Finite Group Databasebeta

← #25134358

Subgroups — #25134358

Order 11008.

1438 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic86C211yesmaximal, characteristic
2C2×#14583140C211yesmaximal, characteristic, complemented
3C2×#14583057C211yesmaximal, characteristic, complemented
4C2×#14583057C211yesmaximal, characteristic, complemented
5C22×#13063250C211yesmaximal, characteristic, complemented
6#19138046C211yesmaximal, characteristic
7#19135842C211yesmaximal, characteristic, complemented
8#19135799C211yesmaximal, characteristic, complemented
9#19135697C211yesmaximal, characteristic, complemented
10#19135605C211yesmaximal, characteristic, complemented
11#19134935C211yesmaximal, characteristic, complemented
12#19134900C211yesmaximal, characteristic, complemented
13#19134852C211yesmaximal, characteristic, complemented
14#19134531C211yesmaximal, characteristic, complemented
15C43×#1869C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×Dic172C2211yescharacteristic
20C22×Dic172C2211yescharacteristic
21D4×Dic86—24no—
22D4×Dic86—24no—
23C2×#13063325C2211yescharacteristic
24C2×#13063324—21no—
25C2×#13063304C2211yescharacteristic
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×#13063304C2211yescharacteristic
29C2×#13063302—21no—
30C2×#13063302—21no—
31C2×C4×Dic86C2211yescharacteristic
32C2×D4×Dic43—21no—
33C22×C4⋊Dic43C2211yescharacteristic
34#14583140—24no—
35#14583057—24no—
36#14583057—24no—
37C2×#13063259C2211yescharacteristic
38C2×#13063250—24no—
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063250C2211yescharacteristic
43C2×#13063250C2211yescharacteristic
44C2×#13063250C2211yescharacteristic
45C2×#13063250C2211yescharacteristic
46C2×#13063250C2211yescharacteristic
47C2×#13063250C2211yescharacteristic
48C2×#13063250C2211yescharacteristic
49#14582832—21no—
50#14582822—21no—
51#14582805C2211yescharacteristic
52#14582797C2211yescharacteristic
53#14582779—21no—
54#14582759C2211yescharacteristic
55#14582757—21no—
56#14582662C2211yescharacteristic
57#14582662C2211yescharacteristic
58C23×C8×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C43×#336C2211yescharacteristic
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—22no—
68C22×Dic86—21no—
69C22×Dic86—21no—
70C22×Dic86—22no—
71C22×Dic86—22no—
72C22×Dic86—22no—
73C22×Dic86—22no—
74C22×Dic86—41no—
75C22×Dic86—41no—
76C22×Dic86—41no—
77C22×Dic86—41no—
78C22×Dic86D414yes—
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C22×Dic86C2311yescharacteristic
82C22×Dic86C2311yescharacteristic
83C23×Dic43—21no—
84C23×Dic43—21no—
85C23×Dic43—21no—
86C2×Dic172—22no—
87C2×Dic172—22no—
88C2×Dic172—22no—
89C2×Dic172—22no—
90C2×Dic172—22no—
91C2×Dic172—22no—
92C2×Dic172—41no—
93C2×Dic172—41no—
94C2×Dic172—41no—
95#13063325—22no—
96#13063325—22no—
97#13063324—28no—
98#13063304—22no—
99#13063304—22no—
100#13063304—22no—
101#13063304—22no—
102#13063304—22no—
103#13063304—22no—
104#13063304—41no—
105#13063304D414yes—
106#13063302—28no—
107#13063302—28no—
108C4×Dic86—22no—
109C4×Dic86—22no—
110D4×Dic43—28no—
111C2×C4⋊Dic43—21no—
112C2×C4⋊Dic43—21no—
113C2×C4⋊Dic43—22no—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43—41no—
116C2×C4⋊Dic43C2311yescharacteristic
117C2×C4⋊Dic43C2311yescharacteristic
118C2×C4⋊Dic43C2311yescharacteristic
119C2×C4⋊Dic43C2311yescharacteristic
120C2×Dic43⋊C4—21no—
121C2×Dic43⋊C4—21no—
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×C22⋊Dic43—21no—
127C2×C22⋊Dic43—21no—
128C2×C22⋊Dic43—21no—
129C2×C22⋊Dic43—21no—
130C2×C22⋊Dic43—21no—
131C2×C4×Dic43—21no—
132#13063259—22no—
133#13063250—22no—
134#13063250—22no—
135#13063250—22no—
136#13063250—22no—
137#13063250—22no—
138#13063250—22no—
139#13063250—22no—
140#13063250—22no—
141#13063250—41no—
142#13063250D414yescomplemented
