Finite Group Databasebeta

← #25025948

Subgroups — #25025948

Order 11008.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582802C211yesmaximal, characteristic, complemented
2C2×#14582792C211yesmaximal, characteristic, complemented
3C2×#14582779C211yesmaximal, characteristic, complemented
4C2×#14582779C211yesmaximal, characteristic, complemented
5#19132852C211yesmaximal, characteristic, complemented
6#19132844C211yesmaximal, characteristic, complemented
7#19132836C211yesmaximal, characteristic, complemented
8#19132836C211yesmaximal, characteristic, complemented
9#19132836C211yesmaximal, characteristic, complemented
10#19132832C211yesmaximal, characteristic, complemented
11#19132832C211yesmaximal, characteristic, complemented
12#19132832C211yesmaximal, characteristic, complemented
13#19132820C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C2×C43×#392C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31#14582802—24no—
32#14582792—24no—
33#14582779—24no—
34#14582779—24no—
35C2×C43⋊#95C2211yescharacteristic
36C2×C43⋊#95C2211yescharacteristic
37C2×C43⋊#95C2211yescharacteristic
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C23×D4×C43C2211yescharacteristic
49C23×D4×C43C2211yescharacteristic
50C23×D4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C43×#392C418yescomplemented
55C2×#95×C43C2211yescharacteristic
56C23×Dic43—22no—
57C23×Dic43—22no—
58C23×Dic43—22no—
59C23×Dic43—41no—
60C23×Dic43—41no—
61C23×Dic43—41no—
62C23×Dic43—41no—
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43—41no—
74C2×C22⋊Dic43—22no—
75C2×C22⋊Dic43—22no—
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—22no—
78C2×C22⋊Dic43—22no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—22no—
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—22no—
85C2×C22⋊Dic43—22no—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43—22no—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—41no—
91C2×C22⋊Dic43—41no—
92C2×C22⋊Dic43—41no—
93C2×C22⋊Dic43—41no—
94C2×C22⋊Dic43—41no—
95C2×C22⋊Dic43—41no—
96C2×C22⋊Dic43—41no—
97C2×C22⋊Dic43—41no—
98C2×C22⋊Dic43—41no—
99C2×C22⋊Dic43—41no—
100C2×C22⋊Dic43—41no—
101C2×C22⋊Dic43—41no—
102C2×C22⋊Dic43—41no—
103C2×C22⋊Dic43—41no—
104C2×C22⋊Dic43—41no—
105C2×C22⋊Dic43—41no—
106C2×C22⋊Dic43D414yescomplemented
107C2×C4×Dic43—22no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—22no—
110C2×C4×Dic43—41no—
111C2×C4×Dic43—41no—
112C2×C4×Dic43—41no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—41no—
118C43⋊#95—41no—
119C43⋊#95—41no—
120C43⋊#95—41no—
121C43⋊#95—41no—
122C43⋊#95—41no—
123C43⋊#95—41no—
124C43⋊#95—41no—
125C43⋊#95D414yescomplemented
126C25×C43C2311yescharacteristic
127C25×C43C2311yescharacteristic
128C25×C43C2311yescharacteristic
129C22×D4×C43—22no—
130C22×D4×C43—22no—
131C22×D4×C43—22no—
132C22×D4×C43—22no—
133C22×D4×C43—22no—
134C22×D4×C43—22no—
135C22×D4×C43—41no—
136C22×D4×C43—41no—
137C22×D4×C43—41no—
