Finite Group Databasebeta

← #25138970

Subgroups — #25138970

Order 11008.

1076 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583149C211yesmaximal, characteristic, complemented
2C2×#14582975C211yesmaximal, characteristic, complemented
3C2×#14582938C211yesmaximal, characteristic, complemented
4#19138031C211yesmaximal, characteristic, complemented
5#19138009C211yesmaximal, characteristic, complemented
6#19135979C211yesmaximal, characteristic, complemented
7#19135965C211yesmaximal, characteristic, complemented
8#19135781C211yesmaximal, characteristic, complemented
9#19135774C211yesmaximal, characteristic, complemented
10#19135462C211yesmaximal, characteristic, complemented
11#19135324C211yesmaximal, characteristic, complemented
12#19134914C211yesmaximal, characteristic, complemented
13#19134909C211yesmaximal, characteristic, complemented
14#19134628C211yesmaximal, characteristic, complemented
15C2×C43×#469C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063296—21no—
18C2×#13063296C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14583149—24no—
24#14582975—24no—
25#14582938—24no—
26C2×#13063259C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582822—21no—
39#14582815—21no—
40#14582813—21no—
41#14582807—21no—
42#14582802—21no—
43#14582802C2211yescharacteristic
44#14582802C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582798C2211yescharacteristic
47#14582787—21no—
48#14582775—21no—
49#14582759C2211yescharacteristic
50#14582759C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×D8×C43C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C43×#469—24no—
60C2×#106×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43—21no—
65C22×C22⋊D43D411yescharacteristic
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C2×#10621872—22no—
69C2×#10621872—22no—
70C2×#10621872D414yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063296—22no—
74#13063296—22no—
75#13063296—22no—
76#13063296—22no—
77#13063296—44no—
78C4×C22⋊D43—22no—
79C4×C22⋊D43—22no—
80#13063283—22no—
81#13063283—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4D411yescharacteristic
90C4⋊C4×D43—22no—
91C4⋊C4×D43—41no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43D411yescharacteristic
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4D411yescharacteristic
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105#13063259—22no—
106#13063258—22no—
107#13063257—22no—
108#13063256—22no—
109Dic43⋊C8—22no—
110#13063246—22no—
111#13063246—22no—
112#13063246—41no—
113#13063246—41no—
114C22⋊(C43⋊C8)—22no—
115(C2×D43)⋊C8—22no—
116C8×Dic43—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×D4×C43—21no—
122C22×D4×C43—21no—
123C22×D4×C43C2311yescharacteristic
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C2×D8×C43—22no—
127C2×D8×C43—22no—
128C2×D8×C43—22no—
129C2×M16×C43—22no—
130C2×M16×C43—22no—
131C2×M16×C43—22no—
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134#121×C43—22no—
135#121×C43—22no—
136#121×C43—41no—
137#121×C43—41no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142#106×C43D414yescomplemented
143#102×C43—22no—
144#102×C43—22no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43C2×D411yescharacteristic
148C23×D43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—81no—
166C2×D4×C43—81no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—22no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—81no—
185C2×C22⋊D43—81no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×C4×D43—81no—
200C2×C4×D43C2×D412yes—
201C2×C4×D43#4112yes—
202D8×C43—44no—
203M16×C43—44no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43C2×D412yes—
208C2×C8×C43C2×D412yes—
209C2×C8×C43#4112yes—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43C2×D412yes—
213C4⋊C4×C43C2×D412yes—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—42no—
216C22⋊Dic43—22no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—81no—
223C22⋊Dic43—81no—
224C22⋊Dic43—81no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—42no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—42no—
236C4⋊Dic43—81no—
