Finite Group Databasebeta

← #25003651

Subgroups — #25003651

Order 11008.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063245C211yesmaximal, characteristic
2C22×#13063245C211yesmaximal, characteristic
3C2×#14582801C211yesmaximal, characteristic
4C2×#14582661C211yesmaximal, characteristic, complemented
5C2×#14582661C211yesmaximal, characteristic, complemented
6C2×#14582654C211yesmaximal, characteristic, complemented
7C2×C43×#389C211yesmaximal, characteristic, complemented
8C23×D172C2211yescharacteristic
9C23×C43⋊C8C2211yescharacteristic
10C23×C43⋊C8C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×(C2×D43)⋊C4—21no—
13C22×(C2×D43)⋊C4—21no—
14C2×#13063245—22no—
15C2×#13063245—22no—
16C2×#13063245—22no—
17C2×#13063245—22no—
18C2×#13063245—22no—
19C2×#13063245C414yescomplemented
20#14582801—22no—
21#14582801—22no—
22#14582661—22no—
23#14582661—22no—
24#14582654—22no—
25C22×C4⋊C4×C43—21no—
26C22×C4⋊C4×C43C2211yescharacteristic
27C22×C4⋊C4×C43C2211yescharacteristic
28C22×C42×C43C2211yescharacteristic
29C43×#389—22no—
30C43×#389—22no—
31C2×#95×C43—21no—
32C24×D43—21no—
33C22×D172—21no—
34C22×D172—21no—
35C22×D172—21no—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172—21no—
39C22×D172—21no—
40C22×D172—21no—
41C22×D172—21no—
42C22×D172—21no—
43C22×D172—21no—
44C22×D172C2×C412yes—
45C22×D172D412yes—
46C22×D172Q812yes—
47C23×Dic43—21no—
48C22×C43⋊C8—21no—
49C22×C43⋊C8—21no—
50C22×C43⋊C8—21no—
51C22×C43⋊C8—21no—
52C22×C43⋊C8—21no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59C22×C43⋊C8—21no—
60C22×C43⋊C8C2×C412yes—
61C22×C43⋊C8D412yes—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43D412yes—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—42no—
71C2×(C2×D43)⋊C4—42no—
72C2×(C2×D43)⋊C4—42no—
73C2×(C2×D43)⋊C4—42no—
74#13063245—28no—
75#13063245—28no—
76C23×C4×C43—21no—
77C23×C4×C43—21no—
78C23×C4×C43D411yescharacteristic
79C23×C4×C43D411yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—24no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—42no—
91C2×C4⋊C4×C43—42no—
92C2×C4⋊C4×C43C2×C412yes—
93C2×C4⋊C4×C43D412yes—
94C2×C4⋊C4×C43D412yes—
95C2×C4⋊C4×C43D412yes—
96C2×C42×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43—21no—
100C2×C42×C43—21no—
101C2×C42×C43—21no—
102#95×C43—24no—
103C24×C43C2×D411yescharacteristic
104C23×D43—22no—
105C23×D43—22no—
106C23×D43—22no—
107C23×D43—41no—
108C23×D43—41no—
109C23×D43—41no—
110C23×D43—41no—
111C23×D43—41no—
112C23×D43—41no—
113C23×D43—41no—
114C23×D43—41no—
115C23×D43—41no—
116C23×D43—41no—
117C23×D43—41no—
118C23×D43—41no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—41no—
136C22×C4×C43—41no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43—41no—
140C22×C4×C43—41no—
141C22×C4×C43—41no—
142C22×C4×C43—41no—
143C22×C4×C43—41no—
144C22×C4×C43—41no—
145C22×C4×C43D812yes—
146C22×C4×C43SD1612yes—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×Q811yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43#4111yescharacteristic
161C22×Dic43—22no—
162C22×Dic43—41no—
163C22×Dic43—41no—