138C22×D4×C43—41no—
139C22×D4×C43—41no—
140C22×D4×C43—41no—
141C22×D4×C43—41no—
142C22×D4×C43—41no—
143C22×D4×C43—41no—
144C22×D4×C43—41no—
145C22×D4×C43—41no—
146C22×D4×C43—41no—
147C22×D4×C43C2×C414yes—
148C22×D4×C43C2×C414yes—
149C22×D4×C43C2×C414yescomplemented
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×C22⋊C4×C43—22no—
155C2×C22⋊C4×C43—22no—
156C2×C22⋊C4×C43—41no—
157C2×C22⋊C4×C43—41no—
158C2×C22⋊C4×C43—41no—
159C2×C22⋊C4×C43—41no—
160C2×C22⋊C4×C43C2×C414yes—
161C2×C22⋊C4×C43C2×C414yescomplemented
162C2×C22⋊C4×C43C2×C414yescomplemented
163#95×C43C2×C414yescomplemented
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43—21no—
178C24×C43—21no—
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×C43C22×C412yes—
205C24×C43C22×C412yes—
206C24×C43C22×C412yes—
207C24×C43C2×D412yes—
208C24×C43#4112yes—
209C24×C43C2411yescharacteristic
210C2×D4×C43—28no—
211C2×D4×C43—28no—
212C2×D4×C43—28no—
213C2×D4×C43—44no—
214C2×D4×C43—44no—
215C2×D4×C43—44no—
216C2×D4×C43—44no—
217C2×D4×C43—44no—
218C2×D4×C43—44no—
219C2×D4×C43—44no—
220C2×D4×C43—44no—
221C2×D4×C43—44no—
222C2×D4×C43—44no—
223C2×D4×C43—44no—
224C2×D4×C43—44no—
225C2×D4×C43—44no—
226C2×D4×C43—44no—
227C2×D4×C43—44no—
228C2×D4×C43—44no—
229C2×D4×C43—44no—
230C2×D4×C43—44no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
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×C43C22×C412yes—
254C22×C4×C43C22×C412yes—
255C22×C4×C43C22×C412yes—
256C22×C4×C43C22×C412yes—
257C22×C4×C43C2×D412yes—
258C22×C4×C43#4112yes—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
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—44no—
310C22×Dic43—44no—
311C22×Dic43—44no—
312C22×Dic43—44no—
313C22×Dic43—44no—
314C22×Dic43—44no—
315C22×Dic43—44no—
316C22×Dic43C2×D412yes—
317C22×Dic43C2×D412yes—
318C22×Dic43C2×D412yes—
319C22×Dic43C2×D412yes—
320C22×Dic43#4112yes—
321C22×Dic43#4112yes—
322C22⋊C4×C43—28no—
323C22⋊C4×C43—44no—
324C22⋊C4×C43—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⋊Dic43—44no—
336C4⋊Dic43—44no—
337C4×Dic43—44no—
338C4×Dic43—44no—
339C23×C43—22no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—22no—
360C23×C43—22no—
361C23×C43—22no—
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—41no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43—41no—
377C23×C43—41no—
378C23×C43—41no—
379C23×C43—41no—
380C23×C43—41no—
381C23×C43—41no—
382C23×C43—41no—
383C23×C43—41no—
384C23×C43—41no—
385C23×C43—41no—
386C23×C43—41no—
387C23×C43—41no—
388C23×C43—41no—
389C23×C43—41no—
390C23×C43—41no—
391C23×C43—41no—
392C23×C43—41no—
393C23×C43—41no—
394C23×C43—41no—
395C23×C43—41no—
396C23×C43—41no—
397C23×C43—41no—
398C23×C43—41no—
399C23×C43—41no—
400C23×C43—41no—
401C23×C43—41no—
402C23×C43—41no—
403C23×C43—41no—
404C23×C43—41no—
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×C43C4×D414yes—
444C23×C43C23×C411yescharacteristic
445C23×C43C22×D411yescharacteristic
