#1893—431no—
431#1892—431no—
432#1875—431no—
433#1874—431no—
434#1873—431no—
435#1872—431no—
436#1824—431no—
437#1823—431no—
438#1788—431no—
439#1788D4311yescharacteristic, complemented
440C2×C43—42no—
441C2×C43—82no—
442C2×C43#230811yescharacteristic
443C2×C43#289711yescharacteristic
444C2×C43#289811yescharacteristic
445C2×C43#319811yescharacteristic
446C2×C43#320111yescharacteristic
447C2×C43#320311yescharacteristic
448C2×C43#320411yescharacteristic
449D43—42no—
450D43—42no—
451C22×#41—431no—
452C22×#41C2×D4311yescharacteristic
453C22×M16—431no—
454C23×C8—431no—
455#537—438no—
456#537—864no—
457C2×C22⋊Q8—431no—
458C2×C22⋊Q8—431no—
459C2×C22⋊Q8—861no—
460C2×#121—431no—
461C2×#121—431no—
462C2×#121—861no—
463C2×#121—861no—
464C2×#121—861no—
465C2×#117—431no—
466C22×C4⋊C4—431no—
467C22×C4⋊C4—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103C2×D4311yescharacteristic
471C2×#103C2×D4311yescharacteristic
472C2×#102—431no—
473C2×#102—431no—
474C2×#102C2×D4311yescharacteristic
475C2×#102C2×D4311yescharacteristic
476#408—864no—
477C2×C22⋊C8—431no—
478C2×C22⋊C8—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8C2×D4311yescharacteristic
481#391—861no—
482#390—861no—
483#386—861no—
484#386—861no—
485#380—431no—
486#380—431no—
487#380—431no—
488#380C2×D4311yescharacteristic
489#340—431no—
490#340—431no—
491#340—431no—
492#340—431no—
493#340—431no—
494#340—431no—
495#340—431no—
496#340—431no—
497C43#2177211yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—434no—
504C2×#41—434no—
505C2×#41—1721no—
506C2×#41—1721no—
507C2×#41—1721no—
508C2×#41—1721no—
509C2×#41C4×D4314yescomplemented
510C22×Q8—431no—
511C22×Q8C22×D4311yescharacteristic
512C22×D4—21no—
513C22×D4—431no—
514C22×D4—431no—
515C22×D4—431no—
516C22×D4—861no—
517C22×D4—861no—
518C22×D4C22×D4311yescharacteristic
519C23×C4—21no—
520C23×C4—431no—
521C23×C4—431no—
522C23×C4—861no—
523C23×C4—861no—
524C23×C4C22×D4311yescharacteristic
525C2×M16—862no—
526C2×M16—1721no—
527C2×M16—1721no—
528C22×C8—431no—
529C22×C8—431no—
530C22×C8—862no—
531C22×C8—1721no—
532C22×C8—1721no—
533C22×C8C22×D4311yescharacteristic
534C22×C8C22×D4311yescharacteristic
535C22⋊Q8—434no—
536C22⋊Q8—434no—
537C22⋊Q8—868no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540#121—434no—
541#121—434no—
542#121—868no—
543#121—862no—
544#121—862no—
545#121—868no—
546#121—868no—
547#117—1721no—
548#117—1721no—
549C2×C4⋊C4—434no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—862no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—1721no—
560C2×C4⋊C4—1721no—
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C42—861no—
573#103—41no—
574#103—41no—
575#103—1721no—
576#103—1721no—
577#102—41no—
578#102—41no—
579#102—1721no—
580#102—1721no—
581C22⋊C8—22no—
582C22⋊C8—862no—
583C22⋊C8—862no—
584C22⋊C8—862no—
585#95—21no—
586#95—861no—
587#95—861no—
588#95—861no—
589C24—21no—
590C24—431no—
591C24—431no—
592C24D4×D4311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—1724no—
598#41—1724no—
599#41—1724no—
600#41—1724no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—434no—
607C2×Q8—1721no—
608C2×Q8—1721no—
609C2×Q8C2×C4×D4312yes—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—434no—
619C2×D4—434no—
620C2×D4—434no—
621C2×D4—864no—
622C2×D4—864no—
623C2×D4—3441no—
624C2×D4—3441no—
625C2×D4—3441no—
626C2×D4—3441no—
627C2×D4—1721no—
628C2×D4—1721no—
629C2×D4—1721no—
630C2×D4—1721no—
631C2×D4—1721no—
632C2×D4—1721no—
633C2×D4C2×C4×D4312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—432no—
647C22×C4—432no—
648C22×C4—432no—
649C22×C4—432no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—864no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—3441no—
664C22×C4—3441no—
