Finite Group Databasebeta

← #25125299

Subgroups — #25125299

Order 11008.

1318 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582940C211yesmaximal, characteristic, complemented
2C2×#14582921C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic
4C2×#14582902C211yesmaximal, characteristic
5#19137076C211yesmaximal, characteristic, complemented
6#390×D43C211yesmaximal, characteristic
7#19135980C211yesmaximal, characteristic, complemented
8#19135979C211yesmaximal, characteristic, complemented
9#19135978C211yesmaximal, characteristic, complemented
10#19135970C211yesmaximal, characteristic, complemented
11#19135969C211yesmaximal, characteristic, complemented
12#19135968C211yesmaximal, characteristic, complemented
13#19135967C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#2067C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23C2×C22⋊C4×D43—21no—
24C2×C42×D43C2211yescharacteristic
25#14582940—24no—
26C2×#13063258C2211yescharacteristic, complemented
27C2×#13063257C2211yescharacteristic, complemented
28C2×#13063256C2211yescharacteristic, complemented
29#14582921—24no—
30C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
31C2×Dic43⋊C8C2211yescharacteristic, complemented
32C2×Dic43⋊C8C2211yescharacteristic, complemented
33#14582902—24no—
34#14582902—24no—
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582800C2211yescharacteristic
44#14582799—21no—
45#14582799—21no—
46#14582798C2211yescharacteristic, complemented
47#14582797C2211yescharacteristic, complemented
48#14582795C2211yescharacteristic, complemented
49#14582773—21no—
50#14582770—21no—
51C4⋊C4×Dic43—21no—
52#14582750—21no—
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C2×#107×C43C2211yescharacteristic, complemented
57C2×C4⋊C8×C43C2211yescharacteristic, complemented
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C43×#390C2211yescharacteristic
61C43×#389C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C24×D43—21no—
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43Q814yes—
72C22×C4×D43—21no—
73C22×C4×D43D411yescharacteristic
74C22×C4×D43D411yescharacteristic
75C22×C4×D43C2311yescharacteristic
76C2×#10621872—22no—
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—22no—
80C2×#10621872—22no—
81C2×#10621872D414yes—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84#13063283—22no—
85#13063283—22no—
86#13063283—22no—
87#13063283D414yes—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—22no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C22⋊C4×D43—44no—
106C22⋊C4×D43—44no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112C42×D43—22no—
113C42×D43—22no—
114#13063258—22no—
115#13063257—22no—
116#13063256—22no—
117C4⋊(C43⋊C8)—22no—
118Dic43⋊C8—22no—
119Dic43⋊C8—22no—
120#13063247—22no—
121#13063247—22no—
122#13063246—22no—
123#13063246—22no—
124#13063245—22no—
125#13063245—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C22×D4×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43C2311yescharacteristic
139#107×C43—22no—
140C4⋊C8×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#95×C43—21no—
144C24×C43—21no—
145C23×D43—21no—
146C23×D43—24no—
147C23×D43—42no—
148C23×D43—42no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43—42no—
152C23×D43—42no—
153C23×D43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43C2×Q812yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—24no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175D4×D43—28no—
176D4×D43—28no—
177D4×D43—44no—
178D4×D43—44no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172C2×Q812yes—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—22no—
189C2×C4×D43—41no—
190C2×C4×D43—41no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43C2×D412yes—
195C2×C4×D43C2×D412yes—
196C2×C4×D43C2×Q812yes—
197C2×C4×D43#4112yes—
198C2×C4×D43#4112yes—
199C2×C4×D43#4112yes—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43C2×D412yes—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43C2×D412yes—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C42×C43—21no—
216C42×C43—21no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219(C2×D43)⋊C4—24no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—42no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—42no—
231C4⋊Dic43C2×D412yes—
232Dic43⋊C4—42no—
233Dic43⋊C4—42no—
234Dic43⋊C4—42no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—22no—
238C4×Dic43—22no—
239C4×Dic43—24no—
240C4×Dic43—42no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C2×D412yes—
247#10621872—28no—
248#10621872—44no—
249C23×C43—22no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43C22×D411yescharacteristic
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—22no—
262C22×D43—48no—
263C22×D43—48no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—48no—
271C22×D43—84no—
272C22×D43—84no—
273C22×D43—84no—
274C22×D43—84no—
275C22×D43#12112yes—
276C22×D43#12112yes—
277C22×D43C22⋊Q812yes—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—41no—
281D4×C43—41no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43AGL(1,ℤ/8)12yes—
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×Q811yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C22⋊D43—48no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—22no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43#12112yes—
319C2×Dic43#12112yes—
320C2×Dic43C22⋊Q812yes—
321C2×Dic43AGL(1,ℤ/8)12yes—
322D172—22no—
323D172—22no—
324D172—41no—
325D172—41no—
326C4×D43—44no—
327C4×D43—44no—
328C4×D43—84no—
329C4×D43#12114yes—
330C4×D43C22⋊Q814yes—
331C4×D43C22⋊Q814yes—
332C4×D43#12614yes—
333C8×C43—22no—
334C8×C43—41no—
335C43⋊C8—22no—
336C43⋊C8—41no—
337#23618—431nomaximal, Sylow
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43C2×#12111yescharacteristic
346C22×C43C2×#12111yescharacteristic
347C22×C43C2×C22⋊Q811yescharacteristic
348C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C43#57511yescharacteristic
351C22×C43#57511yescharacteristic
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—816no—
362C2×D43—81no—
363C2×D43—81no—
364C2×D43—81no—
365C2×D43—81no—
366C2×D43#39614yes—
367C4×C43—22no—
368C4×C43—42no—
369C4×C43—41no—
370C4×C43—81no—
371C4×C43—81no—
372C4×C43C2×#12111yescharacteristic
373C4×C43C2×C22⋊Q811yescharacteristic
374C4×C43C2×C22⋊Q811yescharacteristic
375C4×C43C2×#12611yescharacteristic
376Dic43—22no—
377Dic43—42no—
378Dic43—41no—
379Dic43—81no—
380Dic43—81no—
381Dic43#39614yes—
382C2×#428—431no—
383C2×#423—431no—
384C2×#418—431no—
