Finite Group Databasebeta

← #25022064

Subgroups — #25022064

Order 11008.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×#14582815C211yesmaximal, characteristic
3C2×#14582795C211yesmaximal, characteristic, complemented
4C2×#14582788C211yesmaximal, characteristic, complemented
5C2×#14582771C211yesmaximal, characteristic, complemented
6C2×#14582770C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
8#19132842C211yesmaximal, characteristic, complemented
9#19132834C211yesmaximal, characteristic
10#19132831C211yesmaximal, characteristic, complemented
11#19132829C211yesmaximal, characteristic, complemented
12#19132826C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×(C22⋊D43)⋊C4—24no—
20C2×(C22⋊D43)⋊C4—24no—
21C2×(C22⋊D43)⋊C4—24no—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36#14582815C418yescomplemented
37#14582795—24no—
38#14582788—24no—
39#14582771—24no—
40#14582770—24no—
41C22⋊C4×Dic43—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
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43—22no—
66C22×C22⋊D43—22no—
67C22×C22⋊D43C2×C414yes—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—22no—
71C23×Dic43—22no—
72C23×Dic43—41no—
73C23×Dic43—41no—
74C23×Dic43D414yes—
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—22no—
87C22×C4×D43—41no—
88C22×C4×D43—41no—
89(C22⋊D43)⋊C4—232no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2×C414yescomplemented
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4D414yes—
102C2×C22⋊Dic43—22no—
103C2×C22⋊Dic43—22no—
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43C2×C414yescomplemented
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—22no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4—41no—
120C2×(C2×D43)⋊C4C2×C414yescomplemented
121C2×(C2×D43)⋊C4C2×C414yescomplemented
122C2×(C2×D43)⋊C4D414yes—
123C2×C4×Dic43—22no—
124C2×C4×Dic43—22no—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—22no—
127C2×C4×Dic43—22no—
128C2×C4×Dic43—22no—
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—22no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95C2×C414yescomplemented
142C43⋊#95D414yescomplemented
143C25×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43—22no—
151C2×C4⋊C4×C43—22no—
152C2×C4⋊C4×C43—41no—
153C2×C22⋊C4×C43—22no—
154C2×C22⋊C4×C43—22no—
155C2×C22⋊C4×C43—22no—
156C2×C22⋊C4×C43—22no—
157C2×C22⋊C4×C43—22no—
158C2×C22⋊C4×C43—22no—
159C2×C22⋊C4×C43—41no—
160C2×C22⋊C4×C43—41no—
161C2×C22⋊C4×C43C2×C414yescomplemented
162#95×C43—22no—
163#95×C43—22no—
164#95×C43—41no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43C22×C412yes—
178C24×C43C2×D412yes—
179C24×C43#4112yes—
180C24×C43C2411yescharacteristic
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43C22×C412yes—
194C23×D43C2×D412yes—
195C23×D43#4112yes—
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×C43—21no—
232C22×C4×C43C22×C412yes—
233C22×C4×C43C22×C412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43C2×D412yes—
237C22×C4×C43#4112yes—
238C2×C22⋊D43—28no—
239C2×C22⋊D43—28no—
240C2×C22⋊D43—28no—
