Finite Group Databasebeta

← #25028050

Subgroups — #25028050

Order 11008.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063302C211yesmaximal, characteristic, complemented
2C22×D4×Dic43C211yesmaximal, characteristic
3C2×#14582820C211yesmaximal, characteristic, complemented
4C2×#14582811C211yesmaximal, characteristic, complemented
5C2×#14582774C211yesmaximal, characteristic, complemented
6C2×#14582771C211yesmaximal, characteristic, complemented
7#19132847C211yesmaximal, characteristic, complemented
8#19132840C211yesmaximal, characteristic, complemented
9#19132838C211yesmaximal, characteristic, complemented
10#19132838C211yesmaximal, characteristic, complemented
11#19132836C211yesmaximal, characteristic
12#19132829C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C43×#1438C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C2×#13063302—24no—
20C2×#13063302—24no—
21C2×#13063302—24no—
22C2×D4×Dic43—24no—
23C2×D4×Dic43—24no—
24C2×D4×Dic43—24no—
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×C4⋊Dic43C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×C22⋊Dic43C2211yescharacteristic
36C22×C22⋊Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38#14582820—24no—
39#14582811—24no—
40#14582774—24no—
41#14582771—24no—
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C23×D4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C22×Dic86—22no—
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—22no—
71C23×Dic43—22no—
72C23×Dic43—22no—
73C23×Dic43—22no—
74C23×Dic43—22no—
75C23×Dic43—22no—
76C23×Dic43—22no—
77C23×Dic43—41no—
78C23×Dic43—41no—
79C23×Dic43—41no—
80C23×Dic43—41no—
81C23×Dic43D414yes—
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90#13063302—232no—
91D4×Dic43—232no—
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—41no—
99C2×C4⋊Dic43D414yes—
100C2×C4⋊Dic43D414yescomplemented
101C2×Dic43⋊C4—22no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4—22no—
104C2×Dic43⋊C4—22no—
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4—41no—
109C2×Dic43⋊C4D414yescomplemented
110C2×C22⋊Dic43—22no—
111C2×C22⋊Dic43—22no—
112C2×C22⋊Dic43—22no—
113C2×C22⋊Dic43—22no—
114C2×C22⋊Dic43—22no—
115C2×C22⋊Dic43—22no—
116C2×C22⋊Dic43—22no—
117C2×C22⋊Dic43—22no—
118C2×C22⋊Dic43—22no—
119C2×C22⋊Dic43—22no—
120C2×C22⋊Dic43—22no—
121C2×C22⋊Dic43—22no—
122C2×C22⋊Dic43—22no—
123C2×C22⋊Dic43—22no—
124C2×C22⋊Dic43—22no—
125C2×C22⋊Dic43—41no—
126C2×C22⋊Dic43—41no—
127C2×C22⋊Dic43D414yes—
128C2×C4×Dic43—22no—
129C2×C4×Dic43—22no—
130C2×C4×Dic43—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95—22no—
142C43⋊#95—22no—
143C25×C43C2311yescharacteristic
144C25×C43C2311yescharacteristic
145C22×D4×C43—22no—
146C22×D4×C43—22no—
147C22×D4×C43—22no—
148C22×D4×C43—22no—
149C22×D4×C43—22no—
150C22×D4×C43—22no—
151C22×D4×C43Q814yescomplemented
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43—22no—
158C2×C22⋊C4×C43—22no—
159C2×C22⋊C4×C43—22no—
160C2×C22⋊C4×C43—22no—
161C2×C22⋊C4×C43—22no—
162C2×C22⋊C4×C43—22no—
163C2×C22⋊C4×C43—22no—
164C2×C22⋊C4×C43—22no—
165C2×C22⋊C4×C43—22no—
166C2×C22⋊C4×C43—22no—
167C2×C22⋊C4×C43—41no—
168C2×C22⋊C4×C43—41no—
169#95×C43—22no—