164C22×Dic43—41no—
165C22×Dic43—41no—
166C22×Dic43—41no—
167C22×Dic43—41no—
168C2×D172—22no—
169C2×D172—22no—
170C2×D172—22no—
171C2×D172—22no—
172C2×D172—22no—
173C2×D172—22no—
174C2×D172—22no—
175C2×D172—22no—
176C2×D172—22no—
177C2×D172—22no—
178C2×D172—22no—
179C2×D172—22no—
180C2×D172—22no—
181C2×D172—22no—
182C2×D172—22no—
183C2×D172—41no—
184C2×D172—41no—
185C2×D172—41no—
186C2×D172—41no—
187C2×D172—41no—
188C2×D172—41no—
189C2×D172—41no—
190C2×D172—41no—
191C2×D172—41no—
192C2×D172—41no—
193C2×D172—41no—
194C2×D172—41no—
195C2×D172C4⋊C414yescomplemented
196C4⋊C4×C43—22no—
197C4⋊C4×C43—22no—
198C4⋊C4×C43—22no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—48no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43C22⋊C414yescomplemented
205C42×C43—41no—
206C42×C43—41no—
207C42×C43—41no—
208C42×C43—41no—
209(C2×D43)⋊C4—48no—
210(C2×D43)⋊C4—48no—
211C4⋊Dic43—22no—
212C4⋊Dic43—22no—
213C4⋊Dic43—41no—
214C4⋊Dic43—41no—
215C2×C43⋊C8—22no—
216C2×C43⋊C8—22no—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—22no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—41no—
222C2×C43⋊C8—41no—
223C2×C43⋊C8—41no—
224C2×C43⋊C8—41no—
225C2×C43⋊C8—41no—
226C2×C43⋊C8—41no—
227C2×C43⋊C8—41no—
228C2×C43⋊C8—41no—
229C23×C43C4×D411yescharacteristic
230C23×C43#12011yescharacteristic
231C23×C43#12011yescharacteristic
232C23×C43#12111yescharacteristic
233C23×C43#12111yescharacteristic
234C23×C43C22⋊Q811yescharacteristic
235C23×C43#12411yescharacteristic
236C23×C43C2×D811yescharacteristic
237C23×C43C2×SD1611yescharacteristic
238C23×C43#13511yescharacteristic
239C23×C43#13511yescharacteristic
240C23×C43AGL(1,ℤ/8)11yescharacteristic
241C23×C43AGL(1,ℤ/8)11yescharacteristic
242C23×C43AGL(1,ℤ/8)11yescharacteristic
243C23×C43#13711yescharacteristic
244C22×D43—24no—
245C22×D43—42no—
246C22×D43—42no—
247C22×D43—42no—
248C22×D43—42no—
249C22×D43—42no—
250C22×D43—42no—
251C22×D43—42no—
252C22×D43—42no—
253C22×D43—42no—
254C22×D43—42no—
255C22×D43—42no—
256C22×D43—42no—
257C22×D43—42no—
258C22×D43—42no—
259C22×D43—42no—
260C22×D43—42no—
261C22×D43—42no—
262C22×D43—42no—
263C22×D43—81no—
264C22×D43—81no—
265C22×D43—81no—
266C22×D43—81no—
267C22×D43—81no—
268C22×D43—81no—
269C22×D43—81no—
270C22×D43—81no—
271C22×D43—81no—
272C22×D43—81no—
273C22×D43—81no—
274C22×D43—81no—
275C22×D43—81no—
276C22×D43—81no—
277C22×D43—81no—
278C22×D43—81no—
279C2×C4×C43—24no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—42no—
295C2×C4×C43—41no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—81no—
304C2×C4×C43—81no—
305C2×C4×C43—81no—
306C2×C4×C43—81no—
307C2×C4×C43C2×C22⋊C411yescharacteristic
308C2×C4×C43C2×C4⋊C411yescharacteristic
309C2×C4×C43#11711yescharacteristic
310C2×C4×C43C4×D411yescharacteristic
311C2×C4×C43C4×D411yescharacteristic
312C2×C4×C43C4×D411yescharacteristic
313C2×C4×C43#12011yescharacteristic
314C2×C4×C43#12111yescharacteristic
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12111yescharacteristic
318C2×C4×C43#12111yescharacteristic
319C2×C4×C43#12111yescharacteristic
