Finite Group Databasebeta

← #25002588

Subgroups — #25002588

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063235C211yesmaximal, characteristic
2C2×#14582795C211yesmaximal, characteristic
3C2×#14582662C211yesmaximal, characteristic
4C2×#14582661C211yesmaximal, characteristic
5C2×#14582661C211yesmaximal, characteristic
6#19132824C211yesmaximal, characteristic
7C2×C43×#340C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×Dic43⋊C4—21no—
12C22×C4×Dic43C2211yescharacteristic
13C2×#13063235—22no—
14C2×#13063235—22no—
15C2×#13063235—22no—
16#14582795—22no—
17#14582795C414yescomplemented
18C2×C43⋊#95—21no—
19C2×C43⋊#95—21no—
20C2×C43⋊#95—21no—
21#14582662C414yescomplemented
22#14582661—22no—
23#14582661C414yescomplemented
24C23×C8×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#340—22no—
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⋊C8C2×C412yes—
37C22×C43⋊C8D412yes—
38C22×C43⋊C8Q812yes—
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⋊Dic43C2×C412yes—
48C2×C4⋊Dic43C2×C412yes—
49C2×C4⋊Dic43C2×C412yes—
50C2×C4⋊Dic43C2×C412yes—
51C2×Dic43⋊C4—24no—
52C2×Dic43⋊C4—42no—
53C2×Dic43⋊C4—42no—
54C2×C4×Dic43—21no—
55C2×C4×Dic43—21no—
56C2×C4×Dic43—21no—
57C2×C4×Dic43—21no—
58C2×C4×Dic43C2×C412yes—
59C2×C4×Dic43D412yes—
60#13063235—28no—
61C43⋊#95—24no—
62C43⋊#95—42no—
63C43⋊#95—42no—
64C23×C4×C43—21no—
65C23×C4×C43—21no—
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43—21no—
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C22×C8×C43—21no—
71C22×C8×C43C2×C412yes—
72C22×C8×C43D412yes—
73C22×C8×C43Q812yes—
74C2×C4⋊C4×C43—21no—
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×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43C2×C412yes—
85C2×C4⋊C4×C43C2×C412yes—
86C24×C43C2×D411yescharacteristic
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
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×C43C22×C411yescharacteristic
102C22×C4×C43C22×C411yescharacteristic
103C22×C4×C43C22×C411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×Q811yescharacteristic
108C22×C4×C43C2×Q811yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×Dic43—22no—
116C22×Dic43—22no—
117C22×Dic43—22no—
118C22×Dic43—22no—
119C22×Dic43—21no—
120C22×Dic43—21no—
121C22×Dic43—21no—
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—21no—
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×Dic43—41no—
141C22×Dic43C22⋊C412yes—
142C22×Dic43C22⋊C412yes—
143C2×C8×C43—22no—
144C2×C8×C43—22no—
145C2×C8×C43—22no—
146C2×C8×C43—22no—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C2×C8×C43C4⋊C414yescomplemented
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43—41no—
156C4⋊C4×C43—41no—
157C4⋊C4×C43—41no—
158C4⋊Dic43—22no—
159C4⋊Dic43—22no—
160C4⋊Dic43—22no—
161C4⋊Dic43—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43—41no—
164C4⋊Dic43—41no—
165C4⋊Dic43C4214yes—
166Dic43⋊C4—48no—
167C4×Dic43—22no—
168C4×Dic43—22no—
169C4×Dic43—22no—
170C4×Dic43—22no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8C4⋊C414yescomplemented
178C23×C43C2×C22⋊C411yescharacteristic
179C23×C43C4×D411yescharacteristic
180C23×C43C4×D411yescharacteristic
181C23×C43#12111yescharacteristic
182C23×C43#12111yescharacteristic
183C23×C43#12411yescharacteristic
184C23×C43C4⋊Q811yescharacteristic
185C23×C43AGL(1,ℤ/8)11yescharacteristic
186C23×C43AGL(1,ℤ/8)11yescharacteristic
187C23×C43AGL(1,ℤ/8)11yescharacteristic
188C23×C43AGL(1,ℤ/8)11yescharacteristic
189C23×C43#13711yescharacteristic
190C23×C43#13711yescharacteristic
