Finite Group Databasebeta

← #25021932

Subgroups — #25021932

Order 11008.

2854 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic, complemented
2C2×#14582807C211yesmaximal, characteristic
3C2×#14582779C211yesmaximal, characteristic, complemented
4C2×#14582776C211yesmaximal, characteristic, complemented
5C2×#14582775C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
7#19132850C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic, complemented
9#19132834C211yesmaximal, characteristic, complemented
10#19132832C211yesmaximal, characteristic, complemented
11#19132831C211yesmaximal, characteristic, complemented
12#19132821C211yesmaximal, characteristic, complemented
13#19132818C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×C4×C22⋊D43—24no—
21C2×C4×C22⋊D43—24no—
22C2×C4×C22⋊D43—24no—
23C22×Dic43⋊C4C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582807C418yescomplemented
36#14582779—24no—
37#14582776—24no—
38#14582775—24no—
39C22⋊C4×Dic43—24no—
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
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C23×D4×C43C2211yescharacteristic
53C24×C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C43×#386—24no—
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43—22no—
66C22×C22⋊D43—22no—
67C22×C22⋊D43—22no—
68C22×C22⋊D43—22no—
69C22×C22⋊D43—22no—
70C22×C22⋊D43—22no—
71C22×C22⋊D43—41no—
72C22×C22⋊D43—41no—
73C22×C22⋊D43C2×C414yescomplemented
74C22×C22⋊D43C2×C414yescomplemented
75C23×Dic43—22no—
76C23×Dic43—22no—
77C23×Dic43—22no—
78C23×Dic43—22no—
79C23×Dic43—22no—
80C23×Dic43—41no—
81C23×Dic43—41no—
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C22×C4×D43—22no—
90C22×C4×D43—22no—
91C22×C4×D43—22no—
92C22×C4×D43—22no—
93C22×C4×D43—22no—
94C22×C4×D43—41no—
95C22×C4×D43—41no—
96C4×C22⋊D43—232no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—22no—
102C2×C22⋊Dic43—22no—
103C2×C22⋊Dic43—22no—
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—41no—
109C2×C22⋊Dic43—41no—
110C2×C22⋊Dic43—41no—
111C2×C22⋊Dic43—41no—
112C2×C22⋊Dic43C2×C414yescomplemented
113C2×C22⋊Dic43C2×C414yescomplemented
114C2×C22⋊Dic43D414yescomplemented
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—22no—
118C2×(C2×D43)⋊C4—22no—
119C2×(C2×D43)⋊C4—22no—
120C2×(C2×D43)⋊C4—22no—
121C2×(C2×D43)⋊C4—41no—
122C2×(C2×D43)⋊C4—41no—
123C2×(C2×D43)⋊C4—41no—
124C2×(C2×D43)⋊C4—41no—
125C2×(C2×D43)⋊C4C2×C414yescomplemented
126C2×(C2×D43)⋊C4D414yescomplemented
127C2×C4×Dic43—22no—
128C2×C4×Dic43—22no—
129C2×C4×Dic43—22no—
130C2×C4×Dic43—41no—
131C2×C4×Dic43—41no—
132C2×C4×Dic43D414yescomplemented
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—41no—
143C43⋊#95—41no—
144C43⋊#95C2×C414yescomplemented
145C25×C43C2311yescharacteristic
146C25×C43C2311yescharacteristic
147C22×D4×C43—22no—
148C22×D4×C43—22no—
149C22×D4×C43—22no—
150C22×D4×C43—22no—
151C22×D4×C43—41no—
152C22×D4×C43—41no—
153C22×D4×C43C2×C414yescomplemented
154C23×C4×C43—22no—
155C23×C4×C43—22no—
156C23×C4×C43—22no—
157C23×C4×C43—22no—
158C23×C4×C43—22no—
159C23×C4×C43—41no—
160C23×C4×C43—41no—