241C2×C22⋊D43—28no—
242C2×C22⋊D43—28no—
243C2×C22⋊D43—28no—
244C2×C22⋊D43—28no—
245C22×Dic43—28no—
246C22×Dic43—28no—
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×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—44no—
284C22×Dic43—44no—
285C22×Dic43—44no—
286C22×Dic43—44no—
287C22×Dic43—44no—
288C22×Dic43C22×C412yes—
289C22×Dic43C22×C412yes—
290C22×Dic43C22×C412yes—
291C22×Dic43C2×D412yes—
292C22×Dic43C2×D412yes—
293C22×Dic43C2×D412yes—
294C22×Dic43C2×D412yes—
295C22×Dic43C2×D412yes—
296C22×Dic43C2×D412yes—
297C22×Dic43C2×D412yes—
298C22×Dic43#4112yes—
299C22×Dic43#4112yes—
300C22×Dic43#4112yes—
301C2×C4×D43—28no—
302C2×C4×D43—44no—
303C2×C4×D43—44no—
304C2×C4×D43—44no—
305C2×C4×D43—44no—
306C2×C4×D43—44no—
307C2×C4×D43—44no—
308C4⋊C4×C43—44no—
309C22⋊C4×C43—28no—
310C22⋊C4×C43—28no—
311C22⋊C4×C43—44no—
312C22⋊Dic43—28no—
313C22⋊Dic43—28no—
314(C2×D43)⋊C4—28no—
315(C2×D43)⋊C4—28no—
316(C2×D43)⋊C4—28no—
317(C2×D43)⋊C4—44no—
318(C2×D43)⋊C4—44no—
319C4⋊Dic43—28no—
320Dic43⋊C4—28no—
321Dic43⋊C4—44no—
322Dic43⋊C4—44no—
323C4×Dic43—28no—
324C4×Dic43—44no—
325C4×Dic43—44no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43—22no—
335C23×C43—22no—
336C23×C43—22no—
337C23×C43—22no—
338C23×C43—22no—
339C23×C43—22no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—41no—
354C23×C43—41no—
355C23×C43—41no—
356C23×C43—41no—
357C23×C43—41no—
358C23×C43—41no—
359C23×C43—41no—
360C23×C43C4×D414yes—
361C23×C43C23×C411yescharacteristic
362C23×C43C22×D411yescharacteristic
363C23×C43C22×D411yescharacteristic
364C23×C43C22×D411yescharacteristic
365C23×C43C22×D411yescharacteristic
366C23×C43C2×#4111yescharacteristic
367C23×C43C2×#4111yescharacteristic
368C23×C43C2×#4111yescharacteristic
369C23×C43C2×#4111yescharacteristic
370C23×C43C2×#4111yescharacteristic
371C23×C43C2×#4111yescharacteristic
372C23×C43H(5,𝔽2)11yescharacteristic
373C23×C43H(5,𝔽2)11yescharacteristic
374C23×C432−1+411yescharacteristic
375C23×C432−1+411yescharacteristic
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—22no—
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
386C22×D43—22no—
387C22×D43—22no—
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—22no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43—41no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43—41no—
403C22×D43—41no—
404C22×D43—41no—
405C22×D43—41no—
406C22×D43—41no—
407C22×D43—41no—
408C22×D43—41no—
409C22×D43—41no—
410C22×D43C4×D414yes—
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—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43C4×D414yescomplemented
453C22⋊D43—232no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
473C2×Dic43—22no—
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—22no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—416no—
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×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43C4×D414yes—
502C2×Dic43#12014yes—
503C2×Dic43#12114yes—
504C4×D43—416no—
505#14185—431nomaximal, Sylow
506C22×C43—24no—
507C22×C43—24no—
508C22×C43—24no—
