Finite Group Databasebeta

← #25021053

Subgroups — #25021053

Order 11008.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063306C211yesmaximal, characteristic
2C2×#14582787C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
5#19132861C211yesmaximal, characteristic, complemented
6#19132842C211yesmaximal, characteristic, complemented
7#19132838C211yesmaximal, characteristic, complemented
8#19132836C211yesmaximal, characteristic
9#19132832C211yesmaximal, characteristic, complemented
10#19132826C211yesmaximal, characteristic, complemented
11#19132826C211yesmaximal, characteristic, complemented
12Dic43⋊#95C211yesmaximal, characteristic, complemented
13#19132818C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C2×C43×#386C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C2×#13063306—24no—
18C2×#13063306—24no—
19C2×#13063306C418yescomplemented
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582787—24no—
34C22⋊C4×Dic43—24no—
35C4×C22⋊Dic43—24no—
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
49C2×C43⋊#95C2211yescharacteristic
50C23×D4×C43C2211yescharacteristic
51C24×C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C43×#386—24no—
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C23×Dic43—22no—
59C23×Dic43—22no—
60C23×Dic43—22no—
61C23×Dic43—22no—
62C23×Dic43—41no—
63C23×Dic43—41no—
64C23×Dic43C2×C414yescomplemented
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73#13063306—232no—
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—41no—
81C2×Dic43⋊C4C2×C414yescomplemented
82C2×Dic43⋊C4C2×C414yescomplemented
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—22no—
91C2×C22⋊Dic43—22no—
92C2×C22⋊Dic43—22no—
93C2×C22⋊Dic43—22no—
94C2×C22⋊Dic43—22no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—41no—
98C2×C22⋊Dic43—41no—
99C2×C22⋊Dic43C2×C414yes—
100C2×C22⋊Dic43C2×C414yes—
101C2×C22⋊Dic43C2×C414yescomplemented
102C2×C22⋊Dic43D414yes—
103C2×C22⋊Dic43D414yes—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43—22no—
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—22no—
118C43⋊#95—22no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—41no—
124C43⋊#95—41no—
125C43⋊#95—41no—
126C43⋊#95—41no—
127C25×C43C2311yescharacteristic
128C25×C43C2311yescharacteristic
129C22×D4×C43—22no—
130C22×D4×C43—22no—
131C22×D4×C43—22no—
132C22×D4×C43—22no—
133C22×D4×C43—41no—
134C22×D4×C43—41no—
135C22×D4×C43C2×C414yes—
136C23×C4×C43—22no—
137C23×C4×C43—22no—
138C23×C4×C43—22no—
139C23×C4×C43—22no—
140C23×C4×C43—22no—
141C23×C4×C43—41no—
142C23×C4×C43—41no—
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—22no—
149C2×C22⋊C4×C43—22no—
150C2×C22⋊C4×C43—22no—
151C2×C22⋊C4×C43—22no—
152C2×C22⋊C4×C43—22no—
153C2×C22⋊C4×C43—22no—
154C2×C22⋊C4×C43—41no—
155C2×C22⋊C4×C43—41no—
156C2×C22⋊C4×C43D414yes—
157#95×C43—22no—
158#95×C43—22no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
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×C43C22×C412yes—
184C24×C43C22×C412yes—
185C24×C43C2×D412yes—
186C24×C43C2×D412yes—
187C24×C43C2×D412yes—
188C24×C43#4112yes—
189C24×C43C2411yescharacteristic
190C2×D4×C43—28no—
191C2×D4×C43—28no—
192C2×D4×C43—44no—
193C2×D4×C43—44no—
194C2×D4×C43—44no—
195C2×D4×C43—44no—
196C2×D4×C43—44no—
197C22×C4×C43—28no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—44no—
228C22×C4×C43—44no—
229C22×C4×C43—44no—
230C22×C4×C43—44no—
231C22×C4×C43—44no—