161C23×C4×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C23×C4×C43C2311yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C2×C22⋊C4×C43—22no—
167C2×C22⋊C4×C43—22no—
168C2×C22⋊C4×C43—22no—
169C2×C22⋊C4×C43—22no—
170C2×C22⋊C4×C43—22no—
171C2×C22⋊C4×C43—22no—
172C2×C22⋊C4×C43—41no—
173C2×C22⋊C4×C43—41no—
174C2×C22⋊C4×C43D414yescomplemented
175#95×C43—22no—
176#95×C43—22no—
177C24×C43—21no—
178C24×C43—21no—
179C24×C43—21no—
180C24×C43—21no—
181C24×C43—21no—
182C24×C43—21no—
183C24×C43—21no—
184C24×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43—21no—
191C24×C43—21no—
192C24×C43—21no—
193C24×C43—21no—
194C24×C43—21no—
195C24×C43—21no—
196C24×C43—21no—
197C24×C43—21no—
198C24×C43—21no—
199C24×C43—21no—
200C24×C43—21no—
201C24×C43C22×C412yes—
202C24×C43C22×C412yes—
203C24×C43C2×D412yes—
204C24×C43C2×D412yes—
205C24×C43#4112yes—
206C24×C43#4112yes—
207C24×C43C2411yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C23×D43—21no—
211C23×D43—21no—
212C23×D43—21no—
213C23×D43—21no—
214C23×D43—21no—
215C23×D43—21no—
216C23×D43—21no—
217C23×D43—21no—
218C23×D43—21no—
219C23×D43—21no—
220C23×D43C22×C412yes—
221C23×D43C2×D412yes—
222C23×D43#4112yes—
223C2×D4×C43—28no—
224C2×D4×C43—28no—
225C2×D4×C43—44no—
226C2×D4×C43—44no—
227C2×D4×C43—44no—
228C2×D4×C43—44no—
229C2×D4×C43—44no—
230C22×C4×C43—28no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—44no—
261C22×C4×C43—44no—
262C22×C4×C43—44no—
263C22×C4×C43—44no—
264C22×C4×C43—44no—
265C22×C4×C43—44no—
266C22×C4×C43C22×C412yes—
267C22×C4×C43C2×D412yes—
268C22×C4×C43C2×D412yes—
269C22×C4×C43C2×D412yes—
270C22×C4×C43C2×D412yes—
271C22×C4×C43#4112yes—
272C2×C22⋊D43—28no—
273C2×C22⋊D43—28no—
274C2×C22⋊D43—28no—
275C2×C22⋊D43—28no—
276C2×C22⋊D43—28no—
277C2×C22⋊D43—28no—
278C2×C22⋊D43—28no—
279C2×C22⋊D43—28no—
280C2×C22⋊D43—28no—
281C2×C22⋊D43—44no—
282C2×C22⋊D43—44no—
283C2×C22⋊D43—44no—
284C2×C22⋊D43—44no—
285C2×C22⋊D43—44no—
286C22×Dic43—28no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—21no—
294C22×Dic43—21no—
295C22×Dic43—21no—
296C22×Dic43—21no—
297C22×Dic43—21no—
298C22×Dic43—21no—
299C22×Dic43—21no—
300C22×Dic43—21no—
301C22×Dic43—21no—
302C22×Dic43—21no—
303C22×Dic43—21no—
304C22×Dic43—21no—
305C22×Dic43—21no—
306C22×Dic43—21no—
307C22×Dic43—21no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43—21no—
312C22×Dic43—21no—
313C22×Dic43—21no—
314C22×Dic43—21no—
315C22×Dic43—21no—
316C22×Dic43—21no—
317C22×Dic43—21no—
318C22×Dic43—21no—
319C22×Dic43—21no—
320C22×Dic43—21no—
321C22×Dic43—21no—
322C22×Dic43—21no—
323C22×Dic43—21no—
324C22×Dic43—21no—
325C22×Dic43—21no—
326C22×Dic43—44no—
327C22×Dic43—44no—
328C22×Dic43—44no—
329C22×Dic43—44no—
330C22×Dic43—44no—
331C22×Dic43—44no—
332C22×Dic43C22×C412yes—
333C22×Dic43C22×C412yes—
334C22×Dic43C22×C412yes—
335C22×Dic43C2×D412yes—
336C22×Dic43C2×D412yes—
337C22×Dic43C2×D412yes—
338C22×Dic43C2×D412yes—
339C22×Dic43C2×D412yes—
340C22×Dic43#4112yes—
341C22×Dic43#4112yes—
342C2×C4×D43—28no—
343C2×C4×D43—44no—
344C2×C4×D43—44no—
345C2×C4×D43—44no—
346C2×C4×D43—44no—
347C2×C4×D43—44no—