320C2×C4×C43C22⋊Q811yescharacteristic
321C2×C4×C43C22⋊Q811yescharacteristic
322C2×C4×C43C22⋊Q811yescharacteristic
323C2×C4×C43C22⋊Q811yescharacteristic
324C2×C4×C43C22⋊Q811yescharacteristic
325C2×C4×C43#12311yescharacteristic
326C2×C4×C43#12311yescharacteristic
327C2×C4×C43#12311yescharacteristic
328C2×C4×C43#12311yescharacteristic
329C2×C4×C43#12311yescharacteristic
330C2×C4×C43#12411yescharacteristic
331C2×C4×C43#12411yescharacteristic
332C2×C4×C43#12611yescharacteristic
333C2×C4×C43#12611yescharacteristic
334C2×C4×C43#12711yescharacteristic
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—81no—
339C2×Dic43—81no—
340C2×Dic43—81no—
341C2×Dic43—81no—
342D172—24no—
343D172—24no—
344D172—42no—
345D172—42no—
346D172—42no—
347D172—42no—
348D172—42no—
349D172—42no—
350C43⋊C8—42no—
351C43⋊C8—42no—
352#11066—431nomaximal, Sylow
353C22×C43#38511yescharacteristic
354C22×C43#38611yescharacteristic
355C22×C43#38811yescharacteristic
356C22×C43#39211yescharacteristic
357C22×C43#39311yescharacteristic
358C22×C43#39411yescharacteristic
359C22×C43#39611yescharacteristic
360C22×C43C4×D811yescharacteristic
361C22×C43C4×SD1611yescharacteristic
362C22×C43#44011yescharacteristic
363C22×C43#44211yescharacteristic
364C22×C43#44711yescharacteristic
365C22×C43#44711yescharacteristic
366C22×C43#44811yescharacteristic
367C22×C43#44911yescharacteristic
368C22×C43#44911yescharacteristic
369C22×C43#44911yescharacteristic
370C22×C43#45011yescharacteristic
371C22×C43#45211yescharacteristic
372C22×C43#45911yescharacteristic
373C22×C43#46011yescharacteristic
374C22×C43#46311yescharacteristic
375C22×C43#46411yescharacteristic
376C22×C43#46511yescharacteristic
377C22×C43#46611yescharacteristic
378C22×C43#46811yescharacteristic
379C22×C43#46911yescharacteristic
380C22×C43#47411yescharacteristic
381C22×C43#47611yescharacteristic
382C22×C43#47811yescharacteristic
383C22×C43#47811yescharacteristic
384C22×C43#48611yescharacteristic
385C22×C43#48811yescharacteristic
386C22×C43#48911yescharacteristic
387C22×C43#49011yescharacteristic
388C2×D43—44no—
389C2×D43—44no—
390C2×D43—44no—
391C2×D43—82no—
392C2×D43—82no—
393C2×D43—82no—
394C2×D43—82no—
395C2×D43—82no—
396C2×D43—82no—
397C2×D43—82no—
398C2×D43—82no—
399C2×D43—82no—
400C2×D43—82no—
401C2×D43—82no—
402C2×D43—82no—
403C4×C43—44no—
404C4×C43—42no—
405C4×C43—42no—
406C4×C43—82no—
407C4×C43#38011yescharacteristic
408C4×C43#38511yescharacteristic
409C4×C43#38811yescharacteristic
410C4×C43#39011yescharacteristic
411C4×C43#39411yescharacteristic
412C4×C43#39611yescharacteristic
413C4×C43#39711yescharacteristic
414C4×C43#39911yescharacteristic
415Dic43—82no—
416C22×#102—431no—
417C22×#102—431no—
418C2×#390—431no—
419C2×#389D4311yescharacteristic, complemented
420C2×#340—431no—
421C2×#340—431no—
422C2×#336—431no—
423C2×C43#143911yescharacteristic
424C2×C43#186211yescharacteristic
425C2×C43#186411yescharacteristic
426C2×C43#187911yescharacteristic
427C2×C43#188011yescharacteristic
428C2×C43#193411yescharacteristic
429C2×C43#193611yescharacteristic
