Finite Group Databasebeta

← #25019622

Subgroups — #25019622

Order 11008.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582789C211yesmaximal, characteristic, complemented
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582770C211yesmaximal, characteristic, complemented
5C2×#14582758C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
8#19132853C211yesmaximal, characteristic, complemented
9#19132843C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132835C211yesmaximal, characteristic
12#19132831C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14#19132820C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582789—24no—
34#14582777—24no—
35#14582777C418yescomplemented
36#14582770—24no—
37#14582758—24no—
38C4×(C2×D43)⋊C4—24no—
39C4×(C2×D43)⋊C4—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
50C2×C43⋊#95C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C24×D43C2311yescharacteristic
60C22×D172—22no—
61C22×D172—22no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—41no—
65C22×D172—41no—
66C22×D172C2×C414yes—
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—41no—
83C22×C4×D43—41no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43C2×C414yescomplemented
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—41no—
92C2×Dic43⋊C4—41no—
93C2×(C2×D43)⋊C4—22no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
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—22no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4—41no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4C2×C414yes—
120C2×(C2×D43)⋊C4C2×C414yes—
121C2×(C2×D43)⋊C4C2×C414yescomplemented
122C2×(C2×D43)⋊C4D414yes—
123C2×C4×Dic43—22no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—22no—
127C2×C4×Dic43—41no—
128C2×C4×Dic43—41no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—41no—
136C43⋊#95—41no—
137C43⋊#95C2×C414yescomplemented
138C43⋊#95D414yescomplemented
139C43⋊#95D414yescomplemented
140C23×C4×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—22no—
150C2×C42×C43—22no—
151C2×C42×C43—22no—
152C2×C42×C43—41no—
153#95×C43—22no—
154#95×C43—22no—
155#95×C43—22no—
156#95×C43—41no—
157#95×C43C2×C414yescomplemented
158C24×C43C2411yescharacteristic
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43C22×C412yes—
184C23×D43C22×C412yes—
185C23×D43C2×D412yes—
186C23×D43#4112yes—
187C23×D43#4112yes—
188C23×D43#4112yes—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
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×C43—21no—
229C22×C4×C43C22×C412yes—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C22×C412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43#4112yes—
236C22×C4×C43#4112yes—
237C22×C4×C43#4112yes—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
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×Dic43C22×C412yes—
273C22×Dic43C22×C412yes—
274C22×Dic43C2×D412yes—
275C22×Dic43C2×D412yes—
276C22×Dic43C2×D412yes—
277C22×Dic43C2×D412yes—
278C22×Dic43C2×D412yes—
279C22×Dic43#4112yes—
280C2×D172—28no—
281C2×D172—28no—
282C2×D172—44no—
283C2×D172—44no—
284C2×D172—44no—
285C2×D172—44no—
286C2×D172—44no—
287C2×C4×D43—28no—
288C2×C4×D43—28no—
289C2×C4×D43—28no—
290C2×C4×D43—44no—
291C2×C4×D43—44no—
292C2×C4×D43—44no—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43—44no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C4⋊C4×C43—44no—
302C42×C43—44no—
303(C2×D43)⋊C4—28no—
304(C2×D43)⋊C4—28no—
305(C2×D43)⋊C4—28no—
306(C2×D43)⋊C4—28no—
307(C2×D43)⋊C4—28no—
308(C2×D43)⋊C4—28no—
309(C2×D43)⋊C4—44no—
310(C2×D43)⋊C4—44no—
311(C2×D43)⋊C4—44no—
312(C2×D43)⋊C4—44no—
313Dic43⋊C4—44no—
314Dic43⋊C4—44no—
315C4×Dic43—44no—
316C4×Dic43—44no—
317C23×C43C23×C411yescharacteristic
318C23×C43C22×D411yescharacteristic
319C23×C43C22×D411yescharacteristic
320C23×C43C22×D411yescharacteristic
321C23×C43C2×#4111yescharacteristic
322C23×C43C2×#4111yescharacteristic
323C23×C43C2×#4111yescharacteristic
324C23×C43C2×#4111yescharacteristic
325C23×C43C2×#4111yescharacteristic