446C23×C43C22×D411yescharacteristic
447C23×C43C2×#4111yescharacteristic
448C23×C43C2×#4111yescharacteristic
449C23×C43C2×#4111yescharacteristic
450C23×C43C2×#4111yescharacteristic
451C23×C43H(5,𝔽2)11yescharacteristic
452C23×C43H(5,𝔽2)11yescharacteristic
453C23×C43H(5,𝔽2)11yescharacteristic
454C23×C43H(5,𝔽2)11yescharacteristic
455C23×C43H(5,𝔽2)11yescharacteristic
456C23×C43H(5,𝔽2)11yescharacteristic
457C23×C43H(5,𝔽2)11yescharacteristic
458C23×C43H(5,𝔽2)11yescharacteristic
459D4×C43—416no—
460D4×C43—416no—
461D4×C43—416no—
462C2×C4×C43—22no—
463C2×C4×C43—22no—
464C2×C4×C43—22no—
465C2×C4×C43—22no—
466C2×C4×C43—22no—
467C2×C4×C43—22no—
468C2×C4×C43—22no—
469C2×C4×C43—22no—
470C2×C4×C43—22no—
471C2×C4×C43—22no—
472C2×C4×C43—22no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—22no—
476C2×C4×C43—22no—
477C2×C4×C43—41no—
478C2×C4×C43—41no—
479C2×C4×C43—41no—
480C2×C4×C43—41no—
481C2×C4×C43—41no—
482C2×C4×C43—41no—
483C2×C4×C43—41no—
484C2×C4×C43—41no—
485C2×C4×C43—41no—
486C2×C4×C43—41no—
487C2×C4×C43—41no—
488C2×C4×C43—41no—
489C2×C4×C43C4×D414yes—
490C2×Dic43—22no—
491C2×Dic43—22no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—22no—
495C2×Dic43—22no—
496C2×Dic43—22no—
497C2×Dic43—22no—
498C2×Dic43—22no—
499C2×Dic43—22no—
500C2×Dic43—22no—
501C2×Dic43—22no—
502C2×Dic43—22no—
503C2×Dic43—22no—
504C2×Dic43—22no—
505C2×Dic43—22no—
506C2×Dic43—22no—
507C2×Dic43—22no—
508C2×Dic43—416no—
509C2×Dic43—41no—
510C2×Dic43—41no—
511C2×Dic43—41no—
512C2×Dic43—41no—
513C2×Dic43—41no—
514C2×Dic43—41no—
515C2×Dic43—41no—
516C2×Dic43—41no—
517C2×Dic43—41no—
518C2×Dic43—41no—
519C2×Dic43—41no—
520C2×Dic43—41no—
521C2×Dic43—41no—
522C2×Dic43—41no—
523C2×Dic43—41no—
524C2×Dic43—41no—
525C2×Dic43—41no—
526C2×Dic43—41no—
527C2×Dic43—41no—
528C2×Dic43—41no—
529C2×Dic43—41no—
530C2×Dic43—41no—
531C2×Dic43—41no—
532C2×Dic43—41no—
533C2×Dic43—41no—
534C2×Dic43—41no—
535C2×Dic43—41no—
536C2×Dic43—41no—
537C2×Dic43—41no—
538C2×Dic43—41no—
539C2×Dic43—41no—
540C2×Dic43—41no—
541C2×Dic43—41no—
542C2×Dic43—41no—
543C2×Dic43—41no—
544C2×Dic43—41no—
545C2×Dic43—41no—
546C2×Dic43—41no—
547#14520—431nomaximal, Sylow
548C22×C43—24no—
549C22×C43—24no—
550C22×C43—24no—
551C22×C43—42no—
552C22×C43—42no—
553C22×C43—42no—
554C22×C43—42no—
555C22×C43—42no—
556C22×C43—42no—
557C22×C43—42no—
558C22×C43—42no—
559C22×C43—42no—
560C22×C43—42no—
561C22×C43—42no—
562C22×C43—42no—
563C22×C43—42no—
564C22×C43—42no—
565C22×C43—42no—
566C22×C43—42no—
567C22×C43—42no—
568C22×C43—42no—
569C22×C43—42no—
570C22×C43—42no—
571C22×C43—42no—
572C22×C43—42no—
573C22×C43—42no—
574C22×C43—42no—
575C22×C43—42no—
576C22×C43—42no—
577C22×C43—81no—
578C22×C43—81no—
579C22×C43—81no—
580C22×C43—81no—
581C22×C43—81no—
582C22×C43—81no—
583C22×C43—81no—
584C22×C43—81no—
585C22×C43—81no—
586C22×C43—81no—
587C22×C43—81no—
588C22×C43—81no—
589C22×C43—81no—
590C22×C43—81no—
591C22×C43—81no—
592C22×C43—81no—
