Finite Group Databasebeta

← #25023930

Subgroups — #25023930

Order 11008.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063297C211yesmaximal, characteristic
2C2×#14582790C211yesmaximal, characteristic, complemented
3C2×#14582775C211yesmaximal, characteristic, complemented
4C2×#14582775C211yesmaximal, characteristic, complemented
5C2×#14582770C211yesmaximal, characteristic, complemented
6C2×#14582757C211yesmaximal, characteristic, complemented
7#19132845C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic, complemented
9#19132838C211yesmaximal, characteristic, complemented
10#19132836C211yesmaximal, characteristic, complemented
11#19132834C211yesmaximal, characteristic, complemented
12#19132834C211yesmaximal, characteristic, complemented
13#19132828C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C2×C43×#390C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063297—24no—
21C2×#13063297—24no—
22C2×#13063297C418yescomplemented
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35#14582790—24no—
36#14582775—24no—
37#14582775—24no—
38#14582770—24no—
39#14582757—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
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C22×C42×C43C2211yescharacteristic
59C43×#390—24no—
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—41no—
70C22×C22⋊D43—41no—
71C22×C22⋊D43—41no—
72C22×C22⋊D43—41no—
73C22×C22⋊D43C2×C414yes—
74C22×C22⋊D43C2×C414yes—
75C23×Dic43—22no—
76C23×Dic43—22no—
77C23×Dic43—22no—
78C23×Dic43—22no—
79C23×Dic43—41no—
80C23×Dic43—41no—
81C23×Dic43C2×C414yescomplemented
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—41no—
93C22×C4×D43—41no—
94C22×C4×D43—41no—
95C22×C4×D43—41no—
96#13063297—232no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—22no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4—41no—
104C2×Dic43⋊C4—41no—
105C2×Dic43⋊C4C2×C414yescomplemented
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—22no—
109C2×C22⋊Dic43—22no—
110C2×C22⋊Dic43—22no—
111C2×C22⋊Dic43—22no—
112C2×C22⋊Dic43—41no—
113C2×C22⋊Dic43—41no—
114C2×C22⋊Dic43—41no—
115C2×C22⋊Dic43—41no—
116C2×C22⋊Dic43—41no—
117C2×C22⋊Dic43—41no—
118C2×C22⋊Dic43—41no—
119C2×C22⋊Dic43—41no—
120C2×C22⋊Dic43C2×C414yescomplemented
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×(C2×D43)⋊C4—41no—
129C2×(C2×D43)⋊C4—41no—
130C2×(C2×D43)⋊C4C2×C414yes—
131C2×(C2×D43)⋊C4D414yes—
132C2×(C2×D43)⋊C4D414yes—
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⋊#95D414yescomplemented
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×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43—22no—
160C2×C4⋊C4×C43—22no—
161C2×C4⋊C4×C43—41no—
162C2×C22⋊C4×C43—22no—
163C2×C22⋊C4×C43—22no—
164C2×C22⋊C4×C43—22no—
165C2×C22⋊C4×C43—22no—
166C2×C22⋊C4×C43—22no—
167C2×C22⋊C4×C43—41no—
168C2×C22⋊C4×C43—41no—
169C2×C22⋊C4×C43—41no—
170C2×C22⋊C4×C43—41no—
171C2×C22⋊C4×C43—41no—
172C2×C22⋊C4×C43—41no—
173C2×C22⋊C4×C43D414yescomplemented
174C2×C42×C43—22no—
175C2×C42×C43—22no—
176C2×C42×C43—41no—
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×C43—21no—
202C24×C43—21no—
203C24×C43C22×C412yes—
204C24×C43C22×C412yes—
205C24×C43C2×D412yes—
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×D43C2×D412yes—
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—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—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×C43C22×C412yes—
