Finite Group Databasebeta

← #25025012

Subgroups — #25025012

Order 11008.

2118 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582801C211yesmaximal, characteristic
2C2×#14582777C212yesmaximal
3C2×#14582773C212yesmaximal, complemented
4C2×#14582770C212yesmaximal, complemented
5#19132847C212yesmaximal, complemented
6#19132841C212yesmaximal, complemented
7#19132837C212yesmaximal, complemented
8#19132825C211yesmaximal, characteristic, complemented
9C43×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D172C2211yescharacteristic
11C23×C4×D43C2212yes—
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2212yes—
21#14582801C418yescomplemented
22#14582777—28no—
23#14582773—28no—
24#14582770—28no—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C22×C4⋊C4×C43C2211yescharacteristic
31C22×C4⋊C4×C43C2211yescharacteristic
32C22×C42×C43C2211yescharacteristic
33C2×#95×C43C2212yes—
34C2×#95×C43C2212yes—
35C24×D43C2312yes—
36C22×D172—41no—
37C22×D172—41no—
38C22×D172—41no—
39C22×D172—41no—
40C22×D172C2×C414yes—
41C22×D172D414yes—
42C22×D172Q814yes—
43C23×Dic43C2312yes—
44C23×Dic43C2312yes—
45C23×Dic43C2312yes—
46C22×C4×D43—24no—
47C22×C4×D43—24no—
48C22×C4×D43—24no—
49C22×C4×D43—42no—
50C22×C4×D43—42no—
51C22×C4×D43—42no—
52C22×C4×D43—42no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—41no—
55C2×C4⋊Dic43—41no—
56C2×C4⋊Dic43—41no—
57C2×C4⋊Dic43—41no—
58C2×C4⋊Dic43—41no—
59C2×C4⋊Dic43—41no—
60C2×C4⋊Dic43C2×C414yescomplemented
61C2×C4⋊Dic43D414yescomplemented
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—24no—
64C2×Dic43⋊C4—42no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—24no—
67C2×(C2×D43)⋊C4—24no—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—24no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—42no—
75C2×(C2×D43)⋊C4—42no—
76C2×(C2×D43)⋊C4—42no—
77C2×(C2×D43)⋊C4—42no—
78C2×(C2×D43)⋊C4C2×C418yescomplemented
79C2×(C2×D43)⋊C4C2×C418yescomplemented
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—42no—
85C23×C4×C43C2312yes—
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—41no—
92C2×C4⋊C4×C43—41no—
93C2×C4⋊C4×C43—41no—
94C2×C4⋊C4×C43—41no—
95C2×C4⋊C4×C43D414yescomplemented
96C2×C42×C43—41no—
97C2×C42×C43—41no—
98C2×C42×C43C2×C414yescomplemented
99#95×C43—24no—
100#95×C43—24no—
101C24×C43C2411yescharacteristic
102C23×D43—22no—
103C23×D43—22no—
104C23×D43—22no—
105C23×D43—22no—
106C23×D43—22no—
107C23×D43—22no—
108C23×D43—22no—
109C23×D43—22no—
110C23×D43—22no—
111C23×D43—22no—
112C23×D43—22no—
113C23×D43—22no—
114C23×D43C22×C414yes—
115C23×D43C2×D414yes—
116C23×D43C2×Q814yes—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43C22×C412yes—
143C22×C4×C43C22×C412yes—
144C22×C4×C43C22×C412yes—
145C22×C4×C43C2×D414yes—
146C22×C4×C43C2×D412yes—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×Q812yes—
150C22×C4×C43#4112yes—
151C22×C4×C43#4112yes—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43C22×C414yes—
172C22×Dic43C2×D414yes—
173C2×D172—44no—
174C2×D172—44no—
175C2×D172—44no—
