Finite Group Databasebeta

← #25132160

Subgroups — #25132160

Order 11008.

1392 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D43C211yesmaximal, characteristic
2C2×#14583107C211yesmaximal, characteristic, complemented
3C2×#14583053C211yesmaximal, characteristic, complemented
4C2×#14583006C211yesmaximal, characteristic, complemented
5#19139502C211yesmaximal, characteristic
6#19135792C211yesmaximal, characteristic, complemented
7#19135790C211yesmaximal, characteristic, complemented
8#19135603C211yesmaximal, characteristic, complemented
9#19135602C211yesmaximal, characteristic, complemented
10#19135413C211yesmaximal, characteristic, complemented
11#19135391C211yesmaximal, characteristic
12#19134608C211yesmaximal, characteristic, complemented
13#19134530C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C2×C43×#451C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18Q8×C22⋊D43—24no—
19Q8×C22⋊D43—24no—
20C2×#13063323—21no—
21C2×#13063323C2211yescharacteristic
22C2×#13063304—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063301—21no—
25C2×#13063301C2211yescharacteristic
26C2×#13063301C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×Q8×Dic43C2211yescharacteristic
29C2×C4×C22⋊D43—21no—
30C2×C4×C22⋊D43C2211yescharacteristic
31#14583107—24no—
32#14583053—24no—
33#14583006—24no—
34C2×#13063257C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×#13063235C2211yescharacteristic
48#14582832—21no—
49#14582815—21no—
50#14582793—21no—
51#14582789—21no—
52#14582764C2211yescharacteristic
53#14582759C2211yescharacteristic
54#14582756C2211yescharacteristic
55#14582662C2211yescharacteristic
56#14582661C2211yescharacteristic
57C23×Q8×C43C2211yescharacteristic
58C22×Q16×C43C2211yescharacteristic
59C22×Q16×C43C2211yescharacteristic
60C2×C22⋊Q8×C43C2211yescharacteristic
61C43×#451—24no—
62C2×#103×C43C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×C22⋊C8×C43C2211yescharacteristic
65C22×Dic86—21no—
66C22×Dic86C2311yescharacteristic
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—41no—
72C2×Q8×D43—41no—
73C22×C22⋊D43D411yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43C2311yescharacteristic
76C2×#10621885—22no—
77C2×#10621885—22no—
78C2×#10621885—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063323—28no—
82#13063323—22no—
83#13063323D414yes—
84#13063304—28no—
85#13063304—22no—
86#13063304—22no—
87#13063301—28no—
88#13063301—22no—
89#13063301—22no—
90#13063301—22no—
91#13063301—41no—
92Q8×Dic43—22no—
93Q8×Dic43—22no—
94Q8×Dic43—22no—
95Q8×Dic43D414yes—
96C4×C22⋊D43—28no—
97C4×C22⋊D43—22no—
98C4×C22⋊D43—22no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4D411yescharacteristic
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43D411yescharacteristic
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43C2311yescharacteristic
120#13063257—22no—
121Dic43⋊C8—22no—
122#13063250—22no—
123#13063250—22no—
124#13063249—22no—
125#13063249—22no—
126#13063249—22no—
127#13063249—22no—
128#13063249—41no—
129#13063248—41no—
130C22⋊(C43⋊C8)—41no—
131(C2×D43)⋊C8—22no—
132(C2×D43)⋊C8—41no—
133#13063235—22no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C22×Q8×C43—22no—
139C22×Q8×C43—22no—
140C22×Q8×C43—21no—
141C22×Q8×C43—22no—
142C22×Q8×C43—22no—
143C22×Q8×C43—41no—
144C22×Q8×C43—41no—
145C22×Q8×C43C2311yescharacteristic
146C22×Q8×C43C2311yescharacteristic
147C22×Q8×C43C2311yescharacteristic
148C23×C4×C43—21no—
149C23×C4×C43C2311yescharacteristic
150C2×Q16×C43—22no—
151C2×Q16×C43—22no—
152C2×Q16×C43—22no—
153C2×Q16×C43—22no—