430C2×C43#199911yescharacteristic
431C2×C43#200011yescharacteristic
432C2×C43#202311yescharacteristic
433C2×C43#202511yescharacteristic
434C2×C43#204111yescharacteristic
435C2×C43#204211yescharacteristic
436C2×C43#206511yescharacteristic
437C2×C43#206711yescharacteristic
438D43—84no—
439C23×D4—431no—
440C23×C8—431no—
441C23×C8—431no—
442C22×C4⋊C4—21no—
443C22×C4⋊C4—431no—
444C22×C4⋊C4C2×D4311yescharacteristic
445C22×C4⋊C4C2×D4311yescharacteristic
446C22×C22⋊C4—861no—
447C22×C22⋊C4—861no—
448C22×C42C2×D4311yescharacteristic
449C2×#102—434no—
450C2×#102—862no—
451C2×#102—862no—
452C2×#102—862no—
453C2×#102—862no—
454C2×#102—862no—
455#390—862no—
456#390—862no—
457#389—22no—
458#389—22no—
459C2×#95—21no—
460#340—862no—
461#340—862no—
462#336—862no—
463C43#1106611yescharacteristic, complemented, Sylow
464C25—861no—
465C22×D4—432no—
466C22×D4—432no—
467C22×D4—432no—
468C22×D4—861no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4—861no—
473C22×D4—861no—
474C22×D4—861no—
475C22×D4—861no—
476C22×D4—861no—
477C22×D4—861no—
478C22×D4—861no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—861no—
482C23×C4C22⋊D4311yescharacteristic
483C23×C4C22⋊D4311yescharacteristic
484C23×C4C22×D4311yescharacteristic
485C22×C8—432no—
486C22×C8—432no—
487C22×C8—861no—
488C22×C8—861no—
489C22×C8—861no—
490C22×C8—861no—
491C22×C8—861no—
492C22×C8—861no—
493C22×C8—861no—
494C22×C8—861no—
495C22×C8—861no—
496C22×C8—861no—
497C22×C8—861no—
498C22×C8—861no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4—432no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4C4×D4312yes—
517C2×C4⋊C4D17212yes—
518C2×C4⋊C4C22⋊D4312yes—
519C2×C4⋊C4C22⋊D4312yes—
520C2×C22⋊C4—864no—
521C2×C22⋊C4—864no—
522C2×C22⋊C4—1722no—
523C2×C22⋊C4—1722no—
524C2×C22⋊C4—1722no—
525C2×C22⋊C4—1722no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532#102—868no—
533#102—868no—
534#95—24no—
535C24—862no—
536C24—862no—
537C24—862no—
538C24—1721no—
539C24—1721no—
540C24—1721no—
541C24—1721no—
542C24—1721no—
543C24—1721no—
544C24—1721no—
545C24—1721no—
546C24—1721no—
547C24—1721no—
548C24—1721no—
549C24—1721no—
550C24C2×C22⋊D4311yescharacteristic
551C2×D4—434no—
552C2×D4—862no—
553C2×D4—862no—
554C2×D4—862no—
555C2×D4—862no—
556C2×D4—862no—
557C2×D4—862no—
558C2×D4—862no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—862no—
565C2×D4—862no—
566C2×D4—862no—
567C2×D4—1721no—
568C2×D4—1721no—
569C2×D4—1721no—
570C2×D4—1721no—
571C2×D4—1721no—
572C2×D4—1721no—
573C2×D4—1721no—
574C2×D4—1721no—
575C2×D4—1721no—
576C2×D4—1721no—
577C2×D4—1721no—
578C2×D4—1721no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—862no—
606C22×C4—1721no—
607C22×C4—1721no—
608C22×C4—1721no—
609C22×C4—1721no—
610C22×C4—1721no—
611C22×C4—1721no—
612C22×C4#1062188212yes—
613C22×C4#1062188412yes—
614C22×C4C2×C4×D4311yescharacteristic
615C22×C4C2×D17211yescharacteristic
616C22×C4#1062189811yescharacteristic
617C22×C4#1062189811yescharacteristic
618C22×C4D4×D4311yescharacteristic
619C22×C4D4×D4311yescharacteristic
620C22×C4D4×D4311yescharacteristic