170#95×C43—22no—
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×C43C2×D412yes—
196C24×C43C2×D412yes—
197C24×C43C2×Q812yes—
198C24×C43C2×Q812yes—
199C24×C43#4112yes—
200C24×C43#4112yes—
201C24×C43C2411yescharacteristic
202C2×D4×C43—28no—
203C2×D4×C43—28no—
204C2×D4×C43—28no—
205C2×D4×C43—28no—
206C2×D4×C43—28no—
207C2×D4×C43—28no—
208C2×D4×C43—28no—
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—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
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×C43C2×D412yes—
239C22×C4×C43C2×D412yes—
240C22×C4×C43C2×D412yes—
241C22×C4×C43C2×Q812yes—
242C22×C4×C43#4112yes—
243C22×C4×C43#4112yes—
244C22×Dic43—28no—
245C22×Dic43—28no—
246C22×Dic43—28no—
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—21no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43—21no—
292C22×Dic43—44no—
293C22×Dic43—44no—
294C22×Dic43—44no—
295C22×Dic43—44no—
296C22×Dic43—44no—
297C22×Dic43—44no—
298C22×Dic43—44no—
299C22×Dic43—44no—
300C22×Dic43—44no—
301C22×Dic43—44no—
302C22×Dic43—44no—
303C22×Dic43C2×D412yes—
304C22×Dic43C2×D412yes—
305C22×Dic43C2×D412yes—
306C22×Dic43C2×D412yes—
307C22×Dic43C2×D412yes—
308C22×Dic43C2×D412yes—
309C22×Dic43C2×D412yes—
310C22×Dic43C2×D412yes—
311C22×Dic43C2×D412yes—
312C22×Dic43C2×D412yes—
313C22×Dic43#4112yes—
314C2×Dic86—28no—
315C2×Dic86—44no—
316C2×Dic86—44no—
317C2×Dic86—44no—
318C2×Dic86—44no—
319C2×Dic86—44no—
320C2×Dic86—44no—
321C22⋊C4×C43—28no—
322C22⋊C4×C43—28no—
323C22⋊C4×C43—44no—
324C22⋊C4×C43—44no—
325C22⋊Dic43—28no—
326C22⋊Dic43—28no—
327C22⋊Dic43—28no—
328C22⋊Dic43—28no—
329C22⋊Dic43—44no—
330C22⋊Dic43—44no—
331C4⋊Dic43—28no—
332C4⋊Dic43—28no—
333C4⋊Dic43—44no—
334Dic43⋊C4—28no—
335Dic43⋊C4—28no—
336Dic43⋊C4—44no—
337C4×Dic43—28no—
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—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—22no—
372C23×C43—22no—
373C23×C43—22no—
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×C43C22⋊Q814yes—
407C23×C43C22⋊Q814yescomplemented
408C23×C43C22×D411yescharacteristic
409C23×C43C22×D411yescharacteristic
410C23×C43C22×D411yescharacteristic
411C23×C43C22×D411yescharacteristic
412C23×C43C22×D411yescharacteristic
413C23×C43C22×Q811yescharacteristic
414C23×C43C2×#4111yescharacteristic
415C23×C43C2×#4111yescharacteristic
416C23×C43C2×#4111yescharacteristic
417C23×C43C2×#4111yescharacteristic
418C23×C43C2×#4111yescharacteristic
419C23×C43H(5,𝔽2)11yescharacteristic
420C23×C43H(5,𝔽2)11yescharacteristic
421C23×C432−1+411yescharacteristic
422C23×C432−1+411yescharacteristic
423D4×C43—232no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43C22⋊Q814yescomplemented
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—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
473C2×Dic43—22no—
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—22no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—22no—
486C2×Dic43—416no—
487C2×Dic43—416no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43—41no—
504C2×Dic43—41no—
505C2×Dic43—41no—
506C2×Dic43—41no—
507C2×Dic43—41no—
508C2×Dic43—41no—
509C2×Dic43—41no—
510C2×Dic43—41no—
511C2×Dic43—41no—
512C2×Dic43—41no—
