Finite Group Databasebeta

← #25028049

Subgroups — #25028049

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×#13063303C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D43C211yesmaximal, characteristic
3C2×#14582819C211yesmaximal, characteristic, complemented
4C2×#14582811C211yesmaximal, characteristic, complemented
5C2×#14582772C211yesmaximal, characteristic, complemented
6#19132846C211yesmaximal, characteristic, complemented
7#19132839C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic, complemented
9#19132837C211yesmaximal, characteristic, complemented
10#19132834C211yesmaximal, characteristic
11#19132834C211yesmaximal, characteristic
12#19132830C211yesmaximal, characteristic, complemented
13#19132827C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#385C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063303—24no—
20C2×#13063303—24no—
21C2×#13063303—24no—
22C2×C4×C22⋊D43—24no—
23C2×C4×C22⋊D43—24no—
24C2×C4×C22⋊D43—24no—
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38#14582819—24no—
39#14582811—24no—
40#14582772—24no—
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
52C2×C43⋊#95C2211yescharacteristic
53C24×C4×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C43×#385—24no—
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C24×D43C2311yescharacteristic
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—41no—
68C22×Dic86—41no—
69C22×C22⋊D43—22no—
70C22×C22⋊D43—22no—
71C22×C22⋊D43—22no—
72C22×C22⋊D43—22no—
73C22×C22⋊D43—22no—
74C22×C22⋊D43—22no—
75C22×C22⋊D43Q814yescomplemented
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—22no—
87C22×C4×D43—41no—
88C22×C4×D43—41no—
89C22×C4×D43D414yes—
90#13063303—232no—
91C4×C22⋊D43—232no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—41no—
102C2×Dic43⋊C4D414yes—
103C2×Dic43⋊C4D414yescomplemented
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—22no—
109C2×C22⋊Dic43—22no—
110C2×C22⋊Dic43—22no—
111C2×C22⋊Dic43—41no—
112C2×C22⋊Dic43D414yes—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
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—22no—
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—22no—
124C2×(C2×D43)⋊C4—22no—
125C2×(C2×D43)⋊C4—22no—
126C2×(C2×D43)⋊C4—41no—
127C2×(C2×D43)⋊C4—41no—
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
144C23×C4×C43—22no—
145C23×C4×C43—22no—
146C23×C4×C43—22no—
147C23×C4×C43—22no—
148C23×C4×C43—22no—
149C23×C4×C43—41no—
150C23×C4×C43—41no—
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C2×C4⋊C4×C43—22no—
158C2×C4⋊C4×C43—22no—
159C2×C4⋊C4×C43—22no—
160C2×C4⋊C4×C43—22no—
161C2×C4⋊C4×C43—41no—
162C2×C4⋊C4×C43D414yescomplemented
163C2×C22⋊C4×C43—22no—
164C2×C22⋊C4×C43—22no—
165C2×C22⋊C4×C43—22no—
166C2×C22⋊C4×C43—22no—
167C2×C22⋊C4×C43—22no—
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×C43C2×D412yes—
184C24×C43C2×Q812yes—
185C24×C43#4112yes—
186C24×C43C2411yescharacteristic
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—21no—
195C23×D43—21no—
196C23×D43—21no—
197C23×D43—21no—
198C23×D43—21no—
199C23×D43C2×D412yes—
200C23×D43C2×Q812yes—
201C23×D43#4112yes—
202C22×C4×C43—28no—
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—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×C43—44no—
239C22×C4×C43—44no—
240C22×C4×C43—44no—
241C22×C4×C43—44no—
242C22×C4×C43—44no—
243C22×C4×C43—44no—
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2×D412yes—
247C22×C4×C43C2×D412yes—