143C43⋊#95—21no—
144C43⋊#95—21no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C22×D4×C43D411yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C22×C8×C43—22no—
151C22×C8×C43—22no—
152C22×C8×C43—41no—
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C22×C8×C43C2311yescharacteristic
157C4×D4×C43—22no—
158C4×D4×C43—22no—
159C2×C4⋊C4×C43D411yescharacteristic
160C2×C22⋊C4×C43D411yescharacteristic
161C2×C22⋊C4×C43D411yescharacteristic
162C2×C42×C43C2311yescharacteristic
163C22⋊C8×C43—22no—
164C22⋊C8×C43—22no—
165C22⋊C8×C43—41no—
166C24×C43C2×D411yescharacteristic
167C24×C43C2×D411yescharacteristic
168C2×D4×C43—22no—
169C2×D4×C43—22no—
170C2×D4×C43Q1614yescomplemented
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
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—21no—
181C22×C4×C43C2×D412yes—
182C22×C4×C43C2×D412yes—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—24no—
189C22×Dic43—24no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—42no—
199C22×Dic43—42no—
200C22×Dic43—42no—
201C22×Dic43—42no—
202C22×Dic43—42no—
203C22×Dic43—42no—
204C22×Dic43—81no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—28no—
217C2×Dic86—24no—
218C2×Dic86—24no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—44no—
228C2×Dic86—44no—
229C2×Dic86—44no—
230C2×Dic86—44no—
231C2×Dic86—44no—
232C2×Dic86—44no—
233C2×Dic86—42no—
234C2×Dic86—42no—
235C2×Dic86—42no—
236C2×Dic86—42no—
237C2×Dic86—44no—
238C2×Dic86C2×D412yes—
239C2×Dic86C2×D412yes—
240C2×Dic86C2×D412yes—
241C2×Dic86C2×D412yes—
242C2×Dic86#4112yes—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—44no—
255C2×C8×C43C2×D412yes—
256C4⋊C4×C43—22no—
257C22⋊C4×C43—22no—
258C22⋊C4×C43—22no—
259C42×C43—21no—
260C42×C43—21no—
261C22⋊Dic43—24no—
262C22⋊Dic43—24no—
263C22⋊Dic43—42no—
264C22⋊Dic43—42no—
265C22⋊Dic43—81no—
266C4⋊Dic43—24no—
267C4⋊Dic43—24no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—42no—
275C4⋊Dic43C2×D412yes—
276C4⋊Dic43C2×D412yes—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—42no—
281Dic43⋊C4—42no—
282Dic43⋊C4—81no—
283C4×Dic43—24no—
284Dic172—44no—
285Dic172—44no—
286Dic172—44no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43#12012yes—
298C23×C43C2×Q1612yes—
299C23×C43C2×Q1612yes—
300C23×C43#13712yes—
301C23×C43C22×D411yescharacteristic
302D4×C43—28no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
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—21no—
316C2×C4×C43—21no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43#12012yes—
322C2×C4×C43C2×Q1612yes—
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—48no—
337C2×Dic43—48no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
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—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—84no—
356Dic86—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—22no—
360Dic86—22no—
361Dic86—22no—
362Dic86—22no—
363Dic86—48no—
364Dic86—48no—
365Dic86—41no—
366Dic86—41no—
367Dic86—41no—
368Dic86—41no—
369Dic86—41no—
370Dic86—41no—
371Dic86—41no—
372Dic86—41no—
373Dic86#12114yes—
374C8×C43—22no—
375C8×C43—41no—
376C8×C43—41no—
377C8×C43—41no—
378#24437—431nomaximal, Sylow
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43#45114yescomplemented
393C22×C43C2×#12011yescharacteristic
394C22×C43D4211yescharacteristic
395C22×C43#54611yescharacteristic
396C22×C43C22×Q1611yescharacteristic
397C22×C43C2×#13711yescharacteristic
398C22×C43#57711yescharacteristic
399C22×C43#57811yescharacteristic
400C4×C43—22no—
401C4×C43—22no—
402C4×C43—41no—
403C4×C43—41no—
404C4×C43C2×#12111yescharacteristic
405C4×C43#53411yescharacteristic
406C4×C43D4211yescharacteristic
407C4×C43#54611yescharacteristic
408Dic43—24no—
409Dic43—42no—
410Dic43—42no—
411Dic43—42no—
412Dic43—42no—
