Finite Group Databasebeta

← #25021882

Subgroups — #25021882

Order 11008.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic43C211yesmaximal, characteristic, complemented
2C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
3C2×#14582807C211yesmaximal, characteristic
4C2×#14582776C211yesmaximal, characteristic, complemented
5C2×#14582775C211yesmaximal, characteristic, complemented
6C2×#14582773C211yesmaximal, characteristic, complemented
7C2×#14582771C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic, complemented
9#19132834C211yesmaximal, characteristic, complemented
10#19132832C211yesmaximal, characteristic, complemented
11#19132831C211yesmaximal, characteristic, complemented
12#19132829C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C43×#1438C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×D4×Dic43—24no—
22C2×D4×Dic43—24no—
23C2×D4×Dic43—24no—
24C2×(C22⋊D43)⋊C4—24no—
25C2×(C22⋊D43)⋊C4—24no—
26C2×(C22⋊D43)⋊C4—24no—
27C22×C4⋊Dic43C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40#14582807C418yescomplemented
41#14582776—24no—
42#14582775—24no—
43#14582773—24no—
44#14582771—24no—
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C23×D4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C22×C22⋊C4×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C2×#95×C43C2211yescharacteristic
62C24×D43C2311yescharacteristic
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—22no—
73C22×C22⋊D43—41no—
74C22×C22⋊D43—41no—
75C22×C22⋊D43C2×C414yescomplemented
76C22×C22⋊D43C2×C414yescomplemented
77C23×Dic43—22no—
78C23×Dic43—22no—
79C23×Dic43—22no—
80C23×Dic43—22no—
81C23×Dic43—22no—
82C23×Dic43—22no—
83C23×Dic43—22no—
84C23×Dic43—22no—
85C23×Dic43—22no—
86C23×Dic43—41no—
87C23×Dic43—41no—
88C23×Dic43—41no—
89C23×Dic43—41no—
90C23×Dic43D414yescomplemented
91C23×Dic43C2311yescharacteristic
92C23×Dic43C2311yescharacteristic
93C23×Dic43C2311yescharacteristic
94C23×Dic43C2311yescharacteristic
95C23×Dic43C2311yescharacteristic
96C23×Dic43C2311yescharacteristic
97C23×Dic43C2311yescharacteristic
98C22×C4×D43—22no—
99C22×C4×D43—22no—
100C22×C4×D43—22no—
101C22×C4×D43—22no—
102C22×C4×D43—22no—
103C22×C4×D43—41no—
104C22×C4×D43—41no—
105D4×Dic43—232no—
106(C22⋊D43)⋊C4—232no—
107C2×C4⋊Dic43—22no—
108C2×C4⋊Dic43—22no—
109C2×C4⋊Dic43D414yescomplemented
110C2×Dic43⋊C4—22no—
111C2×Dic43⋊C4—22no—
112C2×Dic43⋊C4—22no—
113C2×Dic43⋊C4—22no—
114C2×Dic43⋊C4—41no—
115C2×Dic43⋊C4D414yescomplemented
116C2×C22⋊Dic43—22no—
117C2×C22⋊Dic43—22no—
118C2×C22⋊Dic43—22no—
119C2×C22⋊Dic43—22no—
120C2×C22⋊Dic43—22no—
121C2×C22⋊Dic43—22no—
122C2×C22⋊Dic43—22no—
123C2×C22⋊Dic43—41no—
124C2×C22⋊Dic43—41no—
125C2×C22⋊Dic43C2×C414yescomplemented
126C2×C22⋊Dic43C2×C414yescomplemented
127C2×C22⋊Dic43D414yescomplemented
128C2×(C2×D43)⋊C4—22no—
129C2×(C2×D43)⋊C4—22no—
130C2×(C2×D43)⋊C4—22no—
131C2×(C2×D43)⋊C4—22no—
132C2×(C2×D43)⋊C4—22no—
133C2×(C2×D43)⋊C4—22no—
134C2×(C2×D43)⋊C4—22no—
135C2×(C2×D43)⋊C4—22no—
136C2×(C2×D43)⋊C4—41no—
137C2×(C2×D43)⋊C4—41no—
138C2×(C2×D43)⋊C4C2×C414yescomplemented