232C22×C4×C43—44no—
233C22×C4×C43C22×C412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43#4112yes—
237C22×C4×C43#4112yes—
238C22×C4×C43#4112yes—
239C22×Dic43—28no—
240C22×Dic43—28no—
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—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
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—44no—
287C22×Dic43—44no—
288C22×Dic43—44no—
289C22×Dic43—44no—
290C22×Dic43—44no—
291C22×Dic43C22×C412yes—
292C22×Dic43C22×C412yes—
293C22×Dic43C22×C412yes—
294C22×Dic43C22×C412yes—
295C22×Dic43C2×D412yes—
296C22×Dic43C2×D412yes—
297C22×Dic43C2×D412yes—
298C22×Dic43C2×D412yes—
299C22×Dic43#4112yes—
300C22×Dic43#4112yes—
301C22×Dic43#4112yes—
302C22⋊C4×C43—28no—
303C22⋊C4×C43—44no—
304C22⋊C4×C43—44no—
305C22⋊Dic43—28no—
306C22⋊Dic43—28no—
307C22⋊Dic43—28no—
308C22⋊Dic43—28no—
309C22⋊Dic43—44no—
310C22⋊Dic43—44no—
311C22⋊Dic43C22⋊C4116yescomplemented
312Dic43⋊C4—28no—
313Dic43⋊C4—28no—
314Dic43⋊C4—44no—
315C4×Dic43—44no—
316C4×Dic43—44no—
317C4×Dic43—44no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—22no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43—22no—
335C23×C43—22no—
336C23×C43—22no—
337C23×C43—22no—
338C23×C43—22no—
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—41no—
355C23×C43—41no—
356C23×C43—41no—
357C23×C43—41no—
358C23×C43—41no—
359C23×C43—41no—
360C23×C43—41no—
361C23×C43—41no—
362C23×C43—41no—
363C23×C43—41no—
364C23×C43—41no—
365C23×C43—41no—
366C23×C43—41no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43—41no—
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×C43C2×C22⋊C414yes—
387C23×C43C4×D414yes—
388C23×C43C23×C411yescharacteristic
389C23×C43C22×D411yescharacteristic
390C23×C43C22×D411yescharacteristic
391C23×C43C22×D411yescharacteristic
392C23×C43C2×#4111yescharacteristic
393C23×C43C2×#4111yescharacteristic
394C23×C43C2×#4111yescharacteristic
395C23×C43C2×#4111yescharacteristic
396C23×C43C2×#4111yescharacteristic
397C23×C43C2×#4111yescharacteristic
398C23×C43C2×#4111yescharacteristic
399C23×C43H(5,𝔽2)11yescharacteristic
400C23×C43H(5,𝔽2)11yescharacteristic
401C23×C43H(5,𝔽2)11yescharacteristic
402C23×C432−1+411yescharacteristic
403D4×C43—416no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—416no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43#12314yescomplemented
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—416no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43C2×C22⋊C414yes—
496C2×Dic43C2×C22⋊C414yes—
497#14096—431nomaximal, Sylow
498C22×C43—24no—
499C22×C43—24no—
500C22×C43—24no—
501C22×C43—24no—
502C22×C43—24no—
503C22×C43—24no—
504C22×C43—42no—
505C22×C43—42no—
506C22×C43—42no—
507C22×C43—42no—
508C22×C43—42no—
509C22×C43—42no—
510C22×C43—42no—
511C22×C43—42no—
512C22×C43—42no—
513C22×C43—42no—
514C22×C43—42no—
515C22×C43—42no—
516C22×C43—42no—
517C22×C43—42no—
518C22×C43—42no—
519C22×C43—42no—
520C22×C43—42no—
521C22×C43—42no—
522C22×C43—42no—
523C22×C43—42no—
524C22×C43—42no—
525C22×C43—42no—
526C22×C43—42no—
527C22×C43—42no—
528C22×C43C22×C22⋊C411yescharacteristic
529C22×C43C2×C4×D411yescharacteristic
530C22×C43C4×#4111yescharacteristic
531C22×C43C4×#4111yescharacteristic
532C22×C43C4×#4111yescharacteristic
533C22×C43#51811yescharacteristic
534C22×C43#52011yescharacteristic
535C22×C43C2×#12311yescharacteristic
536C22×C43#52511yescharacteristic
537C22×C43#52511yescharacteristic
