Finite Group Databasebeta

← #25023957

Subgroups — #25023957

Order 11008.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063296C211yesmaximal, characteristic
2C2×#14582799C211yesmaximal, characteristic, complemented
3C2×#14582778C211yesmaximal, characteristic, complemented
4C2×#14582761C211yesmaximal, characteristic, complemented
5#19132847C211yesmaximal, characteristic, complemented
6#19132842C211yesmaximal, characteristic, complemented
7#19132838C211yesmaximal, characteristic, complemented
8#19132836C211yesmaximal, characteristic, complemented
9#19132834C211yesmaximal, characteristic, complemented
10#19132834C211yesmaximal, characteristic, complemented
11#19132832C211yesmaximal, characteristic, complemented
12#19132829C211yesmaximal, characteristic, complemented
13#19132818C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063296—24no—
20C2×#13063296—24no—
21C2×#13063296C418yescomplemented
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582799—24no—
36#14582778—24no—
37#14582761—24no—
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
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
50C23×D4×C43C2211yescharacteristic
51C24×C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C43×#386—24no—
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C22×C22⋊D43—22no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—41no—
62C22×C22⋊D43—41no—
63C22×C22⋊D43—41no—
64C22×C22⋊D43—41no—
65C22×C22⋊D43—41no—
66C22×C22⋊D43—41no—
67C22×C22⋊D43—41no—
68C22×C22⋊D43—41no—
69C22×C22⋊D43C2×C414yes—
70C22×C22⋊D43C2×C414yescomplemented
71C22×C22⋊D43D414yes—
72C22×C22⋊D43D414yes—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
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#13063296—232no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43C2×C414yescomplemented
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—41no—
93C2×Dic43⋊C4—41no—
94C2×C22⋊Dic43—22no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—22no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—22no—
102C2×C22⋊Dic43—41no—
103C2×C22⋊Dic43—41no—
104C2×C22⋊Dic43—41no—
105C2×C22⋊Dic43—41no—
106C2×C22⋊Dic43—41no—
107C2×C22⋊Dic43—41no—
108C2×C22⋊Dic43—41no—
109C2×C22⋊Dic43—41no—
110C2×C22⋊Dic43C2×C414yes—
111C2×C22⋊Dic43C2×C414yescomplemented
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—41no—
121C2×(C2×D43)⋊C4—41no—
122C2×(C2×D43)⋊C4—41no—
123C2×(C2×D43)⋊C4—41no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—41no—
126C2×C4×Dic43—41no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C43⋊#95—41no—
136C43⋊#95—41no—
137C43⋊#95—41no—
138C43⋊#95—41no—
139C25×C43C2311yescharacteristic
140C25×C43C2311yescharacteristic
141C22×D4×C43—22no—
142C22×D4×C43—22no—
143C22×D4×C43—22no—
144C22×D4×C43—22no—
145C22×D4×C43—41no—
146C22×D4×C43—41no—
147C22×D4×C43C2×C414yes—
148C23×C4×C43—22no—
149C23×C4×C43—22no—
150C23×C4×C43—22no—
151C23×C4×C43—41no—
152C23×C4×C43—41no—
153C23×C4×C43—41no—
154C23×C4×C43—41no—
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—22no—
