Finite Group Databasebeta

← #25024165

Subgroups — #25024165

Order 11008.

1866 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×#14582801C211yesmaximal, characteristic
2C2×#14582791C211yesmaximal, characteristic, complemented
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582773C211yesmaximal, characteristic, complemented
5C2×#14582765C211yesmaximal, characteristic, complemented
6#19132847C211yesmaximal, characteristic, complemented
7#19132843C211yesmaximal, characteristic, complemented
8#19132841C211yesmaximal, characteristic, complemented
9#19132841C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132835C211yesmaximal, characteristic
12#19132831C211yesmaximal, characteristic, complemented
13#19132829C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1434C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34#14582801C418yescomplemented
35#14582791—24no—
36#14582777—24no—
37#14582773—24no—
38#14582765—24no—
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×C42×C43C2211yescharacteristic
50C2×#95×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—22no—
61C22×D172—22no—
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—41no—
75C22×C4×D43—41no—
76C22×C4×D43—41no—
77C22×C4×D43—41no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—41no—
83C2×C4⋊Dic43—41no—
84C2×C4⋊Dic43—41no—
85C2×C4⋊Dic43—41no—
86C2×C4⋊Dic43C2×C414yescomplemented
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—41no—
89C2×Dic43⋊C4—41no—
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—41no—
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)⋊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)⋊C4—41no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4C2×C414yes—
120C2×(C2×D43)⋊C4C2×C414yes—
121C2×(C2×D43)⋊C4C2×C414yescomplemented
122C2×(C2×D43)⋊C4C2×C414yescomplemented
123C2×C4×Dic43—22no—
124C2×C4×Dic43—41no—
125C2×C4×Dic43—41no—
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—
135C43⋊#95D414yes—
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C2×C42×C43—22no—
144C2×C42×C43—22no—
145C2×C42×C43C2×C414yescomplemented
146#95×C43—22no—
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×D43#4112yes—
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×C43—21no—
223C22×C4×C43C22×C412yes—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D412yes—
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×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43C22×C412yes—
271C22×Dic43C22×C412yes—
272C22×Dic43C2×D412yes—
273C22×Dic43C2×D412yes—
274C2×D172—28no—
275C2×D172—28no—
276C2×D172—44no—
277C2×D172—44no—
278C2×D172—44no—
279C2×D172—44no—
280C2×D172—44no—
281C2×C4×D43—44no—
282C2×C4×D43—44no—
283C2×C4×D43—44no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
287C2×C4×D43—44no—
288C42×C43—28no—
289(C2×D43)⋊C4—28no—
290(C2×D43)⋊C4—28no—
291(C2×D43)⋊C4—44no—
292(C2×D43)⋊C4—44no—
293(C2×D43)⋊C4—44no—
294(C2×D43)⋊C4—44no—
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—
300C4⋊Dic43—44no—
301C4⋊Dic43—44no—
302C4⋊Dic43—44no—
303Dic43⋊C4—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×C43H(5,𝔽2)11yescharacteristic
313C23×C43H(5,𝔽2)11yescharacteristic
314C23×C43H(5,𝔽2)11yescharacteristic
315C23×C43H(5,𝔽2)11yescharacteristic
316C23×C43H(5,𝔽2)11yescharacteristic
317C23×C43H(5,𝔽2)11yescharacteristic
318C23×C432−1+411yescharacteristic
319C23×C432−1+411yescharacteristic
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×D43#11714yes—
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—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
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×C43C4×D414yes—
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—41no—
452C2×Dic43—41no—
453C2×Dic43—41no—
454C2×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
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—41no—
481D172—416no—
482C4×D43—416no—
483#14377—431nomaximal, Sylow
484C22×C43C2×#11711yescharacteristic
485C22×C43C2×C4×D411yescharacteristic
486C22×C43C2×C4×D411yescharacteristic
487C22×C43#51811yescharacteristic
488C22×C43#51811yescharacteristic
489C22×C43#52011yescharacteristic
490C22×C43#52011yescharacteristic
491C22×C43#53511yescharacteristic
492C22×C43#53511yescharacteristic
493C22×C43#53511yescharacteristic
