Finite Group Databasebeta

← #25105706

Subgroups — #25105706

Order 11008.

1326 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583472C211yesmaximal, characteristic
2C2×#14582864C211yesmaximal, characteristic
3#19137188C211yesmaximal, characteristic
4#19135027C211yesmaximal, characteristic, complemented
5#19135025C211yesmaximal, characteristic, complemented
6#19135017C211yesmaximal, characteristic, complemented
7#19135015C211yesmaximal, characteristic, complemented
8#19134908C211yesmaximal, characteristic, complemented
9#19134905C211yesmaximal, characteristic, complemented
10#19134902C211yesmaximal, characteristic, complemented
11#19134689C211yesmaximal, characteristic, complemented
12#19134688C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C43×#1872C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583472—24no—
21#14583472C418yescomplemented
22C2×#13063324—21no—
23C2×#13063311—21no—
24C2×#13063310—21no—
25C2×#13063307—21no—
26C2×#13063305C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×#13063301C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37#14582864—24no—
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41#14582804—21no—
42#14582800—21no—
43#14582778—21no—
44#14582778—21no—
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×C22⋊Q8×C43C2211yescharacteristic
56C22×C4⋊C4×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C2×#10621898—41no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898C2×C414yes—
67C2×#10621898D414yes—
68C22×Dic86—21no—
69C22×Dic86D411yescharacteristic
70C22×Dic86C2311yescharacteristic
71C2×Q8×D43—22no—
72C2×Q8×D43—41no—
73C2×Q8×D43—41no—
74C2×Q8×D43—41no—
75C2×Q8×D43—41no—
76C2×Q8×D43C2×C414yescomplemented
77C22×D172D411yescharacteristic
78C22×C22⋊D43D411yescharacteristic
79C22×C22⋊D43D411yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43C2311yescharacteristic
82C22×C4×D43C2311yescharacteristic
83C2×#10621872—22no—
84C2×#10621872—41no—
85C2×#10621872—41no—
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C2×C8×D43—22no—
89C2×C8×D43—41no—
90C2×C8×D43—41no—
91#13063324—28no—
92#13063311—28no—
93#13063310—28no—
94#13063307—28no—
95#13063305—22no—
96#13063305C2×C414yescomplemented
97#13063304—22no—
98#13063304C2×C414yes—
99#13063301—22no—
100#13063301C2×C414yescomplemented
101#13063284—41no—
102#13063284—41no—
103#13063283—22no—
104#13063283C2×C414yescomplemented
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122#13063250—41no—
123#13063250—41no—
124#13063249—41no—
125#13063249—41no—
126#13063248—41no—
127#13063248—41no—
128C22⋊(C43⋊C8)—22no—
129(C2×D43)⋊C8—22no—
130(C2×D43)⋊C8—22no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×Q8×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C23×C4×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22⋊Q8×C43—22no—
141C22⋊Q8×C43C2×C414yes—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43—41no—
145C2×C4⋊C4×C43—41no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150#103×C43—41no—
151#103×C43—41no—
152C22⋊C8×C43—22no—
153C24×C43C2×D411yescharacteristic
154C23×D43C2×D411yescharacteristic
155C23×D43C2×D411yescharacteristic
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43C22×C412yes—
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—42no—
171C22×C4×C43—81no—
172C22×C4×C43—81no—
173C22×C4×C43C22×C412yes—
174C22×C4×C43C2×D412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—41no—
178C2×C22⋊D43—41no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43—41no—
