Finite Group Databasebeta

← #25021112

Subgroups — #25021112

Order 11008.

2690 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
1C2×#14582802C211yesmaximal, characteristic, complemented
2C2×#14582792C211yesmaximal, characteristic, complemented
3C2×#14582779C211yesmaximal, characteristic, complemented
4C2×#14582779C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
7#19132848C211yesmaximal, characteristic, complemented
8#19132836C211yesmaximal, characteristic, complemented
9#19132836C211yesmaximal, characteristic, complemented
10#19132836C211yesmaximal, characteristic, complemented
11#19132832C211yesmaximal, characteristic, complemented
12#19132832C211yesmaximal, characteristic, complemented
13#19132827C211yesmaximal, characteristic, complemented
14#19132818C211yesmaximal, characteristic, complemented
15C22×#121×C43C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32#14582802—24no—
33#14582792—24no—
34#14582779—24no—
35#14582779—24no—
36C22⋊C4×Dic43—24no—
37C4×C22⋊Dic43—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
51C23×D4×C43C2211yescharacteristic
52C23×D4×C43C2211yescharacteristic
53C24×C4×C43C2211yescharacteristic
54C2×#121×C43—24no—
55C2×#121×C43—24no—
56C2×#121×C43C418yescomplemented
57C22×C4⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C22×C22⋊C4×C43C2211yescharacteristic
60C23×Dic43—22no—
61C23×Dic43—22no—
62C23×Dic43—22no—
63C23×Dic43—22no—
64C23×Dic43—22no—
65C23×Dic43—41no—
66C23×Dic43—41no—
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C2×C4⋊Dic43—22no—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43—41no—
78C2×C22⋊Dic43—22no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—22no—
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—22no—
85C2×C22⋊Dic43—22no—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43—22no—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—22no—
91C2×C22⋊Dic43—22no—
92C2×C22⋊Dic43—22no—
93C2×C22⋊Dic43—22no—
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⋊Dic43D414yescomplemented
111C2×C4×Dic43—22no—
112C2×C4×Dic43—22no—
113C2×C4×Dic43—22no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—41no—
118C2×C4×Dic43—41no—
119C2×C4×Dic43—41no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—41no—
130C43⋊#95—41no—
131C43⋊#95D414yescomplemented
132C25×C43C2311yescharacteristic
133C25×C43C2311yescharacteristic
134C25×C43C2311yescharacteristic
135C22×D4×C43—22no—
136C22×D4×C43—22no—
137C22×D4×C43—22no—
138C22×D4×C43—22no—
139C22×D4×C43—22no—
140C22×D4×C43—22no—
141C22×D4×C43—22no—
142C22×D4×C43—22no—
143C22×D4×C43—22no—
144C22×D4×C43—22no—
145C22×D4×C43—22no—
146C22×D4×C43—22no—
147C22×D4×C43—41no—
148C22×D4×C43—41no—
149C22×D4×C43—41no—
150C22×D4×C43—41no—
151C22×D4×C43—41no—
152C22×D4×C43—41no—
153C22×D4×C43C2×C414yes—
154C22×D4×C43C2×C414yes—
155C22×D4×C43C2×C414yescomplemented
156C23×C4×C43—22no—
157C23×C4×C43—22no—
158C23×C4×C43—22no—
159C23×C4×C43—22no—
160C23×C4×C43—41no—
161C23×C4×C43—41no—
162C23×C4×C43C2×C414yescomplemented
163C23×C4×C43C2311yescharacteristic
164C23×C4×C43C2311yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167#121×C43—232no—
168C2×C4⋊C4×C43—22no—
169C2×C4⋊C4×C43—22no—
170C2×C4⋊C4×C43C2×C414yescomplemented