161C2×C22⋊C4×C43—22no—
162C2×C22⋊C4×C43—22no—
163C2×C22⋊C4×C43—22no—
164C2×C22⋊C4×C43—22no—
165C2×C22⋊C4×C43—41no—
166C2×C22⋊C4×C43—41no—
167C2×C22⋊C4×C43—41no—
168C2×C22⋊C4×C43—41no—
169#95×C43—22no—
170#95×C43D414yescomplemented
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×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×C43C22×C412yes—
198C24×C43C22×C412yes—
199C24×C43C2×D412yes—
200C24×C43C2×D412yes—
201C24×C43C2411yescharacteristic
202C23×D43—21no—
203C23×D43—21no—
204C23×D43—21no—
205C23×D43—21no—
206C23×D43—21no—
207C23×D43—21no—
208C23×D43—21no—
209C23×D43—21no—
210C23×D43—21no—
211C23×D43—21no—
212C23×D43—21no—
213C23×D43—21no—
214C23×D43C22×C412yes—
215C23×D43C2×D412yes—
216C23×D43C2×D412yes—
217C2×D4×C43—28no—
218C2×D4×C43—28no—
219C2×D4×C43—44no—
220C2×D4×C43—44no—
221C2×D4×C43—44no—
222C2×D4×C43—44no—
223C2×D4×C43—44no—
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—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—44no—
254C22×C4×C43—44no—
255C22×C4×C43—44no—
256C22×C4×C43—44no—
257C22×C4×C43—44no—
258C22×C4×C43—44no—
259C22×C4×C43—44no—
260C22×C4×C43C22×C412yes—
261C22×C4×C43C2×D412yes—
262C22×C4×C43C2×D412yes—
263C22×C4×C43C2×D412yes—
264C22×C4×C43#4112yes—
265C22×C4×C43#4112yes—
266C2×C22⋊D43—28no—
267C2×C22⋊D43—44no—
268C2×C22⋊D43—44no—
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—
279C2×C22⋊D43C22⋊C4116yescomplemented
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×Dic43—21no—
298C22×Dic43—21no—
299C22×Dic43—21no—
300C22×Dic43—21no—
301C22×Dic43—21no—
302C22×Dic43—21no—
303C22×Dic43—21no—
304C22×Dic43—21no—
305C22×Dic43—21no—
306C22×Dic43—21no—
307C22×Dic43—21no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43—21no—
312C22×Dic43—21no—
313C22×Dic43—21no—
314C22×Dic43—21no—
315C22×Dic43—21no—
316C22×Dic43—21no—
317C22×Dic43—21no—
318C22×Dic43—21no—
319C22×Dic43—21no—
320C22×Dic43—21no—
321C22×Dic43—21no—
322C22×Dic43—21no—
323C22×Dic43C22×C412yes—
324C22×Dic43C22×C412yes—
325C22×Dic43C22×C412yes—
326C22×Dic43C2×D412yes—
327C22×Dic43C2×D412yes—
328C22×Dic43#4112yes—
329C2×C4×D43—28no—
330C2×C4×D43—28no—
331C2×C4×D43—44no—
332C2×C4×D43—44no—
333C2×C4×D43—44no—
334C2×C4×D43—44no—
335C2×C4×D43—44no—
336C22⋊C4×C43—44no—
337C22⋊C4×C43—44no—
338C22⋊C4×C43—44no—
339C22⋊Dic43—28no—
340C22⋊Dic43—28no—
341C22⋊Dic43—44no—
342C22⋊Dic43—44no—
343C22⋊Dic43—44no—
344C22⋊Dic43—44no—
345(C2×D43)⋊C4—44no—
346(C2×D43)⋊C4—44no—
347(C2×D43)⋊C4—44no—
348(C2×D43)⋊C4—44no—
349C4⋊Dic43—28no—
350Dic43⋊C4—44no—
351C4×Dic43—44no—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—22no—
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—41no—
378C23×C43—41no—
379C23×C43—41no—
380C23×C43—41no—
381C23×C43—41no—
382C23×C43—41no—
383C23×C43—41no—
384C23×C43—41no—
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×C43C2×C22⋊C414yes—
422C23×C43C23×C411yescharacteristic
423C23×C43C22×D411yescharacteristic
424C23×C43C22×D411yescharacteristic
425C23×C43C22×D411yescharacteristic
