Finite Group Databasebeta

← #25022257

Subgroups — #25022257

Order 11008.

1954 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582816C211yesmaximal, characteristic
2C2×#14582791C211yesmaximal, characteristic, complemented
3C2×#14582777C211yesmaximal, characteristic
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5C2×#14582746C211yesmaximal, characteristic, complemented
6#19132843C211yesmaximal, characteristic, complemented
7#19132841C211yesmaximal, characteristic, complemented
8#19132835C211yesmaximal, characteristic
9#19132833C211yesmaximal, characteristic, complemented
10#19132831C211yesmaximal, characteristic, complemented
11#19132831C211yesmaximal, characteristic, complemented
12#19132824C211yesmaximal, characteristic, complemented
13#19132819C211yesmaximal, characteristic, complemented
14#19132819C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊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×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582816C418yescomplemented
34#14582791—24no—
35#14582777—24no—
36C4×(C2×D43)⋊C4—24no—
37#14582746—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
49C22×C4⋊C4×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C24×D43C2311yescharacteristic
58C22×D172—22no—
59C22×D172—22no—
60C22×D172—41no—
61C22×D172—41no—
62C22×D172—41no—
63C22×D172—41no—
64C22×D172C2×C414yes—
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—41no—
76C22×C4×D43—41no—
77C22×C4×D43D414yes—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—41no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—22no—
84C2×(C2×D43)⋊C4—22no—
85C2×(C2×D43)⋊C4—22no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
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—41no—
105C2×(C2×D43)⋊C4—41no—
106C2×(C2×D43)⋊C4—41no—
107C2×(C2×D43)⋊C4—41no—
108C2×(C2×D43)⋊C4—41no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4C2×C414yes—
111C2×(C2×D43)⋊C4C2×C414yes—
112C2×(C2×D43)⋊C4C2×C414yescomplemented
113C2×(C2×D43)⋊C4C2×C414yescomplemented
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—41no—
122C2×C4×Dic43—41no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—41no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95C2×C414yescomplemented
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43—41no—
142C2×C4⋊C4×C43—41no—
143C2×C4⋊C4×C43C2×C414yescomplemented
144C2×C42×C43—22no—
145C2×C42×C43—41no—
146C2×C42×C43—41no—
147#95×C43—22no—
148#95×C43—22no—
149#95×C43—41no—
150#95×C43—41no—
151#95×C43D414yescomplemented
152C24×C43C2411yescharacteristic
153C23×D43—21no—
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—21no—
157C23×D43—21no—
158C23×D43—21no—
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×D43C22×C412yes—
180C23×D43C22×C412yes—
181C23×D43C2×D412yes—
182C23×D43#4112yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
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×C43C22×C412yes—
223C22×C4×C43C22×C412yes—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C2×D412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43#4112yes—
230C22×C4×C43#4112yes—
231C22×C4×C43#4112yes—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
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×Dic43C22×C412yes—
268C22×Dic43C22×C412yes—
269C22×Dic43C2×D412yes—
270C22×Dic43#4112yes—
271C22×Dic43#4112yes—
272C22×Dic43#4112yes—
273C22×Dic43#4112yes—
274C2×D172—28no—
275C2×D172—44no—
276C2×D172—44no—
277C2×D172—44no—
278C2×D172—44no—
279C2×D172—44no—
280C2×D172—44no—
281C2×C4×D43—28no—
282C2×C4×D43—28no—