139C2×(C2×D43)⋊C4D414yescomplemented
140C2×C4×Dic43—22no—
141C2×C4×Dic43—22no—
142C2×C4×Dic43—22no—
143C2×C4×Dic43—22no—
144C2×C4×Dic43—22no—
145C2×C4×Dic43—22no—
146C43⋊#95—22no—
147C43⋊#95—22no—
148C43⋊#95—22no—
149C43⋊#95—22no—
150C43⋊#95—22no—
151C43⋊#95—22no—
152C43⋊#95—22no—
153C43⋊#95—22no—
154C43⋊#95—41no—
155C43⋊#95C2×C414yescomplemented
156C25×C43C2311yescharacteristic
157C25×C43C2311yescharacteristic
158C22×D4×C43—22no—
159C22×D4×C43—22no—
160C22×D4×C43—22no—
161C22×D4×C43—22no—
162C22×D4×C43—22no—
163C22×D4×C43—22no—
164C22×D4×C43C2×C414yescomplemented
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C23×C4×C43C2311yescharacteristic
168C23×C4×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
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×C43—22no—
176C2×C22⋊C4×C43—22no—
177C2×C22⋊C4×C43—22no—
178C2×C22⋊C4×C43—41no—
179C2×C22⋊C4×C43—41no—
180C2×C22⋊C4×C43—41no—
181C2×C22⋊C4×C43—41no—
182#95×C43—22no—
183#95×C43—22no—
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×C43C2×D412yes—
211C24×C43C2×D412yes—
212C24×C43#4112yes—
213C24×C43#4112yes—
214C24×C43C2411yescharacteristic
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×D43—21no—
225C23×D43—21no—
226C23×D43—21no—
227C23×D43C22×C412yes—
228C23×D43C2×D412yes—
229C23×D43#4112yes—
230C2×D4×C43—28no—
231C2×D4×C43—28no—
232C2×D4×C43—28no—
233C2×D4×C43—28no—
234C2×D4×C43—28no—
235C2×D4×C43—28no—
236C2×D4×C43—28no—
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—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43C22×C412yes—
268C22×C4×C43C2×D412yes—
269C22×C4×C43C2×D412yes—
270C22×C4×C43C2×D412yes—
271C22×C4×C43#4112yes—
272C2×C22⋊D43—28no—
273C2×C22⋊D43—28no—
274C2×C22⋊D43—28no—
275C2×C22⋊D43—28no—
276C2×C22⋊D43—28no—
277C2×C22⋊D43—28no—
278C2×C22⋊D43—28no—
279C2×C22⋊D43—28no—
280C2×C22⋊D43—28no—
281C2×C22⋊D43—44no—
282C2×C22⋊D43—44no—
283C2×C22⋊D43—44no—
284C2×C22⋊D43—44no—
285C2×C22⋊D43—44no—
286C22×Dic43—28no—
287C22×Dic43—28no—
288C22×Dic43—28no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—21no—
294C22×Dic43—21no—
295C22×Dic43—21no—
296C22×Dic43—21no—
297C22×Dic43—21no—
298C22×Dic43—21no—
299C22×Dic43—21no—
300C22×Dic43—21no—
301C22×Dic43—21no—
302C22×Dic43—21no—
303C22×Dic43—21no—
304C22×Dic43—21no—
305C22×Dic43—21no—
306C22×Dic43—21no—
307C22×Dic43—21no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43—21no—
312C22×Dic43—21no—
313C22×Dic43—21no—
314C22×Dic43—21no—
315C22×Dic43—21no—
316C22×Dic43—21no—
317C22×Dic43—21no—
318C22×Dic43—21no—
319C22×Dic43—21no—
320C22×Dic43—21no—
321C22×Dic43—21no—
322C22×Dic43—21no—
323C22×Dic43—21no—
324C22×Dic43—21no—
325C22×Dic43—44no—
326C22×Dic43—44no—
327C22×Dic43—44no—
328C22×Dic43—44no—
329C22×Dic43—44no—
330C22×Dic43—44no—
331C22×Dic43—44no—
332C22×Dic43—44no—
333C22×Dic43—44no—
334C22×Dic43—44no—
335C22×Dic43—44no—
336C22×Dic43C22×C412yes—
337C22×Dic43C22×C412yes—
338C22×Dic43C22×C412yes—
339C22×Dic43C2×D412yes—
340C22×Dic43C2×D412yes—
341C22×Dic43C2×D412yes—
342C22×Dic43C2×D412yes—
343C22×Dic43C2×D412yes—
