Finite Group Databasebeta

← #25028020

Subgroups — #25028020

Order 11008.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063306C211yesmaximal, characteristic, complemented
2C22×D4×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582813C211yesmaximal, characteristic, complemented
4C2×#14582779C211yesmaximal, characteristic, complemented
5C2×#14582771C211yesmaximal, characteristic, complemented
6#19132859C211yesmaximal, characteristic, complemented
7#19132842C211yesmaximal, characteristic, complemented
8#19132840C211yesmaximal, characteristic, complemented
9#19132838C211yesmaximal, characteristic, complemented
10#19132836C211yesmaximal, characteristic, complemented
11#19132836C211yesmaximal, characteristic, complemented
12#19132832C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C2×C43×#392C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C2×#13063306—24no—
19C2×#13063306—24no—
20C2×#13063306—24no—
21C2×D4×Dic43—24no—
22C2×D4×Dic43—24no—
23C2×D4×Dic43—24no—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×C22⋊Dic43C2211yescharacteristic
36C22×C22⋊Dic43C2211yescharacteristic
37C22×C22⋊Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39#14582813—24no—
40#14582779—24no—
41#14582771—24no—
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C23×D4×C43C2211yescharacteristic
54C23×D4×C43C2211yescharacteristic
55C23×D4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C43×#392—24no—
60C2×#95×C43C2211yescharacteristic
61C23×Dic43—22no—
62C23×Dic43—22no—
63C23×Dic43—22no—
64C23×Dic43—22no—
65C23×Dic43—22no—
66C23×Dic43—22no—
67C23×Dic43—22no—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—41no—
71C23×Dic43—41no—
72C23×Dic43—41no—
73C23×Dic43—41no—
74C23×Dic43D414yescomplemented
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83#13063306—232no—
84D4×Dic43—232no—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—41no—
96C2×Dic43⋊C4D414yescomplemented
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—22no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—22no—
102C2×C22⋊Dic43—22no—
103C2×C22⋊Dic43—22no—
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—22no—
109C2×C22⋊Dic43—22no—
110C2×C22⋊Dic43—22no—
111C2×C22⋊Dic43—22no—
112C2×C22⋊Dic43—22no—
113C2×C22⋊Dic43—22no—
114C2×C22⋊Dic43—22no—
115C2×C22⋊Dic43—22no—
116C2×C22⋊Dic43—22no—
117C2×C22⋊Dic43—22no—
118C2×C22⋊Dic43—22no—
119C2×C22⋊Dic43—22no—
120C2×C22⋊Dic43—22no—
121C2×C22⋊Dic43—41no—
122C2×C22⋊Dic43—41no—
123C2×C22⋊Dic43—41no—
124C2×C22⋊Dic43—41no—
125C2×C22⋊Dic43D414yescomplemented
126C2×C22⋊Dic43D414yescomplemented
127C2×C4×Dic43—22no—
128C2×C4×Dic43—22no—
129C2×C4×Dic43—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—41no—
139C43⋊#95—41no—
140C43⋊#95—41no—
141C25×C43C2311yescharacteristic
142C25×C43C2311yescharacteristic
143C25×C43C2311yescharacteristic
144C22×D4×C43—22no—
145C22×D4×C43—22no—
146C22×D4×C43—22no—
147C22×D4×C43—22no—
