Finite Group Databasebeta

← #25129013

Subgroups — #25129013

Order 11008.

1300 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583606C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic, complemented
3C2×#14582900C211yesmaximal, characteristic, complemented
4#19135736C211yesmaximal, characteristic, complemented
5#19135731C211yesmaximal, characteristic, complemented
6#19135603C211yesmaximal, characteristic, complemented
7#19135598C211yesmaximal, characteristic, complemented
8#19135026C211yesmaximal, characteristic, complemented
9#19134953C211yesmaximal, characteristic, complemented
10#19134939C211yesmaximal, characteristic, complemented
11#19134913C211yesmaximal, characteristic, complemented
12#19134903C211yesmaximal, characteristic, complemented
13#19134893C211yesmaximal, characteristic, complemented
14#19134679C211yesmaximal, characteristic, complemented
15C43×#2407C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19#14583606—24no—
20#14583606—24no—
21C2×#13063325C2211yescharacteristic
22C2×#13063316—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×#13063302—21no—
26C2×#13063302—21no—
27C2×C4×Dic86C2211yescharacteristic
28C2×D4×Dic43—21no—
29C22×C4⋊Dic43C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31#14583061—24no—
32#14582900—24no—
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#394—21no—
57C43×#392—21no—
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#386—21no—
61C43×#385—21no—
62C43×#380C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—41no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—41no—
73C2×#10621877—22no—
74C2×#10621877—41no—
75C2×#10621877—41no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063325—22no—
81#13063325—22no—
82#13063316—28no—
83#13063304—22no—
84#13063304—22no—
85#13063304—22no—
86#13063304D414yescomplemented
87#13063302—28no—
88#13063302—28no—
89C4×Dic86—22no—
90C4×Dic86—22no—
91D4×Dic43—28no—
92C2×C4⋊Dic43—22no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—22no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43D414yescomplemented
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C4×Dic43—21no—
108#13063249—22no—
109#13063249—22no—
110#13063249—22no—
111#13063248—41no—
112#13063248—41no—
113#13063246—22no—
114#13063246—22no—
115#13063246—22no—
116C22⋊(C43⋊C8)—22no—
117C22⋊(C43⋊C8)—41no—
118C22⋊(C43⋊C8)—41no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—41no—
124C2×#41×C43—41no—
125C22×Q8×C43C2311yescharacteristic
126C22×D4×C43—21no—
127C22×D4×C43—21no—
128C22×D4×C43D411yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C22⋊Q8×C43—22no—
134C22⋊Q8×C43—41no—
135#121×C43—22no—
136#121×C43—41no—
137C4×D4×C43—22no—
138C4×D4×C43—22no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43D411yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43D411yescharacteristic
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C42×C43C2311yescharacteristic
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157#41×C43—28no—
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×C43#4112yes—
167C2×D4×C43—22no—
168C2×D4×C43—21no—
169C2×D4×C43—22no—
170C2×D4×C43—22no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—42no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—81no—
181C2×D4×C43#4112yes—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43—42no—
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2411yescharacteristic
205C22×Dic43—24no—
206C22×Dic43—24no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—81no—
212C22×Dic43—81no—
213C22×Dic43—81no—
214C22×Dic43—81no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—24no—
221C2×Dic86—81no—
222C2×Dic86—81no—
223C2×Dic86C2×D412yes—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—42no—
230C22⋊C4×C43—22no—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—81no—
236C22⋊C4×C43—81no—
237C42×C43—21no—
238C42×C43—21no—
239C22⋊Dic43—24no—
240C22⋊Dic43—24no—
241#10621885—44no—
242#10621883—44no—
243C4⋊Dic43—24no—
244C4⋊Dic43—24no—
245C4⋊Dic43—24no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43C2×D412yes—
250C4⋊Dic43C2×D412yes—
251C4⋊Dic43C2×D412yes—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255C4×Dic43—24no—
256#10621877—44no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—22no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43#12012yes—