513C2×Dic43—41no—
514C2×Dic43—41no—
515C2×Dic43#12014yes—
516C2×Dic43#12014yes—
517Dic86—416no—
518#14723—431nomaximal, Sylow
519C22×C43—24no—
520C22×C43—24no—
521C22×C43—24no—
522C22×C43—24no—
523C22×C43—24no—
524C22×C43—24no—
525C22×C43—42no—
526C22×C43—42no—
527C22×C43—42no—
528C22×C43—42no—
529C22×C43—42no—
530C22×C43—42no—
531C22×C43—42no—
532C22×C43—42no—
533C22×C43—42no—
534C22×C43—42no—
535C22×C43—42no—
536C22×C43—42no—
537C22×C43—42no—
538C22×C43—42no—
539C22×C43—42no—
540C22×C43—42no—
541C22×C43—42no—
542C22×C43—42no—
543C22×C43—42no—
544C22×C43—42no—
545C22×C43—42no—
546C22×C43—42no—
547C22×C43—42no—
548C22×C43—42no—
549C22×C43C2×#12011yescharacteristic
550C22×C43C2×#12011yescharacteristic
551C22×C43C2×C22⋊Q811yescharacteristic
552C22×C43C2×C22⋊Q811yescharacteristic
553C22×C43C2×C22⋊Q811yescharacteristic
554C22×C43#52511yescharacteristic
555C22×C43#52511yescharacteristic
556C22×C43#52511yescharacteristic
557C22×C43#52511yescharacteristic
558C22×C43#52511yescharacteristic
559C22×C43#53211yescharacteristic
560C22×C43#53211yescharacteristic
561C22×C43#53211yescharacteristic
562C22×C43#53411yescharacteristic
563C22×C43#53611yescharacteristic
564C22×C43#53911yescharacteristic
565C22×C43#53911yescharacteristic
566C22×C43#54211yescharacteristic
567C22×C43#54211yescharacteristic
568C22×C43D4211yescharacteristic
569C22×C43D4211yescharacteristic
570C22×C43D4211yescharacteristic
571C22×C43D4211yescharacteristic
572C22×C43#54711yescharacteristic
573C22×C43#54711yescharacteristic
574C22×C43#54811yescharacteristic
575C22×C43#54811yescharacteristic
576C22×C43#54811yescharacteristic
577C22×C43#54811yescharacteristic
578C22×C43D4×Q811yescharacteristic
579C22×C43D4×Q811yescharacteristic
580C22×C43#55111yescharacteristic
581C22×C43#55111yescharacteristic
582C22×C43#55411yescharacteristic
583C22×C43#55411yescharacteristic
584C4×C43—24no—
585C4×C43—42no—
586C4×C43—42no—
587C4×C43—42no—
588C4×C43—81no—
589Dic43—24no—
590Dic43—24no—
591Dic43—42no—
592Dic43—42no—
593Dic43—42no—
594Dic43—42no—
595Dic43—42no—
596Dic43—81no—
597C22×C22⋊Q8—431no—
598C22×C4×D4—431no—
599C2×#395—431no—
600C2×#393—431no—
601C2×#385—431no—
602C2×#385—431no—
603#1441—431no—
604#1439—431no—
605#1439—431no—
606#1439—431no—
607#1438—431no—
608#1438D4311yescharacteristic
609#1436—431no—
610#1436—431no—
611C22⋊#95—431no—
612C2×C43—44no—
613C2×C43—44no—
614C2×C43#238811yescharacteristic
615C2×C43#240311yescharacteristic
616C2×C43#240911yescharacteristic
617C2×C43#243211yescharacteristic
618C2×C43#244911yescharacteristic
619C2×C43#244911yescharacteristic
620C2×C43#245211yescharacteristic
621C2×C43#245211yescharacteristic
622C2×C43#246111yescharacteristic
623C2×C43#246111yescharacteristic
624C2×C43#246311yescharacteristic
625C2×C43#246311yescharacteristic
626C2×C43#256411yescharacteristic
627C2×C43#263811yescharacteristic
628C2×C43#284811yescharacteristic
629C23×Q8—431no—
630C23×D4C2×D4311yescharacteristic
631C24×C4—431no—
632C24×C4—431no—
633C2×C22⋊Q8—864no—
634C2×C22⋊Q8—864no—
635C2×C22⋊Q8—864no—
636C2×C4×D4—864no—
637C2×C4×D4—864no—
638C2×C4×D4—864no—
639C22×C4⋊C4—431no—
640C22×C4⋊C4—431no—
641C22×C4⋊C4—431no—