260C22×C4×C43C2×D412yes—
261C22×C4×C43C2×D412yes—
262C22×C4×C43C2×D412yes—
263C22×C4×C43C2×D412yes—
264C22×C4×C43C2×D412yes—
265C2×C22⋊D43—28no—
266C2×C22⋊D43—28no—
267C2×C22⋊D43—28no—
268C2×C22⋊D43—28no—
269C2×C22⋊D43—44no—
270C2×C22⋊D43—44no—
271C2×C22⋊D43—44no—
272C2×C22⋊D43—44no—
273C2×C22⋊D43—44no—
274C2×C22⋊D43—44no—
275C2×C22⋊D43—44no—
276C2×C22⋊D43—44no—
277C2×C22⋊D43—44no—
278C2×C22⋊D43—44no—
279C22×Dic43—28no—
280C22×Dic43—28no—
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×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—44no—
323C22×Dic43—44no—
324C22×Dic43—44no—
325C22×Dic43—44no—
326C22×Dic43—44no—
327C22×Dic43C22×C412yes—
328C22×Dic43C22×C412yes—
329C22×Dic43C22×C412yes—
330C22×Dic43C2×D412yes—
331C22×Dic43C2×D412yes—
332C22×Dic43C2×D412yes—
333C22×Dic43C2×D412yes—
334C22×Dic43#4112yes—
335C2×C4×D43—44no—
336C2×C4×D43—44no—
337C2×C4×D43—44no—
338C2×C4×D43—44no—
339C2×C4×D43—44no—
340C2×C4×D43—44no—
341C2×C4×D43—44no—
342C4⋊C4×C43—44no—
343C22⋊C4×C43—44no—
344C22⋊C4×C43—44no—
345C22⋊C4×C43—44no—
346C22⋊C4×C43—44no—
347C42×C43—44no—
348C22⋊Dic43—28no—
349C22⋊Dic43—44no—
350C22⋊Dic43—44no—
351C22⋊Dic43—44no—
352C22⋊Dic43—44no—
353(C2×D43)⋊C4—44no—
354(C2×D43)⋊C4—44no—
355(C2×D43)⋊C4—44no—
356(C2×D43)⋊C4C22⋊C4116yescomplemented
357Dic43⋊C4—28no—
358Dic43⋊C4—44no—
359Dic43⋊C4—44no—
360C23×C43—22no—
361C23×C43—22no—
362C23×C43—22no—
363C23×C43—22no—
364C23×C43—22no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—22no—
368C23×C43—22no—
369C23×C43—22no—
370C23×C43—22no—
371C23×C43—22no—
372C23×C43—22no—
373C23×C43—22no—
374C23×C43—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—41no—
386C23×C43—41no—
387C23×C43—41no—
388C23×C43—41no—
389C23×C43—41no—
390C23×C43—41no—
391C23×C43—41no—
392C23×C43—41no—
393C23×C43—41no—
394C23×C43—41no—
395C23×C43—41no—
396C23×C43—41no—
397C23×C43—41no—
398C23×C43—41no—
399C23×C43—41no—
400C23×C43—41no—
401C23×C43—41no—
402C23×C43—41no—
403C23×C43—41no—
404C23×C43—41no—
405C23×C43—41no—
406C23×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×C43C4×D414yes—
430C23×C43C23×C411yescharacteristic
431C23×C43C22×D411yescharacteristic
432C23×C43C22×D411yescharacteristic
433C23×C43C22×D411yescharacteristic
434C23×C43C22×D411yescharacteristic
435C23×C43C2×#4111yescharacteristic
436C23×C43C2×#4111yescharacteristic
437C23×C43H(5,𝔽2)11yescharacteristic
438C23×C43H(5,𝔽2)11yescharacteristic
439C23×C43H(5,𝔽2)11yescharacteristic
440C23×C43H(5,𝔽2)11yescharacteristic
441C23×C43H(5,𝔽2)11yescharacteristic
442C23×C43H(5,𝔽2)11yescharacteristic
443C23×C432−1+411yescharacteristic
444C23×C432−1+411yescharacteristic
445C22×D43—22no—
446C22×D43—22no—
447C22×D43—22no—
448C22×D43—22no—
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—41no—
464C22×D43—41no—
465C22×D43—41no—
466C22×D43—41no—
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×D43C2×C22⋊C414yes—
480D4×C43—416no—
481C2×C4×C43—22no—
482C2×C4×C43—22no—
483C2×C4×C43—22no—
484C2×C4×C43—22no—
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—41no—
497C2×C4×C43—41no—
498C2×C4×C43—41no—
499C2×C4×C43—41no—
500C2×C4×C43—41no—
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×C43C2×C22⋊C414yes—
516C22⋊D43—416no—
517C22⋊D43—416no—
518C2×Dic43—22no—
519C2×Dic43—22no—