171C2×C22⋊C4×C43—22no—
172C2×C22⋊C4×C43—22no—
173C2×C22⋊C4×C43C2×C414yes—
174C2×C22⋊C4×C43C2×C414yescomplemented
175C2×C22⋊C4×C43D414yes—
176C2×C22⋊C4×C43D414yes—
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×C43—21no—
204C24×C43—21no—
205C24×C43—21no—
206C24×C43—21no—
207C24×C43—21no—
208C24×C43—21no—
209C24×C43—21no—
210C24×C43—21no—
211C24×C43—21no—
212C24×C43—21no—
213C24×C43—21no—
214C24×C43—21no—
215C24×C43C22×C412yes—
216C24×C43C22×C412yes—
217C24×C43C22×C412yes—
218C24×C43C2×D412yes—
219C24×C43C2×D412yes—
220C24×C43C2×D412yes—
221C24×C43#4112yes—
222C24×C43C2411yescharacteristic
223C2×D4×C43—28no—
224C2×D4×C43—28no—
225C2×D4×C43—28no—
226C2×D4×C43—28no—
227C2×D4×C43—28no—
228C2×D4×C43—28no—
229C2×D4×C43—44no—
230C2×D4×C43—44no—
231C2×D4×C43—44no—
232C2×D4×C43—44no—
233C2×D4×C43—44no—
234C2×D4×C43—44no—
235C2×D4×C43—44no—
236C2×D4×C43—44no—
237C2×D4×C43—44no—
238C2×D4×C43—44no—
239C2×D4×C43—44no—
240C2×D4×C43—44no—
241C2×D4×C43—44no—
242C2×D4×C43—44no—
243C2×D4×C43—44no—
244C22×C4×C43—28no—
245C22×C4×C43—28no—
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×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—44no—
265C22×C4×C43—44no—
266C22×C4×C43—44no—
267C22×C4×C43—44no—
268C22×C4×C43—44no—
269C22×C4×C43C22×C412yes—
270C22×C4×C43C22×C412yes—
271C22×C4×C43C22×C412yes—
272C22×C4×C43C22×C412yes—
273C22×C4×C43C2×D412yes—
274C22×C4×C43C2×D412yes—
275C22×C4×C43C2×D412yes—
276C22×C4×C43C2×D412yes—
277C22×C4×C43C2×D412yes—
278C22×C4×C43#4112yes—
279C22×Dic43—28no—
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×Dic43—21no—
324C22×Dic43—21no—
325C22×Dic43—21no—
326C22×Dic43—21no—
327C22×Dic43—21no—
328C22×Dic43—44no—
329C22×Dic43—44no—
330C22×Dic43—44no—
331C22×Dic43—44no—
332C22×Dic43—44no—
333C22×Dic43—44no—
334C22×Dic43C2×D412yes—
335C22×Dic43C2×D412yes—
336C22×Dic43C2×D412yes—
337C22×Dic43C2×D412yes—
338C22×Dic43#4112yes—
339C22×Dic43#4112yes—
340C22×Dic43#4112yes—
341C22×Dic43#4112yes—
342C4⋊C4×C43—28no—
343C22⋊C4×C43—28no—
344C22⋊C4×C43C22⋊C4116yescomplemented
345C22⋊Dic43—28no—
346C22⋊Dic43—28no—
347C22⋊Dic43—28no—
348C22⋊Dic43—44no—
349C22⋊Dic43—44no—
350C22⋊Dic43—44no—
351C22⋊Dic43—44no—
352C22⋊Dic43—44no—
353C22⋊Dic43—44no—
354C22⋊Dic43—44no—
355C22⋊Dic43—44no—
356C4⋊Dic43—44no—
357C4×Dic43—44no—
358C4×Dic43—44no—
359C4×Dic43—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—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—22no—
393C23×C43—22no—
394C23×C43—22no—
395C23×C43—22no—
396C23×C43—22no—
397C23×C43—22no—
398C23×C43—22no—
399C23×C43—22no—
400C23×C43—22no—
401C23×C43—22no—
402C23×C43—22no—
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×C43—41no—
430C23×C43—41no—
431C23×C43—41no—
432C23×C43—41no—
433C23×C43—41no—
434C23×C43—41no—
435C23×C43—41no—
436C23×C43—41no—
437C23×C43—41no—
438C23×C43—41no—
439C23×C43—41no—
440C23×C43—41no—
441C23×C43—41no—
442C23×C43—41no—
443C23×C43—41no—
444C23×C43—41no—
445C23×C43—41no—
446C23×C43—41no—
447C23×C43—41no—
448C23×C43—41no—
449C23×C43—41no—
450C23×C43—41no—
451C23×C43—41no—
452C23×C43—41no—
453C23×C43—41no—
454C23×C43—41no—
455C23×C43—41no—
456C23×C43—41no—
457C23×C43—41no—
458C23×C43—41no—
459C23×C43—41no—
