Finite Group Databasebeta

← #25020571

Subgroups — #25020571

Order 11008.

2330 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×#13063283C211yesmaximal, characteristic, complemented
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582773C211yesmaximal, characteristic, complemented
5C2×#14582746C211yesmaximal, characteristic, complemented
6#19132839C211yesmaximal, characteristic, complemented
7#19132837C211yesmaximal, characteristic, complemented
8#19132835C211yesmaximal, characteristic
9#19132831C211yesmaximal, characteristic, complemented
10#19132831C211yesmaximal, characteristic, complemented
11#19132829C211yesmaximal, characteristic, complemented
12#19132826C211yesmaximal, characteristic, complemented
13#19132821C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1442C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063283—24no—
20C2×#13063283—24no—
21C2×#13063283—24no—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582777—24no—
38#14582777C418yescomplemented
39#14582773—24no—
40#14582746—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
51C22×C4⋊C4×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C24×D43C2311yescharacteristic
60C22×D172—22no—
61C22×D172—22no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—41no—
65C22×D172—41no—
66C22×D172C2×C414yes—
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43C2×C414yescomplemented
87#13063283—232no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43D414yescomplemented
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—41no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4—41no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4—41no—
120C2×(C2×D43)⋊C4C2×C414yes—
121C2×(C2×D43)⋊C4C2×C414yes—
122C2×(C2×D43)⋊C4C2×C414yescomplemented
123C2×(C2×D43)⋊C4D414yes—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—22no—
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—41no—
140C43⋊#95—41no—
141C43⋊#95—41no—
142C43⋊#95C2×C414yescomplemented
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43—22no—
151C2×C4⋊C4×C43—22no—
152C2×C4⋊C4×C43—22no—
153#95×C43—22no—
154#95×C43—22no—
155#95×C43—22no—
156#95×C43—41no—
157#95×C43—41no—
158#95×C43C2×C414yescomplemented
159C24×C43C2411yescharacteristic
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43C22×C412yes—
185C23×D43C22×C412yes—
186C23×D43C2×D412yes—
187C23×D43#4112yes—
188C23×D43#4112yes—
189C23×D43#4112yes—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
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—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43C22×C412yes—
232C22×C4×C43C22×C412yes—
233C22×C4×C43C22×C412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43C2×D412yes—
237C22×C4×C43#4112yes—
238C22×C4×C43#4112yes—
239C22×Dic43—21no—
240C22×Dic43—21no—
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×Dic43C22×C412yes—
273C22×Dic43C22×C412yes—
274C22×Dic43C2×D412yes—
275C22×Dic43C2×D412yes—
276C22×Dic43C2×D412yes—
277C22×Dic43C2×D412yes—
278C22×Dic43C2×D412yes—
279C22×Dic43#4112yes—
280C22×Dic43#4112yes—
281C2×D172—28no—
282C2×D172—28no—
283C2×D172—44no—
284C2×D172—44no—
285C2×D172—44no—
286C2×D172—44no—
287C2×D172—44no—
288C2×C4×D43—28no—
289C2×C4×D43—28no—
290C2×C4×D43—28no—
291C2×C4×D43—28no—
292C2×C4×D43—28no—
293C2×C4×D43—28no—
294C2×C4×D43—28no—