509C22×C43—42no—
510C22×C43—42no—
511C22×C43—42no—
512C22×C43—42no—
513C22×C43—42no—
514C22×C43—42no—
515C22×C43—42no—
516C22×C43—42no—
517C22×C43—42no—
518C22×C43—42no—
519C22×C43—42no—
520C22×C43—42no—
521C22×C43C2×C4×D411yescharacteristic
522C22×C43C2×C4×D411yescharacteristic
523C22×C43C2×C4×D411yescharacteristic
524C22×C43C2×C4×D411yescharacteristic
525C22×C43C4×#4111yescharacteristic
526C22×C43#52011yescharacteristic
527C22×C43#52011yescharacteristic
528C22×C43C2×#12011yescharacteristic
529C22×C43C2×#12111yescharacteristic
530C22×C43#52511yescharacteristic
531C22×C43#52511yescharacteristic
532C22×C43#52511yescharacteristic
533C22×C43#52511yescharacteristic
534C22×C43#52911yescharacteristic
535C22×C43#53211yescharacteristic
536C22×C43#53411yescharacteristic
537C22×C43#53611yescharacteristic
538C22×C43#53911yescharacteristic
539C22×C43#53911yescharacteristic
540C22×C43D4211yescharacteristic
541C22×C43D4211yescharacteristic
542C22×C43#54611yescharacteristic
543C22×C43#54611yescharacteristic
544C22×C43#54711yescharacteristic
545C22×C43#54711yescharacteristic
546C22×C43#54711yescharacteristic
547C22×C43#54811yescharacteristic
548C22×C43#54811yescharacteristic
549C22×C43#54811yescharacteristic
550C22×C43#55111yescharacteristic
551C22×C43#55211yescharacteristic
552C22×C43#55311yescharacteristic
553C22×C43#55311yescharacteristic
554C22×C43#55611yescharacteristic
555C22×C43#55911yescharacteristic
556C2×D43—24no—
557C2×D43—24no—
558C2×D43—24no—
559C2×D43—42no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
563C2×D43—42no—
564C2×D43—42no—
565C2×D43—42no—
566C2×D43—42no—
567C2×D43—42no—
568C2×D43—42no—
569C2×D43—42no—
570C2×D43—42no—
571C4×C43—24no—
572C4×C43—42no—
573C4×C43—42no—
574C4×C43—42no—
575C4×C43—81no—
576C4×C43—81no—
577Dic43—24no—
578Dic43—24no—
579Dic43—24no—
580Dic43—42no—
581Dic43—42no—
582Dic43—42no—
583Dic43—42no—
584C22×C4×D4—431no—
585C2×#394—431no—
586C2×#389—431no—
587C2×#388—431no—
588C2×#385—431no—
589C2×#385—431no—
590C2×C4×C22⋊C4—431no—
591#1440—431no—
592#1439D4311yescharacteristic, complemented
593#1438—431no—
594#1437—431no—
595#1436—431no—
596#1436—431no—
597#1436—431no—
598C22⋊#95—431no—
599C2×C43—44no—
600C2×C43C4×#12011yescharacteristic
601C2×C43C4×#12111yescharacteristic
602C2×C43#232211yescharacteristic
603C2×C43#235911yescharacteristic
604C2×C43#236111yescharacteristic
605C2×C43#236111yescharacteristic
606C2×C43#236711yescharacteristic
607C2×C43#241011yescharacteristic
608C2×C43#241511yescharacteristic
609C2×C43#243211yescharacteristic
610C2×C43#245511yescharacteristic
611C2×C43#246011yescharacteristic
612C2×C43#246311yescharacteristic
613C2×C43#246611yescharacteristic
614C2×C43#260211yescharacteristic
615D43—44no—
616C23×D4—431no—
617C24×C4—431no—
618C24×C4—431no—
619C2×C4×D4—864no—
620C2×C4×D4—864no—
621C2×C4×D4—864no—
622C22×C4⋊C4—431no—
623C22×C4⋊C4—431no—
624C22×C4⋊C4—431no—
625C22×C4⋊C4—431no—
626C22×C4⋊C4C2×D4311yescharacteristic
627C22×C22⋊C4—431no—
628C22×C22⋊C4—431no—
629C22×C22⋊C4—431no—
630C22×C22⋊C4—431no—
631C22×C22⋊C4—431no—
