Finite Group Databasebeta

← #25102373

Subgroups — #25102373

Order 11008.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583376C211yesmaximal, characteristic, complemented
2C2×#14583040C211yesmaximal, characteristic
3C2×#14582998C211yesmaximal, characteristic, complemented
4C2×#14582986C211yesmaximal, characteristic, complemented
5#19137284C211yesmaximal, characteristic
6#19134951C211yesmaximal, characteristic, complemented
7#19134951C211yesmaximal, characteristic, complemented
8#19134917C211yesmaximal, characteristic
9#19134860C211yesmaximal, characteristic, complemented
10#19134846C211yesmaximal, characteristic, complemented
11#19134529C211yesmaximal, characteristic, complemented
12#19134424C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20#14583376—24no—
21#14583376—24no—
22C2×C4×Dic86—21no—
23C2×C4×Dic86—21no—
24C2×#13063290C2211yescharacteristic
25C2×#13063290C2211yescharacteristic
26C2×#13063290C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×#13063287C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063281—21no—
31C2×#13063281—21no—
32#14583040C418yescomplemented
33#14582998—24no—
34#14582986—24no—
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×#13063235C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582800C2211yescharacteristic
47#14582799—21no—
48#14582795C2211yescharacteristic
49#14582791—21no—
50#14582775—21no—
51#14582773—21no—
52C4⋊C4×Dic43C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×#117×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—22no—
68C22×Dic86—22no—
69C22×Dic86—22no—
70C22×Dic86C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×Dic86C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C22⋊D43—21no—
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C2×#10621873—22no—
78C2×#10621873—22no—
79C2×#10621873—22no—
80C2×#10621873—22no—
81C2×#10621873C2×C414yes—
82C2×#10621873C2×C414yes—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063299—22no—
86#13063299C2×C414yes—
87C4×Dic86—28no—
88C4×Dic86—28no—
89#13063290—22no—
90#13063290—22no—
91#13063290—22no—
92#13063290—22no—
93#13063290—22no—
94#13063290—22no—
95#13063290D414yescomplemented
96#13063290D414yescomplemented
97#13063287—22no—
98#13063287—22no—
99#13063284—22no—
100#13063284—22no—
101#13063281—28no—
102#13063281—28no—
103C2×C4⋊Dic43D411yescharacteristic
104C2×C4⋊Dic43D411yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×C22⋊Dic43D411yescharacteristic
112C2×C22⋊Dic43D411yescharacteristic
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123C2×C4×Dic43C2311yescharacteristic
124#13063250C2×C414yescomplemented
125#13063250C2×C414yescomplemented
126#13063248—22no—
127#13063248—22no—
128#13063248—22no—
129#13063248—22no—
130#13063245—22no—
131#13063245—22no—
132C22⋊(C43⋊C8)—22no—
133#13063235—22no—
134C8×Dic43—22no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C23×C4×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140#117×C43—22no—
141#117×C43—22no—
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C42×C43—21no—
149#107×C43—22no—
150#106×C43—22no—
151C22⋊C8×C43C2×C414yescomplemented
152#95×C43—21no—
153C24×C43C2×D411yescharacteristic
154C23×D43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C22×C412yes—
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43#4112yes—
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43—81no—
170C22×Dic43—24no—
171C22×Dic43—24no—
172C22×Dic43—24no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172C22×C412yes—
186C2×C4×D43—42no—
187C2×C4×D43—81no—
188C2×C4×D43—81no—
189C2×Dic86—24no—
190C2×Dic86—24no—
191C2×Dic86—28no—
192C2×Dic86—28no—
193C2×Dic86—24no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—28no—
201C2×Dic86—28no—
202C2×Dic86C22×C412yes—
203C2×Dic86C22×C412yes—
204C2×Dic86C2×D412yes—
205C2×Dic86C2×D412yes—
206C2×Dic86#4112yes—
207C2×Dic86#4112yes—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43C22×C412yes—
213C2×C8×C43C22×C412yes—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43C2×D412yes—
221C4⋊C4×C43C2×D412yes—
222C22⋊C4×C43—24no—
223C22⋊C4×C43—81no—
224C42×C43—24no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227(C2×D43)⋊C4—24no—
228(C2×D43)⋊C4—42no—
