Finite Group Databasebeta

← #25019583

Subgroups — #25019583

Order 11008.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582792C211yesmaximal, characteristic
2C2×#14582784C211yesmaximal, characteristic, complemented
3C2×#14582771C211yesmaximal, characteristic
4C2×#14582763C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic
6#19132855C211yesmaximal, characteristic, complemented
7#19132847C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic
9#19132832C211yesmaximal, characteristic
10#19132826C211yesmaximal, characteristic, complemented
11#19132826C211yesmaximal, characteristic, complemented
12#19132821C211yesmaximal, characteristic, complemented
13#19132817C211yesmaximal, characteristic
14#95×Dic43C211yesmaximal, characteristic, complemented
15C43×#1440C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28#14582792C418yescomplemented
29#14582784—24no—
30#14582771—24no—
31#14582763—24no—
32C22⋊C4×Dic43—24no—
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
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C22×C22⋊C4×C43C2211yescharacteristic
50C22×C22⋊C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C23×Dic43—22no—
57C23×Dic43—22no—
58C23×Dic43—22no—
59C23×Dic43—22no—
60C23×Dic43—22no—
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⋊Dic43C2×C414yescomplemented
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—41no—
82C2×Dic43⋊C4—41no—
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—41no—
90C2×C22⋊Dic43C2×C414yes—
91C2×C22⋊Dic43C2×C414yes—
92C2×C4×Dic43—22no—
93C2×C4×Dic43—22no—
94C2×C4×Dic43—22no—
95C2×C4×Dic43—22no—
96C2×C4×Dic43—22no—
97C2×C4×Dic43—22no—
98C2×C4×Dic43—22no—
99C2×C4×Dic43—22no—
100C2×C4×Dic43—41no—
101C2×C4×Dic43—41no—
102C2×C4×Dic43—41no—
103C2×C4×Dic43C2×C414yescomplemented
104C43⋊#95—22no—
105C43⋊#95—22no—
106C43⋊#95—22no—
107C43⋊#95—22no—
108C43⋊#95—22no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—41no—
115C43⋊#95—41no—
116C43⋊#95C2×C414yescomplemented
117C43⋊#95C2×C414yescomplemented
118C43⋊#95D414yes—
119C43⋊#95D414yes—
120C25×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—22no—
128C2×C22⋊C4×C43—22no—
129C2×C22⋊C4×C43—22no—
130C2×C22⋊C4×C43—22no—
131C2×C22⋊C4×C43—22no—
132C2×C22⋊C4×C43—22no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—41no—
135C2×C22⋊C4×C43C2×C414yes—
136#95×C43—22no—
137#95×C43—22no—
138#95×C43—22no—
139#95×C43—41no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—21no—
143C24×C43—21no—
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—21no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43C22×C412yes—
153C24×C43#4112yes—
154C24×C43#4112yes—
155C24×C43C2411yescharacteristic
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—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43C22×C412yes—
194C22×C4×C43C22×C412yes—
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2×D412yes—
197C22×C4×C43#4112yes—
198C22×Dic43—28no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
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—44no—
243C22×Dic43—44no—
244C22×Dic43—44no—
245C22×Dic43—44no—
246C22×Dic43—44no—
247C22×Dic43—44no—
248C22×Dic43C22×C412yes—
249C22×Dic43C22×C412yes—
250C22×Dic43C22×C412yes—
251C22×Dic43C22×C412yes—
252C22×Dic43C2×D412yes—
253C22×Dic43C2×D412yes—
254C22×Dic43C2×D412yes—
255C22×Dic43C2×D412yes—
256C22×Dic43#4112yes—
257C22×Dic43#4112yes—
258C22×Dic43#4112yes—
259C22×Dic43#4112yes—
260C22×Dic43#4112yes—
261C22⋊C4×C43—28no—
262C22⋊C4×C43—28no—
263C22⋊C4×C43—44no—
264C22⋊Dic43—28no—
