Finite Group Databasebeta

← #25129003

Subgroups — #25129003

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×#14583059C211yesmaximal, characteristic, complemented
2C2×#14582898C211yesmaximal, characteristic, complemented
3#19137940C211yesmaximal, characteristic
4#19135733C211yesmaximal, characteristic, complemented
5#19135728C211yesmaximal, characteristic, complemented
6#19135603C211yesmaximal, characteristic, complemented
7#19135596C211yesmaximal, characteristic, complemented
8#19135029C211yesmaximal, characteristic, complemented
9#19134950C211yesmaximal, characteristic, complemented
10#19134936C211yesmaximal, characteristic, complemented
11#19134912C211yesmaximal, characteristic, complemented
12#19134902C211yesmaximal, characteristic, complemented
13#19134893C211yesmaximal, characteristic, complemented
14#19134681C211yesmaximal, characteristic, complemented
15C2×C43×#554C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22#14583059—24no—
23#14582898—24no—
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35#14582814—21no—
36#14582807—21no—
37#14582805C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582775—21no—
40#14582770—21no—
41#14582759C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C43×#554—24no—
51C43×#554—24no—
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#125×C43—21no—
54C2×C22⋊Q8×C43—21no—
55C2×C22⋊Q8×C43—21no—
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C2×C4×D4×C43—21no—
60C2×C4×D4×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C22×Dic86C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C4×D43—21no—
74C2×#10621885—22no—
75C2×#10621885—22no—
76C2×#10621885—41no—
77C2×#10621884—22no—
78C2×#10621884—22no—
79C2×#10621884—41no—
80C2×#10621877—22no—
81C2×#10621877—41no—
82C2×#10621877—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063304—22no—
88#13063304—41no—
89#13063299—22no—
90#13063299—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99#13063249—41no—
100#13063249—41no—
101#13063248—22no—
102#13063248—22no—
103#13063248—22no—
104#13063245—22no—
105#13063245—22no—
106#13063245—22no—
107C22⋊(C43⋊C8)—22no—
108C22⋊(C43⋊C8)—41no—
109C22⋊(C43⋊C8)—41no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×Q8×C43—21no—
114C22×Q8×C43C2311yescharacteristic
115C22×D4×C43D411yescharacteristic
116C23×C4×C43—21no—
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C4⋊Q8×C43—22no—
121C4⋊Q8×C43—22no—
122#125×C43—28no—
123C22⋊Q8×C43—28no—
124C22⋊Q8×C43—28no—
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—22no—
127C22⋊Q8×C43—22no—
128C22⋊Q8×C43D414yescomplemented
129C4×Q8×C43—22no—
130C4×Q8×C43—22no—
131C4×D4×C43—28no—
132C4×D4×C43—22no—
133C4×D4×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—22no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43—22no—
142C2×C4⋊C4×C43—22no—
143C2×C4⋊C4×C43D411yescharacteristic
144C2×C4⋊C4×C43D414yescomplemented
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C42×C43—21no—
153C2×C42×C43C2311yescharacteristic
154C24×C43C2×D411yescharacteristic
155C24×C43C2×D411yescharacteristic
156C23×D43—21no—
157C2×Q8×C43—24no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—81no—
164C2×Q8×C43—81no—
165C2×Q8×C43C2×D412yes—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—24no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
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—21no—
185C22×C4×C43—81no—
186C22×C4×C43—81no—
187C22×C4×C43—81no—
188C22×C4×C43—81no—
189C22×C4×C43C2×D412yes—
190C22×C4×C43C2×D412yes—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—42no—
199C2×C22⋊D43—42no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43—81no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205#10621898—28no—
206#10621898—44no—
207#10621898—44no—
208#10621898—44no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172#4112yes—
215C2×C4×D43—42no—
216C2×C4×D43—42no—
217C2×C4×D43—42no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86#4112yes—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—22no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C2×D412yes—
235C4⋊C4×C43C2×D412yes—