344C22×Dic43C2×D412yes—
345C22×Dic43C2×D412yes—
346C22×Dic43C2×D412yes—
347C22×Dic43C2×D412yes—
348C22×Dic43#4112yes—
349C2×C4×D43—28no—
350C2×C4×D43—44no—
351C2×C4×D43—44no—
352C2×C4×D43—44no—
353C2×C4×D43—44no—
354C2×C4×D43—44no—
355C2×C4×D43—44no—
356C22⋊C4×C43—28no—
357C22⋊C4×C43—44no—
358C22⋊C4×C43—44no—
359C22⋊C4×C43—44no—
360C22⋊Dic43—28no—
361C22⋊Dic43—28no—
362C22⋊Dic43—28no—
363C22⋊Dic43—44no—
364(C2×D43)⋊C4—28no—
365(C2×D43)⋊C4—28no—
366(C2×D43)⋊C4—44no—
367(C2×D43)⋊C4—44no—
368C4⋊Dic43—28no—
369Dic43⋊C4—28no—
370Dic43⋊C4—44no—
371C4×Dic43—28no—
372C4×Dic43—28no—
373C23×C43—22no—
374C23×C43—22no—
375C23×C43—22no—
376C23×C43—22no—
377C23×C43—22no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—22no—
393C23×C43—22no—
394C23×C43—22no—
395C23×C43—22no—
396C23×C43—22no—
397C23×C43—22no—
398C23×C43—22no—
399C23×C43—22no—
400C23×C43—22no—
401C23×C43—22no—
402C23×C43—22no—
403C23×C43—22no—
404C23×C43—22no—
405C23×C43—22no—
406C23×C43—22no—
407C23×C43—22no—
408C23×C43—22no—
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×C43C4×D414yes—
442C23×C43C4×D414yescomplemented
443C23×C43C23×C411yescharacteristic
444C23×C43C22×D411yescharacteristic
445C23×C43C22×D411yescharacteristic
446C23×C43C22×D411yescharacteristic
447C23×C43C22×D411yescharacteristic
448C23×C43C22×D411yescharacteristic
449C23×C43C2×#4111yescharacteristic
450C23×C43C2×#4111yescharacteristic
451C23×C43C2×#4111yescharacteristic
452C23×C43C2×#4111yescharacteristic
453C23×C43C2×#4111yescharacteristic
454C23×C43H(5,𝔽2)11yescharacteristic
455C23×C43H(5,𝔽2)11yescharacteristic
456C23×C43H(5,𝔽2)11yescharacteristic
457C23×C432−1+411yescharacteristic
458C22×D43—22no—
459C22×D43—22no—
460C22×D43—22no—
461C22×D43—22no—
462C22×D43—22no—
463C22×D43—22no—
464C22×D43—22no—
465C22×D43—22no—
466C22×D43—22no—
467C22×D43—22no—
468C22×D43—22no—
469C22×D43—22no—
470C22×D43—22no—
471C22×D43—22no—
472C22×D43—22no—
473C22×D43—22no—
474C22×D43—22no—
475C22×D43—22no—
476C22×D43—41no—
477C22×D43—41no—
478C22×D43—41no—
479C22×D43—41no—
480C22×D43—41no—
481C22×D43—41no—
482C22×D43—41no—
483C22×D43—41no—
484C22×D43—41no—
485C22×D43—41no—
486C22×D43—41no—
487C22×D43—41no—
488C22×D43—41no—
489C22×D43—41no—
490C22×D43—41no—
491C22×D43—41no—
492C22×D43C4×D414yescomplemented
493D4×C43—232no—
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—22no—
505C2×C4×C43—22no—
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—41no—
519C2×C4×C43—41no—
520C2×C4×C43—41no—
521C2×C4×C43—41no—
522C2×C4×C43—41no—
523C2×C4×C43—41no—
524C2×C4×C43—41no—
525C2×C4×C43—41no—
526C2×C4×C43—41no—
527C2×C4×C43—41no—
528C2×C4×C43C4×D414yescomplemented
529C22⋊D43—232no—
530C22⋊D43—416no—
531C2×Dic43—22no—
532C2×Dic43—22no—
533C2×Dic43—22no—
534C2×Dic43—22no—
535C2×Dic43—22no—
536C2×Dic43—22no—
537C2×Dic43—22no—
538C2×Dic43—22no—
539C2×Dic43—22no—
540C2×Dic43—22no—
541C2×Dic43—22no—
542C2×Dic43—22no—
543C2×Dic43—22no—
544C2×Dic43—22no—
545C2×Dic43—22no—
546C2×Dic43—22no—
547C2×Dic43—22no—
548C2×Dic43—22no—
549C2×Dic43—22no—
550C2×Dic43—22no—
