Finite Group Databasebeta

← #25129582

Subgroups — #25129582

Order 11008.

1344 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×#14583556C211yesmaximal, characteristic
2C2×#14583216C211yesmaximal, characteristic, complemented
3C2×#103×D43C211yesmaximal, characteristic, complemented
4#19138908C211yesmaximal, characteristic, complemented
5#19135835C211yesmaximal, characteristic, complemented
6#19135834C211yesmaximal, characteristic, complemented
7#19135792C211yesmaximal, characteristic, complemented
8#19135791C211yesmaximal, characteristic, complemented
9#19135020C211yesmaximal, characteristic, complemented
10#19134884C211yesmaximal, characteristic, complemented
11#19134865C211yesmaximal, characteristic, complemented
12#19134861C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583556—24no—
19#14583556—24no—
20C2×#13063312—21no—
21C2×#13063312C2211yescharacteristic
22C2×#13063304—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063296—21no—
25C2×#13063296C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14583216—24no—
31C2×#13063257C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39#103×D43—24no—
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44#14582840—21no—
45#14582835—21no—
46#14582798C2211yescharacteristic
47#14582795C2211yescharacteristic
48#14582775—21no—
49#14582773—21no—
50#14582759C2211yescharacteristic
51#14582756C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×#41×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—41no—
69C2×Q8×D43—41no—
70C2×Q8×D43D414yes—
71C22×C22⋊D43—21no—
72C22×C22⋊D43D411yescharacteristic
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—22no—
79C2×C8×D43—41no—
80C2×C8×D43—41no—
81#13063312—28no—
82#13063312—22no—
83#13063312—22no—
84#13063304—28no—
85#13063304—22no—
86#13063304—22no—
87#13063296—28no—
88#13063296—22no—
89#13063296D414yes—
90Q8×Dic43—22no—
91Q8×Dic43—22no—
92C4×C22⋊D43—28no—
93C4×C22⋊D43—22no—
94C4×C22⋊D43—22no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4D411yescharacteristic
104C4⋊C4×D43—22no—
105C4⋊C4×D43—22no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116#13063257—22no—
117#13063256—22no—
118#13063250—22no—
119#13063250—41no—
120#13063249—22no—
121#13063249—22no—
122#13063248—22no—
123#13063248—41no—
124#13063246—22no—
125#13063246—41no—
126C22⋊(C43⋊C8)—41no—
127(C2×D43)⋊C8—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C2×#41×C43—22no—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—41no—
137C2×#41×C43—41no—
138C22×Q8×C43C2311yescharacteristic
139C22×D4×C43—21no—
140C22×D4×C43C2311yescharacteristic
141C23×C4×C43—21no—
142C23×C4×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C22⋊C4×C43—21no—
148#103×C43—22no—
149#103×C43—22no—
150#102×C43—22no—
151#102×C43—41no—
152C22⋊C8×C43—41no—
153#95×C43—21no—
154C24×C43—21no—
155C24×C43C2×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×C43C2×D412yes—
165C2×Q8×C43#4112yes—
166C2×Q8×C43#4112yes—
167C2×D4×C43—24no—
168C2×D4×C43—21no—
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×C43C2×D412yes—
176C22×C4×C43—24no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—22no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—22no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203Q8×D43—28no—
204Q8×D43—44no—
205Q8×D43—44no—
206Q8×D43—44no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—24no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43—42no—
215C2×C4×D43—81no—
216C2×C4×D43—81no—
217C2×C4×D43C2×D412yes—
218C2×C4×D43C2×D412yes—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—24no—
225C2×Dic86—42no—
226C2×Dic86—42no—
227C2×Dic86C2×D412yes—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C22⋊C4×C43—81no—
239C22⋊Dic43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43—22no—
244C22⋊Dic43—81no—
245(C2×D43)⋊C4—22no—
246(C2×D43)⋊C4—42no—
247C4⋊Dic43—24no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—81no—
254C4⋊Dic43C2×D412yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—22no—
257Dic43⋊C4—42no—
258Dic43⋊C4—81no—
259C4×Dic43—24no—
260C4×Dic43—21no—
261C4×Dic43—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—
268C8×D43—44no—
269C23×C43—21no—
270C23×C43—22no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43C22×D411yescharacteristic
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43#12012yes—