593C22×C43C2×C4×D411yescharacteristic
594C22×C43C2×C4×D411yescharacteristic
595C22×C43C4×#4111yescharacteristic
596C22×C43#51811yescharacteristic
597C22×C43#51811yescharacteristic
598C22×C43#51811yescharacteristic
599C22×C43#51811yescharacteristic
600C22×C43#53411yescharacteristic
601C22×C43#53511yescharacteristic
602C22×C43#53511yescharacteristic
603C22×C43#53511yescharacteristic
604C22×C43#53811yescharacteristic
605C22×C43#53811yescharacteristic
606C22×C43#53811yescharacteristic
607C22×C43#53811yescharacteristic
608C22×C43#54011yescharacteristic
609C22×C43#54011yescharacteristic
610C22×C43#54011yescharacteristic
611C22×C43#54011yescharacteristic
612C22×C43D4211yescharacteristic
613C22×C43#54611yescharacteristic
614C22×C43#54611yescharacteristic
615C22×C43#54611yescharacteristic
616C22×C43#54611yescharacteristic
617C22×C43#54611yescharacteristic
618C22×C43#55011yescharacteristic
619C22×C43#55111yescharacteristic
620C22×C43#55311yescharacteristic
621C22×C43#55311yescharacteristic
622C22×C43#55311yescharacteristic
623C22×C43#55511yescharacteristic
624C22×C43#56011yescharacteristic
625C22×C43#56011yescharacteristic
626C22×C43#56011yescharacteristic
627C22×C43H(3,𝔽4)11yescharacteristic
628C4×C43—24no—
629C4×C43—42no—
630C4×C43—42no—
631C4×C43—42no—
632Dic43—42no—
633Dic43—42no—
634Dic43—42no—
635Dic43—42no—
636Dic43—42no—
637Dic43—42no—
638Dic43—81no—
639Dic43—81no—
640C2×#392D4311yescharacteristic
641C2×#390—431no—
642C2×#388—431no—
643C2×#386—431no—
644C2×#386—431no—
645#1442—431no—
646#1440—431no—
647#1438—431no—
648#1438—431no—
649#1438—431no—
650#1437—431no—
651#1437—431no—
652#1437—431no—
653#1434—431no—
654C22⋊#95—431no—
655C2×C43—44no—
656C2×C43—82no—
657C2×C43—82no—
658C2×C43#232111yescharacteristic
659C2×C43#232811yescharacteristic
660C2×C43#233311yescharacteristic
661C2×C43#235811yescharacteristic
662C2×C43#236311yescharacteristic
663C2×C43#236411yescharacteristic
664C2×C43#237511yescharacteristic
665C2×C43#267011yescharacteristic
666C2×C43#267311yescharacteristic
667C2×C43#269911yescharacteristic
668C2×C43#270311yescharacteristic
669C2×C43#270311yescharacteristic
670C2×C43#271411yescharacteristic
671C2×C43#275311yescharacteristic
672C2×C43#275611yescharacteristic
673C23×D4C2×D4311yescharacteristic
674C23×D4C2×D4311yescharacteristic
675C23×D4C2×D4311yescharacteristic
676C24×C4—431no—
677C22×C4⋊C4—431no—
678C22×C22⋊C4—431no—
679C22×C22⋊C4—431no—
680C22×C22⋊C4—431no—
681C22×C22⋊C4—431no—
682C22×C22⋊C4—431no—
683C22×C22⋊C4—431no—
684C22×C22⋊C4—431no—
685C22×C22⋊C4—431no—
686C22×C22⋊C4—431no—
687C22×C22⋊C4—431no—
688C22×C22⋊C4—431no—
689C22×C22⋊C4C2×D4311yescharacteristic
690C22×C22⋊C4C2×D4311yescharacteristic
691C22×C22⋊C4C2×D4311yescharacteristic
692C22×C42—431no—
693C22×C42—431no—
694#392Dic4318yescomplemented
695#390—864no—
696#388—864no—
697#386—864no—
698#386—864no—
699C2×#95—431no—
700C2×#95—431no—
701C2×#95—431no—
702C2×#95—431no—
703C2×#95—431no—