148C22×D4×C43—22no—
149C22×D4×C43—22no—
150C22×D4×C43—22no—
151C22×D4×C43—22no—
152C22×D4×C43—22no—
153C22×D4×C43—22no—
154C22×D4×C43—22no—
155C22×D4×C43—22no—
156C22×D4×C43—22no—
157C22×D4×C43—22no—
158C22×D4×C43—22no—
159C22×D4×C43—22no—
160C22×D4×C43—41no—
161C22×D4×C43—41no—
162C22×D4×C43—41no—
163C22×D4×C43—41no—
164C22×D4×C43D414yes—
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C23×C4×C43C2311yescharacteristic
168C23×C4×C43C2311yescharacteristic
169C2×C22⋊C4×C43—22no—
170C2×C22⋊C4×C43—22no—
171C2×C22⋊C4×C43—22no—
172C2×C22⋊C4×C43—22no—
173C2×C22⋊C4×C43—22no—
174C2×C22⋊C4×C43—22no—
175C2×C22⋊C4×C43—22no—
176C2×C22⋊C4×C43—41no—
177C2×C22⋊C4×C43—41no—
178#95×C43—22no—
179C24×C43—21no—
180C24×C43—21no—
181C24×C43—21no—
182C24×C43—21no—
183C24×C43—21no—
184C24×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43—21no—
191C24×C43—21no—
192C24×C43—21no—
193C24×C43—21no—
194C24×C43—21no—
195C24×C43—21no—
196C24×C43—21no—
197C24×C43—21no—
198C24×C43—21no—
199C24×C43—21no—
200C24×C43—21no—
201C24×C43—21no—
202C24×C43—21no—
203C24×C43—21no—
204C24×C43—21no—
205C24×C43—21no—
206C24×C43—21no—
207C24×C43—21no—
208C24×C43—21no—
209C24×C43—21no—
210C24×C43—21no—
211C24×C43—21no—
212C24×C43—21no—
213C24×C43—21no—
214C24×C43—21no—
215C24×C43—21no—
216C24×C43—21no—
217C24×C43C2×D412yes—
218C24×C43C2×D412yes—
219C24×C43C2×D412yes—
220C24×C43C2×D412yes—
221C24×C43C2×D412yes—
222C24×C43#4112yes—
223C24×C43#4112yes—
224C24×C43C2411yescharacteristic
225C2×D4×C43—28no—
226C2×D4×C43—28no—
227C2×D4×C43—28no—
228C2×D4×C43—28no—
229C2×D4×C43—28no—
230C2×D4×C43—28no—
231C2×D4×C43—28no—
232C2×D4×C43—28no—
233C2×D4×C43—28no—
234C2×D4×C43—44no—
235C2×D4×C43—44no—
236C2×D4×C43—44no—
237C2×D4×C43—44no—
238C2×D4×C43—44no—
239C2×D4×C43—44no—
240C2×D4×C43—44no—
241C2×D4×C43—44no—
242C2×D4×C43—44no—
243C2×D4×C43—44no—
244C2×D4×C43—44no—
245C2×D4×C43—44no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43—21no—
268C22×C4×C43—21no—
269C22×C4×C43C2×D412yes—
270C22×C4×C43C2×D412yes—
271C22×C4×C43#4112yes—
272C22×C4×C43#4112yes—
273C22×C4×C43#4112yes—
274C22×Dic43—28no—
275C22×Dic43—28no—
276C22×Dic43—28no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43—21no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—21no—
294C22×Dic43—21no—
295C22×Dic43—21no—
296C22×Dic43—21no—
297C22×Dic43—21no—
298C22×Dic43—21no—
299C22×Dic43—21no—
300C22×Dic43—21no—
301C22×Dic43—21no—
302C22×Dic43—21no—
303C22×Dic43—21no—
304C22×Dic43—21no—
305C22×Dic43—21no—
306C22×Dic43—21no—
307C22×Dic43—21no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43—21no—
312C22×Dic43—21no—
313C22×Dic43—21no—
314C22×Dic43—21no—
315C22×Dic43—21no—
316C22×Dic43—21no—
317C22×Dic43—21no—
318C22×Dic43—21no—
319C22×Dic43—21no—
320C22×Dic43—21no—
321C22×Dic43—21no—
322C22×Dic43—21no—
323C22×Dic43—21no—
324C22×Dic43—44no—
325C22×Dic43—44no—
326C22×Dic43—44no—
327C22×Dic43—44no—
