Finite Group Databasebeta

← #25028027

Subgroups — #25028027

Order 11008.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063308C211yesmaximal, characteristic, complemented
2C2×#14582814C211yesmaximal, characteristic, complemented
3C2×#14582807C211yesmaximal, characteristic
4C2×#14582778C211yesmaximal, characteristic, complemented
5C2×#14582772C211yesmaximal, characteristic, complemented
6#19132858C211yesmaximal, characteristic, complemented
7#19132844C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic, complemented
9#19132837C211yesmaximal, characteristic, complemented
10#19132836C211yesmaximal, characteristic, complemented
11#19132834C211yesmaximal, characteristic, complemented
12#19132833C211yesmaximal, characteristic, complemented
13#19132828C211yesmaximal, characteristic, complemented
14#19132818C211yesmaximal, characteristic, complemented
15C22×C4×D4×C43C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C2×#13063308—24no—
19C2×#13063308—24no—
20C2×#13063308—24no—
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
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×(C2×D43)⋊C4C2211yescharacteristic
35#14582814—24no—
36#14582807—24no—
37#14582778—24no—
38#14582772—24no—
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
50C2×C43⋊#95C2211yescharacteristic
51C23×D4×C43C2211yescharacteristic
52C24×C4×C43C2211yescharacteristic
53C24×C4×C43C2211yescharacteristic
54C2×C4×D4×C43—24no—
55C2×C4×D4×C43—24no—
56C2×C4×D4×C43—24no—
57C22×C4⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C22×C22⋊C4×C43C2211yescharacteristic
60C22×C42×C43C2211yescharacteristic
61C24×D43C2311yescharacteristic
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—22no—
70C22×C22⋊D43—22no—
71C22×C22⋊D43—22no—
72C22×C22⋊D43—41no—
73C22×C22⋊D43—41no—
74C22×C22⋊D43—41no—
75C22×C22⋊D43—41no—
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83#13063308—232no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—41no—
92C2×Dic43⋊C4D414yescomplemented
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—22no—
103C2×C22⋊Dic43—22no—
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—41no—
108C2×C22⋊Dic43—41no—
109C2×C22⋊Dic43—41no—
110C2×C22⋊Dic43—41no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—22no—
118C2×(C2×D43)⋊C4—22no—
119C2×(C2×D43)⋊C4—22no—
120C2×(C2×D43)⋊C4—22no—
121C2×(C2×D43)⋊C4—22no—
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—41no—
124C2×(C2×D43)⋊C4—41no—
125C2×(C2×D43)⋊C4D414yescomplemented
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—41no—
136C43⋊#95—41no—
137C43⋊#95—41no—
138C25×C43C2311yescharacteristic
139C25×C43C2311yescharacteristic
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×C43D414yes—
147C23×C4×C43—22no—
148C23×C4×C43—22no—
149C23×C4×C43—22no—
150C23×C4×C43—22no—
151C23×C4×C43—22no—
152C23×C4×C43—22no—
153C23×C4×C43—22no—
154C23×C4×C43—22no—
155C23×C4×C43—22no—
156C23×C4×C43—41no—
157C23×C4×C43—41no—
158C23×C4×C43—41no—
159C23×C4×C43—41no—
160C23×C4×C43D414yescomplemented
161C23×C4×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C23×C4×C43C2311yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C4×D4×C43—232no—
167C2×C4⋊C4×C43—22no—
168C2×C4⋊C4×C43—22no—
169C2×C4⋊C4×C43—22no—
