Finite Group Databasebeta

← #25025955

Subgroups — #25025955

Order 11008.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582807C211yesmaximal, characteristic
2C2×#14582802C211yesmaximal, characteristic, complemented
3C2×#14582799C211yesmaximal, characteristic, complemented
4C2×#14582793C211yesmaximal, characteristic, complemented
5C2×#14582788C211yesmaximal, characteristic, complemented
6C2×#14582778C211yesmaximal, characteristic, complemented
7#19132841C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic, complemented
9#19132838C211yesmaximal, characteristic, complemented
10#19132834C211yesmaximal, characteristic, complemented
11#19132834C211yesmaximal, characteristic, complemented
12#19132829C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14#19132818C211yesmaximal, characteristic, complemented
15C2×C43×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34#14582807C418yescomplemented
35#14582802—24no—
36#14582799—24no—
37#14582793—24no—
38#14582788—24no—
39#14582778—24no—
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
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—22no—
62C22×C22⋊D43—22no—
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⋊D43—41no—
70C22×C22⋊D43—41no—
71C22×C22⋊D43C2×C414yes—
72C22×C22⋊D43C2×C414yescomplemented
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—41no—
83C2×Dic43⋊C4—22no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—41no—
88C2×Dic43⋊C4—41no—
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—41no—
97C2×C22⋊Dic43—41no—
98C2×C22⋊Dic43—41no—
99C2×C22⋊Dic43—41no—
100C2×C22⋊Dic43—41no—
101C2×C22⋊Dic43—41no—
102C2×C22⋊Dic43—41no—
103C2×C22⋊Dic43—41no—
104C2×C22⋊Dic43C2×C414yes—
105C2×C22⋊Dic43C2×C414yescomplemented
106C2×C22⋊Dic43D414yescomplemented
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4—41no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4—41no—
120C2×(C2×D43)⋊C4—41no—
121C2×(C2×D43)⋊C4C2×C414yescomplemented
122C2×C4×Dic43—22no—
123C2×C4×Dic43—22no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—41no—
127C2×C4×Dic43—41no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C43⋊#95—41no—
136C43⋊#95C2×C414yescomplemented
137C43⋊#95D414yescomplemented
138C25×C43C2311yescharacteristic
139C25×C43C2311yescharacteristic
140C22×D4×C43—22no—
141C22×D4×C43—22no—
142C22×D4×C43—22no—
143C22×D4×C43—22no—
144C22×D4×C43—41no—
145C22×D4×C43—41no—
146C22×D4×C43C2×C414yes—
147C23×C4×C43—22no—
148C23×C4×C43—22no—
149C23×C4×C43—22no—
150C23×C4×C43—41no—
151C23×C4×C43—41no—
152C23×C4×C43—41no—
153C23×C4×C43—41no—
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159C2×C22⋊C4×C43—22no—
160C2×C22⋊C4×C43—22no—
161C2×C22⋊C4×C43—22no—
162C2×C22⋊C4×C43—22no—
163C2×C22⋊C4×C43—22no—
164C2×C22⋊C4×C43—41no—
165C2×C22⋊C4×C43—41no—
166C2×C22⋊C4×C43—41no—
167C2×C22⋊C4×C43—41no—
168#95×C43—22no—
169#95×C43D414yescomplemented
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×C43C22×C412yes—
197C24×C43C22×C412yes—
198C24×C43C2×D412yes—
199C24×C43#4112yes—
200C24×C43C2411yescharacteristic
201C23×D43—21no—
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×D43—21no—
215C23×D43C22×C412yes—
216C2×D4×C43—28no—
217C2×D4×C43—28no—
218C2×D4×C43—44no—
219C2×D4×C43—44no—
220C2×D4×C43—44no—
221C2×D4×C43—44no—
222C2×D4×C43—44no—
223C22×C4×C43—21no—
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—44no—
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×C43C22×C412yes—
260C22×C4×C43C2×D412yes—
261C22×C4×C43C2×D412yes—
262C22×C4×C43C2×D412yes—
263C22×C4×C43C2×D412yes—
264C22×C4×C43#4112yes—
265C2×C22⋊D43—28no—
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—
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—21no—
