Finite Group Databasebeta

← #25018804

Subgroups — #25018804

Order 11008.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582766C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×Dic43C211yesmaximal, characteristic
3C22×C43⋊#95C211yesmaximal, characteristic
4#19132856C211yesmaximal, characteristic, complemented
5#19132856C211yesmaximal, characteristic, complemented
6#19132855C211yesmaximal, characteristic, complemented
7#19132855C211yesmaximal, characteristic, complemented
8#19132821C211yesmaximal, characteristic, complemented
9#19132820C211yesmaximal, characteristic, complemented
10#19132819C211yesmaximal, characteristic, complemented
11#19132818C211yesmaximal, characteristic
12#19132817C211yesmaximal, characteristic
13#19132817C211yesmaximal, characteristic
14#19132817C211yesmaximal, characteristic
15C43×C22⋊#95C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14582766—24no—
23C22⋊C4×Dic43C418yescomplemented
24C2×C43⋊#95—24no—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
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
47C24×C4×C43C2211yescharacteristic
48C22×C22⋊C4×C43C2211yescharacteristic
49C22×C22⋊C4×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C23×Dic43—22no—
55C23×Dic43—22no—
56C23×Dic43—22no—
57C23×Dic43—22no—
58C23×Dic43—22no—
59C23×Dic43—22no—
60C23×Dic43—22no—
61C23×Dic43—22no—
62C23×Dic43—22no—
63C23×Dic43—41no—
64C23×Dic43—41no—
65C23×Dic43—41no—
66C23×Dic43—41no—
67C23×Dic43C2×C414yes—
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—22no—
78C2×C22⋊Dic43—22no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—22no—
81C2×C22⋊Dic43C2×C414yes—
82C2×C4×Dic43—22no—
83C2×C4×Dic43—22no—
84C2×C4×Dic43—41no—
85C2×C4×Dic43—41no—
86C2×C4×Dic43C2×C414yescomplemented
87C2×C4×Dic43C2×C414yescomplemented
88C43⋊#95—22no—
89C43⋊#95—22no—
90C43⋊#95—22no—
91C43⋊#95—22no—
92C43⋊#95—22no—
93C43⋊#95—22no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C43⋊#95—22no—
99C43⋊#95—41no—
100C43⋊#95—41no—
101C43⋊#95—41no—
102C43⋊#95—41no—
103C43⋊#95—41no—
104C43⋊#95—41no—
105C43⋊#95—41no—
106C43⋊#95—41no—
107C43⋊#95C2×C414yescomplemented
108C43⋊#95C2×C414yescomplemented
109C43⋊#95D414yes—
110C25×C43C2311yescharacteristic
111C23×C4×C43—22no—
112C23×C4×C43—22no—
113C23×C4×C43—22no—
114C23×C4×C43—22no—
115C23×C4×C43—22no—
116C23×C4×C43—41no—
117C23×C4×C43—41no—
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—22no—
125C2×C22⋊C4×C43—22no—
126C2×C22⋊C4×C43—22no—
127C2×C22⋊C4×C43—22no—
128C2×C22⋊C4×C43—22no—
129C2×C22⋊C4×C43C2×C414yes—
130#95×C43—22no—
131#95×C43—22no—
132#95×C43—41no—
133#95×C43—41no—
134C24×C43—21no—
135C24×C43—21no—
136C24×C43—21no—
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43C22×C412yes—
143C24×C43#4112yes—
144C24×C43#4112yes—
145C24×C43#4112yes—
146C24×C43#4112yes—
147C24×C43#4112yes—
148C24×C43#4112yes—
149C24×C43C2411yescharacteristic
150C22×C4×C43—28no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
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×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—44no—
190C22×C4×C43—44no—
191C22×C4×C43—44no—
192C22×C4×C43—44no—
193C22×C4×C43—44no—
194C22×C4×C43—44no—
195C22×C4×C43C22×C412yes—
196C22×C4×C43C22×C412yes—
197C22×C4×C43C2×D412yes—
198C22×C4×C43#4112yes—
199C22×Dic43—28no—
200C22×Dic43—28no—
201C22×Dic43—28no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—44no—
251C22×Dic43—44no—
252C22×Dic43—44no—
253C22×Dic43—44no—
254C22×Dic43—44no—
255C22×Dic43—44no—
256C22×Dic43—44no—
257C22×Dic43—44no—
258C22×Dic43—44no—
259C22×Dic43—44no—
260C22×Dic43—44no—
261C22×Dic43C22×C412yes—
262C22×Dic43C22×C412yes—
263C22×Dic43C22×C412yes—
264C22×Dic43C22×C412yes—
