Finite Group Databasebeta

← #25019752

Subgroups — #25019752

Order 11008.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582790C211yesmaximal, characteristic, complemented
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582777C211yesmaximal, characteristic
5C2×#14582758C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
7C2×#95×D43C211yesmaximal, characteristic, complemented
8#19132857C211yesmaximal, characteristic, complemented
9#19132853C211yesmaximal, characteristic, complemented
10#19132843C211yesmaximal, characteristic, complemented
11#19132839C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1434C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊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
32#14582790—24no—
33#14582777—24no—
34#14582777—24no—
35#14582777C418yescomplemented
36#14582758—24no—
37C4×(C2×D43)⋊C4—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
50#95×D43—24no—
51C22×C42×C43C2211yescharacteristic
52C2×#95×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—22no—
65C22×D172—22no—
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—22no—
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—41no—
87C22×C4×D43—41no—
88C22×C4×D43—41no—
89C22×C4×D43—41no—
90C22×C4×D43—41no—
91C22×C4×D43—41no—
92C22×C4×D43C2×C414yes—
93C22×C4×D43D414yes—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—41no—
99C2×Dic43⋊C4—41no—
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—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)⋊C4—41no—
122C2×(C2×D43)⋊C4—41no—
123C2×(C2×D43)⋊C4C2×C414yes—
124C2×(C2×D43)⋊C4C2×C414yescomplemented
125C2×(C2×D43)⋊C4C2×C414yescomplemented
126C2×(C2×D43)⋊C4D414yes—
127C2×C4×Dic43—22no—
128C2×C4×Dic43—41no—
129C2×C4×Dic43—41no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—41no—
139C43⋊#95—41no—
140C43⋊#95C2×C414yescomplemented
141C43⋊#95D414yescomplemented
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C2×C42×C43—22no—
150C2×C42×C43—22no—
151C2×C42×C43—22no—
152#95×C43—22no—
153#95×C43—22no—
154#95×C43—22no—
155#95×C43—22no—
156#95×C43—22no—
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×D43C22×C412yes—
182C23×D43C22×C412yes—
183C23×D43C2×D412yes—
184C23×D43C2×D412yes—
185C23×D43#4112yes—
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×C43—21no—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C22×C412yes—
232C22×C4×C43C22×C412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
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×Dic43—21no—
273C22×Dic43C22×C412yes—
274C22×Dic43C22×C412yes—
275C22×Dic43C2×D412yes—
276C22×Dic43C2×D412yes—
277C22×Dic43C2×D412yes—
278C22×Dic43C2×D412yes—
279C22×Dic43#4112yes—
280C2×D172—28no—
281C2×D172—28no—
282C2×D172—28no—
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—28no—
291C2×C4×D43—28no—
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—
301C2×C4×D43—44no—
302C2×C4×D43—44no—
303C2×C4×D43—44no—
304C2×C4×D43—44no—
305C2×C4×D43—44no—
306C2×C4×D43—44no—
307C2×C4×D43—44no—
308C42×C43—44no—
309(C2×D43)⋊C4—28no—
310(C2×D43)⋊C4—28no—
311(C2×D43)⋊C4—28no—
312(C2×D43)⋊C4—44no—
313(C2×D43)⋊C4—44no—
314(C2×D43)⋊C4—44no—
315(C2×D43)⋊C4—44no—
316(C2×D43)⋊C4—44no—
317(C2×D43)⋊C4—44no—
318Dic43⋊C4—44no—
319Dic43⋊C4—44no—
320C4×Dic43—44no—