248C22×C4×C43C2×D412yes—
249C22×C4×C43C2×D412yes—
250C22×C4×C43#4112yes—
251C2×C22⋊D43—28no—
252C2×C22⋊D43—28no—
253C2×C22⋊D43—28no—
254C2×C22⋊D43—28no—
255C2×C22⋊D43—28no—
256C2×C22⋊D43—28no—
257C2×C22⋊D43—28no—
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—21no—
293C22×Dic43—21no—
294C22×Dic43—21no—
295C22×Dic43—21no—
296C22×Dic43—21no—
297C22×Dic43C2×D412yes—
298C22×Dic43C2×D412yes—
299C22×Dic43C2×D412yes—
300C22×Dic43C2×D412yes—
301C22×Dic43C2×D412yes—
302C22×Dic43C2×D412yes—
303C22×Dic43C2×D412yes—
304C22×Dic43C2×Q812yes—
305C22×Dic43#4112yes—
306C22×Dic43#4112yes—
307C2×C4×D43—28no—
308C2×C4×D43—28no—
309C2×C4×D43—44no—
310C2×C4×D43—44no—
311C2×C4×D43—44no—
312C2×C4×D43—44no—
313C2×C4×D43—44no—
314C2×Dic86—28no—
315C2×Dic86—44no—
316C2×Dic86—44no—
317C2×Dic86—44no—
318C2×Dic86—44no—
319C2×Dic86—44no—
320C2×Dic86—44no—
321C4⋊C4×C43—28no—
322C4⋊C4×C43—44no—
323C22⋊C4×C43—28no—
324C22⋊C4×C43—44no—
325C22⋊Dic43—28no—
326C22⋊Dic43—28no—
327C22⋊Dic43—44no—
328(C2×D43)⋊C4—28no—
329(C2×D43)⋊C4—28no—
330(C2×D43)⋊C4—28no—
331(C2×D43)⋊C4—44no—
332(C2×D43)⋊C4—44no—
333Dic43⋊C4—28no—
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—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×C43C22⋊Q814yescomplemented
373C23×C43C22×D411yescharacteristic
374C23×C43C22×D411yescharacteristic
375C23×C43C22×D411yescharacteristic
376C23×C43C22×D411yescharacteristic
377C23×C43C22×D411yescharacteristic
378C23×C43C22×Q811yescharacteristic
379C23×C43C2×#4111yescharacteristic
380C23×C43C2×#4111yescharacteristic
381C23×C43C2×#4111yescharacteristic
382C23×C43C2×#4111yescharacteristic
383C23×C43C2×#4111yescharacteristic
384C23×C43H(5,𝔽2)11yescharacteristic
385C23×C43H(5,𝔽2)11yescharacteristic
386C23×C432−1+411yescharacteristic
387C23×C432−1+411yescharacteristic
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—22no—
394C22×D43—22no—
395C22×D43—22no—
396C22×D43—22no—
397C22×D43—22no—
398C22×D43—22no—
399C22×D43—22no—
400C22×D43—22no—
401C22×D43—22no—
402C22×D43—22no—
403C22×D43—22no—
404C22×D43—22no—
405C22×D43—22no—
406C22×D43—41no—
407C22×D43—41no—
408C22×D43—41no—
409C22×D43—41no—
410C22×D43—41no—
411C22×D43—41no—
412C22×D43—41no—
413C22×D43—41no—
414C22×D43—41no—
415C22×D43—41no—
416C22×D43—41no—
417C22×D43—41no—
418C22×D43—41no—
419C22×D43—41no—
420C22×D43—41no—
421C22×D43—41no—
422C22×D43C22⋊Q814yes—
423C2×C4×C43—22no—
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—22no—
440C2×C4×C43—22no—
441C2×C4×C43—416no—
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×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—41no—
465C2×C4×C43#12014yes—
466C22⋊D43—232no—
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—22no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—22no—
490C2×Dic43—22no—
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#12014yes—
515C2×Dic43C22⋊Q814yescomplemented
516C4×D43—416no—
517Dic86—416no—
518#14723—431nomaximal, Sylow
519C22×C43—24no—
520C22×C43—24no—
521C22×C43—24no—
522C22×C43—42no—
523C22×C43—42no—
524C22×C43—42no—
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×C43C2×#12011yescharacteristic
535C22×C43C2×#12011yescharacteristic
536C22×C43C2×C22⋊Q811yescharacteristic
537C22×C43C2×C22⋊Q811yescharacteristic
538C22×C43C2×C22⋊Q811yescharacteristic
539C22×C43#52511yescharacteristic
540C22×C43#52511yescharacteristic
541C22×C43#52511yescharacteristic
542C22×C43#52511yescharacteristic
