Finite Group Databasebeta

← #25135384

Subgroups — #25135384

Order 11008.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583032C211yesmaximal, characteristic
2C2×#14582960C211yesmaximal, characteristic, complemented
3#19137175C211yesmaximal, characteristic, complemented
4#19135980C211yesmaximal, characteristic, complemented
5#19135966C211yesmaximal, characteristic, complemented
6#19135905C211yesmaximal, characteristic, complemented
7#19135905C211yesmaximal, characteristic, complemented
8#19135470C211yesmaximal, characteristic, complemented
9#19135460C211yesmaximal, characteristic, complemented
10#19135291C211yesmaximal, characteristic, complemented
11#19135277C211yesmaximal, characteristic, complemented
12#19134918C211yesmaximal, characteristic, complemented
13#19134792C211yesmaximal, characteristic, complemented
14#19134525C211yesmaximal, characteristic, complemented
15C43×#2624C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20#14583032—24no—
21#14582960—24no—
22C2×#13063258C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
25C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
26C2×#13063246C2211yescharacteristic, complemented
27C2×#13063246C2211yescharacteristic, complemented
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic, complemented
37C2×C4×C43⋊C8C2211yescharacteristic, complemented
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582800—21no—
43#14582800—21no—
44#14582754—21no—
45#14582754—21no—
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50C2×#121×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C43×#399—21no—
53C43×#397—21no—
54C43×#394—21no—
55C43×#394—21no—
56C43×#390C2211yescharacteristic, complemented
57C43×#390C2211yescharacteristic, complemented
58C43×#389C2211yescharacteristic, complemented
59C43×#389C2211yescharacteristic, complemented
60C43×#380C2211yescharacteristic
61C24×D43—21no—
62C22×D172—21no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C2×#10621882—22no—
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882—41no—
76C2×#10621882—41no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063284—41no—
82#13063284—41no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×C4×Dic43—21no—
95#13063258—41no—
96#13063256—41no—
97C4⋊(C43⋊C8)—22no—
98C4⋊(C43⋊C8)—22no—
99#13063246—41no—
100#13063246—41no—
101#13063245—22no—
102#13063245—22no—
103#13063245—22no—
104#13063245—22no—
105#13063245—41no—
106#13063245—41no—
107C22⋊(C43⋊C8)—22no—
108C22⋊(C43⋊C8)D414yes—
109#13063236—22no—
110C4×C43⋊C8—22no—
111C22×D4×C43—21no—
112C22×D4×C43C2311yescharacteristic
113C23×C4×C43C2311yescharacteristic
114#121×C43—22no—
115#121×C43—22no—
116#117×C43—22no—
117#117×C43—22no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—24no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—81no—
146C23×D43—81no—
147C23×D43—81no—
148C23×D43—81no—
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—42no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43#4112yes—
172C22×C4×C43C2411yescharacteristic
173C22×Dic43—21no—
174C22×Dic43—21no—
175C2×D172—24no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—44no—
187C2×D172—44no—
188C2×D172—44no—
189C2×D172—44no—
190C2×D172—42no—
191C2×D172—42no—
192C2×D172#4112yes—
193C2×D172#4112yes—
194C4⋊C4×C43—22no—
195C4⋊C4×C43—22no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—81no—
203C4⋊C4×C43—81no—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—81no—
208C22⋊C4×C43—81no—
209C22⋊C4×C43—81no—
210C22⋊C4×C43—81no—
211C22⋊C4×C43—81no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C22⋊Dic43—42no—
217#10621882—44no—
218#10621882—44no—
219(C2×D43)⋊C4—81no—
220(C2×D43)⋊C4—81no—
221(C2×D43)⋊C4—81no—
222(C2×D43)⋊C4—81no—
223(C2×D43)⋊C4—81no—
224(C2×D43)⋊C4—81no—
225(C2×D43)⋊C4—81no—
226(C2×D43)⋊C4—81no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4×Dic43—42no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8C2×D412yes—
243C2×C43⋊C8C2×D412yes—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43#12112yes—
258C23×C43C22×D411yescharacteristic
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—48no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—84no—
275C22×D43—84no—
276C22×D43—84no—
277C22×D43—84no—
278C22×D43—84no—
279C22×D43—84no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43—84no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43#12112yes—
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325D172—22no—
326D172—22no—
327D172—22no—
328D172—22no—
329D172—48no—
330D172—41no—
331D172—41no—
332D172—41no—
333D172—41no—
334C43⋊C8—22no—
335C43⋊C8—22no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338#24512—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43C2×#12111yescharacteristic
354C22×C43#52511yescharacteristic
355C22×C43#53511yescharacteristic
356C22×C43#57611yescharacteristic
357C22×C43#57611yescharacteristic
358C22×C43#57611yescharacteristic
359C22×C43#57711yescharacteristic
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—816no—
367C2×D43—81no—
368C2×D43—81no—
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43—81no—
373C2×D43—81no—
374C2×D43—81no—
375C4×C43—22no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—81no—
381C4×C43—81no—
382C4×C43—81no—
383C4×C43#54611yescharacteristic
384C4×C43#54611yescharacteristic
385C4×C43#55111yescharacteristic
386C4×C43#55111yescharacteristic
387Dic43—81no—
388Dic43—81no—
389C2×#447—431no—
390C2×#433—431no—
391#2624D4311yescharacteristic, complemented
392#2309—431no—
393#2067—431no—
394#2065—431no—
395#2054—431no—
396#2054—431no—
397#1972—431no—
398#1970—431no—