326C23×C43C2×#4111yescharacteristic
327C23×C43C2×#4111yescharacteristic
328C23×C43H(5,𝔽2)11yescharacteristic
329C23×C43H(5,𝔽2)11yescharacteristic
330C23×C43H(5,𝔽2)11yescharacteristic
331C23×C432−1+411yescharacteristic
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
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#11714yes—
401C22×D43C4×D414yes—
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×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43C4×D414yes—
450C2×C4×C43#12114yes—
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—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
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—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43C4×D414yes—
493D172—416no—
494C4×D43—416no—
495C4×D43—416no—
496#13988—431nomaximal, Sylow
497C22×C43C2×#11711yescharacteristic
498C22×C43C2×C4×D411yescharacteristic
499C22×C43C2×C4×D411yescharacteristic
500C22×C43C2×C4×D411yescharacteristic
501C22×C43C4×#4111yescharacteristic
502C22×C43#51811yescharacteristic
503C22×C43#52011yescharacteristic
504C22×C43C2×#12111yescharacteristic
505C22×C43#52511yescharacteristic
506C22×C43#52511yescharacteristic
507C22×C43#52511yescharacteristic
508C22×C43#52911yescharacteristic
509C22×C43#52911yescharacteristic
510C22×C43#52911yescharacteristic
511C22×C43#53211yescharacteristic
512C22×C43#53811yescharacteristic
513C22×C43#53911yescharacteristic
514C22×C43#54011yescharacteristic
515C22×C43#54211yescharacteristic
516C22×C43D4211yescharacteristic
517C22×C43D4211yescharacteristic
518C22×C43#54611yescharacteristic
519C22×C43#54611yescharacteristic
520C22×C43#54611yescharacteristic
521C22×C43#54611yescharacteristic
522C22×C43#54611yescharacteristic
523C22×C43#54711yescharacteristic
524C22×C43#54811yescharacteristic
525C22×C43#54811yescharacteristic
526C22×C43#55111yescharacteristic
527C22×C43#55111yescharacteristic
528C22×C43#55111yescharacteristic
529C22×C43#55211yescharacteristic
530C22×C43#55311yescharacteristic
531C22×C43#55311yescharacteristic
532C2×D43—24no—
533C2×D43—24no—
534C2×D43—24no—
535C2×D43—24no—
536C2×D43—24no—
537C2×D43—24no—
538C2×D43—42no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43—42no—
560C2×D43—42no—
561C2×D43—42no—
562C4×C43—24no—
563C4×C43—24no—
564C4×C43—42no—
565C4×C43—42no—
566C4×C43—42no—
567C4×C43—81no—
568C4×C43—81no—
569Dic43—24no—
570Dic43—42no—
571Dic43—42no—
572Dic43—42no—
573Dic43—42no—
574Dic43—42no—
575C2×#388—431no—
576C2×#386—431no—
577C2×#386—431no—
578C2×#385—431no—
579C2×#380—431no—
580C2×C4×C22⋊C4—431no—
581C2×C4×C22⋊C4—431no—
582#1442—431no—
583#1440—431no—
584#1439—431no—
585#1438—431no—
586#1437—431no—
587#1436—431no—
588#1436D4311yescharacteristic, complemented
589#1434—431no—
590C2×C43#229011yescharacteristic
591C2×C43C4×#12111yescharacteristic
592C2×C43#233511yescharacteristic
593C2×C43#234211yescharacteristic
594C2×C43#235211yescharacteristic
595C2×C43#235811yescharacteristic
596C2×C43#236111yescharacteristic
597C2×C43#242411yescharacteristic
598C2×C43#242711yescharacteristic
599C2×C43#245711yescharacteristic
600C2×C43#246311yescharacteristic
601C2×C43#246411yescharacteristic
602C2×C43#247711yescharacteristic
603C2×C43#255311yescharacteristic
604C2×C43#257811yescharacteristic
605D43—44no—
606D43—44no—
607C23×D4—431no—
608C24×C4—431no—
609C24×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⋊C4—431no—
623C22×C42—431no—
624C22×C42—431no—
625C22×C42C2×D4311yescharacteristic
626#388—864no—
627#386—438no—
628#386—864no—
629#385—864no—
630#380—864no—
631C4×C22⋊C4—864no—
632C4×C22⋊C4—864no—
633C2×#95—431no—
634C2×#95—431no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—431no—
638C2×#95—431no—
639C2×#95—431no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95—431no—
643C2×#95—431no—
644C2×#95C2×D4311yescharacteristic
645C2×#95C2×D4311yescharacteristic
646C2×#95C2×D4311yescharacteristic
647C2×#95C2×D4311yescharacteristic
648C2×#95C2×D4311yescharacteristic
649C43#1398811yescharacteristic, complemented, Sylow