176C2×D172—44no—
177C2×D172—44no—
178C2×D172—44no—
179C2×D172C4⋊C4116yescomplemented
180C2×C4×D43—48no—
181C2×C4×D43—48no—
182C2×C4×D43—48no—
183C2×C4×D43—48no—
184C2×C4×D43—48no—
185C2×C4×D43—48no—
186C2×C4×D43—48no—
187C4⋊C4×C43—44no—
188C4⋊C4×C43—44no—
189C42×C43—44no—
190(C2×D43)⋊C4—216no—
191(C2×D43)⋊C4—216no—
192(C2×D43)⋊C4—48no—
193(C2×D43)⋊C4—48no—
194(C2×D43)⋊C4—48no—
195C4⋊Dic43—44no—
196C4⋊Dic43—44no—
197C4⋊Dic43—44no—
198Dic43⋊C4—48no—
199C23×C43C23×C411yescharacteristic
200C23×C43C22×D411yescharacteristic
201C23×C43C22×D411yescharacteristic
202C23×C43C22×D411yescharacteristic
203C23×C43C22×Q811yescharacteristic
204C23×C43C2×#4111yescharacteristic
205C23×C43C2×#4111yescharacteristic
206C23×C43H(5,𝔽2)11yescharacteristic
207C23×C43H(5,𝔽2)11yescharacteristic
208C23×C43H(5,𝔽2)11yescharacteristic
209C23×C43H(5,𝔽2)11yescharacteristic
210C23×C43H(5,𝔽2)11yescharacteristic
211C23×C43H(5,𝔽2)11yescharacteristic
212C23×C432−1+411yescharacteristic
213C23×C432−1+411yescharacteristic
214C22×D43—24no—
215C22×D43—24no—
216C22×D43—24no—
217C22×D43—24no—
218C22×D43—24no—
219C22×D43—24no—
220C22×D43—24no—
221C22×D43—24no—
222C22×D43—24no—
223C22×D43—24no—
224C22×D43—24no—
225C22×D43—24no—
226C22×D43—24no—
227C22×D43—24no—
228C22×D43—24no—
229C22×D43—24no—
230C22×D43—24no—
231C22×D43—24no—
232C22×D43—42no—
233C22×D43—42no—
234C22×D43—42no—
235C22×D43—42no—
236C22×D43—42no—
237C22×D43—42no—
238C22×D43—42no—
239C22×D43—42no—
240C22×D43—42no—
241C22×D43—42no—
242C22×D43—42no—
243C22×D43—42no—
244C22×D43—42no—
245C22×D43—42no—
246C22×D43—42no—
247C22×D43—42no—
248C22×D43C2×C4⋊C418yes—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—24no—
268C2×C4×C43—24no—
269C2×C4×C43—24no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—42no—
281C2×C4×C43C2×C4⋊C414yes—
282C2×C4×C43C4×D414yes—
283C2×C4×C43C4×D414yes—
284C2×Dic43—24no—
285C2×Dic43—24no—
286C2×Dic43—24no—
287C2×Dic43—24no—
288C2×Dic43—24no—
289C2×Dic43—24no—
290C2×Dic43—42no—
291C2×Dic43—42no—
292C2×Dic43—42no—
293C2×Dic43—42no—
294C2×Dic43—42no—
295C2×Dic43—42no—
296C2×Dic43—42no—
297C2×Dic43—42no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—42no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305D172—416no—
306C4×D43—432no—
307#14440—431nomaximal, Sylow
308C22×C43C22×C4⋊C411yescharacteristic
309C22×C43C2×C4×D411yescharacteristic
310C22×C43C2×C4×D411yescharacteristic
311C22×C43#51811yescharacteristic
312C22×C43#51811yescharacteristic
313C22×C43#52011yescharacteristic
314C22×C43#52011yescharacteristic
315C22×C43#53411yescharacteristic
316C22×C43#53411yescharacteristic
317C22×C43#53411yescharacteristic
318C22×C43#53411yescharacteristic
319C22×C43#53711yescharacteristic
320C22×C43#53711yescharacteristic
321C22×C43#53811yescharacteristic
322C22×C43#53811yescharacteristic
323C22×C43#53911yescharacteristic
324C22×C43#53911yescharacteristic
325C22×C43#54311yescharacteristic
326C22×C43#54311yescharacteristic
327C22×C43D4211yescharacteristic
328C22×C43D4211yescharacteristic