181C2×C22⋊D43C22⋊C414yes—
182C2×C22⋊D43C22⋊C414yes—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43C2×D411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189Q8×D43—44no—
190Q8×D43—44no—
191Q8×D43—44no—
192Q8×D43—44no—
193#10621898—44no—
194#10621898—44no—
195#10621898—44no—
196#10621898—44no—
197C2×D172—41no—
198C2×D172—41no—
199C2×D172C22⋊C414yes—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—24no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43C22×C412yes—
212C2×C4×D43C22×C412yes—
213C2×C4×D43C2×D412yes—
214C2×C4×D43C2×D412yes—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—24no—
221C2×Dic86—41no—
222C2×Dic86—41no—
223C2×Dic86—42no—
224C2×Dic86—42no—
225C2×Dic86C22⋊C414yes—
226C2×Dic86C22×C412yes—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—42no—
240C4⋊C4×C43C22×C412yes—
241C22⋊C4×C43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43—42no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—81no—
248(C2×D43)⋊C4—81no—
249(C2×D43)⋊C4—81no—
250(C2×D43)⋊C4—81no—
251C4⋊Dic43—21no—
252C4⋊Dic43—24no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43C22×C412yes—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260C4×Dic43—24no—
261C4×Dic43—42no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268#10621872—44no—
269C8×D43—44no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43C2×C22⋊C412yes—
277C23×C43C22×D411yescharacteristic
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—21no—
290C22×D43C2×C22⋊C412yes—
291C22×D43C2×C22⋊C412yes—
292Q8×C43—22no—
293Q8×C43—22no—
294Q8×C43—41no—
295Q8×C43—41no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
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—84no—
315C2×C4×C43C2×C22⋊C412yes—
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C22⋊D43—44no—
323C22⋊D43—44no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43C2×C22⋊C412yes—
341C2×Dic43C2×C22⋊C412yes—
342D172—44no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—48no—
352Dic86—22no—
353Dic86—22no—
354Dic86—44no—
355Dic86—48no—
356Dic86—41no—
357Dic86—41no—
358C8×C43—41no—
359C8×C43—41no—
360C43⋊C8—41no—
361C43⋊C8—41no—
362#21771—431nomaximal, Sylow
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43C22×C22⋊C411yescharacteristic
371C22×C43#53411yescharacteristic
372C22×C43#53411yescharacteristic
373C22×C43#57711yescharacteristic
374C22×C43#57711yescharacteristic
375C22×C43#57811yescharacteristic
376C22×C43#57811yescharacteristic
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C2×D43—41no—
389C2×D43—41no—
390C2×D43—41no—
391C4×C43—22no—
392C4×C43—42no—
393C4×C43—42no—
394C4×C43—81no—
395C4×C43—81no—
396C4×C43#51811yescharacteristic
397C4×C43#51811yescharacteristic
398C4×C43#53411yescharacteristic
399C4×C43#53411yescharacteristic
400Dic43—22no—
401Dic43—22no—
402Dic43—42no—
403Dic43—42no—
404Dic43—81no—
405Dic43—81no—
406C2×#536—431no—
407C2×#408—431no—
408#2311—431no—
409#1894—431no—
410#1894—431no—
411#1892—431no—
412#1892—431no—
413#1873—431no—
414#1873—431no—
415#1872—431no—
416#1872D4311yescharacteristic, complemented
417#1825—431no—
418#1825—431no—
419#1787—431no—
420#1787—431no—
421C2×C43—42no—
422C2×C43#230811yescharacteristic
423C2×C43#289811yescharacteristic
424C2×C43#289811yescharacteristic
425C2×C43#320011yescharacteristic
426C2×C43#320111yescharacteristic
427C2×C43#320111yescharacteristic
428C2×C43#320211yescharacteristic
429D43—42no—
430D43—42no—
431C22×#41—431no—
432C23×Q8—431no—
433C22×M16—431no—
434C23×C8—431no—