328C22×Dic43—44no—
329C22×Dic43—44no—
330C22×Dic43—44no—
331C22×Dic43—44no—
332C22×Dic43—44no—
333C22×Dic43—44no—
334C22×Dic43—44no—
335C22×Dic43C2×D412yes—
336C22×Dic43C2×D412yes—
337C22×Dic43C2×D412yes—
338C22×Dic43C2×D412yes—
339C22×Dic43C2×D412yes—
340C22×Dic43C2×D412yes—
341C22×Dic43C2×D412yes—
342C22×Dic43C2×D412yes—
343C22×Dic43#4112yes—
344C22⋊C4×C43—44no—
345C22⋊C4×C43—44no—
346C22⋊C4×C43—44no—
347C22⋊Dic43—28no—
348C22⋊Dic43—28no—
349C22⋊Dic43—28no—
350C22⋊Dic43—28no—
351C22⋊Dic43—28no—
352C22⋊Dic43—28no—
353C22⋊Dic43—44no—
354C22⋊Dic43—44no—
355C22⋊Dic43—44no—
356C22⋊Dic43—44no—
357C4⋊Dic43—28no—
358Dic43⋊C4—28no—
359Dic43⋊C4—28no—
360Dic43⋊C4—44no—
361C4×Dic43—28no—
362C23×C43—22no—
363C23×C43—22no—
364C23×C43—22no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—22no—
368C23×C43—22no—
369C23×C43—22no—
370C23×C43—22no—
371C23×C43—22no—
372C23×C43—22no—
373C23×C43—22no—
374C23×C43—22no—
375C23×C43—22no—
376C23×C43—22no—
377C23×C43—22no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—22no—
393C23×C43—22no—
394C23×C43—22no—
395C23×C43—22no—
396C23×C43—22no—
397C23×C43—22no—
398C23×C43—22no—
399C23×C43—22no—
400C23×C43—22no—
401C23×C43—22no—
402C23×C43—22no—
403C23×C43—22no—
404C23×C43—22no—
405C23×C43—41no—
406C23×C43—41no—
407C23×C43—41no—
408C23×C43—41no—
409C23×C43—41no—
410C23×C43—41no—
411C23×C43—41no—
412C23×C43—41no—
413C23×C43—41no—
414C23×C43—41no—
415C23×C43—41no—
416C23×C43—41no—
417C23×C43—41no—
418C23×C43—41no—
419C23×C43—41no—
420C23×C43—41no—
421C23×C43—41no—
422C23×C43—41no—
423C23×C43—41no—
424C23×C43—41no—
425C23×C43—41no—
426C23×C43—41no—
427C23×C43—41no—
428C23×C43—41no—
429C23×C43—41no—
430C23×C43—41no—
431C23×C43—41no—
432C23×C43—41no—
433C23×C43—41no—
434C23×C43—41no—
435C23×C43—41no—
436C23×C43—41no—
437C23×C43—41no—
438C23×C43—41no—
439C23×C43—41no—
440C23×C43—41no—
441C23×C43—41no—
442C23×C43—41no—
443C23×C43—41no—
444C23×C43—41no—
445C23×C43—41no—
446C23×C43—41no—
447C23×C43—41no—
448C23×C43—41no—
449C23×C43—41no—
450C23×C43—41no—
451C23×C43—41no—
452C23×C43—41no—
453C23×C43—41no—
454C23×C43—41no—
455C23×C43—41no—
456C23×C43—41no—
457C23×C43—41no—
458C23×C43—41no—
459C23×C43—41no—
460C23×C43—41no—
461C23×C43—41no—
462C23×C43—41no—
463C23×C43—41no—
464C23×C43—41no—
465C23×C43#12014yes—
466C23×C43#12314yescomplemented
467C23×C43C22×D411yescharacteristic
468C23×C43C22×D411yescharacteristic
469C23×C43C22×D411yescharacteristic
470C23×C43C22×D411yescharacteristic
471C23×C43C22×D411yescharacteristic
472C23×C43C2×#4111yescharacteristic
473C23×C43C2×#4111yescharacteristic
474C23×C43C2×#4111yescharacteristic
475C23×C43C2×#4111yescharacteristic
476C23×C43C2×#4111yescharacteristic
477C23×C43C2×#4111yescharacteristic
478C23×C43H(5,𝔽2)11yescharacteristic
479C23×C43H(5,𝔽2)11yescharacteristic
480C23×C43H(5,𝔽2)11yescharacteristic
481C23×C432−1+411yescharacteristic
482D4×C43—232no—
483D4×C43—416no—