170C2×C22⋊C4×C43—22no—
171C2×C22⋊C4×C43—22no—
172C2×C22⋊C4×C43—22no—
173C2×C22⋊C4×C43—22no—
174C2×C22⋊C4×C43—22no—
175C2×C22⋊C4×C43D414yescomplemented
176C2×C42×C43—22no—
177C2×C42×C43—22no—
178C2×C42×C43—22no—
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×C43C2×D412yes—
204C24×C43C2×D412yes—
205C24×C43C2×D412yes—
206C24×C43C2×D412yes—
207C24×C43#4112yes—
208C24×C43#4112yes—
209C24×C43C2411yescharacteristic
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×D43—21no—
221C23×D43—21no—
222C23×D43—21no—
223C23×D43—21no—
224C23×D43C2×D412yes—
225C2×D4×C43—28no—
226C2×D4×C43—28no—
227C2×D4×C43—28no—
228C2×D4×C43—28no—
229C2×D4×C43—28no—
230C2×D4×C43—28no—
231C2×D4×C43—28no—
232C22×C4×C43—28no—
233C22×C4×C43—28no—
234C22×C4×C43—28no—
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×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—44no—
262C22×C4×C43—44no—
263C22×C4×C43—44no—
264C22×C4×C43—44no—
265C22×C4×C43—44no—
266C22×C4×C43—44no—
267C22×C4×C43—44no—
268C22×C4×C43—44no—
269C22×C4×C43—44no—
270C22×C4×C43—44no—
271C22×C4×C43—44no—
272C22×C4×C43C2×D412yes—
273C22×C4×C43C2×D412yes—
274C22×C4×C43C2×D412yes—
275C22×C4×C43C2×D412yes—
276C22×C4×C43C2×D412yes—
277C22×C4×C43C2×D412yes—
278C22×C4×C43C2×D412yes—
279C22×C4×C43#4112yes—
280C22×C4×C43#4112yes—
281C2×C22⋊D43—28no—
282C2×C22⋊D43—28no—
283C2×C22⋊D43—44no—
284C2×C22⋊D43—44no—
285C2×C22⋊D43—44no—
286C2×C22⋊D43—44no—
287C2×C22⋊D43—44no—
288C2×C22⋊D43—44no—
289C2×C22⋊D43—44no—
290C2×C22⋊D43—44no—
291C2×C22⋊D43—44no—
292C2×C22⋊D43—44no—
293C2×C22⋊D43—44no—
294C2×C22⋊D43—44no—
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—21no—
329C22×Dic43—21no—
330C22×Dic43—21no—
331C22×Dic43—21no—
332C22×Dic43—21no—
333C22×Dic43—21no—
334C22×Dic43—21no—
335C22×Dic43—21no—
336C22×Dic43—21no—
337C22×Dic43—21no—
338C22×Dic43—21no—
339C22×Dic43C2×D412yes—
340C22×Dic43C2×D412yes—
341C22×Dic43C2×D412yes—
342C22×Dic43#4112yes—
343C22×Dic43#4112yes—
344C4⋊C4×C43—28no—
345C22⋊C4×C43—28no—
346C22⋊C4×C43—28no—
347C42×C43—28no—
348C22⋊Dic43—28no—
349C22⋊Dic43—28no—
350C22⋊Dic43—44no—
351C22⋊Dic43—44no—
352C22⋊Dic43—44no—
353C22⋊Dic43—44no—
354(C2×D43)⋊C4—28no—
355(C2×D43)⋊C4—28no—
356(C2×D43)⋊C4—44no—
357(C2×D43)⋊C4—44no—
358(C2×D43)⋊C4—44no—
359Dic43⋊C4—28no—
360Dic43⋊C4—28no—
361Dic43⋊C4—44no—
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—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#12014yes—
431C23×C43#12314yescomplemented
432C23×C43C22×D411yescharacteristic
433C23×C43C22×D411yescharacteristic
434C23×C43C22×D411yescharacteristic
435C23×C43C22×D411yescharacteristic
436C23×C43C22×D411yescharacteristic
437C23×C43C2×#4111yescharacteristic
438C23×C43C2×#4111yescharacteristic
439C23×C43C2×#4111yescharacteristic
440C23×C43C2×#4111yescharacteristic
441C23×C43C2×#4111yescharacteristic
442C23×C43C2×#4111yescharacteristic
443C23×C43H(5,𝔽2)11yescharacteristic
444C23×C43H(5,𝔽2)11yescharacteristic
445C23×C43H(5,𝔽2)11yescharacteristic
446C23×C432−1+411yescharacteristic
447C22×D43—22no—
448C22×D43—22no—
449C22×D43—22no—
450C22×D43—22no—
451C22×D43—22no—
452C22×D43—22no—
453C22×D43—22no—
454C22×D43—41no—
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×D43—41no—
472C22×D43—41no—
473C22×D43—41no—
