Finite Group Databasebeta

← #25025932

Subgroups — #25025932

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×#14582807C211yesmaximal, characteristic
2C2×#14582802C211yesmaximal, characteristic, complemented
3C2×#14582778C211yesmaximal, characteristic, complemented
4C2×#14582775C211yesmaximal, characteristic, complemented
5C2×#14582775C211yesmaximal, characteristic, complemented
6C2×#14582773C211yesmaximal, characteristic, complemented
7#19132851C211yesmaximal, characteristic, complemented
8#19132842C211yesmaximal, characteristic, complemented
9#19132838C211yesmaximal, characteristic, complemented
10#19132838C211yesmaximal, characteristic, complemented
11#19132834C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13#19132820C211yesmaximal, characteristic, complemented
14#19132818C211yesmaximal, characteristic, complemented
15C2×C43×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
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×C4×Dic43C2211yescharacteristic
32#14582807C418yescomplemented
33#14582802—24no—
34#14582778—24no—
35#14582775—24no—
36#14582775—24no—
37#14582773—24no—
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C23×D4×C43C2211yescharacteristic
51C24×C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C43×#386—24no—
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C22×C22⋊D43—22no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
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
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—41no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43—41no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—41no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—41no—
92C2×Dic43⋊C4—41no—
93C2×C22⋊Dic43—22no—
94C2×C22⋊Dic43—22no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
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⋊Dic43—41no—
105C2×C22⋊Dic43—41no—
106C2×C22⋊Dic43—41no—
107C2×C22⋊Dic43—41no—
108C2×C22⋊Dic43C2×C414yescomplemented
109C2×C22⋊Dic43C2×C414yescomplemented
110C2×C22⋊Dic43D414yescomplemented
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—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4—41no—
120C2×(C2×D43)⋊C4—41no—
121C2×(C2×D43)⋊C4C2×C414yescomplemented
122C2×(C2×D43)⋊C4D414yescomplemented
123C2×C4×Dic43—22no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—41no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C43⋊#95—41no—
136C43⋊#95—41no—
137C43⋊#95C2×C414yescomplemented
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×C414yescomplemented
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×D43C22×C412yes—
214C23×D43C2×D412yes—
215C23×D43#4112yes—
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—28no—
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×Dic43—21no—
321C22×Dic43—21no—
322C22×Dic43C22×C412yes—
323C22×Dic43C22×C412yes—
324C22×Dic43C22×C412yes—
325C22×Dic43C2×D412yes—
326C22×Dic43C2×D412yes—
327C22×Dic43C2×D412yes—
328C2×C4×D43—44no—
329C2×C4×D43—44no—
330C2×C4×D43—44no—
331C2×C4×D43—44no—
332C2×C4×D43—44no—
333C2×C4×D43—44no—
334C2×C4×D43—44no—
335C22⋊C4×C43—44no—
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—
344(C2×D43)⋊C4—28no—
345(C2×D43)⋊C4—44no—
346(C2×D43)⋊C4—44no—
347(C2×D43)⋊C4—44no—
348C4⋊Dic43—44no—