621C22×C4#1062190011yescharacteristic
622C22×C4Q8×D4311yescharacteristic
623C22×C4#1062190211yescharacteristic
624C22×C4#1062190211yescharacteristic
625C22×C4#1062190211yescharacteristic
626C22×C4C2×C22⋊D4311yescharacteristic
627C22×C4C2×C22⋊D4311yescharacteristic
628C2×C8—862no—
629C2×C8—862no—
630C2×C8—862no—
631C2×C8—862no—
632C2×C8—862no—
633C2×C8—862no—
634C2×C8—1721no—
635C2×C8—1721no—
636C2×C8—1721no—
637C2×C8—1721no—
638C2×C8—1721no—
639C2×C8—1721no—
640C2×C8—1721no—
641C2×C8—1721no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—48no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—862no—
651C4⋊C4—862no—
652C4⋊C4—1721no—
653C4⋊C4—1721no—
654C4⋊C4(C2×D43)⋊C414yescomplemented
655C22⋊C4—1728no—
656C22⋊C4—1728no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—41no—
661C23—864no—
662C23—3441no—
663C23—3441no—
664C23—3441no—
665C23—3441no—
666C23—3441no—
667C23—3441no—
668C23—3441no—
669C23—3441no—
670C23—3441no—
671C23—3441no—
672C23—3441no—
673C23—3441no—
674C23—3441no—
675C23—3441no—
676C23—3441no—
677C23—3441no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23—1722no—
688C23—1722no—
689C23—1722no—
690C23—1722no—
691C23—1722no—
692C23—1722no—
693C23—1722no—
694C23—1722no—
695C23—1722no—
696C23C4×C22⋊D4311yescharacteristic
697C23#1306329311yescharacteristic
698C23#1306329411yescharacteristic
699C23#1306329711yescharacteristic
700C23#1306329911yescharacteristic
701C23#1306330111yescharacteristic
702C23#1306331411yescharacteristic
703C23C2×#1062188211yescharacteristic
704C23C2×#1062188411yescharacteristic
705C23#1306334511yescharacteristic
706C23#1306334511yescharacteristic
707C23#1306335011yescharacteristic
708C23#1306335011yescharacteristic
709C23#1306335111yescharacteristic
710C23#1306335611yescharacteristic
711D4—864no—
712D4—864no—
713D4—1722no—
714D4—1722no—
715D4—1722no—
716D4—1722no—
717D4—1722no—
718D4—1722no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—3441no—
748C2×C4—3441no—
749C2×C4—3441no—
750C2×C4—3441no—
751C2×C4—1722no—
752C2×C4—1722no—
753C2×C4—1722no—
754C2×C4C2×(C2×D43)⋊C411yescharacteristic
755C2×C4C4⋊C4×D4311yescharacteristic
756C2×C4#1306328311yescharacteristic
757C2×C4C4×C22⋊D4311yescharacteristic
758C2×C4#1306328711yescharacteristic
759C2×C4#1306328711yescharacteristic
760C2×C4#1306329311yescharacteristic
761C2×C4#1306329611yescharacteristic
762C2×C4#1306329711yescharacteristic
763C2×C4#1306329911yescharacteristic
764C2×C4#1306330011yescharacteristic
765C2×C4#1306330011yescharacteristic
766C2×C4#1306330011yescharacteristic
767C2×C4#1306330111yescharacteristic
768C2×C4#1306330111yescharacteristic
769C2×C4#1306330311yescharacteristic
770C2×C4#1306330311yescharacteristic
771C2×C4#1306330511yescharacteristic
772C2×C4#1306330811yescharacteristic
773C2×C4#1306331011yescharacteristic
774C2×C4#1306331011yescharacteristic
775C2×C4#1306331011yescharacteristic
776C2×C4#1306331011yescharacteristic
777C2×C4#1306331411yescharacteristic
778C2×C4#1306331411yescharacteristic
779C2×C4#1306332011yescharacteristic
780C2×C4#1306332011yescharacteristic