289C23×C43#13712yes—
290C23×C43C22×D411yescharacteristic
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—41no—
294Q8×C43—41no—
295D4×C43—28no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—48no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—84no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—48no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
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×C43#12012yes—
331C2×C4×C43#13712yes—
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C2×#4111yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43H(5,𝔽2)11yescharacteristic
337C2×C4×C43H(5,𝔽2)11yescharacteristic
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—84no—
351C2×Dic43—84no—
352Dic86—22no—
353Dic86—22no—
354Dic86—41no—
355Dic86—41no—
356Dic86—84no—
357C43⋊C8—41no—
358C43⋊C8—41no—
359C43⋊C8—41no—
360C43⋊C8—41no—
361#23981—431nomaximal, Sylow
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43C2×#12011yescharacteristic
384C22×C43#54611yescharacteristic
385C22×C43#54611yescharacteristic
386C22×C43C2×#13711yescharacteristic
387C22×C43C2×#13711yescharacteristic
388C22×C43#57611yescharacteristic
389C22×C43#57711yescharacteristic
390C4×C43—22no—
391C4×C43—22no—
392C4×C43—41no—
393C4×C43—42no—
394C4×C43—41no—
395C4×C43—81no—
396C4×C43—81no—
397C4×C43#52511yescharacteristic
398C4×C43#53511yescharacteristic
399C4×C43#54611yescharacteristic
400C4×C43#54611yescharacteristic
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404Dic43—42no—
405C2×#554—431no—
406C2×#452—431no—
407C2×#417—431no—
408#2407D4311yescharacteristic
409#2024—431no—
410#2023—431no—
411#2001—431no—
412#2000—431no—
413#1894—431no—
414#1880—431no—
415#1878—431no—
416#1874—431no—
417#1872—431no—
418#1870—431no—
419#1823—431no—
420C2×C43—42no—
421C2×C43—42no—
422C2×C43—82no—
423C2×C43#240411yescharacteristic
424C2×C43#300411yescharacteristic
425C2×C43#301211yescharacteristic
426C2×C43#331411yescharacteristic
427C2×C43#331611yescharacteristic
428C2×C43#333111yescharacteristic
429C2×C43#333311yescharacteristic
430C22×#41C2×D4311yescharacteristic
431C22×Q16—431no—
432C22×SD16—431no—
433C22×M16—431no—
434#554—864no—
435#554—864no—
436C2×C4⋊Q8—431no—
437C2×#125—861no—
438C2×C22⋊Q8—431no—
439C2×C22⋊Q8—431no—
440C2×C22⋊Q8—861no—
441C2×C22⋊Q8—861no—
442C2×C22⋊Q8C2×D4311yescharacteristic
443C2×#121C2×D4311yescharacteristic
444C2×C4×Q8—431no—
445C2×C4×D4—861no—
446C2×C4×D4C2×D4311yescharacteristic
447C22×C4⋊C4—431no—
448C22×C4⋊C4—431no—
449#452—864no—
450#417—864no—
451C2×#103—431no—
452C2×#103—431no—
453C2×#103—431no—
454C2×#103—431no—
455C2×#103—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461C2×C22⋊C8—431no—
462#394—21no—
463#392—21no—
464#391C2×D4311yescharacteristic
465#390C2×D4311yescharacteristic
466#386—21no—
467#385—21no—
468#380C2×D4311yescharacteristic
469#340—431no—
470#340—431no—
471#340—431no—
472#340—431no—
473#340—431no—
474#340—431no—
475#336—431no—
476#336—431no—
477C43#2398111yescharacteristic, complemented, Sylow
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C22×Q8—431no—
485C22×Q8—861no—
486C22×Q8C22×D4311yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4C22⋊D4311yescharacteristic
490C22×D4C22×D4311yescharacteristic
491C23×C4—21no—
492C23×C4—861no—
493C23×C4—861no—
494C23×C4C22×D4311yescharacteristic
495C23×C4C22×D4311yescharacteristic
496C2×Q16—862no—
497C2×Q16—862no—
498C2×Q16—1721no—
499C2×SD16—862no—
500C2×SD16—862no—
501C2×SD16—1721no—
502C2×M16—862no—
503C2×M16—1721no—
504C2×M16—1721no—
505C22×C8—431no—
506C22×C8—431no—
507C22×C8—431no—
508C22×C8—431no—
509C4⋊Q8—862no—
510C4⋊Q8—862no—
511#125—868no—
512C22⋊Q8—22no—
513C22⋊Q8—41no—
514C22⋊Q8—434no—
515C22⋊Q8—868no—
516C22⋊Q8—868no—
517C22⋊Q8—862no—
518C22⋊Q8—862no—
519C22⋊Q8—862no—
520#121—22no—
521#121—41no—
522C4×Q8—862no—
523C4×Q8—862no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—868no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—434no—
529C2×C4⋊C4—431no—
530C2×C4⋊C4—431no—
531C2×C4⋊C4—431no—
532C2×C4⋊C4—862no—
533C2×C4⋊C4—862no—
534C2×C4⋊C4—862no—
535C2×C4⋊C4—861no—
536C2×C4⋊C4—861no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4C22⋊D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4C22⋊D4311yescharacteristic