289C22×D43#13512yes—
290C22×D43#13712yes—
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—22no—
294Q8×C43#12314yes—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—48no—
298D4×C43—41no—
299D4×C43—41no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—48no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C22⋊D43—44no—
324C22⋊D43—48no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43#12012yes—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—48no—
351C4×D43—84no—
352Dic86—22no—
353Dic86—22no—
354Dic86—48no—
355Dic86—41no—
356Dic86—41no—
357C8×C43—41no—
358C8×C43—41no—
359C43⋊C8—41no—
360C43⋊C8—41no—
361#24036—431nomaximal, Sylow
362C22×C43—41no—
363C22×C43—42no—
364C22×C43—41no—
365C22×C43—42no—
366C22×C43—41no—
367C22×C43—42no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43C2×#12011yescharacteristic
377C22×C43#54611yescharacteristic
378C22×C43#54611yescharacteristic
379C22×C43C2×#13511yescharacteristic
380C22×C43C2×#13711yescharacteristic
381C22×C43#57711yescharacteristic
382C22×C43#57711yescharacteristic
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43#45214yes—
390C4×C43—24no—
391C4×C43—41no—
392C4×C43—81no—
393C4×C43—81no—
394C4×C43C2×#12311yescharacteristic
395C4×C43#53411yescharacteristic
396C4×C43#54611yescharacteristic
397C4×C43#54611yescharacteristic
398Dic43—22no—
399Dic43—42no—
400Dic43—41no—
401Dic43—42no—
402Dic43—41no—
403Dic43—81no—
404Dic43—81no—
405C2×#548—431no—
406C2×#481—431no—
407C22×#103—431no—
408#2487—431no—
409#2042—431no—
410#2042—431no—
411#2035—431no—
412#2035—431no—
413#1893—431no—
414#1869—431no—
415#1865—431no—
416#1865—431no—
417#1788—431no—
418#1788D4311yescharacteristic, complemented
419#1787—431no—
420C2×C43—81no—
421C2×C43—82no—
422C2×C43#240511yescharacteristic
423C2×C43C2×#45211yescharacteristic
424C2×C43#301011yescharacteristic
425C2×C43#330111yescharacteristic
426C2×C43#330111yescharacteristic
427C2×C43#331611yescharacteristic
428C2×C43#331611yescharacteristic
429D43—24no—
430C22×#41C2×D4311yescharacteristic
431C23×Q8—431no—
432C23×C8—431no—
433#548—864no—
434#548—864no—
435C2×#124—431no—
436C2×#124—861no—
437C2×C22⋊Q8—431no—
438C2×C22⋊Q8—861no—
439C2×#121—431no—
440C2×#121—861no—
441C2×C4×Q8—431no—
442C2×C4×D4—431no—
443C2×C4×D4—861no—
444C22×C4⋊C4—431no—
445#481—864no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#103—431no—
453C2×#103—431no—
454C2×#103—864no—
455C2×#103C2×D4311yescharacteristic
456C2×#103C2×D4311yescharacteristic
457C2×#102—431no—
458C2×#102—431no—
459C2×#102C2×D4311yescharacteristic
460C2×#102C2×D4311yescharacteristic
461C2×C22⋊C8—431no—
462C2×C22⋊C8—431no—
463C2×C22⋊C8C2×D4311yescharacteristic
464#400—861no—
465#399—861no—
466#389—431no—
467#389—431no—
468#386—861no—
469#385—861no—
470#380—431no—
471#380—431no—
472#380C2×D4311yescharacteristic
473#340—431no—
474#340—431no—
475#336—431no—
476#336—431no—
477C43#2403611yescharacteristic, complemented, Sylow
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C22×Q8—434no—
485C22×Q8—431no—
486C22×Q8—861no—
487C22×Q8—862no—
488C22×Q8—862no—
489C22×Q8—862no—
490C22×Q8—1721no—
491C22×Q8—1721no—
492C22×Q8C22×D4311yescharacteristic
493C22×D4—21no—
494C22×D4—431no—
495C22×D4—861no—
496C22×D4C22×D4311yescharacteristic
497C23×C4—21no—
498C23×C4—431no—
499C23×C4—861no—
500C23×C4—861no—
501C23×C4C22×D4311yescharacteristic
502C22×C8—431no—
503C22×C8—431no—
504C22×C8—862no—
505C22×C8—1721no—
506C22×C8—1721no—
507C22×C8C22×D4311yescharacteristic
508C22×C8C22×D4311yescharacteristic
509#124—862no—
510#124—868no—
511#124—862no—
512C22⋊Q8—862no—
513C22⋊Q8—862no—
514C22⋊Q8—868no—
515#121—434no—
516#121—862no—
517#121—868no—
518C4×Q8—862no—
519C4×Q8—862no—
520C4×D4—862no—
521C4×D4—862no—
522C4×D4—868no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—431no—
526C2×C4⋊C4—431no—
527C2×C4⋊C4—862no—
528C2×C4⋊C4—862no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C42—431no—
546C2×C42—861no—
547#106—862no—
548#106—862no—
549#103—22no—
550#103—22no—
551#103—862no—
552#103—862no—
553#103—862no—
554#103—862no—
555#103—1721no—
556#103—1721no—
557#102—22no—
558#102—41no—
559#102—862no—
560#102—1721no—
561C22⋊C8—41no—
562C22⋊C8—862no—
563C22⋊C8—1721no—
564#95—21no—
565#95—861no—
566#95—861no—
567#95—861no—
568#95—861no—