295C2×C4×D43—28no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C4⋊C4×C43—28no—
303(C2×D43)⋊C4—28no—
304(C2×D43)⋊C4—28no—
305(C2×D43)⋊C4—28no—
306(C2×D43)⋊C4—28no—
307(C2×D43)⋊C4—28no—
308(C2×D43)⋊C4—44no—
309(C2×D43)⋊C4—44no—
310(C2×D43)⋊C4—44no—
311(C2×D43)⋊C4—44no—
312(C2×D43)⋊C4—44no—
313C4⋊Dic43—28no—
314Dic43⋊C4—44no—
315C4×Dic43—28no—
316C4×Dic43—28no—
317C4×Dic43—44no—
318C23×C43C23×C411yescharacteristic
319C23×C43C22×D411yescharacteristic
320C23×C43C22×D411yescharacteristic
321C23×C43C22×D411yescharacteristic
322C23×C43C2×#4111yescharacteristic
323C23×C43C2×#4111yescharacteristic
324C23×C43C2×#4111yescharacteristic
325C23×C43C2×#4111yescharacteristic
326C23×C43C2×#4111yescharacteristic
327C23×C43C2×#4111yescharacteristic
328C23×C43C2×#4111yescharacteristic
329C23×C43H(5,𝔽2)11yescharacteristic
330C23×C43H(5,𝔽2)11yescharacteristic
331C23×C43H(5,𝔽2)11yescharacteristic
332C23×C432−1+411yescharacteristic
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43—41no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43—41no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43#11714yescomplemented
402C22×D43C4×D414yes—
403C2×C4×C43—22no—
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—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
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—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×C43C4×D414yes—
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—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
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×Dic43C4×D414yes—
493C2×Dic43#12014yes—
494D172—416no—
495C4×D43—232no—
496C4×D43—416no—
497#14064—431nomaximal, Sylow
498C22×C43C2×#11711yescharacteristic
499C22×C43C2×C4×D411yescharacteristic
500C22×C43C2×C4×D411yescharacteristic
501C22×C43C2×C4×D411yescharacteristic
502C22×C43C4×#4111yescharacteristic
503C22×C43#51811yescharacteristic
504C22×C43#52011yescharacteristic
505C22×C43C2×#12011yescharacteristic
506C22×C43#52511yescharacteristic
507C22×C43#52511yescharacteristic
508C22×C43#52511yescharacteristic
509C22×C43#52511yescharacteristic
510C22×C43#52511yescharacteristic
511C22×C43#52911yescharacteristic
512C22×C43#52911yescharacteristic
513C22×C43#53511yescharacteristic
514C22×C43#53711yescharacteristic
515C22×C43#54011yescharacteristic
516C22×C43#54211yescharacteristic
517C22×C43#54611yescharacteristic
518C22×C43#54611yescharacteristic
519C22×C43#54611yescharacteristic
520C22×C43#54611yescharacteristic
521C22×C43#54611yescharacteristic
522C22×C43#54711yescharacteristic
523C22×C43#54811yescharacteristic
524C22×C43#55011yescharacteristic
525C22×C43#55111yescharacteristic
526C22×C43#55111yescharacteristic
527C22×C43#55111yescharacteristic
528C22×C43#55211yescharacteristic
529C22×C43#55211yescharacteristic
530C22×C43#55311yescharacteristic
531C22×C43#55311yescharacteristic
532C22×C43#55511yescharacteristic
533C2×D43—24no—
534C2×D43—24no—
535C2×D43—24no—
536C2×D43—24no—
537C2×D43—24no—
538C2×D43—24no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43—42no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
563C4×C43—24no—
564C4×C43—42no—
565C4×C43—42no—
566C4×C43—42no—
567C4×C43—42no—
568C4×C43—42no—
569C4×C43—81no—
570Dic43—24no—
571Dic43—24no—
572Dic43—42no—
573Dic43—42no—
574Dic43—42no—
575Dic43—81no—
576C22×#117—431no—
577C2×#386—431no—