460C23×C43—41no—
461C23×C43—41no—
462C23×C43—41no—
463C23×C43C2×C22⋊C414yes—
464C23×C43C4×D414yes—
465C23×C43C23×C411yescharacteristic
466C23×C43C22×D411yescharacteristic
467C23×C43C22×D411yescharacteristic
468C23×C43C22×D411yescharacteristic
469C23×C43C22×D411yescharacteristic
470C23×C43C2×#4111yescharacteristic
471C23×C43C2×#4111yescharacteristic
472C23×C43C2×#4111yescharacteristic
473C23×C43C2×#4111yescharacteristic
474C23×C43C2×#4111yescharacteristic
475C23×C43C2×#4111yescharacteristic
476C23×C43H(5,𝔽2)11yescharacteristic
477C23×C43H(5,𝔽2)11yescharacteristic
478C23×C43H(5,𝔽2)11yescharacteristic
479C23×C43H(5,𝔽2)11yescharacteristic
480D4×C43—416no—
481D4×C43—416no—
482D4×C43—416no—
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—22no—
497C2×C4×C43—22no—
498C2×C4×C43—22no—
499C2×C4×C43—22no—
500C2×C4×C43—22no—
501C2×C4×C43—22no—
502C2×C4×C43—22no—
503C2×C4×C43—22no—
504C2×C4×C43—416no—
505C2×C4×C43—41no—
506C2×C4×C43—41no—
507C2×C4×C43—41no—
508C2×C4×C43—41no—
509C2×C4×C43C2×C22⋊C414yes—
510C2×C4×C43C2×C22⋊C414yes—
511C2×C4×C43C4×D414yes—
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—22no—
527C2×Dic43—22no—
528C2×Dic43—22no—
529C2×Dic43—22no—
530C2×Dic43—22no—
531C2×Dic43—22no—
532C2×Dic43—22no—
533C2×Dic43—416no—
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×Dic43—41no—
560C2×Dic43—41no—
561C2×Dic43—41no—
562C2×Dic43—41no—
563C2×Dic43—41no—
564C2×Dic43—41no—
565C2×Dic43—41no—
566C2×Dic43—41no—
567C2×Dic43—41no—
568C2×Dic43#12114yescomplemented
569#14100—431nomaximal, Sylow
570C22×C43—24no—
571C22×C43—24no—
572C22×C43—24no—
573C22×C43—24no—
574C22×C43—24no—
575C22×C43—24no—
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—42no—
593C22×C43—42no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—42no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43—42no—
600C22×C43—42no—
601C22×C43—42no—
602C22×C43—42no—
603C22×C43—42no—
604C22×C43—42no—
605C22×C43—42no—
606C22×C43—42no—
607C22×C43—81no—
608C22×C43—81no—
609C22×C43—81no—
610C22×C43—81no—
611C22×C43—81no—
612C22×C43—81no—
613C22×C43—81no—
614C22×C43—81no—
615C22×C43C22×C22⋊C411yescharacteristic
616C22×C43C2×C4×D411yescharacteristic
617C22×C43C2×C4×D411yescharacteristic
618C22×C43C4×#4111yescharacteristic
619C22×C43C4×#4111yescharacteristic
620C22×C43#51811yescharacteristic
621C22×C43#51811yescharacteristic
622C22×C43C2×#12111yescharacteristic
623C22×C43#52511yescharacteristic
624C22×C43#52511yescharacteristic
625C22×C43#52511yescharacteristic
626C22×C43#52911yescharacteristic
627C22×C43#53211yescharacteristic
628C22×C43#53211yescharacteristic
629C22×C43#53211yescharacteristic
630C22×C43#53811yescharacteristic
631C22×C43#53811yescharacteristic
632C22×C43#54011yescharacteristic
633C22×C43#54011yescharacteristic
634C22×C43D4211yescharacteristic
635C22×C43D4211yescharacteristic
636C22×C43D4211yescharacteristic
637C22×C43D4211yescharacteristic
638C22×C43#54611yescharacteristic
639C22×C43#54611yescharacteristic
640C22×C43#54611yescharacteristic
641C22×C43#54611yescharacteristic
642C22×C43#54611yescharacteristic
643C22×C43#54611yescharacteristic
644C22×C43#54611yescharacteristic
645C22×C43#55011yescharacteristic
646C22×C43#55311yescharacteristic
