Finite Group Databasebeta

← #25002610

Subgroups — #25002610

Order 11008.

986 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582798C211yesmaximal, characteristic
2C2×C4⋊C4×Dic43C211yesmaximal, characteristic
3C2×#14582662C211yesmaximal, characteristic
4C2×#14582661C211yesmaximal, characteristic
5C2×#14582661C211yesmaximal, characteristic
6C2×#14582653C211yesmaximal, characteristic
7C2×C43×#340C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C22×C4⋊Dic43—21no—
10C22×C4⋊Dic43C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×C4×Dic43—21no—
13C22×C4×Dic43C2211yescharacteristic
14#14582798—22no—
15#14582798C414yescomplemented
16C4⋊C4×Dic43—22no—
17C4⋊C4×Dic43—22no—
18C2×C43⋊#95—21no—
19C2×C43⋊#95—21no—
20#14582662—22no—
21#14582661—22no—
22#14582661C414yescomplemented
23#14582653—22no—
24C23×C8×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#340C414yescomplemented
28C23×Dic43—21no—
29C23×Dic43—21no—
30C23×Dic43D411yescharacteristic
31C23×Dic43D411yescharacteristic
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8C2×C412yes—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—24no—
48C2×C4⋊Dic43—42no—
49C2×C4⋊Dic43—42no—
50C2×C4⋊Dic43C2×C412yes—
51C2×C4⋊Dic43C2×C412yes—
52C2×C4⋊Dic43D412yes—
53C2×C4⋊Dic43Q812yes—
54C2×C4×Dic43—21no—
55C2×C4×Dic43—21no—
56C2×C4×Dic43—21no—
57C2×C4×Dic43—21no—
58C2×C4×Dic43—24no—
59C2×C4×Dic43—42no—
60C2×C4×Dic43—42no—
61C2×C4×Dic43C2×C412yes—
62C2×C4×Dic43D412yes—
63C43⋊#95—24no—
64C43⋊#95—24no—
65C23×C4×C43—21no—
66C23×C4×C43—21no—
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C22×C8×C43—21no—
71C22×C8×C43—21no—
72C22×C8×C43—21no—
73C22×C8×C43—21no—
74C22×C8×C43C2×C412yes—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43C2×C412yes—
82C2×C4⋊C4×C43C2×C412yes—
83C2×C4⋊C4×C43C2×C412yes—
84C2×C4⋊C4×C43C2×C412yes—
85C2×C4⋊C4×C43D412yes—
86C2×C4⋊C4×C43Q812yes—
87C24×C43C2×D411yescharacteristic
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43—22no—
91C22×C4×C43—22no—
92C22×C4×C43—22no—
93C22×C4×C43—22no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43C22×C411yescharacteristic
103C22×C4×C43C22×C411yescharacteristic
104C22×C4×C43C22×C411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×Q811yescharacteristic
109C22×C4×C43C2×Q811yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×Dic43—22no—
117C22×Dic43—22no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—22no—
121C22×Dic43—22no—
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—41no—
131C22×Dic43—41no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134C22×Dic43—41no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43—41no—
140C22×Dic43C22⋊C412yes—
141C22×Dic43C22⋊C412yes—
142C22×Dic43D812yes—
143C22×Dic43SD1612yes—
144C2×C8×C43—22no—
145C2×C8×C43—22no—
146C2×C8×C43—22no—
147C2×C8×C43—41no—
148C2×C8×C43—41no—
149C2×C8×C43—41no—
150C2×C8×C43—41no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43C4214yescomplemented
158C4⋊C4×C43C4⋊C414yescomplemented
159C4⋊Dic43—22no—
160C4⋊Dic43—22no—
161C4⋊Dic43—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43—22no—
164C4⋊Dic43—41no—
165C4⋊Dic43—41no—
166C4⋊Dic43—48no—
167C4⋊Dic43C4⋊C414yescomplemented
168C4×Dic43—22no—
169C4×Dic43—22no—
170C4×Dic43—22no—
171C4×Dic43—22no—
172C4×Dic43—48no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—41no—
177C2×C43⋊C8—41no—
178C2×C43⋊C8—41no—
179C2×C43⋊C8—41no—
180C23×C43C2×C22⋊C411yescharacteristic
181C23×C43C4×D411yescharacteristic
182C23×C43C4×D411yescharacteristic
183C23×C43#12011yescharacteristic
184C23×C43C22⋊Q811yescharacteristic
185C23×C43C22⋊Q811yescharacteristic
186C23×C43#12311yescharacteristic