474C22×D43—41no—
475C22×D43—41no—
476C22×D43—41no—
477C22×D43—41no—
478C22×D43—41no—
479C22×D43—41no—
480C22×D43—41no—
481C22×D43—41no—
482D4×C43—232no—
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—416no—
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×C43—41no—
516C2×C4×C43—41no—
517C2×C4×C43—41no—
518C2×C4×C43#12014yes—
519C2×C4×C43#12314yescomplemented
520C22⋊D43—416no—
521C22⋊D43—416no—
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—22no—
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—41no—
569C2×Dic43—41no—
570C2×Dic43—41no—
571#14721—431nomaximal, Sylow
572C22×C43—24no—
573C22×C43—24no—
574C22×C43—24no—
575C22×C43—24no—
576C22×C43—24no—
577C22×C43—24no—
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×C43C2×#12011yescharacteristic
603C22×C43C2×#12011yescharacteristic
604C22×C43C2×#12311yescharacteristic
605C22×C43C2×#12311yescharacteristic
606C22×C43#52511yescharacteristic
607C22×C43#52511yescharacteristic
608C22×C43#52511yescharacteristic
609C22×C43#52511yescharacteristic
610C22×C43#52511yescharacteristic
611C22×C43#52511yescharacteristic
612C22×C43#53211yescharacteristic
613C22×C43#53211yescharacteristic
614C22×C43#53211yescharacteristic
615C22×C43#53411yescharacteristic
616C22×C43#53711yescharacteristic
617C22×C43#53811yescharacteristic
618C22×C43#53911yescharacteristic
619C22×C43#54011yescharacteristic
620C22×C43#54211yescharacteristic
621C22×C43D4211yescharacteristic
622C22×C43D4211yescharacteristic
623C22×C43D4211yescharacteristic
624C22×C43D4211yescharacteristic
625C22×C43#54611yescharacteristic
626C22×C43#54611yescharacteristic
627C22×C43#54611yescharacteristic
628C22×C43#54711yescharacteristic
629C22×C43#54711yescharacteristic
630C22×C43#54711yescharacteristic
631C22×C43#54811yescharacteristic
632C22×C43#55011yescharacteristic
633C22×C43#55111yescharacteristic
634C22×C43#55311yescharacteristic
635C22×C43#55311yescharacteristic
636C22×C43#55911yescharacteristic
637C2×D43—42no—
638C2×D43—42no—
639C2×D43—42no—
640C2×D43—42no—
641C2×D43—42no—
642C2×D43—42no—
643C2×D43—42no—
644C2×D43—81no—
645C2×D43—81no—
646C2×D43—81no—
647C2×D43—81no—
648C2×D43—81no—
649C2×D43—81no—
650C2×D43—81no—
651C2×D43—81no—
652C4×C43—24no—
653C4×C43—24no—
654C4×C43—42no—
655C4×C43—42no—
656C4×C43—42no—
657Dic43—42no—
658Dic43—42no—
659Dic43—42no—
660Dic43—42no—
661Dic43—42no—
662Dic43—81no—
663Dic43—81no—
664C22×#123—431no—
665C22×C4×D4D4311yescharacteristic, complemented
666C2×#394—431no—
667C2×#392—431no—
668C2×#386—431no—
669C2×#385—431no—
670#1444—431no—
671#1440—431no—
672#1439—431no—
673#1439—431no—
674#1438—431no—
675#1438—431no—
676#1437—431no—
677#1436—431no—
678C22⋊#95—431no—
679C2×C43—44no—
680C2×C43—44no—
681C2×C43#238811yescharacteristic
682C2×C43#240311yescharacteristic
683C2×C43#240711yescharacteristic
684C2×C43#241811yescharacteristic
685C2×C43#242211yescharacteristic
686C2×C43#243011yescharacteristic
687C2×C43#244311yescharacteristic
688C2×C43#244511yescharacteristic
689C2×C43#245511yescharacteristic
690C2×C43#245611yescharacteristic
691C2×C43#246111yescharacteristic
692C2×C43#246411yescharacteristic
693C2×C43#260211yescharacteristic
694C2×C43#263011yescharacteristic
695C2×C43#284911yescharacteristic
