Finite Group Databasebeta

← #25020414

Subgroups — #25020414

Order 11008.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063324C211yesmaximal, characteristic
2C2×#14582804C212yesmaximal
3C2×C4⋊C4×Dic43C211yesmaximal, characteristic
4#19132865C212yesmaximal
5#19132845C212yesmaximal
6#19132830C212yesmaximal
7#19132825C211yesmaximal, characteristic
8#19132824C211yesmaximal, characteristic
9#19132824C211yesmaximal, characteristic
10C4×C43⋊#95C211yesmaximal, characteristic
11C2×C43×#389C211yesmaximal, characteristic
12C23×Dic86C2212yes—
13C2×#13063324—24no—
14C2×#13063324—24no—
15C2×#13063324C418yescomplemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2212yes—
19C22×C4×Dic43C2212yes—
20C22×C4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14582804—28no—
23C4⋊C4×Dic43—24no—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2212yes—
37C22×C4⋊C4×C43C2211yescharacteristic
38C22×C42×C43C2211yescharacteristic
39C43×#389—24no—
40C2×#95×C43C2212yes—
41C22×Dic86—24no—
42C22×Dic86—24no—
43C22×Dic86—24no—
44C22×Dic86—24no—
45C22×Dic86—42no—
46C22×Dic86—42no—
47C22×Dic86C2×C418yes—
48C23×Dic43C2312yes—
49C23×Dic43C2312yes—
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54#13063324—232no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43—22no—
58C2×C4⋊Dic43—22no—
59C2×C4⋊Dic43C2×C414yes—
60C2×C4⋊Dic43Q814yescomplemented
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4C2×C418yes—
64C2×C4×Dic43—22no—
65C2×C4×Dic43—22no—
66C2×C4×Dic43—22no—
67C2×C4×Dic43—22no—
68C2×C4×Dic43—24no—
69C2×C4×Dic43—24no—
70C2×C4×Dic43—42no—
71C2×C4×Dic43C2×C414yes—
72C2×C4×Dic43Q814yescomplemented
73C43⋊#95—24no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—22no—
78C43⋊#95—22no—
79C43⋊#95—24no—
80C43⋊#95—42no—
81C43⋊#95—42no—
82C43⋊#95D414yes—
83C43⋊#95Q814yescomplemented
84C23×C4×C43C2312yes—
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2312yes—
88C23×C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43—24no—
90C2×C4⋊C4×C43—24no—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—42no—
95C2×C4⋊C4×C43C2×C414yes—
96C2×C4⋊C4×C43D414yes—
97C2×C4⋊C4×C43D414yes—
98C2×C42×C43—22no—
99C2×C42×C43—22no—
100C2×C42×C43—22no—
101#95×C43—24no—
102C24×C43C2411yescharacteristic
103C22×C4×C43—22no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43C22×C414yes—
127C22×C4×C43C22×C412yes—
128C22×C4×C43C2×D414yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D414yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×Q812yes—
134C22×C4×C43C2×Q812yes—
135C22×C4×C43C2×Q812yes—
136C22×C4×C43#4112yes—
137C22×C4×C43#4112yes—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43—21no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—22no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—22no—
168C22×Dic43C22×C414yes—
169C22×Dic43C22×C412yes—
170C22×Dic43C22×C412yes—
171C22×Dic43C2×D412yes—
172C22×Dic43C2×D412yes—
173C22×Dic43C2×Q812yes—
174C22×Dic43C2×Q814yes—
175C22×Dic43C2×Q812yes—
176C22×Dic43C2×Q812yes—
177C22×Dic43C2×Q812yes—
178C22×Dic43#4112yes—
179C22×Dic43#4112yes—
180C2×Dic86—216no—
181C2×Dic86—216no—
182C2×Dic86—48no—
183C2×Dic86—48no—
184C2×Dic86—48no—
185C2×Dic86—48no—
186C2×Dic86—48no—
187C4⋊C4×C43—48no—
188C4⋊C4×C43—44no—
189C4⋊C4×C43C22⋊C4116yes—
190C42×C43—44no—
191C4⋊Dic43—28no—
192C4⋊Dic43—28no—
193Dic43⋊C4—216no—
194C4×Dic43—28no—