569C24—21no—
570C24—431no—
571C24D4×D4311yescharacteristic
572#41—44no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—432no—
580C2×Q8—864no—
581C2×Q8—861no—
582C2×Q8—868no—
583C2×Q8—861no—
584C2×Q8—861no—
585C2×Q8—861no—
586C2×Q8—861no—
587C2×Q8—1722no—
588C2×Q8—1722no—
589C2×Q8—1724no—
590C2×Q8—1724no—
591C2×Q8—1724no—
592C2×Q8#1062189812yes—
593C2×Q8D4×D4312yes—
594C2×Q8#1062190012yes—
595C2×D4—24no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—864no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—1722no—
608C2×D4—1722no—
609C2×D4D4×D4312yes—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—431no—
623C22×C4—432no—
624C22×C4—432no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—864no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—3441no—
637C22×C4—3441no—
638C22×C4—1722no—
639C22×C4—1722no—
640C22×C4—1722no—
641C22×C4D4×D4311yescharacteristic
642C22×C4C23×D4311yescharacteristic
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—861no—
650C2×C8—861no—
651C2×C8—861no—
652C2×C8—861no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—1724no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—432no—
661C4⋊C4—862no—
662C4⋊C4—864no—
663C4⋊C4—864no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—3441no—
670C4⋊C4—3441no—
671C4⋊C4—1722no—
672C22⋊C4—81no—
673C22⋊C4—862no—
674C22⋊C4—862no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—3441no—
680C22⋊C4—1722no—
681C42—864no—
682C42—861no—
683C42—861no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—432no—
699C23—432no—
700C23—432no—
701C23—861no—
702C23—861no—
703C23—861no—
704C23—861no—
705C23C2×D4×D4311yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—862no—
710Q8—862no—
711Q8—1728no—
712Q8—1721no—
713Q8—1721no—
714Q8#1306330714yes—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—1724no—
721D4—1728no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—48no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—432no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—861no—
747C2×C4—862no—
748C2×C4—861no—
749C2×C4—862no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—3444no—
755C2×C4—1728no—
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—1721no—
765C2×C4—1721no—
766C2×C4C2×D4×D4311yescharacteristic
767C2×C4C2×D4×D4311yescharacteristic
768C2×C4C2×#1062190011yescharacteristic
769C2×C4C2×#1062189811yescharacteristic
770C2×C4#1306337011yescharacteristic
771C2×C4#1306337011yescharacteristic
772C8—41no—
773C8—41no—
774C8—1721no—
775C8—1721no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—434no—
791C22—862no—
792C22—862no—
793C22—862no—
794C22—862no—
795C22—862no—
796C22—862no—
797C22#120×D4311yescharacteristic
798C22#1458353611yescharacteristic
799C22#1458353911yescharacteristic
800C22#135×D4311yescharacteristic
801C22#137×D4311yescharacteristic
802C22#1458370611yescharacteristic
803C22#1458370911yescharacteristic
804C4—24no—
805C4—41no—
806C4—81no—
807C4—81no—
808C4—862no—
809C4—3441no—
810C4—3441no—
811C4—1721no—
812C4—1722no—
813C4—1722no—
814C4—1721no—
815C4C2×#1306330711yescharacteristic
816C4#1458345911yescharacteristic
817C4#1458353611yescharacteristic
818C4#1458353911yescharacteristic
819C2—81no—
820C2—82no—
821C2—864no—
822C2#1913792011yescharacteristic
823C2#452×D4311yescharacteristic
824C2#1914387811yescharacteristic
825C2#1914649011yescharacteristic
826C2#1914649811yescharacteristic
827C2#1914669911yescharacteristic
828C2#1914670711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583556C2
hypercenter#1788D43
hypocenterC43#24036
LCSG ▷ C22×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×#14583216C2semidirect
3. C2×#103×D43C2semidirect
4. #19138908C2semidirect
5. #19135835C2semidirect
6. #19135834C2semidirect
7. #19135792C2semidirect
8. #19135791C2semidirect
9. #19135020C2semidirect
10. #19134884C2semidirect
11. #19134865C2semidirect
12. #19134861C2semidirect
13. #19134535C2semidirect
14. #19134528C2semidirect
15. C43×#1788C2semidirect
418. #1788D43semidirect
477. C43#24036semidirect

Maximal subgroups

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

subgroupindex
C2×#145835562
C2×#145832162
C2×#103×D432
#191389082
#191358352
#191358342
#191357922
#191357912
#191350202
#191348842
#191348652
#191348612
#191345352
#191345282
C43×#17882
#2403643