316C22×Dic43—21no—
317C22×Dic43—21no—
318C22×Dic43—21no—
319C22×Dic43—21no—
320C22×Dic43C22×C412yes—
321C22×Dic43C22×C412yes—
322C22×Dic43C22×C412yes—
323C22×Dic43C2×D412yes—
324C22×Dic43C2×D412yes—
325C22×Dic43C2×D412yes—
326C22×Dic43C2×D412yes—
327C22×Dic43#4112yes—
328C22⋊C4×C43—44no—
329C22⋊C4×C43—44no—
330C22⋊C4×C43—44no—
331C22⋊Dic43—28no—
332C22⋊Dic43—44no—
333C22⋊Dic43—44no—
334C22⋊Dic43—44no—
335C22⋊Dic43—44no—
336C22⋊Dic43—44no—
337(C2×D43)⋊C4—28no—
338(C2×D43)⋊C4—44no—
339(C2×D43)⋊C4—44no—
340(C2×D43)⋊C4—44no—
341(C2×D43)⋊C4—44no—
342C4⋊Dic43—44no—
343Dic43⋊C4—44no—
344Dic43⋊C4—44no—
345C4×Dic43—44no—
346C4×Dic43—44no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—22no—
350C23×C43—22no—
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—41no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43—41no—
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×C43C4×D414yes—
417C23×C43C23×C411yescharacteristic
418C23×C43C22×D411yescharacteristic
419C23×C43C22×D411yescharacteristic
420C23×C43C22×D411yescharacteristic
421C23×C43C2×#4111yescharacteristic
422C23×C43C2×#4111yescharacteristic
423C23×C43C2×#4111yescharacteristic
424C23×C43H(5,𝔽2)11yescharacteristic
425C23×C43H(5,𝔽2)11yescharacteristic
426C23×C43H(5,𝔽2)11yescharacteristic
427C23×C43H(5,𝔽2)11yescharacteristic
428C23×C43H(5,𝔽2)11yescharacteristic
429C23×C43H(5,𝔽2)11yescharacteristic
430C23×C43H(5,𝔽2)11yescharacteristic
431C23×C432−1+411yescharacteristic
432C22×D43—22no—
433C22×D43—22no—
434C22×D43—22no—
435C22×D43—22no—
436C22×D43—22no—
437C22×D43—22no—
438C22×D43—22no—
439C22×D43—41no—
440C22×D43—41no—
441C22×D43—41no—
442C22×D43—41no—
443C22×D43—41no—
444C22×D43—41no—
445C22×D43—41no—
446C22×D43—41no—
447C22×D43—41no—
448C22×D43—41no—
449C22×D43—41no—
450C22×D43—41no—
451C22×D43—41no—
452C22×D43—41no—
453C22×D43—41no—
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—
467D4×C43—416no—
468C2×C4×C43—22no—
469C2×C4×C43—22no—
470C2×C4×C43—22no—
471C2×C4×C43—22no—
472C2×C4×C43—22no—
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—416no—
484C2×C4×C43—41no—
485C2×C4×C43—41no—
486C2×C4×C43—41no—
487C2×C4×C43—41no—
488C2×C4×C43—41no—
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×C43C4×D414yes—
504C22⋊D43—416no—
505C22⋊D43—416no—
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—22no—
521C2×Dic43—22no—
522C2×Dic43—22no—
523C2×Dic43—22no—
524C2×Dic43—22no—
525C2×Dic43—22no—
526C2×Dic43—22no—
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×Dic43C4×D414yes—
555#14521—431nomaximal, Sylow
556C22×C43—24no—
557C22×C43—24no—
558C22×C43—24no—
559C22×C43—42no—
560C22×C43—42no—
561C22×C43—42no—
562C22×C43—42no—
563C22×C43—42no—
564C22×C43—42no—
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—81no—
579C22×C43—81no—
580C22×C43—81no—
581C22×C43—81no—
582C22×C43—81no—
583C22×C43—81no—
584C22×C43—81no—
585C22×C43—81no—
586C22×C43C2×C4×D411yescharacteristic
587C22×C43C2×C4×D411yescharacteristic
588C22×C43C2×C4×D411yescharacteristic
589C22×C43#51811yescharacteristic
590C22×C43#51811yescharacteristic
591C22×C43#51811yescharacteristic
592C22×C43#52011yescharacteristic
593C22×C43#53411yescharacteristic
594C22×C43#53511yescharacteristic
595C22×C43#53511yescharacteristic
596C22×C43#53711yescharacteristic
597C22×C43#53711yescharacteristic
598C22×C43#53711yescharacteristic
599C22×C43#53811yescharacteristic
600C22×C43#53911yescharacteristic
601C22×C43#54011yescharacteristic
602C22×C43#54011yescharacteristic
603C22×C43#54211yescharacteristic
604C22×C43#54211yescharacteristic
605C22×C43D4211yescharacteristic
606C22×C43D4211yescharacteristic
607C22×C43D4211yescharacteristic
