Finite Group Databasebeta

← #25027828

Subgroups — #25027828

Order 11008.

2746 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D43C211yesmaximal, characteristic, complemented
2C2×#14582789C211yesmaximal, characteristic, complemented
3C2×#14582788C211yesmaximal, characteristic, complemented
4C2×#14582777C211yesmaximal, characteristic
5C2×#14582777C211yesmaximal, characteristic
6C2×#14582777C211yesmaximal, characteristic
7C2×#14582770C211yesmaximal, characteristic, complemented
8#19132833C211yesmaximal, characteristic, complemented
9#19132831C211yesmaximal, characteristic, complemented
10#19132826C211yesmaximal, characteristic, complemented
11#19132821C211yesmaximal, characteristic, complemented
12#19132820C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊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×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C2×C42×D43—24no—
34C2×C42×D43—24no—
35C2×C42×D43—24no—
36#14582789—24no—
37#14582788—24no—
38#14582777—24no—
39#14582777—24no—
40#14582777C418yescomplemented
41#14582770—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
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C24×D43C2311yescharacteristic
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172C2×C414yes—
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
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—22no—
85C22×C4×D43—22no—
86C22×C4×D43—22no—
87C22×C4×D43—22no—
88C22×C4×D43—22no—
89C22×C4×D43—22no—
90C22×C4×D43—22no—
91C22×C4×D43—22no—
92C22×C4×D43—22no—
93C22×C4×D43C2×C414yes—
94C22×C4×D43D414yes—
95C22×C4×D43D414yes—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊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—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)⋊C4C2×C414yes—
124C2×(C2×D43)⋊C4C2×C414yescomplemented
125C2×(C2×D43)⋊C4C2×C414yescomplemented
126C2×C4×Dic43—22no—
127C2×C4×Dic43—22no—
128C2×C4×Dic43—22no—
129C2×C4×Dic43—22no—
130C2×C4×Dic43—22no—
131C2×C4×Dic43—22no—
132C2×C4×Dic43—22no—
133C2×C4×Dic43D414yescomplemented
134C2×C4×Dic43D414yescomplemented
135C42×D43—232no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95—22no—
142C43⋊#95—22no—
143C43⋊#95—22no—
144C43⋊#95—22no—
145C43⋊#95—22no—
146C43⋊#95C2×C414yescomplemented
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43—22no—
155C2×C4⋊C4×C43—22no—
156C2×C4⋊C4×C43—22no—
157C2×C42×C43—22no—
158C2×C42×C43—22no—
159C2×C42×C43—22no—
160#95×C43—22no—
161#95×C43—22no—
162#95×C43—22no—
163#95×C43—22no—
164#95×C43C2×C414yescomplemented
165C24×C43C2411yescharacteristic
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×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43C22×C412yes—
189C23×D43C22×C412yes—
190C23×D43C2×D412yes—
191C23×D43C2×D412yes—
192C23×D43#4112yes—
193C23×D43#4112yes—
194C23×D43#4112yes—
195C23×D43#4112yes—
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×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43C22×C412yes—
235C22×C4×C43C22×C412yes—
236C22×C4×C43C22×C412yes—
237C22×C4×C43C2×D412yes—
238C22×C4×C43C2×D412yes—
239C22×C4×C43C2×D412yes—
240C22×C4×C43C2×D412yes—