283C2×C4×D43—44no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
287C2×C4×D43—44no—
288C4⋊C4×C43—44no—
289C42×C43—44no—
290(C2×D43)⋊C4—28no—
291(C2×D43)⋊C4—28no—
292(C2×D43)⋊C4—28no—
293(C2×D43)⋊C4—28no—
294(C2×D43)⋊C4—28no—
295(C2×D43)⋊C4—44no—
296(C2×D43)⋊C4—44no—
297(C2×D43)⋊C4—44no—
298(C2×D43)⋊C4—44no—
299(C2×D43)⋊C4—44no—
300(C2×D43)⋊C4—44no—
301C4⋊Dic43—44no—
302C4×Dic43—44no—
303C4×Dic43—44no—
304C4×Dic43—44no—
305C23×C43C23×C411yescharacteristic
306C23×C43C22×D411yescharacteristic
307C23×C43C22×D411yescharacteristic
308C23×C43C2×#4111yescharacteristic
309C23×C43C2×#4111yescharacteristic
310C23×C43C2×#4111yescharacteristic
311C23×C43C2×#4111yescharacteristic
312C23×C43C2×#4111yescharacteristic
313C23×C43C2×#4111yescharacteristic
314C23×C43C2×#4111yescharacteristic
315C23×C43C2×#4111yescharacteristic
316C23×C43H(5,𝔽2)11yescharacteristic
317C23×C43H(5,𝔽2)11yescharacteristic
318C23×C43H(5,𝔽2)11yescharacteristic
319C23×C43H(5,𝔽2)11yescharacteristic
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
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—41no—
346C22×D43—41no—
347C22×D43—41no—
348C22×D43—41no—
349C22×D43—41no—
350C22×D43—41no—
351C22×D43—41no—
352C22×D43—41no—
353C22×D43—41no—
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×D43C4×D414yes—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
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—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
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×C43C4×D414yes—
438C2×C4×C43#12114yes—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
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—41no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—41no—
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#12314yes—
481D172—416no—
482C4×D43—416no—
483#14199—431nomaximal, Sylow
484C22×C43C2×C4×D411yescharacteristic
485C22×C43C2×C4×D411yescharacteristic
486C22×C43C4×#4111yescharacteristic
487C22×C43C4×#4111yescharacteristic
488C22×C43C4×#4111yescharacteristic
489C22×C43#51811yescharacteristic
490C22×C43#51811yescharacteristic
491C22×C43C2×#12111yescharacteristic
492C22×C43C2×#12311yescharacteristic
493C22×C43#52511yescharacteristic
494C22×C43#52511yescharacteristic
495C22×C43#52911yescharacteristic
496C22×C43#52911yescharacteristic
497C22×C43#52911yescharacteristic
498C22×C43#53211yescharacteristic
499C22×C43#53411yescharacteristic
500C22×C43#53511yescharacteristic
501C22×C43#53811yescharacteristic
502C22×C43#53811yescharacteristic
503C22×C43#54611yescharacteristic
504C22×C43#54611yescharacteristic
505C22×C43#54611yescharacteristic
506C22×C43#55011yescharacteristic
507C22×C43#55111yescharacteristic
508C22×C43#55111yescharacteristic
509C22×C43#55111yescharacteristic
510C22×C43#55311yescharacteristic
511C22×C43#55311yescharacteristic
512C22×C43#55311yescharacteristic
513C22×C43#55311yescharacteristic
514C22×C43#55311yescharacteristic
515C22×C43#55511yescharacteristic
516C22×C43#55511yescharacteristic
517C22×C43#55511yescharacteristic
518C22×C43#55911yescharacteristic
519C2×D43—24no—
520C2×D43—24no—
521C2×D43—24no—
522C2×D43—42no—
523C2×D43—42no—
524C2×D43—42no—
525C2×D43—42no—
526C2×D43—42no—
527C2×D43—42no—
528C2×D43—42no—
529C2×D43—42no—
530C2×D43—42no—
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—81no—
542C2×D43—81no—
543C2×D43—81no—
544C2×D43—81no—
545C2×D43—81no—
546C2×D43—81no—
547C2×D43—81no—
548C2×D43—81no—
549C4×C43—24no—
550C4×C43—24no—
551C4×C43—42no—
552C4×C43—42no—
553C4×C43—42no—
554C4×C43—42no—
555C4×C43—81no—
556Dic43—24no—
