Finite Group Databasebeta

← #25140166

Subgroups — #25140166

Order 11008.

1168 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×#14583212C211yesmaximal, characteristic, complemented
2C2×#14582903C211yesmaximal, characteristic, complemented
3#19137951C211yesmaximal, characteristic
4#19136119C211yesmaximal, characteristic, complemented
5#19136009C211yesmaximal, characteristic, complemented
6#19135784C211yesmaximal, characteristic, complemented
7#19135784C211yesmaximal, characteristic, complemented
8#19135222C211yesmaximal, characteristic, complemented
9#19135215C211yesmaximal, characteristic, complemented
10#19134912C211yesmaximal, characteristic, complemented
11#19134893C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic, complemented
14#19134525C211yesmaximal, characteristic, complemented
15C43×#2352C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063293—21no—
21#14583212—24no—
22C2×#13063258C2211yescharacteristic, complemented
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063256C2211yescharacteristic, complemented
25C2×#13063256C2211yescharacteristic, complemented
26#14582903—24no—
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
37C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
38#14582816—21no—
39#14582808—21no—
40#14582801C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582754—21no—
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C2×C4×D4×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic, complemented
53C43×#388—21no—
54C43×#387—21no—
55C43×#386—21no—
56C43×#382C2211yescharacteristic, complemented
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic, complemented
59C4×C4⋊C4×C43C2211yescharacteristic, complemented
60C4×C22⋊C4×C43—21no—
61C24×D43—21no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—21no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C2×#10621877—22no—
74C2×#10621877—22no—
75C2×#10621877—41no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063299—22no—
81#13063299—22no—
82#13063299—41no—
83#13063299—41no—
84#13063293—44no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C22⋊Dic43—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—
94#13063258—22no—
95#13063258—22no—
96#13063256—41no—
97#13063256—41no—
98#13063245—22no—
99#13063245—22no—
100#13063245—22no—
101#13063245—22no—
102#13063245—22no—
103#13063245—41no—
104#13063245—41no—
105#13063245D414yescomplemented
106C22⋊(C43⋊C8)—22no—
107C22⋊(C43⋊C8)—22no—
108C22⋊(C43⋊C8)—41no—
109C43⋊#95—21no—
110C22×D4×C43D411yescharacteristic
111C23×C4×C43—21no—
112C23×C4×C43C2311yescharacteristic
113C23×C4×C43C2311yescharacteristic
114C4×D4×C43—22no—
115C4×D4×C43—22no—
116#117×C43—22no—
117#117×C43—41no—
118C2×C4⋊C4×C43—22no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—41no—
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43C2×D411yescharacteristic
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—42no—
148C23×D43—81no—
149C23×D43—81no—
150C2×D4×C43—22no—
151C2×D4×C43—22no—
152C2×D4×C43—41no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
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×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—42no—
168C22×C4×C43—42no—
169C22×C4×C43—81no—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43#4112yes—
175C22×C4×C43#4112yes—
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—42no—
178C2×C22⋊D43—42no—
179C2×C22⋊D43—42no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—81no—
182C2×C22⋊D43—81no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—28no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—42no—
197C2×D172—42no—
198C2×D172—44no—
199C2×D172—44no—
200C2×D172—44no—
201C2×D172—42no—
202C2×D172C2×D412yes—
203C2×D172#4112yes—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43C2×D412yes—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—81no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43—42no—
222C42×C43—81no—
223C22⋊Dic43—42no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—81no—
229(C2×D43)⋊C4—81no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234#10621877—44no—
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⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C2×D412yes—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43#12312yes—
260C23×C43AGL(1,ℤ/8)12yes—
261C23×C43C22×D411yescharacteristic