241C22×C4×C43#4112yes—
242C22×C4×C43#4112yes—
243C22×C4×C43#4112yes—
244C22×C4×C43#4112yes—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43C22×C412yes—
278C22×Dic43C22×C412yes—
279C22×Dic43C2×D412yes—
280C22×Dic43C2×D412yes—
281C22×Dic43C2×D412yes—
282C22×Dic43C2×D412yes—
283C22×Dic43C2×D412yes—
284C22×Dic43C2×D412yes—
285C22×Dic43#4112yes—
286C22×Dic43#4112yes—
287C2×D172—28no—
288C2×D172—28no—
289C2×D172—28no—
290C2×D172—44no—
291C2×D172—44no—
292C2×D172—44no—
293C2×D172—44no—
294C2×C4×D43—28no—
295C2×C4×D43—28no—
296C2×C4×D43—28no—
297C2×C4×D43—28no—
298C2×C4×D43—28no—
299C2×C4×D43—28no—
300C2×C4×D43—28no—
301C2×C4×D43—28no—
302C2×C4×D43—28no—
303C2×C4×D43—28no—
304C2×C4×D43—28no—
305C2×C4×D43—28no—
306C2×C4×D43—28no—
307C2×C4×D43—28no—
308C2×C4×D43—28no—
309C2×C4×D43—28no—
310C2×C4×D43—28no—
311C2×C4×D43—28no—
312C2×C4×D43—28no—
313C2×C4×D43—28no—
314C2×C4×D43—28no—
315C4⋊C4×C43—44no—
316C42×C43—28no—
317(C2×D43)⋊C4—28no—
318(C2×D43)⋊C4—28no—
319(C2×D43)⋊C4—28no—
320(C2×D43)⋊C4—44no—
321(C2×D43)⋊C4—44no—
322(C2×D43)⋊C4—44no—
323(C2×D43)⋊C4—44no—
324(C2×D43)⋊C4—44no—
325(C2×D43)⋊C4—44no—
326Dic43⋊C4—44no—
327C4×Dic43—28no—
328C4×Dic43—28no—
329C4×Dic43—28no—
330C23×C43C23×C411yescharacteristic
331C23×C43C22×D411yescharacteristic
332C23×C43C22×D411yescharacteristic
333C23×C43C22×D411yescharacteristic
334C23×C43C22×D411yescharacteristic
335C23×C43C2×#4111yescharacteristic
336C23×C43C2×#4111yescharacteristic
337C23×C43C2×#4111yescharacteristic
338C23×C43C2×#4111yescharacteristic
339C23×C43C2×#4111yescharacteristic
340C23×C43C2×#4111yescharacteristic
341C23×C43C2×#4111yescharacteristic
342C23×C43C2×#4111yescharacteristic
343C23×C43C2×#4111yescharacteristic
344C23×C43C2×#4111yescharacteristic
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—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
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—41no—
402C22×D43—41no—
403C22×D43—41no—
404C22×D43—41no—
405C22×D43—41no—
406C22×D43—41no—
407C22×D43—41no—
408C22×D43#11714yes—
409C22×D43C4×D414yes—
410C22×D43C4×D414yes—
411C22×D43#12114yes—
412C22×D43#12314yes—
413C22×D43#12414yes—
414C22×D43#12614yes—
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—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×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43C4×D414yes—
462C2×C4×C43#12114yes—
463C2×C4×C43#12314yes—
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—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43C4×D414yes—
504C2×Dic43#12014yes—
505C2×Dic43#12114yes—
506D172—416no—
507C4×D43—232no—
508C4×D43—232no—
509C4×D43—232no—
510#14696—431nomaximal, Sylow
511C22×C43C2×#11711yescharacteristic
512C22×C43C2×C4×D411yescharacteristic
513C22×C43C2×C4×D411yescharacteristic
514C22×C43C2×C4×D411yescharacteristic
515C22×C43C2×C4×D411yescharacteristic
516C22×C43C4×#4111yescharacteristic
517C22×C43C4×#4111yescharacteristic
518C22×C43C2×#12011yescharacteristic
519C22×C43C2×#12111yescharacteristic
520C22×C43C2×#12111yescharacteristic
521C22×C43C2×#12111yescharacteristic
522C22×C43C2×#12311yescharacteristic
523C22×C43C2×#12311yescharacteristic
