Finite Group Databasebeta

← #25025933

Subgroups — #25025933

Order 11008.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582802C211yesmaximal, characteristic, complemented
2C2×#14582779C211yesmaximal, characteristic, complemented
3C2×#14582779C211yesmaximal, characteristic, complemented
4C2×#14582779C211yesmaximal, characteristic, complemented
5C2×#14582779C211yesmaximal, characteristic, complemented
6C2×#14582774C211yesmaximal, characteristic, complemented
7#19132852C211yesmaximal, characteristic, complemented
8#19132844C211yesmaximal, characteristic, complemented
9#19132840C211yesmaximal, characteristic, complemented
10#19132840C211yesmaximal, characteristic, complemented
11#19132836C211yesmaximal, characteristic, complemented
12#19132832C211yesmaximal, characteristic, complemented
13#19132820C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C2×C43×#392C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊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×C22⋊Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31#14582802—24no—
32#14582779—24no—
33#14582779—24no—
34#14582779—24no—
35#14582779—24no—
36#14582774—24no—
37C2×C43⋊#95C2211yescharacteristic
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
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C43×#392C418yescomplemented
57C2×#95×C43C2211yescharacteristic
58C23×Dic43—22no—
59C23×Dic43—22no—
60C23×Dic43—22no—
61C23×Dic43—22no—
62C23×Dic43—22no—
63C23×Dic43—22no—
64C23×Dic43—41no—
65C23×Dic43—41no—
66C23×Dic43—41no—
67C23×Dic43—41no—
68C23×Dic43—41no—
69C23×Dic43—41no—
70C23×Dic43—41no—
71C23×Dic43—41no—
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—41no—
84C2×C4⋊Dic43—41no—
85C2×C4⋊Dic43—41no—
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—41no—
101C2×C22⋊Dic43—41no—
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⋊Dic43—41no—
111C2×C22⋊Dic43—41no—
112C2×C22⋊Dic43—41no—
113C2×C22⋊Dic43—41no—
114C2×C22⋊Dic43D414yescomplemented
115C2×C22⋊Dic43D414yescomplemented
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—41no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—41no—
128C43⋊#95—41no—
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—41no—
146C22×D4×C43—41no—
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×C414yescomplemented
155C22×D4×C43C2×C414yescomplemented
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—41no—
163C2×C22⋊C4×C43—41no—
164C2×C22⋊C4×C43—41no—
165C2×C22⋊C4×C43—41no—
166C2×C22⋊C4×C43C2×C414yescomplemented
167C2×C22⋊C4×C43C2×C414yescomplemented
168C2×C22⋊C4×C43C2×C414yescomplemented
169#95×C43C2×C414yescomplemented
170C24×C43—21no—
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×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×C43C22×C412yes—
209C24×C43C22×C412yes—
210C24×C43C22×C412yes—
211C24×C43C2×D412yes—
212C24×C43C2×D412yes—
213C24×C43#4112yes—
214C24×C43#4112yes—
215C24×C43C2411yescharacteristic
216C2×D4×C43—28no—
217C2×D4×C43—28no—
218C2×D4×C43—28no—
219C2×D4×C43—28no—
220C2×D4×C43—28no—
221C2×D4×C43—44no—
222C2×D4×C43—44no—
223C2×D4×C43—44no—
224C2×D4×C43—44no—
225C2×D4×C43—44no—
226C2×D4×C43—44no—
227C2×D4×C43—44no—
228C2×D4×C43—44no—
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—
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×C43C22×C412yes—
261C22×C4×C43C22×C412yes—
262C22×C4×C43C22×C412yes—
263C22×C4×C43C2×D412yes—
264C22×C4×C43#4112yes—
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×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