557Dic43—42no—
558Dic43—42no—
559Dic43—42no—
560Dic43—42no—
561Dic43—81no—
562C2×#394—431no—
563C2×#388—431no—
564C2×#386—431no—
565C2×C4×C22⋊C4—431no—
566C2×C4×C22⋊C4—431no—
567#1440—431no—
568#1439—431no—
569#1438—431no—
570#1437—431no—
571#1437—431no—
572#1437—431no—
573#1436D4311yescharacteristic, complemented
574C4⋊#95—431no—
575#1434—431no—
576#1434—431no—
577C2×C43C4×#12111yescharacteristic
578C2×C43C4×#12311yescharacteristic
579C2×C43#232111yescharacteristic
580C2×C43#236311yescharacteristic
581C2×C43#236411yescharacteristic
582C2×C43#237211yescharacteristic
583C2×C43#237411yescharacteristic
584C2×C43#241211yescharacteristic
585C2×C43#241411yescharacteristic
586C2×C43#245911yescharacteristic
587C2×C43#246711yescharacteristic
588C2×C43#250011yescharacteristic
589C2×C43#251811yescharacteristic
590C2×C43#251811yescharacteristic
591C2×C43#260211yescharacteristic
592D43—44no—
593D43—82no—
594C23×D4—431no—
595C24×C4—431no—
596C22×C4⋊C4—431no—
597C22×C4⋊C4C2×D4311yescharacteristic
598C22×C22⋊C4—431no—
599C22×C22⋊C4—431no—
600C22×C22⋊C4—431no—
601C22×C22⋊C4—431no—
602C22×C22⋊C4—431no—
603C22×C22⋊C4—431no—
604C22×C22⋊C4—431no—
605C22×C22⋊C4—431no—
606C22×C22⋊C4—431no—
607C22×C22⋊C4—431no—
608C22×C22⋊C4—431no—
609C22×C42—431no—
610C22×C42—431no—
611C22×C42—431no—
612C22×C42C2×D4311yescharacteristic
613#394—438no—
614#388—864no—
615#386—864no—
616C4×C22⋊C4—864no—
617C4×C22⋊C4—864no—
618C2×#95—431no—
619C2×#95—431no—
620C2×#95—431no—
621C2×#95—431no—
622C2×#95—431no—
623C2×#95—431no—
624C2×#95—431no—
625C2×#95—431no—
626C2×#95—431no—
627C2×#95—431no—
628C2×#95—431no—
629C2×#95C2×D4311yescharacteristic
630C2×#95C2×D4311yescharacteristic
631C2×#95C2×D4311yescharacteristic
632C2×#95C2×D4311yescharacteristic
633C2×#95C2×D4311yescharacteristic
634C43#1419911yescharacteristic, complemented, Sylow
635C25—431no—
636C25—431no—
637C22×D4—434no—
638C22×D4—862no—
639C22×D4—862no—
640C22×D4—1721no—
641C22×D4—1721no—
642C22×D4—1721no—
643C22×D4—1721no—
644C23×C4—431no—
645C23×C4—431no—
646C23×C4—431no—
647C23×C4—431no—
648C23×C4—431no—
649C23×C4—434no—
650C23×C4—431no—
651C23×C4—862no—
652C23×C4—862no—
653C23×C4—862no—
654C23×C4—862no—
655C23×C4—1721no—
656C23×C4—1721no—
657C23×C4C22×D4311yescharacteristic
658C23×C4C22×D4311yescharacteristic
659C23×C4C22×D4311yescharacteristic
660C23×C4C22×D4311yescharacteristic
661C23×C4C22×D4311yescharacteristic
662C23×C4C22×D4311yescharacteristic
663C23×C4C22×D4311yescharacteristic
664C2×C4⋊C4—41no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4—862no—
667C2×C4⋊C4—862no—
668C2×C4⋊C4—1721no—
669C2×C4⋊C4C4×D4314yescomplemented
670C2×C22⋊C4—434no—
671C2×C22⋊C4—434no—
672C2×C22⋊C4—434no—
673C2×C22⋊C4—434no—
674C2×C22⋊C4—862no—
675C2×C22⋊C4—862no—
676C2×C22⋊C4—862no—
677C2×C22⋊C4—862no—
678C2×C22⋊C4—862no—
679C2×C22⋊C4—862no—
680C2×C22⋊C4—862no—
681C2×C22⋊C4—862no—
682C2×C22⋊C4—862no—
683C2×C22⋊C4—862no—
684C2×C22⋊C4—862no—
685C2×C22⋊C4—862no—
686C2×C22⋊C4—862no—
687C2×C22⋊C4—862no—
688C2×C22⋊C4—862no—
689C2×C22⋊C4—862no—
690C2×C22⋊C4—862no—
691C2×C22⋊C4—862no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4—862no—
695C2×C22⋊C4—862no—
696C2×C22⋊C4—862no—
697C2×C22⋊C4—1721no—
698C2×C22⋊C4—1721no—
699C2×C22⋊C4—1721no—
700C2×C22⋊C4—1721no—
701C2×C22⋊C4—1721no—
702C2×C22⋊C4—1721no—
703C2×C42—22no—
704C2×C42—41no—
705C2×C42—41no—
706C2×C42—862no—
707C2×C42—862no—
708C2×C42—862no—
709C2×C42—862no—
710C2×C42—862no—
711C2×C42—862no—
712C2×C42—862no—
713C2×C42—1721no—
714C2×C42—1721no—
715#95—22no—
716#95—22no—
717#95—41no—
718#95—41no—