632C22×C22⋊C4—431no—
633C22×C22⋊C4—431no—
634C22×C22⋊C4C2×D4311yescharacteristic
635C22×C22⋊C4C2×D4311yescharacteristic
636C22×C22⋊C4C2×D4311yescharacteristic
637C22×C42—431no—
638C22×C42—431no—
639C22×C42—431no—
640#394—438no—
641#389—864no—
642#388—864no—
643#385—864no—
644#385—864no—
645C4×C22⋊C4—864no—
646C2×#95—431no—
647C2×#95—431no—
648C2×#95—431no—
649C2×#95—431no—
650C2×#95—431no—
651C2×#95—431no—
652C2×#95—431no—
653C2×#95—431no—
654C2×#95—431no—
655C2×#95—431no—
656C2×#95—431no—
657C2×#95C2×D4311yescharacteristic
658C2×#95C2×D4311yescharacteristic
659C2×#95C2×D4311yescharacteristic
660C43#1418511yescharacteristic, complemented, Sylow
661C25—431no—
662C25C22×D4311yescharacteristic
663C22×D4—434no—
664C22×D4—862no—
665C22×D4—862no—
666C22×D4—862no—
667C22×D4—862no—
668C22×D4—862no—
669C22×D4—862no—
670C23×C4—431no—
671C23×C4—431no—
672C23×C4—431no—
673C23×C4—431no—
674C23×C4—431no—
675C23×C4—431no—
676C23×C4—431no—
677C23×C4—434no—
678C23×C4—862no—
679C23×C4—862no—
680C23×C4—862no—
681C23×C4—862no—
682C23×C4—862no—
683C23×C4—862no—
684C23×C4—862no—
685C23×C4—862no—
686C23×C4—862no—
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
697C4×D4—8632no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4—434no—
702C2×C4⋊C4—434no—
703C2×C4⋊C4—862no—
704C2×C4⋊C4—862no—
705C2×C4⋊C4—862no—
706C2×C4⋊C4—862no—
707C2×C4⋊C4—862no—
708C2×C4⋊C4—862no—
709C2×C4⋊C4—862no—
710C2×C4⋊C4—862no—
711C2×C4⋊C4—862no—
712C2×C4⋊C4—862no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—434no—
722C2×C22⋊C4—434no—
723C2×C22⋊C4—434no—
724C2×C22⋊C4—434no—
725C2×C22⋊C4—862no—
726C2×C22⋊C4—862no—
727C2×C22⋊C4—862no—
728C2×C22⋊C4—862no—
729C2×C22⋊C4—862no—
730C2×C22⋊C4—862no—
731C2×C22⋊C4—862no—
732C2×C22⋊C4—862no—
733C2×C22⋊C4—862no—
734C2×C22⋊C4—862no—
735C2×C22⋊C4—862no—
736C2×C22⋊C4—862no—
737C2×C22⋊C4—862no—
738C2×C22⋊C4—862no—
739C2×C22⋊C4—862no—
740C2×C22⋊C4—1721no—
741C2×C22⋊C4—1721no—
742C2×C22⋊C4C4×D4314yescomplemented
743C2×C42—862no—
744C2×C42—862no—
745C2×C42—862no—
746C2×C42—862no—
747C2×C42—862no—
748C2×C42—862no—
749C2×C42—862no—
750C2×C42—1721no—
751C2×C42—1721no—
752#95—22no—
753#95—22no—
754#95—41no—
755#95—434no—
756#95—434no—
757#95—862no—
758#95—862no—
759#95—862no—
760#95—862no—
761#95—862no—
762#95—862no—
763#95—862no—
764#95—862no—
765#95—862no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—432no—
779C24—432no—
780C24—432no—
781C24—861no—
782C24—861no—
783C24—861no—
784C24—861no—
785C24—861no—
786C24—861no—
787C24—861no—
788C24—861no—
789C24—861no—
790C24—861no—
791C24—861no—
792C24—861no—
793C24C2×C4×D4312yes—
794C24D4×D4312yes—
795C24#1062190212yes—
796C24C23×D4311yescharacteristic
797C2×D4—868no—
798C2×D4—868no—
799C2×D4—868no—
800C2×D4—868no—
801C2×D4—868no—
802C2×D4—868no—
803C2×D4—868no—
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—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—432no—
841C22×C4—432no—
842C22×C4—432no—
843C22×C4—432no—
844C22×C4—432no—
845C22×C4—432no—
846C22×C4—432no—
847C22×C4—432no—
848C22×C4—432no—
849C22×C4—432no—
850C22×C4—432no—