329C22×C43D4211yescharacteristic
330C22×C43#54711yescharacteristic
331C22×C43#54711yescharacteristic
332C22×C43D4×Q811yescharacteristic
333C22×C43D4×Q811yescharacteristic
334C22×C43#55011yescharacteristic
335C22×C43#55011yescharacteristic
336C22×C43#55411yescharacteristic
337C22×C43#55411yescharacteristic
338C22×C43#55911yescharacteristic
339C22×C43H(3,𝔽4)11yescharacteristic
340C22×C43#56211yescharacteristic
341C22×C43#56211yescharacteristic
342C22×C43#56311yescharacteristic
343C2×D43—28no—
344C2×D43—28no—
345C2×D43—28no—
346C2×D43—44no—
347C2×D43—44no—
348C2×D43—44no—
349C2×D43—44no—
350C2×D43—44no—
351C2×D43—44no—
352C2×D43—44no—
353C2×D43—44no—
354C2×D43—44no—
355C2×D43—44no—
356C2×D43—44no—
357C2×D43—44no—
358C4×C43—24no—
359C4×C43—24no—
360C4×C43—24no—
361C4×C43—44no—
362C4×C43—82no—
363Dic43—44no—
364Dic43—44no—
365Dic43—82no—
366C2×#390—431no—
367C2×#386—432no—
368C2×#385—432no—
369C2×#385—432no—
370#1441—432no—
371#1439—432no—
372#1439—432no—
373C4⋊#95—431no—
374C4⋊#95D4311yescharacteristic, complemented
375C2×C43#231511yescharacteristic
376C2×C43#232511yescharacteristic
377C2×C43#232511yescharacteristic
378C2×C43D4×C4⋊C411yescharacteristic
379C2×C43D4×C4⋊C411yescharacteristic
380C2×C43#236611yescharacteristic
381C2×C43#237911yescharacteristic
382C2×C43#267911yescharacteristic
383C2×C43#268211yescharacteristic
384C2×C43#268211yescharacteristic
385C2×C43#268311yescharacteristic
386C2×C43#272411yescharacteristic
387C2×C43#273211yescharacteristic
388C2×C43#273211yescharacteristic
389C2×C43#280411yescharacteristic
390D43—48no—
391C23×D4—431no—
392C24×C4—432no—
393C22×C4⋊C4—431no—
394C22×C4⋊C4—431no—
395C22×C4⋊C4—432no—
396C22×C4⋊C4—431no—
397C22×C4⋊C4C2×D4311yescharacteristic
398C22×C4⋊C4C2×D4311yescharacteristic
399C22×C22⋊C4—432no—
400C22×C22⋊C4—432no—
401C22×C22⋊C4—432no—
402C22×C22⋊C4—432no—
403C22×C22⋊C4—432no—
404C22×C42C2×D4311yescharacteristic
405#390—438no—
406#386—868no—
407#385—868no—
408#385—868no—
409C2×#95—432no—
410C2×#95—432no—
411C2×#95—432no—
412C2×#95—432no—
413C2×#95—432no—
414C2×#95C2×D4312yes—
415C2×#95C2×D4312yes—
416C43#1444011yescharacteristic, complemented, Sylow
417C25—432no—
418C22×D4—434no—
419C22×D4—434no—
420C22×D4—434no—
421C22×D4—1721no—
422C22×D4—1721no—
423C22×D4—1721no—
424C22×D4—1721no—
425C23×C4—432no—
426C23×C4—432no—
427C23×C4—432no—
428C23×C4—864no—
429C23×C4—864no—
430C23×C4—864no—
431C23×C4—1722no—
432C23×C4—1722no—
433C23×C4—1722no—
434C23×C4—1722no—
435C23×C4C22×D4312yes—
436C23×C4C22×D4312yes—
437C23×C4C22×D4311yescharacteristic
438C23×C4C22×D4311yescharacteristic
439C23×C4C22×D4311yescharacteristic
440C2×C4⋊C4—22no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—434no—
446C2×C4⋊C4—434no—
447C2×C4⋊C4—864no—
448C2×C4⋊C4—864no—
449C2×C4⋊C4—862no—
450C2×C4⋊C4—1722no—
451C2×C4⋊C4—1721no—
452C2×C4⋊C4—1721no—
453C2×C4⋊C4—1721no—
454C2×C4⋊C4—1721no—
455C2×C4⋊C4—1721no—
456C2×C4⋊C4—1721no—
457C2×C4⋊C4D17214yescomplemented
458C2×C22⋊C4—438no—
459C2×C22⋊C4—438no—