696D43—82no—
697C23×D4—431no—
698C23×D4—431no—
699C23×D4C2×D4311yescharacteristic
700C24×C4C2×D4311yescharacteristic
701C24×C4C2×D4311yescharacteristic
702C2×#123—864no—
703C2×#123—864no—
704C2×#123—864no—
705C2×C4×D4—24no—
706C2×C4×D4—24no—
707C2×C4×D4—24no—
708C22×C4⋊C4—431no—
709C22×C4⋊C4—431no—
710C22×C4⋊C4—431no—
711C22×C4⋊C4C2×D4311yescharacteristic
712C22×C22⋊C4—431no—
713C22×C22⋊C4—431no—
714C22×C22⋊C4—431no—
715C22×C22⋊C4—431no—
716C22×C22⋊C4—431no—
717C22×C22⋊C4—431no—
718C22×C22⋊C4—431no—
719C22×C22⋊C4—431no—
720C22×C22⋊C4—431no—
721C22×C22⋊C4—431no—
722C22×C22⋊C4—431no—
723C22×C22⋊C4C2×D4311yescharacteristic
724C22×C22⋊C4C2×D4311yescharacteristic
725C22×C42C2×D4311yescharacteristic
726#394—864no—
727#392—864no—
728#386—864no—
729#385—864no—
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—
739C2×#95—431no—
740C2×#95—431no—
741C2×#95—431no—
742C43#1472111yescharacteristic, complemented, Sylow
743C25—431no—
744C25C22×D4311yescharacteristic
745C25C22×D4311yescharacteristic
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—862no—
753C22×D4—862no—
754C22×D4—862no—
755C22×D4—862no—
756C22×D4—862no—
757C22×D4—862no—
758C22×D4—862no—
759C22×D4—862no—
760C22×D4—862no—
761C22×D4—862no—
762C22×D4—1721no—
763C22×D4—1721no—
764C22×D4—1721no—
765C22×D4—1721no—
766C22×D4C22⋊D4314yes—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—22no—
775C23×C4—22no—
776C23×C4—41no—
777C23×C4—41no—
778C23×C4—41no—
779C23×C4—41no—
780C23×C4—431no—
781C23×C4—431no—
782C23×C4—431no—
783C23×C4—431no—
784C23×C4—431no—
785C23×C4—431no—
786C23×C4—431no—
787C23×C4C22⋊D4314yescomplemented
788C23×C4C22×D4311yescharacteristic
789C23×C4C22×D4311yescharacteristic
790C23×C4C22×D4311yescharacteristic
791C23×C4C22×D4311yescharacteristic
792C23×C4C22×D4311yescharacteristic
793#123—8632no—
794C4×D4—232no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—434no—
799C2×C4⋊C4—862no—
800C2×C4⋊C4—862no—
801C2×C4⋊C4—862no—
802C2×C4⋊C4—862no—
803C2×C4⋊C4—862no—
804C2×C4⋊C4—862no—
805C2×C4⋊C4—862no—
806C2×C4⋊C4—1721no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—434no—
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—862no—
825C2×C22⋊C4—862no—
826C2×C22⋊C4—862no—
827C2×C22⋊C4—862no—
828C2×C22⋊C4—862no—
829C2×C22⋊C4—862no—
830C2×C22⋊C4—862no—
831C2×C22⋊C4—862no—
832C2×C22⋊C4—862no—
833C2×C22⋊C4—862no—
834C2×C22⋊C4—862no—
835C2×C22⋊C4—862no—
836C2×C22⋊C4—862no—
837C2×C22⋊C4—862no—
838C2×C22⋊C4—862no—
839C2×C22⋊C4—1721no—
840C2×C22⋊C4—1721no—
841C2×C22⋊C4—1721no—
842C2×C22⋊C4—1721no—
843C2×C22⋊C4—1721no—
844C2×C22⋊C4—1721no—
845C2×C22⋊C4C22⋊D4314yescomplemented
846C2×C42—22no—
847C2×C42—22no—
848C2×C42—22no—
849#95—862no—
850#95—862no—
851#95—862no—
852#95—862no—
853#95—862no—
854#95—862no—
855#95—862no—
856#95—862no—
857#95—862no—
858#95—1721no—
859#95—1721no—
860#95—1721no—
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—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—
898C24—861no—
899C24—861no—
900C24#1062189812yes—
901C24#1062189812yes—
902C24C2×C22⋊D4312yes—
903C24C2×C22⋊D4312yes—
904C24C2×C22⋊D4312yes—
905C24C2×C22⋊D4312yes—
906C24C23×D4311yescharacteristic
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—868no—
915C2×D4—868no—
