Finite Group Databasebeta

← #25130549

Subgroups — #25130549

Order 11008.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic
2C2×#14583192C211yesmaximal, characteristic, complemented
3C2×Q16×Dic43C211yesmaximal, characteristic, complemented
4#19139514C211yesmaximal, characteristic
5#19135797C211yesmaximal, characteristic, complemented
6#19135795C211yesmaximal, characteristic, complemented
7#19135602C211yesmaximal, characteristic, complemented
8#19135554C211yesmaximal, characteristic, complemented
9#19135387C211yesmaximal, characteristic
10#19134903C211yesmaximal, characteristic, complemented
11#19134899C211yesmaximal, characteristic, complemented
12#19134785C211yesmaximal, characteristic, complemented
13#19134784C211yesmaximal, characteristic, complemented
14#19134598C211yesmaximal, characteristic, complemented
15C43×#2001C211yesmaximal, characteristic, complemented
16#14583607—24no—
17#14583607—24no—
18C2×#13063324C2211yescharacteristic
19C2×#13063315—21no—
20C2×#13063305—21no—
21C2×#13063302—21no—
22C2×#13063301C2211yescharacteristic
23C2×#13063301C2211yescharacteristic
24C2×Q8×Dic43C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×C4×C22⋊D43C2211yescharacteristic
27C2×(C22⋊D43)⋊C4—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14583192—24no—
31Q16×Dic43—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44#14582822—21no—
45#14582821—21no—
46#14582799—21no—
47#14582794—21no—
48#14582768C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×C22⋊D43D411yescharacteristic
65C23×Dic43—21no—
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063324—22no—
71#13063324D414yes—
72#13063315—28no—
73#13063305—28no—
74#13063302—28no—
75#13063301—22no—
76#13063301—22no—
77#13063301—22no—
78#13063301—41no—
79Q8×Dic43—22no—
80Q8×Dic43—22no—
81Q8×Dic43—22no—
82Q8×Dic43D414yes—
83C4×C22⋊D43—22no—
84C4×C22⋊D43—22no—
85(C22⋊D43)⋊C4—28no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4D411yescharacteristic
102C4⋊C4×D43—22no—
103C4⋊C4×D43—22no—
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×Dic43C2311yescharacteristic
113#13063259—22no—
114#13063259—22no—
115#13063258—22no—
116Dic43⋊C8—22no—
117#13063249—22no—
118#13063249—22no—
119#13063249—22no—
120#13063249—41no—
121C22⋊(C43⋊C8)—41no—
122(C2×D43)⋊C8—22no—
123(C2×D43)⋊C8—41no—
124C8×Dic43—22no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×Q8×C43C2311yescharacteristic
128C22×Q8×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C2×Q16×C43—22no—
131C2×Q16×C43—22no—
132C2×Q16×C43—22no—
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22⋊Q8×C43—22no—
136C22⋊Q8×C43—22no—
137C22⋊Q8×C43—22no—
138C22⋊Q8×C43—41no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145#103×C43—22no—
146#103×C43—41no—
147C22⋊C8×C43—22no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C2×D412yes—
161C2×Q8×C43#4112yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2411yescharacteristic
174C2×C22⋊D43—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43Q1614yescomplemented
177C22×Dic43—24no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—81no—
183C22×Dic43—81no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—24no—
194C2×C4×D43—81no—
195C2×C4×D43—81no—
196C2×Dic86—24no—
197C2×Dic86—81no—
198C2×Dic86—81no—
199Q16×C43—28no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43#4112yes—
206C4⋊C4×C43—24no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—42no—
211C4⋊C4×C43C2×D412yes—
212C22⋊C4×C43—24no—
213C22⋊C4×C43—42no—
214C22⋊Dic43—22no—
215C22⋊Dic43—81no—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—22no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—81no—
220C4⋊Dic43—24no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—24no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—42no—
229C4⋊Dic43C2×D412yes—
230C4⋊Dic43C2×D412yes—
231Dic43⋊C4—24no—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4—22no—
235Dic43⋊C4—42no—
236Dic43⋊C4—42no—
237Dic43⋊C4—81no—
238C4×Dic43—24no—
239C4×Dic43—42no—