551C2×Dic43—22no—
552C2×Dic43—22no—
553C2×Dic43—22no—
554C2×Dic43—22no—
555C2×Dic43—22no—
556C2×Dic43—22no—
557C2×Dic43—22no—
558C2×Dic43—22no—
559C2×Dic43—22no—
560C2×Dic43—22no—
561C2×Dic43—416no—
562C2×Dic43—416no—
563C2×Dic43—41no—
564C2×Dic43—41no—
565C2×Dic43—41no—
566C2×Dic43—41no—
567C2×Dic43—41no—
568C2×Dic43—41no—
569C2×Dic43—41no—
570C2×Dic43—41no—
571C2×Dic43—41no—
572C2×Dic43—41no—
573C2×Dic43—41no—
574C2×Dic43—41no—
575C2×Dic43—41no—
576C2×Dic43—41no—
577C2×Dic43—41no—
578C2×Dic43—41no—
579C2×Dic43C4×D414yescomplemented
580C2×Dic43#12014yes—
581C2×Dic43#12014yes—
582C4×D43—416no—
583#14171—431nomaximal, Sylow
584C22×C43—24no—
585C22×C43—24no—
586C22×C43—24no—
587C22×C43—24no—
588C22×C43—24no—
589C22×C43—24no—
590C22×C43—42no—
591C22×C43—42no—
592C22×C43—42no—
593C22×C43—42no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—42no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43—42no—
600C22×C43—42no—
601C22×C43—42no—
602C22×C43—42no—
603C22×C43—42no—
604C22×C43—42no—
605C22×C43—42no—
606C22×C43—42no—
607C22×C43—42no—
608C22×C43—42no—
609C22×C43—42no—
610C22×C43—42no—
611C22×C43—42no—
612C22×C43—42no—
613C22×C43—42no—
614C22×C43C2×C4×D411yescharacteristic
615C22×C43C2×C4×D411yescharacteristic
616C22×C43C2×C4×D411yescharacteristic
617C22×C43C2×C4×D411yescharacteristic
618C22×C43C2×C4×D411yescharacteristic
619C22×C43#51811yescharacteristic
620C22×C43#52011yescharacteristic
621C22×C43C2×#12011yescharacteristic
622C22×C43C2×#12011yescharacteristic
623C22×C43#52511yescharacteristic
624C22×C43#52511yescharacteristic
625C22×C43#52511yescharacteristic
626C22×C43#52511yescharacteristic
627C22×C43#52511yescharacteristic
628C22×C43#52511yescharacteristic
629C22×C43#53411yescharacteristic
630C22×C43#53711yescharacteristic
631C22×C43#53811yescharacteristic
632C22×C43#53911yescharacteristic
633C22×C43D4211yescharacteristic
634C22×C43D4211yescharacteristic
635C22×C43D4211yescharacteristic
636C22×C43D4211yescharacteristic
637C22×C43#54611yescharacteristic
638C22×C43#54611yescharacteristic
639C22×C43#54711yescharacteristic
640C22×C43#54711yescharacteristic
641C22×C43#54811yescharacteristic
642C22×C43#54811yescharacteristic
643C22×C43#55011yescharacteristic
644C22×C43#55011yescharacteristic
645C22×C43#55111yescharacteristic
646C22×C43#55311yescharacteristic
647C22×C43#55311yescharacteristic
648C22×C43#55911yescharacteristic
649C2×D43—24no—
650C2×D43—24no—
651C2×D43—24no—
652C2×D43—42no—
653C2×D43—42no—
654C2×D43—42no—
655C2×D43—42no—
656C2×D43—42no—
657C2×D43—42no—
658C2×D43—42no—
659C2×D43—42no—
660C2×D43—42no—
661C2×D43—42no—
662C2×D43—42no—
663C2×D43—42no—
664C4×C43—24no—
665C4×C43—42no—
666C4×C43—42no—
667C4×C43—81no—
668C4×C43—81no—
669Dic43—24no—
670Dic43—24no—
671Dic43—24no—
672Dic43—42no—
673Dic43—42no—
674Dic43—42no—
675Dic43—42no—
676C22×C4×D4—431no—
677C22×C4×D4—431no—
678C2×#392—431no—
679C2×#386—431no—
680C2×#386—431no—
681C2×#385—431no—
682C2×#385—431no—
683#1439—431no—
684#1438—431no—
685#1438D4311yescharacteristic, complemented
686#1437—431no—