191C23×C43#13711yescharacteristic
192C23×C43#13711yescharacteristic
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—81no—
200C2×C4×C43—81no—
201C2×C4×C43—81no—
202C2×C4×C43—81no—
203C2×C4×C43—81no—
204C2×C4×C43—81no—
205C2×C4×C43—81no—
206C2×C4×C43—81no—
207C2×C4×C43C2×C4211yescharacteristic
208C2×C4×C43C2×C4⋊C411yescharacteristic
209C2×C4×C43C2×C4⋊C411yescharacteristic
210C2×C4×C43#11711yescharacteristic
211C2×C4×C43#11711yescharacteristic
212C2×C4×C43#11711yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43C4×D411yescharacteristic
219C2×C4×C43C4×Q811yescharacteristic
220C2×C4×C43C4×Q811yescharacteristic
221C2×C4×C43C4×Q811yescharacteristic
222C2×C4×C43C4×Q811yescharacteristic
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43C22⋊Q811yescharacteristic
225C2×C4×C43C22⋊Q811yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12511yescharacteristic
232C2×C4×C43#12511yescharacteristic
233C2×C4×C43#12611yescharacteristic
234C2×C4×C43#12611yescharacteristic
235C2×Dic43—24no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—81no—
260C2×Dic43—81no—
261C2×Dic43—81no—
262C2×Dic43—81no—
263C8×C43—24no—
264C43⋊C8—24no—
265#10881—431nomaximal, Sylow
266C22×C43C4×C22⋊C411yescharacteristic
267C22×C43#38611yescharacteristic
268C22×C43#38811yescharacteristic
269C22×C43#38811yescharacteristic
270C22×C43#38911yescharacteristic
271C22×C43#38911yescharacteristic
272C22×C43#39111yescharacteristic
273C22×C43#41711yescharacteristic
274C22×C43#41711yescharacteristic
275C22×C43#41811yescharacteristic
276C22×C43#41911yescharacteristic
277C22×C43#44011yescharacteristic
278C22×C43#44011yescharacteristic
279C22×C43#44011yescharacteristic
280C22×C43#44011yescharacteristic
281C22×C43#44111yescharacteristic
282C22×C43#44111yescharacteristic
283C22×C43#44211yescharacteristic
284C22×C43#44211yescharacteristic
285C22×C43#46811yescharacteristic
286C22×C43#46811yescharacteristic
287C22×C43#46811yescharacteristic
288C22×C43#46811yescharacteristic
289C22×C43#46911yescharacteristic
290C22×C43#46911yescharacteristic
291C22×C43#47011yescharacteristic
292C22×C43#47011yescharacteristic
293C22×C43#48911yescharacteristic
294C22×C43#48911yescharacteristic
295C22×C43#49011yescharacteristic
296C22×C43#49111yescharacteristic
297C22×C43#50111yescharacteristic
298C22×C43#50111yescharacteristic
299C22×C43#50111yescharacteristic
300C22×C43#50111yescharacteristic
301C4×C43—82no—
302C4×C43—82no—
303C4×C43C4×C4⋊C411yescharacteristic
304C4×C43C4×C4⋊C411yescharacteristic
305C4×C43#38511yescharacteristic
306C4×C43#38511yescharacteristic
307C4×C43#38711yescharacteristic
308C4×C43#38711yescharacteristic
309C4×C43#38711yescharacteristic
310C4×C43#38711yescharacteristic
311Dic43—42no—
312Dic43—42no—
313Dic43—44no—
314Dic43—82no—
315C22×#97—431no—
316C2×#389—431no—
317C2×#340—431no—
318C2×#340—431no—
319C2×#340—431no—
320C2×#340D4311yescharacteristic
321C4⋊#95—431no—
322C2×C43#143611yescharacteristic
323C2×C43#176211yescharacteristic
324C2×C43#176311yescharacteristic
325C2×C43#189411yescharacteristic
326C2×C43#189511yescharacteristic
327C2×C43#193511yescharacteristic
328C2×C43#193511yescharacteristic
329C2×C43#193611yescharacteristic
330C2×C43#193611yescharacteristic
331C2×C43#194311yescharacteristic
332C2×C43#194311yescharacteristic
333C2×C43#194411yescharacteristic
334C2×C43#194411yescharacteristic
335C2×C43#199211yescharacteristic
336C2×C43#199311yescharacteristic
337C23×C8—431no—
338C23×C8C2×D4311yescharacteristic
339C22×C4⋊C4—431no—