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—44no—
316C22×Dic43—44no—
317C22×Dic43—44no—
318C22×Dic43—44no—
319C22×Dic43—44no—
320C22×Dic43—44no—
321C22×Dic43—44no—
322C22×Dic43—44no—
323C22×Dic43—44no—
324C22×Dic43—44no—
325C22×Dic43—44no—
326C22×Dic43—44no—
327C22×Dic43—44no—
328C22×Dic43—44no—
329C22×Dic43C2×D412yes—
330C22×Dic43C2×D412yes—
331C22×Dic43C2×D412yes—
332C22×Dic43C2×D412yes—
333C22×Dic43C2×D412yes—
334C22×Dic43C2×D412yes—
335C22⋊C4×C43—28no—
336C22⋊C4×C43—44no—
337C22⋊C4×C43—44no—
338C22⋊Dic43—44no—
339C22⋊Dic43—44no—
340C22⋊Dic43—44no—
341C22⋊Dic43—44no—
342C22⋊Dic43—44no—
343C22⋊Dic43—44no—
344C22⋊Dic43—44no—
345C22⋊Dic43—44no—
346C22⋊Dic43—44no—
347C22⋊Dic43—44no—
348C4⋊Dic43—44no—
349C4⋊Dic43—44no—
350C4×Dic43—44no—
351C23×C43—22no—
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—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—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×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×C43C4×D414yes—
455C23×C43C4×D414yes—
456C23×C43C23×C411yescharacteristic
457C23×C43C22×D411yescharacteristic
458C23×C43C22×D411yescharacteristic
459C23×C43C22×D411yescharacteristic
460C23×C43C2×#4111yescharacteristic
461C23×C43C2×#4111yescharacteristic
462C23×C43C2×#4111yescharacteristic
463C23×C43H(5,𝔽2)11yescharacteristic
464C23×C43H(5,𝔽2)11yescharacteristic
465C23×C43H(5,𝔽2)11yescharacteristic
466C23×C43H(5,𝔽2)11yescharacteristic
467C23×C43H(5,𝔽2)11yescharacteristic
468C23×C43H(5,𝔽2)11yescharacteristic
469C23×C43H(5,𝔽2)11yescharacteristic
470C23×C432−1+411yescharacteristic
471D4×C43—416no—
472D4×C43—416no—
473D4×C43—416no—
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—22no—
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×C43C4×D414yes—
502C2×Dic43—22no—
503C2×Dic43—22no—
504C2×Dic43—22no—
505C2×Dic43—22no—
506C2×Dic43—22no—
507C2×Dic43—22no—
508C2×Dic43—22no—
509C2×Dic43—22no—
510C2×Dic43—22no—
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—416no—
521C2×Dic43—416no—
522C2×Dic43—41no—
523C2×Dic43—41no—
524C2×Dic43—41no—
525C2×Dic43—41no—
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×Dic43—41no—
560#14519—431nomaximal, Sylow
561C22×C43—24no—
562C22×C43—24no—
563C22×C43—24no—
564C22×C43—24no—
565C22×C43—24no—
566C22×C43—24no—
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—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—81no—
599C22×C43—81no—
600C22×C43—81no—
601C22×C43—81no—
602C22×C43—81no—
603C22×C43—81no—
604C22×C43—81no—
605C22×C43—81no—
606C22×C43C2×C4×D411yescharacteristic
607C22×C43C2×C4×D411yescharacteristic
608C22×C43C2×C4×D411yescharacteristic
609C22×C43#51811yescharacteristic
610C22×C43#51811yescharacteristic
611C22×C43#51811yescharacteristic
612C22×C43#52011yescharacteristic
613C22×C43#53411yescharacteristic
614C22×C43#53411yescharacteristic
615C22×C43#53511yescharacteristic
616C22×C43#53511yescharacteristic
617C22×C43#53511yescharacteristic
618C22×C43#53711yescharacteristic
619C22×C43#53811yescharacteristic
620C22×C43#53811yescharacteristic
621C22×C43#53811yescharacteristic
622C22×C43#53911yescharacteristic
623C22×C43#54011yescharacteristic
624C22×C43#54011yescharacteristic
625C22×C43D4211yescharacteristic
626C22×C43D4211yescharacteristic
627C22×C43D4211yescharacteristic
628C22×C43#54611yescharacteristic
629C22×C43#54611yescharacteristic
630C22×C43#54611yescharacteristic
631C22×C43#54611yescharacteristic