426C23×C43C2×#4111yescharacteristic
427C23×C43C2×#4111yescharacteristic
428C23×C43C2×#4111yescharacteristic
429C23×C43H(5,𝔽2)11yescharacteristic
430C23×C43H(5,𝔽2)11yescharacteristic
431C23×C43H(5,𝔽2)11yescharacteristic
432C23×C43H(5,𝔽2)11yescharacteristic
433C23×C43H(5,𝔽2)11yescharacteristic
434C23×C43H(5,𝔽2)11yescharacteristic
435C23×C43H(5,𝔽2)11yescharacteristic
436C23×C432−1+411yescharacteristic
437C22×D43—22no—
438C22×D43—22no—
439C22×D43—22no—
440C22×D43—22no—
441C22×D43—22no—
442C22×D43—22no—
443C22×D43—22no—
444C22×D43—22no—
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—41no—
456C22×D43—41no—
457C22×D43—41no—
458C22×D43—41no—
459C22×D43—41no—
460C22×D43—41no—
461C22×D43—41no—
462C22×D43—41no—
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×D43C2×C22⋊C414yes—
472D4×C43—416no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—22no—
476C2×C4×C43—22no—
477C2×C4×C43—22no—
478C2×C4×C43—22no—
479C2×C4×C43—22no—
480C2×C4×C43—22no—
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—416no—
489C2×C4×C43—41no—
490C2×C4×C43—41no—
491C2×C4×C43—41no—
492C2×C4×C43—41no—
493C2×C4×C43—41no—
494C2×C4×C43—41no—
495C2×C4×C43—41no—
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×C43C4×D414yes—
509C22⋊D43—416no—
510C22⋊D43—416no—
511C2×Dic43—22no—
512C2×Dic43—22no—
513C2×Dic43—22no—
514C2×Dic43—22no—
515C2×Dic43—22no—
516C2×Dic43—22no—
517C2×Dic43—22no—
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—41no—
527C2×Dic43—41no—
528C2×Dic43—41no—
529C2×Dic43—41no—
530C2×Dic43—41no—
531C2×Dic43—41no—
532C2×Dic43—41no—
533C2×Dic43—41no—
534C2×Dic43—41no—
535C2×Dic43—41no—
536C2×Dic43—41no—
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×Dic43C2×C22⋊C414yes—
560C4×D43—416no—
561#14363—431nomaximal, Sylow
562C22×C43—24no—
563C22×C43—24no—
564C22×C43—24no—
565C22×C43—42no—
566C22×C43—42no—
567C22×C43—42no—
568C22×C43—42no—
569C22×C43—42no—
570C22×C43—42no—
571C22×C43—42no—
572C22×C43—42no—
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—81no—
585C22×C43—81no—
586C22×C43—81no—
587C22×C43—81no—
588C22×C43—81no—
589C22×C43—81no—
590C22×C43—81no—
591C22×C43—81no—
592C22×C43C22×C22⋊C411yescharacteristic
593C22×C43C2×C4×D411yescharacteristic
594C22×C43C4×#4111yescharacteristic
595C22×C43#51811yescharacteristic
596C22×C43#51811yescharacteristic
597C22×C43#51811yescharacteristic
598C22×C43#52011yescharacteristic
599C22×C43#53411yescharacteristic
600C22×C43#53411yescharacteristic
601C22×C43#53411yescharacteristic
602C22×C43#53411yescharacteristic
603C22×C43#53511yescharacteristic
604C22×C43#53711yescharacteristic
605C22×C43#53811yescharacteristic
606C22×C43#53811yescharacteristic
607C22×C43#54011yescharacteristic
608C22×C43#54011yescharacteristic
609C22×C43#54011yescharacteristic
610C22×C43#54211yescharacteristic
611C22×C43D4211yescharacteristic
612C22×C43D4211yescharacteristic
613C22×C43#54611yescharacteristic
614C22×C43#54611yescharacteristic
615C22×C43#54611yescharacteristic
616C22×C43#54611yescharacteristic
