Finite Group Databasebeta

← #25135388

Subgroups — #25135388

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×#14582957C211yesmaximal, characteristic, complemented
3#19140385C211yesmaximal, characteristic, complemented
4#19137175C211yesmaximal, characteristic, complemented
5#19135984C211yesmaximal, characteristic, complemented
6#19135970C211yesmaximal, characteristic, complemented
7#19135904C211yesmaximal, characteristic, complemented
8#19135904C211yesmaximal, characteristic, complemented
9#19135468C211yesmaximal, characteristic, complemented
10#19135458C211yesmaximal, characteristic, complemented
11#19135290C211yesmaximal, characteristic, complemented
12#19135276C211yesmaximal, characteristic, complemented
13#19134794C211yesmaximal, characteristic, complemented
14#19134527C211yesmaximal, characteristic, complemented
15C43×#1875C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20#14583032—24no—
21#14582957—24no—
22C2×#13063258C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24C2×Dic43⋊C8C2211yescharacteristic, complemented
25C2×Dic43⋊C8C2211yescharacteristic, complemented
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063235C2211yescharacteristic, complemented
34C2×C8×Dic43C2211yescharacteristic, complemented
35#14582835—21no—
36#14582824—21no—
37#14582813—21no—
38#14582813—21no—
39#14582802C2211yescharacteristic, complemented
40#14582802C2211yescharacteristic, complemented
41#14582801—21no—
42#14582801—21no—
43#14582800C2211yescharacteristic
44#14582800C2211yescharacteristic
45#14582800C2211yescharacteristic
46#14582800C2211yescharacteristic
47#14582795C2211yescharacteristic, complemented
48#14582795C2211yescharacteristic, complemented
49#14582759C2211yescharacteristic
50#14582754—21no—
51#14582754—21no—
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54C2×#121×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic, complemented
57C2×#102×C43C2211yescharacteristic, complemented
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
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
79#13063284—22no—
80#13063284—22no—
81C2×C4⋊Dic43D411yescharacteristic
82C2×C4⋊Dic43D411yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43D411yescharacteristic
93C2×C22⋊Dic43D411yescharacteristic
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104#13063258—41no—
105#13063256—41no—
106Dic43⋊C8—22no—
107Dic43⋊C8—22no—
108#13063247—22no—
109#13063247—22no—
110#13063247—41no—
111#13063247—41no—
112#13063245—22no—
113#13063245—22no—
114C22⋊(C43⋊C8)D414yes—
115#13063235—22no—
116C8×Dic43—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×D4×C43—21no—
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125#121×C43—22no—
126#121×C43—22no—
127#117×C43—41no—
128#117×C43—41no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43—21no—
135#102×C43—41no—
136#102×C43—41no—
137C22⋊C8×C43—22no—
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×C43#4112yes—
168C22×C4×C43C2411yescharacteristic
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
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—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C42×C43—42no—
209C22⋊Dic43—22no—
210C22⋊Dic43—22no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213C22⋊Dic43—81no—
214C22⋊Dic43—81no—
215C22⋊Dic43—81no—
216#10621882—44no—
217#10621882—44no—
218(C2×D43)⋊C4—81no—
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—
226C4⋊Dic43—22no—
227C4⋊Dic43—22no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232Dic43⋊C4—81no—
233Dic43⋊C4—81no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—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—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—41no—
299C2×C4×C43—41no—
300C2×C4×C43#12112yes—
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
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—
334C8×C43—41no—
335C8×C43—41no—
336C43⋊C8—22no—
337C43⋊C8—22no—
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—81no—
377C4×C43—81no—
378C4×C43—81no—
379C4×C43#54611yescharacteristic
380C4×C43#54611yescharacteristic
381C4×C43#55111yescharacteristic
382C4×C43#55111yescharacteristic
383Dic43—41no—
384Dic43—41no—
385Dic43—41no—
386Dic43—41no—
387Dic43—81no—
388Dic43—81no—
389C2×#447—431no—
390C2×#433—431no—
391#2624—431no—
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#1875D4311yescharacteristic, complemented
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×#102C2×D4311yescharacteristic, complemented
434C2×#102C2×D4311yescharacteristic, complemented
435C2×C22⋊C8—431no—
436C2×C22⋊C8C2×D4311yescharacteristic
437C2×#97—431no—
438C2×C4×C8—431no—
439#399—861no—
440#397—861no—
441#394—861no—
442#394—861no—
443#390—431no—
444#390—431no—
445#390—431no—
446#390—431no—
447#390—431no—
448#390—431no—
449#390—861no—
450#390—861no—