348C2×C4×D43—44no—
349C22⋊C4×C43—28no—
350C22⋊C4×C43—44no—
351C22⋊C4×C43—44no—
352C22⋊Dic43—28no—
353C22⋊Dic43—28no—
354C22⋊Dic43—44no—
355C22⋊Dic43—44no—
356C22⋊Dic43—44no—
357(C2×D43)⋊C4—28no—
358(C2×D43)⋊C4—44no—
359(C2×D43)⋊C4—44no—
360(C2×D43)⋊C4—44no—
361Dic43⋊C4—28no—
362C4×Dic43—28no—
363C4×Dic43—44no—
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—22no—
375C23×C43—22no—
376C23×C43—22no—
377C23×C43—22no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—22no—
393C23×C43—22no—
394C23×C43—22no—
395C23×C43—22no—
396C23×C43—22no—
397C23×C43—22no—
398C23×C43—22no—
399C23×C43—22no—
400C23×C43—41no—
401C23×C43—41no—
402C23×C43—41no—
403C23×C43—41no—
404C23×C43—41no—
405C23×C43—41no—
406C23×C43—41no—
407C23×C43—41no—
408C23×C43—41no—
409C23×C43—41no—
410C23×C43—41no—
411C23×C43—41no—
412C23×C43—41no—
413C23×C43—41no—
414C23×C43—41no—
415C23×C43—41no—
416C23×C43—41no—
417C23×C43—41no—
418C23×C43—41no—
419C23×C43—41no—
420C23×C43—41no—
421C23×C43—41no—
422C23×C43—41no—
423C23×C43—41no—
424C23×C43—41no—
425C23×C43—41no—
426C23×C43—41no—
427C23×C43—41no—
428C23×C43—41no—
429C23×C43—41no—
430C23×C43—41no—
431C23×C43—41no—
432C23×C43C4×D414yes—
433C23×C43C4×D414yescomplemented
434C23×C43C23×C411yescharacteristic
435C23×C43C22×D411yescharacteristic
436C23×C43C22×D411yescharacteristic
437C23×C43C22×D411yescharacteristic
438C23×C43C22×D411yescharacteristic
439C23×C43C2×#4111yescharacteristic
440C23×C43C2×#4111yescharacteristic
441C23×C43C2×#4111yescharacteristic
442C23×C43C2×#4111yescharacteristic
443C23×C43C2×#4111yescharacteristic
444C23×C43C2×#4111yescharacteristic
445C23×C43H(5,𝔽2)11yescharacteristic
446C23×C43H(5,𝔽2)11yescharacteristic
447C23×C43H(5,𝔽2)11yescharacteristic
448C23×C43H(5,𝔽2)11yescharacteristic
449C22×D43—22no—
450C22×D43—22no—
451C22×D43—22no—
452C22×D43—22no—
453C22×D43—22no—
454C22×D43—22no—
455C22×D43—22no—
456C22×D43—22no—
457C22×D43—22no—
458C22×D43—22no—
459C22×D43—22no—
460C22×D43—22no—
461C22×D43—22no—
462C22×D43—22no—
463C22×D43—22no—
464C22×D43—22no—
465C22×D43—22no—
466C22×D43—22no—
467C22×D43—41no—
468C22×D43—41no—
469C22×D43—41no—
470C22×D43—41no—
471C22×D43—41no—
472C22×D43—41no—
473C22×D43—41no—
474C22×D43—41no—
475C22×D43—41no—
476C22×D43—41no—
477C22×D43—41no—
478C22×D43—41no—
479C22×D43—41no—
480C22×D43—41no—
481C22×D43—41no—
482C22×D43—41no—
483C22×D43C4×D414yes—
484D4×C43—416no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—22no—
491C2×C4×C43—22no—
492C2×C4×C43—22no—
493C2×C4×C43—22no—
494C2×C4×C43—22no—
495C2×C4×C43—22no—
496C2×C4×C43—22no—
497C2×C4×C43—22no—
498C2×C4×C43—22no—
499C2×C4×C43—22no—
500C2×C4×C43—416no—
501C2×C4×C43—41no—
502C2×C4×C43—41no—
503C2×C4×C43—41no—
504C2×C4×C43—41no—
505C2×C4×C43—41no—
506C2×C4×C43—41no—
507C2×C4×C43—41no—
508C2×C4×C43—41no—
509C2×C4×C43—41no—
510C2×C4×C43—41no—
511C2×C4×C43—41no—
512C2×C4×C43—41no—
513C2×C4×C43—41no—
514C2×C4×C43—41no—
515C2×C4×C43—41no—
516C2×C4×C43—41no—
517C2×C4×C43—41no—
518C2×C4×C43—41no—
519C2×C4×C43—41no—
520C2×C4×C43#12114yes—
521C22⋊D43—232no—
522C22⋊D43—416no—
523C2×Dic43—22no—
