Finite Group Databasebeta

← #25019773

Subgroups — #25019773

Order 11008.

2038 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582799C211yesmaximal, characteristic
2C2×#14582799C211yesmaximal, characteristic
3C2×#14582799C211yesmaximal, characteristic
4C2×#14582791C211yesmaximal, characteristic, complemented
5C2×#14582790C211yesmaximal, characteristic, complemented
6C2×#14582787C211yesmaximal, characteristic, complemented
7C2×#14582768C211yesmaximal, characteristic, complemented
8C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
9#19132840C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132838C211yesmaximal, characteristic, complemented
12#19132837C211yesmaximal, characteristic, complemented
13Dic43⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
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
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36#14582799—24no—
37#14582799—24no—
38#14582799C418yescomplemented
39#14582791—24no—
40#14582790—24no—
41#14582787—24no—
42#14582768—24no—
43C4×Dic43⋊C4—24no—
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C42×C43C2211yescharacteristic
57C43×#388—24no—
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43—22no—
66C22×C22⋊D43—22no—
67C22×C22⋊D43C2×C414yes—
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C2×C4⋊Dic43—22no—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43—41no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—22no—
82C2×Dic43⋊C4—22no—
83C2×Dic43⋊C4—22no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—41no—
90C2×Dic43⋊C4—41no—
91C2×Dic43⋊C4C2×C414yes—
92C2×Dic43⋊C4D414yes—
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⋊Dic43C2×C414yes—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×(C2×D43)⋊C4—22no—
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—41no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4—41no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4C2×C414yes—
119C2×(C2×D43)⋊C4C2×C414yes—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—22no—
122C2×C4×Dic43—22no—
123C2×C4×Dic43—22no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—22no—
127C2×C4×Dic43—22no—
128C2×C4×Dic43—22no—
129C2×C4×Dic43—22no—
130C2×C4×Dic43C2×C414yes—
131C2×C4×Dic43D414yes—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95D414yescomplemented
140C25×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43—22no—
148C2×C4⋊C4×C43—22no—
149C2×C4⋊C4×C43—41no—
150C2×C22⋊C4×C43—22no—
151C2×C22⋊C4×C43—22no—
152C2×C22⋊C4×C43—22no—
153C2×C22⋊C4×C43—22no—
154C2×C22⋊C4×C43—22no—
155C2×C22⋊C4×C43—22no—
156C2×C22⋊C4×C43—22no—
157C2×C22⋊C4×C43—41no—
158C2×C22⋊C4×C43C2×C414yes—
159C2×C42×C43—22no—
160C2×C42×C43—22no—
161C2×C42×C43—22no—
162#95×C43—22no—
163#95×C43D414yescomplemented
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
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×C43C22×C412yes—
179C24×C43C2411yescharacteristic
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43C22×C412yes—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43C22×C412yes—
229C22×C4×C43C22×C412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2×D412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43#4112yes—
237C2×C22⋊D43—28no—
238C2×C22⋊D43—28no—
239C2×C22⋊D43—28no—
240C2×C22⋊D43—44no—
241C2×C22⋊D43—44no—
242C2×C22⋊D43—44no—
243C2×C22⋊D43—44no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43C22×C412yes—