451#389—431no—
452#389—431no—
453#380—431no—
454#379—861no—
455#379—861no—
456#340—431no—
457#340—431no—
458#340C2×D4311yescharacteristic, complemented
459#340C2×D4311yescharacteristic, complemented
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—861no—
469C22×D4—862no—
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×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484#121—22no—
485#121—22no—
486#117—41no—
487#117—41no—
488#117—862no—
489#117—862no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4C22×D4311yescharacteristic
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—431no—
502C2×C22⋊C4—431no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
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⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C42—21no—
517C2×C42—431no—
518C2×C42—431no—
519#107—1721no—
520#106—1721no—
521C4⋊C8—862no—
522C4⋊C8—862no—
523#102—41no—
524#102—41no—
525#102—862no—
526#102—862no—
527#102—862no—
528#102—862no—
529#102—1721no—
530#102—1721no—
531C22⋊C8—22no—
532C22⋊C8—434no—
533#97—862no—
534C4×C8—862no—
535#95—861no—
536#95—861no—
537#95—861no—
538C24—21no—
539C24—864no—
540C24—861no—
541C24—861no—
542C24—3441no—
543C24—3441no—
544C24—3441no—
545C24—3441no—
546C24—1722no—
547C24—1722no—
548C24D4×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—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4#1062189812yes—
591C22×C4D4×D4311yescharacteristic
592C22×C4D4×D4312yes—
593C22×C4C23×D4311yescharacteristic
594D8—1724no—
595D8—1724no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—432no—
603C2×C8—432no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—862no—
615C4⋊C4—862no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—3441no—
621C4⋊C4—3441no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—862no—
625C22⋊C4—862no—
626C22⋊C4—3441no—
627C22⋊C4—3441no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
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—3441no—
639C42—42no—
640C42—861no—
641C42—861no—
642C42—861no—
643C42—861no—
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#1306329812yes—
679C23C2×D4×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—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
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—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4#1306329812yes—
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4#41×D4311yescharacteristic
730C2×C4#41×D4311yescharacteristic
731C2×C4C2×#1062189811yescharacteristic
732C2×C4#1306337011yescharacteristic
733C2×C4#1306337011yescharacteristic
734C8—41no—
735C8—41no—
736C8—862no—
737C8—862no—
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×#1306329811yescharacteristic
768C22#1458340711yescharacteristic
769C22#1458346411yescharacteristic
770C22#1458370111yescharacteristic
771C22#1458370311yescharacteristic
772C22#1458370311yescharacteristic
773C22#1458370611yescharacteristic
774C4—22no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4—3441no—
779C4—3441no—
780C4—1721no—
781C4—1721no—
782C4—1721no—
783C4—1721no—
784C4#1458353811yescharacteristic
785C4#1458353811yescharacteristic
786C4#1458357811yescharacteristic
787C4#1458357811yescharacteristic
788C2—42no—
789C2—161no—
790C2—3442no—
791C2—3442no—
792C2#1913798311yescharacteristic
793C2#1914424211yescharacteristic
794C2#1914427811yescharacteristic
795C2#1914477411yescharacteristic
796C2#1914483411yescharacteristic
797C2#1914564311yescharacteristic
798C2#1914568711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1875C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
hypercenter#1875D43
hypocenterC43#24512
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. C2×#14582957C2semidirect
3. #19140385C2semidirect
4. #19137175C2semidirect
5. #19135984C2semidirect
6. #19135970C2semidirect
7. #19135904C2semidirect
8. #19135904C2semidirect
9. #19135468C2semidirect
10. #19135458C2semidirect
11. #19135290C2semidirect
12. #19135276C2semidirect
13. #19134794C2semidirect
14. #19134527C2semidirect
15. C43×#1875C2semidirect
22. C2×#13063258C22semidirect
23. C2×#13063256C22semidirect
24. C2×Dic43⋊C8C22semidirect
25. C2×Dic43⋊C8C22semidirect
33. C2×#13063235C22semidirect
34. C2×C8×Dic43C22semidirect
39. #14582802C22semidirect
40. #14582802C22semidirect
47. #14582795C22semidirect
48. #14582795C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
56. C2×#102×C43C22semidirect
57. C2×#102×C43C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
401. #1875D43semidirect
433. C2×#102C2×D43semidirect
434. C2×#102C2×D43semidirect
458. #340C2×D43semidirect
459. #340C2×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×#145829572
#191403852
#191371752
#191359842
#191359702
#191359042
#191354682
#191354582
#191352902
#191352762
#191347942
#191345272
C43×#18752
#2451243