Finite Group Databasebeta

← #25021027

Subgroups — #25021027

Order 11008.

2158 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×#14582785C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5#19132849C211yesmaximal, characteristic, complemented
6#19132837C211yesmaximal, characteristic, complemented
7#19132837C211yesmaximal, characteristic, complemented
8#19132835C211yesmaximal, characteristic
9#19132833C211yesmaximal, characteristic, complemented
10#19132833C211yesmaximal, characteristic, complemented
11#19132833C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13#19132828C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C2×#13063310—24no—
19C2×#13063310—24no—
20C2×#13063310C418yescomplemented
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊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×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582801—24no—
36#14582785—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
50C22×C4⋊C4×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C22×C42×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C4×C4⋊C4×C43—24no—
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⋊C4C2×C414yes—
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—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—41no—
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)⋊C4C2×C414yes—
117C2×(C2×D43)⋊C4C2×C414yes—
118C2×(C2×D43)⋊C4C2×C414yes—
119C2×(C2×D43)⋊C4D414yes—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—22no—
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—22no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43—22no—
143C2×C4⋊C4×C43—22no—
144C2×C4⋊C4×C43—22no—
145C2×C4⋊C4×C43C2×C414yes—
146C2×C4⋊C4×C43D414yes—
147C2×C4⋊C4×C43D414yes—
148C2×C42×C43—22no—
149C2×C42×C43—22no—
150C2×C42×C43—22no—
151C2×C42×C43—22no—
152C2×C42×C43—22no—
153C2×C42×C43—22no—
154C2×C42×C43—22no—
155C2×C42×C43—41no—
156C2×C42×C43—41no—
157#95×C43—22no—
158#95×C43—22no—
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×C43C22×C412yes—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C22×C412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2×D412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43#4112yes—
235C22×C4×C43#4112yes—
236C22×C4×C43#4112yes—
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×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43C22×C412yes—
278C22×Dic43C22×C412yes—
279C22×Dic43C2×D412yes—
280C22×Dic43#4112yes—
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—
296C4⋊C4×C43C22⋊C4116yescomplemented
297C42×C43—28no—
298C42×C43—44no—
299C42×C43—44no—
300(C2×D43)⋊C4—28no—
301(C2×D43)⋊C4—28no—
302(C2×D43)⋊C4—28no—
303(C2×D43)⋊C4—28no—
304(C2×D43)⋊C4—28no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307(C2×D43)⋊C4—44no—
308(C2×D43)⋊C4—44no—
309(C2×D43)⋊C4—44no—
310(C2×D43)⋊C4—44no—
311C4⋊Dic43—44no—
312Dic43⋊C4—28no—
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×C43C2×#4111yescharacteristic
322C23×C43C2×#4111yescharacteristic
323C23×C43C2×#4111yescharacteristic
324C23×C43C2×#4111yescharacteristic
325C23×C43H(5,𝔽2)11yescharacteristic
326C23×C43H(5,𝔽2)11yescharacteristic
327C23×C43H(5,𝔽2)11yescharacteristic
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—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—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
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×C43C2×C22⋊C414yes—
445C2×C4×C43C2×C22⋊C414yes—
446C2×C4×C43C2×C22⋊C414yes—
447C2×C4×C43#12314yescomplemented
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—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—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—
490D172—416no—
491C4×D43—416no—
492#14095—431nomaximal, Sylow
493C22×C43C22×C22⋊C411yescharacteristic
494C22×C43C2×C4×D411yescharacteristic
495C22×C43C4×#4111yescharacteristic
496C22×C43C4×#4111yescharacteristic
497C22×C43C4×#4111yescharacteristic
498C22×C43#51811yescharacteristic
499C22×C43#52011yescharacteristic
500C22×C43C2×#12311yescharacteristic