240C4×Dic43C2×D412yes—
241C4×Dic43C2×D412yes—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43C2×Q1612yes—
255C23×C43C22×D411yescharacteristic
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43C2×Q1612yes—
263Q8×C43—22no—
264Q8×C43—22no—
265Q8×C43—22no—
266Q8×C43—22no—
267Q8×C43—41no—
268Q8×C43—41no—
269Q8×C43—41no—
270Q8×C43—41no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—21no—
274C2×C4×C43—22no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C432−1+411yescharacteristic
296C22⋊D43—28no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—22no—
300C2×Dic43—21no—
301C2×Dic43—22no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—84no—
315C2×Dic43#12012yes—
316C2×Dic43#12012yes—
317C2×Dic43C2×Q1612yes—
318C2×Dic43#13712yes—
319C4×D43—41no—
320C4×D43—41no—
321C4×D43—41no—
322C4×D43—41no—
323C4×D43—84no—
324Dic86—84no—
325C8×C43—22no—
326C8×C43—41no—
327C43⋊C8—41no—
328C43⋊C8—41no—
329#24122—431nomaximal, Sylow
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43C2×#12011yescharacteristic
338C22×C43#54611yescharacteristic
339C22×C43#54711yescharacteristic
340C22×C43C22×Q1611yescharacteristic
341C22×C43C2×#13711yescharacteristic
342C22×C43#57611yescharacteristic
343C22×C43#57711yescharacteristic
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—41no—
351C4×C43—41no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43—81no—
356C4×C43#52511yescharacteristic
357C4×C43#53711yescharacteristic
358C4×C43#54811yescharacteristic
359C4×C43#55011yescharacteristic
360Dic43—22no—
361Dic43—41no—
362Dic43—42no—
363Dic43—42no—
364Dic43—81no—
365Dic43—81no—
366Dic43#45114yes—
367C2×#554—431no—
368C2×#477—431no—
369C2×C4×Q16—431no—
370#2538—431no—
371#2036—431no—
372#2036—431no—
373#2001—431no—
374#2001D4311yescharacteristic, complemented
375#1990—431no—
376#1954—431no—
377#1872—431no—
378#1872—431no—
379#1852—431no—
380#1852—431no—
381#1803—431no—
382C2×C43—42no—
383C2×C43#240711yescharacteristic
384C2×C43C2×#45111yescharacteristic
385C2×C43#301211yescharacteristic
386C2×C43#329911yescharacteristic
387C2×C43#333311yescharacteristic
388C2×C43#333811yescharacteristic
389C2×C43#335611yescharacteristic
390D43—42no—
391C22×Q16C2×D4311yescharacteristic
392#554—864no—
393#554—864no—
394C2×C4⋊Q8—431no—
395C2×#125—861no—
396C2×C22⋊Q8—431no—
397C2×C22⋊Q8—431no—
398C2×C22⋊Q8—861no—
399C2×C22⋊Q8—861no—
400C2×C22⋊Q8C2×D4311yescharacteristic
401C2×C22⋊Q8C2×D4311yescharacteristic
402C2×C4×Q8—431no—
403C2×C4×Q8—431no—
404C2×C4×D4—431no—
405C2×C4×D4—861no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4—431no—
408#477—864no—
409C4×Q16—864no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×C4⋊C8—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103C2×D4311yescharacteristic
419C2×#103C2×D4311yescharacteristic
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422C2×C22⋊C8—431no—
423C2×C22⋊C8C2×D4311yescharacteristic
424C2×C4×C8—431no—
425#396—861no—
426#396—861no—
427#390—861no—
428#389—861no—
429#384—431no—
430#380—431no—
431#380—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#340—431no—
437#340C2×D4311yescharacteristic
438C43#2412211yescharacteristic, complemented, Sylow
439C22×Q8—861no—
440C22×Q8C22×D4311yescharacteristic
441C22×Q8C22×D4311yescharacteristic
442C22×D4—431no—
443C23×C4—431no—
444C23×C4—861no—
445C23×C4—861no—
446C23×C4C22×D4311yescharacteristic
447C2×Q16—22no—
448C2×Q16—22no—
449C2×Q16—22no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8C22×D4311yescharacteristic
453C22×C8C22×D4311yescharacteristic
454C4⋊Q8—434no—
455C4⋊Q8—862no—
456#125—868no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—41no—
461C22⋊Q8—868no—
462C22⋊Q8—868no—
463C22⋊Q8—862no—
464C22⋊Q8—862no—
465C22⋊Q8—862no—
466C22⋊Q8—1721no—
467C4×Q8—434no—
468C4×Q8—862no—
469C4×Q8—862no—
470C4×Q8—862no—
471C4×D4—862no—
472C4×D4—862no—
473C4×D4—868no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—862no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4C22×D4311yescharacteristic