236C4⋊C4×C43C2×D412yes—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—22no—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—22no—
241C42×C43—24no—
242C42×C43—21no—
243C42×C43—21no—
244C22⋊Dic43—42no—
245C22⋊Dic43—81no—
246#10621885—44no—
247#10621884—44no—
248(C2×D43)⋊C4—42no—
249(C2×D43)⋊C4—42no—
250(C2×D43)⋊C4—81no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255Dic43⋊C4—42no—
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#12012yes—
282C23×C43#13712yes—
283C23×C43C22×D411yescharacteristic
284C22×D43—22no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—41no—
294Q8×C43—41no—
295Q8×C43—84no—
296D4×C43—28no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—21no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
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—84no—
328C2×C4×C43—84no—
329C2×C4×C43#12012yes—
330C2×C4×C43#13712yes—
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C2×#4111yescharacteristic
334C2×C4×C43C2×#4111yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C2×C4×C43H(5,𝔽2)11yescharacteristic
337C22⋊D43—48no—
338C22⋊D43—84no—
339C2×Dic43—22no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348D172—22no—
349D172—22no—
350D172—41no—
351D172—41no—
352C4×D43—48no—
353Dic86—22no—
354Dic86—22no—
355Dic86—41no—
356Dic86—41no—
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×C43C2×#12011yescharacteristic
377C22×C43#54611yescharacteristic
378C22×C43#54611yescharacteristic
379C22×C43C2×#13711yescharacteristic
380C22×C43C2×#13711yescharacteristic
381C22×C43#57611yescharacteristic
382C22×C43#57711yescharacteristic
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43—81no—
389C2×D43—81no—
390C4×C43—22no—
391C4×C43—22no—
392C4×C43—41no—
393C4×C43—42no—
394C4×C43—41no—
395C4×C43—42no—
396C4×C43—42no—
397C4×C43—42no—
398C4×C43#52511yescharacteristic
399C4×C43#53511yescharacteristic
400C4×C43#54611yescharacteristic
401C4×C43#54611yescharacteristic
402Dic43—42no—
403Dic43—81no—
404Dic43—81no—
405C2×#554D4311yescharacteristic, complemented
406C2×#452—431no—
407C2×#417—431no—
408#2407—431no—
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#240411yescharacteristic
423C2×C43#300411yescharacteristic
424C2×C43#301211yescharacteristic
425C2×C43#331411yescharacteristic
426C2×C43#331611yescharacteristic
427C2×C43#333111yescharacteristic
428C2×C43#333311yescharacteristic
429D43—82no—
430C22×#41—431no—
431C22×Q16—431no—
432C22×SD16—431no—
433C22×M16—431no—
434#554—24no—
435#554—24no—
436C2×C4⋊Q8C2×D4311yescharacteristic
437C2×#125—21no—
438C2×C22⋊Q8—21no—
439C2×C22⋊Q8—21no—
440C2×C22⋊Q8—431no—
441C2×C22⋊Q8C2×D4311yescharacteristic
442C2×C22⋊Q8C2×D4311yescharacteristic
443C2×#121—431no—
444C2×C4×Q8C2×D4311yescharacteristic
445C2×C4×D4—21no—
446C2×C4×D4C2×D4311yescharacteristic
447C22×C4⋊C4C2×D4311yescharacteristic
448C22×C4⋊C4C2×D4311yescharacteristic
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—861no—
463#392—861no—
464#391—431no—
465#390—431no—
466#386—861no—
467#385—861no—
468#380—431no—
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—862no—
479C2×#41—862no—
480C2×#41—862no—
481C2×#41—862no—
482C2×#41—1721no—
483C2×#41—1721no—
484C22×Q8—21no—
485C22×Q8—431no—
486C22×Q8C22×D4311yescharacteristic
487C22×D4—431no—
488C22×D4—861no—
489C22×D4—861no—
490C22×D4C22⋊D4311yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
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—22no—
510C4⋊Q8—22no—
511#125—28no—
512C22⋊Q8—28no—
513C22⋊Q8—28no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—862no—
518C22⋊Q8—1721no—
519C22⋊Q8C22⋊D4314yescomplemented
520#121—862no—
521#121—1721no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×D4—28no—
525C4×D4—22no—
526C4×D4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4C22⋊D4311yescharacteristic
540C2×C4⋊C4C22⋊D4314yescomplemented
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4C22⋊D4311yescharacteristic
552C2×C22⋊C4C22⋊D4311yescharacteristic
553C2×C42—21no—
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—861no—
567#95—861no—
568#95—861no—
569C24—861no—
570C24C2×C22⋊D4311yescharacteristic
571C24C2×C22⋊D4311yescharacteristic
572#41—868no—
573#41—1724no—