229(C2×D43)⋊C4—81no—
230(C2×D43)⋊C4—81no—
231C4⋊Dic43—21no—
232C4⋊Dic43—22no—
233C4⋊Dic43—22no—
234C4⋊Dic43C22×C412yes—
235Dic43⋊C4—24no—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239Dic43⋊C4—81no—
240C4×Dic43—24no—
241C4×Dic43—24no—
242C4×Dic43—21no—
243C4×Dic43—21no—
244C4×Dic43—24no—
245C4×Dic43—24no—
246C4×Dic43—81no—
247C4×Dic43C2×D412yes—
248C4×Dic43C2×D412yes—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255#10621873—28no—
256#10621873—28no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43C4×D412yes—
264C23×C43C22×D411yescharacteristic
265C22×D43—22no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43C4×D412yes—
291C2×C4×C43C23×C411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C22⋊D43—84no—
298C2×Dic43—216no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43#12012yes—
319C2×Dic43#12012yes—
320D172—22no—
321D172—22no—
322D172—41no—
323D172—41no—
324C4×D43—84no—
325Dic86—216no—
326Dic86—22no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86C4×D414yes—
333Dic86C4×D414yes—
334C8×C43—22no—
335C8×C43—22no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338#21462—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43C2×C4×D411yescharacteristic
347C22×C43C2×#12011yescharacteristic
348C22×C43#52511yescharacteristic
349C22×C43#57711yescharacteristic
350C22×C43#57711yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57811yescharacteristic
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C4×C43—22no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43—81no—
364C4×C43—81no—
365C4×C43C2×C4×D411yescharacteristic
366C4×C43C2×C4×D411yescharacteristic
367C4×C43#52511yescharacteristic
368C4×C43#52511yescharacteristic
369Dic43—22no—
370Dic43—22no—
371Dic43—24no—
372Dic43—24no—
373Dic43—42no—
374Dic43—41no—
375Dic43—41no—
376C2×#519—431no—
377C2×#448—431no—
378C2×#440—431no—
379C2×C4×SD16—431no—
380#2324—431no—
381#1880—431no—
382#1880—431no—
383#1875—431no—
384#1865—431no—
385#1863—431no—
386#1854D4311yescharacteristic, complemented
387#1787—431no—
388#1763—431no—
389C4×#103—431no—
390#1750—431no—
391C2×C43—42no—
392C2×C43C4×#12011yescharacteristic
393C2×C43#294711yescharacteristic
394C2×C43#294911yescharacteristic
395C2×C43#301011yescharacteristic
396C2×C43#301311yescharacteristic
397C2×C43#312111yescharacteristic
398C2×C43#312611yescharacteristic
399D43—82no—
400C23×Q8—431no—
401C22×SD16—431no—
402C22×SD16—431no—
403C2×#121—431no—
404#519—864no—
405#519—864no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—861no—
411C2×C4×Q8—861no—
412C2×C4×D4—431no—
413C2×#117—431no—
414C2×#117—861no—
415C2×#117—861no—
416C2×#117C2×D4311yescharacteristic
417#448—438no—
418#440—864no—
419C4×SD16—864no—
420C2×#107C2×D4311yescharacteristic
421C2×#106C2×D4311yescharacteristic
422C2×#103—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×C22⋊C8—431no—
431C2×C22⋊C8C2×D4311yescharacteristic
432C2×#97—431no—
433C2×C4×C8—431no—
434#390—431no—
435#390—861no—
436#389—431no—
437#388—861no—
438#386—861no—
439#385—861no—
440#380C2×D4311yescharacteristic
441C4×C4⋊C4—431no—
442#340—431no—
443#340—431no—
444#340C2×D4311yescharacteristic
445#340C2×D4311yescharacteristic
446#336—431no—
447#336—431no—
448C43#2146211yescharacteristic, complemented, Sylow
449C22×Q8—434no—
450C22×Q8—431no—
451C22×Q8—431no—
452C22×Q8—862no—
453C22×Q8—862no—
454C22×Q8—862no—
455C22×Q8—862no—
456C22×Q8—861no—
457C22×Q8—862no—
458C22×D4—431no—
459C22×D4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C2×SD16—434no—
464C2×SD16—434no—
465C2×SD16—862no—
466C2×SD16—862no—
467C2×SD16—862no—
468C2×SD16—862no—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473#121—434no—
474#121—862no—
475C4×Q8—434no—
476C4×Q8—434no—
477C4×Q8—868no—
478C4×Q8—868no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×Q8—862no—
485C4×D4—862no—
486C4×D4—862no—
487#117—22no—
488#117—22no—
489#117—862no—
490#117—862no—
491#117—868no—
492#117—868no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C42—21no—
514C2×C42—431no—
515C2×C42—431no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42—861no—
521#107—22no—
522#106—22no—
523#103—434no—
524#103—434no—
525#103—862no—
526#103—862no—
