Finite Group Databasebeta

← #25130516

Subgroups — #25130516

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583620C211yesmaximal, characteristic, complemented
2C2×#14583177C211yesmaximal, characteristic, complemented
3C2×SD16×Dic43C211yesmaximal, characteristic, complemented
4#19139509C211yesmaximal, characteristic
5#19135797C211yesmaximal, characteristic, complemented
6#19135795C211yesmaximal, characteristic, complemented
7#19135595C211yesmaximal, characteristic, complemented
8#19135554C211yesmaximal, characteristic, complemented
9#19135387C211yesmaximal, characteristic, complemented
10#19134918C211yesmaximal, characteristic, complemented
11#19134914C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134795C211yesmaximal, characteristic, complemented
14#19134598C211yesmaximal, characteristic, complemented
15C43×#2000C211yesmaximal, characteristic, complemented
16#14583620—24no—
17#14583620—24no—
18C2×#13063324C2211yescharacteristic
19C2×#13063320—21no—
20C2×#13063318—21no—
21C2×#13063311—21no—
22C2×#13063301C2211yescharacteristic
23C2×#13063297—21no—
24C2×#13063296C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×#13063290—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31#14583177—24no—
32SD16×Dic43—24no—
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×#13063257C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582814—21no—
46#14582813—21no—
47#14582768C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582757—21no—
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×C22⋊D43—21no—
65C22×C22⋊D43D411yescharacteristic
66C23×Dic43—21no—
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063324—22no—
71#13063324D414yescomplemented
72#13063320—28no—
73#13063318—28no—
74#13063311—28no—
75#13063301—22no—
76#13063301—22no—
77#13063297—44no—
78#13063296—22no—
79#13063296—41no—
80Q8×Dic43—22no—
81Q8×Dic43D414yescomplemented
82#13063290—28no—
83D4×Dic43—22no—
84D4×Dic43—22no—
85C4×C22⋊D43—22no—
86C4×C22⋊D43—22no—
87#13063284—22no—
88#13063284—22no—
89#13063283—22no—
90#13063283—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4D411yescharacteristic
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43D411yescharacteristic
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114#13063259—22no—
115#13063258—22no—
116#13063257—22no—
117Dic43⋊C8—22no—
118#13063249—22no—
119#13063249—41no—
120#13063246—22no—
121#13063246—22no—
122C22⋊(C43⋊C8)—41no—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—41no—
125C8×Dic43—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×Q8×C43C2311yescharacteristic
129C22×D4×C43—21no—
130C22×D4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C2×SD16×C43—22no—
133C2×SD16×C43—22no—
134C2×SD16×C43—22no—
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22⋊Q8×C43—22no—
138C22⋊Q8×C43—22no—
139#121×C43—22no—
140#121×C43—41no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146#103×C43—41no—
147#102×C43—22no—
148C22⋊C8×C43—22no—
149C24×C43—21no—
150C24×C43C2×D411yescharacteristic
151C23×D43C2×D411yescharacteristic
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43C2×D412yes—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—81no—
166C2×D4×C43#4112yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2411yescharacteristic
178C2×C22⋊D43—22no—
179C2×C22⋊D43—22no—
180C2×C22⋊D43—22no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—81no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×Dic86—24no—
201C2×Dic86—42no—
202C2×Dic86—42no—
203SD16×C43—28no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43#4112yes—
210C4⋊C4×C43—24no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43C2×D412yes—
215C22⋊C4×C43—24no—
216C22⋊C4×C43—42no—
217C22⋊Dic43—24no—
218C22⋊Dic43—22no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—42no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—24no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43C2×D412yes—
234C4⋊Dic43C2×D412yes—
235Dic43⋊C4—24no—
236Dic43⋊C4—24no—
237Dic43⋊C4—22no—
238Dic43⋊C4—42no—
239Dic43⋊C4—81no—
240C4×Dic43—24no—
241C4×Dic43—24no—
242C4×Dic43—24no—