608C22×C43#54611yescharacteristic
609C22×C43#54611yescharacteristic
610C22×C43#54611yescharacteristic
611C22×C43#54611yescharacteristic
612C22×C43#55011yescharacteristic
613C22×C43#55011yescharacteristic
614C22×C43#55111yescharacteristic
615C22×C43#55111yescharacteristic
616C22×C43#55911yescharacteristic
617C22×C43#56011yescharacteristic
618C22×C43#56011yescharacteristic
619C22×C43#56011yescharacteristic
620C22×C43H(3,𝔽4)11yescharacteristic
621C2×D43—42no—
622C2×D43—42no—
623C2×D43—42no—
624C2×D43—42no—
625C2×D43—42no—
626C2×D43—42no—
627C2×D43—42no—
628C2×D43—81no—
629C2×D43—81no—
630C2×D43—81no—
631C2×D43—81no—
632C2×D43—81no—
633C2×D43—81no—
634C2×D43—81no—
635C2×D43—81no—
636C4×C43—24no—
637C4×C43—42no—
638C4×C43—42no—
639C4×C43—42no—
640C4×C43—81no—
641Dic43—24no—
642Dic43—42no—
643Dic43—42no—
644Dic43—42no—
645Dic43—42no—
646Dic43—42no—
647Dic43—81no—
648C2×#392—431no—
649C2×#390—431no—
650C2×#390—431no—
651C2×#388—431no—
652C2×#388—431no—
653C2×#386—431no—
654C2×#386D4311yescharacteristic, complemented
655#1439—431no—
656#1439—431no—
657#1439—431no—
658#1438—431no—
659#1438—431no—
660#1436—431no—
661#1436—431no—
662C22⋊#95—431no—
663C2×C43—44no—
664C2×C43—82no—
665C2×C43#232411yescharacteristic
666C2×C43#232411yescharacteristic
667C2×C43#232511yescharacteristic
668C2×C43#235811yescharacteristic
669C2×C43#235811yescharacteristic
670C2×C43#236611yescharacteristic
671C2×C43#237511yescharacteristic
672C2×C43#267011yescharacteristic
673C2×C43#267311yescharacteristic
674C2×C43#267311yescharacteristic
675C2×C43#267511yescharacteristic
676C2×C43#270511yescharacteristic
677C2×C43#270511yescharacteristic
678C2×C43#271211yescharacteristic
679C2×C43#275211yescharacteristic
680D43—82no—
681C23×D4—431no—
682C23×D4—431no—
683C23×D4C2×D4311yescharacteristic
684C24×C4C2×D4311yescharacteristic
685C22×C4⋊C4—431no—
686C22×C4⋊C4—431no—
687C22×C4⋊C4—431no—
688C22×C22⋊C4—431no—
689C22×C22⋊C4—431no—
690C22×C22⋊C4—431no—
691C22×C22⋊C4—431no—
692C22×C22⋊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⋊C4C2×D4311yescharacteristic
700C22×C22⋊C4C2×D4311yescharacteristic
701C22×C22⋊C4C2×D4311yescharacteristic
702C22×C42—431no—
703C22×C42—431no—
704#392—438no—
705#390—864no—
706#390—864no—
707#388—864no—
708#388—864no—
709#386—24no—
710#386—864no—
711C2×#95—431no—
712C2×#95—431no—
713C2×#95—431no—
714C2×#95—431no—
715C2×#95—431no—
716C2×#95—431no—
717C2×#95—431no—
718C2×#95—431no—
719C2×#95—431no—
720C2×#95—431no—
721C2×#95C2×D4311yescharacteristic
722C2×#95C2×D4311yescharacteristic
723C43#1452111yescharacteristic, complemented, Sylow
724C25—431no—
725C25C22×D4311yescharacteristic
726C25C22×D4311yescharacteristic
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—434no—
734C22×D4—434no—
735C22×D4—862no—
736C22×D4—862no—
737C22×D4—862no—
738C22×D4—862no—
739C22×D4—1721no—
740C22×D4—1721no—
741C22×D4—1721no—
742C22×D4—1721no—
743C22×D4—1721no—
744C22×D4—1721no—
745C22×D4—1721no—
746C22×D4—1721no—
747C22×D4C4×D4314yes—
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—41no—
752C23×C4—41no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4—431no—
756C23×C4—431no—
757C23×C4—431no—
758C23×C4—431no—
759C23×C4—431no—
760C23×C4—431no—
761C23×C4—431no—
762C23×C4C22×D4311yescharacteristic
763C23×C4C22×D4311yescharacteristic
764C23×C4C22×D4311yescharacteristic
765C23×C4C22×D4311yescharacteristic
766C23×C4C22×D4311yescharacteristic
767C2×C4⋊C4—862no—
768C2×C4⋊C4—862no—
769C2×C4⋊C4—862no—
770C2×C4⋊C4—862no—
771C2×C4⋊C4—862no—
772C2×C4⋊C4—862no—
773C2×C4⋊C4—1721no—
774C2×C4⋊C4—1721no—
775C2×C4⋊C4—1721no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—434no—
786C2×C22⋊C4—434no—