413Dic43—81no—
414Dic43—81no—
415Dic43—81no—
416C2×D4×Q8—431no—
417C2×#467—431no—
418C2×#451—431no—
419C2×#451—431no—
420C22×#103—431no—
421#2417—431no—
422#2043—431no—
423#2036—431no—
424#2016—431no—
425#2001—431no—
426#1878—431no—
427#1872—431no—
428#1869D4311yescharacteristic
429#1863—431no—
430#1787—431no—
431C2×C43—24no—
432C2×C43—42no—
433C2×C43#241011yescharacteristic
434C2×C43C2×#45111yescharacteristic
435C2×C43#301311yescharacteristic
436C2×C43#326611yescharacteristic
437C2×C43D4×Q1611yescharacteristic
438C2×C43#329911yescharacteristic
439C2×C43#331211yescharacteristic
440C23×Q8—431no—
441C23×Q8—431no—
442C22×Q16—431no—
443C22×Q16—431no—
444C22×Q16—431no—
445C23×C8C2×D4311yescharacteristic
446D4×Q8—864no—
447D4×Q8—864no—
448C2×C4⋊Q8—431no—
449C2×C4⋊Q8—861no—
450C2×C22⋊Q8—431no—
451C2×C22⋊Q8—431no—
452C2×C22⋊Q8—431no—
453C2×C22⋊Q8—431no—
454C2×C22⋊Q8—861no—
455C2×C22⋊Q8—861no—
456C2×C4×Q8—431no—
457C2×C4×D4—861no—
458C2×C4×D4C2×D4311yescharacteristic
459C22×C4⋊C4—431no—
460#467—864no—
461#451—864no—
462#451—864no—
463C2×#107—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—864no—
475C2×C22⋊C8C2×D4311yescharacteristic
476C2×C22⋊C8C2×D4311yescharacteristic
477C2×C22⋊C8C2×D4311yescharacteristic
478#398—861no—
479#396—861no—
480#391—431no—
481#389—431no—
482#386—861no—
483#380—431no—
484#380—861no—
485#340—431no—
486#340—431no—
487#336C2×D4311yescharacteristic
488#336C2×D4311yescharacteristic
489C43#2443711yescharacteristic, complemented, Sylow
490C22×Q8—434no—
491C22×Q8—431no—
492C22×Q8—431no—
493C22×Q8—431no—
494C22×Q8—431no—
495C22×Q8—862no—
496C22×Q8—862no—
497C22×Q8—862no—
498C22×Q8—862no—
499C22×Q8—862no—
500C22×Q8—862no—
501C22×Q8—861no—
502C22×Q8—861no—
503C22×Q8—862no—
504C22×Q8—1721no—
505C22×Q8—1721no—
506C22×Q8—1721no—
507C22×Q8—1721no—
508C22×D4D17211yescharacteristic
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512C23×C4C22×D4311yescharacteristic
513C23×C4C22×D4311yescharacteristic
514C2×Q16—862no—
515C2×Q16—862no—
516C2×Q16—862no—
517C2×Q16—862no—
518C2×Q16—862no—
519C2×Q16—862no—
520C2×Q16—1721no—
521C2×Q16—1721no—
522C2×Q16—1721no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—41no—
526C22×C8C22×D4311yescharacteristic
527C22×C8C22×D4311yescharacteristic
528C22×C8C22×D4311yescharacteristic
529C22×C8C22×D4311yescharacteristic
530C4⋊Q8—862no—
531C4⋊Q8—862no—
532C4⋊Q8—868no—
533C22⋊Q8—434no—
534C22⋊Q8—868no—
535C22⋊Q8—868no—
536C22⋊Q8—862no—
537C22⋊Q8—862no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
541C22⋊Q8—862no—
542C22⋊Q8—1721no—
543C4×Q8—862no—
544C4×Q8—862no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—868no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—862no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—1721no—
563C2×C4⋊C4D17211yescharacteristic
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4D17211yescharacteristic
570C2×C22⋊C4D17211yescharacteristic
571C2×C42—861no—
572C2×C42C22×D4311yescharacteristic
573#107—862no—
574#103—434no—
575#103—862no—
576#103—862no—
577#103—862no—
578#103—862no—
579#103—862no—
580#103—862no—
581#103—862no—
582#103—862no—
583#103—1721no—
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—41no—
587#95—861no—
588#95—861no—
589#95—861no—
590#95—861no—
591C24C2×D17211yescharacteristic
592C24C2×D17211yescharacteristic
593C2×Q8—432no—
594C2×Q8—432no—
595C2×Q8—432no—
596C2×Q8—432no—
597C2×Q8—432no—
598C2×Q8—864no—
599C2×Q8—868no—
600C2×Q8—864no—
601C2×Q8—861no—
602C2×Q8—861no—
603C2×Q8—861no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8—861no—
615C2×Q8—861no—
616C2×Q8—861no—
617C2×Q8—861no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×Q8—1722no—
621C2×Q8—1722no—
622C2×Q8—1722no—
623C2×Q8—1722no—
624C2×Q8—1724no—
625C2×Q8—1724no—
626C2×Q8—1724no—
627C2×Q8—1724no—