243C4×Dic43C2×D412yes—
244C4×Dic43C2×D412yes—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C23×C43—21no—
252C23×C43—22no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43C22×D411yescharacteristic
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43—41no—
276Q8×C43—41no—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—84no—
282C2×C4×C43—21no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C432−1+411yescharacteristic
304C22⋊D43—44no—
305C22⋊D43—84no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—22no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—84no—
324C2×Dic43#12012yes—
325C2×Dic43#12012yes—
326C2×Dic43#13512yes—
327C2×Dic43AGL(1,ℤ/8)12yes—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—41no—
331C4×D43—41no—
332Dic86—48no—
333C8×C43—22no—
334C8×C43—41no—
335C43⋊C8—41no—
336C43⋊C8—41no—
337#24119—431nomaximal, Sylow
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—42no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43C2×#12011yescharacteristic
353C22×C43#54611yescharacteristic
354C22×C43#54711yescharacteristic
355C22×C43C2×#13511yescharacteristic
356C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C43#57711yescharacteristic
358C22×C43#57811yescharacteristic
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—41no—
363C2×D43—41no—
364C2×D43—41no—
365C2×D43—41no—
366C4×C43—41no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—81no—
370C4×C43#52511yescharacteristic
371C4×C43#53711yescharacteristic
372C4×C43#54811yescharacteristic
373C4×C43#55011yescharacteristic
374Dic43—22no—
375Dic43—41no—
376Dic43—42no—
377Dic43—42no—
378Dic43—81no—
379Dic43—81no—
380Dic43#44914yes—
381C2×#556—431no—
382C2×#474—431no—
383C2×C4×SD16—431no—
384#2537—431no—
385#2036—431no—
386#2036—431no—
387#2000—431no—
388#2000D4311yescharacteristic, complemented
389#1990—431no—
390#1954—431no—
391#1875—431no—
392#1875—431no—
393#1854—431no—
394#1854—431no—
395#1803—431no—
396C2×C43—81no—
397C2×C43—82no—
398C2×C43#240711yescharacteristic
399C2×C43C2×#44911yescharacteristic
400C2×C43#301311yescharacteristic
401C2×C43#330211yescharacteristic
402C2×C43#332411yescharacteristic
403C2×C43#334011yescharacteristic
404C2×C43#335311yescharacteristic
405D43—81no—
406C22×SD16C2×D4311yescharacteristic
407#556—864no—
408#556—864no—
409C2×C4⋊Q8—431no—
410C2×#126—861no—
411C2×#126—861no—
412C2×#124—861no—
413C2×C22⋊Q8—431no—
414C2×C22⋊Q8C2×D4311yescharacteristic
415C2×#121—431no—
416C2×#121—861no—
417C2×#121C2×D4311yescharacteristic
418C2×C4×Q8—431no—
419C2×C4×Q8—861no—
420C2×C4×D4—431no—
421C2×C4×D4—431no—
422C2×#117—431no—
423C2×#117—431no—
424#474—864no—
425C4×SD16—864no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#106—431no—
429C2×C4⋊C8—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103C2×D4311yescharacteristic
433C2×#102—431no—
434C2×#102—431no—
435C2×#102C2×D4311yescharacteristic
436C2×C22⋊C8—431no—
437C2×C22⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8C2×D4311yescharacteristic
440C2×C4×C8—431no—
441#394—861no—
442#394—861no—
443#384—431no—
444#380—431no—
445#380—431no—
446#380—861no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452#340C2×D4311yescharacteristic
453C43#2411911yescharacteristic, complemented, Sylow
454C22×Q8—861no—
455C22×Q8C22×D4311yescharacteristic
456C22×D4—21no—
457C22×D4—431no—
458C22×D4—861no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—431no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C22×C8—431no—
467C22×C8—431no—
468C22×C8C22×D4311yescharacteristic
469C22×C8C22×D4311yescharacteristic
470C4⋊Q8—434no—
471C4⋊Q8—862no—
472#126—868no—
473#126—868no—
474#124—868no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—862no—
478C22⋊Q8—862no—
479#121—22no—
480#121—41no—
481#121—862no—
482#121—1721no—
483#121—1724no—
484C4×Q8—434no—
485C4×Q8—862no—
486C4×Q8—868no—
487C4×D4—862no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—862no—
491#117—862no—
492#117—862no—
493#117—862no—
494#117—862no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C42—431no—
520C2×C42—861no—
521C2×C42—861no—
522C2×C42—861no—
523#107—862no—