704C2×#95—431no—
705C2×#95—431no—
706C2×#95—431no—
707C2×#95—431no—
708C2×#95—431no—
709C2×#95—431no—
710C2×#95—431no—
711C2×#95—431no—
712C2×#95C2×D4311yescharacteristic
713C43#1452011yescharacteristic, complemented, Sylow
714C25C22×D4311yescharacteristic
715C25C22×D4311yescharacteristic
716C25C22×D4311yescharacteristic
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4C2×Dic4314yes—
736C22×D4C2×Dic4314yes—
737C22×D4C2×Dic4314yescomplemented
738C23×C4—431no—
739C23×C4—431no—
740C23×C4—431no—
741C23×C4—431no—
742C23×C4—431no—
743C23×C4—431no—
744C23×C4—431no—
745C23×C4—431no—
746C23×C4—862no—
747C23×C4—862no—
748C23×C4—862no—
749C23×C4—1721no—
750C23×C4—1721no—
751C23×C4—1721no—
752C23×C4—1721no—
753C23×C4C22×D4311yescharacteristic
754C23×C4C22×D4311yescharacteristic
755C23×C4C22×D4311yescharacteristic
756C23×C4C22×D4311yescharacteristic
757C2×C4⋊C4—862no—
758C2×C4⋊C4—862no—
759C2×C4⋊C4—1721no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—434no—
767C2×C22⋊C4—862no—
768C2×C22⋊C4—862no—
769C2×C22⋊C4—862no—
770C2×C22⋊C4—862no—
771C2×C22⋊C4—862no—
772C2×C22⋊C4—862no—
773C2×C22⋊C4—862no—
774C2×C22⋊C4—862no—
775C2×C22⋊C4—862no—
776C2×C22⋊C4—862no—
777C2×C22⋊C4—862no—
778C2×C22⋊C4—862no—
779C2×C22⋊C4—862no—
780C2×C22⋊C4—862no—
781C2×C22⋊C4—862no—
782C2×C22⋊C4—862no—
783C2×C22⋊C4—1721no—
784C2×C22⋊C4—1721no—
785C2×C22⋊C4—1721no—
786C2×C22⋊C4—1721no—
787C2×C22⋊C4—1721no—
788C2×C22⋊C4—1721no—
789C2×C22⋊C4—1721no—
790C2×C22⋊C4—1721no—
791C2×C22⋊C4—1721no—
792C2×C22⋊C4—1721no—
793C2×C22⋊C4—1721no—
794C2×C22⋊C4—1721no—
795C2×C22⋊C4—1721no—
796C2×C22⋊C4—1721no—
797C2×C22⋊C4—1721no—
798C2×C22⋊C4—1721no—
799C2×C22⋊C4C2×Dic4314yes—
800C2×C22⋊C4C2×Dic4314yescomplemented
801C2×C22⋊C4C2×Dic4314yescomplemented
802C2×C42—862no—
803C2×C42—862no—
804C2×C42—862no—
805C2×C42—1721no—
806C2×C42—1721no—
807C2×C42—1721no—
808#95—434no—
809#95—862no—
810#95—862no—
811#95—862no—
812#95—862no—
813#95—1721no—
814#95—1721no—
815#95—1721no—
816#95—1721no—
817#95—1721no—
818#95—1721no—
819#95—1721no—
820#95—1721no—
821#95C2×Dic4314yescomplemented
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24D4×D4312yes—
863C24#1062190012yes—
864C24C22×Dic4312yes—
865C24C22×Dic4312yes—
866C24C22×Dic4312yes—
867C24C23×D4311yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—432no—
912C22×C4—432no—
913C22×C4—432no—
914C22×C4—432no—
915C22×C4—432no—
916C22×C4—432no—
917C22×C4—861no—
918C22×C4—861no—
919C22×C4—861no—
920C22×C4—861no—
921C22×C4—861no—
922C22×C4—861no—
923C22×C4—861no—
924C22×C4—861no—
925C22×C4—861no—
926C22×C4—861no—
927C22×C4—861no—
928C22×C4—861no—
929C22×C4—861no—
930C22×C4—861no—
931C22×C4—861no—
932C22×C4—861no—
933C22×C4—861no—
934C22×C4—861no—
935C22×C4—861no—
936C22×C4—861no—
937C22×C4—861no—
938C22×C4—861no—
939C22×C4—861no—
940C22×C4—861no—
941C22×C4—861no—
942C22×C4—861no—
943C22×C4—861no—
944C22×C4—861no—
945C22×C4—861no—
946C22×C4—861no—
947C22×C4—861no—