647C22×C43#55311yescharacteristic
648C22×C43#55311yescharacteristic
649C22×C43#55511yescharacteristic
650C4×C43—24no—
651C4×C43—24no—
652C4×C43—24no—
653C4×C43—42no—
654Dic43—24no—
655Dic43—42no—
656Dic43—42no—
657Dic43—42no—
658Dic43—42no—
659Dic43—42no—
660Dic43—81no—
661Dic43—81no—
662C22×#121D4311yescharacteristic
663C2×#390—431no—
664C2×#388—431no—
665C2×#386—431no—
666C2×#386—431no—
667C2×C4×C22⋊C4—431no—
668C2×C4×C22⋊C4—431no—
669#1441—431no—
670#1438—431no—
671#1438—431no—
672#1438—431no—
673#1437—431no—
674#1437—431no—
675#1436—431no—
676C22⋊#95—431no—
677C2×C43—44no—
678C2×C43—44no—
679C2×C43—82no—
680C2×C43#229711yescharacteristic
681C2×C43C4×#12111yescharacteristic
682C2×C43#233311yescharacteristic
683C2×C43D4×C22⋊C411yescharacteristic
684C2×C43D4×C22⋊C411yescharacteristic
685C2×C43#236311yescharacteristic
686C2×C43#236411yescharacteristic
687C2×C43#242411yescharacteristic
688C2×C43#242811yescharacteristic
689C2×C43#245611yescharacteristic
690C2×C43#246411yescharacteristic
691C2×C43#246411yescharacteristic
692C2×C43#247611yescharacteristic
693C2×C43#255511yescharacteristic
694C2×C43#255911yescharacteristic
695C23×D4C2×D4311yescharacteristic
696C23×D4C2×D4311yescharacteristic
697C23×D4C2×D4311yescharacteristic
698C24×C4—431no—
699C24×C4C2×D4311yescharacteristic
700C2×#121—24no—
701C2×#121—24no—
702C2×#121Dic4318yescomplemented
703C22×C4⋊C4—431no—
704C22×C4⋊C4C2×D4311yescharacteristic
705C22×C22⋊C4—431no—
706C22×C22⋊C4—431no—
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×C42—431no—
719C22×C42—431no—
720C22×C42—431no—
721#390—864no—
722#388—864no—
723#386—864no—
724#386—864no—
725C4×C22⋊C4—864no—
726C4×C22⋊C4—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#1410011yescharacteristic, complemented, Sylow
740C25C22×D4311yescharacteristic
741C25C22×D4311yescharacteristic
742C25C22×D4311yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4—41no—
761C22×D4C2×Dic4314yes—
762C22×D4C2×Dic4314yes—
763C22×D4C2×Dic4314yescomplemented
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—41no—
769C23×C4—41no—
770C23×C4—431no—
771C23×C4—431no—
772C23×C4—431no—
773C23×C4—431no—
774C23×C4—431no—
775C23×C4—431no—
776C23×C4—431no—
777C23×C4—431no—
778C23×C4—862no—
779C23×C4—862no—
780C23×C4—862no—
781C23×C4—862no—
782C23×C4—862no—
783C23×C4—1721no—
784C23×C4—1721no—
785C23×C4C2×Dic4314yescomplemented
786C23×C4C22×D4311yescharacteristic
787C23×C4C22×D4311yescharacteristic
788C23×C4C22×D4311yescharacteristic
789C23×C4C22×D4311yescharacteristic
790#121—232no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—862no—
794C2×C4⋊C4—862no—
795C2×C4⋊C4—1721no—
796C2×C4⋊C4C2×Dic4314yescomplemented
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—434no—
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—862no—
815C2×C22⋊C4—862no—
816C2×C22⋊C4—862no—
817C2×C22⋊C4—862no—
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—1721no—
825C2×C22⋊C4—1721no—
826C2×C22⋊C4—1721no—
827C2×C22⋊C4—1721no—
828C2×C22⋊C4—1721no—
829C2×C22⋊C4—1721no—
830C2×C22⋊C4—1721no—
831C2×C22⋊C4—1721no—
832C2×C22⋊C4C2×Dic4314yes—
833C2×C22⋊C4C2×Dic4314yescomplemented
834C2×C22⋊C4C22⋊D4314yes—
835C2×C22⋊C4C22⋊D4314yes—
836C2×C42—862no—