484D4×C43—416no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—22no—
491C2×C4×C43—22no—
492C2×C4×C43—22no—
493C2×C4×C43—22no—
494C2×C4×C43—22no—
495C2×C4×C43—22no—
496C2×C4×C43—22no—
497C2×C4×C43—41no—
498C2×C4×C43—41no—
499C2×C4×C43—41no—
500C2×C4×C43—41no—
501C2×C4×C43—41no—
502C2×C4×C43—41no—
503C2×C4×C43—41no—
504C2×C4×C43—41no—
505C2×C4×C43—41no—
506C2×C4×C43—41no—
507C2×C4×C43—41no—
508C2×C4×C43—41no—
509C2×C4×C43—41no—
510C2×C4×C43—41no—
511C2×C4×C43—41no—
512C2×C4×C43#12314yescomplemented
513C2×Dic43—22no—
514C2×Dic43—22no—
515C2×Dic43—22no—
516C2×Dic43—22no—
517C2×Dic43—22no—
518C2×Dic43—22no—
519C2×Dic43—22no—
520C2×Dic43—22no—
521C2×Dic43—22no—
522C2×Dic43—22no—
523C2×Dic43—22no—
524C2×Dic43—22no—
525C2×Dic43—22no—
526C2×Dic43—22no—
527C2×Dic43—22no—
528C2×Dic43—22no—
529C2×Dic43—22no—
530C2×Dic43—22no—
531C2×Dic43—22no—
532C2×Dic43—22no—
533C2×Dic43—22no—
534C2×Dic43—22no—
535C2×Dic43—22no—
536C2×Dic43—22no—
537C2×Dic43—416no—
538C2×Dic43—416no—
539C2×Dic43—41no—
540C2×Dic43—41no—
541C2×Dic43—41no—
542C2×Dic43—41no—
543C2×Dic43—41no—
544C2×Dic43—41no—
545C2×Dic43—41no—
546C2×Dic43—41no—
547C2×Dic43—41no—
548C2×Dic43—41no—
549C2×Dic43—41no—
550C2×Dic43—41no—
551C2×Dic43—41no—
552C2×Dic43—41no—
553C2×Dic43—41no—
554C2×Dic43—41no—
555C2×Dic43—41no—
556C2×Dic43—41no—
557C2×Dic43—41no—
558C2×Dic43—41no—
559C2×Dic43—41no—
560C2×Dic43—41no—
561C2×Dic43—41no—
562C2×Dic43—41no—
563C2×Dic43—41no—
564C2×Dic43—41no—
565C2×Dic43—41no—
566C2×Dic43—41no—
567C2×Dic43—41no—
568C2×Dic43—41no—
569C2×Dic43—41no—
570C2×Dic43#12014yes—
571#14721—431nomaximal, Sylow
572C22×C43—24no—
573C22×C43—24no—
574C22×C43—24no—
575C22×C43—24no—
576C22×C43—24no—
577C22×C43—24no—
578C22×C43—42no—
579C22×C43—42no—
580C22×C43—42no—
581C22×C43—42no—
582C22×C43—42no—
583C22×C43—42no—
584C22×C43—42no—
585C22×C43—42no—
586C22×C43—42no—
587C22×C43—42no—
588C22×C43—42no—
589C22×C43—42no—
590C22×C43—42no—
591C22×C43—42no—
592C22×C43—42no—
593C22×C43—42no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—42no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43—42no—
600C22×C43—42no—
601C22×C43—42no—
602C22×C43—42no—
603C22×C43—42no—
604C22×C43—42no—
605C22×C43—42no—
606C22×C43—42no—
607C22×C43—42no—
608C22×C43—42no—
609C22×C43—81no—
610C22×C43—81no—
611C22×C43—81no—
612C22×C43—81no—
613C22×C43—81no—
614C22×C43—81no—
615C22×C43—81no—
616C22×C43—81no—
617C22×C43C2×#12011yescharacteristic
618C22×C43C2×#12011yescharacteristic
619C22×C43C2×#12311yescharacteristic
620C22×C43C2×#12311yescharacteristic
621C22×C43#52511yescharacteristic
622C22×C43#52511yescharacteristic
623C22×C43#52511yescharacteristic
624C22×C43#52511yescharacteristic
625C22×C43#52511yescharacteristic
626C22×C43#52511yescharacteristic
627C22×C43#53211yescharacteristic
628C22×C43#53211yescharacteristic
629C22×C43#53211yescharacteristic
630C22×C43#53411yescharacteristic
631C22×C43#53711yescharacteristic