187C23×C43C2×D811yescharacteristic
188C23×C43C2×SD1611yescharacteristic
189C23×C43#13511yescharacteristic
190C23×C43#13511yescharacteristic
191C23×C43AGL(1,ℤ/8)11yescharacteristic
192C23×C43#13711yescharacteristic
193C23×C43#13711yescharacteristic
194C23×C43#13711yescharacteristic
195C2×C4×C43—24no—
196C2×C4×C43—24no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43C2×C4211yescharacteristic
210C2×C4×C43C2×C4⋊C411yescharacteristic
211C2×C4×C43C2×C4⋊C411yescharacteristic
212C2×C4×C43#11711yescharacteristic
213C2×C4×C43#11711yescharacteristic
214C2×C4×C43#11711yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43C4×D411yescharacteristic
219C2×C4×C43C4×D411yescharacteristic
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43C4×Q811yescharacteristic
222C2×C4×C43C4×Q811yescharacteristic
223C2×C4×C43C4×Q811yescharacteristic
224C2×C4×C43C4×Q811yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43C22⋊Q811yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12411yescharacteristic
232C2×C4×C43#12511yescharacteristic
233C2×C4×C43#12511yescharacteristic
234C2×C4×C43#12611yescharacteristic
235C2×C4×C43#12611yescharacteristic
236C2×C4×C43C4⋊Q811yescharacteristic
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—24no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—81no—
261C2×Dic43—81no—
262C2×Dic43—81no—
263C2×Dic43—81no—
264C2×Dic43#10214yes—
265C8×C43—42no—
266C43⋊C8—42no—
267#10884—431nomaximal, Sylow
268C22×C43C4×C22⋊C411yescharacteristic
269C22×C43#38511yescharacteristic
270C22×C43#38511yescharacteristic
271C22×C43#38611yescharacteristic
272C22×C43#38711yescharacteristic
273C22×C43#38711yescharacteristic
274C22×C43#39111yescharacteristic
275C22×C43C2×#10211yescharacteristic
276C22×C43#41611yescharacteristic
277C22×C43#41711yescharacteristic
278C22×C43#41911yescharacteristic
279C22×C43C4×D811yescharacteristic
280C22×C43C4×D811yescharacteristic
281C22×C43C4×SD1611yescharacteristic
282C22×C43C4×SD1611yescharacteristic
283C22×C43#44011yescharacteristic
284C22×C43#44011yescharacteristic
285C22×C43#44111yescharacteristic
286C22×C43#44111yescharacteristic
287C22×C43#44711yescharacteristic
288C22×C43#44811yescharacteristic
289C22×C43#45211yescharacteristic
290C22×C43#45211yescharacteristic
291C22×C43#47411yescharacteristic
292C22×C43#47411yescharacteristic
293C22×C43#47511yescharacteristic
294C22×C43#47511yescharacteristic
295C22×C43#47811yescharacteristic
296C22×C43#47811yescharacteristic
297C22×C43#47911yescharacteristic
298C22×C43#47911yescharacteristic
299C22×C43#48011yescharacteristic
300C22×C43#48111yescharacteristic
301C22×C43#48511yescharacteristic
302C22×C43#48511yescharacteristic
303C4×C43—44no—
304C4×C43—44no—
305C4×C43C4×C4⋊C411yescharacteristic
306C4×C43C4×C4⋊C411yescharacteristic
307C4×C43#38711yescharacteristic
308C4×C43#38711yescharacteristic
309C4×C43#38811yescharacteristic
310C4×C43#38811yescharacteristic
311C4×C43#38911yescharacteristic
312C4×C43#38911yescharacteristic
313Dic43—24no—
314Dic43—44no—
315Dic43—42no—
316Dic43—82no—
317C2×#389—431no—
318C2×C4×C4⋊C4—431no—
319C2×#340—431no—
320C2×#340—431no—
321C2×#340—431no—
322C2×#340D4311yescharacteristic
323C2×#336—431no—
324C2×C43#143611yescharacteristic
325C2×C43C4×#10211yescharacteristic
326C2×C43#176311yescharacteristic
327C2×C43#186211yescharacteristic
328C2×C43#186211yescharacteristic
329C2×C43#186511yescharacteristic
330C2×C43#186511yescharacteristic
331C2×C43#187311yescharacteristic
332C2×C43#187411yescharacteristic
333C2×C43#191811yescharacteristic
334C2×C43#191811yescharacteristic
335C2×C43#191911yescharacteristic
336C2×C43#191911yescharacteristic
337C2×C43#198811yescharacteristic