524C22×C43#52511yescharacteristic
525C22×C43#52511yescharacteristic
526C22×C43#52511yescharacteristic
527C22×C43#52511yescharacteristic
528C22×C43#52511yescharacteristic
529C22×C43#52511yescharacteristic
530C22×C43#52511yescharacteristic
531C22×C43#52511yescharacteristic
532C22×C43#52511yescharacteristic
533C22×C43#52511yescharacteristic
534C22×C43C2×#12411yescharacteristic
535C22×C43C2×#12611yescharacteristic
536C22×C43#52911yescharacteristic
537C22×C43#52911yescharacteristic
538C22×C43#52911yescharacteristic
539C22×C43#52911yescharacteristic
540C22×C43#52911yescharacteristic
541C22×C43#52911yescharacteristic
542C22×C43#52911yescharacteristic
543C22×C43#52911yescharacteristic
544C22×C43#53211yescharacteristic
545C22×C43#53211yescharacteristic
546C2×D43—24no—
547C2×D43—24no—
548C2×D43—24no—
549C2×D43—24no—
550C2×D43—24no—
551C2×D43—24no—
552C2×D43—24no—
553C2×D43—24no—
554C2×D43—24no—
555C2×D43—24no—
556C2×D43—24no—
557C2×D43—24no—
558C2×D43—24no—
559C2×D43—24no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
563C2×D43—42no—
564C2×D43—42no—
565C2×D43—42no—
566C2×D43—42no—
567C2×D43—81no—
568C2×D43—81no—
569C2×D43—81no—
570C2×D43—81no—
571C2×D43—81no—
572C2×D43—81no—
573C2×D43—81no—
574C2×D43—81no—
575C2×D43#38818yescomplemented
576C4×C43—24no—
577C4×C43—24no—
578C4×C43—24no—
579C4×C43—42no—
580C4×C43—42no—
581C4×C43—81no—
582C4×C43—81no—
583Dic43—24no—
584Dic43—24no—
585Dic43—24no—
586Dic43—42no—
587Dic43—81no—
588Dic43—81no—
589C23×C42—431no—
590C2×#388—431no—
591C2×#388—431no—
592C2×#386—431no—
593C2×#386—431no—
594C2×#386—431no—
595C2×#385—431no—
596#1437—431no—
597#1437—431no—
598#1436—431no—
599#1436D4311yescharacteristic, complemented
600#1434—431no—
601#1434—431no—
602C22⋊#95—431no—
603C22⋊#95—431no—
604C2×C43C2×#38811yescharacteristic
605C2×C43#229011yescharacteristic
606C2×C43#229011yescharacteristic
607C2×C43C4×#12011yescharacteristic
608C2×C43C4×#12111yescharacteristic
609C2×C43C4×#12111yescharacteristic
610C2×C43C4×#12311yescharacteristic
611C2×C43#284711yescharacteristic
612C2×C43#284911yescharacteristic
613C2×C43#285011yescharacteristic
614C2×C43#285011yescharacteristic
615C2×C43#285211yescharacteristic
616C2×C43#285211yescharacteristic
617C2×C43#285311yescharacteristic
618C2×C43#285411yescharacteristic
619D43—28no—
620D43—82no—
621C23×D4—431no—
622C24×C4—431no—
623C24×C4—431no—
624C24×C4—431no—
625C22×C4⋊C4—431no—
626C22×C4⋊C4C2×D4311yescharacteristic
627C22×C22⋊C4—431no—
628C22×C22⋊C4—431no—
629C22×C22⋊C4—431no—
630C22×C22⋊C4—431no—
631C22×C22⋊C4—431no—
632C22×C22⋊C4—431no—
633C22×C22⋊C4—431no—
634C22×C22⋊C4—431no—
635C22×C22⋊C4—431no—
636C22×C42—431no—
637C22×C42—431no—
638C22×C42—431no—
639C22×C42—864no—
640C22×C42—864no—
641C22×C42—864no—
642C22×C42C2×D4311yescharacteristic
643#388—864no—
644#388—864no—
645#386—438no—
646#386—864no—
647#386—864no—
648#385—864no—
649C2×#95—431no—
650C2×#95—431no—
651C2×#95—431no—
652C2×#95—431no—
653C2×#95—431no—
654C2×#95—431no—
655C2×#95—431no—
656C2×#95—431no—
657C2×#95—431no—
658C2×#95—431no—
659C2×#95—431no—
660C2×#95C2×D4311yescharacteristic
661C2×#95C2×D4311yescharacteristic