665C22×C4—3441no—
666C22×C4—3441no—
667C22×C4—1722no—
668C22×C4C2×C4×D4312yes—
669C22×C4D4×D4311yescharacteristic
670C22×C4D4×D4312yes—
671C22×C4C23×D4311yescharacteristic
672M16—1724no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—1724no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—432no—
691C4⋊C4—432no—
692C4⋊C4—864no—
693C4⋊C4—864no—
694C4⋊C4—864no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—1722no—
702C22⋊C4—81no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—3441no—
708C22⋊C4—3441no—
709C22⋊C4—3441no—
710C22⋊C4—1722no—
711C42—1722no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—432no—
726C23—432no—
727C23—861no—
728C23—861no—
729C23—861no—
730C23—861no—
731C23—861no—
732C23—861no—
733C23—861no—
734C23—861no—
735C23—861no—
736C23—861no—
737C23—861no—
738C23—861no—
739C23C22⋊C4×D4312yes—
740C23C2×D4×D4311yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—41no—
744Q8—41no—
745Q8—1724no—
746D4—22no—
747D4—22no—
748D4—48no—
749D4—41no—
750D4—41no—
751D4—3444no—
752D4—3444no—
753D4—1724no—
754D4—1724no—
755D4—1724no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—48no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—432no—
773C2×C4—432no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—861no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—3444no—
789C2×C4—3444no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4C22⋊C4×D4312yes—
801C2×C4C22×C4×D4311yescharacteristic
802C2×C4C2×D4×D4311yescharacteristic
803C2×C4#1306337011yescharacteristic
804C2×C4#1306337011yescharacteristic
805C2×C4#1306337011yescharacteristic
806C2×C4#1306337011yescharacteristic
807C8—41no—
808C8—41no—
809C8—1721no—
810C8—1721no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—862no—
826C22—862no—
827C22—862no—
828C22—862no—
829C22—862no—
830C22—862no—
831C22—1721no—
832C22—1721no—
833C22—1721no—
834C22—1721no—
835C22—1721no—
836C22—1721no—
837C22—1721no—
838C22—1721no—
839C22C2×C22⋊C4×D4311yescharacteristic
840C22#1458345911yescharacteristic
841C22#1458345911yescharacteristic
842C22#1458370311yescharacteristic
843C22#1458370611yescharacteristic
844C22#1458370811yescharacteristic
845C22#1458371311yescharacteristic
846C4—22no—
847C4—42no—
848C4—81no—
849C4—81no—
850C4—862no—
851C4—862no—
852C4—3441no—
853C4—3441no—
854C4—1722no—
855C4—1722no—
856C4#1458337211yescharacteristic
857C4#1458337211yescharacteristic
858C4#1458345911yescharacteristic
859C4#1458345911yescharacteristic
860C2—42no—
861C2—82no—
862C2—1722no—
863C2—1722no—
864C2#1913717111yescharacteristic
865C2#1914311911yescharacteristic
866C2#1914312411yescharacteristic
867C2#1914544611yescharacteristic
868C2#1914547611yescharacteristic
869C2#1914549411yescharacteristic
870C2#1914550311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583477C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#21772
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14582864C2semidirect
3. #19137184C2semidirect
4. #19135030C2semidirect
5. #19135025C2semidirect
6. #19135020C2semidirect
7. #19135015C2semidirect
8. #19134914C2semidirect
9. #19134909C2semidirect
10. #19134904C2semidirect
11. #19134899C2semidirect
12. #19134686C2semidirect
13. #19134679C2semidirect
14. #19134535C2semidirect
15. C43×#1788C2semidirect
20. #14583477C4semidirect
90. #13063301C2×C4semidirect
97. #13063296C2×C4semidirect
102. C2×C4⋊Dic43C2×C4semidirect
136. C2×#41×C43C2×C4semidirect
439. #1788D43semidirect
497. C43#21772semidirect
509. C2×#41C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
C2×#145828642
#191371842
#191350302
#191350252
#191350202
#191350152
#191349142
#191349092
#191349042
#191348992
#191346862
#191346792
#191345352
C43×#17882
#2177243