Finite Group Databasebeta

← #25023919

Subgroups — #25023919

Order 11008.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063310C211yesmaximal, characteristic
2C2×#14582801C211yesmaximal, characteristic
3C2×#14582796C211yesmaximal, characteristic, complemented
4C2×#14582783C211yesmaximal, characteristic, complemented
5C2×#14582758C211yesmaximal, characteristic, complemented
6#19132848C211yesmaximal, characteristic, complemented
7#19132839C211yesmaximal, characteristic, complemented
8#19132839C211yesmaximal, characteristic, complemented
9#19132839C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132835C211yesmaximal, characteristic
12#19132831C211yesmaximal, characteristic, complemented
13#19132831C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C2×#13063310—24no—
19C2×#13063310—24no—
20C2×#13063310C418yescomplemented
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
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×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38#14582801—24no—
39#14582796—24no—
40#14582783—24no—
41#14582758—24no—
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—41no—
78C22×C4×D43—41no—
79C22×C4×D43C2×C414yes—
80#13063310—232no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—41no—
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⋊C4—41no—
92C2×Dic43⋊C4—41no—
93C2×Dic43⋊C4C2×C414yes—
94C2×Dic43⋊C4D414yes—
95C2×Dic43⋊C4D414yes—
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—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4—41no—
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)⋊C4—41no—
124C2×(C2×D43)⋊C4—41no—
125C2×(C2×D43)⋊C4C2×C414yes—
126C2×(C2×D43)⋊C4C2×C414yes—
127C2×(C2×D43)⋊C4C2×C414yes—
128C2×(C2×D43)⋊C4D414yes—
129C2×C4×Dic43—22no—
130C2×C4×Dic43—41no—
131C2×C4×Dic43—41no—
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⋊#95—41no—
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43—22no—
149C2×C4⋊C4×C43—22no—
150C2×C4⋊C4×C43C2×C414yes—
151C2×C42×C43—22no—
152C2×C42×C43—22no—
153C2×C42×C43—41no—
154#95×C43—22no—
155#95×C43—22no—
156#95×C43—22no—
157#95×C43—22no—
158#95×C43—41no—
159C24×C43C2411yescharacteristic
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×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43C22×C412yes—
187C23×D43C22×C412yes—
188C23×D43C2×D412yes—
189C23×D43#4112yes—
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×C43—21no—
231C22×C4×C43C22×C412yes—
232C22×C4×C43C22×C412yes—
233C22×C4×C43C22×C412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43C2×D412yes—
237C22×C4×C43#4112yes—
238C22×C4×C43#4112yes—
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×Dic43—21no—
274C22×Dic43C22×C412yes—
275C22×Dic43C22×C412yes—
276C22×Dic43C2×D412yes—
277C22×Dic43C2×D412yes—
278C22×Dic43C2×D412yes—
279C22×Dic43C2×D412yes—
280C22×Dic43C2×D412yes—
281C2×D172—28no—
282C2×D172—28no—
283C2×D172—44no—
284C2×D172—44no—
285C2×D172—44no—
286C2×D172—44no—
287C2×D172—44no—
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—
295C4⋊C4×C43—28no—
296C42×C43—44no—
297(C2×D43)⋊C4—28no—
298(C2×D43)⋊C4—28no—
299(C2×D43)⋊C4—28no—
300(C2×D43)⋊C4—44no—
301(C2×D43)⋊C4—44no—
302(C2×D43)⋊C4—44no—
303(C2×D43)⋊C4—44no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307(C2×D43)⋊C4—44no—
308C4⋊Dic43—44no—
309Dic43⋊C4—44no—
310Dic43⋊C4—44no—
311Dic43⋊C4—44no—
312Dic43⋊C4C22⋊C4116yescomplemented
313C4×Dic43—44no—
314C23×C43C23×C411yescharacteristic
315C23×C43C22×D411yescharacteristic
316C23×C43C22×D411yescharacteristic
317C23×C43C22×D411yescharacteristic
318C23×C43C2×#4111yescharacteristic
319C23×C43C2×#4111yescharacteristic
320C23×C43C2×#4111yescharacteristic
321C23×C43H(5,𝔽2)11yescharacteristic
322C23×C43H(5,𝔽2)11yescharacteristic
323C23×C43H(5,𝔽2)11yescharacteristic
324C23×C43H(5,𝔽2)11yescharacteristic
325C23×C43H(5,𝔽2)11yescharacteristic
326C23×C432−1+411yescharacteristic
327C23×C432−1+411yescharacteristic