520C2×Dic43—22no—
521C2×Dic43—22no—
522C2×Dic43—22no—
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—416no—
537C2×Dic43—41no—
538C2×Dic43—41no—
539C2×Dic43—41no—
540C2×Dic43—41no—
541C2×Dic43—41no—
542C2×Dic43—41no—
543C2×Dic43—41no—
544C2×Dic43—41no—
545C2×Dic43—41no—
546C2×Dic43—41no—
547C2×Dic43—41no—
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×Dic43C2×C22⋊C414yes—
567C2×Dic43C4×D414yes—
568C4×D43—416no—
569#14361—431nomaximal, Sylow
570C22×C43—24no—
571C22×C43—24no—
572C22×C43—24no—
573C22×C43—42no—
574C22×C43—42no—
575C22×C43—42no—
576C22×C43—42no—
577C22×C43—42no—
578C22×C43—42no—
579C22×C43—42no—
580C22×C43—42no—
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—81no—
593C22×C43—81no—
594C22×C43—81no—
595C22×C43—81no—
596C22×C43—81no—
597C22×C43—81no—
598C22×C43—81no—
599C22×C43—81no—
600C22×C43C22×C22⋊C411yescharacteristic
601C22×C43C2×C4×D411yescharacteristic
602C22×C43C2×C4×D411yescharacteristic
603C22×C43#51811yescharacteristic
604C22×C43#51811yescharacteristic
605C22×C43#52011yescharacteristic
606C22×C43#52011yescharacteristic
607C22×C43#53411yescharacteristic
608C22×C43#53511yescharacteristic
609C22×C43#53511yescharacteristic
610C22×C43#53611yescharacteristic
611C22×C43#53711yescharacteristic
612C22×C43#53711yescharacteristic
613C22×C43#53711yescharacteristic
614C22×C43#53711yescharacteristic
615C22×C43#53811yescharacteristic
616C22×C43#53911yescharacteristic
617C22×C43#54011yescharacteristic
618C22×C43#54211yescharacteristic
619C22×C43D4211yescharacteristic
620C22×C43D4211yescharacteristic
621C22×C43D4211yescharacteristic
622C22×C43D4211yescharacteristic
623C22×C43D4211yescharacteristic
624C22×C43#54611yescharacteristic
625C22×C43#54611yescharacteristic
626C22×C43#54611yescharacteristic
627C22×C43#54611yescharacteristic
628C22×C43#54711yescharacteristic
629C22×C43#54811yescharacteristic
630C22×C43#55311yescharacteristic
631C22×C43#56011yescharacteristic
632C22×C43#56011yescharacteristic
633C22×C43#56211yescharacteristic
634C22×C43#56211yescharacteristic
635C2×D43—24no—
636C2×D43—24no—
637C2×D43—24no—
638C2×D43—42no—
639C2×D43—42no—
640C2×D43—42no—
641C2×D43—42no—
642C2×D43—42no—
643C2×D43—42no—
644C2×D43—42no—
645C2×D43—42no—
646C2×D43—42no—
647C2×D43—42no—
648C2×D43—42no—
649C2×D43—42no—
650C4×C43—24no—
651C4×C43—42no—
652C4×C43—42no—
653C4×C43—42no—
654C4×C43—81no—
655Dic43—24no—
656Dic43—24no—
657Dic43—42no—
658Dic43—42no—
659Dic43—81no—
660Dic43—81no—
661Dic43—81no—
662C22×#121—431no—
663C2×#390D4311yescharacteristic, complemented
664C2×#388—431no—
665C2×#386—431no—
666C2×#386—431no—
667C2×#385—431no—
668C2×#380—431no—
669#1441—431no—
670#1439—431no—
671#1439—431no—
672#1438—431no—
673#1438—431no—
674#1438—431no—
675#1436—431no—
676C22⋊#95—431no—
677C2×C43—44no—
678C2×C43—82no—
679C2×C43#231111yescharacteristic
680C2×C43#232411yescharacteristic
681C2×C43#232511yescharacteristic
682C2×C43D4×C22⋊C411yescharacteristic
683C2×C43D4×C22⋊C411yescharacteristic
684C2×C43#236111yescharacteristic
685C2×C43#237711yescharacteristic
686C2×C43#266911yescharacteristic
687C2×C43#267111yescharacteristic
688C2×C43#267211yescharacteristic
689C2×C43#267511yescharacteristic
690C2×C43#267611yescharacteristic
691C2×C43#268111yescharacteristic
692C2×C43#269111yescharacteristic
693C2×C43#270311yescharacteristic
694D43—44no—