265C22⋊Dic43—28no—
266C22⋊Dic43—44no—
267C4⋊Dic43—28no—
268Dic43⋊C4—44no—
269Dic43⋊C4—44no—
270Dic43⋊C4—44no—
271C4×Dic43—28no—
272C4×Dic43—44no—
273C4×Dic43—44no—
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—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43#11714yes—
310C23×C43C23×C411yescharacteristic
311C23×C43C22×D411yescharacteristic
312C23×C43C22×D411yescharacteristic
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×C432−1+411yescharacteristic
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—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
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×Dic43—22no—
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—22no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—416no—
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×Dic43C4×D414yes—
422C2×Dic43C4×D414yes—
423C2×Dic43#12414yes—
424#13986—431nomaximal, Sylow
425C22×C43—24no—
426C22×C43—24no—
427C22×C43—24no—
428C22×C43—42no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43—42no—
432C22×C43—42no—
433C22×C43—42no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—42no—
437C22×C43—42no—
438C22×C43—42no—
439C22×C43—42no—
440C22×C43C2×#11711yescharacteristic
441C22×C43C2×C4×D411yescharacteristic
442C22×C43C2×C4×D411yescharacteristic
443C22×C43C4×#4111yescharacteristic
444C22×C43C4×#4111yescharacteristic
445C22×C43#52011yescharacteristic
446C22×C43#52011yescharacteristic
447C22×C43#52511yescharacteristic
448C22×C43#52511yescharacteristic
449C22×C43C2×#12411yescharacteristic
450C22×C43#52911yescharacteristic
451C22×C43#52911yescharacteristic
452C22×C43#52911yescharacteristic
453C22×C43#52911yescharacteristic
454C22×C43#53211yescharacteristic
455C22×C43#53811yescharacteristic
456C22×C43#53911yescharacteristic
457C22×C43#54111yescharacteristic
458C22×C43#54211yescharacteristic
459C22×C43D4211yescharacteristic
460C22×C43#54611yescharacteristic
461C22×C43#54611yescharacteristic
462C22×C43#54711yescharacteristic
463C22×C43#54711yescharacteristic
464C22×C43#54811yescharacteristic
465C22×C43#54811yescharacteristic
466C22×C43#55111yescharacteristic
467C22×C43#55111yescharacteristic
468C22×C43#55111yescharacteristic
469C22×C43#55211yescharacteristic
470C22×C43#55211yescharacteristic
471C22×C43#55211yescharacteristic
472C22×C43#55211yescharacteristic
473C22×C43#55311yescharacteristic
474C22×C43#55311yescharacteristic
475C4×C43—42no—
476C4×C43—42no—
477C4×C43—42no—
478C4×C43—42no—
479C4×C43—42no—
480C4×C43—81no—
481Dic43—24no—
482Dic43—24no—
483Dic43—24no—
484Dic43—42no—
485Dic43—42no—
486Dic43—42no—
487Dic43—42no—
488Dic43—81no—
489C2×#388—431no—
490C2×#387—431no—
491C2×#385—431no—
492C2×#382—431no—
493C2×C4×C22⋊C4—431no—
494#1443—431no—
495#1441—431no—
496#1440D4311yescharacteristic
497#1439—431no—
498#1437—431no—
499#1436—431no—
500#1436—431no—
501#1434—431no—
502C22⋊#95—431no—
503C4×#95—431no—
504C2×C43—44no—
505C2×C43#229011yescharacteristic
506C2×C43C4×#12411yescharacteristic
507C2×C43#233411yescharacteristic
508C2×C43#234311yescharacteristic
509C2×C43#235211yescharacteristic
510C2×C43#235911yescharacteristic
511C2×C43#236111yescharacteristic
512C2×C43#246011yescharacteristic
513C2×C43#246111yescharacteristic
514C2×C43#247211yescharacteristic
515C2×C43#247511yescharacteristic
516C2×C43#248911yescharacteristic
517C2×C43#251511yescharacteristic
518C2×C43#255311yescharacteristic
519C2×C43#257611yescharacteristic
520C24×C4—431no—
521C22×C4⋊C4—431no—
522C22×C4⋊C4—431no—
523C22×C4⋊C4—431no—