837C2×C42—862no—
838C2×C42—862no—
839C2×C42—862no—
840C2×C42—862no—
841C2×C42—862no—
842C2×C42—1721no—
843C2×C42—1721no—
844C2×C42—1721no—
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—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24D4×D4312yes—
896C24#1062190012yes—
897C24C22×Dic4312yes—
898C24C22×Dic4312yes—
899C24C22×Dic4312yes—
900C24C2×C22⋊D4312yes—
901C24C2×C22⋊D4312yes—
902C24C23×D4311yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
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—28no—
943C22×C4—28no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—432no—
950C22×C4—432no—
951C22×C4—432no—
952C22×C4—432no—
953C22×C4—432no—
954C22×C4—432no—
955C22×C4—432no—
956C22×C4—432no—
957C22×C4—861no—
958C22×C4—861no—
959C22×C4—861no—
960C22×C4—861no—
961C22×C4—868no—
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—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—861no—
1005C22×C4—861no—
1006C22×C4—1724no—
1007C22×C4—1724no—
1008C22×C4—1724no—
1009C22×C4—1724no—
1010C22×C4—1724no—
1011C22×C4—1724no—
1012C22×C4D4×D4312yes—
1013C22×C4#1062190012yes—
1014C22×C4C22×Dic4312yes—
1015C22×C4C22×Dic4312yes—
1016C22×C4C22×Dic4312yes—
1017C22×C4C22×Dic4312yes—
1018C22×C4C2×C22⋊D4312yes—
1019C22×C4C2×C22⋊D4312yes—
1020C22×C4C2×C22⋊D4312yes—
1021C22×C4C2×C22⋊D4312yes—
1022C4⋊C4—28no—
1023C4⋊C4—1724no—
1024C22⋊C4—28no—
1025C22⋊C4—868no—
1026C22⋊C4—868no—
1027C22⋊C4—868no—
1028C22⋊C4—1724no—
1029C22⋊C4—1724no—
1030C22⋊C4—1724no—
1031C22⋊C4—1724no—
1032C22⋊C4—1724no—
1033C22⋊C4—1724no—
1034C22⋊C4—1724no—
1035C22⋊C4—1724no—
1036C22⋊C4C22⋊Dic43116yescomplemented
1037C42—1724no—
1038C42—1724no—
1039C42—1724no—
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—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
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—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C22⋊Dic4314yes—
1144C23D4×Dic4314yes—
1145C23C23×Dic4311yescharacteristic
1146C23C2×D4×D4311yescharacteristic
1147C23C2×D4×D4311yescharacteristic
1148C23C22×C22⋊D4311yescharacteristic
1149C23C22×C22⋊D4311yescharacteristic
1150C23#41×D4311yescharacteristic
1151C23#41×D4311yescharacteristic
1152C23#41×D4311yescharacteristic
1153C23#41×D4311yescharacteristic
1154C23C2×#1062190011yescharacteristic
1155C23C2×#1062190011yescharacteristic
1156C23#1306337011yescharacteristic
1157C23#1306337011yescharacteristic
1158C23#1306337011yescharacteristic
1159C23#1306337011yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
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—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—416no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—434no—
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—862no—
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—17216no—
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×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×C4C2×C22⋊Dic4314yes—
1247C2×C4C2×C22⋊Dic4314yes—
1248C2×C4D4×Dic4314yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
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—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C22⋊Dic4311yescharacteristic