650C25—431no—
651C25—431no—
652C22×D4—434no—
653C22×D4—862no—
654C22×D4—862no—
655C22×D4—862no—
656C22×D4—862no—
657C22×D4—1721no—
658C22×D4—1721no—
659C23×C4—431no—
660C23×C4—431no—
661C23×C4—431no—
662C23×C4—431no—
663C23×C4—431no—
664C23×C4—431no—
665C23×C4—434no—
666C23×C4—862no—
667C23×C4—862no—
668C23×C4—862no—
669C23×C4—862no—
670C23×C4—862no—
671C23×C4—862no—
672C23×C4—862no—
673C23×C4—862no—
674C23×C4—862no—
675C23×C4—1721no—
676C23×C4—1721no—
677C23×C4—1721no—
678C23×C4—1721no—
679C23×C4C22×D4311yescharacteristic
680C23×C4C22×D4311yescharacteristic
681C23×C4C22×D4311yescharacteristic
682C23×C4C22×D4311yescharacteristic
683C23×C4C22×D4311yescharacteristic
684C23×C4C22×D4311yescharacteristic
685C23×C4C22×D4311yescharacteristic
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—862no—
690C2×C4⋊C4—862no—
691C2×C4⋊C4—862no—
692C2×C4⋊C4—862no—
693C2×C4⋊C4—1721no—
694C2×C4⋊C4—1721no—
695C2×C22⋊C4—434no—
696C2×C22⋊C4—434no—
697C2×C22⋊C4—434no—
698C2×C22⋊C4—434no—
699C2×C22⋊C4—862no—
700C2×C22⋊C4—862no—
701C2×C22⋊C4—862no—
702C2×C22⋊C4—862no—
703C2×C22⋊C4—862no—
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×C42—22no—
726C2×C42—22no—
727C2×C42—41no—
728C2×C42—862no—
729C2×C42—862no—
730C2×C42—862no—
731C2×C42—862no—
732C2×C42—1721no—
733C2×C42—1721no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—41no—
738#95—434no—
739#95—434no—
740#95—434no—
741#95—862no—
742#95—862no—
743#95—862no—
744#95—862no—
745#95—862no—
746#95—862no—
747#95—1721no—
748#95—1721no—
749#95C4×D4314yescomplemented
750C24—432no—
751C24—432no—
752C24—432no—
753C24—432no—
754C24—432no—
755C24—432no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
760C24—861no—
761C24—861no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24—861no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24—861no—
780C24C23×D4311yescharacteristic
781C2×D4—868no—
782C2×D4—868no—
783C2×D4—1724no—
784C2×D4—1724no—
785C2×D4—1724no—
786C2×D4—1724no—
787C2×D4—1724no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
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—21no—
826C22×C4—21no—
827C22×C4—21no—
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—868no—
837C22×C4—868no—
838C22×C4—861no—
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—868no—
873C22×C4—1724no—
874C22×C4—1724no—
875C22×C4—1724no—
876C22×C4—1724no—
877C22×C4—1724no—
878C22×C4—1724no—
879C22×C4—1724no—
880C22×C4—1724no—
881C22×C4—1724no—
882C22×C4—1724no—
883C22×C4—1724no—
884C22×C4C2×C4×D4312yes—
885C22×C4C2×C4×D4312yes—
886C22×C4C2×C4×D4312yes—
887C22×C4#1062189812yes—
888C22×C4#1062189812yes—
889C22×C4D4×D4312yes—
890C22×C4D4×D4312yes—
891C22×C4D4×D4312yes—
892C22×C4#1062190212yes—
893C4⋊C4—44no—
894C4⋊C4—1724no—
895C4⋊C4—1724no—
896C22⋊C4—868no—
897C22⋊C4—868no—
898C22⋊C4—868no—
899C22⋊C4—868no—
900C22⋊C4—868no—
901C22⋊C4—868no—
902C22⋊C4—1724no—
903C22⋊C4—1724no—
904C22⋊C4—1724no—
905C22⋊C4—1724no—
906C42—44no—
907C42—1724no—
908C42—1724no—
909C23—434no—
910C23—434no—
911C23—862no—
912C23—862no—
913C23—862no—
914C23—862no—
915C23—862no—
916C23—862no—
917C23—862no—
918C23—862no—
919C23—862no—
920C23—862no—
921C23—862no—
922C23—862no—
923C23—862no—
924C23—862no—
925C23—862no—
926C23—862no—
927C23—862no—
928C23—862no—
929C23—862no—
930C23—862no—
931C23—862no—
932C23—862no—
933C23—862no—
934C23—862no—
935C23—862no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—862no—
940C23—862no—
941C23—862no—
942C23—862no—
943C23—862no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—1721no—
948C23—1721no—
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—
977C23—1721no—
978C23—1721no—
979C23C22×C4×D4311yescharacteristic
980C23C2×D4×D4311yescharacteristic
981C23C2×D4×D4311yescharacteristic
982C23C2×D4×D4311yescharacteristic
983C23#41×D4311yescharacteristic
984C23#41×D4311yescharacteristic
985C23#41×D4311yescharacteristic
986C23#41×D4311yescharacteristic
987C23C2×#1062189811yescharacteristic
988C23C2×#1062189811yescharacteristic