321C23×C43C23×C411yescharacteristic
322C23×C43C22×D411yescharacteristic
323C23×C43C22×D411yescharacteristic
324C23×C43C22×D411yescharacteristic
325C23×C43C2×#4111yescharacteristic
326C23×C43C2×#4111yescharacteristic
327C23×C43C2×#4111yescharacteristic
328C23×C43C2×#4111yescharacteristic
329C23×C43C2×#4111yescharacteristic
330C23×C43C2×#4111yescharacteristic
331C23×C43C2×#4111yescharacteristic
332C23×C43H(5,𝔽2)11yescharacteristic
333C23×C43H(5,𝔽2)11yescharacteristic
334C23×C43H(5,𝔽2)11yescharacteristic
335C23×C432−1+411yescharacteristic
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—22no—
369C22×D43—22no—
370C22×D43—22no—
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#11714yes—
400C22×D43C4×D414yes—
401C22×D43C4×D414yes—
402C22×D43#12114yes—
403C22×D43#12314yes—
404C22×D43#12414yes—
405C22×D43#12614yes—
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—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
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×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43#12114yes—
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—22no—
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×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43C4×D414yes—
497D172—416no—
498C4×D43—416no—
499C4×D43—416no—
500C4×D43—416no—
501#13999—431nomaximal, Sylow
502C22×C43C2×#11711yescharacteristic
503C22×C43C2×C4×D411yescharacteristic
504C22×C43C2×C4×D411yescharacteristic
505C22×C43C2×C4×D411yescharacteristic
506C22×C43C4×#4111yescharacteristic
507C22×C43#51811yescharacteristic
508C22×C43#52011yescharacteristic
509C22×C43C2×#12111yescharacteristic
510C22×C43C2×#12111yescharacteristic
511C22×C43C2×#12311yescharacteristic
512C22×C43#52511yescharacteristic
513C22×C43C2×#12411yescharacteristic
514C22×C43C2×#12611yescharacteristic
515C22×C43#52911yescharacteristic
516C22×C43#53211yescharacteristic
517C22×C43#53411yescharacteristic
518C22×C43#53711yescharacteristic
519C22×C43#53811yescharacteristic
520C22×C43#53911yescharacteristic
521C22×C43D4211yescharacteristic
522C22×C43#54611yescharacteristic
523C22×C43#54611yescharacteristic
524C22×C43#54611yescharacteristic
525C22×C43#54611yescharacteristic
526C22×C43#54711yescharacteristic
527C22×C43#54811yescharacteristic
528C22×C43#55111yescharacteristic
529C22×C43#55111yescharacteristic
530C22×C43#55111yescharacteristic
531C22×C43#55111yescharacteristic
532C22×C43#55211yescharacteristic
533C22×C43#55211yescharacteristic
534C22×C43#55311yescharacteristic
535C22×C43#55311yescharacteristic
536C22×C43#55311yescharacteristic
537C2×D43—24no—
538C2×D43—24no—
539C2×D43—24no—
540C2×D43—24no—
541C2×D43—24no—
542C2×D43—24no—
543C2×D43—24no—
544C2×D43—24no—
545C2×D43—24no—
546C2×D43—24no—
547C2×D43—24no—
548C2×D43—24no—
549C2×D43—24no—
550C2×D43—24no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—81no—
559C2×D43—81no—
560C2×D43—81no—
561C2×D43—81no—
562C2×D43—81no—
563C2×D43—81no—
564C2×D43—81no—
565C2×D43—81no—
566C2×D43#38818yescomplemented
567C4×C43—24no—
568C4×C43—42no—
569C4×C43—42no—
570C4×C43—42no—
571C4×C43—42no—
572C4×C43—42no—
573C4×C43—81no—
574Dic43—24no—
575Dic43—42no—
576Dic43—42no—
577Dic43—42no—
578Dic43—42no—
579Dic43—81no—
580C2×#388—431no—
581C2×#386—431no—
582C2×#386—431no—
583C2×#386—431no—