1295C22C2×D4×Dic4311yescharacteristic
1296C22C2×D4×Dic4311yescharacteristic
1297C22#41×Dic4311yescharacteristic
1298C22#41×Dic4311yescharacteristic
1299C22#1458337411yescharacteristic
1300C22#1458337411yescharacteristic
1301C22#121×D4311yescharacteristic
1302C22#1458340611yescharacteristic
1303C22#1458340611yescharacteristic
1304C22#1458340911yescharacteristic
1305C22#1458343011yescharacteristic
1306C22#1458344411yescharacteristic
1307C22#1458344511yescharacteristic
1308C22#1458344511yescharacteristic
1309C22#1458348111yescharacteristic
1310C22#1458348111yescharacteristic
1311C22#1458349911yescharacteristic
1312C22#1458349911yescharacteristic
1313C22D4×C22⋊D4311yescharacteristic
1314C22D4×C22⋊D4311yescharacteristic
1315C22D4×C22⋊D4311yescharacteristic
1316C22D4×C22⋊D4311yescharacteristic
1317C22#1458353811yescharacteristic
1318C22#1458353811yescharacteristic
1319C22#1458354311yescharacteristic
1320C22#1458354311yescharacteristic
1321C22#1458354311yescharacteristic
1322C22#1458354311yescharacteristic
1323C22#1458354611yescharacteristic
1324C22#1458356711yescharacteristic
1325C22#1458359211yescharacteristic
1326C22#1458359211yescharacteristic
1327C22#1458359611yescharacteristic
1328C22#1458361311yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—864no—
1334C4—3441no—
1335C4—3441no—
1336C4—1722no—
1337C4—1722no—
1338C4—1722no—
1339C4—1722no—
1340C4—1722no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2#1913708611yescharacteristic
1345C2#121×Dic4311yescharacteristic
1346C2#1913736211yescharacteristic
1347C2D4×C22⋊Dic4311yescharacteristic
1348C2D4×C22⋊Dic4311yescharacteristic
1349C2#1913763711yescharacteristic
1350C2#1913764711yescharacteristic
1351C2#1913812811yescharacteristic
1352C2#1913818011yescharacteristic
1353C2#1913849211yescharacteristic
1354C2#1913859711yescharacteristic
1355C2#1913860611yescharacteristic
1356C2#1913877711yescharacteristic
1357C2#1913966811yescharacteristic
1358C2#1913972011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
Fitting, prime radicalC22×#121×C43C2
socle, cosocleC24×C43C24
hypercenterC22×#121D43
hypocenterC43#14100
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14582802C2semidirect
2. C2×#14582792C2semidirect
3. C2×#14582779C2semidirect
4. C2×#14582779C2semidirect
5. C2×C22⋊C4×Dic43C2semidirect
6. C2×C4×C22⋊Dic43C2semidirect
7. #19132848C2semidirect
8. #19132836C2semidirect
9. #19132836C2semidirect
10. #19132836C2semidirect
11. #19132832C2semidirect
12. #19132832C2semidirect
13. #19132827C2semidirect
14. #19132818C2semidirect
56. C2×#121×C43C4semidirect
110. C2×C22⋊Dic43D4semidirect
131. C43⋊#95D4semidirect
155. C22×D4×C43C2×C4semidirect
162. C23×C4×C43C2×C4semidirect
170. C2×C4⋊C4×C43C2×C4semidirect
174. C2×C22⋊C4×C43C2×C4semidirect
344. C22⋊C4×C43C22⋊C4semidirect
568. C2×Dic43#121semidirect
702. C2×#121Dic43semidirect
739. C43#14100semidirect
763. C22×D4C2×Dic43semidirect
785. C23×C4C2×Dic43semidirect
796. C2×C4⋊C4C2×Dic43semidirect
833. C2×C22⋊C4C2×Dic43semidirect
1036. C22⋊C4C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828022
C2×#145827922
C2×#145827792
C2×C22⋊C4×Dic432
C2×C4×C22⋊Dic432
#191328482
#191328362
#191328322
#191328272
#191328182
C22×#121×C432
#1410043