349Dic43⋊C4—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—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×C43—41no—
417C23×C43—41no—
418C23×C43—41no—
419C23×C43—41no—
420C23×C43C4×D414yes—
421C23×C43C23×C411yescharacteristic
422C23×C43C22×D411yescharacteristic
423C23×C43C22×D411yescharacteristic
424C23×C43C22×D411yescharacteristic
425C23×C43C2×#4111yescharacteristic
426C23×C43C2×#4111yescharacteristic
427C23×C43C2×#4111yescharacteristic
428C23×C43H(5,𝔽2)11yescharacteristic
429C23×C43H(5,𝔽2)11yescharacteristic
430C23×C43H(5,𝔽2)11yescharacteristic
431C23×C43H(5,𝔽2)11yescharacteristic
432C23×C43H(5,𝔽2)11yescharacteristic
433C23×C43H(5,𝔽2)11yescharacteristic
434C23×C43H(5,𝔽2)11yescharacteristic
435C23×C432−1+411yescharacteristic
436C22×D43—22no—
437C22×D43—22no—
438C22×D43—22no—
439C22×D43—22no—
440C22×D43—22no—
441C22×D43—22no—
442C22×D43—22no—
443C22×D43—22no—
444C22×D43—22no—
445C22×D43—22no—
446C22×D43—22no—
447C22×D43—22no—
448C22×D43—22no—
449C22×D43—22no—
450C22×D43—22no—
451C22×D43—22no—
452C22×D43—22no—
453C22×D43—22no—
454C22×D43—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×D43C4×D414yes—
471D4×C43—416no—
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—22no—
484C2×C4×C43—22no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—416no—
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×C43—41no—
504C2×C4×C43—41no—
505C2×C4×C43—41no—
506C2×C4×C43—41no—
507C2×C4×C43C4×D414yes—
508C22⋊D43—416no—
509C22⋊D43—416no—
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—22no—
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—
559C4×D43—416no—
560#14519—431nomaximal, Sylow
561C22×C43—24no—
562C22×C43—24no—
563C22×C43—24no—
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—42no—
579C22×C43—42no—
580C22×C43—42no—
581C22×C43—42no—
582C22×C43—42no—
583C22×C43—81no—
584C22×C43—81no—
585C22×C43—81no—
586C22×C43—81no—
587C22×C43—81no—
588C22×C43—81no—
589C22×C43—81no—
590C22×C43—81no—
591C22×C43C2×C4×D411yescharacteristic
592C22×C43C2×C4×D411yescharacteristic
593C22×C43C2×C4×D411yescharacteristic
594C22×C43#51811yescharacteristic
595C22×C43#51811yescharacteristic
596C22×C43#51811yescharacteristic
597C22×C43#52011yescharacteristic
598C22×C43#53411yescharacteristic
599C22×C43#53411yescharacteristic
600C22×C43#53511yescharacteristic
601C22×C43#53511yescharacteristic
602C22×C43#53511yescharacteristic
603C22×C43#53711yescharacteristic
604C22×C43#53811yescharacteristic
605C22×C43#53811yescharacteristic
606C22×C43#53811yescharacteristic
607C22×C43#53911yescharacteristic
608C22×C43#54011yescharacteristic
609C22×C43#54011yescharacteristic
610C22×C43D4211yescharacteristic
611C22×C43D4211yescharacteristic
612C22×C43D4211yescharacteristic
613C22×C43#54611yescharacteristic
614C22×C43#54611yescharacteristic
615C22×C43#54611yescharacteristic
616C22×C43#54611yescharacteristic
617C22×C43#54711yescharacteristic
618C22×C43#54811yescharacteristic
619C22×C43#55111yescharacteristic
620C22×C43#55111yescharacteristic
621C22×C43#55311yescharacteristic
622C22×C43#56011yescharacteristic
623C22×C43#56011yescharacteristic
624C22×C43#56211yescharacteristic
625C22×C43#56211yescharacteristic
626C2×D43—24no—
627C2×D43—24no—
628C2×D43—24no—
629C2×D43—42no—
630C2×D43—42no—
631C2×D43—42no—
632C2×D43—42no—
633C2×D43—42no—
634C2×D43—42no—
635C2×D43—42no—