578C2×#386—431no—
579C2×#385—431no—
580C2×C4×C22⋊C4—431no—
581#1442D4311yescharacteristic, complemented
582#1439—431no—
583#1439—431no—
584#1438—431no—
585#1437—431no—
586#1437—431no—
587#1436—431no—
588#1436—431no—
589#1434—431no—
590C22⋊#95—431no—
591C2×C43#229011yescharacteristic
592C2×C43C4×#12011yescharacteristic
593C2×C43#232411yescharacteristic
594C2×C43#234211yescharacteristic
595C2×C43#235211yescharacteristic
596C2×C43#235911yescharacteristic
597C2×C43#236311yescharacteristic
598C2×C43#240411yescharacteristic
599C2×C43#240711yescharacteristic
600C2×C43#247011yescharacteristic
601C2×C43#247111yescharacteristic
602C2×C43#247611yescharacteristic
603C2×C43#247711yescharacteristic
604C2×C43#259811yescharacteristic
605C2×C43#260911yescharacteristic
606D43—44no—
607D43—44no—
608C23×D4—431no—
609C24×C4—431no—
610C24×C4—431no—
611C2×#117—864no—
612C2×#117—864no—
613C2×#117—864no—
614C22×C4⋊C4—431no—
615C22×C4⋊C4—431no—
616C22×C4⋊C4C2×D4311yescharacteristic
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⋊C4—431no—
625C22×C22⋊C4—431no—
626C22×C22⋊C4—431no—
627C22×C42—431no—
628C22×C42—431no—
629C22×C42—431no—
630#386—438no—
631#386—864no—
632#385—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×#95C2×D4311yescharacteristic
645C2×#95C2×D4311yescharacteristic
646C2×#95C2×D4311yescharacteristic
647C2×#95C2×D4311yescharacteristic
648C2×#95C2×D4311yescharacteristic
649C2×#95C2×D4311yescharacteristic
650C43#1406411yescharacteristic, complemented, Sylow
651C25—431no—
652C25—431no—
653C22×D4—434no—
654C22×D4—862no—
655C22×D4—862no—
656C22×D4—862no—
657C22×D4—862no—
658C22×D4—1721no—
659C22×D4—1721no—
660C23×C4—431no—
661C23×C4—431no—
662C23×C4—431no—
663C23×C4—431no—
664C23×C4—431no—
665C23×C4—434no—
666C23×C4—431no—
667C23×C4—862no—
668C23×C4—862no—
669C23×C4—862no—
670C23×C4—862no—
671C23×C4—862no—
672C23×C4—862no—
673C23×C4—862no—
674C23×C4—862no—
675C23×C4—862no—
676C23×C4—862no—
677C23×C4—862no—
678C23×C4—1721no—
679C23×C4—1721no—
680C23×C4C22×D4311yescharacteristic
681C23×C4C22×D4311yescharacteristic
682C23×C4C22×D4311yescharacteristic
683C23×C4C22×D4311yescharacteristic
684C23×C4C22×D4311yescharacteristic
685C23×C4C22×D4311yescharacteristic
686C23×C4C22×D4311yescharacteristic
687#117—8632no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—434no—
692C2×C4⋊C4—862no—
693C2×C4⋊C4—862no—
694C2×C4⋊C4—862no—
695C2×C4⋊C4—862no—
696C2×C4⋊C4—1721no—
697C2×C22⋊C4—434no—
698C2×C22⋊C4—434no—
699C2×C22⋊C4—434no—
700C2×C22⋊C4—434no—
701C2×C22⋊C4—862no—
702C2×C22⋊C4—862no—
703C2×C22⋊C4—862no—
704C2×C22⋊C4—862no—
705C2×C22⋊C4—862no—
706C2×C22⋊C4—862no—
707C2×C22⋊C4—862no—
708C2×C22⋊C4—862no—
709C2×C22⋊C4—862no—
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—1721no—
722C2×C22⋊C4—1721no—
723C2×C22⋊C4—1721no—
724C2×C22⋊C4—1721no—
725C2×C22⋊C4—1721no—
726C2×C22⋊C4—1721no—
727C2×C42—434no—
728C2×C42—862no—
729C2×C42—862no—
730C2×C42—862no—
731C2×C42—862no—
732C2×C42—862no—
733C2×C42—862no—
734C2×C42—1721no—
735C2×C42—1721no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—41no—
740#95—41no—
741#95—434no—
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#95C4×D4314yescomplemented
752C24—432no—
753C24—432no—
754C24—432no—
755C24—432no—
756C24—432no—
757C24—432no—
758C24—861no—
759C24—861no—
760C24—861no—