617C22×C43#54611yescharacteristic
618C22×C43#54711yescharacteristic
619C22×C43#54711yescharacteristic
620C22×C43#55011yescharacteristic
621C22×C43#55311yescharacteristic
622C22×C43#55511yescharacteristic
623C22×C43#56011yescharacteristic
624C22×C43#56011yescharacteristic
625C22×C43#56211yescharacteristic
626C22×C43#56211yescharacteristic
627C2×D43—24no—
628C2×D43—24no—
629C2×D43—24no—
630C2×D43—42no—
631C2×D43—42no—
632C2×D43—42no—
633C2×D43—42no—
634C2×D43—42no—
635C2×D43—42no—
636C2×D43—42no—
637C2×D43—42no—
638C2×D43—42no—
639C2×D43—42no—
640C2×D43—42no—
641C2×D43—42no—
642C4×C43—24no—
643C4×C43—42no—
644C4×C43—42no—
645C4×C43—42no—
646C4×C43—81no—
647Dic43—24no—
648Dic43—42no—
649Dic43—42no—
650Dic43—42no—
651Dic43—81no—
652Dic43—81no—
653Dic43—81no—
654C22×#121—431no—
655C2×#390—431no—
656C2×#386—431no—
657C2×#386D4311yescharacteristic, complemented
658C2×#381—431no—
659#1441—431no—
660#1440—431no—
661#1439—431no—
662#1438—431no—
663#1438—431no—
664#1438—431no—
665#1437—431no—
666#1436—431no—
667C22⋊#95—431no—
668C22⋊#95—431no—
669C2×C43—44no—
670C2×C43—82no—
671C2×C43#230811yescharacteristic
672C2×C43#232411yescharacteristic
673C2×C43#233311yescharacteristic
674C2×C43D4×C22⋊C411yescharacteristic
675C2×C43#233911yescharacteristic
676C2×C43#236311yescharacteristic
677C2×C43#237711yescharacteristic
678C2×C43#267111yescharacteristic
679C2×C43#267311yescharacteristic
680C2×C43#267811yescharacteristic
681C2×C43#268211yescharacteristic
682C2×C43#268611yescharacteristic
683C2×C43#268811yescharacteristic
684C2×C43#269911yescharacteristic
685C2×C43#270111yescharacteristic
686D43—44no—
687C23×D4—431no—
688C23×D4—431no—
689C23×D4C2×D4311yescharacteristic
690C24×C4—431no—
691C24×C4C2×D4311yescharacteristic
692C2×#121—438no—
693C2×#121—864no—
694C2×#121—864no—
695C22×C4⋊C4—431no—
696C22×C4⋊C4—431no—
697C22×C22⋊C4—431no—
698C22×C22⋊C4—431no—
699C22×C22⋊C4—431no—
700C22×C22⋊C4—431no—
701C22×C22⋊C4—431no—
702C22×C22⋊C4—431no—
703C22×C22⋊C4—431no—
704C22×C22⋊C4—431no—
705C22×C22⋊C4—431no—
706C22×C22⋊C4—431no—
707C22×C22⋊C4C2×D4311yescharacteristic
708C22×C22⋊C4C2×D4311yescharacteristic
709C22×C22⋊C4C2×D4311yescharacteristic
710C22×C42—431no—
711#390—864no—
712#386—24no—
713#386—864no—
714#381—864no—
715C2×#95—431no—
716C2×#95—431no—
717C2×#95—431no—
718C2×#95—431no—
719C2×#95—431no—
720C2×#95—431no—
721C2×#95—431no—
722C2×#95—431no—
723C2×#95—431no—
724C2×#95—431no—
725C2×#95—431no—
726C2×#95—431no—
727C2×#95C2×D4311yescharacteristic
728C2×#95C2×D4311yescharacteristic
729C43#1436311yescharacteristic, complemented, Sylow
730C25—431no—
731C25C22×D4311yescharacteristic
732C25C22×D4311yescharacteristic
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—434no—
740C22×D4—434no—
741C22×D4—434no—
742C22×D4—434no—
743C22×D4—862no—
744C22×D4—862no—
745C22×D4—1721no—
746C22×D4—1721no—
747C22×D4—1721no—
748C22×D4—1721no—
749C22×D4—1721no—
750C22×D4—1721no—
751C22×D4—1721no—
752C22×D4—1721no—