636C2×D43—42no—
637C2×D43—42no—
638C2×D43—42no—
639C2×D43—42no—
640C2×D43—42no—
641C4×C43—24no—
642C4×C43—42no—
643C4×C43—42no—
644C4×C43—42no—
645C4×C43—81no—
646Dic43—42no—
647Dic43—42no—
648Dic43—42no—
649Dic43—42no—
650Dic43—42no—
651Dic43—42no—
652Dic43—81no—
653C2×#392—431no—
654C2×#390—431no—
655C2×#386—431no—
656C2×#386—431no—
657C2×#386—431no—
658C2×#386D4311yescharacteristic, complemented
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—82no—
670C2×C43#232111yescharacteristic
671C2×C43#232511yescharacteristic
672C2×C43#232811yescharacteristic
673C2×C43#235811yescharacteristic
674C2×C43#235811yescharacteristic
675C2×C43#236111yescharacteristic
676C2×C43#237711yescharacteristic
677C2×C43#266911yescharacteristic
678C2×C43#267111yescharacteristic
679C2×C43#267611yescharacteristic
680C2×C43#267811yescharacteristic
681C2×C43#268811yescharacteristic
682C2×C43#269611yescharacteristic
683C2×C43#270611yescharacteristic
684C2×C43#274911yescharacteristic
685D43—44no—
686C23×D4—431no—
687C23×D4—431no—
688C23×D4C2×D4311yescharacteristic
689C24×C4—431no—
690C24×C4C2×D4311yescharacteristic
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#392—438no—
708#390—864no—
709#386—24no—
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×#95C2×D4311yescharacteristic
727C2×#95C2×D4311yescharacteristic
728C43#1451911yescharacteristic, complemented, Sylow
729C25—431no—
730C25C22×D4311yescharacteristic
731C25C22×D4311yescharacteristic
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—434no—
739C22×D4—434no—
740C22×D4—862no—
741C22×D4—862no—
742C22×D4—862no—
743C22×D4—862no—
744C22×D4—862no—
745C22×D4—862no—
746C22×D4—1721no—
747C22×D4—1721no—
748C22×D4—1721no—
749C22×D4—1721no—
750C22×D4—1721no—
751C22×D4—1721no—
752C22×D4C4×D4314yescomplemented
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—41no—
757C23×C4—41no—
758C23×C4—41no—
759C23×C4—41no—
760C23×C4—431no—
761C23×C4—431no—
762C23×C4—431no—
763C23×C4—431no—
764C23×C4—431no—
765C23×C4—431no—
766C23×C4—431no—
767C23×C4—862no—
768C23×C4—862no—
769C23×C4—862no—
770C23×C4—1721no—
771C23×C4—1721no—
772C23×C4—1721no—
773C23×C4—1721no—
774C23×C4C22×D4311yescharacteristic
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—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—434no—
795C2×C22⋊C4—434no—
796C2×C22⋊C4—434no—
797C2×C22⋊C4—434no—
798C2×C22⋊C4—434no—
799C2×C22⋊C4—862no—
800C2×C22⋊C4—862no—
801C2×C22⋊C4—862no—
802C2×C22⋊C4—862no—
803C2×C22⋊C4—862no—
804C2×C22⋊C4—862no—
805C2×C22⋊C4—862no—
806C2×C22⋊C4—862no—
807C2×C22⋊C4—862no—
808C2×C22⋊C4—862no—
809C2×C22⋊C4—862no—
810C2×C22⋊C4—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⋊C4—1721no—
822C2×C22⋊C4—1721no—
823C2×C22⋊C4—1721no—
824C2×C42—862no—
825C2×C42—862no—
826C2×C42—1721no—
827#95—22no—
828#95—434no—
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#95C22⋊D4314yescomplemented
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—432no—
868C24—432no—
869C24—432no—
870C24—861no—
871C24—861no—
872C24—861no—
873C24—861no—
874C24—861no—
875C24—861no—
876C24—861no—
877C24—861no—
878C24—861no—
879C24—861no—
880C24—861no—
881C24—861no—
882C24C2×C4×D4312yes—
883C24C2×C4×D4312yes—
884C24D4×D4312yes—
885C24#1062190012yes—
886C24C23×D4311yescharacteristic
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—868no—