340C22×C4⋊C4—431no—
341C22×C4⋊C4—861no—
342C22×C4⋊C4C2×D4311yescharacteristic
343C22×C4⋊C4C2×D4311yescharacteristic
344C22×C42—431no—
345C2×#97—862no—
346C2×#97—862no—
347C2×#97—862no—
348#389—434no—
349#389—862no—
350C2×#95—861no—
351C2×#95—861no—
352C2×#95—861no—
353#340—22no—
354#340—434no—
355#340—434no—
356#340—862no—
357C43#1088111yescharacteristic, complemented, Sylow
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—431no—
361C23×C4—431no—
362C23×C4—861no—
363C23×C4—861no—
364C23×C4C22×D4311yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—432no—
370C22×C8—432no—
371C22×C8—432no—
372C22×C8—861no—
373C22×C8—861no—
374C22×C8—861no—
375C22×C8—861no—
376C22×C8Dic8612yes—
377C22×C8C4×D4312yes—
378C22×C8C22⋊D4312yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
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—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—432no—
390C2×C4⋊C4—432no—
391C2×C4⋊C4—432no—
392C2×C4⋊C4—432no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—864no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—1722no—
403C2×C4⋊C4—1722no—
404C2×C4⋊C4C4×D4312yes—
405C2×C4⋊C4C4×D4312yes—
406C2×C42—432no—
407C2×C42—432no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412#97—868no—
413#95—864no—
414#95—1722no—
415#95—1722no—
416C24D4×D4311yescharacteristic
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—432no—
432C22×C4—432no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—862no—
449C22×C4—1721no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4—1721no—
455C22×C4—1721no—
456C22×C4—1721no—
457C22×C4—1721no—
458C22×C4—1721no—
459C22×C4C2×Dic8611yescharacteristic
460C22×C4C2×C4×D4311yescharacteristic
461C22×C4C2×C4×D4311yescharacteristic
462C22×C4C2×C4×D4311yescharacteristic
463C22×C4#1062189811yescharacteristic
464C22×C4#1062189811yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4#1062190011yescharacteristic
468C22×C4#1062190011yescharacteristic
469C22×C4#1062190011yescharacteristic
470C22×C4Q8×D4311yescharacteristic
471C22×C4#1062190211yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—434no—
480C2×C8—862no—
481C2×C8—862no—
482C2×C8—862no—
483C2×C8—862no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8Dic43⋊C414yescomplemented
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—434no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—1728no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C42—862no—
505C42—862no—
506C42—862no—
507C42—862no—
508C23C22⋊C4×D4311yescharacteristic
509C23(C22⋊D43)⋊C411yescharacteristic
510C23#1306328711yescharacteristic
511C23#1306329611yescharacteristic
512C23#1306329811yescharacteristic
513C23#1306331111yescharacteristic
514C23#1306332411yescharacteristic
515C23#1306334911yescharacteristic
516C23#1306334911yescharacteristic
517C23#1306335211yescharacteristic
518C23#1306335211yescharacteristic
519C23#1306335411yescharacteristic
520C23#1306335411yescharacteristic
521C23#1306335711yescharacteristic
522C23#1306335711yescharacteristic
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—862no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—862no—
541C2×C4—864no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—3441no—
545C2×C4—3441no—
546C2×C4—3441no—
547C2×C4—3441no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1722no—
559C2×C4—1721no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4C42×D4311yescharacteristic
566C2×C4C4⋊C4×D4311yescharacteristic
567C2×C4C2×Dic43⋊C411yescharacteristic