687#1437—431no—
688#1436—431no—
689#1436—431no—
690C22⋊#95—431no—
691C2×C43—44no—
692C2×C43—44no—
693C2×C43C4×#12011yescharacteristic
694C2×C43C4×#12011yescharacteristic
695C2×C43#232511yescharacteristic
696C2×C43#235811yescharacteristic
697C2×C43#236111yescharacteristic
698C2×C43#236111yescharacteristic
699C2×C43#236611yescharacteristic
700C2×C43#240311yescharacteristic
701C2×C43#240711yescharacteristic
702C2×C43#240711yescharacteristic
703C2×C43#245511yescharacteristic
704C2×C43#245611yescharacteristic
705C2×C43#245611yescharacteristic
706C2×C43#246311yescharacteristic
707C2×C43#260011yescharacteristic
708D43—44no—
709C23×D4—431no—
710C23×D4—431no—
711C23×D4C2×D4311yescharacteristic
712C24×C4—431no—
713C24×C4—431no—
714C24×C4—431no—
715C2×C4×D4—864no—
716C2×C4×D4—864no—
717C2×C4×D4—864no—
718C2×C4×D4—864no—
719C2×C4×D4—864no—
720C2×C4×D4—864no—
721C22×C4⋊C4—431no—
722C22×C4⋊C4—431no—
723C22×C4⋊C4—431no—
724C22×C22⋊C4—431no—
725C22×C22⋊C4—431no—
726C22×C22⋊C4—431no—
727C22×C22⋊C4—431no—
728C22×C22⋊C4—431no—
729C22×C22⋊C4—431no—
730C22×C22⋊C4—431no—
731C22×C22⋊C4—431no—
732C22×C22⋊C4C2×D4311yescharacteristic
733C22×C22⋊C4C2×D4311yescharacteristic
734C22×C22⋊C4C2×D4311yescharacteristic
735C22×C22⋊C4C2×D4311yescharacteristic
736C22×C42—431no—
737C22×C42—431no—
738#392—438no—
739#386—864no—
740#386—864no—
741#385—864no—
742#385—864no—
743C2×#95—431no—
744C2×#95—431no—
745C2×#95—431no—
746C2×#95—431no—
747C2×#95—431no—
748C2×#95—431no—
749C2×#95—431no—
750C2×#95—431no—
751C2×#95—431no—
752C2×#95—431no—
753C2×#95C2×D4311yescharacteristic
754C2×#95C2×D4311yescharacteristic
755C43#1417111yescharacteristic, complemented, Sylow
756C25—431no—
757C25C22×D4311yescharacteristic
758C25C22×D4311yescharacteristic
759C22×D4—22no—
760C22×D4—22no—
761C22×D4—22no—
762C22×D4—22no—
763C22×D4—22no—
764C22×D4—22no—
765C22×D4—434no—
766C22×D4—434no—
767C22×D4—862no—
768C22×D4—862no—
769C22×D4—862no—
770C22×D4—862no—
771C22×D4—862no—
772C22×D4—862no—
773C22×D4—862no—
774C22×D4—862no—
775C22×D4—862no—
776C22×D4—862no—
777C22×D4—1721no—
778C22×D4—1721no—
779C22×D4C4×D4314yescomplemented
780C23×C4—431no—
781C23×C4—431no—
782C23×C4—431no—
783C23×C4—431no—
784C23×C4—431no—
785C23×C4—431no—
786C23×C4—431no—
787C23×C4—434no—
788C23×C4—862no—
789C23×C4—862no—
790C23×C4—862no—
791C23×C4—862no—
792C23×C4—862no—
793C23×C4—862no—
794C23×C4—862no—
795C23×C4—862no—
796C23×C4—862no—
797C23×C4—862no—
798C23×C4—862no—
799C23×C4—862no—
800C23×C4—862no—
801C23×C4—862no—
802C23×C4—1721no—
803C23×C4—1721no—
804C23×C4—1721no—
805C23×C4—1721no—
806C23×C4—1721no—
807C23×C4—1721no—
808C23×C4C22×D4311yescharacteristic
809C23×C4C22×D4311yescharacteristic
810C23×C4C22×D4311yescharacteristic
811C23×C4C22×D4311yescharacteristic
812C23×C4C22×D4311yescharacteristic
813C4×D4—8632no—
814C4×D4—8632no—
815C2×C4⋊C4—434no—
816C2×C4⋊C4—434no—
817C2×C4⋊C4—862no—
818C2×C4⋊C4—862no—
819C2×C4⋊C4—862no—
820C2×C4⋊C4—862no—
821C2×C4⋊C4—862no—
822C2×C4⋊C4—862no—
823C2×C4⋊C4—1721no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—22no—