524C2×Dic43—22no—
525C2×Dic43—22no—
526C2×Dic43—22no—
527C2×Dic43—22no—
528C2×Dic43—22no—
529C2×Dic43—22no—
530C2×Dic43—22no—
531C2×Dic43—22no—
532C2×Dic43—22no—
533C2×Dic43—22no—
534C2×Dic43—22no—
535C2×Dic43—22no—
536C2×Dic43—22no—
537C2×Dic43—22no—
538C2×Dic43—22no—
539C2×Dic43—22no—
540C2×Dic43—22no—
541C2×Dic43—22no—
542C2×Dic43—22no—
543C2×Dic43—22no—
544C2×Dic43—22no—
545C2×Dic43—22no—
546C2×Dic43—22no—
547C2×Dic43—416no—
548C2×Dic43—41no—
549C2×Dic43—41no—
550C2×Dic43—41no—
551C2×Dic43—41no—
552C2×Dic43—41no—
553C2×Dic43—41no—
554C2×Dic43—41no—
555C2×Dic43—41no—
556C2×Dic43—41no—
557C2×Dic43—41no—
558C2×Dic43—41no—
559C2×Dic43—41no—
560C2×Dic43—41no—
561C2×Dic43—41no—
562C2×Dic43—41no—
563C2×Dic43—41no—
564C2×Dic43—41no—
565C2×Dic43—41no—
566C2×Dic43—41no—
567C2×Dic43—41no—
568C2×Dic43—41no—
569C2×Dic43—41no—
570C2×Dic43—41no—
571C2×Dic43C4×D414yes—
572C2×Dic43#12014yes—
573C4×D43—416no—
574#14175—431nomaximal, Sylow
575C22×C43—24no—
576C22×C43—24no—
577C22×C43—24no—
578C22×C43—24no—
579C22×C43—24no—
580C22×C43—24no—
581C22×C43—42no—
582C22×C43—42no—
583C22×C43—42no—
584C22×C43—42no—
585C22×C43—42no—
586C22×C43—42no—
587C22×C43—42no—
588C22×C43—42no—
589C22×C43—42no—
590C22×C43—42no—
591C22×C43—42no—
592C22×C43—42no—
593C22×C43—42no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—42no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43—42no—
600C22×C43—42no—
601C22×C43—42no—
602C22×C43—42no—
603C22×C43—42no—
604C22×C43—42no—
605C22×C43C2×C4×D411yescharacteristic
606C22×C43C2×C4×D411yescharacteristic
607C22×C43C2×C4×D411yescharacteristic
608C22×C43C2×C4×D411yescharacteristic
609C22×C43C4×#4111yescharacteristic
610C22×C43#51811yescharacteristic
611C22×C43#51811yescharacteristic
612C22×C43C2×#12011yescharacteristic
613C22×C43C2×#12111yescharacteristic
614C22×C43#52511yescharacteristic
615C22×C43#52511yescharacteristic
616C22×C43#52511yescharacteristic
617C22×C43#52511yescharacteristic
618C22×C43#52911yescharacteristic
619C22×C43#53211yescharacteristic
620C22×C43#53511yescharacteristic
621C22×C43#53511yescharacteristic
622C22×C43#54011yescharacteristic
623C22×C43#54011yescharacteristic
624C22×C43D4211yescharacteristic
625C22×C43D4211yescharacteristic
626C22×C43#54611yescharacteristic
627C22×C43#54611yescharacteristic
628C22×C43#54611yescharacteristic
629C22×C43#54611yescharacteristic
630C22×C43#54611yescharacteristic
631C22×C43#54611yescharacteristic
632C22×C43#54611yescharacteristic
633C22×C43#54611yescharacteristic
634C22×C43#55111yescharacteristic
635C22×C43#55111yescharacteristic
636C22×C43#55311yescharacteristic
637C22×C43#55311yescharacteristic
638C22×C43#55311yescharacteristic
639C22×C43#55311yescharacteristic
640C2×D43—24no—
641C2×D43—24no—
642C2×D43—24no—
643C2×D43—42no—
644C2×D43—42no—
645C2×D43—42no—
646C2×D43—42no—
647C2×D43—42no—
648C2×D43—42no—
649C2×D43—42no—
650C2×D43—42no—
651C2×D43—42no—
652C2×D43—42no—
653C2×D43—42no—
654C2×D43—42no—
655C4×C43—24no—
656C4×C43—42no—
657C4×C43—42no—
658C4×C43—42no—
659C4×C43—81no—
660Dic43—24no—
661Dic43—24no—
662Dic43—42no—