642C22×C4⋊C4—431no—
643C22×C4⋊C4—431no—
644C22×C4⋊C4—431no—
645C22×C22⋊C4—431no—
646C22×C22⋊C4—431no—
647C22×C22⋊C4—431no—
648C22×C22⋊C4—431no—
649C22×C22⋊C4—431no—
650C22×C22⋊C4—431no—
651C22×C22⋊C4C2×D4311yescharacteristic
652C22×C22⋊C4C2×D4311yescharacteristic
653C22×C22⋊C4C2×D4311yescharacteristic
654C22×C22⋊C4C2×D4311yescharacteristic
655C22×C42—431no—
656#395—864no—
657#393—864no—
658#385—864no—
659#385—864no—
660C2×#95—431no—
661C2×#95—431no—
662C2×#95—431no—
663C2×#95—431no—
664C2×#95—431no—
665C2×#95—431no—
666C2×#95—431no—
667C2×#95—431no—
668C2×#95—431no—
669C2×#95—431no—
670C2×#95—431no—
671C2×#95—431no—
672C2×#95C2×D4311yescharacteristic
673C2×#95C2×D4311yescharacteristic
674C43#1472311yescharacteristic, complemented, Sylow
675C25C22×D4311yescharacteristic
676C25C22×D4311yescharacteristic
677C22×Q8—862no—
678C22×Q8—862no—
679C22×Q8—862no—
680C22×Q8—862no—
681C22×Q8—862no—
682C22×Q8—1721no—
683C22×Q8—1721no—
684C22×D4—22no—
685C22×D4—22no—
686C22×D4—22no—
687C22×D4—22no—
688C22×D4—22no—
689C22×D4—22no—
690C22×D4Dic8614yescomplemented
691C23×C4—431no—
692C23×C4—431no—
693C23×C4—431no—
694C23×C4—431no—
695C23×C4—431no—
696C23×C4—431no—
697C23×C4—431no—
698C23×C4—434no—
699C23×C4—431no—
700C23×C4—862no—
701C23×C4—862no—
702C23×C4—862no—
703C23×C4—862no—
704C23×C4—862no—
705C23×C4—862no—
706C23×C4—862no—
707C23×C4—862no—
708C23×C4—862no—
709C23×C4—1721no—
710C23×C4—1721no—
711C23×C4—1721no—
712C23×C4—1721no—
713C23×C4C22×D4311yescharacteristic
714C23×C4C22×D4311yescharacteristic
715C23×C4C22×D4311yescharacteristic
716C23×C4C22×D4311yescharacteristic
717C23×C4C22×D4311yescharacteristic
718C22⋊Q8—8632no—
719C4×D4—8632no—
720C2×C4⋊C4—434no—
721C2×C4⋊C4—434no—
722C2×C4⋊C4—434no—
723C2×C4⋊C4—862no—
724C2×C4⋊C4—862no—
725C2×C4⋊C4—862no—
726C2×C4⋊C4—862no—
727C2×C4⋊C4—862no—
728C2×C4⋊C4—862no—
729C2×C4⋊C4—862no—
730C2×C4⋊C4—862no—
731C2×C4⋊C4—862no—
732C2×C4⋊C4—862no—
733C2×C4⋊C4—862no—
734C2×C4⋊C4—862no—
735C2×C4⋊C4—862no—
736C2×C4⋊C4—1721no—
737C2×C4⋊C4—1721no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—41no—
750C2×C22⋊C4—434no—
751C2×C22⋊C4—862no—
752C2×C22⋊C4—862no—
753C2×C22⋊C4—862no—
754C2×C22⋊C4—862no—
755C2×C22⋊C4—862no—
756C2×C22⋊C4—862no—
757C2×C22⋊C4—862no—
758C2×C22⋊C4—862no—
759C2×C22⋊C4—862no—
760C2×C22⋊C4—862no—
761C2×C22⋊C4—862no—
762C2×C22⋊C4—862no—
763C2×C22⋊C4—862no—
764C2×C22⋊C4—862no—
765C2×C22⋊C4—862no—
766C2×C22⋊C4—1721no—
767C2×C22⋊C4—1721no—
768C2×C42—862no—
769C2×C42—862no—
770C2×C42—862no—
771#95—22no—
772#95—22no—
773#95—862no—
774#95—862no—
775#95—862no—
776#95—862no—
777#95—862no—
778#95—862no—
779#95—862no—
780#95—862no—
781#95—862no—
782#95—862no—
783#95—862no—
784#95—862no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24C2×Dic8612yes—
810C24C2×Dic8612yes—
811C24D4×D4312yes—
812C24D4×D4312yes—
813C24#1062190012yes—
814C24#1062190012yes—
815C24C23×D4311yescharacteristic
816C2×Q8—868no—
817C2×Q8—1724no—
818C2×Q8—1724no—
819C2×Q8—1724no—
820C2×Q8—1724no—
821C2×Q8—1724no—
822C2×Q8—1724no—
823C2×D4—28no—
824C2×D4—28no—
825C2×D4—28no—
826C2×D4—28no—
827C2×D4—28no—
828C2×D4—28no—
829C2×D4—28no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—432no—