830C2×C22⋊C4—22no—
831C2×C22⋊C4—22no—
832C2×C22⋊C4—41no—
833C2×C22⋊C4—41no—
834C2×C22⋊C4—41no—
835C2×C22⋊C4—41no—
836C2×C22⋊C4—434no—
837C2×C22⋊C4—434no—
838C2×C22⋊C4—434no—
839C2×C22⋊C4—434no—
840C2×C22⋊C4—434no—
841C2×C22⋊C4—862no—
842C2×C22⋊C4—862no—
843C2×C22⋊C4—862no—
844C2×C22⋊C4—862no—
845C2×C22⋊C4—862no—
846C2×C22⋊C4—862no—
847C2×C22⋊C4—862no—
848C2×C22⋊C4—862no—
849C2×C22⋊C4—862no—
850C2×C22⋊C4—862no—
851C2×C22⋊C4—862no—
852C2×C22⋊C4—862no—
853C2×C22⋊C4—862no—
854C2×C22⋊C4—862no—
855C2×C22⋊C4—862no—
856C2×C22⋊C4—1721no—
857C2×C22⋊C4—1721no—
858C2×C22⋊C4—1721no—
859C2×C22⋊C4—1721no—
860C2×C42—862no—
861C2×C42—862no—
862C2×C42—862no—
863C2×C42—862no—
864C2×C42—862no—
865C2×C42—862no—
866#95—22no—
867#95—22no—
868#95—434no—
869#95—862no—
870#95—862no—
871#95—862no—
872#95—862no—
873#95—862no—
874#95—862no—
875#95—862no—
876#95—862no—
877#95—1721no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—432no—
903C24—432no—
904C24—432no—
905C24—861no—
906C24—861no—
907C24—861no—
908C24—861no—
909C24—861no—
910C24—861no—
911C24—861no—
912C24—861no—
913C24—861no—
914C24—861no—
915C24—861no—
916C24—861no—
917C24C2×C4×D4312yes—
918C24C2×C4×D4312yes—
919C24D4×D4312yes—
920C24D4×D4312yes—
921C24#1062190012yes—
922C24#1062190012yes—
923C24C23×D4311yescharacteristic
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—28no—
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—868no—
932C2×D4—868no—
933C2×D4—868no—
934C2×D4—868no—
935C2×D4—868no—
936C2×D4—868no—
937C2×D4—868no—
938C2×D4—868no—
939C2×D4—868no—
940C2×D4—1724no—
941C2×D4—1724no—
942C2×D4—1724no—
943C2×D4—1724no—
944C2×D4—1724no—
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—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—432no—
976C22×C4—432no—
977C22×C4—432no—
978C22×C4—432no—
979C22×C4—432no—
980C22×C4—432no—
981C22×C4—432no—
982C22×C4—432no—
983C22×C4—432no—
984C22×C4—432no—
985C22×C4—432no—
986C22×C4—432no—
987C22×C4—432no—
988C22×C4—868no—
989C22×C4—868no—
990C22×C4—868no—
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—868no—
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—861no—
1018C22×C4—861no—
1019C22×C4—861no—
1020C22×C4—861no—
1021C22×C4—861no—
1022C22×C4—861no—
1023C22×C4—861no—
1024C22×C4—861no—
1025C22×C4—861no—
1026C22×C4—861no—
1027C22×C4—861no—
1028C22×C4—1724no—
1029C22×C4—1724no—
1030C22×C4—1724no—
1031C22×C4—1724no—
1032C22×C4—1724no—
1033C22×C4—1724no—
1034C22×C4—1724no—
1035C22×C4—1724no—
1036C22×C4—1724no—
1037C22×C4—1724no—
1038C22×C4—1724no—
1039C22×C4—1724no—
1040C22×C4—1724no—
1041C22×C4—1724no—
1042C22×C4—1724no—
1043C22×C4—1724no—
1044C22×C4—1724no—
1045C22×C4C2×C4×D4312yes—
1046C22×C4D4×D4312yes—
1047C22×C4D4×D4312yes—
1048C22×C4D4×D4312yes—
1049C22×C4#1062190012yes—
1050C4⋊C4—868no—
1051C4⋊C4—868no—
1052C4⋊C4—1724no—
1053C22⋊C4—28no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—868no—
1058C22⋊C4—868no—
1059C22⋊C4—868no—
1060C22⋊C4—868no—
1061C22⋊C4—868no—
1062C22⋊C4—1724no—
1063C22⋊C4—1724no—
1064C22⋊C4—1724no—
1065C42—868no—