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—48no—
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—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—84no—
278C22×D43—84no—
279C22×D43—84no—
280C22×D43—84no—
281C22×D43—84no—
282C22×D43—84no—
283D4×C43—44no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
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×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—84no—
316C2×C4×C43#12312yes—
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C22⋊D43—84no—
324C22⋊D43—84no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331D172—22no—
332D172—22no—
333D172—22no—
334D172—22no—
335D172—48no—
336D172—41no—
337D172—41no—
338D172—41no—
339D172—41no—
340C43⋊C8—22no—
341C43⋊C8—41no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344#24882—431nomaximal, Sylow
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43C2×#12311yescharacteristic
360C22×C43D4211yescharacteristic
361C22×C43#54611yescharacteristic
362C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C43#57511yescharacteristic
364C22×C43#57611yescharacteristic
365C22×C43#57711yescharacteristic
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—816no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C2×D43—81no—
377C2×D43—81no—
378C2×D43—81no—
379C2×D43—81no—
380C2×D43—81no—
381C4×C43—22no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—42no—
386C4×C43—81no—
387C4×C43—81no—
388C4×C43—81no—
389C4×C43#52511yescharacteristic
390C4×C43#53811yescharacteristic
391C4×C43#54611yescharacteristic
392C4×C43#55111yescharacteristic
393Dic43—81no—
394Dic43—81no—
395C2×#480—431no—
396C2×#418—431no—
397#2408—431no—
398#2352D4311yescharacteristic, complemented
399#2092—431no—
400#2073—431no—
401#2034—431no—
402#2034—431no—
403#1926—431no—
404#1925—431no—
405#1874—431no—
406#1870—431no—
407#1854—431no—
408#1809—431no—
409#1786—431no—
410C2×C43—42no—
411C2×C43—42no—
412C2×C43#241811yescharacteristic
413C2×C43#309411yescharacteristic
414C2×C43#309611yescharacteristic
415C2×C43#326411yescharacteristic
416C2×C43#327511yescharacteristic
417C2×C43#331011yescharacteristic
418C2×C43#332211yescharacteristic
419D43—82no—
420D43—82no—
421C23×D4—431no—
422C22×M16—431no—
423C2×#121—431no—
424C2×#121—431no—
425C2×#120—861no—
426C2×C4×D4C2×D4311yescharacteristic
427C2×#117C2×D4311yescharacteristic
428C22×C4⋊C4C2×D4311yescharacteristic, complemented
429#480—864no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#106—431no—
433C2×#106—431no—
434#418—864no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446#394—861no—
447#392—861no—
448#390—431no—
449#390—431no—
450#388—21no—
451#387—21no—
452#386—21no—
453#382C2×D4311yescharacteristic, complemented
454#380—431no—
455#380C2×D4311yescharacteristic
456#380C2×D4311yescharacteristic, complemented
457#379—861no—
458C4×C4⋊C4C2×D4311yescharacteristic, complemented
459C4×C22⋊C4—21no—
460#340—431no—
461#340—431no—
462#340—431no—
463#340—431no—
464#336—431no—
465#336—431no—
466C43#2488211yescharacteristic, complemented, Sylow
467C25—861no—
468C22×D4—431no—
469C22×D4—431no—
470C22×D4—862no—
471C22×D4—862no—
472C22×D4—861no—
473C22×D4—861no—
474C22×D4—862no—
475C22×D4—862no—
476C22×D4—861no—
477C22×D4—1721no—
478C22×D4—1721no—
479C22×D4C22⋊D4311yescharacteristic
480C23×C4—21no—
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483C2×M16—862no—
484C2×M16—862no—
485C2×M16—1721no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8—431no—
489C22×C8—431no—
490#121—862no—
491#121—862no—
492#121—1721no—
493#121—1721no—
494#120—1724no—
495C4×D4—22no—
496C4×D4—22no—
497#117—22no—
498#117—41no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4C22⋊D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
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⋊C4C22⋊D4311yescharacteristic
520C2×C22⋊C4C22⋊D4311yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42C22×D4311yescharacteristic
524#107—862no—
525#107—862no—
526#106—1721no—
527#106—1721no—
528#102—434no—
529#102—862no—
530#102—862no—
531#102—862no—
532#102—862no—
533#102—862no—
534#102—1721no—
535#102—1721no—
536C22⋊C8—862no—
537C22⋊C8—862no—
538C22⋊C8—1721no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—861no—
545C24—861no—
546C24—861no—
547C24—3441no—
548C24—3441no—
549C24—1722no—
550C24—1722no—