787C2×C22⋊C4—434no—
788C2×C22⋊C4—434no—
789C2×C22⋊C4—862no—
790C2×C22⋊C4—862no—
791C2×C22⋊C4—862no—
792C2×C22⋊C4—862no—
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—1721no—
805C2×C22⋊C4—1721no—
806C2×C22⋊C4—1721no—
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×C42—862no—
819C2×C42—862no—
820C2×C42—862no—
821C2×C42—862no—
822C2×C42—1721no—
823C2×C42—1721no—
824#95—22no—
825#95—434no—
826#95—434no—
827#95—862no—
828#95—862no—
829#95—862no—
830#95—1721no—
831#95—1721no—
832#95—1721no—
833#95—1721no—
834#95—1721no—
835#95C22⋊D4314yescomplemented
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
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—432no—
863C24—861no—
864C24—861no—
865C24—861no—
866C24—861no—
867C24—861no—
868C24—861no—
869C24—861no—
870C24—861no—
871C24—861no—
872C24—861no—
873C24—861no—
874C24—861no—
875C24—861no—
876C24—861no—
877C24C2×C4×D4312yes—
878C24C2×C4×D4312yes—
879C24D4×D4312yes—
880C24#1062190012yes—
881C24C23×D4311yescharacteristic
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—868no—
890C2×D4—868no—
891C2×D4—1724no—
892C2×D4—1724no—
893C2×D4—1724no—
894C2×D4—1724no—
895C2×D4—1724no—
896C2×D4—1724no—
897C2×D4—1724no—
898C2×D4—1724no—
899C2×D4—1724no—
900C2×D4—1724no—
901C2×D4—1724no—
902C2×D4—1724no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
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—21no—
931C22×C4—21no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—432no—
940C22×C4—432no—
941C22×C4—432no—
942C22×C4—432no—
943C22×C4—432no—
944C22×C4—432no—
945C22×C4—432no—
946C22×C4—432no—
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—861no—
987C22×C4—861no—
988C22×C4C2×C4×D4312yes—
989C22×C4#1062189812yes—
990C22×C4D4×D4312yes—
991C22×C4C2×C22⋊D4312yes—
992C22×C4C2×C22⋊D4312yes—
993C22×C4C2×C22⋊D4312yes—
994C4⋊C4—1724no—
995C4⋊C4—1724no—
996C4⋊C4—1724no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—868no—
1001C22⋊C4—868no—
1002C22⋊C4—1724no—
1003C22⋊C4—1724no—
1004C22⋊C4—1724no—
1005C22⋊C4—1724no—
1006C22⋊C4—1724no—
1007C22⋊C4—1724no—
1008C22⋊C4—1724no—
1009C22⋊C4—1724no—
1010C22⋊C4—1724no—
1011C42—1724no—
1012C42—1724no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
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—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
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—862no—
1083C23—862no—
1084C23—862no—
1085C23—862no—
1086C23—862no—
1087C23—862no—
1088C23—862no—
1089C23—1721no—
1090C23—1721no—
1091C23—1721no—
1092C23—1721no—
1093C23—1721no—
1094C23—1721no—
1095C23—1721no—
1096C23—1721no—
1097C23—1721no—
1098C23—1721no—
1099C23—1721no—
1100C23—1721no—
1101C23—1721no—
1102C23—1721no—
1103C23—1721no—
1104C23—1721no—
1105C23—1721no—
1106C23—1721no—
1107C23—1721no—
1108C23—1721no—
1109C23—1721no—
1110C23—1721no—
1111C23—1721no—
1112C23—1721no—
1113C23—1721no—
1114C23—1721no—
1115C23—1721no—
1116C23—1721no—
1117C23(C22⋊D43)⋊C414yes—
1118C23C22×C4×D4311yescharacteristic
1119C23C2×D4×D4311yescharacteristic
1120C23C2×D4×D4311yescharacteristic
1121C23C22×C22⋊D4311yescharacteristic
1122C23#41×D4311yescharacteristic
1123C23C2×#1062190011yescharacteristic
1124C23C2×#1062189811yescharacteristic
1125C23#1306337011yescharacteristic
1126C23#1306337011yescharacteristic
1127C23#1306337011yescharacteristic
1128C23#1306337011yescharacteristic
1129C23#1306337011yescharacteristic
1130C23#1306337111yescharacteristic
1131C23#1306337111yescharacteristic
1132C23#1306337211yescharacteristic
1133D4—416no—
1134D4—17216no—
1135D4—17216no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—416no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