435#536—438no—
436#536—864no—
437C2×C4⋊Q8—861no—
438C2×#124—861no—
439C2×#123—861no—
440C2×#123—861no—
441C2×C22⋊Q8—431no—
442C2×C22⋊Q8—431no—
443C2×C22⋊Q8—431no—
444C2×C22⋊Q8C2×D4311yescharacteristic
445C2×#117—431no—
446C2×#117—431no—
447C22×C4⋊C4C2×D4311yescharacteristic
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#103—431no—
453C2×#103—431no—
454C2×#103C2×D4311yescharacteristic
455C2×#103C2×D4311yescharacteristic
456#408—864no—
457C2×C22⋊C8—431no—
458C2×C22⋊C8—431no—
459C2×C22⋊C8—431no—
460C2×C22⋊C8C2×D4311yescharacteristic
461#391—861no—
462#390—861no—
463#386—861no—
464#386—861no—
465#380—431no—
466#380—431no—
467#380—431no—
468#380—431no—
469#340—431no—
470#340—431no—
471#340—431no—
472#340—431no—
473#340—431no—
474#340—431no—
475#340C2×D4311yescharacteristic
476#340C2×D4311yescharacteristic
477C43#2177111yescharacteristic, complemented, Sylow
478C2×#41—434no—
479C2×#41—434no—
480C2×#41—1721no—
481C2×#41—1721no—
482C2×#41—1721no—
483C2×#41—1721no—
484C22×Q8—431no—
485C22×Q8—434no—
486C22×Q8—431no—
487C22×Q8—861no—
488C22×Q8—862no—
489C22×Q8—1721no—
490C22×Q8—1721no—
491C22×Q8—1721no—
492C22×Q8—1721no—
493C22×Q8C22×D4311yescharacteristic
494C22×D4—431no—
495C22×D4—431no—
496C22×D4—431no—
497C23×C4—21no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—861no—
501C23×C4C22×D4311yescharacteristic
502C2×M16—862no—
503C2×M16—1721no—
504C2×M16—1721no—
505C22×C8—431no—
506C22×C8—431no—
507C22×C8—862no—
508C22×C8—1721no—
509C22×C8—1721no—
510C22×C8C22×D4311yescharacteristic
511C22×C8C22×D4311yescharacteristic
512C4⋊Q8—868no—
513#124—868no—
514#123—868no—
515#123—868no—
516C22⋊Q8—22no—
517C22⋊Q8—434no—
518C22⋊Q8—434no—
519C22⋊Q8—434no—
520C22⋊Q8—862no—
521C22⋊Q8—862no—
522C22⋊Q8—862no—
523C22⋊Q8C4×D4314yes—
524#117—434no—
525#117—862no—
526#117—1721no—
527#117—1721no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—41no—
531C2×C4⋊C4—41no—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—861no—
536C2×C4⋊C4—861no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4C22×D4311yescharacteristic
539C2×C4⋊C4C22×D4311yescharacteristic
540C2×C4⋊C4C22×D4311yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C42—861no—
552C2×C42—861no—
553#103—41no—
554#103—41no—
555#103—1721no—
556#103—1721no—
557#103—1721no—
558#103—1721no—
559#103—1721no—
560#103—1721no—
561C22⋊C8—22no—
562C22⋊C8—862no—
563C22⋊C8—862no—
564C22⋊C8—862no—
565#95—861no—
566#95—861no—
567#95—861no—
568#95—861no—
569C24—431no—
570C24—431no—
571C24D4×D4311yescharacteristic
572#41—1724no—
573#41—1724no—
574#41—1724no—
575#41—1724no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—434no—
582C2×Q8—432no—
583C2×Q8—864no—
584C2×Q8—861no—
585C2×Q8—861no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—1721no—
590C2×Q8—1721no—
591C2×Q8—1722no—
592C2×Q8—1722no—
593C2×Q8—1724no—
594C2×Q8—1724no—
595C2×Q8—1724no—
596C2×Q8—1724no—
597C2×Q8C2×C4×D4312yes—
598C2×D4—434no—
599C2×D4—434no—
600C2×D4—434no—
601C2×D4—1721no—
602C2×D4—1721no—
603C2×D4—1721no—
604C2×D4—1721no—
605C2×D4—1721no—
606C2×D4—1721no—
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—42no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—864no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
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—861no—
637C22×C4—1722no—
638C22×C4—1722no—
639C22×C4C2×C4×D4312yes—
640C22×C4D4×D4311yescharacteristic
641C22×C4D4×D4312yes—
642C22×C4C23×D4311yescharacteristic
643M16—1724no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—861no—