695C23×D4—431no—
696C23×D4—431no—
697C23×D4C2×D4311yescharacteristic
698C24×C4—431no—
699C24×C4—431no—
700C2×#121—438no—
701C2×#121—864no—
702C2×#121—864no—
703C22×C4⋊C4—431no—
704C22×C4⋊C4—431no—
705C22×C4⋊C4—431no—
706C22×C4⋊C4C2×D4311yescharacteristic
707C22×C22⋊C4—431no—
708C22×C22⋊C4—431no—
709C22×C22⋊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⋊C4C2×D4311yescharacteristic
717C22×C22⋊C4C2×D4311yescharacteristic
718C22×C22⋊C4C2×D4311yescharacteristic
719C22×C22⋊C4C2×D4311yescharacteristic
720C22×C42C2×D4311yescharacteristic
721#390—24no—
722#388—864no—
723#386—864no—
724#386—864no—
725#385—864no—
726#380—864no—
727C2×#95—431no—
728C2×#95—431no—
729C2×#95—431no—
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—
739C43#1436111yescharacteristic, complemented, Sylow
740C25—431no—
741C25C22×D4311yescharacteristic
742C25C22×D4311yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—434no—
750C22×D4—434no—
751C22×D4—862no—
752C22×D4—862no—
753C22×D4—862no—
754C22×D4—862no—
755C22×D4—862no—
756C22×D4—862no—
757C22×D4—862no—
758C22×D4—862no—
759C22×D4—1721no—
760C22×D4—1721no—
761C22×D4—1721no—
762C22×D4—1721no—
763C22×D4C4×D4314yescomplemented
764C23×C4—431no—
765C23×C4—431no—
766C23×C4—431no—
767C23×C4—431no—
768C23×C4—434no—
769C23×C4—431no—
770C23×C4—431no—
771C23×C4—431no—
772C23×C4—862no—
773C23×C4—862no—
774C23×C4—862no—
775C23×C4—862no—
776C23×C4—862no—
777C23×C4—862no—
778C23×C4—862no—
779C23×C4—1721no—
780C23×C4—1721no—
781C23×C4—1721no—
782C23×C4—1721no—
783C23×C4—1721no—
784C23×C4—1721no—
785C23×C4C22×D4311yescharacteristic
786C23×C4C22×D4311yescharacteristic
787C23×C4C22×D4311yescharacteristic
788C23×C4C22×D4311yescharacteristic
789C23×C4C22×D4311yescharacteristic
790#121—8632no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—41no—
794C2×C4⋊C4—434no—
795C2×C4⋊C4—862no—
796C2×C4⋊C4—862no—
797C2×C4⋊C4—862no—
798C2×C4⋊C4—862no—
799C2×C4⋊C4—862no—
800C2×C4⋊C4—862no—
801C2×C4⋊C4—1721no—
802C2×C4⋊C4—1721no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
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—862no—
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—1721no—
830C2×C22⋊C4—1721no—
831C2×C22⋊C4—1721no—
832C2×C22⋊C4—1721no—
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—22no—
843C2×C42—22no—
844C2×C42—41no—
845#95—434no—
846#95—862no—
847#95—862no—
848#95—862no—
849#95—862no—
850#95—862no—
851#95—862no—
852#95—862no—
853#95—862no—
854#95—862no—
855#95—1721no—
856#95—1721no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
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—432no—
884C24—432no—
885C24—432no—
886C24—861no—
887C24—861no—
888C24—861no—
889C24—861no—
890C24—861no—
891C24—861no—
892C24—861no—
893C24—861no—
894C24—861no—
895C24—861no—
896C24—861no—
897C24—861no—
898C24C2×C4×D4312yes—
899C24C2×C4×D4312yes—
900C24#1062189812yes—
901C24C2×C22⋊D4312yes—
902C24C23×D4311yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—868no—
911C2×D4—868no—
912C2×D4—868no—
913C2×D4—868no—
914C2×D4—1724no—
915C2×D4—1724no—
916C2×D4—1724no—
917C2×D4—1724no—
918C2×D4—1724no—
919C2×D4—1724no—
920C2×D4—1724no—
921C2×D4—1724no—
922C2×D4—1724no—
923C2×D4—1724no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
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—432no—
954C22×C4—432no—
955C22×C4—432no—