628C2×Q8—1724no—
629C2×Q8—1724no—
630C2×Q8—1724no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4Dic17214yescomplemented
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—861no—
645C22×C4—864no—
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—3441no—
655C22×C4—1722no—
656C22×C4—1722no—
657C22×C4—1722no—
658C22×C4—1722no—
659C22×C4—1722no—
660C22×C4—1722no—
661C22×C4C2×D17211yescharacteristic
662C22×C4C2×D17211yescharacteristic
663C22×C4C2×D17211yescharacteristic
664C22×C4C2×D17211yescharacteristic
665C22×C4D4×D4312yes—
666C22×C4D4×D4312yes—
667C22×C4C23×D4311yescharacteristic
668Q16—1724no—
669Q16—1724no—
670Q16—1724no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—44no—
683C2×C8D4×D4312yes—
684C4⋊C4—22no—
685C4⋊C4—432no—
686C4⋊C4—432no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—864no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—3441no—
699C4⋊C4—1722no—
700C4⋊C4—1722no—
701C4⋊C4—1722no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—3441no—
707C22⋊C4—1722no—
708C22⋊C4—1722no—
709C42—21no—
710C42—21no—
711C42—864no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23#1306329512yes—
723C23C2×Dic17212yes—
724C23C2×Dic17212yes—
725C23#1306335812yes—
726C23C22×D17211yescharacteristic
727Q8—434no—
728Q8—862no—
729Q8—862no—
730Q8—862no—
731Q8—862no—
732Q8—862no—
733Q8—862no—
734Q8—862no—
735Q8—1728no—
736Q8—1728no—
737Q8—1721no—
738Q8—1721no—
739Q8—1721no—
740Q8—1721no—
741Q8—1721no—
742Q8—1721no—
743Q8—1721no—
744Q8—1721no—
745D4—28no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—3444no—
772C2×C4—1728no—
773C2×C4—1728no—
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×C4—1721no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4#1306329512yes—
792C2×C4C2×Dic17212yes—
793C2×C4C2×D4×D4311yescharacteristic
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4C2×D4×D4311yescharacteristic
796C2×C4#41×D4311yescharacteristic
797C2×C4#1306337011yescharacteristic
798C2×C4#1306337111yescharacteristic
799C8—22no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22#1458305714yescomplemented
817C22C2×#1306329511yescharacteristic
818C22D4×D17211yescharacteristic
819C22#1458354411yescharacteristic
820C22C22×Dic17211yescharacteristic
821C22C2×#1306335811yescharacteristic
822C22#1458371111yescharacteristic
823C22#1458371611yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—864no—
829C4—3441no—
830C4—3441no—
831C4—3441no—
832C4—1722no—
833C4—1722no—
834C4—1722no—
835C4—1722no—
836C4#121×D4311yescharacteristic
837C4#1458345711yescharacteristic
838C4#1458353111yescharacteristic
839C4#1458354111yescharacteristic
840C2—24no—
841C2—42no—
842C2#1913796811yescharacteristic
843C2C2×#1458305711yescharacteristic
844C2#1914391311yescharacteristic
845C2#1914611011yescharacteristic
846C2D4×Dic17211yescharacteristic
847C2#1914647211yescharacteristic
848C2#1914664811yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1869C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#1869D43
hypocenterC43#24437
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#14583140C2semidirect
3. C2×#14583057C2semidirect
4. C2×#14583057C2semidirect
5. C22×#13063250C2semidirect
7. #19135842C2semidirect
8. #19135799C2semidirect
9. #19135697C2semidirect
10. #19135605C2semidirect
11. #19134935C2semidirect
12. #19134900C2semidirect
13. #19134852C2semidirect
14. #19134531C2semidirect
142. #13063250D4semidirect
170. C2×D4×C43Q16semidirect
392. C22×C43#451semidirect
489. C43#24437semidirect
633. C2×D4Dic172semidirect
816. C22#14583057semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic862
C2×#145831402
C2×#145830572
C22×#130632502
#191380462
#191358422
#191357992
#191356972
#191356052
#191349352
#191349002
#191348522
#191345312
C43×#18692
#2443743