948C22×C4—861no—
949C22×C4—861no—
950C22×C4—861no—
951C22×C4—861no—
952C22×C4—861no—
953C22×C4—861no—
954C22×C4—861no—
955C22×C4—861no—
956C22×C4—861no—
957C22×C4—861no—
958C22×C4—861no—
959C22×C4—861no—
960C22×C4—861no—
961C22×C4—861no—
962C22×C4—861no—
963C22×C4—861no—
964C22×C4—861no—
965C22×C4—861no—
966C22×C4—861no—
967C22×C4—1724no—
968C22×C4—1724no—
969C22×C4—1724no—
970C22×C4—1724no—
971C22×C4—1724no—
972C22×C4—1724no—
973C22×C4—1724no—
974C22×C4D4×D4312yes—
975C22×C4#1062190012yes—
976C22×C4C22×Dic4312yes—
977C22×C4C22×Dic4312yes—
978C22×C4C22×Dic4312yes—
979C22×C4C22×Dic4312yes—
980C4⋊C4—1724no—
981C22⋊C4—28no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—1724no—
985C22⋊C4—1724no—
986C22⋊C4—1724no—
987C22⋊C4—1724no—
988C22⋊C4—1724no—
989C22⋊C4—1724no—
990C22⋊C4—1724no—
991C22⋊C4—1724no—
992C22⋊C4—1724no—
993C22⋊C4—1724no—
994C22⋊C4—1724no—
995C42—1724no—
996C42—1724no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
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—
1101C23D4×Dic4314yes—
1102C23C23×Dic4311yescharacteristic
1103C23C2×D4×D4311yescharacteristic
1104C23C2×D4×D4311yescharacteristic
1105C23#41×D4311yescharacteristic
1106C23#41×D4311yescharacteristic
1107C23C2×#1062190011yescharacteristic
1108C23C2×#1062190011yescharacteristic
1109C23#1306337011yescharacteristic
1110C23#1306337011yescharacteristic
1111C23#1306337011yescharacteristic
1112C23#1306337011yescharacteristic
1113C23#1306337011yescharacteristic
1114C23#1306337011yescharacteristic
1115C23#1306337011yescharacteristic
1116C23#1306337011yescharacteristic
1117D4—416no—
1118D4—416no—
1119D4—416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—862no—
1148C2×C4—862no—
1149C2×C4—862no—
1150C2×C4—862no—
1151C2×C4—862no—
1152C2×C4—862no—
1153C2×C4—862no—
1154C2×C4—862no—
1155C2×C4—862no—
1156C2×C4—862no—
1157C2×C4—862no—
1158C2×C4—862no—
1159C2×C4—862no—
1160C2×C4—862no—
1161C2×C4—862no—
1162C2×C4—862no—
1163C2×C4—862no—
1164C2×C4—862no—
1165C2×C4—1721no—
1166C2×C4—1721no—
1167C2×C4—1721no—
1168C2×C4—1721no—
1169C2×C4—1721no—
1170C2×C4—1721no—
1171C2×C4—1721no—
1172C2×C4—1721no—
1173C2×C4—1721no—
1174C2×C4—1721no—
1175C2×C4—1721no—
1176C2×C4—1721no—
1177C2×C4—1721no—
1178C2×C4—1721no—
1179C2×C4—17216no—
1180C2×C4—1721no—
1181C2×C4—1721no—
1182C2×C4—1721no—
1183C2×C4—1721no—
1184C2×C4—1721no—
1185C2×C4—1721no—
1186C2×C4—1721no—
1187C2×C4—1721no—
1188C2×C4—1721no—
1189C2×C4—1721no—
1190C2×C4—1721no—
1191C2×C4—1721no—
1192C2×C4—1721no—
1193C2×C4—1721no—
1194C2×C4—1721no—
1195C2×C4—1721no—
1196C2×C4—1721no—
1197C2×C4—1721no—
1198C2×C4—1721no—
1199C2×C4—1721no—
1200C2×C4—1721no—
1201C2×C4—1721no—
1202C2×C4—1721no—
1203C2×C4—1721no—
1204C2×C4D4×Dic4314yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×D4×Dic4311yescharacteristic
1251C22C2×D4×Dic4311yescharacteristic
1252C22#41×Dic4311yescharacteristic
1253C22#1458337411yescharacteristic
1254C22#1458337411yescharacteristic