574#41—1724no—
575#41—1724no—
576C2×Q8—24no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—81no—
583C2×Q8—81no—
584C2×Q8—432no—
585C2×Q8—861no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8C2×C22⋊D4312yes—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—432no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4—861no—
599C2×D4—861no—
600C2×D4—3441no—
601C2×D4—1722no—
602C2×D4—1722no—
603C2×D4—1722no—
604C2×D4—1722no—
605C2×D4—1722no—
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—24no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—81no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4—81no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—1722no—
630C22×C4—1722no—
631C22×C4—1722no—
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C2×C22⋊D4311yescharacteristic
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C2×C22⋊D4312yes—
636C22×C4C2×C22⋊D4312yes—
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—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—1722no—
669C4⋊C4C2×C22⋊D4312yes—
670C4⋊C4C2×C22⋊D4312yes—
671C4⋊C4C2×C22⋊D4312yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—3441no—
677C22⋊C4—3441no—
678C22⋊C4—1722no—
679C22⋊C4—1722no—
680C22⋊C4—1722no—
681C42—24no—
682C42—21no—
683C42—21no—
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—862no—
697C23—1721no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23#1306329412yes—
704C23#1306335612yes—
705C23C22×C22⋊D4311yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710Q8—84no—
711Q8—862no—
712Q8—862no—
713Q8—1721no—
714Q8—1721no—
715D4—28no—
716D4—862no—
717D4—862no—
718D4—3444no—
719D4—1728no—
720D4—1721no—
721D4—1721no—
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—22no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
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—41no—
751C2×C4—41no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4—862no—
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#1306329412yes—
765C2×C4#1306335612yes—
766C2×C4C22×C22⋊D4311yescharacteristic
767C2×C4C22×C22⋊D4311yescharacteristic
768C2×C4#41×D4311yescharacteristic
769C2×C4#41×D4311yescharacteristic
770C2×C4#1306337111yescharacteristic
771C2×C4#1306337111yescharacteristic
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—3441no—
791C22—3441no—
792C22—3441no—
793C22—3441no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22C2×#1306329411yescharacteristic
798C22#1458353711yescharacteristic
799C22#1458353711yescharacteristic
800C22C2×#1306335611yescharacteristic
801C22C2×#1306335611yescharacteristic
802C22#1458370211yescharacteristic
803C22#1458371011yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—42no—
808C4—41no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—3441no—
813C4—3441no—
814C4—1722no—
815C4#1458340611yescharacteristic
816C4#1458346311yescharacteristic
817C4#1458353711yescharacteristic
818C4#1458353711yescharacteristic
819C2—42no—
820C2—42no—
821C2—3442no—
822C2#1913791011yescharacteristic
823C2#1914382911yescharacteristic
824C2#1914389911yescharacteristic
825C2#1914667011yescharacteristic
826C2#1914670011yescharacteristic
827C2#1914690511yescharacteristic
828C2#1914692711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#554C2
socleC23×C43C22×D4
prime radical#19137940C2
hypercenterC2×#554D43
hypocenterC43#23981
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#14583059C2semidirect
2. C2×#14582898C2semidirect
4. #19135733C2semidirect
5. #19135728C2semidirect
6. #19135603C2semidirect
7. #19135596C2semidirect
8. #19135029C2semidirect
9. #19134950C2semidirect
10. #19134936C2semidirect
11. #19134912C2semidirect
12. #19134902C2semidirect
13. #19134893C2semidirect
14. #19134681C2semidirect
15. C2×C43×#554C2semidirect
128. C22⋊Q8×C43D4semidirect
144. C2×C4⋊C4×C43D4semidirect
405. C2×#554D43semidirect
477. C43#23981semidirect
519. C22⋊Q8C22⋊D43semidirect
540. C2×C4⋊C4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830592
C2×#145828982
#191379402
#191357332
#191357282
#191356032
#191355962
#191350292
#191349502
#191349362
#191349122
#191349022
#191348932
#191346812
C2×C43×#5542
#2398143