280C22×Dic43C22×C412yes—
281C22×Dic43C22×C412yes—
282C22×Dic43C2×D412yes—
283C22×Dic43C2×D412yes—
284C22×Dic43C2×D412yes—
285C22×Dic43C2×D412yes—
286C22×Dic43C2×D412yes—
287C22×Dic43C2×D412yes—
288C22×Dic43#4112yes—
289C22×Dic43#4112yes—
290C22×Dic43#4112yes—
291C22×Dic43#4112yes—
292C22×Dic43#4112yes—
293C4⋊C4×C43—44no—
294C22⋊C4×C43—28no—
295C22⋊C4×C43—44no—
296C22⋊C4×C43—44no—
297C42×C43—44no—
298C22⋊Dic43—28no—
299C22⋊Dic43—44no—
300C22⋊Dic43—44no—
301(C2×D43)⋊C4—28no—
302(C2×D43)⋊C4—28no—
303(C2×D43)⋊C4—44no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307C4⋊Dic43—44no—
308Dic43⋊C4—28no—
309Dic43⋊C4—28no—
310Dic43⋊C4—44no—
311Dic43⋊C4—44no—
312Dic43⋊C4—44no—
313C4×Dic43—28no—
314C4×Dic43—28no—
315C4×Dic43—44no—
316C4×Dic43—44no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—22no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43C23×C411yescharacteristic
353C23×C43C22×D411yescharacteristic
354C23×C43C22×D411yescharacteristic
355C23×C43C22×D411yescharacteristic
356C23×C43C22×D411yescharacteristic
357C23×C43C2×#4111yescharacteristic
358C23×C43C2×#4111yescharacteristic
359C23×C43C2×#4111yescharacteristic
360C23×C43C2×#4111yescharacteristic
361C23×C43C2×#4111yescharacteristic
362C23×C43C2×#4111yescharacteristic
363C23×C43H(5,𝔽2)11yescharacteristic
364C23×C43H(5,𝔽2)11yescharacteristic
365C23×C432−1+411yescharacteristic
366C23×C432−1+411yescharacteristic
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43—41no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43—41no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43—41no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43C4×D414yes—
443C2×C4×C43#12714yes—
444C22⋊D43—416no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43#11714yes—
487C2×Dic43C4×D414yes—
488C2×Dic43C4×D414yes—
489C2×Dic43C4×D414yes—
490C2×Dic43#12114yes—
491C2×Dic43#12314yes—
492C2×Dic43#12414yes—
493C2×Dic43#12614yes—
494#14001—431nomaximal, Sylow
495C22×C43—42no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43—42no—
499C22×C43—42no—
500C22×C43—42no—
501C22×C43—42no—
502C22×C43—81no—
503C22×C43—81no—
504C22×C43—81no—
505C22×C43—81no—
506C22×C43—81no—
507C22×C43—81no—
508C22×C43—81no—
509C22×C43—81no—
510C22×C43C2×#11711yescharacteristic
511C22×C43C2×C4×D411yescharacteristic
512C22×C43C2×C4×D411yescharacteristic
513C22×C43C2×C4×D411yescharacteristic
514C22×C43C2×C4×D411yescharacteristic
515C22×C43#52011yescharacteristic
516C22×C43#52011yescharacteristic
517C22×C43C2×#12111yescharacteristic
518C22×C43C2×#12311yescharacteristic
519C22×C43C2×#12411yescharacteristic
520C22×C43C2×#12611yescharacteristic
521C22×C43C2×#12711yescharacteristic
522C22×C43#53211yescharacteristic
523C22×C43#53211yescharacteristic
524C22×C43#53211yescharacteristic
525C22×C43#53511yescharacteristic
526C22×C43#53611yescharacteristic
527C22×C43#54211yescharacteristic
528C22×C43#54211yescharacteristic
529C22×C43D4211yescharacteristic
530C22×C43D4211yescharacteristic
531C22×C43#54711yescharacteristic
532C22×C43#54711yescharacteristic
533C22×C43#54711yescharacteristic
534C22×C43#54711yescharacteristic
535C22×C43#54811yescharacteristic
536C22×C43#54811yescharacteristic
537C22×C43#55011yescharacteristic
538C22×C43#55011yescharacteristic
539C22×C43#55311yescharacteristic
540C22×C43#55311yescharacteristic
541C22×C43#55511yescharacteristic
542C22×C43#55511yescharacteristic
543C22×C43#55611yescharacteristic