399#1936—431no—
400#1934—431no—
401#1875—431no—
402#1854—431no—
403#1786—431no—
404C2×C43—42no—
405C2×C43—161no—
406C2×C43#241111yescharacteristic
407C2×C43#305811yescharacteristic
408C2×C43#306211yescharacteristic
409C2×C43#311811yescharacteristic
410C2×C43#312211yescharacteristic
411C2×C43#322011yescharacteristic
412C2×C43#322411yescharacteristic
413D43—82no—
414D43—82no—
415C23×D4—431no—
416C22×D8—431no—
417C22×D8—431no—
418C2×#121C2×D4311yescharacteristic
419C2×#117—431no—
420C2×#117C2×D4311yescharacteristic
421#447—864no—
422#433—864no—
423C2×#107—431no—
424C2×#106—431no—
425C2×C4⋊C8—431no—
426C2×C4⋊C8—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×#97—431no—
438C2×C4×C8—431no—
439#399—21no—
440#397—21no—
441#394—21no—
442#394—21no—
443#390—431no—
444#390—431no—
445#390—431no—
446#390—431no—
447#390—861no—
448#390—861no—
449#390C2×D4311yescharacteristic, complemented
450#390C2×D4311yescharacteristic, complemented
451#389C2×D4311yescharacteristic, complemented
452#389C2×D4311yescharacteristic, complemented
453#380C2×D4311yescharacteristic
454#379—861no—
455#379—861no—
456#340—431no—
457#340—431no—
458#340—431no—
459#340—431no—
460C43#2451211yescharacteristic, complemented, Sylow
461C25—861no—
462C22×D4—21no—
463C22×D4—431no—
464C22×D4—431no—
465C22×D4—862no—
466C22×D4—862no—
467C22×D4—862no—
468C22×D4—862no—
469C22×D4—861no—
470C22×D4—1721no—
471C22×D4—1721no—
472C22×D4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C2×D8—862no—
475C2×D8—862no—
476C2×D8—862no—
477C2×D8—862no—
478C2×D8—1721no—
479C2×D8—1721no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8—431no—
483C22×C8—431no—
484#121—22no—
485#121—22no—
486#117—22no—
487#117—22no—
488#117—1721no—
489#117—1721no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4C22⋊D4311yescharacteristic
495C2×C4⋊C4C22⋊D4311yescharacteristic
496C2×C4⋊C4C22×D4311yescharacteristic
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4C22⋊D4311yescharacteristic
515C2×C22⋊C4C22⋊D4311yescharacteristic
516C2×C42—861no—
517C2×C42C22×D4311yescharacteristic
518C2×C42C22×D4311yescharacteristic
519#107—1721no—
520#106—1721no—
521C4⋊C8—862no—
522C4⋊C8—862no—
523#102—862no—
524#102—862no—
525#102—862no—
526#102—862no—
527#102—1721no—
528#102—1721no—
529#102—1721no—
530#102—1721no—
531C22⋊C8—434no—
532C22⋊C8—862no—
533#97—862no—
534C4×C8—862no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24—864no—
540C24—861no—
541C24—861no—
542C24—3441no—
543C24—3441no—
544C24—3441no—
545C24—3441no—
546C24—1722no—
547C24—1722no—
548C24C2×C22⋊D4311yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—432no—
559C2×D4—432no—
560C2×D4—864no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—1724no—
572C2×D4—1724no—
573C2×D4—1724no—
574C2×D4—1724no—
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—861no—
585C22×C4—861no—
586C22×C4D4×D4312yes—
587C22×C4#1062190012yes—
588C22×C4C2×C22⋊D4311yescharacteristic
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C2×C22⋊D4311yescharacteristic
592C22×C4C2×C22⋊D4311yescharacteristic
593C22×C4C23×D4311yescharacteristic
594D8—1724no—
595D8—1724no—
596C2×C8—432no—
597C2×C8—432no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—81no—
617C4⋊C4—81no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—3441no—
631C22⋊C4—3441no—
632C22⋊C4—3441no—
633C22⋊C4—3441no—
634C22⋊C4—3441no—
635C22⋊C4—3441no—
636C22⋊C4—3441no—
637C22⋊C4—3441no—
638C22⋊C4—1722no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—1722no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—862no—
658C23—862no—
659C23—3444no—
660C23—3444no—
661C23—3444no—
662C23—3444no—
663C23—3444no—
664C23—3444no—
665C23—1728no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23—1721no—
672C23—1721no—
673C23—1721no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23#1306329712yes—
679C23C22×C22⋊D4311yescharacteristic
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—862no—
686D4—862no—
687D4—862no—
688D4—862no—
689D4—1728no—
690D4—1721no—
691D4—1721no—
692D4—1721no—
693D4—1721no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4#1306329712yes—
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4#41×D4311yescharacteristic
730C2×C4#41×D4311yescharacteristic
731C2×C4C2×#1062190011yescharacteristic
732C2×C4#1306337111yescharacteristic
733C2×C4#1306337111yescharacteristic
734C8—862no—
735C8—862no—
736C8—1721no—
737C8—1721no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—34416no—
753C22—3441no—
754C22—3441no—
755C22—3441no—
756C22—3441no—
757C22—3441no—
758C22—3441no—
759C22—3441no—
760C22—3441no—
761C22—1722no—
762C22—1722no—
763C22—1722no—
764C22—1722no—
765C22—1722no—
766C22—1722no—
767C22C2×#1306329711yescharacteristic
768C22#1458340611yescharacteristic
769C22#1458346311yescharacteristic
770C22#1458370211yescharacteristic
771C22#1458370211yescharacteristic
772C22#1458370211yescharacteristic
773C22#1458370711yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—3441no—
783C4—3441no—
784C4#1458354111yescharacteristic
785C4#1458354111yescharacteristic
786C4#1458357211yescharacteristic
787C4#1458357211yescharacteristic
788C2—42no—
789C2—161no—
790C2—3442no—
791C2—3442no—
792C2#1913798111yescharacteristic
793C2#1914424011yescharacteristic
794C2#1914427711yescharacteristic
795C2#1914477311yescharacteristic
796C2#1914483311yescharacteristic
797C2#1914563911yescharacteristic
798C2#1914568311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2624C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
hypercenter#2624D43
hypocenterC43#24512
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2624

