Finite Group Databasebeta

← #25130509

Subgroups — #25130509

Order 11008.

1218 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583604C211yesmaximal, characteristic, complemented
2C2×#14583187C211yesmaximal, characteristic, complemented
3C2×#14582990C211yesmaximal, characteristic, complemented
4#19139509C211yesmaximal, characteristic
5#19135794C211yesmaximal, characteristic, complemented
6#19135792C211yesmaximal, characteristic, complemented
7#19135599C211yesmaximal, characteristic, complemented
8#19135598C211yesmaximal, characteristic, complemented
9#19135554C211yesmaximal, characteristic, complemented
10#19135387C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134789C211yesmaximal, characteristic, complemented
13#19134788C211yesmaximal, characteristic, complemented
14#19134599C211yesmaximal, characteristic, complemented
15C43×#1874C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17#14583604—24no—
18#14583604—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063305C2211yescharacteristic
22C2×#13063304—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063303—21no—
25C2×#13063297—21no—
26C2×#13063296C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×D4×Dic43C2211yescharacteristic
29C2×C4×C22⋊D43—21no—
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14583187—24no—
33#14582990—24no—
34C2×#13063257C2211yescharacteristic
35C2×#13063256C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37C2×Dic43⋊C8C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582814—21no—
47#14582813—21no—
48#14582768C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582757—21no—
51#14582756C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C22×C4⋊C4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43D411yescharacteristic
67C23×Dic43—21no—
68C22×C4×D43—21no—
69C22×C4×D43C2311yescharacteristic
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063324—22no—
76#13063324D414yescomplemented
77#13063315—28no—
78#13063305—22no—
79#13063305—22no—
80#13063304—28no—
81#13063304—22no—
82#13063304—22no—
83#13063303—28no—
84#13063297—44no—
85#13063296—22no—
86#13063296—41no—
87#13063290—22no—
88#13063290D414yescomplemented
89D4×Dic43—22no—
90D4×Dic43—22no—
91C4×C22⋊D43—28no—
92C4×C22⋊D43—22no—
93C4×C22⋊D43—22no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4D411yescharacteristic
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4D411yescharacteristic
115C2×C4×Dic43—21no—
116C2×C4×Dic43C2311yescharacteristic
117#13063257—22no—
118#13063256—22no—
119#13063256—22no—
120Dic43⋊C8—22no—
121#13063250—22no—
122#13063250—41no—
123#13063248—41no—
124#13063246—22no—
125C22⋊(C43⋊C8)—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—41no—
128C8×Dic43—22no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×D4×C43—21no—
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134C23×C4×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137#121×C43—22no—
138#121×C43—41no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—22no—
141C2×C4⋊C4×C43—22no—
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43—21no—
146#102×C43—22no—
147#102×C43—22no—
148C22⋊C8×C43—41no—
149C24×C43—21no—
150C24×C43C2×D411yescharacteristic
151C23×D43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43—81no—
160C2×D4×C43#4112yes—
161C22×C4×C43—24no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—81no—
172C22×C4×C43—81no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—42no—
178C2×C22⋊D43—42no—
179C2×C22⋊D43—81no—
180C2×C22⋊D43SD1614yescomplemented
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—42no—
186C22×Dic43—42no—
187C22×Dic43—42no—
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—24no—
198C2×C4×D43—81no—
199C2×C4×D43—81no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—24no—
206C2×Dic86—81no—
207C2×Dic86—81no—
208C2×Dic86C2×D412yes—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C4⋊C4×C43—24no—
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—42no—
223C22⋊Dic43—24no—
224C22⋊Dic43—22no—
225C22⋊Dic43—42no—
226C22⋊Dic43—42no—
227C22⋊Dic43—42no—
228#10621883—28no—
229(C2×D43)⋊C4—24no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—42no—
232C4⋊Dic43—24no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—24no—