662C2×#95C2×D4311yescharacteristic
663C2×#95C2×D4311yescharacteristic
664C2×#95C2×D4311yescharacteristic
665C43#1469611yescharacteristic, complemented, Sylow
666C25—431no—
667C25—431no—
668C22×D4—434no—
669C22×D4—862no—
670C22×D4—862no—
671C22×D4—862no—
672C22×D4—862no—
673C22×D4—862no—
674C22×D4—862no—
675C23×C4—431no—
676C23×C4—431no—
677C23×C4—431no—
678C23×C4—431no—
679C23×C4—434no—
680C23×C4—434no—
681C23×C4—434no—
682C23×C4—431no—
683C23×C4—431no—
684C23×C4—862no—
685C23×C4—862no—
686C23×C4—862no—
687C23×C4—862no—
688C23×C4—862no—
689C23×C4—862no—
690C23×C4—862no—
691C23×C4—862no—
692C23×C4—862no—
693C23×C4—862no—
694C23×C4—862no—
695C23×C4—862no—
696C23×C4—862no—
697C23×C4—862no—
698C23×C4—862no—
699C23×C4—862no—
700C23×C4—862no—
701C23×C4—862no—
702C23×C4C22×D4311yescharacteristic
703C23×C4C22×D4311yescharacteristic
704C23×C4C22×D4311yescharacteristic
705C23×C4C22×D4311yescharacteristic
706C23×C4C22×D4311yescharacteristic
707C23×C4C22×D4311yescharacteristic
708C23×C4C22×D4311yescharacteristic
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—862no—
713C2×C4⋊C4—862no—
714C2×C4⋊C4—862no—
715C2×C22⋊C4—434no—
716C2×C22⋊C4—434no—
717C2×C22⋊C4—434no—
718C2×C22⋊C4—862no—
719C2×C22⋊C4—862no—
720C2×C22⋊C4—862no—
721C2×C22⋊C4—862no—
722C2×C22⋊C4—862no—
723C2×C22⋊C4—862no—
724C2×C22⋊C4—862no—
725C2×C22⋊C4—862no—
726C2×C22⋊C4—862no—
727C2×C22⋊C4—862no—
728C2×C22⋊C4—862no—
729C2×C22⋊C4—862no—
730C2×C22⋊C4—862no—
731C2×C22⋊C4—862no—
732C2×C22⋊C4—862no—
733C2×C22⋊C4—862no—
734C2×C22⋊C4—862no—
735C2×C22⋊C4—862no—
736C2×C22⋊C4—862no—
737C2×C22⋊C4—862no—
738C2×C22⋊C4—862no—
739C2×C22⋊C4—862no—
740C2×C22⋊C4—862no—
741C2×C22⋊C4—862no—
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—434no—
746C2×C42—434no—
747C2×C42—8632no—
748C2×C42—862no—
749C2×C42—862no—
750C2×C42—862no—
751C2×C42—862no—
752C2×C42—862no—
753C2×C42—862no—
754C2×C42—862no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—434no—
760#95—862no—
761#95—862no—
762#95—862no—
763#95—862no—
764#95—862no—
765#95—862no—
766#95—862no—
767#95—862no—
768#95—862no—
769#95—862no—
770#95C4×D4314yescomplemented
771C24—432no—
772C24—432no—
773C24—432no—
774C24—432no—
775C24—432no—
776C24—432no—
777C24—432no—
778C24—432no—
779C24—861no—
780C24—861no—
781C24—861no—
782C24—861no—
783C24—861no—
784C24—861no—
785C24—861no—
786C24—861no—
787C24—861no—
788C24—861no—
789C24—861no—
790C24—861no—
791C24—861no—
792C24—861no—
793C24—861no—
794C24—861no—
795C24—861no—
796C24—861no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24—861no—
801C24C23×D4311yescharacteristic
802C2×D4—868no—
803C2×D4—868no—
804C2×D4—868no—
805C2×D4—1724no—
806C2×D4—1724no—
807C2×D4—1724no—
808C2×D4—1724no—
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—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—432no—
848C22×C4—432no—
849C22×C4—432no—
850C22×C4—432no—
851C22×C4—432no—
852C22×C4—432no—
853C22×C4—432no—
854C22×C4—432no—
855C22×C4—432no—
856C22×C4—432no—
857C22×C4—868no—
858C22×C4—868no—
859C22×C4—868no—
860C22×C4—868no—
861C22×C4—868no—
862C22×C4—868no—
863C22×C4—868no—
864C22×C4—868no—