632C22×C43#54711yescharacteristic
633C22×C43#54811yescharacteristic
634C22×C43#55111yescharacteristic
635C22×C43#55111yescharacteristic
636C22×C43#55311yescharacteristic
637C22×C43#56011yescharacteristic
638C22×C43#56011yescharacteristic
639C22×C43#56211yescharacteristic
640C22×C43#56211yescharacteristic
641C4×C43—24no—
642C4×C43—42no—
643C4×C43—42no—
644C4×C43—42no—
645Dic43—42no—
646Dic43—42no—
647Dic43—42no—
648Dic43—42no—
649Dic43—42no—
650Dic43—42no—
651Dic43—81no—
652Dic43—81no—
653C2×#392D4311yescharacteristic
654C2×#390—431no—
655C2×#386—431no—
656C2×#386—431no—
657C2×#386—431no—
658C2×#386—431no—
659C2×#385—431no—
660#1442—431no—
661#1440—431no—
662#1439—431no—
663#1439—431no—
664#1438—431no—
665#1437—431no—
666#1434—431no—
667C22⋊#95—431no—
668C2×C43—44no—
669C2×C43—44no—
670C2×C43—82no—
671C2×C43#232111yescharacteristic
672C2×C43#232511yescharacteristic
673C2×C43#232811yescharacteristic
674C2×C43#235811yescharacteristic
675C2×C43#235811yescharacteristic
676C2×C43#236111yescharacteristic
677C2×C43#237711yescharacteristic
678C2×C43#266911yescharacteristic
679C2×C43#267111yescharacteristic
680C2×C43#267611yescharacteristic
681C2×C43#267811yescharacteristic
682C2×C43#268811yescharacteristic
683C2×C43#269611yescharacteristic
684C2×C43#270611yescharacteristic
685C2×C43#274911yescharacteristic
686C23×D4C2×D4311yescharacteristic
687C23×D4C2×D4311yescharacteristic
688C23×D4C2×D4311yescharacteristic
689C24×C4—431no—
690C24×C4—431no—
691C22×C4⋊C4—431no—
692C22×C4⋊C4—431no—
693C22×C22⋊C4—431no—
694C22×C22⋊C4—431no—
695C22×C22⋊C4—431no—
696C22×C22⋊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⋊C4C2×D4311yescharacteristic
704C22×C22⋊C4C2×D4311yescharacteristic
705C22×C22⋊C4C2×D4311yescharacteristic
706C22×C42—431no—
707#392Dic4318yescomplemented
708#390—864no—
709#386—864no—
710#386—864no—
711#386—864no—
712#386—864no—
713#385—864no—
714C2×#95—431no—
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
728C43#1451911yescharacteristic, complemented, Sylow
729C25C22×D4311yescharacteristic
730C25C22×D4311yescharacteristic
731C25C22×D4311yescharacteristic
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4C2×Dic4314yes—
751C22×D4C2×Dic4314yescomplemented
752C22×D4C2×Dic4314yescomplemented
753C23×C4—431no—
754C23×C4—431no—
755C23×C4—431no—
756C23×C4—431no—
757C23×C4—431no—
758C23×C4—431no—
759C23×C4—431no—
760C23×C4—431no—
761C23×C4—862no—
762C23×C4—862no—
763C23×C4—862no—
764C23×C4—862no—
765C23×C4—862no—
766C23×C4—862no—
767C23×C4—1721no—
768C23×C4—1721no—
769C23×C4—1721no—
770C23×C4—1721no—
771C23×C4—1721no—
772C23×C4—1721no—
773C23×C4—1721no—
774C23×C4—1721no—
775C23×C4C22×D4311yescharacteristic
776C23×C4C22×D4311yescharacteristic
777C23×C4C22×D4311yescharacteristic
778C23×C4C22×D4311yescharacteristic
779C2×C4⋊C4—862no—
780C2×C4⋊C4—862no—
781C2×C4⋊C4—862no—
782C2×C4⋊C4—1721no—
783C2×C4⋊C4—1721no—
784C2×C4⋊C4—1721no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—434no—
792C2×C22⋊C4—434no—
793C2×C22⋊C4—862no—
794C2×C22⋊C4—862no—
795C2×C22⋊C4—862no—
796C2×C22⋊C4—862no—
797C2×C22⋊C4—862no—
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—1721no—
808C2×C22⋊C4—1721no—
809C2×C22⋊C4—1721no—
810C2×C22⋊C4—1721no—
811C2×C22⋊C4—1721no—
812C2×C22⋊C4—1721no—
813C2×C22⋊C4—1721no—
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⋊C4C2×Dic4314yescomplemented
822C2×C22⋊C4C2×Dic4314yescomplemented
823C2×C22⋊C4C2×Dic4314yescomplemented
824C2×C42—862no—
825C2×C42—862no—