265C22×Dic43C2×D412yes—
266C22×Dic43C2×D412yes—
267C22×Dic43#4112yes—
268C22×Dic43#4112yes—
269C22⋊C4×C43—28no—
270C22⋊C4×C43—44no—
271C22⋊Dic43—28no—
272C22⋊Dic43—44no—
273C4×Dic43—28no—
274C4×Dic43—44no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43#11714yes—
304C23×C43#11714yes—
305C23×C43#11714yes—
306C23×C43#12614yes—
307C23×C43#12614yes—
308C23×C43#12614yes—
309C23×C43#12614yes—
310C23×C43C23×C411yescharacteristic
311C23×C43C22×D411yescharacteristic
312C23×C43C2×#4111yescharacteristic
313C23×C43C2×#4111yescharacteristic
314C23×C43C2×#4111yescharacteristic
315C23×C43C2×#4111yescharacteristic
316C23×C43C2×#4111yescharacteristic
317C23×C43C2×#4111yescharacteristic
318C23×C43C2×#4111yescharacteristic
319C23×C43C2×#4111yescharacteristic
320C23×C43C2×#4111yescharacteristic
321C23×C43H(5,𝔽2)11yescharacteristic
322C23×C43H(5,𝔽2)11yescharacteristic
323C23×C43H(5,𝔽2)11yescharacteristic
324C23×C432−1+411yescharacteristic
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—416no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—416no—
390C2×Dic43—416no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43C4×D414yes—
426#13901—431nomaximal, Sylow
427C22×C43—24no—
428C22×C43—24no—
429C22×C43—24no—
430C22×C43—24no—
431C22×C43—24no—
432C22×C43—24no—
433C22×C43—24no—
434C22×C43—24no—
435C22×C43—24no—
436C22×C43—24no—
437C22×C43—24no—
438C22×C43—24no—
439C22×C43—24no—
440C22×C43—24no—
441C22×C43#38318yescomplemented
442C22×C43C2×#11711yescharacteristic
443C22×C43C2×#11711yescharacteristic
444C22×C43C2×#11711yescharacteristic
445C22×C43C2×C4×D411yescharacteristic
446C22×C43C4×#4111yescharacteristic
447C22×C43#51811yescharacteristic
448C22×C43#52011yescharacteristic
449C22×C43#52511yescharacteristic
450C22×C43#52511yescharacteristic
451C22×C43C2×#12611yescharacteristic
452C22×C43C2×#12611yescharacteristic
453C22×C43C2×#12611yescharacteristic
454C22×C43C2×#12611yescharacteristic
455C22×C43#52911yescharacteristic
456C22×C43#52911yescharacteristic
457C22×C43#53811yescharacteristic
458C22×C43#53811yescharacteristic
459C22×C43#53911yescharacteristic
460C22×C43#53911yescharacteristic
461C22×C43#54611yescharacteristic
462C22×C43#54611yescharacteristic
463C22×C43#54611yescharacteristic
464C22×C43#54811yescharacteristic
465C22×C43#55111yescharacteristic
466C22×C43#55111yescharacteristic
467C22×C43#55111yescharacteristic
468C22×C43#55111yescharacteristic
469C22×C43#55111yescharacteristic
470C22×C43#55111yescharacteristic
471C22×C43#55211yescharacteristic
472C22×C43#55211yescharacteristic
473C22×C43#55211yescharacteristic
474C22×C43#55311yescharacteristic
475C22×C43#55311yescharacteristic
476C22×C43#55311yescharacteristic
477C4×C43—42no—
478C4×C43—42no—
479C4×C43—42no—
480C4×C43—42no—
481C4×C43—81no—
482C4×C43—81no—
483Dic43—24no—
484Dic43—42no—
485Dic43—42no—
486Dic43—42no—
487Dic43—42no—
488Dic43—42no—
489Dic43—81no—
490Dic43—81no—
491C2×#383—431no—
492C2×C4×C22⋊C4—431no—
493C22×#95—431no—
494#1443—431no—
495#1443—431no—
496#1443—431no—
497#1443—431no—
498#1434—431no—
499#1434—431no—
500#1434—431no—
501C22⋊#95—431no—
502C22⋊#95—431no—
503C22⋊#95—431no—
504C22⋊#95—431no—
505C22⋊#95D4311yescharacteristic
506C2×C43—28no—
507C2×C43C2×#38311yescharacteristic
508C2×C43#229011yescharacteristic
509C2×C43#231811yescharacteristic
510C2×C43#234211yescharacteristic
511C2×C43#234311yescharacteristic
512C2×C43#235211yescharacteristic
513C2×C43#235311yescharacteristic
514C2×C43#248011yescharacteristic
515C2×C43#248011yescharacteristic
516C2×C43#248111yescharacteristic
517C2×C43#248111yescharacteristic
518C2×C43#249311yescharacteristic
519C2×C43#249311yescharacteristic
520C2×C43#251011yescharacteristic