154C2×Q16×C43—41no—
155C2×Q16×C43D414yescomplemented
156C22×C8×C43C2311yescharacteristic
157C22×C8×C43C2311yescharacteristic
158C22⋊Q8×C43—22no—
159C22⋊Q8×C43—41no—
160C2×C4⋊C4×C43—21no—
161C2×C4⋊C4×C43C2311yescharacteristic
162C2×C22⋊C4×C43—21no—
163#103×C43—22no—
164#103×C43—22no—
165C22⋊C8×C43—22no—
166C24×C43C2×D411yescharacteristic
167C23×D43C2×D411yescharacteristic
168C2×Q8×C43—24no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—42no—
183C2×Q8×C43—42no—
184C2×Q8×C43—44no—
185C2×Q8×C43—44no—
186C2×Q8×C43—44no—
187C2×Q8×C43—44no—
188C2×Q8×C43C2×D412yes—
189C2×Q8×C43C2×D412yes—
190C2×Q8×C43C2×D412yes—
191C2×Q8×C43C2×D412yes—
192C2×Q8×C43#4112yes—
193C22×C4×C43—24no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—42no—
205C22×C4×C43—42no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—22no—
209C2×C22⋊D43—22no—
210C2×C22⋊D43—22no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218Q8×D43—44no—
219Q8×D43—44no—
220Q8×D43—44no—
221Q8×D43—44no—
222C2×C4×D43—24no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—24no—
236C2×Dic86—21no—
237C2×Dic86—42no—
238C2×Dic86—42no—
239C2×Dic86C2×D412yes—
240Q16×C43—28no—
241Q16×C43—44no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43C2×D412yes—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊Dic43—24no—
253C22⋊Dic43—22no—
254C22⋊Dic43—42no—
255#10621885—44no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—22no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—42no—
260C4⋊Dic43—21no—
261C4⋊Dic43—24no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—42no—
267C4⋊Dic43C2×D412yes—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—22no—
273Dic43⋊C4—42no—
274C4×Dic43—24no—
275C4×Dic43—42no—
276C4×Dic43C2×D412yes—
277C4×Dic43C2×D412yes—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43#13712yes—
291C23×C43C22×D411yescharacteristic
292C22×D43—21no—
293C22×D43—21no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43#13712yes—
299Q8×C43—22no—
300Q8×C43—22no—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—48no—
307Q8×C43—41no—
308Q8×C43—41no—
309Q8×C43—41no—
310Q8×C43—41no—
311Q8×C43#12114yes—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—48no—
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—41no—
331C2×C4×C43—41no—
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43H(5,𝔽2)11yescharacteristic
337C2×C4×C43H(5,𝔽2)11yescharacteristic
338C22⋊D43—28no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—22no—
344C2×Dic43—21no—
345C2×Dic43—22no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43#12012yes—
359C2×Dic43#12012yes—
360C4×D43—48no—
361C4×D43—41no—
362C4×D43—41no—
363C4×D43—41no—
364C4×D43—41no—
365Dic86—22no—
366Dic86—22no—
367Dic86—48no—
368Dic86—41no—
369Dic86—41no—
370C8×C43—22no—
371C8×C43—41no—
372C43⋊C8—41no—
373C43⋊C8—41no—
374#24255—431nomaximal, Sylow
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43C2×#12011yescharacteristic
383C22×C43D4211yescharacteristic
384C22×C43#54611yescharacteristic
385C22×C43C2×#13711yescharacteristic
386C22×C43C2×#13711yescharacteristic
387C22×C43#57811yescharacteristic
388C22×C43#57811yescharacteristic
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C4×C43—24no—
397C4×C43—41no—
398C4×C43—42no—
399C4×C43—42no—
400C4×C43—81no—
401C4×C43C2×#12111yescharacteristic
402C4×C43#53511yescharacteristic
403C4×C43D4211yescharacteristic
404C4×C43#54611yescharacteristic
405Dic43—22no—
406Dic43—22no—
407Dic43—42no—
408Dic43—41no—
409Dic43—42no—
410Dic43—81no—
411Dic43—81no—
412C2×D4×Q8—431no—
413C2×#462—431no—
414C2×#451—431no—