753C22×D4C4×D4314yes—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—41no—
758C23×C4—41no—
759C23×C4—41no—
760C23×C4—41no—
761C23×C4—431no—
762C23×C4—431no—
763C23×C4—431no—
764C23×C4—431no—
765C23×C4—434no—
766C23×C4—431no—
767C23×C4—431no—
768C23×C4—431no—
769C23×C4—862no—
770C23×C4—862no—
771C23×C4—862no—
772C23×C4—862no—
773C23×C4—1721no—
774C23×C4—1721no—
775C23×C4C22×D4311yescharacteristic
776C23×C4C22×D4311yescharacteristic
777C23×C4C22×D4311yescharacteristic
778C23×C4C22×D4311yescharacteristic
779C23×C4C22×D4311yescharacteristic
780#121—8632no—
781C2×C4⋊C4—434no—
782C2×C4⋊C4—862no—
783C2×C4⋊C4—862no—
784C2×C4⋊C4—862no—
785C2×C4⋊C4—1721no—
786C2×C4⋊C4—1721no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—434no—
797C2×C22⋊C4—434no—
798C2×C22⋊C4—862no—
799C2×C22⋊C4—862no—
800C2×C22⋊C4—862no—
801C2×C22⋊C4—862no—
802C2×C22⋊C4—862no—
803C2×C22⋊C4—862no—
804C2×C22⋊C4—862no—
805C2×C22⋊C4—862no—
806C2×C22⋊C4—862no—
807C2×C22⋊C4—862no—
808C2×C22⋊C4—862no—
809C2×C22⋊C4—862no—
810C2×C22⋊C4—862no—
811C2×C22⋊C4—862no—
812C2×C22⋊C4—862no—
813C2×C22⋊C4—862no—
814C2×C22⋊C4—1721no—
815C2×C22⋊C4—1721no—
816C2×C22⋊C4—1721no—
817C2×C22⋊C4—1721no—
818C2×C22⋊C4—1721no—
819C2×C22⋊C4—1721no—
820C2×C22⋊C4—1721no—
821C2×C22⋊C4—1721no—
822C2×C22⋊C4—1721no—
823C2×C22⋊C4—1721no—
824C2×C22⋊C4—1721no—
825C2×C22⋊C4—1721no—
826C2×C42—862no—
827C2×C42—1721no—
828C2×C42—1721no—
829#95—22no—
830#95—862no—
831#95—862no—
832#95—862no—
833#95—862no—
834#95—862no—
835#95—862no—
836#95—1721no—
837#95—1721no—
838#95—1721no—
839#95—1721no—
840#95—1721no—
841#95—1721no—
842#95C22⋊D4314yescomplemented
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
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—432no—
870C24—432no—
871C24—432no—
872C24—861no—
873C24—861no—
874C24—861no—
875C24—861no—
876C24—861no—
877C24—861no—
878C24—861no—
879C24—861no—
880C24—861no—
881C24—861no—
882C24—861no—
883C24—861no—
884C24C2×C4×D4312yes—
885C24C2×C4×D4312yes—
886C24D4×D4312yes—
887C24D4×D4312yes—
888C24C23×D4311yescharacteristic
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—4316no—
897C2×D4—868no—
898C2×D4—1724no—
899C2×D4—1724no—
900C2×D4—1724no—
901C2×D4—1724no—
902C2×D4—1724no—
903C2×D4—1724no—
904C2×D4—1724no—
905C2×D4—1724no—
906C2×D4—1724no—
907C2×D4—1724no—
908C2×D4—1724no—
909C2×D4—1724no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
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—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—432no—
947C22×C4—432no—
948C22×C4—432no—
949C22×C4—432no—
950C22×C4—432no—
951C22×C4—432no—
952C22×C4—868no—
953C22×C4—861no—
954C22×C4—861no—
955C22×C4—861no—
956C22×C4—861no—
957C22×C4—861no—
958C22×C4—861no—
959C22×C4—861no—
960C22×C4—861no—
961C22×C4—861no—
962C22×C4—861no—
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—868no—
976C22×C4—861no—
977C22×C4—861no—
978C22×C4—861no—
979C22×C4—861no—
980C22×C4—861no—
981C22×C4—861no—
982C22×C4—861no—
983C22×C4—861no—
984C22×C4—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—1724no—