538C22×C43#52511yescharacteristic
539C22×C43#52911yescharacteristic
540C22×C43#52911yescharacteristic
541C22×C43#53211yescharacteristic
542C22×C43#53211yescharacteristic
543C22×C43#53811yescharacteristic
544C22×C43#53911yescharacteristic
545C22×C43#54011yescharacteristic
546C22×C43#54211yescharacteristic
547C22×C43D4211yescharacteristic
548C22×C43D4211yescharacteristic
549C22×C43#54611yescharacteristic
550C22×C43#54611yescharacteristic
551C22×C43#54611yescharacteristic
552C22×C43#54611yescharacteristic
553C22×C43#54611yescharacteristic
554C22×C43#54711yescharacteristic
555C22×C43#54711yescharacteristic
556C22×C43#54711yescharacteristic
557C22×C43#55111yescharacteristic
558C22×C43#55111yescharacteristic
559C22×C43#55211yescharacteristic
560C22×C43#55311yescharacteristic
561C22×C43#55311yescharacteristic
562C22×C43#55911yescharacteristic
563C4×C43—24no—
564C4×C43—42no—
565C4×C43—42no—
566C4×C43—42no—
567C4×C43—81no—
568Dic43—24no—
569Dic43—24no—
570Dic43—42no—
571Dic43—42no—
572Dic43—42no—
573Dic43—42no—
574Dic43—42no—
575Dic43—81no—
576C22×#123—431no—
577C2×#388—431no—
578C2×#386D4311yescharacteristic
579C2×C4×C22⋊C4—431no—
580C2×C4×C22⋊C4—431no—
581#1445—431no—
582#1440—431no—
583#1439—431no—
584#1438—431no—
585#1437—431no—
586#1436—431no—
587#1436—431no—
588C4⋊#95—431no—
589C22⋊#95—431no—
590C22⋊#95—431no—
591C2×C43—44no—
592C2×C43—44no—
593C2×C43#229711yescharacteristic
594C2×C43C4×#12311yescharacteristic
595C2×C43#233511yescharacteristic
596C2×C43D4×C22⋊C411yescharacteristic
597C2×C43#233911yescharacteristic
598C2×C43#235911yescharacteristic
599C2×C43#237411yescharacteristic
600C2×C43#241811yescharacteristic
601C2×C43#242211yescharacteristic
602C2×C43#245511yescharacteristic
603C2×C43#245711yescharacteristic
604C2×C43#246411yescharacteristic
605C2×C43#247011yescharacteristic
606C2×C43#255311yescharacteristic
607C2×C43#255711yescharacteristic
608C23×D4C2×D4311yescharacteristic
609C24×C4—431no—
610C24×C4C2×D4311yescharacteristic
611C2×#123—438no—
612C2×#123—864no—
613C2×#123—864no—
614C22×C4⋊C4—431no—
615C22×C4⋊C4—431no—
616C22×C4⋊C4—431no—
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C22⋊C4—431no—
622C22×C22⋊C4—431no—
623C22×C22⋊C4—431no—
624C22×C22⋊C4C2×D4311yescharacteristic
625C22×C22⋊C4C2×D4311yescharacteristic
626C22×C22⋊C4C2×D4311yescharacteristic
627C22×C42—431no—
628C22×C42—431no—
629C22×C42—431no—
630#388—864no—
631#386—24no—
632C4×C22⋊C4—864no—
633C4×C22⋊C4—864no—
634C2×#95—431no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—431no—
638C2×#95—431no—
639C2×#95—431no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95—431no—
643C2×#95—431no—
644C2×#95—431no—
645C2×#95—431no—
646C2×#95—431no—
647C2×#95—431no—
648C2×#95C2×D4311yescharacteristic
649C2×#95C2×D4311yescharacteristic
650C43#1409611yescharacteristic, complemented, Sylow
651C25C22×D4311yescharacteristic
652C25C22×D4311yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C4×D4314yes—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—41no—
666C23×C4—41no—
667C23×C4—431no—
668C23×C4—431no—
669C23×C4—431no—
670C23×C4—431no—
671C23×C4—431no—
672C23×C4—431no—
673C23×C4—431no—
674C23×C4—434no—
675C23×C4—431no—
676C23×C4—862no—
677C23×C4—862no—
678C23×C4—862no—
679C23×C4—862no—
680C23×C4—1721no—
681C23×C4—1721no—
682C23×C4C22×D4311yescharacteristic
683C23×C4C22×D4311yescharacteristic
684C23×C4C22×D4311yescharacteristic