632C22×C43#53811yescharacteristic
633C22×C43#53911yescharacteristic
634C22×C43#54011yescharacteristic
635C22×C43#54211yescharacteristic
636C22×C43D4211yescharacteristic
637C22×C43D4211yescharacteristic
638C22×C43D4211yescharacteristic
639C22×C43D4211yescharacteristic
640C22×C43#54611yescharacteristic
641C22×C43#54611yescharacteristic
642C22×C43#54611yescharacteristic
643C22×C43#54711yescharacteristic
644C22×C43#54711yescharacteristic
645C22×C43#54711yescharacteristic
646C22×C43#54811yescharacteristic
647C22×C43#55011yescharacteristic
648C22×C43#55111yescharacteristic
649C22×C43#55311yescharacteristic
650C22×C43#55311yescharacteristic
651C22×C43#55911yescharacteristic
652C4×C43—24no—
653C4×C43—42no—
654C4×C43—42no—
655C4×C43—81no—
656Dic43—24no—
657Dic43—42no—
658Dic43—42no—
659Dic43—42no—
660Dic43—42no—
661Dic43—42no—
662Dic43—42no—
663Dic43—81no—
664C22×#123—431no—
665C22×C4×D4—431no—
666C2×#394—431no—
667C2×#392D4311yescharacteristic
668C2×#386—431no—
669C2×#385—431no—
670#1444—431no—
671#1440—431no—
672#1439—431no—
673#1439—431no—
674#1438—431no—
675#1438—431no—
676#1437—431no—
677#1436—431no—
678C22⋊#95—431no—
679C2×C43—44no—
680C2×C43—44no—
681C2×C43—82no—
682C2×C43#238811yescharacteristic
683C2×C43#240311yescharacteristic
684C2×C43#240711yescharacteristic
685C2×C43#241811yescharacteristic
686C2×C43#242211yescharacteristic
687C2×C43#243011yescharacteristic
688C2×C43#244311yescharacteristic
689C2×C43#244511yescharacteristic
690C2×C43#245511yescharacteristic
691C2×C43#245611yescharacteristic
692C2×C43#246111yescharacteristic
693C2×C43#246411yescharacteristic
694C2×C43#260211yescharacteristic
695C2×C43#263011yescharacteristic
696C2×C43#284911yescharacteristic
697C23×D4C2×D4311yescharacteristic
698C23×D4C2×D4311yescharacteristic
699C23×D4C2×D4311yescharacteristic
700C24×C4—431no—
701C24×C4—431no—
702C2×#123—864no—
703C2×#123—864no—
704C2×#123—864no—
705C2×C4×D4—864no—
706C2×C4×D4—864no—
707C2×C4×D4—864no—
708C22×C4⋊C4—431no—
709C22×C4⋊C4—431no—
710C22×C4⋊C4—431no—
711C22×C4⋊C4—431no—
712C22×C22⋊C4—431no—
713C22×C22⋊C4—431no—
714C22×C22⋊C4—431no—
715C22×C22⋊C4—431no—
716C22×C22⋊C4—431no—
717C22×C22⋊C4—431no—
718C22×C22⋊C4—431no—
719C22×C22⋊C4—431no—
720C22×C22⋊C4—431no—
721C22×C22⋊C4—431no—
722C22×C22⋊C4C2×D4311yescharacteristic
723C22×C22⋊C4C2×D4311yescharacteristic
724C22×C22⋊C4C2×D4311yescharacteristic
725C22×C42—431no—
726#394—864no—
727#392—24no—
728#386—864no—
729#385—864no—
730C2×#95—431no—
731C2×#95—431no—
732C2×#95—431no—
733C2×#95—431no—
734C2×#95—431no—
735C2×#95—431no—
736C2×#95—431no—
737C2×#95—431no—
738C2×#95—431no—
739C2×#95—431no—
740C2×#95—431no—
741C2×#95C2×D4311yescharacteristic
742C43#1472111yescharacteristic, complemented, Sylow
743C25C22×D4311yescharacteristic
744C25C22×D4311yescharacteristic
745C25C22×D4311yescharacteristic
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—22no—
756C22×D4—22no—