568C2×C4#1306328111yescharacteristic
569C2×C4#1306328211yescharacteristic
570C2×C4#1306328311yescharacteristic
571C2×C4(C22⋊D43)⋊C411yescharacteristic
572C2×C4(C22⋊D43)⋊C411yescharacteristic
573C2×C4(C22⋊D43)⋊C411yescharacteristic
574C2×C4C4×C22⋊D4311yescharacteristic
575C2×C4C4×C22⋊D4311yescharacteristic
576C2×C4#1306328711yescharacteristic
577C2×C4#1306329011yescharacteristic
578C2×C4#1306329011yescharacteristic
579C2×C4C4×Dic8611yescharacteristic
580C2×C4C4×Dic8611yescharacteristic
581C2×C4#1306329311yescharacteristic
582C2×C4#1306330111yescharacteristic
583C2×C4#1306330211yescharacteristic
584C2×C4#1306330211yescharacteristic
585C2×C4#1306330311yescharacteristic
586C2×C4#1306330611yescharacteristic
587C2×C4#1306330711yescharacteristic
588C2×C4#1306331011yescharacteristic
589C2×C4#1306331511yescharacteristic
590C2×C4#1306331611yescharacteristic
591C2×C4#1306331811yescharacteristic
592C2×C4#1306332011yescharacteristic
593C8—24no—
594C8—864no—
595C22#1458274611yescharacteristic
596C22#1458277511yescharacteristic
597C22#1458278711yescharacteristic
598C22#1458278811yescharacteristic
599C22#1458279511yescharacteristic
600C22#1458279611yescharacteristic
601C22#1458280311yescharacteristic
602C22#1458289711yescharacteristic
603C22#1458289911yescharacteristic
604C22#1458290211yescharacteristic
605C22#1458290611yescharacteristic
606C22#1458299611yescharacteristic
607C22#1458299811yescharacteristic
608C22#1458299811yescharacteristic
609C22#1458300211yescharacteristic
610C22#1458300311yescharacteristic
611C22#1458300511yescharacteristic
612C22#1458300811yescharacteristic
613C22#1458301011yescharacteristic
614C22#1458314211yescharacteristic
615C22#1458314211yescharacteristic
616C22#1458314411yescharacteristic
617C22#1458314811yescharacteristic
618C22#1458314911yescharacteristic
619C22#1458315111yescharacteristic
620C22#1458315411yescharacteristic
621C22#1458315611yescharacteristic
622C22#1458325711yescharacteristic
623C22#1458326011yescharacteristic
624C22#1458326211yescharacteristic
625C22#1458326611yescharacteristic
626C22#1458330611yescharacteristic
627C22#1458330611yescharacteristic
628C22#1458330711yescharacteristic
629C22#1458330711yescharacteristic
630C4—82no—
631C4—82no—
632C4—3442no—
633C4—1722no—
634C4—1722no—
635C4—1724no—
636C4#1458275011yescharacteristic
637C4C4×Dic43⋊C411yescharacteristic
638C4#1458277011yescharacteristic
639C4#1458277111yescharacteristic
640C4#1458278011yescharacteristic
641C4#1458278111yescharacteristic
642C4#1458278211yescharacteristic
643C4#1458278611yescharacteristic
644C2#1913282611yescharacteristic
645C2#1913441911yescharacteristic
646C2#1913442411yescharacteristic
647C2#1913502511yescharacteristic
648C2#1913503011yescharacteristic
649C2#1913528211yescharacteristic
650C2#1913528311yescharacteristic
651C2#1913528911yescharacteristic
652C2#1913529011yescharacteristic
653C2#1913533111yescharacteristic
654C2#1913533211yescharacteristic
655C2#1913533611yescharacteristic
656C2#1913533711yescharacteristic
657C2#1913556211yescharacteristic
658C2#1913556611yescharacteristic
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#10881
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
17. #14582795C4semidirect
21. #14582662C4semidirect
23. #14582661C4semidirect
149. C2×C8×C43C4⋊C4semidirect
177. C2×C43⋊C8C4⋊C4semidirect
357. C43#10881semidirect
486. C2×C8Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632352
C2×#145827952
C2×#145826622
C2×#145826612
#191328242
C2×C43×#3402
#1088143