195C4×Dic43—28no—
196C4×Dic43—48no—
197C23×C43C23×C411yescharacteristic
198C23×C43C22×D411yescharacteristic
199C23×C43C22×D411yescharacteristic
200C23×C43C22×D411yescharacteristic
201C23×C43C22×Q811yescharacteristic
202C23×C43C22×Q811yescharacteristic
203C23×C43C22×Q811yescharacteristic
204C23×C43C2×#4111yescharacteristic
205C23×C43C2×#4111yescharacteristic
206C23×C43C2×#4111yescharacteristic
207C23×C43C2×#4111yescharacteristic
208C23×C43H(5,𝔽2)11yescharacteristic
209C23×C43H(5,𝔽2)11yescharacteristic
210C23×C432−1+411yescharacteristic
211C23×C432−1+411yescharacteristic
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43C2×C22⋊C418yes—
240C2×C4×C43C2×C22⋊C414yes—
241C2×C4×C43C4×Q814yes—
242C2×C4×C43C4×Q814yes—
243C2×C4×C43C22⋊Q814yes—
244C2×C4×C43C22⋊Q814yes—
245C2×C4×C43#12414yes—
246C2×C4×C43C4⋊Q814yes—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—24no—
266C2×Dic43—24no—
267C2×Dic43—24no—
268C2×Dic43—22no—
269C2×Dic43—24no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—24no—
273C2×Dic43—24no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—42no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43C4×D414yes—
287C2×Dic43C4×Q814yes—
288C2×Dic43C4⋊Q814yescomplemented
289Dic86—432no—
290#14053—431nomaximal, Sylow
291C22×C43C22×C22⋊C411yescharacteristic
292C22×C43C2×C4×D411yescharacteristic
293C22×C43C2×C4×Q811yescharacteristic
294C22×C43C2×C4×Q811yescharacteristic
295C22×C43C2×C4×Q811yescharacteristic
296C22×C43#51811yescharacteristic
297C22×C43#51911yescharacteristic
298C22×C43C2×C22⋊Q811yescharacteristic
299C22×C43C2×C22⋊Q811yescharacteristic
300C22×C43C2×#12411yescharacteristic
301C22×C43C2×C4⋊Q811yescharacteristic
302C22×C43C2×C4⋊Q811yescharacteristic
303C22×C43#53211yescharacteristic
304C22×C43#53311yescharacteristic
305C22×C43#53311yescharacteristic
306C22×C43#54211yescharacteristic
307C22×C43#54211yescharacteristic
308C22×C43#54411yescharacteristic
309C22×C43#54411yescharacteristic
310C22×C43D4211yescharacteristic
311C22×C43D4211yescharacteristic
312C22×C43#54611yescharacteristic
313C22×C43#54611yescharacteristic
314C22×C43#54711yescharacteristic
315C22×C43#54811yescharacteristic
316C22×C43#54811yescharacteristic
317C22×C43D4×Q811yescharacteristic
318C22×C43D4×Q811yescharacteristic
319C22×C43D4×Q811yescharacteristic
320C22×C43#55411yescharacteristic
321C22×C43#55411yescharacteristic
322C22×C43#55511yescharacteristic
323C22×C43#55611yescharacteristic
324C22×C43#55711yescharacteristic
325C22×C43Q8211yescharacteristic
326C4×C43—28no—
327C4×C43—42no—
328C4×C43—42no—
329C4×C43—82no—
330C4×C43#39118yescomplemented
331Dic43—24no—
332Dic43—24no—
333Dic43—24no—
334Dic43—44no—
335Dic43—42no—
336Dic43—44no—
337C22×C4⋊Q8—431no—
338C2×#391—432no—
339C2×#389D4311yescharacteristic
340C2×C4×C4⋊C4—431no—
341#1446—432no—
342#1441—432no—
343#1436—432no—
344C4⋊#95—431no—
345C4⋊#95—431no—
346C4⋊#95—431no—
347C4×#95—431no—
348C2×C43C2×#39111yescharacteristic
349C2×C43C4×C4⋊Q811yescharacteristic
350C2×C43#233111yescharacteristic
351C2×C43D4×C22⋊C411yescharacteristic
352C2×C43Q8×C22⋊C411yescharacteristic
353C2×C43#236511yescharacteristic
354C2×C43#236911yescharacteristic
355C2×C43#243911yescharacteristic
356C2×C43#244011yescharacteristic
357C2×C43#245111yescharacteristic
358C2×C43#245211yescharacteristic
359C2×C43#249111yescharacteristic