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—434no—
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—862no—
1191C2×C4—862no—
1192C2×C4—862no—
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—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×C4C4×C22⋊D4314yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—3441no—
1252C22—3441no—
1253C22—3441no—
1254C22—3441no—
1255C22—3441no—
1256C22—3441no—
1257C22—3441no—
1258C22—3441no—
1259C22—1722no—
1260C22—1722no—
1261C22—1722no—
1262C22—1722no—
1263C22—1722no—
1264C22—1722no—
1265C22—1722no—
1266C22C4×D4×D4311yescharacteristic
1267C22C2×(C22⋊D43)⋊C411yescharacteristic
1268C22C2×C4×C22⋊D4311yescharacteristic
1269C22#1458337111yescharacteristic
1270C22#1458337111yescharacteristic
1271C22#1458337211yescharacteristic
1272C22#1458337811yescharacteristic
1273C22#1458345711yescharacteristic
1274C22#1458346411yescharacteristic
1275C22#1458346611yescharacteristic
1276C22#1458347611yescharacteristic
1277C22#1458347711yescharacteristic
1278C22#1458347811yescharacteristic
1279C22#1458348411yescharacteristic
1280C22#1458349311yescharacteristic
1281C22#1458349911yescharacteristic
1282C22#1458350011yescharacteristic
1283C22#1458351411yescharacteristic
1284C22#1458351711yescharacteristic
1285C22D4×C22⋊D4311yescharacteristic
1286C22D4×C22⋊D4311yescharacteristic
1287C22#1458353311yescharacteristic
1288C22#1458353611yescharacteristic
1289C22#1458353811yescharacteristic
1290C22#1458353911yescharacteristic
1291C22#1458354311yescharacteristic
1292C22#1458356811yescharacteristic
1293C22#1458357011yescharacteristic
1294C22#1458357211yescharacteristic
1295C22#1458357511yescharacteristic
1296C22#1458363211yescharacteristic
1297C22#1458363711yescharacteristic
1298C22#1458363711yescharacteristic
1299C22#1458363911yescharacteristic
1300C22#1458364211yescharacteristic
1301C4—24no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—81no—
1306C4—864no—
1307C4—3441no—
1308C4—1722no—
1309C4—1722no—
1310C4—1722no—
1311C4—1722no—
1312C4—1722no—
1313C2—44no—
1314C2—82no—
1315C2—3442no—
1316C2#1913728211yescharacteristic
1317C2#1913728511yescharacteristic
1318C2#1913729611yescharacteristic
1319C2#1913757411yescharacteristic
1320C2#1913757511yescharacteristic
1321C2#1913765711yescharacteristic
1322C2#1913773311yescharacteristic
1323C2#1914081711yescharacteristic
1324C2#1914085611yescharacteristic
1325C2#1914085811yescharacteristic
1326C2#1914088511yescharacteristic
1327C2#1914126411yescharacteristic
1328C2#1914127211yescharacteristic
1329C2#1914136211yescharacteristic
1330C2#1914186211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#386C2
socle, cosocleC24×C43C24
prime radicalC2×#14582807C2
hypercenterC2×#386D43
hypocenterC43#14521
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#14582802C2semidirect
3. C2×#14582799C2semidirect
4. C2×#14582793C2semidirect
5. C2×#14582788C2semidirect
6. C2×#14582778C2semidirect
7. #19132841C2semidirect
8. #19132838C2semidirect
9. #19132838C2semidirect
10. #19132834C2semidirect
11. #19132834C2semidirect
12. #19132829C2semidirect
13. #19132826C2semidirect
14. #19132818C2semidirect
15. C2×C43×#386C2semidirect
34. #14582807C4semidirect
72. C22×C22⋊D43C2×C4semidirect
105. C2×C22⋊Dic43C2×C4semidirect
106. C2×C22⋊Dic43D4semidirect
121. C2×(C2×D43)⋊C4C2×C4semidirect
136. C43⋊#95C2×C4semidirect
137. C43⋊#95D4semidirect
169. #95×C43D4semidirect
654. C2×#386D43semidirect
723. C43#14521semidirect
835. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828072
C2×#145828022
C2×#145827992
C2×#145827932
C2×#145827882
C2×#145827782
#191328412
#191328382
#191328342
#191328292
#191328262
#191328182
C2×C43×#3862
#1452143