956C22×C4—432no—
957C22×C4—432no—
958C22×C4—432no—
959C22×C4—432no—
960C22×C4—432no—
961C22×C4—868no—
962C22×C4—868no—
963C22×C4—861no—
964C22×C4—861no—
965C22×C4—861no—
966C22×C4—861no—
967C22×C4—861no—
968C22×C4—861no—
969C22×C4—861no—
970C22×C4—861no—
971C22×C4—861no—
972C22×C4—861no—
973C22×C4—861no—
974C22×C4—861no—
975C22×C4—861no—
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—861no—
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—1724no—
1005C22×C4—1724no—
1006C22×C4—1724no—
1007C22×C4—1724no—
1008C22×C4—1724no—
1009C22×C4—1724no—
1010C22×C4—1724no—
1011C22×C4—1724no—
1012C22×C4—1724no—
1013C22×C4—1724no—
1014C22×C4—1724no—
1015C22×C4—1724no—
1016C22×C4C2×C4×D4312yes—
1017C22×C4D4×D4312yes—
1018C22×C4D4×D4312yes—
1019C22×C4D4×D4312yes—
1020C22×C4C2×C22⋊D4312yes—
1021C22×C4C2×C22⋊D4312yes—
1022C4⋊C4—44no—
1023C4⋊C4—868no—
1024C4⋊C4—1724no—
1025C4⋊C4—1724no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—4316no—
1031C22⋊C4—868no—
1032C22⋊C4—1724no—
1033C22⋊C4—1724no—
1034C22⋊C4—1724no—
1035C22⋊C4—1724no—
1036C22⋊C4—1724no—
1037C22⋊C4—1724no—
1038C22⋊C4—1724no—
1039C42—44no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
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—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
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—434no—
1110C23—862no—
1111C23—862no—
1112C23—862no—
1113C23—862no—
1114C23—862no—
1115C23—862no—
1116C23—862no—
1117C23—862no—
1118C23—862no—
1119C23—862no—
1120C23—862no—
1121C23—862no—
1122C23—862no—
1123C23—862no—
1124C23—862no—
1125C23—862no—
1126C23—862no—
1127C23—862no—
1128C23—1721no—
1129C23—1721no—
1130C23—1721no—
1131C23—1721no—
1132C23—1721no—
1133C23—1721no—
1134C23—1721no—
1135C23—1721no—
1136C23—1721no—
1137C23—1721no—
1138C23—1721no—
1139C23—1721no—
1140C23—1721no—
1141C23—1721no—
1142C23—1721no—
1143C23—1721no—
1144C23C4×C22⋊D4314yes—
1145C23C22×C4×D4311yescharacteristic
1146C23C2×D4×D4311yescharacteristic
1147C23C2×D4×D4311yescharacteristic
1148C23C2×D4×D4311yescharacteristic
1149C23C22×C22⋊D4311yescharacteristic
1150C23#41×D4311yescharacteristic
1151C23C2×#1062189811yescharacteristic
1152C23#1306337011yescharacteristic
1153C23#1306337011yescharacteristic
1154C23#1306337011yescharacteristic
1155C23#1306337011yescharacteristic
1156C23#1306337011yescharacteristic
1157C23#1306337111yescharacteristic
1158C23#1306337211yescharacteristic
1159C23#1306337211yescharacteristic
1160D4—416no—
1161D4—17216no—
1162D4—17216no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
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—434no—
1198C2×C4—434no—
1199C2×C4—862no—
1200C2×C4—862no—
1201C2×C4—862no—
1202C2×C4—862no—
1203C2×C4—862no—
1204C2×C4—862no—
1205C2×C4—862no—
1206C2×C4—862no—
1207C2×C4—862no—
1208C2×C4—862no—
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—17216no—
1218C2×C4—17216no—
1219C2×C4—1721no—
1220C2×C4—1721no—
1221C2×C4—1721no—
1222C2×C4—1721no—
1223C2×C4—1721no—
1224C2×C4—1721no—
1225C2×C4—1721no—
1226C2×C4—1721no—
1227C2×C4—1721no—
1228C2×C4—1721no—
1229C2×C4—1721no—
1230C2×C4—1721no—
1231C2×C4—1721no—
1232C2×C4—1721no—
1233C2×C4—1721no—
1234C2×C4—1721no—
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×C4C22⋊C4×D4314yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—864no—
1280C22—864no—
1281C22—864no—