521C2×C43#251011yescharacteristic
522C24×C4—431no—
523C24×C4—431no—
524C24×C4C2×D4311yescharacteristic
525C22×C22⋊C4—431no—
526C22×C22⋊C4—431no—
527C22×C22⋊C4C2×D4311yescharacteristic
528C22×C22⋊C4C2×D4311yescharacteristic
529C22×C42—431no—
530C22×C42—431no—
531#383—864no—
532C4×C22⋊C4—438no—
533C2×#95—431no—
534C2×#95—431no—
535C2×#95—431no—
536C2×#95—431no—
537C2×#95—431no—
538C2×#95—431no—
539C2×#95—431no—
540C2×#95—431no—
541C2×#95—431no—
542C2×#95—431no—
543C2×#95—431no—
544C2×#95—431no—
545C2×#95—431no—
546C2×#95—431no—
547C2×#95—431no—
548C2×#95—431no—
549C2×#95—431no—
550C2×#95—431no—
551C2×#95—431no—
552C2×#95—431no—
553C2×#95—431no—
554C2×#95—431no—
555C2×#95—864no—
556C2×#95C2×D4311yescharacteristic
557C2×#95C2×D4311yescharacteristic
558C2×#95C2×D4311yescharacteristic
559C2×#95C2×D4311yescharacteristic
560C43#1390111yescharacteristic, complemented, Sylow
561C25C22×D4311yescharacteristic
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—41no—
568C23×C4—41no—
569C23×C4—431no—
570C23×C4—431no—
571C23×C4—431no—
572C23×C4—431no—
573C23×C4—431no—
574C23×C4—431no—
575C23×C4—434no—
576C23×C4—431no—
577C23×C4—431no—
578C23×C4—862no—
579C23×C4—862no—
580C23×C4—862no—
581C23×C4—862no—
582C23×C4—862no—
583C23×C4—862no—
584C23×C4—862no—
585C23×C4—862no—
586C23×C4—862no—
587C23×C4—1721no—
588C23×C4—1721no—
589C23×C4—1721no—
590C23×C4—1721no—
591C23×C4C22×D4311yescharacteristic
592C23×C4C22×D4311yescharacteristic
593C23×C4C22×D4311yescharacteristic
594C23×C4C22×D4311yescharacteristic
595C23×C4C22×D4311yescharacteristic
596C23×C4C22×D4311yescharacteristic
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—434no—
603C2×C22⋊C4—862no—
604C2×C22⋊C4—862no—
605C2×C22⋊C4—862no—
606C2×C22⋊C4—862no—
607C2×C22⋊C4—862no—
608C2×C22⋊C4C4×D4314yes—
609C2×C42—434no—
610C2×C42—434no—
611C2×C42—862no—
612C2×C42—862no—
613C2×C42—1721no—
614C2×C42—1721no—
615#95—22no—
616#95—22no—
617#95—41no—
618#95—41no—
619#95—434no—
620#95—434no—
621#95—434no—
622#95—862no—
623#95—862no—
624#95—862no—
625#95—862no—
626#95—862no—
627#95—862no—
628#95—862no—
629#95—862no—
630#95—862no—
631#95—862no—
632#95—862no—
633#95—1721no—
634#95—1721no—
635#95—1721no—
636#95—1721no—
637#95—1721no—
638#95—1721no—
639#95—1721no—
640#95—1721no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×C4×D4312yes—
650C24#1062189812yes—
651C24#1062189812yes—
652C24#1062190012yes—
653C24#1062190012yes—
654C24#1062190012yes—
655C24#1062190212yes—
656C24C23×D4311yescharacteristic
657C22×C4—28no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—432no—
706C22×C4—432no—
707C22×C4—432no—
708C22×C4—432no—
709C22×C4—432no—
710C22×C4—868no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—868no—
716C22×C4—868no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—1724no—
762C22×C4—1724no—
763C22×C4—1724no—
764C22×C4—1724no—
765C22×C4—1724no—
766C22×C4—1724no—
767C22×C4—1724no—
768C22×C4—1724no—
769C22×C4—1724no—
770C22×C4—1724no—
771C22×C4—1724no—
772C22×C4C2×C4×D4312yes—
773C22×C4C2×C4×D4312yes—
774C22×C4D4×D4312yes—
775C22×C4#1062190012yes—
776C22⋊C4—28no—
777C22⋊C4—44no—
778C22⋊C4—868no—
779C22⋊C4—1724no—
780C42—868no—
781C42—1724no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23#1306328114yes—
811C23#1306328214yes—
812C23#1306328314yes—
813C23#1306331814yes—
814C23#1306331814yes—
815C23#1306332014yes—
816C23#1306332014yes—
817C23C22×C4×D4311yescharacteristic
818C23C2×D4×D4311yescharacteristic
819C23#41×D4311yescharacteristic
820C23#41×D4311yescharacteristic
821C23C2×#1062190011yescharacteristic
822C23C2×#1062190011yescharacteristic
823C23C2×#1062190011yescharacteristic
824C23C2×#1062190011yescharacteristic
825C23C2×#1062189811yescharacteristic