826C2×C42—1721no—
827#95—434no—
828#95—862no—
829#95—862no—
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#95C2×Dic4314yescomplemented
841C24—21no—
842C24—21no—
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—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24D4×D4312yes—
880C24D4×D4312yes—
881C24#1062190012yes—
882C24#1062190012yes—
883C24C22×Dic4312yes—
884C24C22×Dic4312yes—
885C24C22×Dic4312yes—
886C24C23×D4311yescharacteristic
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C22×C4—21no—
909C22×C4—21no—
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—432no—
931C22×C4—432no—
932C22×C4—432no—
933C22×C4—432no—
934C22×C4—432no—
935C22×C4—432no—
936C22×C4—861no—
937C22×C4—861no—
938C22×C4—861no—
939C22×C4—861no—
940C22×C4—861no—
941C22×C4—861no—
942C22×C4—861no—
943C22×C4—861no—
944C22×C4—861no—
945C22×C4—861no—
946C22×C4—861no—
947C22×C4—861no—
948C22×C4—861no—
949C22×C4—861no—
950C22×C4—861no—
951C22×C4—861no—
952C22×C4—861no—
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—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—1724no—
987C22×C4—1724no—
988C22×C4—1724no—
989C22×C4—1724no—
990C22×C4—1724no—
991C22×C4—1724no—
992C22×C4—1724no—
993C22×C4—1724no—
994C22×C4—1724no—
995C22×C4—1724no—
996C22×C4—1724no—
997C22×C4—1724no—
998C22×C4—1724no—
999C22×C4—1724no—
1000C22×C4D4×D4312yes—
1001C22×C4#1062190012yes—
1002C22×C4C22×Dic4312yes—
1003C22×C4C22×Dic4312yes—
1004C22×C4C22×Dic4312yes—
1005C22×C4C22×Dic4312yes—
1006C4⋊C4—1724no—
1007C4⋊C4—1724no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—1724no—
1012C22⋊C4—1724no—
1013C22⋊C4—1724no—
1014C22⋊C4—1724no—
1015C22⋊C4—1724no—
1016C22⋊C4—1724no—
1017C22⋊C4—1724no—
1018C22⋊C4—1724no—
1019C22⋊C4—1724no—
1020C22⋊C4—1724no—
1021C42—1724no—
1022C23—22no—
1023C23—22no—
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—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—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—
1125C23D4×Dic4314yes—
1126C23D4×Dic4314yes—
1127C23C23×Dic4311yescharacteristic
1128C23C2×D4×D4311yescharacteristic
1129C23C2×D4×D4311yescharacteristic
1130C23C2×D4×D4311yescharacteristic
1131C23C2×#1062190011yescharacteristic
1132C23C2×#1062190011yescharacteristic
1133C23C2×#1062190011yescharacteristic
1134C23#1306337011yescharacteristic
1135C23#1306337011yescharacteristic
1136C23#1306337011yescharacteristic
1137C23#1306337011yescharacteristic
1138C23#1306337011yescharacteristic
1139C23#1306337011yescharacteristic
1140C23#1306337111yescharacteristic
1141C23#1306337211yescharacteristic
1142D4—416no—
1143D4—416no—
1144D4—416no—
1145C2×C4—22no—
1146C2×C4—22no—
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—41no—
1161C2×C4—41no—
1162C2×C4—41no—
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—862no—
1173C2×C4—862no—
1174C2×C4—862no—
1175C2×C4—862no—
1176C2×C4—862no—
1177C2×C4—862no—
1178C2×C4—862no—
1179C2×C4—862no—
1180C2×C4—862no—
1181C2×C4—862no—
1182C2×C4—862no—
1183C2×C4—862no—
1184C2×C4—862no—
1185C2×C4—862no—
1186C2×C4—862no—
1187C2×C4—862no—
1188C2×C4—862no—
1189C2×C4—862no—
1190C2×C4—1721no—
1191C2×C4—1721no—
1192C2×C4—1721no—
1193C2×C4—1721no—
1194C2×C4—1721no—
1195C2×C4—1721no—
1196C2×C4—1721no—
1197C2×C4—1721no—
1198C2×C4—1721no—
1199C2×C4—1721no—
1200C2×C4—1721no—
1201C2×C4—1721no—
1202C2×C4—1721no—
1203C2×C4—1721no—
1204C2×C4—17216no—
1205C2×C4—17216no—
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×C4D4×Dic4314yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