851C22×C4—432no—
852C22×C4—432no—
853C22×C4—868no—
854C22×C4—868no—
855C22×C4—868no—
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—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—861no—
890C22×C4—861no—
891C22×C4—861no—
892C22×C4—1724no—
893C22×C4—1724no—
894C22×C4—1724no—
895C22×C4—1724no—
896C22×C4—1724no—
897C22×C4—1724no—
898C22×C4—1724no—
899C22×C4—1724no—
900C22×C4—1724no—
901C22×C4—1724no—
902C22×C4—1724no—
903C22×C4C2×C4×D4312yes—
904C22×C4C2×C4×D4312yes—
905C22×C4D4×D4312yes—
906C22×C4D4×D4312yes—
907C22×C4D4×D4312yes—
908C22×C4#1062190012yes—
909C4⋊C4—44no—
910C4⋊C4—868no—
911C4⋊C4—868no—
912C4⋊C4—1724no—
913C4⋊C4—1724no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—44no—
917C22⋊C4—868no—
918C22⋊C4—868no—
919C22⋊C4—868no—
920C22⋊C4—868no—
921C22⋊C4—868no—
922C22⋊C4—1724no—
923C22⋊C4—1724no—
924C42—868no—
925C42—1724no—
926C42—1724no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—434no—
962C23—862no—
963C23—862no—
964C23—862no—
965C23—862no—
966C23—862no—
967C23—862no—
968C23—862no—
969C23—862no—
970C23—862no—
971C23—862no—
972C23—862no—
973C23—862no—
974C23—862no—
975C23—862no—
976C23—862no—
977C23—862no—
978C23—862no—
979C23—862no—
980C23—1721no—
981C23—1721no—
982C23—1721no—
983C23—1721no—
984C23—1721no—
985C23—1721no—
986C23—1721no—
987C23—1721no—
988C23—1721no—
989C23—1721no—
990C23—1721no—
991C23—1721no—
992C23—1721no—
993C23—1721no—
994C23—1721no—
995C23—1721no—
996C23#1306328714yes—
997C23C22×C4×D4311yescharacteristic
998C23C2×D4×D4311yescharacteristic
999C23C2×D4×D4311yescharacteristic
1000C23C2×D4×D4311yescharacteristic
1001C23C2×D4×D4311yescharacteristic
1002C23#41×D4311yescharacteristic
1003C23#41×D4311yescharacteristic
1004C23#41×D4311yescharacteristic
1005C23#41×D4311yescharacteristic
1006C23C2×#1062190011yescharacteristic
1007C23C2×#1062190211yescharacteristic
1008C23#1306337011yescharacteristic
1009C23#1306337011yescharacteristic
1010C23#1306337211yescharacteristic
1011C23#1306337211yescharacteristic
1012D4—8632no—
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—22no—
1026C2×C4—22no—
1027C2×C4—22no—
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—41no—
1053C2×C4—41no—
1054C2×C4—434no—
1055C2×C4—434no—
1056C2×C4—434no—
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—862no—
1072C2×C4—862no—
1073C2×C4—862no—
1074C2×C4—862no—
1075C2×C4—862no—
1076C2×C4—862no—
1077C2×C4—862no—
1078C2×C4—862no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—862no—
1086C2×C4—862no—
1087C2×C4—17216no—
1088C2×C4—17216no—
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—1721no—
1098C2×C4—1721no—
1099C2×C4—1721no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4—1721no—
1103C2×C4—1721no—
1104C2×C4—1721no—
1105C2×C4(C22⋊D43)⋊C414yescomplemented
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—864no—
1122C22—864no—
1123C22—864no—
1124C22—1722no—
1125C22—1722no—
1126C22—1722no—
1127C22—1722no—
1128C22—1722no—
1129C22—1722no—
1130C22—1722no—
1131C22—1722no—
1132C22—1722no—
1133C22—1722no—
1134C22—1722no—
1135C22—1722no—