543C22×C43#52511yescharacteristic
544C22×C43#53211yescharacteristic
545C22×C43#53211yescharacteristic
546C22×C43#53211yescharacteristic
547C22×C43#53411yescharacteristic
548C22×C43#53611yescharacteristic
549C22×C43#53911yescharacteristic
550C22×C43#53911yescharacteristic
551C22×C43#54211yescharacteristic
552C22×C43#54211yescharacteristic
553C22×C43D4211yescharacteristic
554C22×C43D4211yescharacteristic
555C22×C43D4211yescharacteristic
556C22×C43D4211yescharacteristic
557C22×C43#54711yescharacteristic
558C22×C43#54711yescharacteristic
559C22×C43#54811yescharacteristic
560C22×C43#54811yescharacteristic
561C22×C43#54811yescharacteristic
562C22×C43#54811yescharacteristic
563C22×C43D4×Q811yescharacteristic
564C22×C43D4×Q811yescharacteristic
565C22×C43#55111yescharacteristic
566C22×C43#55111yescharacteristic
567C22×C43#55411yescharacteristic
568C22×C43#55411yescharacteristic
569C2×D43—24no—
570C2×D43—24no—
571C2×D43—24no—
572C2×D43—42no—
573C2×D43—42no—
574C2×D43—42no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—42no—
581C2×D43—42no—
582C2×D43—42no—
583C2×D43—42no—
584C4×C43—24no—
585C4×C43—42no—
586C4×C43—42no—
587C4×C43—42no—
588C4×C43—42no—
589C4×C43—81no—
590Dic43—24no—
591Dic43—24no—
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×#385D4311yescharacteristic, complemented
603#1441—431no—
604#1439—431no—
605#1439—431no—
606#1439—431no—
607#1438—431no—
608#1438—431no—
609#1436—431no—
610#1436—431no—
611C22⋊#95—431no—
612C2×C43—44no—
613C2×C43#238811yescharacteristic
614C2×C43#240311yescharacteristic
615C2×C43#240911yescharacteristic
616C2×C43#243211yescharacteristic
617C2×C43#244911yescharacteristic
618C2×C43#244911yescharacteristic
619C2×C43#245211yescharacteristic
620C2×C43#245211yescharacteristic
621C2×C43#246111yescharacteristic
622C2×C43#246111yescharacteristic
623C2×C43#246311yescharacteristic
624C2×C43#246311yescharacteristic
625C2×C43#256411yescharacteristic
626C2×C43#263811yescharacteristic
627C2×C43#284811yescharacteristic
628D43—44no—
629C23×Q8—431no—
630C23×D4—431no—
631C24×C4—431no—
632C24×C4C2×D4311yescharacteristic
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⋊C4C2×D4311yescharacteristic
644C22×C4⋊C4C2×D4311yescharacteristic
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⋊C4—431no—
652C22×C22⋊C4—431no—
653C22×C22⋊C4C2×D4311yescharacteristic
654C22×C22⋊C4C2×D4311yescharacteristic
655C22×C42—431no—
656#395—864no—
657#393—864no—
658#385—24no—
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
675C25—431no—
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—434no—
685C22×D4—862no—
686C22×D4—862no—
687C22×D4—862no—
688C22×D4—862no—
689C22×D4—862no—
690C22×D4—862no—
691C23×C4—22no—
692C23×C4—22no—
693C23×C4—22no—
694C23×C4—22no—
695C23×C4—22no—
696C23×C4—41no—
697C23×C4—41no—
698C23×C4—431no—
699C23×C4—431no—
700C23×C4—431no—
701C23×C4—431no—
702C23×C4—431no—
703C23×C4—431no—
704C23×C4—434no—
705C23×C4—431no—
706C23×C4—862no—
707C23×C4—862no—
708C23×C4—862no—
709C23×C4—862no—
710C23×C4—1721no—
711C23×C4—1721no—
712C23×C4C22×D4311yescharacteristic
713C23×C4C22×D4311yescharacteristic
714C23×C4C22×D4311yescharacteristic
715C23×C4C22×D4311yescharacteristic
716C23×C4C22×D4311yescharacteristic
717C23×C4C22×D4311yescharacteristic
718C22⋊Q8—8632no—
719C4×D4—8632no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4—41no—
725C2×C4⋊C4—434no—
726C2×C4⋊C4—434no—
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⋊C4C22⋊D4314yescomplemented