460C2×C22⋊C4—864no—
461C2×C22⋊C4—864no—
462C2×C22⋊C4—864no—
463C2×C22⋊C4—864no—
464C2×C22⋊C4—864no—
465C2×C22⋊C4—864no—
466C2×C22⋊C4—864no—
467C2×C22⋊C4—864no—
468C2×C22⋊C4—864no—
469C2×C22⋊C4—1722no—
470C2×C22⋊C4—1722no—
471C2×C22⋊C4—1722no—
472C2×C22⋊C4—1722no—
473C2×C42—41no—
474C2×C42—41no—
475C2×C42C4×D4314yescomplemented
476#95—24no—
477#95—24no—
478#95—864no—
479#95—864no—
480#95—864no—
481#95—864no—
482#95—1722no—
483C24—434no—
484C24—434no—
485C24—434no—
486C24—862no—
487C24—862no—
488C24—862no—
489C24—862no—
490C24—862no—
491C24—862no—
492C24—862no—
493C24—862no—
494C24—862no—
495C24—862no—
496C24—862no—
497C24—862no—
498C24C23×D4311yescharacteristic
499C2×D4—4316no—
500C2×D4—1724no—
501C2×D4—1724no—
502C2×D4—1724no—
503C2×D4—1724no—
504C2×D4—1724no—
505C2×D4—1724no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—434no—
532C22×C4—434no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—1728no—
553C22×C4—1728no—
554C22×C4—1728no—
555C22×C4—1728no—
556C22×C4—1728no—
557C22×C4—1728no—
558C22×C4—1728no—
559C22×C4C2×C4×D4312yes—
560C22×C4C2×C4×D4312yes—
561C22×C4C2×C4×D4312yes—
562C22×C4C2×D17214yes—
563C22×C4C2×D17212yes—
564C22×C4#1062189812yes—
565C22×C4D4×D4312yes—
566C22×C4D4×D4312yes—
567C22×C4Q8×D4312yes—
568C22×C4#1062190212yes—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—1724no—
572C4⋊C4—1724no—
573C4⋊C4—1728no—
574C4⋊C4—1724no—
575C22⋊C4—8616no—
576C22⋊C4—8616no—
577C22⋊C4—1728no—
578C22⋊C4—1728no—
579C22⋊C4—1728no—
580C42—44no—
581C23—438no—
582C23—864no—
583C23—864no—
584C23—864no—
585C23—864no—
586C23—864no—
587C23—864no—
588C23—864no—
589C23—864no—
590C23—864no—
591C23—864no—
592C23—864no—
593C23—864no—
594C23—864no—
595C23—864no—
596C23—864no—
597C23—864no—
598C23—864no—
599C23—864no—
600C23—1722no—
601C23—1722no—
602C23—1722no—
603C23—1722no—
604C23—1722no—
605C23—1722no—
606C23—1722no—
607C23—1722no—
608C23—1722no—
609C23—1722no—
610C23—1722no—
611C23—1722no—
612C23—1722no—
613C23—1722no—
614C23—1722no—
615C23—1722no—
616C23C22×C4×D4311yescharacteristic
617C23C2×D4×D4311yescharacteristic
618C23C2×D4×D4311yescharacteristic
619C23C22×D17211yescharacteristic
620C23C2×Q8×D4311yescharacteristic
621C23C2×#1062189811yescharacteristic
622C23C2×#1062190211yescharacteristic
623C23#1306337011yescharacteristic
624C23#1306337011yescharacteristic
625C23#1306337011yescharacteristic
626C23#1306337111yescharacteristic
627C23#1306337111yescharacteristic
628C23#1306337111yescharacteristic
629C23#1306337211yescharacteristic
630C23#1306337311yescharacteristic
631D4—17216no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—864no—
665C2×C4—864no—
666C2×C4—864no—
667C2×C4—864no—
668C2×C4—864no—
669C2×C4—864no—
670C2×C4—17232no—
671C2×C4—1722no—
672C2×C4—1722no—
673C2×C4—1722no—
674C2×C4—1722no—
675C2×C4—1722no—
676C2×C4—1722no—
677C2×C4—1722no—
678C2×C4—1722no—
679C2×C4—1722no—
680C2×C4—1722no—
681C2×C4—1722no—
682C2×C4—1722no—
683C2×C4—1722no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4C4⋊C4×D4314yes—