685C23×C4C22×D4311yescharacteristic
686C23×C4C22×D4311yescharacteristic
687#123—8632no—
688C2×C4⋊C4—434no—
689C2×C4⋊C4—434no—
690C2×C4⋊C4—862no—
691C2×C4⋊C4—862no—
692C2×C4⋊C4—862no—
693C2×C4⋊C4—862no—
694C2×C4⋊C4—862no—
695C2×C4⋊C4—862no—
696C2×C4⋊C4—1721no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—434no—
706C2×C22⋊C4—434no—
707C2×C22⋊C4—434no—
708C2×C22⋊C4—434no—
709C2×C22⋊C4—434no—
710C2×C22⋊C4—862no—
711C2×C22⋊C4—862no—
712C2×C22⋊C4—862no—
713C2×C22⋊C4—862no—
714C2×C22⋊C4—862no—
715C2×C22⋊C4—862no—
716C2×C22⋊C4—862no—
717C2×C22⋊C4—862no—
718C2×C22⋊C4—862no—
719C2×C22⋊C4—862no—
720C2×C22⋊C4—862no—
721C2×C22⋊C4—862no—
722C2×C22⋊C4—862no—
723C2×C22⋊C4—862no—
724C2×C22⋊C4—1721no—
725C2×C22⋊C4—1721no—
726C2×C22⋊C4C22⋊D4314yes—
727C2×C42—862no—
728C2×C42—862no—
729C2×C42—862no—
730C2×C42—862no—
731C2×C42—862no—
732C2×C42—862no—
733C2×C42—1721no—
734C2×C42—1721no—
735C2×C42—1721no—
736#95—22no—
737#95—22no—
738#95—862no—
739#95—862no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—862no—
744#95—862no—
745#95—862no—
746#95—862no—
747#95—862no—
748#95—1721no—
749#95—1721no—
750#95—1721no—
751#95—1721no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C2×C4×D4312yes—
777C24C2×C4×D4312yes—
778C24#1062189812yes—
779C24D4×D4312yes—
780C24D4×D4312yes—
781C24C2×C22⋊D4312yes—
782C24C23×D4311yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—28no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—432no—
827C22×C4—432no—
828C22×C4—432no—
829C22×C4—432no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—432no—
833C22×C4—432no—
834C22×C4—432no—
835C22×C4—432no—
836C22×C4—432no—
837C22×C4—868no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—868no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—1724no—
885C22×C4—1724no—
886C22×C4—1724no—
887C22×C4—1724no—
888C22×C4—1724no—
889C22×C4C2×C4×D4312yes—
890C22×C4#1062190012yes—
891C22×C4#1062190012yes—
892C22×C4#1062190012yes—
893C22×C4C2×C22⋊D4312yes—
894C22×C4C2×C22⋊D4312yes—
895C4⋊C4—868no—
896C4⋊C4—868no—
897C4⋊C4—1724no—
898C22⋊C4—28no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—4316no—
902C22⋊C4—868no—
903C22⋊C4—868no—
904C22⋊C4—868no—
905C22⋊C4—868no—
906C22⋊C4—1724no—
907C22⋊C4—1724no—
908C42—1724no—
909C42—1724no—
910C42—1724no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C22⋊C4×D4314yes—
980C23C4×C22⋊D4314yes—
981C23C22×C4×D4311yescharacteristic
982C23C2×D4×D4311yescharacteristic
983C23C2×D4×D4311yescharacteristic
984C23C22×C22⋊D4311yescharacteristic
985C23#41×D4311yescharacteristic
986C23#41×D4311yescharacteristic
987C23#41×D4311yescharacteristic
988C23C2×#1062190011yescharacteristic
989C23C2×#1062190011yescharacteristic
990C23C2×#1062190011yescharacteristic
991C23C2×#1062189811yescharacteristic
992C23#1306337011yescharacteristic
993C23#1306337011yescharacteristic
994C23#1306337011yescharacteristic
995C23#1306337211yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—434no—
1033C2×C4—434no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—862no—
1037C2×C4—862no—
1038C2×C4—862no—
1039C2×C4—862no—
1040C2×C4—862no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—862no—
1044C2×C4—862no—
1045C2×C4—862no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—862no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—17216no—
1062C2×C4—1721no—
1063C2×C4—1721no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—1721no—