860C22×C4—432no—
861C22×C4—432no—
862C22×C4—432no—
863C22×C4—432no—
864C22×C4—432no—
865C22×C4—432no—
866C22×C4—432no—
867C22×C4—432no—
868C22×C4—432no—
869C22×C4—432no—
870C22×C4—868no—
871C22×C4—868no—
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—868no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—861no—
890C22×C4—861no—
891C22×C4—861no—
892C22×C4—861no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
897C22×C4—861no—
898C22×C4—861no—
899C22×C4—861no—
900C22×C4—861no—
901C22×C4—861no—
902C22×C4—861no—
903C22×C4—861no—
904C22×C4—861no—
905C22×C4—861no—
906C22×C4—861no—
907C22×C4—861no—
908C22×C4—861no—
909C22×C4—861no—
910C22×C4—861no—
911C22×C4—861no—
912C22×C4—861no—
913C22×C4—861no—
914C22×C4—861no—
915C22×C4—861no—
916C22×C4—861no—
917C22×C4—861no—
918C22×C4—1724no—
919C22×C4—1724no—
920C22×C4—1724no—
921C22×C4—1724no—
922C22×C4—1724no—
923C22×C4—1724no—
924C22×C4—1724no—
925C22×C4—1724no—
926C22×C4—1724no—
927C22×C4—1724no—
928C22×C4—1724no—
929C22×C4C2×Dic8612yes—
930C22×C4D4×D4312yes—
931C22×C4D4×D4312yes—
932C22×C4D4×D4312yes—
933C22×C4#1062190012yes—
934C22×C4#1062190012yes—
935C4⋊C4—868no—
936C4⋊C4—868no—
937C4⋊C4—868no—
938C4⋊C4—868no—
939C4⋊C4—1724no—
940C4⋊C4—1724no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—868no—
946C22⋊C4—868no—
947C22⋊C4—868no—
948C22⋊C4—868no—
949C22⋊C4—1724no—
950C22⋊C4—1724no—
951C42—868no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23#1306330214yes—
1021C23#1306330214yescomplemented
1022C23C2×D4×D4311yescharacteristic
1023C23C2×D4×D4311yescharacteristic
1024C23C2×D4×D4311yescharacteristic
1025C23C2×D4×D4311yescharacteristic
1026C23C2×D4×D4311yescharacteristic
1027C23C22×Dic8611yescharacteristic
1028C23#41×D4311yescharacteristic
1029C23C2×#1062190011yescharacteristic
1030C23C2×#1062190011yescharacteristic
1031C23C2×#1062190011yescharacteristic
1032C23C2×#1062190011yescharacteristic
1033C23#1306337011yescharacteristic
1034C23#1306337111yescharacteristic
1035C23#1306337211yescharacteristic
1036C23#1306337211yescharacteristic
1037Q8—17216no—
1038D4—232no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—434no—
1074C2×C4—434no—
1075C2×C4—862no—
1076C2×C4—862no—
1077C2×C4—862no—
1078C2×C4—862no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—862no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—862no—
1090C2×C4—862no—
1091C2×C4—862no—
1092C2×C4—862no—
1093C2×C4—862no—
1094C2×C4—862no—
1095C2×C4—862no—
1096C2×C4—862no—
1097C2×C4—862no—
1098C2×C4—862no—
1099C2×C4—862no—
1100C2×C4—862no—
1101C2×C4—862no—
1102C2×C4—17216no—
1103C2×C4—17216no—
1104C2×C4—1721no—
1105C2×C4—1721no—
1106C2×C4—1721no—
1107C2×C4—1721no—
1108C2×C4—1721no—
1109C2×C4—1721no—
1110C2×C4—1721no—
1111C2×C4—1721no—
1112C2×C4—1721no—
1113C2×C4—1721no—
1114C2×C4—1721no—
1115C2×C4—1721no—
1116C2×C4—1721no—
1117C2×C4—1721no—
1118C2×C4—1721no—
1119C2×C4—1721no—
1120C2×C4—1721no—
1121C2×C4—1721no—
1122C2×C4—1721no—
1123C2×C4—1721no—
1124C2×C4—1721no—
1125C2×C4—1721no—
1126C2×C4—1721no—
1127C2×C4—1721no—
1128C2×C4—1721no—
1129C2×C4—1721no—
1130C2×C4—1721no—
1131C2×C4#1306330214yescomplemented
1132C22—24no—