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—434no—
745C2×C22⋊C4—862no—
746C2×C22⋊C4—862no—
747C2×C22⋊C4—862no—
748C2×C22⋊C4—862no—
749C2×C22⋊C4—862no—
750C2×C22⋊C4—862no—
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—1721no—
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—432no—
798C24—432no—
799C24—432no—
800C24—861no—
801C24—861no—
802C24—861no—
803C24—861no—
804C24—861no—
805C24—861no—
806C24—861no—
807C24—861no—
808C24—861no—
809C24—861no—
810C24—861no—
811C24—861no—
812C24#1062189812yes—
813C24D4×D4312yes—
814C24Q8×D4312yes—
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—868no—
824C2×D4—868no—
825C2×D4—868no—
826C2×D4—868no—
827C2×D4—868no—
828C2×D4—868no—
829C2×D4—868no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—28no—
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—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—432no—
873C22×C4—432no—
874C22×C4—432no—
875C22×C4—432no—
876C22×C4—432no—
877C22×C4—432no—
878C22×C4—432no—
879C22×C4—432no—
880C22×C4—432no—
881C22×C4—432no—
882C22×C4—868no—
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—868no—
916C22×C4—861no—
917C22×C4—861no—
918C22×C4—861no—
919C22×C4—861no—
920C22×C4—861no—
921C22×C4—861no—
922C22×C4—861no—
923C22×C4—1724no—
924C22×C4—1724no—
925C22×C4—1724no—
926C22×C4—1724no—
927C22×C4—1724no—
928C22×C4#1062189812yes—
929C22×C4D4×D4312yes—
930C22×C4D4×D4312yes—
931C22×C4D4×D4312yes—
932C22×C4C2×C22⋊D4312yes—
933C22×C4C2×C22⋊D4312yes—
934C22×C4C2×C22⋊D4312yes—
935C4⋊C4—28no—
936C4⋊C4—44no—
937C4⋊C4—868no—
938C4⋊C4—868no—
939C4⋊C4—868no—
940C4⋊C4—1724no—
941C22⋊C4—28no—
942C22⋊C4—44no—
943C22⋊C4—868no—
944C22⋊C4—868no—
945C22⋊C4—868no—
946C22⋊C4—868no—
947C22⋊C4—868no—
948C22⋊C4—1724no—
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—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—434no—
987C23—862no—
988C23—862no—
989C23—862no—
990C23—862no—
991C23—862no—
992C23—862no—
993C23—862no—
994C23—862no—
995C23—862no—
996C23—862no—
997C23—862no—
998C23—862no—
999C23—862no—
1000C23—862no—
1001C23—862no—
1002C23—862no—
1003C23—862no—
1004C23—862no—
1005C23—1721no—
1006C23—1721no—
1007C23—1721no—
1008C23—1721no—
1009C23—1721no—
1010C23—1721no—
1011C23—1721no—
1012C23—1721no—
1013C23—1721no—
1014C23—1721no—
1015C23—1721no—
1016C23—1721no—
1017C23—1721no—
1018C23—1721no—
1019C23—1721no—
1020C23—1721no—
1021C23#1306330314yescomplemented
1022C23C2×D4×D4311yescharacteristic
1023C23C2×D4×D4311yescharacteristic
1024C23C2×D4×D4311yescharacteristic
1025C23C2×D4×D4311yescharacteristic
1026C23C22×C22⋊D4311yescharacteristic
1027C23C2×Q8×D4311yescharacteristic
1028C23#41×D4311yescharacteristic
1029C23#41×D4311yescharacteristic
1030C23#41×D4311yescharacteristic
1031C23C2×#1062189811yescharacteristic
1032C23C2×#1062189811yescharacteristic
1033C23#1306337011yescharacteristic
1034C23#1306337011yescharacteristic
1035C23#1306337211yescharacteristic
1036C23#1306337311yescharacteristic
1037Q8—17216no—
1038D4—8632no—
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—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—416no—
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—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—434no—
1082C2×C4—434no—
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—862no—
1103C2×C4—862no—
1104C2×C4—862no—
1105C2×C4—862no—
1106C2×C4—862no—
1107C2×C4—17216no—