415C2×#451D4311yescharacteristic, complemented
416C2×#441—431no—
417#2536—431no—
418#2035—431no—
419#2035—431no—
420#2001—431no—
421#2001—431no—
422#1960—431no—
423#1955—431no—
424#1805—431no—
425#1787—431no—
426#1787—431no—
427C2×C43—42no—
428C2×C43#240811yescharacteristic
429C2×C43#300411yescharacteristic
430C2×C43#301111yescharacteristic
431C2×C43#327011yescharacteristic
432C2×C43#327011yescharacteristic
433C2×C43#331211yescharacteristic
434C2×C43#331211yescharacteristic
435D43—42no—
436C23×Q8—431no—
437C23×Q8C2×D4311yescharacteristic
438C22×Q16—431no—
439C22×Q16C2×D4311yescharacteristic
440C22×Q16C2×D4311yescharacteristic
441D4×Q8—864no—
442D4×Q8—864no—
443C2×C4⋊Q8—431no—
444C2×C4⋊Q8—861no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—431no—
447C2×C22⋊Q8—431no—
448C2×C22⋊Q8—861no—
449C2×C22⋊Q8—861no—
450C2×C22⋊Q8C2×D4311yescharacteristic
451C2×C4×Q8—431no—
452C2×C4×Q8—431no—
453C2×C4×D4—431no—
454C2×C4×D4—861no—
455#462—864no—
456#451—24no—
457#451—864no—
458#441—864no—
459C2×#106—431no—
460C2×C4⋊C8—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103C2×D4311yescharacteristic
470C2×#103C2×D4311yescharacteristic
471C2×C22⋊C8—431no—
472C2×C22⋊C8—431no—
473C2×C22⋊C8—431no—
474C2×C22⋊C8C2×D4311yescharacteristic
475C2×#97—431no—
476#398—861no—
477#394—861no—
478#388—861no—
479#388—861no—
480#382—431no—
481#380—431no—
482#380—431no—
483#340—431no—
484#340—431no—
485C43#2425511yescharacteristic, complemented, Sylow
486C22×Q8—22no—
487C22×Q8—22no—
488C22×Q8—21no—
489C22×Q8—22no—
490C22×Q8—22no—
491C22×Q8—41no—
492C22×Q8—41no—
493C22×Q8—431no—
494C22×Q8—861no—
495C22×Q8—862no—
496C22×Q8—862no—
497C22×Q8—862no—
498C22×Q8—862no—
499C22×Q8—1721no—
500C22×Q8—1721no—
501C22×Q8C22×D4311yescharacteristic
502C22×Q8C22×D4311yescharacteristic
503C22×Q8C22×D4311yescharacteristic
504C22×D4—431no—
505C23×C4—21no—
506C23×C4—431no—
507C23×C4—861no—
508C23×C4C22×D4311yescharacteristic
509C2×Q16—22no—
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—22no—
513C2×Q16—41no—
514C2×Q16—862no—
515C2×Q16—862no—
516C2×Q16—1721no—
517C2×Q16C22⋊D4314yescomplemented
518C22×C8—431no—
519C22×C8—431no—
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522C4⋊Q8—434no—
523C4⋊Q8—862no—
524C4⋊Q8—868no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527C22⋊Q8—862no—
528C22⋊Q8—862no—
529C22⋊Q8—862no—
530C22⋊Q8—868no—
531C22⋊Q8—868no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534C22⋊Q8—1721no—
535C4×Q8—434no—
536C4×Q8—862no—
537C4×Q8—862no—
538C4×Q8—862no—
539C4×D4—862no—
540C4×D4—862no—
541C4×D4—868no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—431no—
557C2×C22⋊C4—431no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C42—431no—
564C2×C42—861no—
565C2×C42—861no—
566#106—862no—
567C4⋊C8—862no—
568#103—22no—
569#103—22no—
570#103—862no—
571#103—862no—
572#103—862no—
573#103—862no—
574#103—862no—
575#103—862no—
576#103—1721no—
577#103—1721no—
578C22⋊C8—22no—
579C22⋊C8—862no—
580C22⋊C8—1721no—
581C22⋊C8—1721no—
582#97—862no—
583#95—861no—
584#95—861no—
585#95—861no—
586#95—861no—
587C24—431no—
588C24D4×D4311yescharacteristic
589C2×Q8—24no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—432no—
610C2×Q8—864no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8—861no—
615C2×Q8—861no—
616C2×Q8—1722no—
617C2×Q8—1722no—
618C2×Q8—1724no—
619C2×Q8—1724no—
620C2×Q8—1724no—
621C2×Q8—1724no—
622C2×Q8D4×D4312yes—
623C2×Q8D4×D4312yes—
624C2×Q8#1062190012yes—
625C2×Q8C2×C22⋊D4312yes—
626C2×Q8C2×C22⋊D4312yes—
627C2×D4—862no—
628C2×D4—862no—
629C2×D4—862no—