663Dic43—42no—
664Dic43—42no—
665Dic43—42no—
666Dic43—81no—
667C22×C4×D4—431no—
668C2×#392—431no—
669C2×#386—431no—
670C2×#386—431no—
671C2×#386—431no—
672C2×#386D4311yescharacteristic, complemented
673C2×C4×C22⋊C4—431no—
674#1442—431no—
675#1439—431no—
676#1438—431no—
677#1437—431no—
678#1437—431no—
679#1434—431no—
680C22⋊#95—431no—
681C22⋊#95—431no—
682C2×C43—44no—
683C2×C43—44no—
684C2×C43C4×#12011yescharacteristic
685C2×C43C4×#12111yescharacteristic
686C2×C43#232811yescharacteristic
687C2×C43#235811yescharacteristic
688C2×C43#235811yescharacteristic
689C2×C43#236411yescharacteristic
690C2×C43#236411yescharacteristic
691C2×C43#240411yescharacteristic
692C2×C43#240811yescharacteristic
693C2×C43#245711yescharacteristic
694C2×C43#245711yescharacteristic
695C2×C43#246411yescharacteristic
696C2×C43#246411yescharacteristic
697C2×C43#253511yescharacteristic
698C2×C43#259811yescharacteristic
699D43—44no—
700C23×D4—431no—
701C23×D4—431no—
702C23×D4C2×D4311yescharacteristic
703C24×C4—431no—
704C24×C4—431no—
705C24×C4C2×D4311yescharacteristic
706C2×C4×D4—864no—
707C2×C4×D4—864no—
708C2×C4×D4—864no—
709C22×C4⋊C4—431no—
710C22×C22⋊C4—431no—
711C22×C22⋊C4—431no—
712C22×C22⋊C4—431no—
713C22×C22⋊C4—431no—
714C22×C22⋊C4—431no—
715C22×C22⋊C4—431no—
716C22×C22⋊C4—431no—
717C22×C22⋊C4—431no—
718C22×C22⋊C4—431no—
719C22×C22⋊C4C2×D4311yescharacteristic
720C22×C22⋊C4C2×D4311yescharacteristic
721C22×C22⋊C4C2×D4311yescharacteristic
722C22×C42—431no—
723C22×C42—431no—
724#392—438no—
725#386—24no—
726#386—864no—
727#386—864no—
728#386—864no—
729C4×C22⋊C4—864no—
730C2×#95—431no—
731C2×#95—431no—
732C2×#95—431no—
733C2×#95—431no—
734C2×#95—431no—
735C2×#95—431no—
736C2×#95—431no—
737C2×#95—431no—
738C2×#95—431no—
739C2×#95—431no—
740C2×#95—431no—
741C2×#95—431no—
742C2×#95C2×D4311yescharacteristic
743C2×#95C2×D4311yescharacteristic
744C43#1417511yescharacteristic, complemented, Sylow
745C25—431no—
746C25C22×D4311yescharacteristic
747C25C22×D4311yescharacteristic
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—434no—
755C22×D4—434no—
756C22×D4—862no—
757C22×D4—862no—
758C22×D4—862no—
759C22×D4—862no—
760C22×D4—862no—
761C22×D4—862no—
762C22×D4—862no—
763C22×D4—862no—
764C22×D4—862no—
765C22×D4—862no—
766C22×D4—1721no—
767C22×D4—1721no—
768C22×D4C4×D4314yescomplemented
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—41no—
775C23×C4—41no—
776C23×C4—431no—
777C23×C4—431no—
778C23×C4—431no—
779C23×C4—431no—
780C23×C4—431no—
781C23×C4—431no—
782C23×C4—431no—
783C23×C4—862no—
784C23×C4—862no—
785C23×C4—862no—
786C23×C4—862no—
787C23×C4—862no—
788C23×C4—862no—
789C23×C4—862no—
790C23×C4—862no—
791C23×C4—862no—
792C23×C4—862no—
793C23×C4—1721no—
794C23×C4—1721no—
795C23×C4—1721no—
796C23×C4—1721no—
797C23×C4C22×D4311yescharacteristic
798C23×C4C22×D4311yescharacteristic
799C23×C4C22×D4311yescharacteristic
800C23×C4C22×D4311yescharacteristic
801C23×C4C22×D4311yescharacteristic
802C4×D4—8632no—
803C2×C4⋊C4—862no—
804C2×C4⋊C4—862no—
805C2×C4⋊C4—862no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—434no—