524C22×C4⋊C4—431no—
525C22×C22⋊C4—431no—
526C22×C22⋊C4—431no—
527C22×C22⋊C4—431no—
528C22×C22⋊C4C2×D4311yescharacteristic
529C22×C22⋊C4C2×D4311yescharacteristic
530C22×C22⋊C4C2×D4311yescharacteristic
531C22×C42—431no—
532C22×C42—431no—
533C22×C42—431no—
534C22×C42—431no—
535#388—438no—
536#387—864no—
537#385—864no—
538#382—864no—
539C4×C22⋊C4—864no—
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—431no—
556C2×#95C2×D4311yescharacteristic
557C2×#95C2×D4311yescharacteristic
558C2×#95C2×D4311yescharacteristic
559C2×#95C2×D4311yescharacteristic
560C43#1398611yescharacteristic, complemented, Sylow
561C25C22×D4311yescharacteristic
562C23×C4—431no—
563C23×C4—431no—
564C23×C4—431no—
565C23×C4—431no—
566C23×C4—431no—
567C23×C4—431no—
568C23×C4—431no—
569C23×C4—431no—
570C23×C4—862no—
571C23×C4—862no—
572C23×C4—862no—
573C23×C4—862no—
574C23×C4—862no—
575C23×C4—1721no—
576C23×C4—1721no—
577C23×C4C22×D4311yescharacteristic
578C23×C4C22×D4311yescharacteristic
579C23×C4C22×D4311yescharacteristic
580C23×C4C22×D4311yescharacteristic
581C23×C4C22×D4311yescharacteristic
582C23×C4C22×D4311yescharacteristic
583C2×C4⋊C4—434no—
584C2×C4⋊C4—862no—
585C2×C4⋊C4—862no—
586C2×C4⋊C4—862no—
587C2×C4⋊C4—862no—
588C2×C4⋊C4—862no—
589C2×C4⋊C4—862no—
590C2×C4⋊C4—862no—
591C2×C4⋊C4—862no—
592C2×C4⋊C4—862no—
593C2×C4⋊C4—1721no—
594C2×C4⋊C4—1721no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—434no—
604C2×C22⋊C4—434no—
605C2×C22⋊C4—862no—
606C2×C22⋊C4—862no—
607C2×C22⋊C4—862no—
608C2×C22⋊C4—862no—
609C2×C22⋊C4—862no—
610C2×C22⋊C4—862no—
611C2×C22⋊C4—1721no—
612C2×C22⋊C4C4×D4314yes—
613C2×C42—434no—
614C2×C42—862no—
615C2×C42—862no—
616C2×C42—862no—
617C2×C42—862no—
618C2×C42—862no—
619C2×C42—862no—
620C2×C42—862no—
621C2×C42—862no—
622C2×C42—1721no—
623C2×C42—1721no—
624C2×C42—1721no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—41no—
629#95—434no—
630#95—434no—
631#95—434no—
632#95—434no—
633#95—862no—
634#95—862no—
635#95—862no—
636#95—862no—
637#95—862no—
638#95—862no—
639#95—862no—
640#95—862no—
641#95—862no—
642#95—862no—
643#95—1721no—
644#95—1721no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24C2×C4×D4312yes—
658C24#1062190012yes—
659C24#1062190012yes—
660C24C23×D4311yescharacteristic
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—21no—
697C22×C4—21no—
698C22×C4—432no—
699C22×C4—432no—
700C22×C4—432no—
701C22×C4—432no—
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—432no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—868no—
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—1724no—
756C22×C4—1724no—
757C22×C4—1724no—
758C22×C4—1724no—
759C22×C4—1724no—
760C22×C4—1724no—
761C22×C4C2×C4×D4312yes—
762C22×C4C2×C4×D4312yes—
763C22×C4D4×D4312yes—
764C22×C4D4×D4312yes—
765C22×C4#1062190012yes—
766C4⋊C4—868no—
767C4⋊C4—1724no—
768C4⋊C4—1724no—
769C4⋊C4—1724no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—44no—
773C22⋊C4—868no—
774C22⋊C4—868no—
775C22⋊C4—1724no—
776C42—868no—
777C42—1724no—
778C42—1724no—
779C42—1724no—
780C23—22no—
781C23—22no—
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—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23#1306328114yes—
815C23C22×C4×D4311yescharacteristic
816C23C2×D4×D4311yescharacteristic
817C23C2×D4×D4311yescharacteristic
818C23#41×D4311yescharacteristic
819C23#41×D4311yescharacteristic
820C23#41×D4311yescharacteristic
821C23#41×D4311yescharacteristic
822C23#41×D4311yescharacteristic
823C23C2×#1062190011yescharacteristic
824C23C2×#1062190011yescharacteristic