237Dic43⋊C4—22no—
238Dic43⋊C4—42no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—42no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8C2×D412yes—
248#10621872—28no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C22×D411yescharacteristic
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43#12112yes—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43—84no—
287D4×C43—84no—
288C2×C4×C43—21no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C432−1+411yescharacteristic
307C22⋊D43—44no—
308C22⋊D43—84no—
309C22⋊D43—84no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43#12112yes—
330C2×Dic43AGL(1,ℤ/8)12yes—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—84no—
336C8×C43—41no—
337C8×C43#12114yescomplemented
338C43⋊C8—22no—
339C43⋊C8—41no—
340#24792—431nomaximal, Sylow
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43C2×#12111yescharacteristic
363C22×C43D4211yescharacteristic
364C22×C43#54711yescharacteristic
365C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C43#57511yescharacteristic
367C22×C43#57611yescharacteristic
368C22×C43#57711yescharacteristic
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C4×C43—41no—
377C4×C43—42no—
378C4×C43—42no—
379C4×C43C2×#12111yescharacteristic
380C4×C43#53711yescharacteristic
381C4×C43#54811yescharacteristic
382C4×C43#55311yescharacteristic
383Dic43—22no—
384Dic43—22no—
385Dic43—41no—
386Dic43—81no—
387Dic43—81no—
388Dic43—81no—
389Dic43—81no—
390C2×#469—431no—
391C2×#469D4311yescharacteristic, complemented
392C2×#436—431no—
393C2×#428—431no—
394#2416—431no—
395#2414—431no—
396#2067—431no—
397#2065—431no—
398#2034—431no—
399#2033—431no—
400#1970—431no—
401#1941—431no—
402#1875—431no—
403#1874—431no—
404#1809—431no—
405C2×C43—81no—
406C2×C43—161no—
407C2×C43—161no—
408C2×C43#241611yescharacteristic
409C2×C43#305511yescharacteristic
410C2×C43#306211yescharacteristic
411C2×C43#327411yescharacteristic
412C2×C43#327511yescharacteristic
413C2×C43#335411yescharacteristic
414C2×C43#335511yescharacteristic
415D43—42no—
416C22×D8C2×D4311yescharacteristic
417C22×M16—431no—
418C22×M16C2×D4311yescharacteristic
419C2×#121—431no—
420C2×#121—431no—
421C2×#121—861no—
422C2×#121C2×D4311yescharacteristic
423C2×#121C2×D4311yescharacteristic
424C2×C4×D4—431no—
425C2×#117—431no—
426C22×C4⋊C4—431no—
427#469—24no—
428#469—864no—
429#436—864no—
430#428—864no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#106—431no—
434C2×#106—431no—
435C2×#106C2×D4311yescharacteristic
436C2×C4⋊C8—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102C2×D4311yescharacteristic
442C2×#102C2×D4311yescharacteristic
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C4×C8—431no—
446#396—861no—
447#394—861no—
448#394—861no—
449#392—861no—
450#390—431no—
451#390—431no—
452#390—861no—
453#389—431no—
454#389—431no—
455#388—861no—
456#386—861no—
457#380—431no—
458#380—431no—
459#340—431no—
460#340—431no—
461#340—431no—
462#340—431no—
463C43#2479211yescharacteristic, complemented, Sylow
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—431no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4C22×D4311yescharacteristic
470C22×D4C22×D4311yescharacteristic
471C23×C4—431no—
472C23×C4—861no—
473C23×C4C22×D4311yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16—434no—
481C2×M16—862no—
482C2×M16—862no—
483C22×C8—431no—
484C22×C8—431no—
485C22×C8C22×D4311yescharacteristic
486C22×C8C22×D4311yescharacteristic
487#121—22no—
488#121—22no—
489#121—41no—
490#121—41no—
491#121—862no—
492#121—862no—
493#121—862no—
494#121—862no—
495#121—1724no—
496C4×D4—862no—
497C4×D4—862no—
498#117—862no—
499#117—1721no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—862no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—1721no—
510C2×C4⋊C4C22×D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—431no—
515C2×C22⋊C4—431no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C42—431no—
526C2×C42—861no—
527#107—862no—
528#107—862no—
529#106—862no—
530#106—862no—
531#106C22⋊D4314yescomplemented
532C4⋊C8—862no—
533#102—22no—
534#102—22no—
535#102—862no—
536#102—862no—