719#95—434no—
720#95—862no—
721#95—862no—
722#95—862no—
723#95—862no—
724#95—862no—
725#95—862no—
726#95—862no—
727#95—1721no—
728#95—1721no—
729#95—1721no—
730#95D17214yescomplemented
731C24—432no—
732C24—432no—
733C24—432no—
734C24—432no—
735C24—861no—
736C24—861no—
737C24—861no—
738C24—861no—
739C24—861no—
740C24—861no—
741C24—861no—
742C24—861no—
743C24—861no—
744C24—861no—
745C24—861no—
746C24—861no—
747C24—861no—
748C24—861no—
749C24—861no—
750C24—861no—
751C24—861no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
760C24—861no—
761C24C23×D4311yescharacteristic
762C2×D4—868no—
763C2×D4—1724no—
764C2×D4—1724no—
765C2×D4—1724no—
766C2×D4—1724no—
767C2×D4—1724no—
768C2×D4—1724no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
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—432no—
809C22×C4—432no—
810C22×C4—432no—
811C22×C4—432no—
812C22×C4—432no—
813C22×C4—432no—
814C22×C4—432no—
815C22×C4—868no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—861no—
821C22×C4—861no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—861no—
826C22×C4—861no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—861no—
834C22×C4—861no—
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—868no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—1724no—
853C22×C4—1724no—
854C22×C4—1724no—
855C22×C4—1724no—
856C22×C4—1724no—
857C22×C4C2×C4×D4312yes—
858C22×C4C2×C4×D4312yes—
859C22×C4C2×C4×D4312yes—
860C22×C4C2×D17212yes—
861C22×C4C2×D17212yes—
862C22×C4C2×D17212yes—
863C22×C4#1062189812yes—
864C22×C4D4×D4312yes—
865C22×C4#1062190212yes—
866C22×C4#1062190212yes—
867C4⋊C4—44no—
868C4⋊C4—1724no—
869C22⋊C4—868no—
870C22⋊C4—868no—
871C22⋊C4—868no—
872C22⋊C4—868no—
873C22⋊C4—868no—
874C22⋊C4—1724no—
875C22⋊C4—1724no—
876C22⋊C4—1724no—
877C22⋊C4—1724no—
878C22⋊C4—1724no—
879C22⋊C4—1724no—
880C42—44no—
881C42—1724no—
882C42—1724no—
883C42—1724no—
884C23—434no—
885C23—862no—
886C23—862no—
887C23—862no—
888C23—862no—
889C23—862no—
890C23—862no—
891C23—862no—
892C23—862no—
893C23—862no—
894C23—862no—
895C23—862no—
896C23—862no—
897C23—862no—
898C23—862no—
899C23—862no—
900C23—862no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—1721no—
911C23—1721no—
912C23—1721no—
913C23—1721no—
914C23—1721no—
915C23—1721no—
916C23—1721no—
917C23—1721no—
918C23—1721no—
919C23—1721no—
920C23—1721no—
921C23—1721no—
922C23—1721no—
923C23—1721no—
924C23—1721no—
925C23—1721no—
926C23—1721no—
927C23—1721no—
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—
954C23C22×C4×D4311yescharacteristic
955C23C2×D4×D4311yescharacteristic
956C23C22×D17211yescharacteristic
957C23#41×D4311yescharacteristic
958C23#41×D4311yescharacteristic
959C23#41×D4311yescharacteristic
960C23#41×D4311yescharacteristic
961C23#41×D4311yescharacteristic
962C23C2×#1062189811yescharacteristic
963C23C2×#1062190211yescharacteristic
964C23C2×#1062190211yescharacteristic
965C23#1306337011yescharacteristic
966C23#1306337011yescharacteristic
967C23#1306337011yescharacteristic
968C23#1306337111yescharacteristic
969D4—17216no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
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—434no—
1018C2×C4—862no—
1019C2×C4—862no—
1020C2×C4—862no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—862no—
1028C2×C4—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—17216no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1721no—
1040C2×C4—1721no—
1041C2×C4—1721no—
1042C2×C4—1721no—
1043C2×C4—1721no—
1044C2×C4—1721no—
1045C2×C4—1721no—
1046C2×C4—1721no—
1047C2×C4—1721no—
1048C2×C4—1721no—