Complements

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

NH ≅ G/Ntype
2. C2×#14582960C2semidirect
3. #19137175C2semidirect
4. #19135980C2semidirect
5. #19135966C2semidirect
6. #19135905C2semidirect
7. #19135905C2semidirect
8. #19135470C2semidirect
9. #19135460C2semidirect
10. #19135291C2semidirect
11. #19135277C2semidirect
12. #19134918C2semidirect
13. #19134792C2semidirect
14. #19134525C2semidirect
15. C43×#2624C2semidirect
22. C2×#13063258C22semidirect
23. C2×#13063256C22semidirect
24. C2×C4⋊(C43⋊C8)C22semidirect
25. C2×C4⋊(C43⋊C8)C22semidirect
26. C2×#13063246C22semidirect
27. C2×#13063246C22semidirect
36. C2×#13063236C22semidirect
37. C2×C4×C43⋊C8C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
56. C43×#390C22semidirect
57. C43×#390C22semidirect
58. C43×#389C22semidirect
59. C43×#389C22semidirect
391. #2624D43semidirect
449. #390C2×D43semidirect
450. #390C2×D43semidirect
451. #389C2×D43semidirect
452. #389C2×D43semidirect
460. C43#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#145830322
C2×#145829602
#191371752
#191359802
#191359662
#191359052
#191354702
#191354602
#191352912
#191352772
#191349182
#191347922
#191345252
C43×#26242
#2451243