584C2×#380—431no—
585C2×C4×C22⋊C4—431no—
586C22×#95—431no—
587#1443—431no—
588#1442—431no—
589#1440—431no—
590#1439—431no—
591#1437—431no—
592#1436—431no—
593#1434D4311yescharacteristic, complemented
594C22⋊#95—431no—
595C2×C43C2×#38811yescharacteristic
596C2×C43C4×#12111yescharacteristic
597C2×C43#232511yescharacteristic
598C2×C43#235211yescharacteristic
599C2×C43#235311yescharacteristic
600C2×C43#235811yescharacteristic
601C2×C43#235911yescharacteristic
602C2×C43#241211yescharacteristic
603C2×C43#241611yescharacteristic
604C2×C43#247211yescharacteristic
605C2×C43#248111yescharacteristic
606C2×C43#248811yescharacteristic
607C2×C43#249811yescharacteristic
608C2×C43#251011yescharacteristic
609C2×C43#254311yescharacteristic
610D43—28no—
611D43—82no—
612C23×D4—431no—
613C24×C4—431no—
614C24×C4—431no—
615C24×C4—431no—
616C22×C4⋊C4—431no—
617C22×C4⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C22⋊C4—431no—
622C22×C22⋊C4—431no—
623C22×C22⋊C4—431no—
624C22×C22⋊C4—431no—
625C22×C22⋊C4—431no—
626C22×C22⋊C4—431no—
627C22×C42—431no—
628C22×C42C2×D4311yescharacteristic
629#388—864no—
630#386—438no—
631#386—864no—
632#386—864no—
633#380—864no—
634C4×C22⋊C4—864no—
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×#95—431no—
645C2×#95—431no—
646C2×#95—431no—
647C2×#95—864no—
648C2×#95C2×D4311yescharacteristic
649C2×#95C2×D4311yescharacteristic
650C2×#95C2×D4311yescharacteristic
651C2×#95C2×D4311yescharacteristic
652C2×#95C2×D4311yescharacteristic
653C2×#95C2×D4311yescharacteristic
654C43#1399911yescharacteristic, complemented, Sylow
655C25—431no—
656C25—431no—
657C22×D4—434no—
658C22×D4—862no—
659C22×D4—862no—
660C22×D4—862no—
661C22×D4—862no—
662C22×D4—862no—
663C22×D4—862no—
664C23×C4—431no—
665C23×C4—431no—
666C23×C4—431no—
667C23×C4—431no—
668C23×C4—431no—
669C23×C4—434no—
670C23×C4—434no—
671C23×C4—431no—
672C23×C4—862no—
673C23×C4—862no—
674C23×C4—862no—
675C23×C4—862no—
676C23×C4—862no—
677C23×C4—862no—
678C23×C4—862no—
679C23×C4—862no—
680C23×C4—862no—
681C23×C4—862no—
682C23×C4—862no—
683C23×C4—862no—
684C23×C4—862no—
685C23×C4—1721no—
686C23×C4—1721no—
687C23×C4—1721no—
688C23×C4—1721no—
689C23×C4—1721no—
690C23×C4—1721no—
691C23×C4C22×D4311yescharacteristic
692C23×C4C22×D4311yescharacteristic
693C23×C4C22×D4311yescharacteristic
694C23×C4C22×D4311yescharacteristic
695C23×C4C22×D4311yescharacteristic
696C23×C4C22×D4311yescharacteristic
697C23×C4C22×D4311yescharacteristic
698C2×C4⋊C4—862no—
699C2×C4⋊C4—862no—
700C2×C4⋊C4—862no—
701C2×C4⋊C4—862no—
702C2×C4⋊C4—1721no—
703C2×C4⋊C4—1721no—
704C2×C22⋊C4—434no—
705C2×C22⋊C4—434no—
706C2×C22⋊C4—434no—
707C2×C22⋊C4—434no—
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—862no—
722C2×C22⋊C4—862no—
723C2×C22⋊C4—862no—
724C2×C22⋊C4—862no—
725C2×C22⋊C4—1721no—
726C2×C22⋊C4—1721no—
727C2×C22⋊C4—1721no—
728C2×C22⋊C4—1721no—
729C2×C22⋊C4—1721no—
730C2×C22⋊C4—1721no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—862no—
735C2×C42—1721no—
736C2×C42—1721no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—434no—
743#95—434no—
744#95—862no—
745#95—862no—
746#95—862no—
747#95—862no—
748#95—862no—
749#95—862no—
750#95—862no—
751#95—862no—
752#95—1721no—
753#95—1721no—
754#95C4×D4314yescomplemented
755C24—432no—
756C24—432no—