815C2×C22⋊C4—434no—
816C2×C22⋊C4—434no—
817C2×C22⋊C4—434no—
818C2×C22⋊C4—434no—
819C2×C22⋊C4—862no—
820C2×C22⋊C4—862no—
821C2×C22⋊C4—862no—
822C2×C22⋊C4—862no—
823C2×C22⋊C4—862no—
824C2×C22⋊C4—862no—
825C2×C22⋊C4—862no—
826C2×C22⋊C4—862no—
827C2×C22⋊C4—862no—
828C2×C22⋊C4—862no—
829C2×C22⋊C4—862no—
830C2×C22⋊C4—862no—
831C2×C22⋊C4—862no—
832C2×C22⋊C4—862no—
833C2×C22⋊C4—1721no—
834C2×C22⋊C4—1721no—
835C2×C22⋊C4—1721no—
836C2×C22⋊C4—1721no—
837C2×C22⋊C4—1721no—
838C2×C22⋊C4—1721no—
839C2×C22⋊C4—1721no—
840C2×C22⋊C4—1721no—
841C2×C22⋊C4C22⋊D4314yescomplemented
842C2×C42—434no—
843C2×C42—862no—
844C2×C42—862no—
845C2×C42—862no—
846C2×C42—1721no—
847C2×C42—1721no—
848#95—22no—
849#95—22no—
850#95—434no—
851#95—862no—
852#95—862no—
853#95—862no—
854#95—862no—
855#95—862no—
856#95—862no—
857#95—862no—
858#95—862no—
859#95—862no—
860#95—1721no—
861#95—1721no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—432no—
887C24—432no—
888C24—432no—
889C24—861no—
890C24—861no—
891C24—861no—
892C24—861no—
893C24—861no—
894C24—861no—
895C24—861no—
896C24—861no—
897C24—861no—
898C24—861no—
899C24—861no—
900C24—861no—
901C24C2×C4×D4312yes—
902C24C2×C4×D4312yes—
903C24#1062189812yes—
904C24D4×D4312yes—
905C24#1062190012yes—
906C24C2×C22⋊D4312yes—
907C24C23×D4311yescharacteristic
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—868no—
916C2×D4—868no—
917C2×D4—868no—
918C2×D4—868no—
919C2×D4—868no—
920C2×D4—868no—
921C2×D4—868no—
922C2×D4—868no—
923C2×D4—868no—
924C2×D4—1724no—
925C2×D4—1724no—
926C2×D4—1724no—
927C2×D4—1724no—
928C2×D4—1724no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—28no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—432no—
966C22×C4—432no—
967C22×C4—432no—
968C22×C4—432no—
969C22×C4—432no—
970C22×C4—432no—
971C22×C4—432no—
972C22×C4—432no—
973C22×C4—432no—
974C22×C4—432no—
975C22×C4—868no—
976C22×C4—861no—
977C22×C4—861no—
978C22×C4—861no—
979C22×C4—861no—
980C22×C4—861no—
981C22×C4—861no—
982C22×C4—861no—
983C22×C4—861no—
984C22×C4—868no—
985C22×C4—861no—
986C22×C4—861no—
987C22×C4—861no—
988C22×C4—861no—
989C22×C4—861no—
990C22×C4—861no—
991C22×C4—861no—
992C22×C4—861no—
993C22×C4—861no—
994C22×C4—861no—
995C22×C4—861no—
996C22×C4—861no—
997C22×C4—861no—
998C22×C4—861no—
999C22×C4—861no—
1000C22×C4—861no—
1001C22×C4—861no—
1002C22×C4—861no—
1003C22×C4—861no—
1004C22×C4—861no—
1005C22×C4—861no—
1006C22×C4—861no—
1007C22×C4—861no—
1008C22×C4—861no—
1009C22×C4—861no—
1010C22×C4—861no—
1011C22×C4—861no—
1012C22×C4—861no—
1013C22×C4—861no—
1014C22×C4—861no—
1015C22×C4—861no—
1016C22×C4—1724no—
1017C22×C4—1724no—
1018C22×C4—1724no—
1019C22×C4—1724no—
1020C22×C4—1724no—
1021C22×C4—1724no—
1022C22×C4—1724no—
1023C22×C4—1724no—
1024C22×C4—1724no—
1025C22×C4—1724no—
1026C22×C4—1724no—
1027C22×C4—1724no—
1028C22×C4C2×C4×D4312yes—
1029C22×C4D4×D4312yes—
1030C22×C4D4×D4312yes—
1031C22×C4#1062190012yes—
1032C22×C4C2×C22⋊D4312yes—
1033C22×C4C2×C22⋊D4312yes—
1034C4⋊C4—868no—
1035C22⋊C4—28no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—868no—
1039C22⋊C4—868no—
1040C22⋊C4—868no—