328C23×C432−1+411yescharacteristic
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
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—41no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—41no—
358C22×D43—41no—
359C22×D43—41no—
360C22×D43—41no—
361C22×D43—41no—
362C22×D43—41no—
363C22×D43—41no—
364C22×D43—41no—
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
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×D43C4×D414yes—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
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—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
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×C43C2×C22⋊C414yes—
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—41no—
487C2×Dic43—41no—
488C2×Dic43C2×C22⋊C414yes—
489C2×Dic43C2×C22⋊C414yes—
490D172—416no—
491C4×D43—416no—
492#14360—431nomaximal, Sylow
493C22×C43C22×C22⋊C411yescharacteristic
494C22×C43C2×C4×D411yescharacteristic
495C22×C43C4×#4111yescharacteristic
496C22×C43#51811yescharacteristic
497C22×C43#52011yescharacteristic
498C22×C43#52011yescharacteristic
499C22×C43#52011yescharacteristic
500C22×C43#53411yescharacteristic
501C22×C43#53511yescharacteristic
502C22×C43#53611yescharacteristic
503C22×C43#53611yescharacteristic
504C22×C43#53711yescharacteristic
505C22×C43#53711yescharacteristic
506C22×C43#53811yescharacteristic
507C22×C43#53911yescharacteristic
508C22×C43#53911yescharacteristic
509C22×C43#53911yescharacteristic
510C22×C43#54011yescharacteristic
511C22×C43#54211yescharacteristic
512C22×C43D4211yescharacteristic
513C22×C43D4211yescharacteristic
514C22×C43#54611yescharacteristic
515C22×C43#54611yescharacteristic
516C22×C43#54611yescharacteristic
517C22×C43#54711yescharacteristic
518C22×C43#54811yescharacteristic
519C22×C43#54811yescharacteristic
520C22×C43#55011yescharacteristic
521C22×C43#55011yescharacteristic
522C22×C43#55111yescharacteristic
523C22×C43#55211yescharacteristic
524C22×C43#56011yescharacteristic
525C22×C43#56211yescharacteristic
526C22×C43#56211yescharacteristic
527C22×C43#56311yescharacteristic
528C2×D43—24no—
529C2×D43—24no—
530C2×D43—24no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—42no—
534C2×D43—42no—
535C2×D43—42no—
536C2×D43—42no—
537C2×D43—42no—
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—81no—
551C2×D43—81no—
552C2×D43—81no—
553C2×D43—81no—
554C2×D43—81no—
555C2×D43—81no—
556C2×D43—81no—
557C2×D43—81no—
558C4×C43—24no—
559C4×C43—42no—
560C4×C43—42no—
561C4×C43—42no—
562C4×C43—42no—
563C4×C43—42no—
564C4×C43—81no—
565Dic43—24no—
566Dic43—24no—
567Dic43—42no—
568Dic43—81no—
569Dic43—81no—
570Dic43—81no—
571C22×#123—431no—
572C2×#390—431no—
573C2×#389—431no—
574C2×#387—431no—
575C2×#380—431no—
576#1441—431no—
577#1439—431no—
578#1439—431no—
579#1439—431no—
580#1439—431no—
581#1438—431no—
582#1437—431no—
583#1437—431no—
584#1436D4311yescharacteristic, complemented
585C22⋊#95—431no—
586C2×C43#231111yescharacteristic
587C2×C43#232211yescharacteristic
588C2×C43#233511yescharacteristic
589C2×C43D4×C22⋊C411yescharacteristic
590C2×C43#234111yescharacteristic
591C2×C43#235911yescharacteristic
592C2×C43#237611yescharacteristic
593C2×C43#267311yescharacteristic
594C2×C43#267411yescharacteristic
595C2×C43#268111yescharacteristic
596C2×C43#268211yescharacteristic
597C2×C43#269411yescharacteristic
598C2×C43#269611yescharacteristic
599C2×C43#270511yescharacteristic
600C2×C43#270711yescharacteristic
601D43—44no—
602D43—82no—
603C23×D4—431no—
604C24×C4—431no—
605C2×#123—438no—
606C2×#123—864no—
607C2×#123—864no—
608C22×C4⋊C4—431no—
609C22×C4⋊C4—431no—
610C22×C4⋊C4—431no—
611C22×C4⋊C4—431no—
612C22×C4⋊C4—431no—
613C22×C4⋊C4C2×D4311yescharacteristic
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×C22⋊C4—431no—
624C22×C22⋊C4—431no—
625C22×C42—431no—
626C22×C42C2×D4311yescharacteristic
627#390—864no—
628#389—864no—
629#387—864no—