1255C22#1458337411yescharacteristic
1256C22#1458337411yescharacteristic
1257C22#1458345911yescharacteristic
1258C22#1458346211yescharacteristic
1259C22#1458346211yescharacteristic
1260C22#1458346411yescharacteristic
1261C22#1458348111yescharacteristic
1262C22#1458348111yescharacteristic
1263C22#1458348411yescharacteristic
1264C22#1458348411yescharacteristic
1265C22#1458349911yescharacteristic
1266C22#1458349911yescharacteristic
1267C22#1458350311yescharacteristic
1268C22#1458350311yescharacteristic
1269C22#1458353111yescharacteristic
1270C22#1458353611yescharacteristic
1271C22#1458353611yescharacteristic
1272C22#1458353811yescharacteristic
1273C22#1458353811yescharacteristic
1274C22#1458354611yescharacteristic
1275C22#1458356711yescharacteristic
1276C22#1458358011yescharacteristic
1277C22#1458359211yescharacteristic
1278C22#1458359211yescharacteristic
1279C22#1458359611yescharacteristic
1280C22#1458361311yescharacteristic
1281C22#1458363811yescharacteristic
1282C22#1458363811yescharacteristic
1283C22#1458363811yescharacteristic
1284C22#1458364211yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—3441no—
1290C4—3441no—
1291C4—1722no—
1292C4—1722no—
1293C4—1722no—
1294C4—1722no—
1295C4—1722no—
1296C4—1722no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2#1913725611yescharacteristic
1301C2#1913732111yescharacteristic
1302C2#1913736211yescharacteristic
1303C2#1913757911yescharacteristic
1304C2#1913763711yescharacteristic
1305C2#1913764711yescharacteristic
1306C2#1913773611yescharacteristic
1307C2#1914082011yescharacteristic
1308C2#1914086311yescharacteristic
1309C2#1914118511yescharacteristic
1310C2#1914123111yescharacteristic
1311C2#1914124511yescharacteristic
1312C2#1914138411yescharacteristic
1313C2#1914187411yescharacteristic
1314C2#1914191911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
Fitting, prime radicalC2×C43×#392C2
socle, cosocleC24×C43C24
hypercenterC2×#392D43
hypocenterC43#14520
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#14582802C2semidirect
2. C2×#14582792C2semidirect
3. C2×#14582779C2semidirect
4. C2×#14582779C2semidirect
5. #19132852C2semidirect
6. #19132844C2semidirect
7. #19132836C2semidirect
8. #19132836C2semidirect
9. #19132836C2semidirect
10. #19132832C2semidirect
11. #19132832C2semidirect
12. #19132832C2semidirect
13. #19132820C2semidirect
14. #19132817C2semidirect
54. C43×#392C4semidirect
106. C2×C22⋊Dic43D4semidirect
125. C43⋊#95D4semidirect
149. C22×D4×C43C2×C4semidirect
161. C2×C22⋊C4×C43C2×C4semidirect
162. C2×C22⋊C4×C43C2×C4semidirect
163. #95×C43C2×C4semidirect
694. #392Dic43semidirect
713. C43#14520semidirect
737. C22×D4C2×Dic43semidirect
800. C2×C22⋊C4C2×Dic43semidirect
801. C2×C22⋊C4C2×Dic43semidirect
821. #95C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828022
C2×#145827922
C2×#145827792
#191328522
#191328442
#191328362
#191328322
#191328202
#191328172
C2×C43×#3922
#1452043