338C2×C43#198911yescharacteristic
339C23×C8—431no—
340C23×C8C2×D4311yescharacteristic
341C22×C4⋊C4—431no—
342C22×C4⋊C4—431no—
343C22×C4⋊C4—861no—
344C22×C4⋊C4C2×D4311yescharacteristic
345C22×C4⋊C4C2×D4311yescharacteristic
346C22×C42—431no—
347C22×C42—861no—
348#389—434no—
349#389—862no—
350C4×C4⋊C4—862no—
351C4×C4⋊C4—862no—
352C2×#95—861no—
353C2×#95—861no—
354#340—434no—
355#340—862no—
356#340—862no—
357#340Dic4314yescomplemented
358#336—862no—
359C43#1088411yescharacteristic, complemented, Sylow
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—431no—
363C23×C4—431no—
364C23×C4—861no—
365C23×C4—861no—
366C23×C4C22×D4311yescharacteristic
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—432no—
374C22×C8—861no—
375C22×C8—861no—
376C22×C8—861no—
377C22×C8—861no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8C2×Dic4312yes—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—432no—
388C2×C4⋊C4—432no—
389C2×C4⋊C4—432no—
390C2×C4⋊C4—432no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—864no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—1722no—
401C2×C4⋊C4—1722no—
402C2×C4⋊C4Dic8612yes—
403C2×C4⋊C4C4×D4312yes—
404C2×C4⋊C4C4×D4312yes—
405C2×C4⋊C4D17212yes—
406C2×C4⋊C4C2×Dic4312yes—
407C2×C4⋊C4C2×Dic4312yes—
408C2×C42—432no—
409C2×C42—432no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—864no—
415C2×C42—1722no—
416C2×C42—1722no—
417#95—864no—
418#95—864no—
419C24D4×D4311yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—862no—
443C22×C4—861no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—862no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4—1721no—
455C22×C4—1721no—
456C22×C4—1721no—
457C22×C4—1721no—
458C22×C4—1721no—
459C22×C4—1721no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4C2×Dic8611yescharacteristic
463C22×C4C2×C4×D4311yescharacteristic
464C22×C4C2×C4×D4311yescharacteristic
465C22×C4C2×D17211yescharacteristic
466C22×C4#1062189811yescharacteristic
467C22×C4#1062189811yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4D4×D4311yescharacteristic
470C22×C4#1062190011yescharacteristic
471C22×C4#1062190011yescharacteristic
472C22×C4#1062190011yescharacteristic
473C22×C4Q8×D4311yescharacteristic
474C22×C4#1062190211yescharacteristic
475C22×C4C22×Dic4311yescharacteristic
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—862no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8—1721no—
487C2×C8—1721no—
488C2×C8—1721no—
489C2×C8—1721no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—434no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—1728no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4C4×Dic4314yescomplemented
506C4⋊C4C4⋊Dic4314yescomplemented
507C42—862no—
508C42—862no—
509C42—862no—
510C42—862no—
511C42—1728no—
512C23C22⋊C4×D4311yescharacteristic
513C23(C22⋊D43)⋊C411yescharacteristic
514C23D4×Dic4311yescharacteristic
515C23#1306329511yescharacteristic
516C23#1306330211yescharacteristic
517C23#1306330311yescharacteristic
518C23#1306331011yescharacteristic
519C23D8×D4311yescharacteristic
520C23SD16×D4311yescharacteristic
521C23#1306334411yescharacteristic
522C23#1306334611yescharacteristic
523C23#1306335211yescharacteristic
524C23#1306335411yescharacteristic
525C23#1306335711yescharacteristic
526C23#1306335711yescharacteristic
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—434no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—864no—
551C2×C4—862no—
552C2×C4—3441no—
553C2×C4—3441no—
554C2×C4—3441no—
555C2×C4—3441no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4C2×C4×Dic4311yescharacteristic
570C2×C4C4⋊C4×D4311yescharacteristic
571C2×C4C2×C4⋊Dic4311yescharacteristic