494C22×C43#53711yescharacteristic
495C22×C43#53811yescharacteristic
496C22×C43#53811yescharacteristic
497C22×C43#53911yescharacteristic
498C22×C43#53911yescharacteristic
499C22×C43#54011yescharacteristic
500C22×C43#54011yescharacteristic
501C22×C43#54011yescharacteristic
502C22×C43#54211yescharacteristic
503C22×C43D4211yescharacteristic
504C22×C43#54611yescharacteristic
505C22×C43#54611yescharacteristic
506C22×C43#54611yescharacteristic
507C22×C43#54711yescharacteristic
508C22×C43#54811yescharacteristic
509C22×C43#54811yescharacteristic
510C22×C43#55111yescharacteristic
511C22×C43#55111yescharacteristic
512C22×C43#55211yescharacteristic
513C22×C43#55311yescharacteristic
514C22×C43#55311yescharacteristic
515C22×C43H(3,𝔽4)11yescharacteristic
516C22×C43#56211yescharacteristic
517C22×C43#56211yescharacteristic
518C22×C43#56311yescharacteristic
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—81no—
555C4×C43—81no—
556Dic43—42no—
557Dic43—42no—
558Dic43—42no—
559Dic43—42no—
560Dic43—81no—
561Dic43—81no—
562C2×#390—431no—
563C2×#388—431no—
564C2×#386—431no—
565C2×#385—431no—
566C2×#382—431no—
567#1441—431no—
568#1440—431no—
569#1439—431no—
570#1439—431no—
571#1439—431no—
572#1438—431no—
573#1437—431no—
574#1436—431no—
575#1434D4311yescharacteristic, complemented
576C22⋊#95—431no—
577C2×C43#231811yescharacteristic
578C2×C43#232411yescharacteristic
579C2×C43#232811yescharacteristic
580C2×C43#234211yescharacteristic
581C2×C43#235211yescharacteristic
582C2×C43#236111yescharacteristic
583C2×C43#237911yescharacteristic
584C2×C43#267011yescharacteristic
585C2×C43#267611yescharacteristic
586C2×C43#270611yescharacteristic
587C2×C43#270711yescharacteristic
588C2×C43#271111yescharacteristic
589C2×C43#272311yescharacteristic
590C2×C43#275311yescharacteristic
591C2×C43#276111yescharacteristic
592D43—44no—
593D43—82no—
594C23×D4—431no—
595C24×C4—431no—
596C22×C4⋊C4—431no—
597C22×C4⋊C4—431no—
598C22×C4⋊C4—431no—
599C22×C4⋊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×C22⋊C4—431no—
610C22×C22⋊C4—431no—
611C22×C42—431no—
612C22×C42C2×D4311yescharacteristic
613#390—438no—
614#388—864no—
615#386—864no—
616#385—864no—
617#382—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×#95C2×D4311yescharacteristic
629C2×#95C2×D4311yescharacteristic
630C2×#95C2×D4311yescharacteristic
631C2×#95C2×D4311yescharacteristic
632C2×#95C2×D4311yescharacteristic
633C2×#95C2×D4311yescharacteristic
634C43#1437711yescharacteristic, complemented, Sylow
635C25—431no—
636C25—431no—
637C22×D4—434no—
638C22×D4—862no—
639C22×D4—862no—
640C22×D4—862no—
641C22×D4—862no—
642C22×D4—1721no—
643C22×D4—1721no—
644C23×C4—431no—
645C23×C4—431no—
646C23×C4—431no—
647C23×C4—431no—
648C23×C4—431no—
649C23×C4—431no—
650C23×C4—862no—
651C23×C4—862no—
652C23×C4—862no—
653C23×C4—1721no—
654C23×C4—1721no—
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—434no—
665C2×C4⋊C4—862no—
666C2×C4⋊C4—862no—
667C2×C4⋊C4—862no—
668C2×C4⋊C4—862no—
669C2×C4⋊C4—862no—
670C2×C4⋊C4—1721no—
671C2×C4⋊C4—1721no—
672C2×C4⋊C4—1721no—
673C2×C4⋊C4—1721no—
674C2×C4⋊C4—1721no—
675C2×C4⋊C4—1721no—
676C2×C22⋊C4—434no—
677C2×C22⋊C4—434no—
678C2×C22⋊C4—434no—
679C2×C22⋊C4—434no—
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—1721no—
694C2×C22⋊C4—1721no—
695C2×C22⋊C4—1721no—
696C2×C22⋊C4—1721no—
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×C22⋊C4—1721no—
704C2×C22⋊C4—1721no—
705C2×C22⋊C4—1721no—
706C2×C22⋊C4—1721no—
707C2×C22⋊C4—1721no—
708C2×C22⋊C4—1721no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—862no—
712C2×C42—1721no—
713C2×C42—1721no—
714C2×C42C4×D4314yescomplemented
715#95—22no—
716#95—22no—
717#95—22no—
718#95—41no—
719#95—41no—
720#95—434no—
721#95—862no—
722#95—862no—
723#95—862no—
724#95—862no—
725#95—862no—
726#95—1721no—
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—868no—
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—21no—
809C22×C4—432no—
810C22×C4—432no—
811C22×C4—432no—
812C22×C4—432no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—861no—
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—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—1724no—
852C22×C4—1724no—
853C22×C4—1724no—
854C22×C4—1724no—
855C22×C4—1724no—
856C22×C4—1724no—
857C22×C4—1724no—
858C22×C4C2×C4×D4312yes—