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#1306329314yes—
1132C22—24no—
1133C22—24no—
1134C22—24no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—864no—
1148C22—864no—
1149C22—864no—
1150C22—1722no—
1151C22—1722no—
1152C22—1722no—
1153C22—1722no—
1154C22—1722no—
1155C22—1722no—
1156C22—1722no—
1157C22—1722no—
1158C22—1722no—
1159C22—1722no—
1160C22—1722no—
1161C22—1722no—
1162C22#120×D4311yescharacteristic
1163C22C2×#1306329311yescharacteristic
1164C22C22⋊Q8×D4311yescharacteristic
1165C22C22⋊Q8×D4311yescharacteristic
1166C22C2×#1306330311yescharacteristic
1167C22#1458340711yescharacteristic
1168C22#1458340811yescharacteristic
1169C22#1458340811yescharacteristic
1170C22#1458340811yescharacteristic
1171C22#1458341011yescharacteristic
1172C22#1458344511yescharacteristic
1173C22#1458344611yescharacteristic
1174C22#1458344611yescharacteristic
1175C22#1458345911yescharacteristic
1176C22#1458347211yescharacteristic
1177C22#1458349111yescharacteristic
1178C22#1458349611yescharacteristic
1179C22#1458351711yescharacteristic
1180C22#1458351911yescharacteristic
1181C22#1458353111yescharacteristic
1182C22#1458353111yescharacteristic
1183C22D4×C22⋊D4311yescharacteristic
1184C22D4×C22⋊D4311yescharacteristic
1185C22#1458354711yescharacteristic
1186C22#1458355011yescharacteristic
1187C22#1458355611yescharacteristic
1188C22#1458355811yescharacteristic
1189C22#1458355911yescharacteristic
1190C22#1458355911yescharacteristic
1191C22#1458356211yescharacteristic
1192C22Q8×C22⋊D4311yescharacteristic
1193C22#1458357711yescharacteristic
1194C22#1458357811yescharacteristic
1195C22#1458360311yescharacteristic
1196C22#1458360411yescharacteristic
1197C4—24no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—81no—
1203C4—864no—
1204C4—864no—
1205C4—3441no—
1206C4—1722no—
1207C4—1722no—
1208C4—1722no—
1209C4—1722no—
1210C2—44no—
1211C2—1724no—
1212C2#1913781011yescharacteristic
1213C2#1913790611yescharacteristic
1214C2#1913795611yescharacteristic
1215C2#1913822111yescharacteristic
1216C2#1913840411yescharacteristic
1217C2#1913840611yescharacteristic
1218C2#1913844211yescharacteristic
1219C2#1913844411yescharacteristic
1220C2#1913855911yescharacteristic
1221C2#1913856111yescharacteristic
1222C2#1913858611yescharacteristic
1223C2#1913859111yescharacteristic
1224C2#1913978011yescharacteristic
1225C2#1914051611yescharacteristic
1226C2#1914288111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC2×C43×#385C2
prime radicalC23×C22⋊D43C22
hypercenterC2×#385D43
hypocenterC43#14723
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13063303C2semidirect
3. C2×#14582819C2semidirect
4. C2×#14582811C2semidirect
5. C2×#14582772C2semidirect
6. #19132846C2semidirect
7. #19132839C2semidirect
8. #19132838C2semidirect
9. #19132837C2semidirect
12. #19132830C2semidirect
13. #19132827C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C43×#385C2semidirect
75. C22×C22⋊D43Q8semidirect
103. C2×Dic43⋊C4D4semidirect
162. C2×C4⋊C4×C43D4semidirect
372. C23×C43C22⋊Q8semidirect
515. C2×Dic43C22⋊Q8semidirect
602. C2×#385D43semidirect
674. C43#14723semidirect
737. C2×C4⋊C4C22⋊D43semidirect
1021. C23#13063303semidirect

Maximal subgroups

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

subgroupindex
C22×#130633032
C22×C4×C22⋊D432
C2×#145828192
C2×#145828112
C2×#145827722
#191328462
#191328392
#191328382
#191328372
#191328342
#191328302
#191328272
(C2×D43)⋊#952
C2×C43×#3852
#1472343