501C22×C43#52511yescharacteristic
502C22×C43#52511yescharacteristic
503C22×C43#52511yescharacteristic
504C22×C43#52911yescharacteristic
505C22×C43#52911yescharacteristic
506C22×C43#53211yescharacteristic
507C22×C43#53211yescharacteristic
508C22×C43#53811yescharacteristic
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#55111yescharacteristic
524C22×C43#55211yescharacteristic
525C22×C43#55311yescharacteristic
526C22×C43#55311yescharacteristic
527C22×C43#55911yescharacteristic
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—24no—
560C4×C43—24no—
561C4×C43—24no—
562C4×C43—42no—
563C4×C43—42no—
564C4×C43—42no—
565Dic43—42no—
566Dic43—42no—
567Dic43—42no—
568Dic43—42no—
569Dic43—81no—
570Dic43—81no—
571C22×#123—431no—
572C2×#390—431no—
573C2×#387—431no—
574C2×C4×C4⋊C4D4311yescharacteristic, complemented
575C2×C4×C22⋊C4—431no—
576#1441—431no—
577#1439—431no—
578#1439—431no—
579#1438—431no—
580#1437—431no—
581#1437—431no—
582#1437—431no—
583#1437—431no—
584#1436—431no—
585C22⋊#95—431no—
586C2×C43#229711yescharacteristic
587C2×C43C4×#12311yescharacteristic
588C2×C43#233511yescharacteristic
589C2×C43D4×C22⋊C411yescharacteristic
590C2×C43#234111yescharacteristic
591C2×C43#235911yescharacteristic
592C2×C43#237411yescharacteristic
593C2×C43#244311yescharacteristic
594C2×C43#244511yescharacteristic
595C2×C43#245611yescharacteristic
596C2×C43#245811yescharacteristic
597C2×C43#246111yescharacteristic
598C2×C43#247111yescharacteristic
599C2×C43#255411yescharacteristic
600C2×C43#255811yescharacteristic
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⋊C4C2×D4311yescharacteristic
611C22×C4⋊C4C2×D4311yescharacteristic
612C22×C22⋊C4—431no—
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×C42C2×D4311yescharacteristic
625C22×C42C2×D4311yescharacteristic
626C22×C42C2×D4311yescharacteristic
627#390—864no—
628#387—864no—
629C4×C4⋊C4—24no—
630C4×C22⋊C4—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×#95—431no—
641C2×#95—431no—
642C2×#95—431no—
643C2×#95C2×D4311yescharacteristic
644C2×#95C2×D4311yescharacteristic
645C43#1409511yescharacteristic, 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—431no—
659C23×C4—434no—
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—22no—
679C2×C4⋊C4—434no—
680C2×C4⋊C4—862no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—862no—
684C2×C4⋊C4—1721no—
685C2×C4⋊C4C4×D4314yes—
686C2×C4⋊C4D17214yes—
687C2×C4⋊C4C22⋊D4314yes—
688C2×C22⋊C4—434no—
689C2×C22⋊C4—434no—
690C2×C22⋊C4—434no—
691C2×C22⋊C4—434no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4—862no—
695C2×C22⋊C4—862no—
696C2×C22⋊C4—862no—
697C2×C22⋊C4—862no—
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—862no—
714C2×C22⋊C4—862no—
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×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—41no—
729C2×C42—41no—
730C2×C42—862no—
731C2×C42—862no—
732C2×C42—1721no—
733#95—22no—
734#95—22no—
735#95—862no—
736#95—862no—
737#95—862no—
738#95—862no—
739#95—862no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—1721no—
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—432no—
820C22×C4—432no—
821C22×C4—432no—
822C22×C4—432no—
823C22×C4—868no—
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—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—868no—
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—1724no—
864C22×C4—1724no—
865C22×C4—1724no—
866C22×C4—1724no—
867C22×C4—1724no—
868C22×C4C2×C4×D4312yes—
869C22×C4C2×C4×D4312yes—
870C22×C4C2×C4×D4312yes—
871C22×C4C2×D17212yes—
872C22×C4C2×D17212yes—
873C22×C4C2×D17212yes—
874C22×C4#1062189812yes—
875C22×C4#1062189812yes—
876C22×C4#1062189812yes—
877C22×C4#1062189812yes—
878C22×C4D4×D4312yes—
879C22×C4#1062190212yes—
880C22×C4C2×C22⋊D4312yes—
881C22×C4C2×C22⋊D4312yes—
882C22×C4C2×C22⋊D4312yes—
883C4⋊C4—28no—
884C4⋊C4—868no—
885C4⋊C4—1724no—
886C4⋊C4(C2×D43)⋊C4116yescomplemented
887C22⋊C4—868no—
888C22⋊C4—868no—
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—
898C42—28no—
899C42—44no—