360C2×C43#249211yescharacteristic
361C2×C43#255011yescharacteristic
362C2×C43#255111yescharacteristic
363C23×Q8—432no—
364C2×C4⋊Q8—438no—
365C2×C4⋊Q8—864no—
366C2×C4⋊Q8—864no—
367C22×C4⋊C4—432no—
368C22×C4⋊C4—431no—
369C22×C4⋊C4—431no—
370C22×C4⋊C4C2×D4311yescharacteristic
371C22×C4⋊C4C2×D4312yes—
372C22×C4⋊C4C2×D4311yescharacteristic
373C22×C42—431no—
374C22×C42—431no—
375C22×C42—432no—
376C22×C42C2×D4311yescharacteristic
377#391—868no—
378#389—24no—
379C4×C4⋊C4—864no—
380C2×#95—431no—
381C2×#95—431no—
382C2×#95—431no—
383C2×#95—431no—
384C2×#95—432no—
385C2×#95—432no—
386C2×#95—432no—
387C2×#95—432no—
388C2×#95—432no—
389C2×#95—432no—
390C2×#95—432no—
391C2×#95C2×D4312yes—
392C43#1405311yescharacteristic, complemented, Sylow
393C22×Q8—438no—
394C22×Q8—864no—
395C22×Q8—864no—
396C22×Q8—864no—
397C22×Q8—864no—
398C22×Q8—1722no—
399C22×Q8—1722no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—431no—
403C23×C4—432no—
404C23×C4—432no—
405C23×C4—431no—
406C23×C4C22×D4312yes—
407C23×C4C22×D4311yescharacteristic
408C23×C4C22×D4311yescharacteristic
409C23×C4C22×D4312yes—
410C23×C4C22×D4311yescharacteristic
411C4⋊Q8—8632no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—438no—
419C2×C4⋊C4—434no—
420C2×C4⋊C4—434no—
421C2×C4⋊C4—864no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—864no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4C4×D4314yes—
428C2×C4⋊C4D17214yes—
429C2×C4⋊C4C22⋊D4314yes—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—434no—
434C2×C42—434no—
435C2×C42—862no—
436C2×C42—862no—
437C2×C42—862no—
438C2×C42—862no—
439C2×C42—864no—
440C2×C42—864no—
441C2×C42—1722no—
442#95—24no—
443#95—434no—
444#95—434no—
445#95—862no—
446#95—862no—
447#95—864no—
448#95—864no—
449#95—864no—
450#95—864no—
451#95—864no—
452#95—1722no—
453#95—1722no—
454C24C23×D4311yescharacteristic
455C2×Q8—8616no—
456C2×Q8—8616no—
457C2×Q8—1728no—
458C2×Q8—1728no—
459C2×Q8—1728no—
460C2×Q8—1728no—
461C2×Q8—1728no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—432no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—432no—
494C22×C4—434no—
495C22×C4—432no—
496C22×C4—434no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4—862no—
512C22×C4—861no—
513C22×C4—862no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—862no—
519C22×C4—861no—
520C22×C4—862no—
521C22×C4—861no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—861no—
527C22×C4C2×C4×D4314yes—
528C22×C4C2×C4×D4312yes—
529C22×C4C2×D17214yes—
530C22×C4C2×D17212yes—
531C22×C4D4×D4312yes—
532C22×C4#1062190012yes—
533C22×C4#1062190012yes—
534C22×C4Q8×D4312yes—
535C22×C4Q8×D4312yes—
536C22×C4Q8×D4312yes—
537C22×C4C2×C22⋊D4314yes—
538C22×C4C2×C22⋊D4312yes—
539C4⋊C4—48no—
540C4⋊C4—44no—
541C4⋊C4—8616no—
542C4⋊C4—868no—
543C4⋊C4—868no—
544C4⋊C4(C2×D43)⋊C4116yes—
545C42—44no—
546C42—868no—
547C42—868no—
548C42—1728no—
549C23C22×C4×D4311yescharacteristic
550C23C2×D4×D4311yescharacteristic
551C23C22×C22⋊D4311yescharacteristic
552C23C22×D17211yescharacteristic
553C23C2×Q8×D4311yescharacteristic
554C23C2×Q8×D4311yescharacteristic
555C23C2×Q8×D4311yescharacteristic
556C23#41×D4311yescharacteristic
557C23#41×D4311yescharacteristic
558C23C2×#1062190011yescharacteristic
559C23C2×#1062190011yescharacteristic
560C23#1306337011yescharacteristic
561C23#1306337111yescharacteristic
562C23#1306337211yescharacteristic