1041C22⋊C4—1724no—
1042C22⋊C4—1724no—
1043C22⋊C4—1724no—
1044C22⋊C4—1724no—
1045C22⋊C4—1724no—
1046C22⋊C4—1724no—
1047C42—868no—
1048C42—1724no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—434no—
1118C23—862no—
1119C23—862no—
1120C23—862no—
1121C23—862no—
1122C23—862no—
1123C23—862no—
1124C23—862no—
1125C23—862no—
1126C23—862no—
1127C23—862no—
1128C23—862no—
1129C23—862no—
1130C23—862no—
1131C23—862no—
1132C23—862no—
1133C23—862no—
1134C23—862no—
1135C23—862no—
1136C23—1721no—
1137C23—1721no—
1138C23—1721no—
1139C23—1721no—
1140C23—1721no—
1141C23—1721no—
1142C23—1721no—
1143C23—1721no—
1144C23—1721no—
1145C23—1721no—
1146C23—1721no—
1147C23—1721no—
1148C23—1721no—
1149C23—1721no—
1150C23—1721no—
1151C23—1721no—
1152C23(C22⋊D43)⋊C414yes—
1153C23C4×C22⋊D4314yescomplemented
1154C23C22×C4×D4311yescharacteristic
1155C23C2×D4×D4311yescharacteristic
1156C23C2×D4×D4311yescharacteristic
1157C23C2×D4×D4311yescharacteristic
1158C23C22×C22⋊D4311yescharacteristic
1159C23#41×D4311yescharacteristic
1160C23#41×D4311yescharacteristic
1161C23#41×D4311yescharacteristic
1162C23C2×#1062190011yescharacteristic
1163C23C2×#1062190011yescharacteristic
1164C23C2×#1062189811yescharacteristic
1165C23#1306337011yescharacteristic
1166C23#1306337011yescharacteristic
1167C23#1306337011yescharacteristic
1168C23#1306337111yescharacteristic
1169D4—416no—
1170D4—8632no—
1171D4—17216no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—416no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—434no—
1208C2×C4—434no—
1209C2×C4—862no—
1210C2×C4—862no—
1211C2×C4—862no—
1212C2×C4—862no—
1213C2×C4—862no—
1214C2×C4—862no—
1215C2×C4—862no—
1216C2×C4—862no—
1217C2×C4—862no—
1218C2×C4—862no—
1219C2×C4—862no—
1220C2×C4—862no—
1221C2×C4—862no—
1222C2×C4—862no—
1223C2×C4—862no—
1224C2×C4—862no—
1225C2×C4—862no—
1226C2×C4—862no—
1227C2×C4—862no—
1228C2×C4—862no—
1229C2×C4—862no—
1230C2×C4—862no—
1231C2×C4—862no—
1232C2×C4—862no—
1233C2×C4—17216no—
1234C2×C4—17216no—
1235C2×C4—1721no—
1236C2×C4—1721no—
1237C2×C4—1721no—
1238C2×C4—1721no—
1239C2×C4—1721no—
1240C2×C4—1721no—
1241C2×C4—1721no—
1242C2×C4—1721no—
1243C2×C4—1721no—
1244C2×C4—1721no—
1245C2×C4—1721no—
1246C2×C4—1721no—
1247C2×C4—1721no—
1248C2×C4—1721no—
1249C2×C4—1721no—
1250C2×C4—1721no—
1251C2×C4—1721no—
1252C2×C4—1721no—
1253C2×C4—1721no—
1254C2×C4—1721no—
1255C2×C4—1721no—
1256C2×C4—1721no—
1257C2×C4—1721no—
1258C2×C4#1306329714yes—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—24no—
1264C22—24no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—864no—
1290C22—864no—
1291C22—864no—
1292C22—1722no—
1293C22—1722no—
1294C22—1722no—
1295C22—1722no—
1296C22—1722no—
1297C22—1722no—
1298C22—1722no—
1299C22—1722no—
1300C22—1722no—
1301C22—1722no—
1302C22—1722no—
1303C22—1722no—
1304C22C4×D4×D4311yescharacteristic
1305C22C4×D4×D4311yescharacteristic
1306C22C2×(C22⋊D43)⋊C411yescharacteristic
1307C22C2×C4×C22⋊D4311yescharacteristic
1308C22C4×#1062190011yescharacteristic
1309C22#1458337111yescharacteristic
1310C22#1458337211yescharacteristic
1311C22#120×D4311yescharacteristic