1133C22—24no—
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—24no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22#120×D4311yescharacteristic
1163C22#120×D4311yescharacteristic
1164C22C2×#1306330211yescharacteristic
1165C22C2×#1306330211yescharacteristic
1166C22C2×#1306330211yescharacteristic
1167C22#1458340511yescharacteristic
1168C22#1458340511yescharacteristic
1169C22#1458340511yescharacteristic
1170C22#1458340511yescharacteristic
1171C22#1458340911yescharacteristic
1172C22#1458344411yescharacteristic
1173C22#1458344411yescharacteristic
1174C22#1458344711yescharacteristic
1175C22#1458345711yescharacteristic
1176C22#1458347111yescharacteristic
1177C22#1458349311yescharacteristic
1178C22#1458349411yescharacteristic
1179C22#1458351611yescharacteristic
1180C22#1458351811yescharacteristic
1181C22#1458353111yescharacteristic
1182C22#1458353311yescharacteristic
1183C22#1458353311yescharacteristic
1184C22#1458353411yescharacteristic
1185C22#1458354711yescharacteristic
1186C22#1458354911yescharacteristic
1187C22#1458355511yescharacteristic
1188C22#1458355511yescharacteristic
1189C22#1458355511yescharacteristic
1190C22#1458355711yescharacteristic
1191C22D4×Dic8611yescharacteristic
1192C22D4×Dic8611yescharacteristic
1193C22#1458357211yescharacteristic
1194C22#1458358011yescharacteristic
1195C22#1458360611yescharacteristic
1196C22#1458360811yescharacteristic
1197C4—24no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—81no—
1202C4—864no—
1203C4—864no—
1204C4—3441no—
1205C4—1722no—
1206C4—1722no—
1207C4—1722no—
1208C4—1722no—
1209C4—1722no—
1210C2—44no—
1211C2—44no—
1212C2#1913780711yescharacteristic
1213C2#1913790411yescharacteristic
1214C2#1913795711yescharacteristic
1215C2#1913821811yescharacteristic
1216C2#1913840811yescharacteristic
1217C2#1913841011yescharacteristic
1218C2#1913844711yescharacteristic
1219C2#1913844811yescharacteristic
1220C2#1913855511yescharacteristic
1221C2#1913855711yescharacteristic
1222C2#1913858511yescharacteristic
1223C2#1913858711yescharacteristic
1224C2#1913977911yescharacteristic
1225C2#1914051111yescharacteristic
1226C2#1914288011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC43×#1438C2
prime radicalC23×D4×C43C22
hypercenter#1438D43
hypocenterC43#14723
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×#13063302C2semidirect
3. C2×#14582820C2semidirect
4. C2×#14582811C2semidirect
5. C2×#14582774C2semidirect
6. C2×#14582771C2semidirect
7. #19132847C2semidirect
8. #19132840C2semidirect
9. #19132838C2semidirect
10. #19132838C2semidirect
12. #19132829C2semidirect
13. #19132826C2semidirect
14. #19132817C2semidirect
100. C2×C4⋊Dic43D4semidirect
109. C2×Dic43⋊C4D4semidirect
151. C22×D4×C43Q8semidirect
407. C23×C43C22⋊Q8semidirect
458. C2×C4×C43C22⋊Q8semidirect
674. C43#14723semidirect
690. C22×D4Dic86semidirect
1021. C23#13063302semidirect
1131. C2×C4#13063302semidirect

Maximal subgroups

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

subgroupindex
C22×#130633022
C22×D4×Dic432
C2×#145828202
C2×#145828112
C2×#145827742
C2×#145827712
#191328472
#191328402
#191328382
#191328362
#191328292
#191328262
#191328172
C43×#14382
#1472343