998C22×C4—1724no—
999C22×C4—1724no—
1000C22×C4—1724no—
1001C22×C4—1724no—
1002C22×C4C2×C4×D4312yes—
1003C22×C4#1062189812yes—
1004C22×C4#1062190012yes—
1005C22×C4C2×C22⋊D4312yes—
1006C22×C4C2×C22⋊D4312yes—
1007C22×C4C2×C22⋊D4312yes—
1008C4⋊C4—868no—
1009C4⋊C4—1724no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—868no—
1014C22⋊C4—868no—
1015C22⋊C4—1724no—
1016C22⋊C4—1724no—
1017C22⋊C4—1724no—
1018C22⋊C4—1724no—
1019C22⋊C4—1724no—
1020C22⋊C4—1724no—
1021C22⋊C4—1724no—
1022C22⋊C4—1724no—
1023C42—1724no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
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—434no—
1094C23—862no—
1095C23—862no—
1096C23—862no—
1097C23—862no—
1098C23—862no—
1099C23—862no—
1100C23—862no—
1101C23—862no—
1102C23—862no—
1103C23—862no—
1104C23—862no—
1105C23—862no—
1106C23—862no—
1107C23—862no—
1108C23—862no—
1109C23—862no—
1110C23—862no—
1111C23—862no—
1112C23—1721no—
1113C23—1721no—
1114C23—1721no—
1115C23—1721no—
1116C23—1721no—
1117C23—1721no—
1118C23—1721no—
1119C23—1721no—
1120C23—1721no—
1121C23—1721no—
1122C23—1721no—
1123C23—1721no—
1124C23—1721no—
1125C23—1721no—
1126C23—1721no—
1127C23—1721no—
1128C23C22⋊C4×D4314yes—
1129C23C22×C4×D4311yescharacteristic
1130C23C2×D4×D4311yescharacteristic
1131C23C2×D4×D4311yescharacteristic
1132C23C22×C22⋊D4311yescharacteristic
1133C23#41×D4311yescharacteristic
1134C23C2×#1062190011yescharacteristic
1135C23C2×#1062189811yescharacteristic
1136C23#1306337011yescharacteristic
1137C23#1306337011yescharacteristic
1138C23#1306337011yescharacteristic
1139C23#1306337011yescharacteristic
1140C23#1306337011yescharacteristic
1141C23#1306337111yescharacteristic
1142C23#1306337111yescharacteristic
1143C23#1306337211yescharacteristic
1144D4—416no—
1145D4—17216no—
1146D4—17216no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—416no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—434no—
1183C2×C4—862no—
1184C2×C4—862no—
1185C2×C4—862no—
1186C2×C4—862no—
1187C2×C4—862no—
1188C2×C4—862no—
1189C2×C4—862no—
1190C2×C4—862no—
1191C2×C4—862no—
1192C2×C4—862no—
1193C2×C4—862no—
1194C2×C4—862no—
1195C2×C4—862no—
1196C2×C4—862no—
1197C2×C4—862no—
1198C2×C4—17216no—
1199C2×C4—1721no—
1200C2×C4—1721no—
1201C2×C4—1721no—
1202C2×C4—1721no—
1203C2×C4—1721no—
1204C2×C4—1721no—
1205C2×C4—1721no—
1206C2×C4—1721no—
1207C2×C4—1721no—
1208C2×C4—1721no—
1209C2×C4—1721no—
1210C2×C4—1721no—
1211C2×C4—1721no—
1212C2×C4—1721no—
1213C2×C4—1721no—
1214C2×C4—1721no—
1215C2×C4—1721no—
1216C2×C4—1721no—
1217C2×C4—1721no—
1218C2×C4—1721no—
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×C4C4×C22⋊D4314yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—864no—
1264C22—864no—
1265C22—864no—
1266C22—1722no—
1267C22—1722no—
1268C22—1722no—
1269C22—1722no—
1270C22—1722no—
1271C22—1722no—
1272C22—1722no—
1273C22—1722no—
1274C22—1722no—
1275C22—1722no—
1276C22—1722no—
1277C22—1722no—
1278C22C2×C22⋊C4×D4311yescharacteristic
1279C22C2×C4×C22⋊D4311yescharacteristic