242Dic43⋊C4—24no—
243Dic43⋊C4—22no—
244Dic43⋊C4—42no—
245Dic43⋊C4—81no—
246C4×Dic43—24no—
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#4112yes—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—22no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43C2×SD1612yes—
269C23×C43C22×D411yescharacteristic
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43C2×SD1612yes—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—84no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—41no—
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×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—84no—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C432−1+411yescharacteristic
305C22⋊D43—28no—
306C22⋊D43—84no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—22no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—84no—
325C2×Dic43#12012yes—
326C2×Dic43#12012yes—
327C2×Dic43C2×SD1612yes—
328C2×Dic43#13712yes—
329C4×D43—41no—
330C4×D43—41no—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—84no—
334Dic86—22no—
335Dic86—22no—
336Dic86—41no—
337Dic86—41no—
338Dic86—84no—
339C8×C43—41no—
340C8×C43—41no—
341C43⋊C8—22no—
342C43⋊C8—41no—
343#24118—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43C2×#12011yescharacteristic
359C22×C43#54611yescharacteristic
360C22×C43#54711yescharacteristic
361C22×C43C22×SD1611yescharacteristic
362C22×C43C2×#13711yescharacteristic
363C22×C43#57611yescharacteristic
364C22×C43#57711yescharacteristic
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C4×C43—41no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—81no—
376C4×C43#52511yescharacteristic
377C4×C43#53711yescharacteristic
378C4×C43#54811yescharacteristic
379C4×C43#55011yescharacteristic
380Dic43—22no—
381Dic43—42no—
382Dic43—41no—
383Dic43—42no—
384Dic43—81no—
385Dic43—81no—
386Dic43#44814yes—
387C2×#554—431no—
388C2×#476—431no—
389C2×C4×SD16—431no—
390#2537—431no—
391#2035—431no—
392#2035—431no—
393#2000—431no—
394#2000—431no—
395#1990—431no—
396#1954—431no—
397#1874—431no—
398#1874D4311yescharacteristic, complemented
399#1853—431no—
400#1853—431no—
401#1803—431no—
402C2×C43—42no—
403C2×C43—82no—
404C2×C43#240711yescharacteristic
405C2×C43C2×#44811yescharacteristic
406C2×C43#301211yescharacteristic
407C2×C43#329511yescharacteristic
408C2×C43#333111yescharacteristic
409C2×C43#333511yescharacteristic
410C2×C43#335711yescharacteristic
411D43—42no—
412C22×SD16—431no—
413#554—864no—
414#554—864no—
415C2×C4⋊Q8—431no—
416C2×#125—861no—
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8—431no—
419C2×C22⋊Q8—861no—
420C2×C22⋊Q8—861no—
421C2×#121—431no—
422C2×#121—861no—
423C2×#121C2×D4311yescharacteristic
424C2×C4×Q8—431no—
425C2×C4×D4—431no—
426C2×C4×D4—431no—
427C2×C4×D4—861no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4C2×D4311yescharacteristic
430#476—864no—
431C4×SD16—864no—
432C2×#106—431no—
433C2×#106—431no—
434C2×#106—431no—
435C2×C4⋊C8—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#102—431no—
440C2×#102C2×D4311yescharacteristic
441C2×#102C2×D4311yescharacteristic
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8C2×D4311yescharacteristic
446C2×C4×C8—431no—
447#394—861no—
448#394—861no—
449#384—431no—
450#380—431no—
451#380—431no—
452#380—861no—
453#340—431no—
454#340—431no—
455#340—431no—
456#340—431no—
457#340C2×D4311yescharacteristic
458#340C2×D4311yescharacteristic
459C43#2411811yescharacteristic, complemented, Sylow
460C22×Q8—431no—
461C22×Q8—861no—
462C22×D4—21no—
463C22×D4—431no—
464C22×D4—861no—
465C22×D4C22×D4311yescharacteristic
466C23×C4—21no—
467C23×C4—431no—
468C23×C4—861no—
469C23×C4—861no—
470C23×C4C22×D4311yescharacteristic
471C2×SD16—862no—
472C2×SD16—862no—
473C2×SD16—862no—
474C22×C8—431no—
475C22×C8—431no—
476C22×C8C22×D4311yescharacteristic
477C22×C8C22×D4311yescharacteristic
478C4⋊Q8—434no—
479C4⋊Q8—862no—
480#125—868no—
481C22⋊Q8—862no—
482C22⋊Q8—868no—
483C22⋊Q8—862no—
484C22⋊Q8—862no—
485C22⋊Q8—868no—
486C22⋊Q8—862no—
487#121—22no—
488#121—41no—
489#121—862no—
490#121—1721no—
491#121—1724no—
492C4×Q8—434no—
493C4×Q8—862no—
494C4×D4—862no—
495C4×D4—862no—
496C4×D4—862no—
497C4×D4—862no—