630C22×C4—21no—
631C22×C4—24no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—431no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—864no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—1722no—
658C22×C4—1722no—
659C22×C4D4×D4311yescharacteristic
660C22×C4C23×D4311yescharacteristic
661Q16—28no—
662Q16—44no—
663Q16—1724no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—861no—
670C2×C8—861no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8C2×C22⋊D4312yes—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—432no—
680C4⋊C4—862no—
681C4⋊C4—864no—
682C4⋊C4—864no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—1722no—
692C4⋊C4—1722no—
693C22⋊C4—42no—
694C22⋊C4—862no—
695C22⋊C4—864no—
696C22⋊C4—862no—
697C22⋊C4—864no—
698C22⋊C4—1722no—
699C22⋊C4—1722no—
700C22⋊C4—1722no—
701C42—432no—
702C42—432no—
703C42—864no—
704C42—1722no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—432no—
712C23—861no—
713C23—861no—
714C23—861no—
715C23—861no—
716C23—861no—
717C23—861no—
718C23#1306335712yes—
719C23C2×D4×D4311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—48no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—862no—
733Q8—862no—
734Q8—1728no—
735Q8—1721no—
736Q8—1721no—
737Q8#1306329714yes—
738D4—868no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—48no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—432no—
760C2×C4—432no—
761C2×C4—861no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—862no—
766C2×C4—861no—
767C2×C4—862no—
768C2×C4—861no—
769C2×C4—861no—
770C2×C4—1728no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4C2×D4×D4311yescharacteristic
786C2×C4C2×D4×D4311yescharacteristic
787C2×C4C22×C22⋊D4311yescharacteristic
788C2×C4C2×#1062190011yescharacteristic
789C2×C4#1306337011yescharacteristic
790C2×C4#1306337011yescharacteristic
791C8—22no—
792C8—41no—
793C8—1721no—
794C8—1721no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—1721no—
806C22—1721no—
807C22—1721no—
808C22—1721no—
809C22#120×D4311yescharacteristic
810C22D4×C22⋊D4311yescharacteristic
811C22#1458353611yescharacteristic
812C22#137×D4311yescharacteristic
813C22C2×#1306335711yescharacteristic
814C22#1458371211yescharacteristic
815C22#1458371511yescharacteristic
816C4—24no—
817C4—41no—
818C4—42no—
819C4—42no—
820C4—81no—
821C4—862no—
822C4—862no—
823C4—3441no—
824C4—3441no—
825C4—1721no—
826C4—1722no—
827C4—1722no—
828C4C2×#1306329711yescharacteristic
829C4#1458346411yescharacteristic
830C4D4×C22⋊D4311yescharacteristic
831C4#1458353611yescharacteristic
832C2—42no—
833C2—1722no—
834C2#1913794811yescharacteristic
835C2#1914383011yescharacteristic
836C2#1914388511yescharacteristic
837C2#1914615911yescharacteristic
838C2#1914616511yescharacteristic
839C2#1914663911yescharacteristic
840C2#1914665011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#451D43
hypocenterC43#24255
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#14583107C2semidirect
3. C2×#14583053C2semidirect
4. C2×#14583006C2semidirect
6. #19135792C2semidirect
7. #19135790C2semidirect
8. #19135603C2semidirect
9. #19135602C2semidirect
10. #19135413C2semidirect
12. #19134608C2semidirect
13. #19134530C2semidirect
14. #19134528C2semidirect
15. C2×C43×#451C2semidirect
155. C2×Q16×C43D4semidirect
415. C2×#451D43semidirect
485. C43#24255semidirect
517. C2×Q16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D432
C2×#145831072
C2×#145830532
C2×#145830062
#191395022
#191357922
#191357902
#191356032
#191356022
#191354132
#191353912
#191346082
#191345302
#191345282
C2×C43×#4512
#2425543