757C22×D4—22no—
758C22×D4—22no—
759C22×D4—22no—
760C22×D4—22no—
761C22×D4—22no—
762C22×D4—41no—
763C22×D4—41no—
764C22×D4—41no—
765C22×D4—41no—
766C22×D4C22⋊D4314yes—
767C23×C4—431no—
768C23×C4—431no—
769C23×C4—431no—
770C23×C4—431no—
771C23×C4—431no—
772C23×C4—431no—
773C23×C4—431no—
774C23×C4—434no—
775C23×C4—431no—
776C23×C4—862no—
777C23×C4—862no—
778C23×C4—862no—
779C23×C4—862no—
780C23×C4—862no—
781C23×C4—862no—
782C23×C4—862no—
783C23×C4—862no—
784C23×C4—862no—
785C23×C4—1721no—
786C23×C4—1721no—
787C23×C4—1721no—
788C23×C4—1721no—
789C23×C4C22×D4311yescharacteristic
790C23×C4C22×D4311yescharacteristic
791C23×C4C22×D4311yescharacteristic
792C23×C4C22×D4311yescharacteristic
793#123—8632no—
794C4×D4—8632no—
795C2×C4⋊C4—434no—
796C2×C4⋊C4—862no—
797C2×C4⋊C4—862no—
798C2×C4⋊C4—862no—
799C2×C4⋊C4—862no—
800C2×C4⋊C4—862no—
801C2×C4⋊C4—862no—
802C2×C4⋊C4—862no—
803C2×C4⋊C4—862no—
804C2×C4⋊C4—862no—
805C2×C4⋊C4—862no—
806C2×C4⋊C4—1721no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—434no—
817C2×C22⋊C4—434no—
818C2×C22⋊C4—862no—
819C2×C22⋊C4—862no—
820C2×C22⋊C4—862no—
821C2×C22⋊C4—862no—
822C2×C22⋊C4—862no—
823C2×C22⋊C4—862no—
824C2×C22⋊C4—862no—
825C2×C22⋊C4—862no—
826C2×C22⋊C4—862no—
827C2×C22⋊C4—862no—
828C2×C22⋊C4—862no—
829C2×C22⋊C4—862no—
830C2×C22⋊C4—862no—
831C2×C22⋊C4—862no—
832C2×C22⋊C4—862no—
833C2×C22⋊C4—862no—
834C2×C22⋊C4—862no—
835C2×C22⋊C4—862no—
836C2×C22⋊C4—862no—
837C2×C22⋊C4—862no—
838C2×C22⋊C4—862no—
839C2×C22⋊C4—862no—
840C2×C22⋊C4—862no—
841C2×C22⋊C4—862no—
842C2×C22⋊C4—1721no—
843C2×C22⋊C4—1721no—
844C2×C22⋊C4—1721no—
845C2×C22⋊C4—1721no—
846C2×C42—862no—
847C2×C42—862no—
848C2×C42—862no—
849#95—22no—
850#95—862no—
851#95—862no—
852#95—862no—
853#95—862no—
854#95—862no—
855#95—862no—
856#95—862no—
857#95—862no—
858#95—1721no—
859#95—1721no—
860#95—1721no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24D4×D4312yes—
900C24D4×D4312yes—
901C24D4×D4312yes—
902C24#1062190012yes—
903C24#1062190012yes—
904C24C2×C22⋊D4312yes—
905C24C2×C22⋊D4312yes—
906C24C23×D4311yescharacteristic
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—432no—
952C22×C4—432no—
953C22×C4—432no—
954C22×C4—432no—
955C22×C4—432no—
956C22×C4—432no—
957C22×C4—432no—
958C22×C4—432no—
959C22×C4—432no—
960C22×C4—868no—
961C22×C4—861no—
962C22×C4—861no—
963C22×C4—861no—
964C22×C4—861no—
965C22×C4—868no—
966C22×C4—868no—
967C22×C4—861no—
968C22×C4—861no—
969C22×C4—861no—
970C22×C4—861no—
971C22×C4—861no—
972C22×C4—861no—
973C22×C4—861no—
974C22×C4—861no—
975C22×C4—861no—
976C22×C4—861no—
977C22×C4—861no—
978C22×C4—861no—
979C22×C4—861no—
980C22×C4—861no—
981C22×C4—861no—
982C22×C4—861no—
983C22×C4—861no—
984C22×C4—861no—
985C22×C4—861no—
986C22×C4—861no—
987C22×C4—861no—
988C22×C4—861no—
989C22×C4—861no—
990C22×C4—861no—
991C22×C4—861no—
992C22×C4—861no—
993C22×C4—861no—
994C22×C4—861no—
995C22×C4—861no—
996C22×C4—861no—
997C22×C4—861no—