1280C22C4×#1062190011yescharacteristic
1281C22#1458337111yescharacteristic
1282C22#1458337111yescharacteristic
1283C22#1458337211yescharacteristic
1284C22#1458337811yescharacteristic
1285C22#1458345711yescharacteristic
1286C22#1458345711yescharacteristic
1287C22#1458345911yescharacteristic
1288C22#1458346011yescharacteristic
1289C22#1458346611yescharacteristic
1290C22#1458347711yescharacteristic
1291C22#1458348411yescharacteristic
1292C22#1458348511yescharacteristic
1293C22#1458349911yescharacteristic
1294C22#1458350011yescharacteristic
1295C22#1458350211yescharacteristic
1296C22#1458351411yescharacteristic
1297C22D4×C22⋊D4311yescharacteristic
1298C22D4×C22⋊D4311yescharacteristic
1299C22#1458353611yescharacteristic
1300C22#1458353811yescharacteristic
1301C22#1458353911yescharacteristic
1302C22#1458353911yescharacteristic
1303C22#1458354311yescharacteristic
1304C22#1458354711yescharacteristic
1305C22#1458354911yescharacteristic
1306C22#1458356811yescharacteristic
1307C22#1458359911yescharacteristic
1308C22#1458361411yescharacteristic
1309C22#1458363711yescharacteristic
1310C22#1458363811yescharacteristic
1311C22#1458364411yescharacteristic
1312C22#1458364611yescharacteristic
1313C4—24no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—81no—
1318C4—864no—
1319C4—3441no—
1320C4—3441no—
1321C4—3441no—
1322C4—1722no—
1323C4—1722no—
1324C4—1722no—
1325C2—44no—
1326C2—82no—
1327C2—1724no—
1328C2#1913716911yescharacteristic
1329C2#1913728211yescharacteristic
1330C2#1913735611yescharacteristic
1331C2C22⋊C4×C22⋊D4311yescharacteristic
1332C2#1913742111yescharacteristic
1333C2#1913762911yescharacteristic
1334C2#1913774711yescharacteristic
1335C2#1914082611yescharacteristic
1336C2#1914085611yescharacteristic
1337C2#1914091611yescharacteristic
1338C2#1914096011yescharacteristic
1339C2#1914099611yescharacteristic
1340C2#1914102611yescharacteristic
1341C2#1914118411yescharacteristic
1342C2#1914121111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#386C2
socle, cosocleC24×C43C24
prime radicalC22×#13063296C2
hypercenterC2×#386D43
hypocenterC43#14363
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#14582799C2semidirect
3. C2×#14582778C2semidirect
4. C2×#14582761C2semidirect
5. #19132847C2semidirect
6. #19132842C2semidirect
7. #19132838C2semidirect
8. #19132836C2semidirect
9. #19132834C2semidirect
10. #19132834C2semidirect
11. #19132832C2semidirect
12. #19132829C2semidirect
13. #19132818C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C43×#386C2semidirect
21. C2×#13063296C4semidirect
70. C22×C22⋊D43C2×C4semidirect
86. C22×C4×D43C2×C4semidirect
90. C2×C4⋊Dic43C2×C4semidirect
111. C2×C22⋊Dic43C2×C4semidirect
170. #95×C43D4semidirect
279. C2×C22⋊D43C22⋊C4semidirect
657. C2×#386D43semidirect
729. C43#14363semidirect
842. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632962
C2×#145827992
C2×#145827782
C2×#145827612
#191328472
#191328422
#191328382
#191328362
#191328342
#191328322
#191328292
#191328182
(C2×D43)⋊#952
C2×C43×#3862
#1436343