687C2×C4#1306328714yes—
688C2×C4C4×D17214yes—
689C22—868no—
690C22—868no—
691C22—868no—
692C22—1724no—
693C22—1724no—
694C22—1724no—
695C22—1724no—
696C22—1724no—
697C22—1724no—
698C22—1724no—
699C22—1724no—
700C22—1724no—
701C22—1724no—
702C22—1724no—
703C22—1724no—
704C22C2×C4⋊C4×D4311yescharacteristic
705C22C2×#1306328711yescharacteristic
706C22C2×C4×D17211yescharacteristic
707C22#1458337211yescharacteristic
708C22#1458337311yescharacteristic
709C22#1458337911yescharacteristic
710C22#1458338011yescharacteristic
711C22#1458345711yescharacteristic
712C22#1458345711yescharacteristic
713C22#1458345711yescharacteristic
714C22#1458346111yescharacteristic
715C22#1458347611yescharacteristic
716C22#1458348011yescharacteristic
717C22#1458348711yescharacteristic
718C22#1458348911yescharacteristic
719C22#1458349611yescharacteristic
720C22#1458349811yescharacteristic
721C22#1458352411yescharacteristic
722C22#1458352411yescharacteristic
723C22#1458353411yescharacteristic
724C22D4×D17211yescharacteristic
725C22D4×D17211yescharacteristic
726C22#1458355211yescharacteristic
727C22#1458355411yescharacteristic
728C22#1458356411yescharacteristic
729C22Q8×D17211yescharacteristic
730C22#1458357011yescharacteristic
731C22#1458357111yescharacteristic
732C22#1458360911yescharacteristic
733C22#1458361011yescharacteristic
734C22#1458363411yescharacteristic
735C22#1458364111yescharacteristic
736C22#1458364311yescharacteristic
737C22#1458364711yescharacteristic
738C22#1458365311yescharacteristic
739C4—24no—
740C4—24no—
741C4—24no—
742C4—44no—
743C4—82no—
744C4—3442no—
745C4—1724no—
746C4—1724no—
747C2—1728no—
748C2#1913720811yescharacteristic
749C2#1913729511yescharacteristic
750C2#1913729811yescharacteristic
751C2#1913749511yescharacteristic
752C2C4⋊C4×D17211yescharacteristic
753C2#1913765911yescharacteristic
754C2#1913776611yescharacteristic
755C2#1914093011yescharacteristic
756C2#1914095711yescharacteristic
757C2#1914095811yescharacteristic
758C2#1914096611yescharacteristic
759C2#1914152411yescharacteristic
760C2#1914161111yescharacteristic
761C2#1914161311yescharacteristic
762C2#1914253911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C4⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenterC4⋊#95D43
hypocenterC43#14440
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#14582773C2semidirect
4. C2×#14582770C2semidirect
5. #19132847C2semidirect
6. #19132841C2semidirect
7. #19132837C2semidirect
8. #19132825C2semidirect
9. C43×C4⋊#95C2semidirect
21. #14582801C4semidirect
60. C2×C4⋊Dic43C2×C4semidirect
61. C2×C4⋊Dic43D4semidirect
78. C2×(C2×D43)⋊C4C2×C4semidirect
79. C2×(C2×D43)⋊C4C2×C4semidirect
95. C2×C4⋊C4×C43D4semidirect
98. C2×C42×C43C2×C4semidirect
179. C2×D172C4⋊C4semidirect
374. C4⋊#95D43semidirect
416. C43#14440semidirect
457. C2×C4⋊C4D172semidirect
475. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828012
C2×#145827772
C2×#145827732
C2×#145827702
#191328472
#191328412
#191328372
#191328252
C43×C4⋊#952
#1444043