998C22×C4—861no—
999C22×C4—861no—
1000C22×C4—861no—
1001C22×C4—861no—
1002C22×C4—861no—
1003C22×C4—861no—
1004C22×C4—861no—
1005C22×C4—861no—
1006C22×C4—861no—
1007C22×C4—861no—
1008C22×C4—861no—
1009C22×C4—861no—
1010C22×C4—1724no—
1011C22×C4—1724no—
1012C22×C4—1724no—
1013C22×C4—1724no—
1014C22×C4—1724no—
1015C22×C4—1724no—
1016C22×C4—1724no—
1017C22×C4—1724no—
1018C22×C4—1724no—
1019C22×C4—1724no—
1020C22×C4—1724no—
1021C22×C4D4×D4312yes—
1022C22×C4#1062190012yes—
1023C22×C4#1062190012yes—
1024C22×C4#1062190012yes—
1025C22×C4C2×C22⋊D4312yes—
1026C4⋊C4—868no—
1027C4⋊C4—868no—
1028C4⋊C4—868no—
1029C4⋊C4—1724no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—868no—
1034C22⋊C4—868no—
1035C22⋊C4—868no—
1036C22⋊C4—868no—
1037C22⋊C4—868no—
1038C22⋊C4—868no—
1039C22⋊C4—1724no—
1040C22⋊C4—1724no—
1041C22⋊C4—1724no—
1042C22⋊C4—1724no—
1043C42—868no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23#1306329314yes—
1148C23#1306330614yescomplemented
1149C23C2×D4×D4311yescharacteristic
1150C23C2×D4×D4311yescharacteristic
1151C23C2×D4×D4311yescharacteristic
1152C23C2×D4×D4311yescharacteristic
1153C23C22×C22⋊D4311yescharacteristic
1154C23#41×D4311yescharacteristic
1155C23C2×#1062190011yescharacteristic
1156C23C2×#1062190011yescharacteristic
1157C23C2×#1062190011yescharacteristic
1158C23C2×#1062190011yescharacteristic
1159C23C2×#1062190011yescharacteristic
1160C23#1306337011yescharacteristic
1161C23#1306337011yescharacteristic
1162C23#1306337011yescharacteristic
1163C23#1306337211yescharacteristic
1164D4—232no—
1165D4—416no—
1166D4—416no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—434no—
1195C2×C4—862no—
1196C2×C4—862no—
1197C2×C4—862no—
1198C2×C4—862no—
1199C2×C4—862no—
1200C2×C4—862no—
1201C2×C4—862no—
1202C2×C4—862no—
1203C2×C4—862no—
1204C2×C4—862no—
1205C2×C4—862no—
1206C2×C4—862no—
1207C2×C4—862no—
1208C2×C4—862no—
1209C2×C4—862no—
1210C2×C4—862no—
1211C2×C4—862no—
1212C2×C4—862no—
1213C2×C4—862no—
1214C2×C4—862no—
1215C2×C4—862no—
1216C2×C4—862no—
1217C2×C4—862no—
1218C2×C4—862no—
1219C2×C4—17216no—
1220C2×C4—17216no—
1221C2×C4—1721no—
1222C2×C4—1721no—
1223C2×C4—1721no—
1224C2×C4—1721no—
1225C2×C4—1721no—
1226C2×C4—1721no—
1227C2×C4—1721no—
1228C2×C4—1721no—
1229C2×C4—1721no—
1230C2×C4—1721no—
1231C2×C4—1721no—
1232C2×C4—1721no—
1233C2×C4—1721no—
1234C2×C4—1721no—
1235C2×C4—1721no—
1236C2×C4—1721no—
1237C2×C4—1721no—
1238C2×C4—1721no—
1239C2×C4—1721no—
1240C2×C4—1721no—
1241C2×C4—1721no—
1242C2×C4—1721no—
1243C2×C4—1721no—
1244C2×C4—1721no—
1245C2×C4—1721no—
1246C2×C4—1721no—
1247C2×C4—1721no—
1248C2×C4—1721no—
1249C2×C4—1721no—
1250C2×C4—1721no—
1251C2×C4—1721no—
1252C2×C4#1306330614yescomplemented
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22#120×D4311yescharacteristic
1299C22C2×#1306329311yescharacteristic
1300C22C2×#1306330611yescharacteristic
1301C22C2×#1306330611yescharacteristic
1302C22#1458340511yescharacteristic