781C2×C4#1306332111yescharacteristic
782C8—1722no—
783C8—1722no—
784C22—3442no—
785C22—3442no—
786C22—3442no—
787C22—3442no—
788C22—3442no—
789C22—3442no—
790C22—3442no—
791C22—3442no—
792C22—3442no—
793C22—3442no—
794C22—3442no—
795C22—3442no—
796C22—1724no—
797C22—1724no—
798C22—1724no—
799C22#1458277011yescharacteristic
800C22#1458277811yescharacteristic
801C22#1458278911yescharacteristic
802C22#1458280711yescharacteristic
803C22#1458281011yescharacteristic
804C22#1458281611yescharacteristic
805C22#1458282111yescharacteristic
806C22C4×#1062188211yescharacteristic
807C22C4×#1062188411yescharacteristic
808C22#1458299711yescharacteristic
809C22#1458300911yescharacteristic
810C22#1458303211yescharacteristic
811C22#1458303311yescharacteristic
812C22#1458303811yescharacteristic
813C22#1458304211yescharacteristic
814C22#1458304411yescharacteristic
815C22#1458304411yescharacteristic
816C22#1458304911yescharacteristic
817C22#1458305911yescharacteristic
818C22#1458309411yescharacteristic
819C22#1458309911yescharacteristic
820C22#1458311411yescharacteristic
821C22#1458312111yescharacteristic
822C22#1458313011yescharacteristic
823C22#1458313311yescharacteristic
824C22#1458314711yescharacteristic
825C22#1458315011yescharacteristic
826C22#1458317611yescharacteristic
827C22#1458318611yescharacteristic
828C22#1458319611yescharacteristic
829C22#1458319611yescharacteristic
830C22#1458324711yescharacteristic
831C22#1458325611yescharacteristic
832C22#1458326111yescharacteristic
833C22#1458326511yescharacteristic
834C4—42no—
835C4—42no—
836C4—44no—
837C4—82no—
838C4—3442no—
839C4#1458275611yescharacteristic
840C4#1458277011yescharacteristic
841C4#1458278911yescharacteristic
842C4#1458280011yescharacteristic
843C4#1458281611yescharacteristic
844C4#1458282111yescharacteristic
845C4#1458282511yescharacteristic
846C4#1458283411yescharacteristic
847C2—3444no—
848C2#1913283711yescharacteristic
849C2#1913484111yescharacteristic
850C2#1913485511yescharacteristic
851C2#1913494311yescharacteristic
852C2#1913495011yescharacteristic
853C2#1913527711yescharacteristic
854C2#1913529111yescharacteristic
855C2#1913559111yescharacteristic
856C2#1913559611yescharacteristic
857C2#1913572811yescharacteristic
858C2#1913573811yescharacteristic
859C2#1913582911yescharacteristic
860C2#1913583611yescharacteristic
861C2#1913596611yescharacteristic
862C2#1913598011yescharacteristic
subgroupG/H
centerC24C2×C22⋊D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#389C2
socleC24×C43C2×D4
prime radicalC23×D172C22
cosocleC23×C4×C43C23
hypercenterC2×#389D43
hypocenterC43#11066
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#14582661C2semidirect
5. C2×#14582661C2semidirect
6. C2×#14582654C2semidirect
7. C2×C43×#389C2semidirect
19. C2×#13063245C4semidirect
195. C2×D172C4⋊C4semidirect
204. C4⋊C4×C43C22⋊C4semidirect
419. C2×#389D43semidirect
463. C43#11066semidirect
654. C4⋊C4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632452
C2×#145828012
C2×#145826612
C2×#145826542
C2×C43×#3892
#1106643