Finite Group Databasebeta

← #25140573

Subgroups — #25140573

Order 11008.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583011C211yesmaximal, characteristic, complemented
2#19138083C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic43C211yesmaximal, characteristic, complemented
4#19136118C211yesmaximal, characteristic, complemented
5#19136028C211yesmaximal, characteristic, complemented
6#19135903C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135289C211yesmaximal, characteristic, complemented
9#19135205C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134945C211yesmaximal, characteristic, complemented
12#19134840C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×C43×#447C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic, complemented
19C22×C22⋊Dic43—21no—
20#14583011—24no—
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063257C2211yescharacteristic, complemented
23C2×Dic43⋊C8C2211yescharacteristic, complemented
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic, complemented
29C2×#13063246C2211yescharacteristic, complemented
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063235C2211yescharacteristic, complemented
32#14582827—21no—
33#14582813—21no—
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic, complemented
37#14582795C2211yescharacteristic, complemented
38#14582779—21no—
39#14582779—21no—
40#14582779—21no—
41#14582764C2211yescharacteristic, complemented
42#14582760—21no—
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582755—21no—
46C4×C22⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C23×D4×C43C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C22×D8×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C43×#447—24no—
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C23×Dic43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66D4×Dic43—22no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—41no—
70D4×Dic43—41no—
71D4×Dic43—41no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—44no—
89C2×C22⋊Dic43D411yescharacteristic
90C2×C22⋊Dic43D411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063258—41no—
94#13063257—22no—
95Dic43⋊C8—41no—
96#13063246—22no—
97#13063246—22no—
98#13063246—22no—
99#13063246—22no—
100#13063246—41no—
101#13063246—41no—
102C22⋊(C43⋊C8)—41no—
103#13063235—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C25×C43—21no—
112C22×D4×C43—22no—
113C22×D4×C43—22no—
114C22×D4×C43—22no—
115C22×D4×C43—22no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—41no—
119C22×D4×C43—41no—
120C22×D4×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C2×D8×C43—22no—
125C2×D8×C43—22no—
126C2×D8×C43—22no—
127C2×D8×C43—22no—
128C2×D8×C43—41no—
129C2×D8×C43D414yes—
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132#121×C43—22no—
133#121×C43—41no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136#102×C43—22no—
137#102×C43—22no—
138C22⋊C8×C43—22no—
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—21no—
142C24×C43—21no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—42no—
147C24×C43—81no—
148C24×C43—81no—
149C24×C43C2×D411yescharacteristic
150C2×D4×C43—24no—
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—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43—44no—
171C2×D4×C43—42no—
172C2×D4×C43—81no—
173C2×D4×C43C2×D412yes—
174C2×D4×C43C2×D412yes—
175C2×D4×C43#4112yes—
176C2×D4×C43#4112yes—
177C2×D4×C43#4112yes—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2411yescharacteristic
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—81no—
198C22×Dic43—81no—
199C22×Dic43—81no—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204D8×C43—28no—
205D8×C43—44no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43C2×D412yes—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C22⋊C4×C43—42no—
215C22⋊Dic43—22no—
216C22⋊Dic43—41no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—42no—
223C22⋊Dic43—81no—
224C22⋊Dic43—81no—
225C22⋊Dic43—81no—
226C22⋊Dic43—81no—
227C22⋊Dic43—81no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236Dic43⋊C4—81no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C23×C43—21no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43—48no—
259C23×C43—48no—
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×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43—84no—
279C23×C43—84no—
280C23×C43—84no—
281C23×C43AGL(1,ℤ/8)12yes—
282C23×C43C22×D411yescharacteristic
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—48no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—84no—
296D4×C43#12314yes—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—84no—
338C2×Dic43—84no—
339C2×Dic43—84no—
340C8×C43—22no—
341C8×C43—41no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344#24909—431nomaximal, Sylow
345C22×C43—22no—
346C22×C43—24no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—41no—
353C22×C43—42no—
354C22×C43—41no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—41no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—816no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43#52511yescharacteristic
375C22×C43D4211yescharacteristic
376C22×C43#54611yescharacteristic
377C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C43#57511yescharacteristic
379C22×C43#57611yescharacteristic
380C22×C43#57611yescharacteristic
381C4×C43—41no—
382C4×C43—81no—
383C4×C43C2×#12311yescharacteristic
384C4×C43#53811yescharacteristic
385C4×C43#54611yescharacteristic
386C4×C43#55111yescharacteristic
387Dic43—41no—
388Dic43—41no—
389Dic43—41no—
390Dic43—41no—
391Dic43—81no—
392Dic43—81no—
393Dic43—81no—
394Dic43—81no—
395C2×#447D4311yescharacteristic
396C2×#442—431no—
397#2420—431no—
398D4×C22⋊C4—431no—
399#2092—431no—
400#2077—431no—
401#2054—431no—
402#2033—431no—
403#1936—431no—
404#1924—431no—
405#1879—431no—
406#1879—431no—
407#1862—431no—