1136C22C4×D4×D4311yescharacteristic
1137C22C4×D4×D4311yescharacteristic
1138C22C2×(C22⋊D43)⋊C411yescharacteristic
1139C22C2×#1306328711yescharacteristic
1140C22#1458336711yescharacteristic
1141C22#1458337811yescharacteristic
1142C22#1458337811yescharacteristic
1143C22#120×D4311yescharacteristic
1144C22#121×D4311yescharacteristic
1145C22#1458340711yescharacteristic
1146C22#1458341211yescharacteristic
1147C22#1458341211yescharacteristic
1148C22#1458341211yescharacteristic
1149C22#1458343511yescharacteristic
1150C22#1458344411yescharacteristic
1151C22#1458345911yescharacteristic
1152C22#1458347111yescharacteristic
1153C22#1458349811yescharacteristic
1154C22#1458349811yescharacteristic
1155C22#1458353111yescharacteristic
1156C22#1458353411yescharacteristic
1157C22#1458353811yescharacteristic
1158C22#1458354611yescharacteristic
1159C22#1458354711yescharacteristic
1160C22#1458354711yescharacteristic
1161C22#1458354911yescharacteristic
1162C22#1458355511yescharacteristic
1163C22#1458355711yescharacteristic
1164C22#1458355711yescharacteristic
1165C22#1458357911yescharacteristic
1166C22#1458358511yescharacteristic
1167C22#1458359211yescharacteristic
1168C22#1458359611yescharacteristic
1169C22#1458361611yescharacteristic
1170C22#1458363311yescharacteristic
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—81no—
1176C4—81no—
1177C4—864no—
1178C4—864no—
1179C4—864no—
1180C4—1722no—
1181C4—1722no—
1182C4—1722no—
1183C4—1722no—
1184C2—44no—
1185C2—1724no—
1186C2#1913709611yescharacteristic
1187C2#1913710111yescharacteristic
1188C2#1913726311yescharacteristic
1189C2#1913758411yescharacteristic
1190C2#1913760611yescharacteristic
1191C2#1913761611yescharacteristic
1192C2#1913766111yescharacteristic
1193C2#1913796211yescharacteristic
1194C2#1913801911yescharacteristic
1195C2#1913821811yescharacteristic
1196C2#1913847811yescharacteristic
1197C2#1913855011yescharacteristic
1198C2#1913859211yescharacteristic
1199C2#1913863411yescharacteristic
1200C2#1914021011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1439D43
hypocenterC43#14185
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#14582795C2semidirect
4. C2×#14582788C2semidirect
5. C2×#14582771C2semidirect
6. C2×#14582770C2semidirect
7. C2×C22⋊C4×Dic43C2semidirect
8. #19132842C2semidirect
10. #19132831C2semidirect
11. #19132829C2semidirect
12. #19132826C2semidirect
13. #19132826C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1439C2semidirect
36. #14582815C4semidirect
92. C2×C4⋊Dic43C2×C4semidirect
107. C2×C22⋊Dic43C2×C4semidirect
120. C2×(C2×D43)⋊C4C2×C4semidirect
121. C2×(C2×D43)⋊C4C2×C4semidirect
141. C43⋊#95C2×C4semidirect
142. C43⋊#95D4semidirect
161. C2×C22⋊C4×C43C2×C4semidirect
452. C2×C4×C43C4×D4semidirect
592. #1439D43semidirect
660. C43#14185semidirect
742. C2×C22⋊C4C4×D43semidirect
1105. C2×C4(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C2×#145828152
C2×#145827952
C2×#145827882
C2×#145827712
C2×#145827702
C2×C22⋊C4×Dic432
#191328422
#191328342
#191328312
#191328292
#191328262
(C2×D43)⋊#952
C43×#14392
#1418543