895C2×D4—868no—
896C2×D4—868no—
897C2×D4—1724no—
898C2×D4—1724no—
899C2×D4—1724no—
900C2×D4—1724no—
901C2×D4—1724no—
902C2×D4—1724no—
903C2×D4—1724no—
904C2×D4—1724no—
905C2×D4—1724no—
906C2×D4—1724no—
907C2×D4—1724no—
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—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—432no—
945C22×C4—432no—
946C22×C4—432no—
947C22×C4—432no—
948C22×C4—432no—
949C22×C4—432no—
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×C4—861no—
989C22×C4—861no—
990C22×C4—861no—
991C22×C4—861no—
992C22×C4—861no—
993C22×C4—1724no—
994C22×C4—1724no—
995C22×C4—1724no—
996C22×C4—1724no—
997C22×C4—1724no—
998C22×C4—1724no—
999C22×C4—1724no—
1000C22×C4C2×C4×D4312yes—
1001C22×C4#1062189812yes—
1002C22×C4D4×D4312yes—
1003C22×C4C2×C22⋊D4312yes—
1004C22×C4C2×C22⋊D4312yes—
1005C22×C4C2×C22⋊D4312yes—
1006C4⋊C4—1724no—
1007C4⋊C4—1724no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—868no—
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—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—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—434no—
1092C23—862no—
1093C23—862no—
1094C23—862no—
1095C23—862no—
1096C23—862no—
1097C23—862no—
1098C23—862no—
1099C23—862no—
1100C23—862no—
1101C23—862no—
1102C23—862no—
1103C23—862no—
1104C23—862no—
1105C23—862no—
1106C23—862no—
1107C23—862no—
1108C23—862no—
1109C23—862no—
1110C23—1721no—
1111C23—1721no—
1112C23—1721no—
1113C23—1721no—
1114C23—1721no—
1115C23—1721no—
1116C23—1721no—
1117C23—1721no—
1118C23—1721no—
1119C23—1721no—
1120C23—1721no—
1121C23—1721no—
1122C23—1721no—
1123C23—1721no—
1124C23—1721no—
1125C23—1721no—
1126C23(C22⋊D43)⋊C414yes—
1127C23C22×C4×D4311yescharacteristic
1128C23C2×D4×D4311yescharacteristic
1129C23C2×D4×D4311yescharacteristic
1130C23C22×C22⋊D4311yescharacteristic
1131C23#41×D4311yescharacteristic
1132C23C2×#1062190011yescharacteristic
1133C23C2×#1062189811yescharacteristic
1134C23#1306337011yescharacteristic
1135C23#1306337011yescharacteristic
1136C23#1306337011yescharacteristic
1137C23#1306337011yescharacteristic
1138C23#1306337011yescharacteristic
1139C23#1306337111yescharacteristic
1140C23#1306337111yescharacteristic
1141C23#1306337211yescharacteristic
1142D4—416no—
1143D4—17216no—
1144D4—17216no—
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—416no—
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—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
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—862no—
1194C2×C4—862no—
1195C2×C4—862no—
1196C2×C4—862no—
1197C2×C4—862no—
1198C2×C4—17216no—
1199C2×C4—1721no—
1200C2×C4—1721no—
1201C2×C4—1721no—
1202C2×C4—1721no—
1203C2×C4—1721no—
1204C2×C4—1721no—
1205C2×C4—1721no—
1206C2×C4—1721no—
1207C2×C4—1721no—
1208C2×C4—1721no—
1209C2×C4—1721no—
1210C2×C4—1721no—
1211C2×C4—1721no—
1212C2×C4—1721no—
1213C2×C4—1721no—
1214C2×C4—1721no—
1215C2×C4—1721no—
1216C2×C4—1721no—
1217C2×C4—1721no—
1218C2×C4—1721no—
1219C2×C4—1721no—
1220C2×C4—1721no—
1221C2×C4—1721no—
1222C2×C4—1721no—
1223C2×C4—1721no—
1224C2×C4—1721no—
1225C2×C4—1721no—
1226C2×C4—1721no—
1227C2×C4—1721no—
1228C2×C4—1721no—
1229C2×C4—1721no—
1230C2×C4C4×C22⋊D4314yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—864no—
1262C22—864no—
1263C22—864no—
1264C22—1722no—