563C23#1306337311yescharacteristic
564Q8—17232no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—434no—
593C2×C4—434no—
594C2×C4—434no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—864no—
614C2×C4—864no—
615C2×C4—864no—
616C2×C4—864no—
617C2×C4—864no—
618C2×C4—862no—
619C2×C4—864no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—1722no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1722no—
627C2×C4—1722no—
628C2×C4—1722no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1722no—
632C2×C4—1722no—
633C2×C4—1721no—
634C2×C4C2×(C2×D43)⋊C418yes—
635C2×C4C2×(C2×D43)⋊C414yes—
636C2×C4#1306329014yes—
637C2×C4#1306329014yes—
638C2×C4#1306330514yes—
639C2×C4#1306330514yes—
640C2×C4#1306331214yes—
641C2×C4#1306332314yes—
642C22C22×(C2×D43)⋊C411yescharacteristic
643C22C4×D4×D4311yescharacteristic
644C22C4×Q8×D4311yescharacteristic
645C22C2×#1306329011yescharacteristic
646C22C2×#1306329011yescharacteristic
647C22#1458337111yescharacteristic
648C22#1458337511yescharacteristic
649C22C2×#1306330511yescharacteristic
650C22C2×#1306330511yescharacteristic
651C22C2×#1306331211yescharacteristic
652C22C4⋊Q8×D4311yescharacteristic
653C22C2×#1306332311yescharacteristic
654C22#1458344411yescharacteristic
655C22#1458345111yescharacteristic
656C22#1458345511yescharacteristic
657C22#1458351611yescharacteristic
658C22#1458352211yescharacteristic
659C22#1458352611yescharacteristic
660C22#1458352911yescharacteristic
661C22D4×C22⋊D4311yescharacteristic
662C22D4×D17211yescharacteristic
663C22#1458353711yescharacteristic
664C22#1458354411yescharacteristic
665C22#1458354911yescharacteristic
666C22#1458355611yescharacteristic
667C22#1458356111yescharacteristic
668C22Q8×C22⋊D4311yescharacteristic
669C22#1458356411yescharacteristic
670C22Q8×D17211yescharacteristic
671C22#1458360511yescharacteristic
672C22#1458360711yescharacteristic
673C22#1458361311yescharacteristic
674C22#1458362011yescharacteristic
675C22#1458362611yescharacteristic
676C22#1458362911yescharacteristic
677C4—28no—
678C4—42no—
679C4—42no—
680C4—82no—
681C4—864no—
682C4—864no—
683C4—864no—
684C4—1724no—
685C4—1724no—
686C4—1722no—
687C4#1458280418yescomplemented
688C2C2×#1458280411yescharacteristic
689C2#1913716611yescharacteristic
690C2#1913734211yescharacteristic
691C2D4×(C2×D43)⋊C411yescharacteristic
692C2Q8×(C2×D43)⋊C411yescharacteristic
693C2#1913764811yescharacteristic
694C2#1913768111yescharacteristic
695C2#1913828411yescharacteristic
696C2#1913829511yescharacteristic
697C2#1913843211yescharacteristic
698C2#1913844311yescharacteristic
699C2#1913896011yescharacteristic
700C2#1913897111yescharacteristic
701C2#1913961411yescharacteristic
702C2#1913962211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#389C2
socle, prime radical, cosocleC24×C43C24
hypercenterC2×#389D43
hypocenterC43#14053
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
15. C2×#13063324C4semidirect
60. C2×C4⋊Dic43Q8semidirect
72. C2×C4×Dic43Q8semidirect
83. C43⋊#95Q8semidirect
288. C2×Dic43C4⋊Q8semidirect
330. C4×C43#391semidirect
392. C43#14053semidirect
687. C4#14582804semidirect

Maximal subgroups

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

subgroupindex
C22×#130633242
C2×#145828042
C2×C4⋊C4×Dic432
#191328652
#191328452
#191328302
#191328252
#191328242
C4×C43⋊#952
C2×C43×#3892
#1405343