826C23C2×#1062189811yescharacteristic
827C23C2×#1062190211yescharacteristic
828C23#1306337011yescharacteristic
829C23#1306337011yescharacteristic
830C23#1306337111yescharacteristic
831C23#1306337211yescharacteristic
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—416no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—434no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—862no—
890C2×C4—862no—
891C2×C4—862no—
892C2×C4—862no—
893C2×C4—862no—
894C2×C4—862no—
895C2×C4—862no—
896C2×C4—862no—
897C2×C4—17216no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—17216no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4—1721no—
916C2×C4—1721no—
917C2×C4—1721no—
918C2×C4—1721no—
919C2×C4—1721no—
920C2×C4—1721no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1721no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4—1721no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22#1458276618yescomplemented
948C22C2×#1306328111yescharacteristic
949C22C2×#1306328211yescharacteristic
950C22C2×#1306328311yescharacteristic
951C22C4×D4×D4311yescharacteristic
952C22C4×#1062190011yescharacteristic
953C22#1458337111yescharacteristic
954C22#1458337811yescharacteristic
955C22#1458340511yescharacteristic
956C22#1458340911yescharacteristic
957C22C2×#1306331811yescharacteristic
958C22C2×#1306331811yescharacteristic
959C22C2×#1306332011yescharacteristic
960C22C2×#1306332011yescharacteristic
961C22#1458342611yescharacteristic
962C22#1458343011yescharacteristic
963C22#1458348411yescharacteristic
964C22#1458348611yescharacteristic
965C22#1458349311yescharacteristic
966C22#1458349411yescharacteristic
967C22#1458353611yescharacteristic
968C22#1458353911yescharacteristic
969C22#1458354011yescharacteristic
970C22#1458355811yescharacteristic
971C22#1458357211yescharacteristic
972C22#1458357311yescharacteristic
973C22#1458357511yescharacteristic
974C22#1458357611yescharacteristic
975C22#1458357611yescharacteristic
976C22#1458358011yescharacteristic
977C22#1458358211yescharacteristic
978C22#1458358611yescharacteristic
979C22#1458359111yescharacteristic
980C22#1458359511yescharacteristic
981C22#1458359811yescharacteristic
982C22#1458359811yescharacteristic
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C4—864no—
990C4—3441no—
991C4—3441no—
992C4—1722no—
993C4—1722no—
994C4—1722no—
995C4—1722no—
996C4—1722no—
997C2—28no—
998C2C2×#1458276611yescharacteristic
999C2#1913703511yescharacteristic
1000C2#1913722111yescharacteristic
1001C2#1913744211yescharacteristic
1002C2#1913745311yescharacteristic
1003C2#1913751811yescharacteristic
1004C2#1913752911yescharacteristic
1005C2#1913883811yescharacteristic
1006C2#1913884611yescharacteristic
1007C2#1913885311yescharacteristic
1008C2#1913886111yescharacteristic
1009C2#1913898411yescharacteristic
1010C2#1913898611yescharacteristic
1011C2#1913915911yescharacteristic
1012C2#1913916111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#13901
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#14582766C2semidirect
4. #19132856C2semidirect
5. #19132856C2semidirect
6. #19132855C2semidirect
7. #19132855C2semidirect
8. #19132821C2semidirect
9. #19132820C2semidirect
10. #19132819C2semidirect
23. C22⋊C4×Dic43C4semidirect
86. C2×C4×Dic43C2×C4semidirect
87. C2×C4×Dic43C2×C4semidirect
107. C43⋊#95C2×C4semidirect
108. C43⋊#95C2×C4semidirect
441. C22×C43#383semidirect
560. C43#13901semidirect
947. C22#14582766semidirect

Maximal subgroups

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

subgroupindex
C2×#145827662
C2×C22⋊C4×Dic432
C22×C43⋊#952
#191328562
#191328552
#191328212
#191328202
#191328192
#191328182
#191328172
C43×C22⋊#952
#1390143