651C2×C8—861no—
652C2×C8—861no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—861no—
656C2×C8—1724no—
657C4⋊C4—24no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—432no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4C2×C4×D4312yes—
674C22⋊C4—24no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—3441no—
680C22⋊C4—3441no—
681C22⋊C4—3441no—
682C22⋊C4—3441no—
683C22⋊C4—1722no—
684C42—864no—
685C42—1722no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—432no—
693C23—432no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23—861no—
698C23—861no—
699C23—861no—
700C23—861no—
701C23—861no—
702C23—861no—
703C23—861no—
704C23—861no—
705C23—861no—
706C23C22⋊C4×D4312yes—
707C23C2×D4×D4311yescharacteristic
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712Q8—862no—
713Q8—862no—
714Q8—1724no—
715Q8—1728no—
716Q8—1721no—
717Q8—1721no—
718D4—1724no—
719D4—1724no—
720D4—1724no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
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—84no—
740C2×C4—432no—
741C2×C4—432no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—861no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—1728no—
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×C4—1721no—
767C2×C4C22⋊C4×D4312yes—
768C2×C4C22×C4×D4311yescharacteristic
769C2×C4C2×D4×D4311yescharacteristic
770C2×C4#1306337011yescharacteristic
771C2×C4#1306337011yescharacteristic
772C2×C4#1306337111yescharacteristic
773C2×C4#1306337111yescharacteristic
774C8—41no—
775C8—41no—
776C8—1721no—
777C8—1721no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—862no—
786C22—862no—
787C22—862no—
788C22—862no—
789C22—862no—
790C22—862no—
791C22—1721no—
792C22—1721no—
793C22—1721no—
794C22—1721no—
795C22—1721no—
796C22—1721no—
797C22—1721no—
798C22—1721no—
799C22C2×C22⋊C4×D4311yescharacteristic
800C22#1458345911yescharacteristic
801C22#1458346011yescharacteristic
802C22#1458370511yescharacteristic
803C22#1458370911yescharacteristic
804C22#1458371211yescharacteristic
805C22#1458371511yescharacteristic
806C4—22no—
807C4—42no—
808C4—42no—
809C4—81no—
810C4—81no—
811C4—862no—
812C4—862no—
813C4—3441no—
814C4—3441no—
815C4—1722no—
816C4—1722no—
817C4#1458337111yescharacteristic
818C4#1458337111yescharacteristic
819C4#1458345711yescharacteristic
820C4#1458345711yescharacteristic
821C2—42no—
822C2—1722no—
823C2—1722no—
824C2#1913716911yescharacteristic
825C2#1914312311yescharacteristic
826C2#1914312611yescharacteristic
827C2#1914546411yescharacteristic
828C2#1914548211yescharacteristic
829C2#1914548411yescharacteristic
830C2#1914548811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1872D43
hypocenterC43#21771
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #19135027C2semidirect
5. #19135025C2semidirect
6. #19135017C2semidirect
7. #19135015C2semidirect
8. #19134908C2semidirect
9. #19134905C2semidirect
10. #19134902C2semidirect
11. #19134689C2semidirect
12. #19134688C2semidirect
13. #19134528C2semidirect
14. #19134528C2semidirect
15. C43×#1872C2semidirect
21. #14583472C4semidirect
76. C2×Q8×D43C2×C4semidirect
96. #13063305C2×C4semidirect
100. #13063301C2×C4semidirect
104. #13063283C2×C4semidirect
416. #1872D43semidirect
477. C43#21771semidirect

Maximal subgroups

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

subgroupindex
C2×#145834722
C2×#145828642
#191371882
#191350272
#191350252
#191350172
#191350152
#191349082
#191349052
#191349022
#191346892
#191346882
#191345282
C43×#18722
#2177143