757C24—432no—
758C24—432no—
759C24—432no—
760C24—432no—
761C24—432no—
762C24—432no—
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—
780C24—861no—
781C24—861no—
782C24—861no—
783C24—861no—
784C24—861no—
785C24C23×D4311yescharacteristic
786C2×D4—868no—
787C2×D4—868no—
788C2×D4—868no—
789C2×D4—1724no—
790C2×D4—1724no—
791C2×D4—1724no—
792C2×D4—1724no—
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—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—432no—
835C22×C4—432no—
836C22×C4—432no—
837C22×C4—432no—
838C22×C4—432no—
839C22×C4—432no—
840C22×C4—432no—
841C22×C4—868no—
842C22×C4—868no—
843C22×C4—868no—
844C22×C4—868no—
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—868no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—1724no—
882C22×C4—1724no—
883C22×C4—1724no—
884C22×C4—1724no—
885C22×C4—1724no—
886C22×C4—1724no—
887C22×C4—1724no—
888C22×C4—1724no—
889C22×C4—1724no—
890C22×C4—1724no—
891C22×C4—1724no—
892C22×C4—1724no—
893C22×C4—1724no—
894C22×C4—1724no—
895C22×C4—1724no—
896C22×C4—1724no—
897C22×C4C2×C4×D4312yes—
898C22×C4C2×C4×D4312yes—
899C22×C4C2×C4×D4312yes—
900C22×C4#1062189812yes—
901C22×C4#1062189812yes—
902C22×C4D4×D4312yes—
903C22×C4D4×D4312yes—
904C22×C4D4×D4312yes—
905C4⋊C4—1724no—
906C4⋊C4—1724no—
907C22⋊C4—868no—
908C22⋊C4—868no—
909C22⋊C4—868no—
910C22⋊C4—1724no—
911C22⋊C4—1724no—
912C22⋊C4—1724no—
913C22⋊C4—1724no—
914C22⋊C4—1724no—
915C22⋊C4—1724no—
916C42—44no—
917C42—1724no—
918C23—434no—
919C23—434no—
920C23—434no—
921C23—434no—
922C23—434no—
923C23—434no—
924C23—434no—
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—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—862no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
959C23—862no—
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—
979C23—1721no—
980C23—1721no—
981C23—1721no—
982C23—1721no—
983C23—1721no—
984C23—1721no—
985C23—1721no—
986C23—1721no—
987C23—1721no—
988C23C22×C4×D4311yescharacteristic
989C23C2×D4×D4311yescharacteristic
990C23C2×D4×D4311yescharacteristic
991C23C2×D4×D4311yescharacteristic
992C23#41×D4311yescharacteristic
993C23#41×D4311yescharacteristic
994C23#41×D4311yescharacteristic
995C23#41×D4311yescharacteristic
996C23#41×D4311yescharacteristic
997C23C2×#1062189811yescharacteristic
998C23C2×#1062189811yescharacteristic
999C23#1306337111yescharacteristic
1000C23#1306337111yescharacteristic
1001C23#1306337111yescharacteristic
1002C23#1306337311yescharacteristic
1003D4—17216no—
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—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
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—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—434no—
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—862no—
1065C2×C4—862no—
1066C2×C4—862no—
1067C2×C4—862no—
1068C2×C4—862no—
1069C2×C4—862no—
1070C2×C4—862no—
1071C2×C4—17216no—
1072C2×C4—17216no—
1073C2×C4—17216no—
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—1721no—
1087C2×C4—1721no—
1088C2×C4—1721no—
1089C2×C4—1721no—
1090C2×C4—1721no—
1091C2×C4—1721no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4—1721no—
1097C2×C4#1306329814yes—
1098C22—438no—
1099C22—864no—
1100C22—864no—
1101C22—864no—
1102C22—864no—
1103C22—864no—
1104C22—864no—