1066C42—868no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—434no—
1136C23—862no—
1137C23—862no—
1138C23—862no—
1139C23—862no—
1140C23—862no—
1141C23—862no—
1142C23—862no—
1143C23—862no—
1144C23—862no—
1145C23—862no—
1146C23—862no—
1147C23—862no—
1148C23—862no—
1149C23—862no—
1150C23—862no—
1151C23—862no—
1152C23—862no—
1153C23—862no—
1154C23—1721no—
1155C23—1721no—
1156C23—1721no—
1157C23—1721no—
1158C23—1721no—
1159C23—1721no—
1160C23—1721no—
1161C23—1721no—
1162C23—1721no—
1163C23—1721no—
1164C23—1721no—
1165C23—1721no—
1166C23—1721no—
1167C23—1721no—
1168C23—1721no—
1169C23—1721no—
1170C23(C22⋊D43)⋊C414yes—
1171C23(C22⋊D43)⋊C414yescomplemented
1172C23C22×C4×D4311yescharacteristic
1173C23C2×D4×D4311yescharacteristic
1174C23C2×D4×D4311yescharacteristic
1175C23C2×D4×D4311yescharacteristic
1176C23C2×D4×D4311yescharacteristic
1177C23C2×D4×D4311yescharacteristic
1178C23#41×D4311yescharacteristic
1179C23#41×D4311yescharacteristic
1180C23C2×#1062190011yescharacteristic
1181C23C2×#1062190011yescharacteristic
1182C23C2×#1062190011yescharacteristic
1183C23#1306337011yescharacteristic
1184C23#1306337011yescharacteristic
1185C23#1306337111yescharacteristic
1186C23#1306337211yescharacteristic
1187D4—232no—
1188D4—8632no—
1189D4—17216no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—434no—
1225C2×C4—434no—
1226C2×C4—434no—
1227C2×C4—862no—
1228C2×C4—862no—
1229C2×C4—862no—
1230C2×C4—862no—
1231C2×C4—862no—
1232C2×C4—862no—
1233C2×C4—862no—
1234C2×C4—862no—
1235C2×C4—862no—
1236C2×C4—862no—
1237C2×C4—862no—
1238C2×C4—862no—
1239C2×C4—862no—
1240C2×C4—862no—
1241C2×C4—862no—
1242C2×C4—862no—
1243C2×C4—862no—
1244C2×C4—862no—
1245C2×C4—862no—
1246C2×C4—862no—
1247C2×C4—862no—
1248C2×C4—862no—
1249C2×C4—862no—
1250C2×C4—862no—
1251C2×C4—862no—
1252C2×C4—862no—
1253C2×C4—862no—
1254C2×C4—862no—
1255C2×C4—862no—
1256C2×C4—862no—
1257C2×C4—17216no—
1258C2×C4—17216no—
1259C2×C4—17216no—
1260C2×C4—1721no—
1261C2×C4—1721no—
1262C2×C4—1721no—
1263C2×C4—1721no—
1264C2×C4—1721no—
1265C2×C4—1721no—
1266C2×C4—1721no—
1267C2×C4—1721no—
1268C2×C4—1721no—
1269C2×C4—1721no—
1270C2×C4—1721no—
1271C2×C4—1721no—
1272C2×C4—1721no—
1273C2×C4—1721no—
1274C2×C4—1721no—
1275C2×C4—1721no—
1276C2×C4(C22⋊D43)⋊C414yescomplemented
1277C22—24no—
1278C22—24no—
1279C22—24no—
1280C22—24no—
1281C22—24no—
1282C22—24no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—864no—
1308C22—864no—
1309C22—864no—
1310C22—1722no—
1311C22—1722no—
1312C22—1722no—
1313C22—1722no—
1314C22—1722no—
1315C22—1722no—
1316C22—1722no—
1317C22—1722no—
1318C22—1722no—
1319C22—1722no—
1320C22—1722no—
1321C22—1722no—
1322C22C4×D4×D4311yescharacteristic
1323C22C4×D4×D4311yescharacteristic
1324C22C2×(C22⋊D43)⋊C411yescharacteristic
1325C22C2×(C22⋊D43)⋊C411yescharacteristic
1326C22C2×(C22⋊D43)⋊C411yescharacteristic
1327C22#1458337111yescharacteristic
1328C22#1458337811yescharacteristic
1329C22#120×D4311yescharacteristic
1330C22#120×D4311yescharacteristic
1331C22#1458340511yescharacteristic
1332C22#1458340511yescharacteristic