524#107—862no—
525#106—862no—
526C4⋊C8—862no—
527#103—41no—
528#103—862no—
529#103—1721no—
530#102—22no—
531#102—862no—
532#102—862no—
533C22⋊C8—22no—
534C22⋊C8—862no—
535C22⋊C8—1721no—
536C22⋊C8—1721no—
537C4×C8—862no—
538#95—861no—
539#95—861no—
540C24—21no—
541C24—431no—
542C24D4×D4311yescharacteristic
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—864no—
549C2×Q8—1722no—
550C2×Q8—1722no—
551C2×Q8D4×D4312yes—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—81no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—3441no—
564C2×D4—1722no—
565C2×D4—1722no—
566C2×D4#1062190012yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—1722no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4D4×D4311yescharacteristic
593C22×C4C23×D4311yescharacteristic
594SD16—28no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8#1062190012yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—432no—
612C4⋊C4—432no—
613C4⋊C4—862no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—3441no—
624C4⋊C4—1722no—
625C4⋊C4D4×D4312yes—
626C22⋊C4—24no—
627C22⋊C4—42no—
628C22⋊C4—862no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—862no—
632C22⋊C4—864no—
633C22⋊C4—1722no—
634C22⋊C4—1722no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C42—432no—
638C42—432no—
639C42—864no—
640C42—864no—
641C42—864no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—861no—
657C23—861no—
658C23—861no—
659C23—861no—
660C23—861no—
661C23—861no—
662C23—861no—
663C23C2×D4×D4311yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—41no—
667Q8—41no—
668Q8—1728no—
669D4—22no—
670D4—22no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—3444no—
675D4—1724no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—432no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—862no—
699C2×C4—861no—
700C2×C4—862no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—3444no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4C2×D4×D4311yescharacteristic
719C2×C4C2×D4×D4311yescharacteristic
720C2×C4C2×#1062190011yescharacteristic
721C2×C4C2×#1062190011yescharacteristic
722C2×C4#1306337011yescharacteristic
723C2×C4#1306337211yescharacteristic
724C8—22no—
725C8—41no—
726C8—1721no—
727C8—1721no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—1721no—
743C22—1721no—
744C22—1721no—
745C22—1721no—
746C22—1721no—
747C22—1721no—
748C22—1721no—
749C22#120×D4311yescharacteristic
750C22#1458353611yescharacteristic
751C22#1458354911yescharacteristic
752C22#135×D4311yescharacteristic
753C22AGL(1,ℤ/8)×D4311yescharacteristic
754C22#1458370511yescharacteristic
755C22#1458371511yescharacteristic
756C4—42no—
757C4—41no—
758C4—42no—
759C4—81no—
760C4—434no—
761C4—862no—
762C4—3441no—
763C4—3441no—
764C4—1722no—
765C4—1721no—
766C4—1722no—
767C4#1458340511yescharacteristic
768C4#1458347611yescharacteristic
769C4#1458355511yescharacteristic
770C4#1458356911yescharacteristic
771C2—81no—
772C2—82no—
773C2—3441no—
774C2#1913793311yescharacteristic
775C2#449×D4311yescharacteristic
776C2#1914390511yescharacteristic
777C2#1914650511yescharacteristic
778C2#1914681911yescharacteristic
779C2#1914700311yescharacteristic
780C2#1914717411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2000C2
socleC23×C43C22×D4
prime radical#19139509C2
hypercenter#2000D43
hypocenterC43#24119
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#14583620C2semidirect
2. C2×#14583177C2semidirect
3. C2×SD16×Dic43C2semidirect
5. #19135797C2semidirect
6. #19135795C2semidirect
7. #19135595C2semidirect
8. #19135554C2semidirect
9. #19135387C2semidirect
10. #19134918C2semidirect
11. #19134914C2semidirect
12. #19134796C2semidirect
13. #19134795C2semidirect
14. #19134598C2semidirect
15. C43×#2000C2semidirect
71. #13063324D4semidirect
81. Q8×Dic43D4semidirect
388. #2000D43semidirect
453. C43#24119semidirect

Maximal subgroups

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

subgroupindex
C2×#145836202
C2×#145831772
C2×SD16×Dic432
#191395092
#191357972
#191357952
#191355952
#191355542
#191353872
#191349182
#191349142
#191347962
#191347952
#191345982
C43×#20002
#2411943