527#103—862no—
528#103—862no—
529#102—862no—
530#102—862no—
531C22⋊C8—862no—
532C22⋊C8C4×D4314yescomplemented
533#97—862no—
534C4×C8—862no—
535#95—21no—
536#95—861no—
537#95—861no—
538C24—861no—
539C24D4×D4311yescharacteristic
540C2×Q8—432no—
541C2×Q8—432no—
542C2×Q8—432no—
543C2×Q8—432no—
544C2×Q8—432no—
545C2×Q8—432no—
546C2×Q8—868no—
547C2×Q8—868no—
548C2×Q8—864no—
549C2×Q8—864no—
550C2×Q8—868no—
551C2×Q8—868no—
552C2×Q8—864no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×D4—432no—
560C2×D4—864no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—3441no—
567C2×D4—3441no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—864no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—3441no—
587C22×C4—3441no—
588C22×C4—1722no—
589C22×C4C2×C4×D4312yes—
590C22×C4D4×D4311yescharacteristic
591C22×C4#1062190212yes—
592C22×C4C23×D4311yescharacteristic
593SD16—868no—
594SD16—868no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8C2×C4×D4312yes—
606C2×C8C2×C4×D4312yes—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—432no—
614C4⋊C4—862no—
615C4⋊C4—862no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—861no—
621C4⋊C4—3441no—
622C4⋊C4D4×D4312yes—
623C4⋊C4D4×D4312yes—
624C22⋊C4—24no—
625C22⋊C4—81no—
626C22⋊C4—862no—
627C22⋊C4—862no—
628C22⋊C4—864no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—1722no—
632C42—24no—
633C42—432no—
634C42—432no—
635C42—864no—
636C42—864no—
637C42—864no—
638C42—864no—
639C42—861no—
640C42—861no—
641C42—3441no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—862no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23#1306328712yes—
656C23C2×D4×D4311yescharacteristic
657Q8—434no—
658Q8—434no—
659Q8—8616no—
660Q8—862no—
661Q8—862no—
662Q8—862no—
663Q8—862no—
664Q8—862no—
665Q8—862no—
666D4—862no—
667D4—862no—
668D4—3444no—
669D4—1721no—
670D4—1721no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—432no—
690C2×C4—432no—
691C2×C4—8616no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—862no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—3444no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4#1306328712yes—
713C2×C4C22×C4×D4311yescharacteristic
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4#41×D4311yescharacteristic
718C2×C4C2×#1062190211yescharacteristic
719C8—22no—
720C8—22no—
721C8—1721no—
722C8—1721no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—3441no—
731C22—3441no—
732C22—3441no—
733C22—3441no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22C2×#1306328711yescharacteristic
738C22#120×D4311yescharacteristic
739C22#1458340711yescharacteristic
740C22#1458370611yescharacteristic
741C22#1458370611yescharacteristic
742C22#1458370911yescharacteristic
743C22#1458371511yescharacteristic
744C4—22no—
745C4—42no—
746C4—42no—
747C4—81no—
748C4—81no—
749C4—864no—
750C4—864no—
751C4—862no—
752C4—862no—
753C4—1722no—
754C4—1721no—
755C4—1721no—
756C4C4×D4×D4311yescharacteristic
757C4C4×D4×D4311yescharacteristic
758C4#1458341211yescharacteristic
759C4#1458341211yescharacteristic
760C2—42no—
761C2—3442no—
762C2#1913709611yescharacteristic
763C2#1914343611yescharacteristic
764C2#1914345311yescharacteristic
765C2#1914387811yescharacteristic
766C2#1914391411yescharacteristic
767C2#1914482711yescharacteristic
768C2#1914488211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#21462
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
1. C2×#14583376C2semidirect
3. C2×#14582998C2semidirect
4. C2×#14582986C2semidirect
6. #19134951C2semidirect
7. #19134951C2semidirect
9. #19134860C2semidirect
10. #19134846C2semidirect
11. #19134529C2semidirect
12. #19134424C2semidirect
13. #19134414C2semidirect
14. #19134363C2semidirect
15. C43×#1854C2semidirect
32. #14583040C4semidirect
70. C22×Dic86C2×C4semidirect
95. #13063290D4semidirect
96. #13063290D4semidirect
124. #13063250C2×C4semidirect
125. #13063250C2×C4semidirect
151. C22⋊C8×C43C2×C4semidirect
386. #1854D43semidirect
448. C43#21462semidirect
532. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833762
C2×#145830402
C2×#145829982
C2×#145829862
#191372842
#191349512
#191349172
#191348602
#191348462
#191345292
#191344242
#191344142
#191343632
C43×#18542
#2146243