1333C22#1458340511yescharacteristic
1334C22#1458340711yescharacteristic
1335C22#1458340911yescharacteristic
1336C22#1458340911yescharacteristic
1337C22#1458345711yescharacteristic
1338C22#1458347611yescharacteristic
1339C22#1458348411yescharacteristic
1340C22#1458349311yescharacteristic
1341C22#1458353111yescharacteristic
1342C22#1458353311yescharacteristic
1343C22#1458353311yescharacteristic
1344C22#1458353411yescharacteristic
1345C22#1458353611yescharacteristic
1346C22#1458353811yescharacteristic
1347C22#1458354711yescharacteristic
1348C22#1458354911yescharacteristic
1349C22#1458355511yescharacteristic
1350C22#1458355711yescharacteristic
1351C22#1458356711yescharacteristic
1352C22#1458356911yescharacteristic
1353C22#1458357211yescharacteristic
1354C22#1458359211yescharacteristic
1355C22#1458359611yescharacteristic
1356C22#1458363111yescharacteristic
1357C4—24no—
1358C4—42no—
1359C4—42no—
1360C4—81no—
1361C4—81no—
1362C4—864no—
1363C4—864no—
1364C4—864no—
1365C4—1722no—
1366C4—1722no—
1367C4—1722no—
1368C4—1722no—
1369C2—44no—
1370C2—44no—
1371C2—1724no—
1372C2#1913709411yescharacteristic
1373C2#1913710011yescharacteristic
1374C2#1913729611yescharacteristic
1375C2#1913757511yescharacteristic
1376C2#1913760611yescharacteristic
1377C2#1913761611yescharacteristic
1378C2#1913765611yescharacteristic
1379C2#1913790411yescharacteristic
1380C2#1913793311yescharacteristic
1381C2#1913793511yescharacteristic
1382C2#1913847311yescharacteristic
1383C2#1913848211yescharacteristic
1384C2#1913848811yescharacteristic
1385C2#1913858711yescharacteristic
1386C2#1914017811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1438C2
socle, cosocleC24×C43C24
prime radicalC2×#14582807C2
hypercenter#1438D43
hypocenterC43#14171
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic43C2semidirect
2. C22×(C22⋊D43)⋊C4C2semidirect
4. C2×#14582776C2semidirect
5. C2×#14582775C2semidirect
6. C2×#14582773C2semidirect
7. C2×#14582771C2semidirect
8. #19132838C2semidirect
9. #19132834C2semidirect
10. #19132832C2semidirect
11. #19132831C2semidirect
12. #19132829C2semidirect
13. #19132826C2semidirect
14. #19132817C2semidirect
15. C43×#1438C2semidirect
40. #14582807C4semidirect
75. C22×C22⋊D43C2×C4semidirect
76. C22×C22⋊D43C2×C4semidirect
90. C23×Dic43D4semidirect
109. C2×C4⋊Dic43D4semidirect
115. C2×Dic43⋊C4D4semidirect
125. C2×C22⋊Dic43C2×C4semidirect
126. C2×C22⋊Dic43C2×C4semidirect
127. C2×C22⋊Dic43D4semidirect
138. C2×(C2×D43)⋊C4C2×C4semidirect
139. C2×(C2×D43)⋊C4D4semidirect
155. C43⋊#95C2×C4semidirect
164. C22×D4×C43C2×C4semidirect
442. C23×C43C4×D4semidirect
492. C22×D43C4×D4semidirect
528. C2×C4×C43C4×D4semidirect
579. C2×Dic43C4×D4semidirect
685. #1438D43semidirect
755. C43#14171semidirect
779. C22×D4C4×D43semidirect
1171. C23(C22⋊D43)⋊C4semidirect
1276. C2×C4(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic432
C22×(C22⋊D43)⋊C42
C2×#145828072
C2×#145827762
C2×#145827752
C2×#145827732
C2×#145827712
#191328382
#191328342
#191328322
#191328312
#191328292
#191328262
#191328172
C43×#14382
#1417143