1265C22—1722no—
1266C22—1722no—
1267C22—1722no—
1268C22—1722no—
1269C22—1722no—
1270C22—1722no—
1271C22—1722no—
1272C22—1722no—
1273C22—1722no—
1274C22—1722no—
1275C22—1722no—
1276C22C4×D4×D4311yescharacteristic
1277C22C2×(C22⋊D43)⋊C411yescharacteristic
1278C22C2×C4×C22⋊D4311yescharacteristic
1279C22#1458337111yescharacteristic
1280C22#1458337111yescharacteristic
1281C22#1458337211yescharacteristic
1282C22#1458337811yescharacteristic
1283C22#1458345711yescharacteristic
1284C22#1458345911yescharacteristic
1285C22#1458346311yescharacteristic
1286C22#1458346511yescharacteristic
1287C22#1458346611yescharacteristic
1288C22#1458347611yescharacteristic
1289C22#1458348111yescharacteristic
1290C22#1458348411yescharacteristic
1291C22#1458348511yescharacteristic
1292C22#1458349311yescharacteristic
1293C22#1458350011yescharacteristic
1294C22#1458350011yescharacteristic
1295C22D4×C22⋊D4311yescharacteristic
1296C22D4×C22⋊D4311yescharacteristic
1297C22#1458353311yescharacteristic
1298C22#1458353611yescharacteristic
1299C22#1458353811yescharacteristic
1300C22#1458353911yescharacteristic
1301C22#1458354311yescharacteristic
1302C22#1458355411yescharacteristic
1303C22#1458355611yescharacteristic
1304C22#1458357211yescharacteristic
1305C22#1458357511yescharacteristic
1306C22#1458359911yescharacteristic
1307C22#1458363711yescharacteristic
1308C22#1458363811yescharacteristic
1309C22#1458364411yescharacteristic
1310C22#1458364611yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—81no—
1316C4—3441no—
1317C4—1722no—
1318C4—1722no—
1319C4—1722no—
1320C4—1722no—
1321C4—1722no—
1322C4—1722no—
1323C2—44no—
1324C2—82no—
1325C2—1724no—
1326C2#1913725111yescharacteristic
1327C2#1913729611yescharacteristic
1328C2#1913731711yescharacteristic
1329C2#1913757411yescharacteristic
1330C2#1913757511yescharacteristic
1331C2#1913760711yescharacteristic
1332C2#1913775311yescharacteristic
1333C2#1914080711yescharacteristic
1334C2#1914083211yescharacteristic
1335C2#1914089011yescharacteristic
1336C2#1914091611yescharacteristic
1337C2#1914102611yescharacteristic
1338C2#1914114111yescharacteristic
1339C2#1914128711yescharacteristic
1340C2#1914182211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#386C2
socle, cosocleC24×C43C24
prime radicalC2×#14582807C2
hypercenterC2×#386D43
hypocenterC43#14519
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×#14582778C2semidirect
4. C2×#14582775C2semidirect
5. C2×#14582775C2semidirect
6. C2×#14582773C2semidirect
7. #19132851C2semidirect
8. #19132842C2semidirect
9. #19132838C2semidirect
10. #19132838C2semidirect
11. #19132834C2semidirect
12. #19132831C2semidirect
13. #19132820C2semidirect
14. #19132818C2semidirect
15. C2×C43×#386C2semidirect
32. #14582807C4semidirect
72. C22×C22⋊D43C2×C4semidirect
108. C2×C22⋊Dic43C2×C4semidirect
109. C2×C22⋊Dic43C2×C4semidirect
110. C2×C22⋊Dic43D4semidirect
121. C2×(C2×D43)⋊C4C2×C4semidirect
122. C2×(C2×D43)⋊C4D4semidirect
137. C43⋊#95C2×C4semidirect
146. C22×D4×C43C2×C4semidirect
169. #95×C43D4semidirect
658. C2×#386D43semidirect
728. C43#14519semidirect
752. C22×D4C4×D43semidirect
840. #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×#145827782
C2×#145827752
C2×#145827732
#191328512
#191328422
#191328382
#191328342
#191328312
#191328202
#191328182
C2×C43×#3862
#1451943