551C24—1722no—
552C24—1722no—
553C24—1722no—
554C24C2×C22⋊D4311yescharacteristic
555C24C2×C22⋊D4311yescharacteristic
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—41no—
559C2×D4—432no—
560C2×D4—432no—
561C2×D4—868no—
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—861no—
572C2×D4—3441no—
573C2×D4—3441no—
574C2×D4—1724no—
575C2×D4—1724no—
576C2×D4—1722no—
577C2×D4—1722no—
578C2×D4—1724no—
579C2×D4—1722no—
580C2×D4—1722no—
581C2×D4—1722no—
582C2×D4—1722no—
583C2×D4—1722no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—81no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4#1062189812yes—
604C22×C4#1062189812yes—
605C22×C4C2×C22⋊D4311yescharacteristic
606C22×C4C2×C22⋊D4311yescharacteristic
607C22×C4C2×C22⋊D4311yescharacteristic
608C22×C4C2×C22⋊D4311yescharacteristic
609C22×C4C23×D4311yescharacteristic
610M16—1724no—
611C2×C8—432no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4D4×D4312yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—81no—
642C22⋊C4—3441no—
643C22⋊C4—3441no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—21no—
650C42—21no—
651C42—42no—
652C42—81no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—862no—
666C23—862no—
667C23—3444no—
668C23—3444no—
669C23—3444no—
670C23—3444no—
671C23—3444no—
672C23—3444no—
673C23—1728no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23—1721no—
682C23—1721no—
683C23—1721no—
684C23—1721no—
685C23—1721no—
686C23#1306330812yes—
687C23#1306335012yes—
688C23C22×C22⋊D4311yescharacteristic
689D4—44no—
690D4—862no—
691D4—862no—
692D4—862no—
693D4—862no—
694D4—3444no—
695D4—3444no—
696D4—1728no—
697D4—1721no—
698D4—1721no—
699D4—1721no—
700D4—1721no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4#1306330812yes—
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4#41×D4311yescharacteristic
742C2×C4C2×#1062189811yescharacteristic
743C2×C4C2×#1062189811yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337111yescharacteristic
746C8—862no—
747C8—1721no—
748C8—1721no—
749C8—1721no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—34416no—
765C22—3441no—
766C22—3441no—
767C22—3441no—
768C22—3441no—
769C22—3441no—
770C22—3441no—
771C22—3441no—
772C22—3441no—
773C22—1722no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22C2×#1306330811yescharacteristic
780C22D4×C22⋊D4311yescharacteristic
781C22#1458353711yescharacteristic
782C22C2×#1306335011yescharacteristic
783C22#1458369711yescharacteristic
784C22#1458370211yescharacteristic
785C22#1458370711yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—3441no—
795C4—3441no—
796C4#1458340811yescharacteristic
797C4#1458348211yescharacteristic
798C4#1458354511yescharacteristic
799C4#1458357811yescharacteristic
800C2—42no—
801C2—42no—
802C2—3442no—
803C2—3442no—
804C2#1913805111yescharacteristic
805C2#1914453511yescharacteristic
806C2#1914455311yescharacteristic
807C2#1914607611yescharacteristic
808C2#1914622711yescharacteristic
809C2#1914661011yescharacteristic
810C2#1914679011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2352C2
socleC23×C43C22×D4
prime radical#19137951C2
hypercenter#2352D43
hypocenterC43#24882
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
1. C2×#14583212C2semidirect
2. C2×#14582903C2semidirect
4. #19136119C2semidirect
5. #19136009C2semidirect
6. #19135784C2semidirect
7. #19135784C2semidirect
8. #19135222C2semidirect
9. #19135215C2semidirect
10. #19134912C2semidirect
11. #19134893C2semidirect
12. #19134794C2semidirect
13. #19134626C2semidirect
14. #19134525C2semidirect
15. C43×#2352C2semidirect
22. C2×#13063258C22semidirect
23. C2×#13063258C22semidirect
24. C2×#13063256C22semidirect
25. C2×#13063256C22semidirect
36. C2×C22⋊(C43⋊C8)C22semidirect
37. C2×C22⋊(C43⋊C8)C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
52. C22×C4⋊C4×C43C22semidirect
56. C43×#382C22semidirect
58. C43×#380C22semidirect
59. C4×C4⋊C4×C43C22semidirect
105. #13063245D4semidirect
398. #2352D43semidirect
428. C22×C4⋊C4C2×D43semidirect
453. #382C2×D43semidirect
456. #380C2×D43semidirect
458. C4×C4⋊C4C2×D43semidirect
466. C43#24882semidirect

Maximal subgroups

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

subgroupindex
C2×#145832122
C2×#145829032
#191379512
#191361192
#191360092
#191357842
#191352222
#191352152
#191349122
#191348932
#191347942
#191346262
#191345252
C43×#23522
#2488243