1312C22C2×#1306329711yescharacteristic
1313C22#1458340711yescharacteristic
1314C22#1458340811yescharacteristic
1315C22#1458340911yescharacteristic
1316C22#1458340911yescharacteristic
1317C22#1458342911yescharacteristic
1318C22#1458344511yescharacteristic
1319C22#1458346411yescharacteristic
1320C22#1458346511yescharacteristic
1321C22#1458349911yescharacteristic
1322C22#1458350111yescharacteristic
1323C22D4×C22⋊D4311yescharacteristic
1324C22D4×C22⋊D4311yescharacteristic
1325C22#1458353611yescharacteristic
1326C22#1458353611yescharacteristic
1327C22#1458353711yescharacteristic
1328C22#1458353911yescharacteristic
1329C22#1458354111yescharacteristic
1330C22#1458354311yescharacteristic
1331C22#1458354511yescharacteristic
1332C22#1458354611yescharacteristic
1333C22#1458357511yescharacteristic
1334C22#1458357811yescharacteristic
1335C22#1458359211yescharacteristic
1336C22#1458359411yescharacteristic
1337C22#1458359611yescharacteristic
1338C22#1458360111yescharacteristic
1339C4—24no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—81no—
1344C4—864no—
1345C4—864no—
1346C4—3441no—
1347C4—1722no—
1348C4—1722no—
1349C4—1722no—
1350C4—1722no—
1351C2—44no—
1352C2—44no—
1353C2—1724no—
1354C2#1913710011yescharacteristic
1355C2C4×#1306329711yescharacteristic
1356C2#1913731611yescharacteristic
1357C2#1913757211yescharacteristic
1358C2#1913757411yescharacteristic
1359C2#1913764311yescharacteristic
1360C2#1913764411yescharacteristic
1361C2#1913791211yescharacteristic
1362C2#1913794811yescharacteristic
1363C2#1913849911yescharacteristic
1364C2#1913850711yescharacteristic
1365C2#1913859811yescharacteristic
1366C2#1913860611yescharacteristic
1367C2#1913949411yescharacteristic
1368C2#1914015811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#386C2
socle, cosocleC24×C43C24
prime radicalC2×#14582807C2
hypercenterC2×#386D43
hypocenterC43#14175
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D43C2semidirect
3. C2×#14582779C2semidirect
4. C2×#14582776C2semidirect
5. C2×#14582775C2semidirect
6. C2×C22⋊C4×Dic43C2semidirect
7. #19132850C2semidirect
8. #19132838C2semidirect
9. #19132834C2semidirect
10. #19132832C2semidirect
11. #19132831C2semidirect
12. #19132821C2semidirect
13. #19132818C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C43×#386C2semidirect
35. #14582807C4semidirect
73. C22×C22⋊D43C2×C4semidirect
74. C22×C22⋊D43C2×C4semidirect
112. C2×C22⋊Dic43C2×C4semidirect
113. C2×C22⋊Dic43C2×C4semidirect
114. C2×C22⋊Dic43D4semidirect
125. C2×(C2×D43)⋊C4C2×C4semidirect
126. C2×(C2×D43)⋊C4D4semidirect
132. C2×C4×Dic43D4semidirect
144. C43⋊#95C2×C4semidirect
153. C22×D4×C43C2×C4semidirect
174. C2×C22⋊C4×C43D4semidirect
433. C23×C43C4×D4semidirect
672. C2×#386D43semidirect
744. C43#14175semidirect
768. C22×D4C4×D43semidirect
841. C2×C22⋊C4C22⋊D43semidirect
1153. C23C4×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C2×#145828072
C2×#145827792
C2×#145827762
C2×#145827752
C2×C22⋊C4×Dic432
#191328502
#191328382
#191328342
#191328322
#191328312
#191328212
#191328182
(C2×D43)⋊#952
C2×C43×#3862
#1417543