825C23C2×#1062190011yescharacteristic
826C23#1306337011yescharacteristic
827C23#1306337111yescharacteristic
828C23#1306337211yescharacteristic
829C23#1306337211yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
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—22no—
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—434no—
873C2×C4—434no—
874C2×C4—434no—
875C2×C4—862no—
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—862no—
898C2×C4—862no—
899C2×C4—862no—
900C2×C4—862no—
901C2×C4—862no—
902C2×C4—862no—
903C2×C4—862no—
904C2×C4—862no—
905C2×C4—17216no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1721no—
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—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×#1306328111yescharacteristic
945C22C4×D4×D4311yescharacteristic
946C22C4×D4×D4311yescharacteristic
947C22C4×#1062190011yescharacteristic
948C22#1458336711yescharacteristic
949C22#1458337811yescharacteristic
950C22#1458337911yescharacteristic
951C22#1458340511yescharacteristic
952C22#1458340911yescharacteristic
953C22#124×D4311yescharacteristic
954C22#1458342611yescharacteristic
955C22#1458342611yescharacteristic
956C22#1458343011yescharacteristic
957C22#1458343211yescharacteristic
958C22#1458344411yescharacteristic
959C22#1458348511yescharacteristic
960C22#1458349411yescharacteristic
961C22#1458350611yescharacteristic
962C22#1458351811yescharacteristic
963C22#1458353311yescharacteristic
964C22#1458353611yescharacteristic
965C22#1458354611yescharacteristic
966C22#1458354711yescharacteristic
967C22#1458354711yescharacteristic
968C22#1458355511yescharacteristic
969C22#1458355711yescharacteristic
970C22#1458357211yescharacteristic
971C22#1458357211yescharacteristic
972C22#1458357911yescharacteristic
973C22#1458358511yescharacteristic
974C22#1458358611yescharacteristic
975C22#1458358611yescharacteristic
976C22#1458358611yescharacteristic
977C22#1458359211yescharacteristic
978C22#1458360011yescharacteristic
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—864no—
986C4—864no—
987C4—864no—
988C4—3441no—
989C4—1722no—
990C4—1722no—
991C4—1722no—
992C4—1722no—
993C2—44no—
994C2#1913703511yescharacteristic
995C2#1913713611yescharacteristic
996C2#1913736711yescharacteristic
997C2#1913745711yescharacteristic
998C2#1913752211yescharacteristic
999C2#1913758411yescharacteristic
1000C2#1913760811yescharacteristic
1001C2#1913854011yescharacteristic
1002C2#1913855511yescharacteristic
1003C2#1913872211yescharacteristic
1004C2#1913876711yescharacteristic
1005C2#1913892911yescharacteristic
1006C2#1913920711yescharacteristic
1007C2#1913963311yescharacteristic
1008C2#1913990211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1440C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1440D43
hypocenterC43#13986
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C2×#14582784C2semidirect
4. C2×#14582763C2semidirect
6. #19132855C2semidirect
7. #19132847C2semidirect
10. #19132826C2semidirect
11. #19132826C2semidirect
12. #19132821C2semidirect
14. #95×Dic43C2semidirect
28. #14582792C4semidirect
73. C2×C4⋊Dic43C2×C4semidirect
103. C2×C4×Dic43C2×C4semidirect
116. C43⋊#95C2×C4semidirect
117. C43⋊#95C2×C4semidirect
560. C43#13986semidirect

Maximal subgroups

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

subgroupindex
C2×#145827922
C2×#145827842
C2×#145827712
C2×#145827632
C2×C22⋊C4×Dic432
#191328552
#191328472
#191328382
#191328322
#191328262
#191328212
#191328172
#95×Dic432
C43×#14402
#1398643