989C23C2×#1062190211yescharacteristic
990C23#1306337011yescharacteristic
991C23#1306337111yescharacteristic
992C23#1306337111yescharacteristic
993C23#1306337311yescharacteristic
994D4—17216no—
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—22no—
1015C2×C4—22no—
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—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—434no—
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—862no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—862no—
1063C2×C4—862no—
1064C2×C4—17216no—
1065C2×C4—17216no—
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×C4—1721no—
1083C2×C4—1721no—
1084C2×C4—1721no—
1085C2×C4—1721no—
1086C2×C4#1306328714yes—
1087C2×C4#1306329814yes—
1088C22—864no—
1089C22—864no—
1090C22—864no—
1091C22—864no—
1092C22—864no—
1093C22—864no—
1094C22—1722no—
1095C22—1722no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22—1722no—
1103C22—1722no—
1104C22—1722no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22—1722no—
1113C22—1722no—
1114C22—1722no—
1115C22—1722no—
1116C22—1722no—
1117C22—1722no—
1118C22#117×D4311yescharacteristic
1119C22C4×D4×D4311yescharacteristic
1120C22C4×D4×D4311yescharacteristic
1121C22C2×#1306328711yescharacteristic
1122C22C4×#1062189811yescharacteristic
1123C22#1458337111yescharacteristic
1124C22#1458338111yescharacteristic
1125C22C2×#1306329811yescharacteristic
1126C22#1458340811yescharacteristic
1127C22#1458340811yescharacteristic
1128C22#1458340811yescharacteristic
1129C22#1458342711yescharacteristic
1130C22#1458343611yescharacteristic
1131C22#1458343611yescharacteristic
1132C22#1458344611yescharacteristic
1133C22#1458348211yescharacteristic
1134C22#1458349611yescharacteristic
1135C22#1458350411yescharacteristic
1136C22#1458352111yescharacteristic
1137C22#1458353111yescharacteristic
1138C22#1458353311yescharacteristic
1139C22#1458353811yescharacteristic
1140C22#1458354011yescharacteristic
1141C22#1458354111yescharacteristic
1142C22#1458354111yescharacteristic
1143C22#1458354211yescharacteristic
1144C22#1458355211yescharacteristic
1145C22#1458355911yescharacteristic
1146C22#1458355911yescharacteristic
1147C22#1458357411yescharacteristic
1148C22#1458357611yescharacteristic
1149C22#1458357711yescharacteristic
1150C22#1458358111yescharacteristic
1151C22#1458360011yescharacteristic
1152C22#1458360211yescharacteristic
1153C4—24no—
1154C4—24no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C4—864no—
1161C4—1722no—
1162C4—1722no—
1163C4—1722no—
1164C4—1722no—
1165C4—1722no—
1166C2—1724no—
1167C2—1724no—
1168C2#1913703611yescharacteristic
1169C2C4×#1306329811yescharacteristic
1170C2#1913737911yescharacteristic
1171C2#1913744311yescharacteristic
1172C2#1913751911yescharacteristic
1173C2#1913757111yescharacteristic
1174C2#1913761011yescharacteristic
1175C2#1913813311yescharacteristic
1176C2#1913817311yescharacteristic
1177C2#1913850411yescharacteristic
1178C2#1913859111yescharacteristic
1179C2#1913860311yescharacteristic
1180C2#1913879811yescharacteristic
1181C2#1913964211yescharacteristic
1182C2#1913993111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#13988
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#14582789C2semidirect
4. C2×#14582770C2semidirect
5. C2×#14582758C2semidirect
6. C2×C4×(C2×D43)⋊C4C2semidirect
7. C2×C4×(C2×D43)⋊C4C2semidirect
8. #19132853C2semidirect
9. #19132843C2semidirect
10. #19132839C2semidirect
12. #19132831C2semidirect
13. #19132826C2semidirect
14. #19132820C2semidirect
15. C43×#1436C2semidirect
35. #14582777C4semidirect
86. C22×C4×D43C2×C4semidirect
121. C2×(C2×D43)⋊C4C2×C4semidirect
137. C43⋊#95C2×C4semidirect
138. C43⋊#95D4semidirect
139. C43⋊#95D4semidirect
157. #95×C43C2×C4semidirect
588. #1436D43semidirect
649. C43#13988semidirect
749. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827892
C2×#145827772
C2×#145827702
C2×#145827582
C2×C4×(C2×D43)⋊C42
#191328532
#191328432
#191328392
#191328352
#191328312
#191328262
#191328202
C43×#14362
#1398843