761C24—861no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24—861no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24—861no—
780C24—861no—
781C24—861no—
782C24C23×D4311yescharacteristic
783C2×D4—868no—
784C2×D4—868no—
785C2×D4—1724no—
786C2×D4—1724no—
787C2×D4—1724no—
788C2×D4—1724no—
789C2×D4—1724no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
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—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—432no—
832C22×C4—432no—
833C22×C4—432no—
834C22×C4—432no—
835C22×C4—432no—
836C22×C4—432no—
837C22×C4—432no—
838C22×C4—432no—
839C22×C4—432no—
840C22×C4—868no—
841C22×C4—868no—
842C22×C4—868no—
843C22×C4—868no—
844C22×C4—868no—
845C22×C4—868no—
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—868no—
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—1724no—
882C22×C4—1724no—
883C22×C4—1724no—
884C22×C4—1724no—
885C22×C4—1724no—
886C22×C4—1724no—
887C22×C4C2×C4×D4312yes—
888C22×C4C2×C4×D4312yes—
889C22×C4C2×C4×D4312yes—
890C22×C4D4×D4312yes—
891C22×C4D4×D4312yes—
892C22×C4D4×D4312yes—
893C22×C4#1062190212yes—
894C22×C4#1062190212yes—
895C4⋊C4—28no—
896C4⋊C4—868no—
897C4⋊C4—1724no—
898C22⋊C4—868no—
899C22⋊C4—868no—
900C22⋊C4—868no—
901C22⋊C4—868no—
902C22⋊C4—868no—
903C22⋊C4—1724no—
904C22⋊C4—1724no—
905C22⋊C4—1724no—
906C22⋊C4—1724no—
907C22⋊C4—1724no—
908C42—868no—
909C42—868no—
910C42—1724no—
911C23—434no—
912C23—434no—
913C23—862no—
914C23—862no—
915C23—862no—
916C23—862no—
917C23—862no—
918C23—862no—
919C23—862no—
920C23—862no—
921C23—862no—
922C23—862no—
923C23—862no—
924C23—862no—
925C23—862no—
926C23—862no—
927C23—862no—
928C23—862no—
929C23—862no—
930C23—862no—
931C23—862no—
932C23—862no—
933C23—862no—
934C23—862no—
935C23—862no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—862no—
940C23—862no—
941C23—862no—
942C23—862no—
943C23—862no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—1721no—
950C23—1721no—
951C23—1721no—
952C23—1721no—
953C23—1721no—
954C23—1721no—
955C23—1721no—
956C23—1721no—
957C23—1721no—
958C23—1721no—
959C23—1721no—
960C23—1721no—
961C23—1721no—
962C23—1721no—
963C23—1721no—
964C23—1721no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23—1721no—
971C23—1721no—
972C23—1721no—
973C23—1721no—
974C23—1721no—
975C23—1721no—
976C23—1721no—
977C23—1721no—
978C23—1721no—
979C23—1721no—
980C23—1721no—
981C23C22×C4×D4311yescharacteristic
982C23C2×D4×D4311yescharacteristic
983C23C2×D4×D4311yescharacteristic
984C23C2×D4×D4311yescharacteristic
985C23#41×D4311yescharacteristic
986C23#41×D4311yescharacteristic
987C23#41×D4311yescharacteristic
988C23#41×D4311yescharacteristic
989C23#41×D4311yescharacteristic
990C23C2×#1062190211yescharacteristic
991C23C2×#1062190211yescharacteristic
992C23#1306337011yescharacteristic
993C23#1306337111yescharacteristic
994C23#1306337111yescharacteristic
995C23#1306337211yescharacteristic
996D4—17216no—
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—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
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—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—434no—
1046C2×C4—434no—
1047C2×C4—8632no—
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—862no—
1062C2×C4—862no—
1063C2×C4—862no—
1064C2×C4—862no—
1065C2×C4—862no—
1066C2×C4—862no—
1067C2×C4—862no—
1068C2×C4—862no—
1069C2×C4—17216no—