859C22×C4C2×C4×D4312yes—
860C22×C4C2×C4×D4312yes—
861C22×C4C2×D17212yes—
862C22×C4C2×D17212yes—
863C22×C4C2×D17212yes—
864C22×C4#1062189812yes—
865C22×C4D4×D4312yes—
866C22×C4#1062190012yes—
867C4⋊C4—1724no—
868C4⋊C4—1724no—
869C4⋊C4—1724no—
870C4⋊C4—1724no—
871C22⋊C4—868no—
872C22⋊C4—868no—
873C22⋊C4—1724no—
874C22⋊C4—1724no—
875C22⋊C4—1724no—
876C22⋊C4—1724no—
877C22⋊C4—1724no—
878C22⋊C4—1724no—
879C22⋊C4—1724no—
880C22⋊C4—1724no—
881C22⋊C4—1724no—
882C42—28no—
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
959C23C2×#1062190011yescharacteristic
960C23C2×#1062189811yescharacteristic
961C23#1306337011yescharacteristic
962C23#1306337111yescharacteristic
963C23#1306337111yescharacteristic
964C23#1306337111yescharacteristic
965C23#1306337111yescharacteristic
966C23#1306337111yescharacteristic
967C23#1306337211yescharacteristic
968C23#1306337311yescharacteristic
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—41no—
992C2×C4—41no—
993C2×C4—41no—
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—862no—
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—17216no—
1030C2×C4—1721no—
1031C2×C4—1721no—
1032C2×C4—1721no—
1033C2×C4—1721no—
1034C2×C4—1721no—
1035C2×C4—1721no—
1036C2×C4—1721no—
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×C4(C22⋊D43)⋊C414yes—
1061C2×C4C4×D17214yes—
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—
1092C22#117×D4311yescharacteristic
1093C22C2×(C22⋊D43)⋊C411yescharacteristic
1094C22C2×C4×D17211yescharacteristic
1095C22#1458337311yescharacteristic
1096C22#1458337311yescharacteristic
1097C22#1458337911yescharacteristic
1098C22#1458338011yescharacteristic
1099C22#1458346511yescharacteristic
1100C22#1458346811yescharacteristic
1101C22#1458346811yescharacteristic
1102C22#1458347911yescharacteristic
1103C22#1458348811yescharacteristic
1104C22#1458348811yescharacteristic
1105C22#1458349011yescharacteristic
1106C22#1458349011yescharacteristic
1107C22#1458350211yescharacteristic
1108C22#1458350411yescharacteristic
1109C22#1458350411yescharacteristic
1110C22#1458352211yescharacteristic
1111C22D4×D17211yescharacteristic
1112C22#1458354111yescharacteristic
1113C22#1458354111yescharacteristic
1114C22#1458354411yescharacteristic
1115C22#1458355311yescharacteristic
1116C22#1458355811yescharacteristic
1117C22#1458356111yescharacteristic
1118C22#1458357211yescharacteristic
1119C22#1458357211yescharacteristic
1120C22#1458359011yescharacteristic
1121C22#1458359511yescharacteristic
1122C22#1458359911yescharacteristic
1123C22#1458364111yescharacteristic
1124C22#1458364311yescharacteristic
1125C22#1458364711yescharacteristic
1126C22#1458365311yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—81no—
1134C4—3441no—
1135C4—3441no—
1136C4—1722no—
1137C4—1722no—
1138C4—1722no—
1139C4—1722no—
1140C2—3442no—
1141C2—1724no—
1142C2#1913722611yescharacteristic
1143C2#1913728411yescharacteristic
1144C2#1913732011yescharacteristic
1145C2#1913743711yescharacteristic
1146C2#1913752711yescharacteristic
1147C2#1913760911yescharacteristic
1148C2#1913776611yescharacteristic
1149C2#1914081911yescharacteristic
1150C2#1914089411yescharacteristic
1151C2#1914128111yescharacteristic
1152C2#1914129911yescharacteristic
1153C2#1914135611yescharacteristic
1154C2#1914151211yescharacteristic
1155C2#1914187611yescharacteristic
1156C2#1914198311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1434D43
hypocenterC43#14377
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#14582791C2semidirect
4. C2×#14582773C2semidirect
5. C2×#14582765C2semidirect
6. #19132847C2semidirect
7. #19132843C2semidirect
8. #19132841C2semidirect
9. #19132841C2semidirect
10. #19132839C2semidirect
12. #19132831C2semidirect
13. #19132829C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1434C2semidirect
34. #14582801C4semidirect
86. C2×C4⋊Dic43C2×C4semidirect
121. C2×(C2×D43)⋊C4C2×C4semidirect
122. C2×(C2×D43)⋊C4C2×C4semidirect
145. C2×C42×C43C2×C4semidirect
151. #95×C43D4semidirect
575. #1434D43semidirect
634. C43#14377semidirect
714. C2×C42C4×D43semidirect
730. #95D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145828012
C2×#145827912
C2×#145827772
C2×#145827732
C2×#145827652
#191328472
#191328432
#191328412
#191328392
#191328352
#191328312
#191328292
(C2×D43)⋊#952
C43×#14342
#1437743