498C4×D4—868no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—862no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4C22×D4311yescharacteristic
516C2×C4⋊C4C22×D4311yescharacteristic
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C42—431no—
528C2×C42—861no—
529#106—862no—
530#106—862no—
531#106—862no—
532C4⋊C8—862no—
533#103—862no—
534#103—1721no—
535#103—1721no—
536#102—22no—
537#102—22no—
538#102—862no—
539C22⋊C8—41no—
540C22⋊C8—862no—
541C22⋊C8—862no—
542C22⋊C8—1721no—
543C4×C8—862no—
544#95—861no—
545#95—861no—
546C24—21no—
547C24—431no—
548C24D4×D4311yescharacteristic
549C2×Q8—432no—
550C2×Q8—864no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—3441no—
557C2×Q8—3441no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—81no—
566C2×D4—434no—
567C2×D4—862no—
568C2×D4—862no—
569C2×D4—3441no—
570C2×D4—1722no—
571C2×D4—1722no—
572C2×D4#1062189812yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—864no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—3441no—
600C22×C4—3441no—
601C22×C4—1722no—
602C22×C4—1722no—
603C22×C4—1722no—
604C22×C4D4×D4311yescharacteristic
605C22×C4C23×D4311yescharacteristic
606SD16—868no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—432no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—432no—
625C4⋊C4—862no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—3441no—
637C4⋊C4—1722no—
638C4⋊C4D4×D4312yes—
639C4⋊C4D4×D4312yes—
640C22⋊C4—42no—
641C22⋊C4—862no—
642C22⋊C4—864no—
643C22⋊C4—862no—
644C22⋊C4—864no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—432no—
650C42—432no—
651C42—864no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—432no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23SD16×D4312yes—
673C23C2×D4×D4311yescharacteristic
674Q8—862no—
675Q8—862no—
676Q8—3444no—
677Q8—1721no—
678Q8—1721no—
679D4—22no—
680D4—22no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4—868no—
685D4—3444no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—84no—
703C2×C4—432no—
704C2×C4—432no—
705C2×C4—432no—
706C2×C4—432no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—3444no—
715C2×C4—3444no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C2×D4×D4311yescharacteristic
732C2×C4#41×D4311yescharacteristic
733C2×C4C2×#1062189811yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337211yescharacteristic
736C8—41no—
737C8—41no—
738C8—862no—
739C8—1721no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22—1721no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22#120×D4311yescharacteristic
762C22#1458353911yescharacteristic
763C22#1458354711yescharacteristic
764C22C2×SD16×D4311yescharacteristic
765C22#137×D4311yescharacteristic
766C22#1458370011yescharacteristic
767C22#1458370911yescharacteristic
768C4—41no—
769C4—42no—
770C4—42no—
771C4—81no—
772C4—434no—
773C4—862no—
774C4—3441no—
775C4—3441no—
776C4—1721no—
777C4—1722no—
778C4—1722no—
779C4#1458340811yescharacteristic
780C4#1458347811yescharacteristic
781C4#1458355811yescharacteristic
782C4#1458356711yescharacteristic
783C2—42no—
784C2—82no—
785C2—1722no—
786C2#1913793711yescharacteristic
787C2#448×D4311yescharacteristic
788C2#1914389411yescharacteristic
789C2#1914641511yescharacteristic
790C2#1914690711yescharacteristic
791C2#1914695011yescharacteristic
792C2#1914721411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radical#19139509C2
hypercenter#1874D43
hypocenterC43#24118
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#14583604C2semidirect
2. C2×#14583187C2semidirect
3. C2×#14582990C2semidirect
5. #19135794C2semidirect
6. #19135792C2semidirect
7. #19135599C2semidirect
8. #19135598C2semidirect
9. #19135554C2semidirect
10. #19135387C2semidirect
11. #19134909C2semidirect
12. #19134789C2semidirect
13. #19134788C2semidirect
14. #19134599C2semidirect
15. C43×#1874C2semidirect
76. #13063324D4semidirect
88. #13063290D4semidirect
180. C2×C22⋊D43SD16semidirect
398. #1874D43semidirect
459. C43#24118semidirect

Maximal subgroups

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

subgroupindex
C2×#145836042
C2×#145831872
C2×#145829902
#191395092
#191357942
#191357922
#191355992
#191355982
#191355542
#191353872
#191349092
#191347892
#191347882
#191345992
C43×#18742
#2411843