495C2×C4⋊C4C22×D4311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—431no—
499C2×C22⋊C4—431no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C42—431no—
505C2×C42—861no—
506C2×C42—861no—
507#107—862no—
508#107—862no—
509#107—862no—
510C4⋊C8—862no—
511#103—22no—
512#103—41no—
513#103—862no—
514#103—862no—
515#103—862no—
516#103—1721no—
517C22⋊C8—22no—
518C22⋊C8—862no—
519C22⋊C8—1721no—
520C22⋊C8—1721no—
521C4×C8—862no—
522#95—861no—
523#95—861no—
524C24—431no—
525C24D4×D4311yescharacteristic
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—864no—
537C2×Q8—3441no—
538C2×Q8—3441no—
539C2×Q8D4×D4312yes—
540C2×Q8#1062190012yes—
541C2×D4—434no—
542C2×D4—862no—
543C2×D4—862no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—864no—
558C22×C4—864no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—3441no—
570C22×C4—3441no—
571C22×C4—3441no—
572C22×C4—3441no—
573C22×C4D4×D4311yescharacteristic
574C22×C4C23×D4311yescharacteristic
575Q16—28no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8#1062190012yes—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—432no—
594C4⋊C4—432no—
595C4⋊C4—862no—
596C4⋊C4—864no—
597C4⋊C4—864no—
598C4⋊C4—864no—
599C4⋊C4—864no—
600C4⋊C4—864no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—3441no—
608C4⋊C4—1722no—
609C4⋊C4—1722no—
610C4⋊C4—1722no—
611C4⋊C4D4×D4312yes—
612C22⋊C4—24no—
613C22⋊C4—42no—
614C22⋊C4—862no—
615C22⋊C4—864no—
616C22⋊C4—862no—
617C22⋊C4—3441no—
618C22⋊C4—3441no—
619C22⋊C4—1722no—
620C42—432no—
621C42—432no—
622C42—864no—
623C42—1722no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—432no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23Q16×D4312yes—
638C23C2×D4×D4311yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—3444no—
648D4—868no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—432no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—3444no—
680C2×C4—3444no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4C2×D4×D4311yescharacteristic
696C2×C4C2×D4×D4311yescharacteristic
697C2×C4C2×#1062190011yescharacteristic
698C2×C4C2×#1062190011yescharacteristic
699C2×C4#1306337011yescharacteristic
700C2×C4#1306337211yescharacteristic
701C8—22no—
702C8—41no—
703C8—1721no—
704C8—1721no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—862no—
713C22—862no—
714C22—862no—
715C22—1721no—
716C22—1721no—
717C22—1721no—
718C22—1721no—
719C22#120×D4311yescharacteristic
720C22#1458353611yescharacteristic
721C22#1458354911yescharacteristic
722C22C2×Q16×D4311yescharacteristic
723C22#137×D4311yescharacteristic
724C22#1458370111yescharacteristic
725C22#1458370811yescharacteristic
726C4—41no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—81no—
731C4—434no—
732C4—862no—
733C4—3441no—
734C4—3441no—
735C4—1721no—
736C4—1722no—
737C4—1722no—
738C4#1458340511yescharacteristic
739C4#1458347611yescharacteristic
740C4#1458355511yescharacteristic
741C4#1458356911yescharacteristic
742C2—42no—
743C2—1722no—
744C2#1913793311yescharacteristic
745C2#451×D4311yescharacteristic
746C2#1914390311yescharacteristic
747C2#1914646411yescharacteristic
748C2#1914692611yescharacteristic
749C2#1914698411yescharacteristic
750C2#1914720511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2001C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#2001D43
hypocenterC43#24122
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#14583192C2semidirect
3. C2×Q16×Dic43C2semidirect
5. #19135797C2semidirect
6. #19135795C2semidirect
7. #19135602C2semidirect
8. #19135554C2semidirect
10. #19134903C2semidirect
11. #19134899C2semidirect
12. #19134785C2semidirect
13. #19134784C2semidirect
14. #19134598C2semidirect
15. C43×#2001C2semidirect
176. C2×C22⋊D43Q16semidirect
374. #2001D43semidirect
438. C43#24122semidirect

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145831922
C2×Q16×Dic432
#191395142
#191357972
#191357952
#191356022
#191355542
#191353872
#191349032
#191348992
#191347852
#191347842
#191345982
C43×#20012
#2412243