544C22×C43#55611yescharacteristic
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—81no—
553C2×D43—81no—
554C2×D43—81no—
555C2×D43—81no—
556C2×D43—81no—
557C2×D43—81no—
558C2×D43—81no—
559C2×D43—81no—
560C4×C43—24no—
561C4×C43—24no—
562C4×C43—42no—
563C4×C43—42no—
564C4×C43—42no—
565C4×C43—81no—
566Dic43—24no—
567Dic43—42no—
568Dic43—42no—
569Dic43—42no—
570Dic43—42no—
571Dic43—81no—
572Dic43#38818yescomplemented
573C2×#390—431no—
574C2×#390—431no—
575C2×#390—431no—
576C2×#388—431no—
577C2×#388—431no—
578C2×#388—431no—
579C2×#388D4311yescharacteristic, complemented
580C2×#384—431no—
581C2×C4×C4⋊C4—431no—
582#1439—431no—
583#1439—431no—
584#1439—431no—
585#1439—431no—
586C4⋊#95—431no—
587C4×#95—431no—
588C2×C43—82no—
589C2×C43C2×#38811yescharacteristic
590C2×C43C4×#12711yescharacteristic
591C2×C43#232611yescharacteristic
592C2×C43#235411yescharacteristic
593C2×C43#235411yescharacteristic
594C2×C43#236111yescharacteristic
595C2×C43#236111yescharacteristic
596C2×C43#249111yescharacteristic
597C2×C43#249111yescharacteristic
598C2×C43#250011yescharacteristic
599C2×C43#250111yescharacteristic
600C2×C43#251211yescharacteristic
601C2×C43#251211yescharacteristic
602C2×C43#254111yescharacteristic
603C2×C43#254511yescharacteristic
604D43—82no—
605C23×D4—431no—
606C22×C4⋊C4—431no—
607C22×C4⋊C4—431no—
608C22×C4⋊C4—431no—
609C22×C4⋊C4—431no—
610C22×C4⋊C4—431no—
611C22×C4⋊C4—431no—
612C22×C4⋊C4C2×D4311yescharacteristic
613C22×C22⋊C4—431no—
614C22×C22⋊C4—431no—
615C22×C22⋊C4—431no—
616C22×C22⋊C4—431no—
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C22⋊C4—431no—
622C22×C22⋊C4C2×D4311yescharacteristic
623C22×C22⋊C4C2×D4311yescharacteristic
624C22×C22⋊C4C2×D4311yescharacteristic
625C22×C42—431no—
626C22×C42—431no—
627C22×C42—431no—
628C22×C42—431no—
629C22×C42C2×D4311yescharacteristic
630#390—438no—
631#390—864no—
632#390—864no—
633#388—24no—
634#388—864no—
635#388—864no—
636#388—864no—
637#384—864no—
638C4×C4⋊C4—864no—
639C2×#95—431no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95—431no—
643C2×#95—431no—
644C2×#95—431no—
645C2×#95—431no—
646C2×#95—431no—
647C2×#95C2×D4311yescharacteristic
648C2×#95C2×D4311yescharacteristic
649C43#1400111yescharacteristic, complemented, Sylow
650C25—431no—
651C25C22×D4311yescharacteristic
652C22×D4—434no—
653C22×D4—862no—
654C22×D4—862no—
655C22×D4—862no—
656C22×D4—862no—
657C22×D4—862no—
658C22×D4—862no—
659C23×C4—431no—
660C23×C4—431no—
661C23×C4—431no—
662C23×C4—431no—
663C23×C4—431no—
664C23×C4—431no—
665C23×C4—431no—
666C23×C4C22×D4311yescharacteristic
667C23×C4C22×D4311yescharacteristic
668C23×C4C22×D4311yescharacteristic
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—434no—
676C2×C4⋊C4—434no—
677C2×C4⋊C4—862no—
678C2×C4⋊C4—862no—
679C2×C4⋊C4—862no—
680C2×C4⋊C4—862no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—862no—
684C2×C4⋊C4—862no—
685C2×C4⋊C4—862no—
686C2×C4⋊C4—862no—
687C2×C4⋊C4—862no—
688C2×C4⋊C4—862no—
689C2×C4⋊C4—862no—
690C2×C4⋊C4—1721no—
691C2×C4⋊C4—1721no—
692C2×C4⋊C4—1721no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—434no—
702C2×C22⋊C4—434no—
703C2×C22⋊C4—434no—
704C2×C22⋊C4—862no—
705C2×C22⋊C4—862no—
706C2×C22⋊C4—862no—
707C2×C22⋊C4—862no—
708C2×C22⋊C4—862no—
709C2×C22⋊C4—862no—
710C2×C22⋊C4—862no—
711C2×C22⋊C4—862no—
712C2×C22⋊C4—862no—
713C2×C22⋊C4—862no—
714C2×C22⋊C4—862no—
715C2×C22⋊C4—862no—
716C2×C22⋊C4—862no—