408#1804—431no—
409#1786—431no—
410C2×C43—42no—
411C2×C43—44no—
412C2×C43—82no—
413C2×C43—82no—
414C2×C43#241811yescharacteristic
415C2×C43#311411yescharacteristic
416C2×C43#312211yescharacteristic
417C2×C43#326411yescharacteristic
418C2×C43#327311yescharacteristic
419C2×C43#331811yescharacteristic
420C2×C43#331911yescharacteristic
421C23×D4C2×D4311yescharacteristic
422C22×D8C2×D4311yescharacteristic
423C22×D8C2×D4311yescharacteristic
424C2×#121C2×D4311yescharacteristic
425C2×C4×D4—431no—
426C2×C4×D4—431no—
427C2×C4×D4—431no—
428C22×C22⋊C4—861no—
429#447—24no—
430#442—864no—
431C2×#107—431no—
432C2×#106—431no—
433C2×C4⋊C8—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102C2×D4311yescharacteristic
441C2×#102C2×D4311yescharacteristic
442C2×C22⋊C8—431no—
443C2×C22⋊C8C2×D4311yescharacteristic
444C2×#97—431no—
445#397—861no—
446#394—861no—
447#390—431no—
448#390—431no—
449#390—431no—
450#389—431no—
451#386—861no—
452#386—861no—
453#386—861no—
454#382—431no—
455#381—861no—
456#380—431no—
457#380—431no—
458#379—861no—
459C4×C22⋊C4—431no—
460#340—431no—
461#340—431no—
462#340—431no—
463#340—431no—
464#336—431no—
465#336—431no—
466C43#2490911yescharacteristic, complemented, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C22×D4311yescharacteristic
477C22×D4C22×D4311yescharacteristic
478C22×D4C22×D4311yescharacteristic
479C23×C4—861no—
480C23×C4—861no—
481C23×C4—861no—
482C23×C4C22×D4311yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8C22⋊D4314yes—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8C22×D4311yescharacteristic
492C22×C8C22×D4311yescharacteristic
493#121—22no—
494#121—41no—
495C4×D4—862no—
496C4×D4—862no—
497C4×D4—862no—
498C4×D4—1721no—
499C4×D4—1721no—
500C4×D4—1721no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—1724no—
522C2×C42—431no—
523C2×C42—431no—
524#107—1721no—
525#106—862no—
526C4⋊C8—1721no—
527#102—22no—
528#102—22no—
529#102—862no—
530#102—862no—
531#102—862no—
532#102—862no—
533#102—1721no—
534#102—1721no—
535C22⋊C8—22no—
536C22⋊C8—1721no—
537#97—862no—
538#95—431no—
539#95—431no—
540#95—861no—
541#95—861no—
542#95—861no—
543#95—861no—
544#95—861no—
545C24—21no—
546C24—24no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24D4×D4311yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4#1062190012yes—
580C2×D4#1062190012yes—
581C2×D4#1062190012yes—
582C2×D4C2×C22⋊D4312yes—
583C2×D4C2×C22⋊D4312yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—431no—
592C22×C4—431no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—3441no—
600C22×C4—3441no—
601C22×C4—3441no—
602C22×C4—1722no—
603C22×C4—1722no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4—1722no—
607C22×C4—1722no—
608C22×C4D4×D4311yescharacteristic
609C22×C4C23×D4311yescharacteristic
610D8—28no—
611D8—44no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8C2×C22⋊D4312yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—3441no—
635C22⋊C4—42no—
636C22⋊C4—862no—
637C22⋊C4—3441no—
638C22⋊C4—3441no—
639C22⋊C4—3441no—
640C22⋊C4—3441no—
641C22⋊C4—3441no—
642C22⋊C4—1721no—
643C22⋊C4—1722no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—861no—
650C42—861no—
651C42—861no—
652C42—861no—
653C23—21no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—21no—
660C23—22no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23#1306334912yes—
688C23C2×D4×D4311yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4#1306330614yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—3444no—
726C2×C4—3444no—
727C2×C4—3444no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4C22×C22⋊D4311yescharacteristic
741C2×C4C2×#1062190011yescharacteristic
742C2×C4C2×#1062190011yescharacteristic
743C2×C4C2×#1062190011yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337011yescharacteristic
746C8—22no—
747C8—41no—
748C8—1721no—
749C8—1721no—
750C22—24no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22#1458340511yescharacteristic
780C22D4×C22⋊D4311yescharacteristic
781C22#1458353611yescharacteristic
782C22C2×#1306334911yescharacteristic
783C22#1458369511yescharacteristic
784C22#1458370011yescharacteristic
785C22#1458370311yescharacteristic
786C4—41no—
787C4—81no—
788C4—3441no—
789C4—3441no—
790C4—3441no—
791C4—3441no—
792C4—1721no—
793C4—1721no—
794C4—1721no—
795C4—1721no—
796C4C2×#1306330611yescharacteristic
797C4#1458348411yescharacteristic
798C4#1458354311yescharacteristic
799C4#1458358011yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—82no—
804C2#1913805311yescharacteristic
805C2#1914472811yescharacteristic
806C2#1914483211yescharacteristic
807C2#1914607511yescharacteristic
808C2#1914620011yescharacteristic
809C2#1914674011yescharacteristic
810C2#1914674411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#447C2
socleC23×C43C22×D4
hypercenterC2×#447D43
hypocenterC43#24909
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#14583011C2semidirect
2. #19138083C2semidirect
3. D4×C22⋊Dic43C2semidirect
4. #19136118C2semidirect
5. #19136028C2semidirect
6. #19135903C2semidirect
7. #19135774C2semidirect
8. #19135289C2semidirect
9. #19135205C2semidirect
10. #19134945C2semidirect
11. #19134945C2semidirect
12. #19134840C2semidirect
13. #19134603C2semidirect
14. #19134526C2semidirect
18. C2×D4×Dic43C22semidirect
21. C2×#13063258C22semidirect
22. C2×#13063257C22semidirect
23. C2×Dic43⋊C8C22semidirect
28. C2×#13063246C22semidirect
29. C2×#13063246C22semidirect
31. C2×#13063235C22semidirect
36. #14582802C22semidirect
37. #14582795C22semidirect
41. #14582764C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
466. C43#24909semidirect

Maximal subgroups

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

subgroupindex
C2×#145830112
#191380832
D4×C22⋊Dic432
#191361182
#191360282
#191359032
#191357742
#191352892
#191352052
#191349452
#191348402
#191346032
#191345262
C2×C43×#4472
#2490943