1282C22—1722no—
1283C22—1722no—
1284C22—1722no—
1285C22—1722no—
1286C22—1722no—
1287C22—1722no—
1288C22—1722no—
1289C22—1722no—
1290C22—1722no—
1291C22—1722no—
1292C22—1722no—
1293C22—1722no—
1294C22C2×C22⋊C4×D4311yescharacteristic
1295C22C4×D4×D4311yescharacteristic
1296C22C2×C4×C22⋊D4311yescharacteristic
1297C22#1458337111yescharacteristic
1298C22#1458337211yescharacteristic
1299C22#1458337811yescharacteristic
1300C22#1458337811yescharacteristic
1301C22#1458345811yescharacteristic
1302C22#1458346211yescharacteristic
1303C22#1458346211yescharacteristic
1304C22#1458346911yescharacteristic
1305C22#1458347611yescharacteristic
1306C22#1458347711yescharacteristic
1307C22#1458347811yescharacteristic
1308C22#1458347811yescharacteristic
1309C22#1458348211yescharacteristic
1310C22#1458349111yescharacteristic
1311C22#1458349911yescharacteristic
1312C22#1458351311yescharacteristic
1313C22D4×C22⋊D4311yescharacteristic
1314C22D4×C22⋊D4311yescharacteristic
1315C22D4×C22⋊D4311yescharacteristic
1316C22#1458353311yescharacteristic
1317C22#1458353411yescharacteristic
1318C22#1458353911yescharacteristic
1319C22#1458353911yescharacteristic
1320C22#1458354211yescharacteristic
1321C22#1458354611yescharacteristic
1322C22#1458354811yescharacteristic
1323C22#1458355811yescharacteristic
1324C22#1458359811yescharacteristic
1325C22#1458363611yescharacteristic
1326C22#1458363711yescharacteristic
1327C22#1458364311yescharacteristic
1328C22#1458364411yescharacteristic
1329C4—24no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—81no—
1334C4—864no—
1335C4—864no—
1336C4—3441no—
1337C4—3441no—
1338C4—3441no—
1339C4—1722no—
1340C4—1722no—
1341C2—44no—
1342C2—82no—
1343C2—1724no—
1344C2#1913718511yescharacteristic
1345C2#1913728111yescharacteristic
1346C2#1913729311yescharacteristic
1347C2C22⋊C4×C22⋊D4311yescharacteristic
1348C2#1913741611yescharacteristic
1349C2#1913761211yescharacteristic
1350C2#1913774611yescharacteristic
1351C2#1914080811yescharacteristic
1352C2#1914082711yescharacteristic
1353C2#1914084111yescharacteristic
1354C2#1914088511yescharacteristic
1355C2#1914089311yescharacteristic
1356C2#1914094411yescharacteristic
1357C2#1914107711yescharacteristic
1358C2#1914123511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#390C2
socle, cosocleC24×C43C24
prime radicalC22×#13063297C2
hypercenterC2×#390D43
hypocenterC43#14361
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#14582790C2semidirect
3. C2×#14582775C2semidirect
4. C2×#14582775C2semidirect
5. C2×#14582770C2semidirect
6. C2×#14582757C2semidirect
7. #19132845C2semidirect
8. #19132838C2semidirect
9. #19132838C2semidirect
10. #19132836C2semidirect
11. #19132834C2semidirect
12. #19132834C2semidirect
13. #19132828C2semidirect
14. #19132817C2semidirect
15. C2×C43×#390C2semidirect
22. C2×#13063297C4semidirect
81. C23×Dic43C2×C4semidirect
105. C2×Dic43⋊C4C2×C4semidirect
120. C2×C22⋊Dic43C2×C4semidirect
144. C43⋊#95D4semidirect
153. C22×D4×C43C2×C4semidirect
173. C2×C22⋊C4×C43D4semidirect
356. (C2×D43)⋊C4C22⋊C4semidirect
663. C2×#390D43semidirect
739. C43#14361semidirect
763. C22×D4C4×D43semidirect
841. C2×C22⋊C4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632972
C2×#145827902
C2×#145827752
C2×#145827702
C2×#145827572
#191328452
#191328382
#191328362
#191328342
#191328282
#191328172
C2×C43×#3902
#1436143