717C2×C22⋊C4—862no—
718C2×C22⋊C4—862no—
719C2×C22⋊C4—862no—
720C2×C22⋊C4—862no—
721C2×C22⋊C4—1721no—
722C2×C22⋊C4—1721no—
723C2×C22⋊C4—1721no—
724C2×C22⋊C4—1721no—
725C2×C22⋊C4—1721no—
726C2×C22⋊C4—1721no—
727C2×C22⋊C4—1721no—
728C2×C22⋊C4C4×D4314yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—434no—
733C2×C42—434no—
734C2×C42—862no—
735C2×C42—862no—
736C2×C42—862no—
737C2×C42—862no—
738C2×C42—862no—
739C2×C42—862no—
740C2×C42—862no—
741C2×C42—862no—
742C2×C42—862no—
743C2×C42—862no—
744#95—22no—
745#95—434no—
746#95—862no—
747#95—862no—
748#95—862no—
749#95—862no—
750#95—862no—
751#95—862no—
752#95—862no—
753#95C22⋊D4314yescomplemented
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—432no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24—861no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24—861no—
780C24—861no—
781C24—861no—
782C24—861no—
783C24C2×C4×D4312yes—
784C24C23×D4311yescharacteristic
785C2×D4—868no—
786C2×D4—868no—
787C2×D4—868no—
788C2×D4—1724no—
789C2×D4—1724no—
790C2×D4—1724no—
791C2×D4—1724no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—432no—
826C22×C4—432no—
827C22×C4—432no—
828C22×C4—432no—
829C22×C4—432no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—432no—
833C22×C4—432no—
834C22×C4—432no—
835C22×C4—432no—
836C22×C4—432no—
837C22×C4—432no—
838C22×C4—432no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4C2×C4×D4312yes—
875C22×C4C2×C4×D4312yes—
876C22×C4#1062189812yes—
877C22×C4D4×D4312yes—
878C22×C4D4×D4312yes—
879C22×C4D4×D4312yes—
880C22×C4C2×C22⋊D4312yes—
881C22×C4C2×C22⋊D4312yes—
882C22×C4C2×C22⋊D4312yes—
883C4⋊C4—44no—
884C4⋊C4—868no—
885C4⋊C4—868no—
886C4⋊C4—1724no—
887C4⋊C4—1724no—
888C4⋊C4—1724no—
889C4⋊C4—1724no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—868no—
894C22⋊C4—868no—
895C22⋊C4—868no—
896C22⋊C4—1724no—
897C22⋊C4—1724no—
898C22⋊C4—1724no—
899C22⋊C4—1724no—
900C22⋊C4—1724no—
901C22⋊C4—1724no—
902C42—44no—
903C42—868no—
904C42—868no—
905C42—1724no—
906C42—1724no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—862no—
943C23—862no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—1721no—
950C23—1721no—
951C23—1721no—
952C23—1721no—
953C23—1721no—
954C23—1721no—
955C23—1721no—
956C23—1721no—
957C23—1721no—
958C23—1721no—
959C23—1721no—
960C23—1721no—
961C23—1721no—
962C23—1721no—
963C23—1721no—
964C23—1721no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23—1721no—
971C23—1721no—
972C23—1721no—
973C23—1721no—
974C23—1721no—
975C23—1721no—
976C23—1721no—
977C23C22×C4×D4311yescharacteristic
978C23C2×D4×D4311yescharacteristic
979C23C2×D4×D4311yescharacteristic
980C23C2×D4×D4311yescharacteristic
981C23C22×C22⋊D4311yescharacteristic
982C23#41×D4311yescharacteristic
983C23#41×D4311yescharacteristic
984C23#41×D4311yescharacteristic
985C23#41×D4311yescharacteristic
986C23#41×D4311yescharacteristic
987C23C2×#1062189811yescharacteristic
988C23#1306337011yescharacteristic
989C23#1306337111yescharacteristic
990C23#1306337211yescharacteristic
991C23#1306337211yescharacteristic
992D4—17216no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—434no—
1034C2×C4—434no—
1035C2×C4—434no—
1036C2×C4—434no—
1037C2×C4—434no—
1038C2×C4—434no—
1039C2×C4—434no—
1040C2×C4—434no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—862no—
1044C2×C4—862no—
1045C2×C4—862no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—862no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4—1721no—