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—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—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22C2×D4×Dic4311yescharacteristic
1277C22C2×D4×Dic4311yescharacteristic
1278C22C2×D4×Dic4311yescharacteristic
1279C22#1458337411yescharacteristic
1280C22#1458337411yescharacteristic
1281C22#1458337411yescharacteristic
1282C22#1458338211yescharacteristic
1283C22#1458345711yescharacteristic
1284C22#1458345911yescharacteristic
1285C22#1458346211yescharacteristic
1286C22#1458346211yescharacteristic
1287C22#1458346411yescharacteristic
1288C22#1458347611yescharacteristic
1289C22#1458348411yescharacteristic
1290C22#1458348411yescharacteristic
1291C22#1458348611yescharacteristic
1292C22#1458349411yescharacteristic
1293C22#1458350311yescharacteristic
1294C22#1458350311yescharacteristic
1295C22#1458353111yescharacteristic
1296C22#1458353111yescharacteristic
1297C22#1458353311yescharacteristic
1298C22#1458353611yescharacteristic
1299C22#1458353611yescharacteristic
1300C22#1458353611yescharacteristic
1301C22#1458353611yescharacteristic
1302C22#1458354911yescharacteristic
1303C22#1458355511yescharacteristic
1304C22#1458358011yescharacteristic
1305C22#1458358011yescharacteristic
1306C22#1458360111yescharacteristic
1307C22#1458363711yescharacteristic
1308C22#1458363711yescharacteristic
1309C22#1458364411yescharacteristic
1310C22#1458364411yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—3441no—
1316C4—3441no—
1317C4—1722no—
1318C4—1722no—
1319C4—1722no—
1320C4—1722no—
1321C4—1722no—
1322C4—1722no—
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2#1913725611yescharacteristic
1327C2#1913730011yescharacteristic
1328C2#1913732111yescharacteristic
1329C2#1913757911yescharacteristic
1330C2#1913757911yescharacteristic
1331C2#1913761511yescharacteristic
1332C2#1913775211yescharacteristic
1333C2#1914080611yescharacteristic
1334C2#1914083311yescharacteristic
1335C2#1914088911yescharacteristic
1336C2#1914091311yescharacteristic
1337C2#1914103011yescharacteristic
1338C2#1914114411yescharacteristic
1339C2#1914129011yescharacteristic
1340C2#1914182011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
Fitting, prime radicalC2×C43×#392C2
socle, cosocleC24×C43C24
hypercenterC2×#392D43
hypocenterC43#14519
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#14582802C2semidirect
2. C2×#14582779C2semidirect
3. C2×#14582779C2semidirect
4. C2×#14582779C2semidirect
5. C2×#14582779C2semidirect
6. C2×#14582774C2semidirect
7. #19132852C2semidirect
8. #19132844C2semidirect
9. #19132840C2semidirect
10. #19132840C2semidirect
11. #19132836C2semidirect
12. #19132832C2semidirect
13. #19132820C2semidirect
14. #19132817C2semidirect
56. C43×#392C4semidirect
114. C2×C22⋊Dic43D4semidirect
115. C2×C22⋊Dic43D4semidirect
131. C43⋊#95D4semidirect
154. C22×D4×C43C2×C4semidirect
155. C22×D4×C43C2×C4semidirect
166. C2×C22⋊C4×C43C2×C4semidirect
167. C2×C22⋊C4×C43C2×C4semidirect
168. C2×C22⋊C4×C43C2×C4semidirect
169. #95×C43C2×C4semidirect
707. #392Dic43semidirect
728. C43#14519semidirect
751. C22×D4C2×Dic43semidirect
752. C22×D4C2×Dic43semidirect
821. C2×C22⋊C4C2×Dic43semidirect
822. C2×C22⋊C4C2×Dic43semidirect
823. C2×C22⋊C4C2×Dic43semidirect
840. #95C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828022
C2×#145827792
C2×#145827742
#191328522
#191328442
#191328402
#191328362
#191328322
#191328202
#191328172
C2×C43×#3922
#1451943