537#102—1721no—
538#102—1721no—
539C22⋊C8—862no—
540C22⋊C8—862no—
541C4×C8—862no—
542#95—861no—
543#95—861no—
544#95—861no—
545#95—861no—
546C24—21no—
547C24—21no—
548C24—431no—
549C24D4×D4311yescharacteristic
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—3441no—
571C2×D4—3441no—
572C2×D4—1721no—
573C2×D4—1722no—
574C2×D4—1722no—
575C2×D4—1722no—
576C2×D4—1722no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—432no—
588C22×C4—432no—
589C22×C4—431no—
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—3441no—
599C22×C4—1722no—
600C22×C4—1722no—
601C22×C4D4×D4311yescharacteristic
602C22×C4C23×D4311yescharacteristic
603D8—44no—
604M16—44no—
605M16—868no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—432no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8D4×D4312yes—
616C2×C8#1062190012yes—
617C2×C8C2×C22⋊D4312yes—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—862no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—3441no—
630C4⋊C4—1722no—
631C4⋊C4—1722no—
632C4⋊C4C2×C22⋊D4312yes—
633C4⋊C4C2×C22⋊D4312yes—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—862no—
637C22⋊C4—862no—
638C22⋊C4—3441no—
639C22⋊C4—3441no—
640C22⋊C4—3441no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C22⋊C4—1722no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C42—861no—
648C42—861no—
649C42—1722no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—432no—
672C23—861no—
673C23—861no—
674C23—861no—
675C23—861no—
676C23—861no—
677C23—861no—
678C23C2×D4×D4311yescharacteristic
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—84no—
689D4—3444no—
690D4—3444no—
691D4—1724no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—432no—
706C2×C4—432no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—3444no—
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×C4—1721no—
731C2×C4C2×D4×D4311yescharacteristic
732C2×C4C22×C22⋊D4311yescharacteristic
733C2×C4#41×D4311yescharacteristic
734C2×C4C2×#1062190011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337211yescharacteristic
737C8—41no—
738C8—862no—
739C8—1721no—
740C8#1306329614yescomplemented
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—862no—
763C22—862no—
764C22—862no—
765C22—1721no—
766C22—1721no—
767C22—1721no—
768C22—1721no—
769C22#121×D4311yescharacteristic
770C22D4×C22⋊D4311yescharacteristic
771C22#1458354911yescharacteristic
772C22AGL(1,ℤ/8)×D4311yescharacteristic
773C22#1458369511yescharacteristic
774C22#1458370311yescharacteristic
775C22#1458370911yescharacteristic
776C4—42no—
777C4—41no—
778C4—42no—
779C4—862no—
780C4—862no—
781C4—3441no—
782C4—3441no—
783C4—3441no—
784C4—3441no—
785C4—1721no—
786C4C2×#1306329611yescharacteristic
787C4#1458347811yescharacteristic
788C4#1458355611yescharacteristic
789C4#1458359611yescharacteristic
790C2—81no—
791C2—161no—
792C2—161no—
793C2—1722no—
794C2#1913803111yescharacteristic
795C2#1914421311yescharacteristic
796C2#1914427211yescharacteristic
797C2#1914620911yescharacteristic
798C2#1914622611yescharacteristic
799C2#1914718511yescharacteristic
800C2#1914719611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#469C2
socleC23×C43C22×D4
hypercenterC2×#469D43
hypocenterC43#24792
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#14583149C2semidirect
2. C2×#14582975C2semidirect
3. C2×#14582938C2semidirect
4. #19138031C2semidirect
5. #19138009C2semidirect
6. #19135979C2semidirect
7. #19135965C2semidirect
8. #19135781C2semidirect
9. #19135774C2semidirect
10. #19135462C2semidirect
11. #19135324C2semidirect
12. #19134914C2semidirect
13. #19134909C2semidirect
14. #19134628C2semidirect
15. C2×C43×#469C2semidirect
70. C2×#10621872D4semidirect
142. #106×C43D4semidirect
337. C8×C43#121semidirect
391. C2×#469D43semidirect
463. C43#24792semidirect
531. #106C22⋊D43semidirect
740. C8#13063296semidirect

Maximal subgroups

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

subgroupindex
C2×#145831492
C2×#145829752
C2×#145829382
#191380312
#191380092
#191359792
#191359652
#191357812
#191357742
#191354622
#191353242
#191349142
#191349092
#191346282
C2×C43×#4692
#2479243