630#380—864no—
631C2×#95—431no—
632C2×#95—431no—
633C2×#95—431no—
634C2×#95—431no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—431no—
638C2×#95—431no—
639C2×#95—431no—
640C2×#95C2×D4311yescharacteristic
641C2×#95C2×D4311yescharacteristic
642C2×#95C2×D4311yescharacteristic
643C2×#95C2×D4311yescharacteristic
644C2×#95C2×D4311yescharacteristic
645C43#1436011yescharacteristic, complemented, Sylow
646C25—431no—
647C25—431no—
648C22×D4—434no—
649C22×D4—862no—
650C22×D4—862no—
651C22×D4—862no—
652C22×D4—862no—
653C22×D4—1721no—
654C22×D4—1721no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—431no—
658C23×C4—434no—
659C23×C4—431no—
660C23×C4—431no—
661C23×C4—431no—
662C23×C4—862no—
663C23×C4—862no—
664C23×C4—862no—
665C23×C4—862no—
666C23×C4—1721no—
667C23×C4—1721no—
668C23×C4C22×D4311yescharacteristic
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C23×C4C22×D4311yescharacteristic
673C23×C4C22×D4311yescharacteristic
674C23×C4C22×D4311yescharacteristic
675#123—8632no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—434no—
679C2×C4⋊C4—434no—
680C2×C4⋊C4—434no—
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—1721no—
689C2×C4⋊C4—1721no—
690C2×C4⋊C4—1721no—
691C2×C4⋊C4—1721no—
692C2×C4⋊C4—1721no—
693C2×C4⋊C4C4×D4314yes—
694C2×C22⋊C4—434no—
695C2×C22⋊C4—434no—
696C2×C22⋊C4—434no—
697C2×C22⋊C4—434no—
698C2×C22⋊C4—862no—
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—1721no—
714C2×C22⋊C4—1721no—
715C2×C22⋊C4—1721no—
716C2×C22⋊C4—1721no—
717C2×C22⋊C4—1721no—
718C2×C22⋊C4—1721no—
719C2×C22⋊C4—1721no—
720C2×C22⋊C4—1721no—
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×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—862no—
731C2×C42—1721no—
732C2×C42—1721no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—41no—
738#95—862no—
739#95—862no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—862no—
744#95—1721no—
745#95—1721no—
746#95—1721no—
747C24—432no—
748C24—432no—
749C24—432no—
750C24—432no—
751C24—861no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
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—
777C24C23×D4311yescharacteristic
778C2×D4—868no—
779C2×D4—868no—
780C2×D4—1724no—
781C2×D4—1724no—
782C2×D4—1724no—
783C2×D4—1724no—
784C2×D4—1724no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
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—432no—
827C22×C4—432no—
828C22×C4—432no—
829C22×C4—432no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—432no—
833C22×C4—868no—
834C22×C4—868no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
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—1724no—
871C22×C4—1724no—
872C22×C4—1724no—
873C22×C4—1724no—
874C22×C4—1724no—
875C22×C4C2×C4×D4312yes—
876C22×C4C2×C4×D4312yes—
877C22×C4C2×C4×D4312yes—
878C22×C4#1062189812yes—
879C22×C4#1062189812yes—
880C22×C4D4×D4312yes—
881C22×C4D4×D4312yes—
882C22×C4D4×D4312yes—
883C4⋊C4—28no—
884C4⋊C4—4316no—
885C4⋊C4—1724no—
886C4⋊C4—1724no—
887C4⋊C4—1724no—
888C4⋊C4—1724no—
889C22⋊C4—868no—
890C22⋊C4—868no—
891C22⋊C4—868no—
892C22⋊C4—1724no—
893C22⋊C4—1724no—
894C22⋊C4—1724no—
895C22⋊C4—1724no—
896C22⋊C4—1724no—
897C22⋊C4—1724no—
898C22⋊C4—1724no—
899C22⋊C4—1724no—
900C42—44no—
901C42—1724no—
902C23—434no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—862no—
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—1721no—
929C23—1721no—
930C23—1721no—
931C23—1721no—
932C23—1721no—
933C23—1721no—
934C23—1721no—
935C23—1721no—
936C23—1721no—
937C23—1721no—
938C23—1721no—
939C23—1721no—
940C23—1721no—
941C23—1721no—
942C23—1721no—
943C23—1721no—
944C23—1721no—
945C23—1721no—
946C23—1721no—
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—
972C23C22×C4×D4311yescharacteristic
973C23C2×D4×D4311yescharacteristic
974C23C2×D4×D4311yescharacteristic
975C23C2×D4×D4311yescharacteristic
976C23#41×D4311yescharacteristic
977C23C2×#1062189811yescharacteristic