865C22×C4—868no—
866C22×C4—868no—
867C22×C4—868no—
868C22×C4—868no—
869C22×C4—868no—
870C22×C4—868no—
871C22×C4—868no—
872C22×C4—868no—
873C22×C4—868no—
874C22×C4—868no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—868no—
888C22×C4—868no—
889C22×C4—868no—
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×C4C2×C4×D4312yes—
911C22×C4C2×C4×D4312yes—
912C22×C4C2×C4×D4312yes—
913C22×C4#1062189812yes—
914C22×C4#1062189812yes—
915C22×C4D4×D4312yes—
916C22×C4D4×D4312yes—
917C22×C4D4×D4312yes—
918C22×C4D4×D4312yes—
919C22×C4#1062190212yes—
920C22×C4#1062190212yes—
921C4⋊C4—44no—
922C4⋊C4—1724no—
923C22⋊C4—868no—
924C22⋊C4—868no—
925C22⋊C4—868no—
926C22⋊C4—1724no—
927C22⋊C4—1724no—
928C22⋊C4—1724no—
929C22⋊C4—1724no—
930C22⋊C4—1724no—
931C22⋊C4—1724no—
932C42—28no—
933C42—868no—
934C42—868no—
935C42—868no—
936C23—434no—
937C23—434no—
938C23—434no—
939C23—434no—
940C23—434no—
941C23—434no—
942C23—434no—
943C23—862no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—862no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
959C23—862no—
960C23—862no—
961C23—862no—
962C23—862no—
963C23—862no—
964C23—862no—
965C23—862no—
966C23—862no—
967C23—862no—
968C23—862no—
969C23—862no—
970C23—862no—
971C23—862no—
972C23—862no—
973C23—862no—
974C23—862no—
975C23—862no—
976C23—862no—
977C23—862no—
978C23—1721no—
979C23—1721no—
980C23—1721no—
981C23—1721no—
982C23—1721no—
983C23—1721no—
984C23—1721no—
985C23—1721no—
986C23—1721no—
987C23—1721no—
988C23—1721no—
989C23—1721no—
990C23—1721no—
991C23—1721no—
992C23—1721no—
993C23—1721no—
994C23—1721no—
995C23—1721no—
996C23—1721no—
997C23—1721no—
998C23—1721no—
999C23—1721no—
1000C23—1721no—
1001C23—1721no—
1002C23—1721no—
1003C23—1721no—
1004C23—1721no—
1005C23—1721no—
1006C23C22×C4×D4311yescharacteristic
1007C23C2×D4×D4311yescharacteristic
1008C23C2×D4×D4311yescharacteristic
1009C23C2×D4×D4311yescharacteristic
1010C23C2×D4×D4311yescharacteristic
1011C23#41×D4311yescharacteristic
1012C23#41×D4311yescharacteristic
1013C23#41×D4311yescharacteristic
1014C23#41×D4311yescharacteristic
1015C23#41×D4311yescharacteristic
1016C23#41×D4311yescharacteristic
1017C23C2×#1062189811yescharacteristic
1018C23C2×#1062189811yescharacteristic
1019C23C2×#1062190211yescharacteristic
1020C23C2×#1062190211yescharacteristic
1021D4—17216no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
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—434no—
1069C2×C4—434no—
1070C2×C4—434no—
1071C2×C4—8632no—
1072C2×C4—8632no—
1073C2×C4—8632no—
1074C2×C4—862no—
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—1721no—
1096C2×C4—1721no—
1097C2×C4—1721no—
1098C2×C4—1721no—
1099C2×C4—1721no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4—1721no—
1103C2×C4—1721no—
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#1306328714yes—
1114C2×C4#1306329814yes—
1115C2×C4#1306331014yes—
1116C22—438no—
1117C22—864no—
1118C22—864no—
1119C22—864no—
1120C22—864no—
1121C22—864no—
1122C22—864no—
1123C22—864no—
1124C22—864no—
1125C22—864no—
1126C22—864no—
1127C22—864no—
1128C22—864no—
1129C22—864no—
1130C22—864no—
1131C22—3441no—
1132C22—3441no—