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#1306328714yes—
1090C22—864no—
1091C22—864no—
1092C22—864no—
1093C22—864no—
1094C22—864no—
1095C22—864no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22—1722no—
1103C22—1722no—
1104C22—1722no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22—1722no—
1113C22—1722no—
1114C22—1722no—
1115C22—1722no—
1116C22—1722no—
1117C22—1722no—
1118C22—1722no—
1119C22—1722no—
1120C22#117×D4311yescharacteristic
1121C22C4×D4×D4311yescharacteristic
1122C22C4×D4×D4311yescharacteristic
1123C22C2×#1306328711yescharacteristic
1124C22C4×#1062190211yescharacteristic
1125C22#1458337111yescharacteristic
1126C22#1458337911yescharacteristic
1127C22#120×D4311yescharacteristic
1128C22#1458340711yescharacteristic
1129C22#1458340711yescharacteristic
1130C22#1458341211yescharacteristic
1131C22#1458341211yescharacteristic
1132C22#1458341211yescharacteristic
1133C22#1458343211yescharacteristic
1134C22#1458343411yescharacteristic
1135C22#1458346711yescharacteristic
1136C22#1458347611yescharacteristic
1137C22#1458350111yescharacteristic
1138C22#1458351511yescharacteristic
1139C22#1458353811yescharacteristic
1140C22#1458354011yescharacteristic
1141C22#1458354011yescharacteristic
1142C22#1458354211yescharacteristic
1143C22#1458354211yescharacteristic
1144C22#1458354711yescharacteristic
1145C22#1458355711yescharacteristic
1146C22#1458356711yescharacteristic
1147C22#1458357411yescharacteristic
1148C22#1458357411yescharacteristic
1149C22#1458357711yescharacteristic
1150C22#1458358711yescharacteristic
1151C22#1458358711yescharacteristic
1152C22#1458360211yescharacteristic
1153C22#1458360211yescharacteristic
1154C22#1458361511yescharacteristic
1155C4—24no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—81no—
1162C4—864no—
1163C4—864no—
1164C4—3441no—
1165C4—1722no—
1166C4—1722no—
1167C4—1722no—
1168C2—1724no—
1169C2—1724no—
1170C2#1913703311yescharacteristic
1171C2#1913709611yescharacteristic
1172C2#1913728311yescharacteristic
1173C2#1913744311yescharacteristic
1174C2#1913752111yescharacteristic
1175C2#1913759411yescharacteristic
1176C2#1913763211yescharacteristic
1177C2#1913791511yescharacteristic
1178C2#1913793511yescharacteristic
1179C2#1913869411yescharacteristic
1180C2#1913870111yescharacteristic
1181C2#1913878411yescharacteristic
1182C2#1913879111yescharacteristic
1183C2#1914016411yescharacteristic
1184C2#1914027311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1442D43
hypocenterC43#14064
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C22×#13063283C2semidirect
4. C2×#14582773C2semidirect
5. C2×#14582746C2semidirect
6. #19132839C2semidirect
7. #19132837C2semidirect
9. #19132831C2semidirect
10. #19132831C2semidirect
11. #19132829C2semidirect
12. #19132826C2semidirect
13. #19132821C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1442C2semidirect
38. #14582777C4semidirect
86. C22×C4×D43C2×C4semidirect
90. C2×C4⋊Dic43D4semidirect
122. C2×(C2×D43)⋊C4C2×C4semidirect
132. C2×C4×Dic43D4semidirect
142. C43⋊#95C2×C4semidirect
158. #95×C43C2×C4semidirect
401. C22×D43#117semidirect
581. #1442D43semidirect
650. C43#14064semidirect
751. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632832
C2×#145827772
C2×#145827732
C2×#145827462
#191328392
#191328372
#191328352
#191328312
#191328292
#191328262
#191328212
(C2×D43)⋊#952
C43×#14422
#1406443