916C2×D4—1724no—
917C2×D4—1724no—
918C2×D4—1724no—
919C2×D4—1724no—
920C2×D4—1724no—
921C2×D4—1724no—
922C2×D4—1724no—
923C2×D4—1724no—
924C2×D4—1724no—
925C2×D4—1724no—
926C2×D4—1724no—
927C2×D4—1724no—
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—28no—
937C22×C4—28no—
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—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—28no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—432no—
969C22×C4—432no—
970C22×C4—432no—
971C22×C4—432no—
972C22×C4—432no—
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—861no—
1007C22×C4—861no—
1008C22×C4—861no—
1009C22×C4—861no—
1010C22×C4—861no—
1011C22×C4—861no—
1012C22×C4—861no—
1013C22×C4—861no—
1014C22×C4—861no—
1015C22×C4—861no—
1016C22×C4—861no—
1017C22×C4#1062189812yes—
1018C22×C4#1062189812yes—
1019C22×C4D4×D4312yes—
1020C22×C4D4×D4312yes—
1021C22×C4C2×C22⋊D4312yes—
1022C22×C4C2×C22⋊D4312yes—
1023C22×C4C2×C22⋊D4312yes—
1024C22×C4C2×C22⋊D4312yes—
1025C22×C4C2×C22⋊D4312yes—
1026C4⋊C4—28no—
1027C4⋊C4—868no—
1028C4⋊C4—868no—
1029C4⋊C4—1724no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—868no—
1033C22⋊C4—868no—
1034C22⋊C4—868no—
1035C22⋊C4—868no—
1036C22⋊C4—1724no—
1037C22⋊C4—1724no—
1038C22⋊C4—1724no—
1039C22⋊C4—1724no—
1040C22⋊C4—1724no—
1041C22⋊C4—1724no—
1042C22⋊C4—1724no—
1043C42—28no—
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—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—862no—
1113C23—862no—
1114C23—862no—
1115C23—862no—
1116C23—862no—
1117C23—862no—
1118C23—862no—
1119C23—1721no—
1120C23—1721no—
1121C23—1721no—
1122C23—1721no—
1123C23—1721no—
1124C23—1721no—
1125C23—1721no—
1126C23—1721no—
1127C23—1721no—
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—
1144C23—1721no—
1145C23—1721no—
1146C23—1721no—
1147C23#1306329414yes—
1148C23#1306330814yescomplemented
1149C23C2×D4×D4311yescharacteristic
1150C23C2×D4×D4311yescharacteristic
1151C23C22×C22⋊D4311yescharacteristic
1152C23C22×C22⋊D4311yescharacteristic
1153C23C22×C22⋊D4311yescharacteristic
1154C23#41×D4311yescharacteristic
1155C23#41×D4311yescharacteristic
1156C23C2×#1062189811yescharacteristic
1157C23C2×#1062189811yescharacteristic
1158C23C2×#1062189811yescharacteristic
1159C23C2×#1062189811yescharacteristic
1160C23#1306337011yescharacteristic
1161C23#1306337011yescharacteristic
1162C23#1306337111yescharacteristic
1163C23#1306337211yescharacteristic
1164D4—232no—
1165D4—17216no—
1166D4—17216no—
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—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—416no—
1189C2×C4—416no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
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—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×C4—1721no—
1247C2×C4—1721no—
1248C2×C4—1721no—
1249C2×C4—1721no—
1250C2×C4—1721no—
1251C2×C4#1306329314yes—
1252C2×C4#1306330814yescomplemented
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
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—3441no—
1284C22—3441no—
1285C22—3441no—
1286C22—3441no—
1287C22—3441no—
1288C22—3441no—
1289C22—3441no—
1290C22—3441no—
1291C22—1722no—
1292C22—1722no—
1293C22—1722no—
1294C22—1722no—
1295C22—1722no—
1296C22—1722no—
1297C22—1722no—