1133C22—3441no—
1134C22—3441no—
1135C22—3441no—
1136C22—3441no—
1137C22—3441no—
1138C22—3441no—
1139C22—1722no—
1140C22—1722no—
1141C22—1722no—
1142C22—1722no—
1143C22—1722no—
1144C22—1722no—
1145C22—1722no—
1146C22#117×D4311yescharacteristic
1147C22C4×D4×D4311yescharacteristic
1148C22C4×D4×D4311yescharacteristic
1149C22C4×D4×D4311yescharacteristic
1150C22C2×#1306328711yescharacteristic
1151C22C4×#1062189811yescharacteristic
1152C22C4×#1062190211yescharacteristic
1153C22#120×D4311yescharacteristic
1154C22#121×D4311yescharacteristic
1155C22#121×D4311yescharacteristic
1156C22C2×#1306329811yescharacteristic
1157C22#123×D4311yescharacteristic
1158C22C2×#1306331011yescharacteristic
1159C22#1458340711yescharacteristic
1160C22#1458340711yescharacteristic
1161C22#1458340811yescharacteristic
1162C22#1458340811yescharacteristic
1163C22#1458340811yescharacteristic
1164C22#1458340811yescharacteristic
1165C22#1458341211yescharacteristic
1166C22#1458341211yescharacteristic
1167C22#1458341211yescharacteristic
1168C22#1458341211yescharacteristic
1169C22#124×D4311yescharacteristic
1170C22#126×D4311yescharacteristic
1171C22#1458342711yescharacteristic
1172C22#1458342711yescharacteristic
1173C22#1458343211yescharacteristic
1174C22#1458343411yescharacteristic
1175C22#1458343411yescharacteristic
1176C22#1458343611yescharacteristic
1177C22#1458343611yescharacteristic
1178C22#1458343611yescharacteristic
1179C22#1458344611yescharacteristic
1180C22#1458345011yescharacteristic
1181C4—24no—
1182C4—24no—
1183C4—24no—
1184C4—42no—
1185C4—42no—
1186C4—81no—
1187C4—81no—
1188C4—864no—
1189C4—864no—
1190C4—864no—
1191C4—3441no—
1192C4—3441no—
1193C4—1722no—
1194C2—868no—
1195C2—3442no—
1196C2#388×D4311yescharacteristic
1197C2#1913703311yescharacteristic
1198C2#1913703611yescharacteristic
1199C2#1913709611yescharacteristic
1200C2#1913710311yescharacteristic
1201C2C4×#1306329811yescharacteristic
1202C2C4×#1306331011yescharacteristic
1203C2#1914287611yescharacteristic
1204C2#1914289011yescharacteristic
1205C2#1914289311yescharacteristic
1206C2#1914289911yescharacteristic
1207C2#1914291311yescharacteristic
1208C2#1914291311yescharacteristic
1209C2#1914291911yescharacteristic
1210C2#1914292811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14696
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×C42×D43C2semidirect
2. C2×#14582789C2semidirect
3. C2×#14582788C2semidirect
7. C2×#14582770C2semidirect
8. #19132833C2semidirect
9. #19132831C2semidirect
10. #19132826C2semidirect
11. #19132821C2semidirect
12. #19132820C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1436C2semidirect
40. #14582777C4semidirect
124. C2×(C2×D43)⋊C4C2×C4semidirect
125. C2×(C2×D43)⋊C4C2×C4semidirect
133. C2×C4×Dic43D4semidirect
134. C2×C4×Dic43D4semidirect
146. C43⋊#95C2×C4semidirect
164. #95×C43C2×C4semidirect
575. C2×D43#388semidirect
599. #1436D43semidirect
665. C43#14696semidirect
770. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D432
C2×#145827892
C2×#145827882
C2×#145827772
C2×#145827702
#191328332
#191328312
#191328262
#191328212
#191328202
(C2×D43)⋊#952
C43×#14362
#1469643