1049C2×C4—1721no—
1050C2×C4—1721no—
1051C2×C4—1721no—
1052C2×C4—1721no—
1053C2×C4—1721no—
1054C2×C4—1721no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4C4×D17214yes—
1061C2×C4#1306330014yes—
1062C22—864no—
1063C22—864no—
1064C22—864no—
1065C22—3441no—
1066C22—3441no—
1067C22—3441no—
1068C22—3441no—
1069C22—3441no—
1070C22—3441no—
1071C22—3441no—
1072C22—3441no—
1073C22—1722no—
1074C22—1722no—
1075C22—1722no—
1076C22—1722no—
1077C22—1722no—
1078C22—1722no—
1079C22—1722no—
1080C22—1722no—
1081C22—1722no—
1082C22—1722no—
1083C22—1722no—
1084C22—1722no—
1085C22—1722no—
1086C22—1722no—
1087C22—1722no—
1088C22—1722no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22C4×D4×D4311yescharacteristic
1093C22C2×C4×D17211yescharacteristic
1094C22#1458336711yescharacteristic
1095C22C4×#1062190211yescharacteristic
1096C22C4×#1062190211yescharacteristic
1097C22#1458337111yescharacteristic
1098C22#1458337211yescharacteristic
1099C22C2×#1306330011yescharacteristic
1100C22#123×D4311yescharacteristic
1101C22#1458341111yescharacteristic
1102C22#1458341211yescharacteristic
1103C22#1458343211yescharacteristic
1104C22#1458343411yescharacteristic
1105C22#1458343611yescharacteristic
1106C22#1458344611yescharacteristic
1107C22#1458345911yescharacteristic
1108C22#1458346511yescharacteristic
1109C22#1458348111yescharacteristic
1110C22#1458348511yescharacteristic
1111C22#1458354411yescharacteristic
1112C22#1458354411yescharacteristic
1113C22#1458354411yescharacteristic
1114C22#1458357111yescharacteristic
1115C22#1458357611yescharacteristic
1116C22#1458357611yescharacteristic
1117C22#1458357611yescharacteristic
1118C22#1458359711yescharacteristic
1119C22#1458359811yescharacteristic
1120C22#1458359811yescharacteristic
1121C22#1458360011yescharacteristic
1122C22#1458360211yescharacteristic
1123C22#1458361111yescharacteristic
1124C22#1458361211yescharacteristic
1125C22#1458361511yescharacteristic
1126C22#1458363311yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—864no—
1135C4—3441no—
1136C4—1722no—
1137C4—1722no—
1138C4—1722no—
1139C4—1722no—
1140C2—3442no—
1141C2—1724no—
1142C2C4×#1306330011yescharacteristic
1143C2#1913711611yescharacteristic
1144C2#1913725111yescharacteristic
1145C2#1913763511yescharacteristic
1146C2#1913764511yescharacteristic
1147C2#1913770611yescharacteristic
1148C2#1913772711yescharacteristic
1149C2#1913798911yescharacteristic
1150C2#1913801111yescharacteristic
1151C2#1913853011yescharacteristic
1152C2#1913864411yescharacteristic
1153C2#1913905511yescharacteristic
1154C2#1913925211yescharacteristic
1155C2#1913925911yescharacteristic
1156C2#1914021111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14199
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#14582791C2semidirect
4. C2×C4×(C2×D43)⋊C4C2semidirect
5. C2×#14582746C2semidirect
6. #19132843C2semidirect
7. #19132841C2semidirect
9. #19132833C2semidirect
10. #19132831C2semidirect
11. #19132831C2semidirect
12. #19132824C2semidirect
13. #19132819C2semidirect
14. #19132819C2semidirect
15. C43×#1436C2semidirect
33. #14582816C4semidirect
112. C2×(C2×D43)⋊C4C2×C4semidirect
113. C2×(C2×D43)⋊C4C2×C4semidirect
133. C43⋊#95C2×C4semidirect
143. C2×C4⋊C4×C43C2×C4semidirect
151. #95×C43D4semidirect
573. #1436D43semidirect
634. C43#14199semidirect
669. C2×C4⋊C4C4×D43semidirect
730. #95D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145828162
C2×#145827912
C2×#145827772
C2×C4×(C2×D43)⋊C42
C2×#145827462
#191328432
#191328412
#191328352
#191328332
#191328312
#191328242
#191328192
C43×#14362
#1419943