385C2×#418—431no—
386#2296—431no—
387C2×#390—431no—
388#2067—431no—
389#2067—431no—
390#2067—431no—
391#2067D4311yescharacteristic, complemented
392#2065—431no—
393#2065—431no—
394#2065—431no—
395#2065—431no—
396#1736—431no—
397C2×C43—82no—
398C2×C43C2×#39611yescharacteristic
399C2×C43#303811yescharacteristic
400C2×C43#304011yescharacteristic
401C2×C43#305511yescharacteristic
402C2×C43#305511yescharacteristic
403C2×C43#307711yescharacteristic
404C2×C43#307711yescharacteristic
405D43—24no—
406D43—82no—
407C23×D4—431no—
408C22×M16—431no—
409C22×M16—431no—
410C2×#117—431no—
411C2×#117—431no—
412C22×C4⋊C4—431no—
413C22×C22⋊C4—861no—
414C22×C22⋊C4—861no—
415C22×C42—431no—
416#428—864no—
417C2×#107—431no—
418C2×#107C2×D4311yescharacteristic, complemented
419C2×#106—431no—
420C2×#106—431no—
421#423—864no—
422C2×C4⋊C8—431no—
423C2×C4⋊C8—431no—
424C2×C4⋊C8—431no—
425C2×C4⋊C8C2×D4311yescharacteristic, complemented
426#418—864no—
427#418—864no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102C2×D4311yescharacteristic
435C2×#102C2×D4311yescharacteristic
436#390—431no—
437#390—431no—
438#390—431no—
439#390—861no—
440#390—861no—
441#390C2×D4311yescharacteristic
442#389—431no—
443#389—431no—
444#389—431no—
445#389C2×D4311yescharacteristic, complemented
446#385—861no—
447#385—861no—
448C4×C4⋊C4—861no—
449C4×C4⋊C4—861no—
450#340—431no—
451#340—431no—
452#340—431no—
453#340C2×D4311yescharacteristic, complemented
454C43#2361811yescharacteristic, complemented, Sylow
455C25—861no—
456C22×D4—434no—
457C22×D4—431no—
458C22×D4—862no—
459C22×D4—862no—
460C22×D4—862no—
461C22×D4—862no—
462C22×D4—862no—
463C22×D4—861no—
464C22×D4C22×D4311yescharacteristic
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—861no—
469C2×M16—434no—
470C2×M16—862no—
471C2×M16—862no—
472C2×M16—862no—
473C2×M16—862no—
474C2×M16—862no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479#117—434no—
480#117—862no—
481#117—862no—
482#117—862no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—862no—
488C2×C4⋊C4—862no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C4⋊C4C22×D4311yescharacteristic
495C2×C4⋊C4C22×D4311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—1724no—
507C2×C22⋊C4—1724no—
508C2×C42—431no—
509C2×C42—431no—
510C2×C42—431no—
511C2×C42—862no—
512C2×C42—862no—
513C2×C42—861no—
514C2×C42—861no—
515C2×C42C22×D4311yescharacteristic
516#107—22no—
517#107—862no—
518#106—862no—
519#106—862no—
520C4⋊C8—22no—
521C4⋊C8—862no—
522C4⋊C8—862no—
523C4⋊C8—862no—
524#102—22no—
525#102—22no—
526#102—862no—
527#102—862no—
528#102—862no—
529#102—862no—
530#102—862no—
531#102—862no—
532#95—21no—
533#95—861no—
534#95—861no—
535#95—861no—
536C24—21no—
537C24—431no—
538C24—864no—
539C24—861no—
540C24—1722no—
541C24—1722no—
542C24—1722no—
543C24—1722no—
544C24—1722no—
545C24—1722no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—432no—
552C2×D4—868no—
553C2×D4—868no—
554C2×D4—864no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—1724no—
561C2×D4—1724no—
562C2×D4—1722no—
563C2×D4—1722no—
564C2×D4Q8×D4312yes—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—431no—
569C22×C4—432no—
570C22×C4—432no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—861no—
581C22×C4—862no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—1721no—
585C22×C4—1721no—
586C22×C4—1722no—
587C22×C4—1722no—
588C22×C4—1722no—
589C22×C4D4×D4311yescharacteristic
590C22×C4D4×D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592M16—868no—
593M16—1724no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—432no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8D4×D4312yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—432no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—1722no—
619C4⋊C4—1722no—
620C4⋊C4—1722no—
621C4⋊C4—1722no—
622C4⋊C4D4×D4312yes—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—864no—
626C22⋊C4—1722no—
627C22⋊C4—1722no—
628C22⋊C4—1722no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C22⋊C4—1722no—
632C22⋊C4—1722no—
633C42—21no—
634C42—21no—
635C42—862no—
636C42—862no—
637C42—864no—
638C42—861no—
639C42—861no—
640C42—1722no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—432no—
649C23—432no—
650C23—432no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—862no—
656C23—3444no—
657C23—3444no—
658C23—3444no—
659C23—3444no—
660C23—1728no—
661C23—1728no—
662C23—1728no—
663C23—1721no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23C2×D4×D4311yescharacteristic
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—862no—
675D4—862no—
676D4—1728no—
677D4—1721no—
678D4—1721no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—432no—
696C2×C4—434no—
697C2×C4—434no—
698C2×C4—434no—
699C2×C4—434no—
700C2×C4—432no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—862no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—3444no—
708C2×C4—1724no—
709C2×C4—1724no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4#1306334912yes—
719C2×C4C2×D4×D4311yescharacteristic
720C2×C4C2×D4×D4311yescharacteristic
721C2×C4C2×Q8×D4311yescharacteristic
722C2×C4#41×D4311yescharacteristic
723C2×C4#41×D4311yescharacteristic
724C2×C4#41×D4311yescharacteristic
725C8—22no—
726C8—41no—
727C8—862no—
728C8—1721no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—434no—
737C22—862no—
738C22—862no—
739C22—862no—
740C22—862no—
741C22—862no—
742C22—862no—
743C22—34416no—
744C22—3441no—
745C22—3441no—
746C22—3441no—
747C22—3441no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22#121×D4311yescharacteristic
752C22#121×D4311yescharacteristic
753C22C22⋊Q8×D4311yescharacteristic
754C22AGL(1,ℤ/8)×D4311yescharacteristic
755C22C2×#1306334911yescharacteristic
756C22#1458369611yescharacteristic
757C22#1458369811yescharacteristic
758C4—22no—
759C4—41no—
760C4—42no—
761C4—81no—
762C4—81no—
763C4—434no—
764C4—862no—
765C4—3441no—
766C4—3441no—
767C4—1721no—
768C4—1722no—
769C4#121×D4311yescharacteristic
770C4C22⋊Q8×D4311yescharacteristic
771C4C22⋊Q8×D4311yescharacteristic
772C4#126×D4311yescharacteristic
773C2—82no—
774C2—864no—
775C2—3442no—
776C2#396×D4311yescharacteristic
777C2#1914407011yescharacteristic
778C2#1914408611yescharacteristic
779C2#1914420911yescharacteristic
780C2#1914421111yescharacteristic
781C2#1914438711yescharacteristic
782C2#1914439011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2067C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
hypercenter#2067D43
hypocenterC43#23618
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2067