572C2×C4#1306328111yescharacteristic
573C2×C4#1306328311yescharacteristic
574C2×C4#1306328411yescharacteristic
575C2×C4(C22⋊D43)⋊C411yescharacteristic
576C2×C4#1306328711yescharacteristic
577C2×C4D4×Dic4311yescharacteristic
578C2×C4D4×Dic4311yescharacteristic
579C2×C4C4×D17211yescharacteristic
580C2×C4C4×D17211yescharacteristic
581C2×C4#1306329011yescharacteristic
582C2×C4C4×Dic8611yescharacteristic
583C2×C4C4×Dic8611yescharacteristic
584C2×C4Q8×Dic4311yescharacteristic
585C2×C4#1306329811yescharacteristic
586C2×C4#1306330011yescharacteristic
587C2×C4#1306330211yescharacteristic
588C2×C4#1306330511yescharacteristic
589C2×C4#1306330711yescharacteristic
590C2×C4#1306330911yescharacteristic
591C2×C4#1306331111yescharacteristic
592C2×C4#1306331511yescharacteristic
593C2×C4#1306331611yescharacteristic
594C2×C4#1306331811yescharacteristic
595C2×C4#1306332011yescharacteristic
596C2×C4#1306332411yescharacteristic
597C8—42no—
598C8—1722no—
599C22C22⋊C4×Dic4311yescharacteristic
600C22#1458277311yescharacteristic
601C22#1458277411yescharacteristic
602C22#1458277711yescharacteristic
603C22#1458278511yescharacteristic
604C22#1458278611yescharacteristic
605C22#1458280311yescharacteristic
606C22#102×D4311yescharacteristic
607C22#1458289211yescharacteristic
608C22#1458289911yescharacteristic
609C22#1458290611yescharacteristic
610C22#1458297911yescharacteristic
611C22D8×Dic4311yescharacteristic
612C22SD16×Dic4311yescharacteristic
613C22#1458299011yescharacteristic
614C22#1458300011yescharacteristic
615C22#1458300211yescharacteristic
616C22#1458300311yescharacteristic
617C22#1458300611yescharacteristic
618C22#1458303411yescharacteristic
619C22#1458303911yescharacteristic
620C22#1458306211yescharacteristic
621C22#1458306411yescharacteristic
622C22#1458317711yescharacteristic
623C22#1458317811yescharacteristic
624C22#1458318211yescharacteristic
625C22#1458318311yescharacteristic
626C22#1458319711yescharacteristic
627C22#1458319811yescharacteristic
628C22#1458320411yescharacteristic
629C22#1458320511yescharacteristic
630C22#1458321411yescharacteristic
631C22#1458321911yescharacteristic
632C22#1458324211yescharacteristic
633C22#1458324311yescharacteristic
634C4—44no—
635C4—44no—
636C4—864no—
637C4—3442no—
638C4—1724no—
639C4—1722no—
640C4C4×C4⋊Dic4311yescharacteristic
641C4C4⋊C4×Dic4311yescharacteristic
642C4#1458278211yescharacteristic
643C4#1458278411yescharacteristic
644C4#1458279111yescharacteristic
645C4#1458279211yescharacteristic
646C4#1458279611yescharacteristic
647C4#1458279811yescharacteristic
648C2#1913282911yescharacteristic
649C2#102×Dic4311yescharacteristic
650C2#1913442711yescharacteristic
651C2#1913484311yescharacteristic
652C2#1913484411yescharacteristic
653C2#1913486411yescharacteristic
654C2#1913486511yescharacteristic
655C2#1913490611yescharacteristic
656C2#1913491111yescharacteristic
657C2#1913516811yescharacteristic
658C2#1913516911yescharacteristic
659C2#1913517511yescharacteristic
660C2#1913517611yescharacteristic
661C2#1913554511yescharacteristic
662C2#1913555111yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×#340C2
socle, prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#340D43
hypocenterC43#10884
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
15. #14582798C4semidirect
22. #14582661C4semidirect
27. C43×#340C4semidirect
157. C4⋊C4×C43C42semidirect
158. C4⋊C4×C43C4⋊C4semidirect
167. C4⋊Dic43C4⋊C4semidirect
357. #340Dic43semidirect
359. C43#10884semidirect
505. C4⋊C4C4×Dic43semidirect
506. C4⋊C4C4⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827982
C2×C4⋊C4×Dic432
C2×#145826622
C2×#145826612
C2×#145826532
C2×C43×#3402
#1088443