978C23C2×#1062189811yescharacteristic
979C23#1306337011yescharacteristic
980C23#1306337111yescharacteristic
981C23#1306337111yescharacteristic
982C23#1306337111yescharacteristic
983C23#1306337111yescharacteristic
984C23#1306337211yescharacteristic
985C23#1306337311yescharacteristic
986C23#1306337311yescharacteristic
987D4—17216no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
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—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
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—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—434no—
1037C2×C4—434no—
1038C2×C4—862no—
1039C2×C4—862no—
1040C2×C4—862no—
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—17216no—
1054C2×C4—1721no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
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×C4C22⋊C4×D4314yes—
1080C22—864no—
1081C22—864no—
1082C22—864no—
1083C22—3441no—
1084C22—3441no—
1085C22—3441no—
1086C22—3441no—
1087C22—3441no—
1088C22—3441no—
1089C22—3441no—
1090C22—3441no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
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—
1110C22C2×C22⋊C4×D4311yescharacteristic
1111C22C4×D4×D4311yescharacteristic
1112C22C4×#1062189811yescharacteristic
1113C22#1458337111yescharacteristic
1114C22#1458337911yescharacteristic
1115C22#1458338111yescharacteristic
1116C22#1458338111yescharacteristic
1117C22#1458346011yescharacteristic
1118C22#1458346711yescharacteristic
1119C22#1458347211yescharacteristic
1120C22#1458347411yescharacteristic
1121C22#1458347911yescharacteristic
1122C22#1458347911yescharacteristic
1123C22#1458348211yescharacteristic
1124C22#1458349011yescharacteristic
1125C22#1458349611yescharacteristic
1126C22#1458349711yescharacteristic
1127C22#1458350411yescharacteristic
1128C22#1458352111yescharacteristic
1129C22#1458353111yescharacteristic
1130C22#1458353311yescharacteristic
1131C22#1458353811yescharacteristic
1132C22#1458354111yescharacteristic
1133C22#1458354511yescharacteristic
1134C22#1458355011yescharacteristic
1135C22#1458355811yescharacteristic
1136C22#1458355811yescharacteristic
1137C22#1458357011yescharacteristic
1138C22#1458357011yescharacteristic
1139C22#1458357311yescharacteristic
1140C22#1458359011yescharacteristic
1141C22#1458364011yescharacteristic
1142C22#1458364511yescharacteristic
1143C22#1458364611yescharacteristic
1144C22#1458365311yescharacteristic
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—81no—
1152C4—864no—
1153C4—864no—
1154C4—3441no—
1155C4—3441no—
1156C4—3441no—
1157C4—1722no—
1158C2—3442no—
1159C2—1724no—
1160C2#1913718611yescharacteristic
1161C2#1913726811yescharacteristic
1162C2#1913737911yescharacteristic
1163C2#1913741311yescharacteristic
1164C2#1913743511yescharacteristic
1165C2#1913759211yescharacteristic
1166C2#1913774211yescharacteristic
1167C2#1914086211yescharacteristic
1168C2#1914087711yescharacteristic
1169C2#1914094811yescharacteristic
1170C2#1914096111yescharacteristic
1171C2#1914111211yescharacteristic
1172C2#1914114211yescharacteristic
1173C2#1914126911yescharacteristic
1174C2#1914129911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14360
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#14582796C2semidirect
4. C2×#14582783C2semidirect
5. C2×#14582758C2semidirect
6. #19132848C2semidirect
7. #19132839C2semidirect
8. #19132839C2semidirect
9. #19132839C2semidirect
10. #19132839C2semidirect
12. #19132831C2semidirect
13. #19132831C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1436C2semidirect
20. C2×#13063310C4semidirect
312. Dic43⋊C4C22⋊C4semidirect
584. #1436D43semidirect
645. C43#14360semidirect

Maximal subgroups

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

subgroupindex
C22×#130633102
C2×#145828012
C2×#145827962
C2×#145827832
C2×#145827582
#191328482
#191328392
#191328352
#191328312
(C2×D43)⋊#952
C43×#14362
#1436043