1072C2×C4—1721no—
1073C2×C4—1721no—
1074C2×C4—1721no—
1075C2×C4—1721no—
1076C2×C4—1721no—
1077C2×C4—1721no—
1078C2×C4—1721no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4—1721no—
1083C2×C4—1721no—
1084C2×C4—1721no—
1085C2×C4—1721no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4—1721no—
1089C2×C4#1306330614yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C2×C22⋊C4×D4311yescharacteristic
1121C22C2×C4×C22⋊D4311yescharacteristic
1122C22C4×#1062190011yescharacteristic
1123C22C4×#1062190011yescharacteristic
1124C22C4×#1062190011yescharacteristic
1125C22#1458337211yescharacteristic
1126C22#1458337811yescharacteristic
1127C22C2×#1306330611yescharacteristic
1128C22#1458340511yescharacteristic
1129C22#1458340611yescharacteristic
1130C22#1458340711yescharacteristic
1131C22#1458342911yescharacteristic
1132C22#1458342911yescharacteristic
1133C22#1458344411yescharacteristic
1134C22#1458344411yescharacteristic
1135C22#1458348411yescharacteristic
1136C22#1458349211yescharacteristic
1137C22#1458349911yescharacteristic
1138C22#1458351611yescharacteristic
1139C22D4×C22⋊D4311yescharacteristic
1140C22D4×C22⋊D4311yescharacteristic
1141C22#1458353611yescharacteristic
1142C22#1458353811yescharacteristic
1143C22#1458353911yescharacteristic
1144C22#1458353911yescharacteristic
1145C22#1458354311yescharacteristic
1146C22#1458354711yescharacteristic
1147C22#1458354811yescharacteristic
1148C22#1458354911yescharacteristic
1149C22#1458357811yescharacteristic
1150C22#1458358011yescharacteristic
1151C22#1458358911yescharacteristic
1152C22#1458359611yescharacteristic
1153C22#1458359611yescharacteristic
1154C22#1458363311yescharacteristic
1155C4—24no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—864no—
1161C4—864no—
1162C4—3441no—
1163C4—1722no—
1164C4—1722no—
1165C4—1722no—
1166C4—1722no—
1167C4—1722no—
1168C2—44no—
1169C2—44no—
1170C2#1913708011yescharacteristic
1171C2C4×#1306330611yescharacteristic
1172C2#1913738611yescharacteristic
1173C2C22⋊C4×C22⋊D4311yescharacteristic
1174C2#1913742111yescharacteristic
1175C2#1913758111yescharacteristic
1176C2#1913772811yescharacteristic
1177C2#1913805311yescharacteristic
1178C2#1913810511yescharacteristic
1179C2#1913847411yescharacteristic
1180C2#1913849911yescharacteristic
1181C2#1913859711yescharacteristic
1182C2#1913868811yescharacteristic
1183C2#1913963711yescharacteristic
1184C2#1913969111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#386C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC2×#386D43
hypocenterC43#14096
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#14582787C2semidirect
3. C2×C22⋊C4×Dic43C2semidirect
4. C2×C4×C22⋊Dic43C2semidirect
5. #19132861C2semidirect
6. #19132842C2semidirect
7. #19132838C2semidirect
9. #19132832C2semidirect
10. #19132826C2semidirect
11. #19132826C2semidirect
12. Dic43⋊#95C2semidirect
13. #19132818C2semidirect
14. #19132817C2semidirect
19. C2×#13063306C4semidirect
64. C23×Dic43C2×C4semidirect
81. C2×Dic43⋊C4C2×C4semidirect
82. C2×Dic43⋊C4C2×C4semidirect
101. C2×C22⋊Dic43C2×C4semidirect
311. C22⋊Dic43C22⋊C4semidirect
439. C2×C4×C43#123semidirect
650. C43#14096semidirect
1089. 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
C2×#145827872
C2×C22⋊C4×Dic432
C2×C4×C22⋊Dic432
#191328612
#191328422
#191328382
#191328362
#191328322
#191328262
Dic43⋊#952
#191328182
#191328172
C2×C43×#3862
#1409643