1062C2×C4—1721no—
1063C2×C4—1721no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—1721no—
1072C2×C4—1721no—
1073C2×C4—1721no—
1074C2×C4—1721no—
1075C2×C4—1721no—
1076C2×C4—1721no—
1077C2×C4—1721no—
1078C2×C4—1721no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4C4×C22⋊D4314yes—
1083C2×C4#1306332114yes—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—3441no—
1100C22—3441no—
1101C22—3441no—
1102C22—3441no—
1103C22—3441no—
1104C22—3441no—
1105C22—3441no—
1106C22—3441no—
1107C22—1722no—
1108C22—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22—1722no—
1113C22—1722no—
1114C22#117×D4311yescharacteristic
1115C22C4×D4×D4311yescharacteristic
1116C22C4×D4×D4311yescharacteristic
1117C22C4×D4×D4311yescharacteristic
1118C22C2×C4×C22⋊D4311yescharacteristic
1119C22#1458337811yescharacteristic
1120C22#1458337911yescharacteristic
1121C22#121×D4311yescharacteristic
1122C22#123×D4311yescharacteristic
1123C22#124×D4311yescharacteristic
1124C22#126×D4311yescharacteristic
1125C22C2×#1306332111yescharacteristic
1126C22#1458344511yescharacteristic
1127C22#1458344611yescharacteristic
1128C22#1458344611yescharacteristic
1129C22#1458346511yescharacteristic
1130C22#1458347111yescharacteristic
1131C22#1458351311yescharacteristic
1132C22#1458351511yescharacteristic
1133C22D4×C22⋊D4311yescharacteristic
1134C22#1458353311yescharacteristic
1135C22#1458354711yescharacteristic
1136C22#1458354711yescharacteristic
1137C22#1458354811yescharacteristic
1138C22#1458354811yescharacteristic
1139C22#1458355711yescharacteristic
1140C22#1458355811yescharacteristic
1141C22#1458356711yescharacteristic
1142C22#1458356811yescharacteristic
1143C22#1458359811yescharacteristic
1144C22#1458360011yescharacteristic
1145C22#1458361111yescharacteristic
1146C22#1458361211yescharacteristic
1147C22#1458361611yescharacteristic
1148C22#1458361711yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—438no—
1156C4—864no—
1157C4—3441no—
1158C4—1722no—
1159C4—1722no—
1160C4—1722no—
1161C4—1722no—
1162C2—82no—
1163C2—3442no—
1164C2#388×D4311yescharacteristic
1165C2C4×#1306332111yescharacteristic
1166C2#1913730411yescharacteristic
1167C2#1913754111yescharacteristic
1168C2#1913754511yescharacteristic
1169C2#1913760811yescharacteristic
1170C2#1913761211yescharacteristic
1171C2#1913895511yescharacteristic
1172C2#1913895711yescharacteristic
1173C2#1913905511yescharacteristic
1174C2#1913906411yescharacteristic
1175C2#1913917811yescharacteristic
1176C2#1913918011yescharacteristic
1177C2#1913953811yescharacteristic
1178C2#1913957311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#14001
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#14582791C2semidirect
5. C2×#14582790C2semidirect
6. C2×#14582787C2semidirect
7. C2×#14582768C2semidirect
8. C2×C4×Dic43⋊C4C2semidirect
9. #19132840C2semidirect
10. #19132839C2semidirect
11. #19132838C2semidirect
12. #19132837C2semidirect
13. Dic43⋊#95C2semidirect
14. #95×Dic43C2semidirect
15. C2×C43×#388C2semidirect
38. #14582799C4semidirect
139. C43⋊#95D4semidirect
163. #95×C43D4semidirect
572. Dic43#388semidirect
579. C2×#388D43semidirect
649. C43#14001semidirect
753. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827992
C2×#145827912
C2×#145827902
C2×#145827872
C2×#145827682
C2×C4×Dic43⋊C42
#191328402
#191328392
#191328382
#191328372
Dic43⋊#952
#95×Dic432
C2×C43×#3882
#1400143