Complements

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

NH ≅ G/Ntype
1. C2×#14582940C2semidirect
2. C2×#14582921C2semidirect
5. #19137076C2semidirect
7. #19135980C2semidirect
8. #19135979C2semidirect
9. #19135978C2semidirect
10. #19135970C2semidirect
11. #19135969C2semidirect
12. #19135968C2semidirect
13. #19135967C2semidirect
14. #19134313C2semidirect
15. C43×#2067C2semidirect
26. C2×#13063258C22semidirect
27. C2×#13063257C22semidirect
28. C2×#13063256C22semidirect
30. C2×C4⋊(C43⋊C8)C22semidirect
31. C2×Dic43⋊C8C22semidirect
32. C2×Dic43⋊C8C22semidirect
46. #14582798C22semidirect
47. #14582797C22semidirect
48. #14582795C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
56. C2×#107×C43C22semidirect
57. C2×C4⋊C8×C43C22semidirect
61. C43×#389C22semidirect
62. C43×#340C22semidirect
391. #2067D43semidirect
418. C2×#107C2×D43semidirect
425. C2×C4⋊C8C2×D43semidirect
445. #389C2×D43semidirect
453. #340C2×D43semidirect
454. C43#23618semidirect

Maximal subgroups

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

subgroupindex
C2×#145829402
C2×#145829212
C2×#145829022
#191370762
#390×D432
#191359802
#191359792
#191359782
#191359702
#191359692
#191359682
#191359672
#191343132
C43×#20672
#2361843