552C2×C22⋊C4C22⋊D4311yescharacteristic
553C2×C42—861no—
554C2×C42C22×D4311yescharacteristic
555#103—862no—
556#103—862no—
557#103—862no—
558#103—1721no—
559#103—1721no—
560#102—862no—
561#102—862no—
562#102—862no—
563C22⋊C8—862no—
564C22⋊C8—1721no—
565C22⋊C8—1721no—
566#95—21no—
567#95—21no—
568#95—21no—
569C24—21no—
570C24C2×C22⋊D4311yescharacteristic
571C24C2×C22⋊D4311yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—432no—
582C2×Q8—864no—
583C2×Q8—861no—
584C2×Q8—861no—
585C2×Q8—861no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—3441no—
589C2×Q8—3441no—
590C2×Q8#1062190012yes—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4#1062190012yes—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—864no—
623C22×C4—864no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—3441no—
629C22×C4—3441no—
630C22×C4—3441no—
631C22×C4—3441no—
632C22×C4D4×D4312yes—
633C22×C4D4×D4312yes—
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C2×C22⋊D4311yescharacteristic
636C22×C4C2×C22⋊D4311yescharacteristic
637C22×C4C2×C22⋊D4311yescharacteristic
638C22×C4C23×D4311yescharacteristic
639Q16—1724no—
640SD16—1724no—
641M16—1724no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8—861no—
650C2×C8—861no—
651C2×C8—861no—
652C2×C8—861no—
653C2×C8—861no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—42no—
660C4⋊C4—432no—
661C4⋊C4—432no—
662C4⋊C4—432no—
663C4⋊C4—864no—
664C4⋊C4—864no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—864no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—861no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—81no—
678C22⋊C4—81no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C42—21no—
682C42—21no—
683C42—864no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23#1306329312yes—
704C23#1306335512yes—
705C23C22×C22⋊D4311yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710Q8—862no—
711Q8—862no—
712Q8—3444no—
713Q8—1721no—
714Q8—1721no—
715D4—28no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—41no—
720D4—41no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—48no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—3444no—
755C2×C4—3444no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4#1306329312yes—
765C2×C4#1306335512yes—
766C2×C4C2×D4×D4311yescharacteristic
767C2×C4C2×D4×D4311yescharacteristic
768C2×C4C2×#1062190011yescharacteristic
769C2×C4C2×#1062190011yescharacteristic
770C2×C4#1306337011yescharacteristic
771C2×C4#1306337011yescharacteristic
772C8—1721no—
773C8—1721no—
774C8—1721no—
775C8—1721no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22C2×#1306329311yescharacteristic
798C22#1458354311yescharacteristic
799C22#1458354311yescharacteristic
800C22C2×#1306335511yescharacteristic
801C22C2×#1306335511yescharacteristic
802C22#1458370211yescharacteristic
803C22#1458370711yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—42no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—1722no—
812C4—1722no—
813C4—1722no—
814C4—1722no—
815C4#1458340511yescharacteristic
816C4#1458346411yescharacteristic
817C4#1458353611yescharacteristic
818C4#1458353611yescharacteristic
819C2—42no—
820C2—42no—
821C2—82no—
822C2#1913791111yescharacteristic
823C2#1914382811yescharacteristic
824C2#1914389611yescharacteristic
825C2#1914667611yescharacteristic
826C2#1914670611yescharacteristic
827C2#1914691111yescharacteristic
828C2#1914693311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2407C2
socleC23×C43C22×D4
hypercenter#2407D43
hypocenterC43#23981
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#14583606C2semidirect
2. C2×#14583061C2semidirect
3. C2×#14582900C2semidirect
4. #19135736C2semidirect
5. #19135731C2semidirect
6. #19135603C2semidirect
7. #19135598C2semidirect
8. #19135026C2semidirect
9. #19134953C2semidirect
10. #19134939C2semidirect
11. #19134913C2semidirect
12. #19134903C2semidirect
13. #19134893C2semidirect
14. #19134679C2semidirect
86. #13063304D4semidirect
98. C2×C4⋊Dic43D4semidirect
477. C43#23981semidirect

Maximal subgroups

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

subgroupindex
C2×#145836062
C2×#145830612
C2×#145829002
#191357362
#191357312
#191356032
#191355982
#191350262
#191349532
#191349392
#191349132
#191349032
#191348932
#191346792
C43×#24072
#2398143