1298C22C2×#1306329311yescharacteristic
1299C22C2×#1306329411yescharacteristic
1300C22C2×#1306330811yescharacteristic
1301C22C2×#1306330811yescharacteristic
1302C22#1458340811yescharacteristic
1303C22#1458340811yescharacteristic
1304C22#1458341011yescharacteristic
1305C22#1458341011yescharacteristic
1306C22#1458341011yescharacteristic
1307C22#1458341011yescharacteristic
1308C22#1458344511yescharacteristic
1309C22#1458344611yescharacteristic
1310C22#1458344611yescharacteristic
1311C22#1458345811yescharacteristic
1312C22#1458347711yescharacteristic
1313C22#1458348211yescharacteristic
1314C22#1458349111yescharacteristic
1315C22#1458350011yescharacteristic
1316C22#1458351411yescharacteristic
1317C22D4×C22⋊D4311yescharacteristic
1318C22D4×C22⋊D4311yescharacteristic
1319C22D4×C22⋊D4311yescharacteristic
1320C22D4×C22⋊D4311yescharacteristic
1321C22#1458353711yescharacteristic
1322C22#1458353711yescharacteristic
1323C22#1458354511yescharacteristic
1324C22#1458354811yescharacteristic
1325C22#1458354811yescharacteristic
1326C22#1458355411yescharacteristic
1327C22#1458355811yescharacteristic
1328C22#1458357011yescharacteristic
1329C22#1458357811yescharacteristic
1330C22#1458359811yescharacteristic
1331C22#1458359911yescharacteristic
1332C22#1458363211yescharacteristic
1333C4—24no—
1334C4—24no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—3441no—
1339C4—3441no—
1340C4—1722no—
1341C4—1722no—
1342C4—1722no—
1343C4—1722no—
1344C4—1722no—
1345C2—44no—
1346C2—44no—
1347C2—3442no—
1348C2#1913781011yescharacteristic
1349C2#1913790511yescharacteristic
1350C2#1913794011yescharacteristic
1351C2#1913805111yescharacteristic
1352C2#1913810311yescharacteristic
1353C2#1913819911yescharacteristic
1354C2#1913832411yescharacteristic
1355C2#1913835411yescharacteristic
1356C2#1913847211yescharacteristic
1357C2#1913848711yescharacteristic
1358C2#1913855611yescharacteristic
1359C2#1913859511yescharacteristic
1360C2#1914020711yescharacteristic
1361C2#1914043211yescharacteristic
1362C2#1914288711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC22×C4×D4×C43C2
prime radicalC2×#14582807C2
hypercenterC22×C4×D4D43
hypocenterC43#14721
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#13063308C2semidirect
2. C2×#14582814C2semidirect
4. C2×#14582778C2semidirect
5. C2×#14582772C2semidirect
6. #19132858C2semidirect
7. #19132844C2semidirect
8. #19132838C2semidirect
9. #19132837C2semidirect
10. #19132836C2semidirect
11. #19132834C2semidirect
12. #19132833C2semidirect
13. #19132828C2semidirect
14. #19132818C2semidirect
15. C22×C4×D4×C43C2semidirect
92. C2×Dic43⋊C4D4semidirect
125. C2×(C2×D43)⋊C4D4semidirect
160. C23×C4×C43D4semidirect
175. C2×C22⋊C4×C43D4semidirect
431. C23×C43#123semidirect
519. C2×C4×C43#123semidirect
665. C22×C4×D4D43semidirect
742. C43#14721semidirect
787. C23×C4C22⋊D43semidirect
845. C2×C22⋊C4C22⋊D43semidirect
1148. C23#13063308semidirect
1252. C2×C4#13063308semidirect

Maximal subgroups

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

subgroupindex
C22×#130633082
C2×#145828142
C2×#145828072
C2×#145827782
C2×#145827722
#191328582
#191328442
#191328382
#191328372
#191328362
#191328342
#191328332
#191328282
#191328182
C22×C4×D4×C432
#1472143