1303C22#1458340511yescharacteristic
1304C22#1458340511yescharacteristic
1305C22#1458340511yescharacteristic
1306C22#1458340511yescharacteristic
1307C22#1458340911yescharacteristic
1308C22#1458344411yescharacteristic
1309C22#1458344411yescharacteristic
1310C22#1458344711yescharacteristic
1311C22#1458345911yescharacteristic
1312C22#1458347611yescharacteristic
1313C22#1458348411yescharacteristic
1314C22#1458349411yescharacteristic
1315C22#1458350311yescharacteristic
1316C22#1458351611yescharacteristic
1317C22#1458353111yescharacteristic
1318C22#1458353111yescharacteristic
1319C22D4×C22⋊D4311yescharacteristic
1320C22D4×C22⋊D4311yescharacteristic
1321C22#1458353611yescharacteristic
1322C22#1458353811yescharacteristic
1323C22#1458354311yescharacteristic
1324C22#1458354811yescharacteristic
1325C22#1458354911yescharacteristic
1326C22#1458354911yescharacteristic
1327C22#1458355511yescharacteristic
1328C22#1458356911yescharacteristic
1329C22#1458358011yescharacteristic
1330C22#1458359211yescharacteristic
1331C22#1458359611yescharacteristic
1332C22#1458363511yescharacteristic
1333C4—24no—
1334C4—42no—
1335C4—42no—
1336C4—81no—
1337C4—864no—
1338C4—3441no—
1339C4—1722no—
1340C4—1722no—
1341C4—1722no—
1342C4—1722no—
1343C4—1722no—
1344C4—1722no—
1345C2—44no—
1346C2—44no—
1347C2—82no—
1348C2#1913780711yescharacteristic
1349C2#1913790611yescharacteristic
1350C2#1913793311yescharacteristic
1351C2#1913805311yescharacteristic
1352C2#1913810511yescharacteristic
1353C2#1913820111yescharacteristic
1354C2#1913832611yescharacteristic
1355C2#1913835611yescharacteristic
1356C2#1913847111yescharacteristic
1357C2#1913848811yescharacteristic
1358C2#1913855711yescharacteristic
1359C2#1913859411yescharacteristic
1360C2#1914020011yescharacteristic
1361C2#1914043111yescharacteristic
1362C2#1914288511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
Fitting, prime radicalC2×C43×#392C2
hypercenterC2×#392D43
hypocenterC43#14721
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#13063306C2semidirect
2. C22×D4×Dic43C2semidirect
3. C2×#14582813C2semidirect
4. C2×#14582779C2semidirect
5. C2×#14582771C2semidirect
6. #19132859C2semidirect
7. #19132842C2semidirect
8. #19132840C2semidirect
9. #19132838C2semidirect
10. #19132836C2semidirect
11. #19132836C2semidirect
12. #19132832C2semidirect
13. #19132826C2semidirect
14. #19132817C2semidirect
74. C23×Dic43D4semidirect
96. C2×Dic43⋊C4D4semidirect
125. C2×C22⋊Dic43D4semidirect
126. C2×C22⋊Dic43D4semidirect
466. C23×C43#123semidirect
512. C2×C4×C43#123semidirect
742. C43#14721semidirect
1148. C23#13063306semidirect
1252. C2×C4#13063306semidirect

Maximal subgroups

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

subgroupindex
C22×#130633062
C22×D4×Dic432
C2×#145828132
C2×#145827792
C2×#145827712
#191328592
#191328422
#191328402
#191328382
#191328362
#191328322
#191328262
#191328172
C2×C43×#3922
#1472143