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
974C23C22×C22⋊D4311yescharacteristic
975C23C22×D17211yescharacteristic
976C23#41×D4311yescharacteristic
977C23#41×D4311yescharacteristic
978C23C2×#1062189811yescharacteristic
979C23C2×#1062189811yescharacteristic
980C23C2×#1062189811yescharacteristic
981C23C2×#1062189811yescharacteristic
982C23C2×#1062190211yescharacteristic
983C23#1306337011yescharacteristic
984C23#1306337111yescharacteristic
985C23#1306337111yescharacteristic
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—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—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—862no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—862no—
1037C2×C4—862no—
1038C2×C4—862no—
1039C2×C4—862no—
1040C2×C4—862no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—862no—
1044C2×C4—862no—
1045C2×C4—17216no—
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×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×C4C2×(C2×D43)⋊C414yes—
1077C2×C4C2×(C2×D43)⋊C414yes—
1078C2×C4C2×(C2×D43)⋊C414yes—
1079C2×C4#1306331014yescomplemented
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—
1110C22C22×(C2×D43)⋊C411yescharacteristic
1111C22C4×D4×D4311yescharacteristic
1112C22C4×#1062189811yescharacteristic
1113C22C4×#1062189811yescharacteristic
1114C22C4×#1062190211yescharacteristic
1115C22#1458337111yescharacteristic
1116C22#1458338111yescharacteristic
1117C22C2×#1306331011yescharacteristic
1118C22#1458340811yescharacteristic
1119C22#1458341011yescharacteristic
1120C22#1458341011yescharacteristic
1121C22#1458342711yescharacteristic
1122C22#1458343611yescharacteristic
1123C22#1458344911yescharacteristic
1124C22#1458344911yescharacteristic
1125C22#1458348211yescharacteristic
1126C22#1458349611yescharacteristic
1127C22#1458350411yescharacteristic
1128C22#1458352111yescharacteristic
1129C22D4×C22⋊D4311yescharacteristic
1130C22D4×D17211yescharacteristic
1131C22#1458353711yescharacteristic
1132C22#1458354411yescharacteristic
1133C22#1458354511yescharacteristic
1134C22#1458355011yescharacteristic
1135C22#1458356011yescharacteristic
1136C22#1458356111yescharacteristic
1137C22#1458356811yescharacteristic
1138C22#1458357111yescharacteristic
1139C22#1458357311yescharacteristic
1140C22#1458357311yescharacteristic
1141C22#1458359011yescharacteristic
1142C22#1458359711yescharacteristic
1143C22#1458359811yescharacteristic
1144C22#1458363411yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—3441no—
1153C4—3441no—
1154C4—1722no—
1155C4—1722no—
1156C4—1722no—
1157C4—1722no—
1158C2—3442no—
1159C2—1724no—
1160C2#1913708511yescharacteristic
1161C2C4×#1306331011yescharacteristic
1162C2#1913737911yescharacteristic
1163C2D4×(C2×D43)⋊C411yescharacteristic
1164C2#1913743311yescharacteristic
1165C2#1913759211yescharacteristic
1166C2#1913772411yescharacteristic
1167C2#1913833011yescharacteristic
1168C2#1913836011yescharacteristic
1169C2#1913848111yescharacteristic
1170C2#1913851111yescharacteristic
1171C2#1913856211yescharacteristic
1172C2#1913870011yescharacteristic
1173C2#1913964911yescharacteristic
1174C2#1913970311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C4×C4⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenterC2×C4×C4⋊C4D43
hypocenterC43#14095
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#14582785C2semidirect
4. C2×C4×(C2×D43)⋊C4C2semidirect
5. #19132849C2semidirect
6. #19132837C2semidirect
7. #19132837C2semidirect
9. #19132833C2semidirect
10. #19132833C2semidirect
11. #19132833C2semidirect
12. #19132831C2semidirect
13. #19132828C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C4×C4⋊C4×C43C2semidirect
20. C2×#13063310C4semidirect
296. C4⋊C4×C43C22⋊C4semidirect
447. C2×C4×C43#123semidirect
574. C2×C4×C4⋊C4D43semidirect
645. C43#14095semidirect
886. C4⋊C4(C2×D43)⋊C4semidirect
1079. C2×C4#13063310semidirect

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×#145827852
C2×C4×(C2×D43)⋊C42
#191328492
#191328372
#191328352
#191328332
#191328312
#191328282
(C2×D43)⋊#952
C2×C4×C4⋊C4×C432
#1409543