1105C22—864no—
1106C22—864no—
1107C22—864no—
1108C22—864no—
1109C22—864no—
1110C22—864no—
1111C22—864no—
1112C22—864no—
1113C22—3441no—
1114C22—3441no—
1115C22—3441no—
1116C22—3441no—
1117C22—3441no—
1118C22—3441no—
1119C22—3441no—
1120C22—3441no—
1121C22—1722no—
1122C22—1722no—
1123C22—1722no—
1124C22—1722no—
1125C22—1722no—
1126C22—1722no—
1127C22—1722no—
1128C22#117×D4311yescharacteristic
1129C22C4×D4×D4311yescharacteristic
1130C22C4×D4×D4311yescharacteristic
1131C22C4×D4×D4311yescharacteristic
1132C22C4×#1062189811yescharacteristic
1133C22#1458337311yescharacteristic
1134C22#1458338111yescharacteristic
1135C22#121×D4311yescharacteristic
1136C22C2×#1306329811yescharacteristic
1137C22#123×D4311yescharacteristic
1138C22#1458340811yescharacteristic
1139C22#124×D4311yescharacteristic
1140C22#126×D4311yescharacteristic
1141C22#1458342711yescharacteristic
1142C22#1458344611yescharacteristic
1143C22#1458346011yescharacteristic
1144C22#1458347911yescharacteristic
1145C22#1458348811yescharacteristic
1146C22#1458349711yescharacteristic
1147C22#1458353311yescharacteristic
1148C22#1458354111yescharacteristic
1149C22#1458354111yescharacteristic
1150C22#1458354211yescharacteristic
1151C22#1458354511yescharacteristic
1152C22#1458355011yescharacteristic
1153C22#1458355911yescharacteristic
1154C22#1458357311yescharacteristic
1155C22#1458357311yescharacteristic
1156C22#1458357311yescharacteristic
1157C22#1458357411yescharacteristic
1158C22#1458358111yescharacteristic
1159C22#1458359011yescharacteristic
1160C22#1458359311yescharacteristic
1161C22#1458359311yescharacteristic
1162C22#1458360011yescharacteristic
1163C4—24no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—81no—
1170C4—864no—
1171C4—3441no—
1172C4—1722no—
1173C4—1722no—
1174C4—1722no—
1175C4—1722no—
1176C2—868no—
1177C2—3442no—
1178C2#388×D4311yescharacteristic
1179C2C4×#1306329811yescharacteristic
1180C2#1913729411yescharacteristic
1181C2#1913751911yescharacteristic
1182C2#1913753611yescharacteristic
1183C2#1913757311yescharacteristic
1184C2#1913759211yescharacteristic
1185C2#1913799311yescharacteristic
1186C2#1913803711yescharacteristic
1187C2#1913872511yescharacteristic
1188C2#1913886011yescharacteristic
1189C2#1913891811yescharacteristic
1190C2#1913903611yescharacteristic
1191C2#1913916211yescharacteristic
1192C2#1913956011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1434D43
hypocenterC43#13999
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#14582790C2semidirect
5. C2×#14582758C2semidirect
6. C2×C4×(C2×D43)⋊C4C2semidirect
7. C2×#95×D43C2semidirect
8. #19132857C2semidirect
9. #19132853C2semidirect
10. #19132843C2semidirect
11. #19132839C2semidirect
12. #19132831C2semidirect
13. #19132826C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1434C2semidirect
35. #14582777C4semidirect
124. C2×(C2×D43)⋊C4C2×C4semidirect
125. C2×(C2×D43)⋊C4C2×C4semidirect
140. C43⋊#95C2×C4semidirect
141. C43⋊#95D4semidirect
157. #95×C43C2×C4semidirect
566. C2×D43#388semidirect
593. #1434D43semidirect
654. C43#13999semidirect
754. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827902
C2×#145827772
C2×#145827582
C2×C4×(C2×D43)⋊C42
C2×#95×D432
#191328572
#191328532
#191328432
#191328392
#191328312
#191328262
(C2×D43)⋊#952
C43×#14342
#1399943