Finite Group Databasebeta

← #25149685

Subgroups — #25149685

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583606C211yesmaximal, characteristic, complemented
2C2×#14583210C211yesmaximal, characteristic, complemented
3C2×#14583143C211yesmaximal, characteristic, complemented
4#19135923C211yesmaximal, characteristic, complemented
5#19135798C211yesmaximal, characteristic, complemented
6#19135731C211yesmaximal, characteristic, complemented
7#19135598C211yesmaximal, characteristic, complemented
8#19134953C211yesmaximal, characteristic, complemented
9#19134913C211yesmaximal, characteristic, complemented
10#19134907C211yesmaximal, characteristic, complemented
11#19134893C211yesmaximal, characteristic, complemented
12#19134848C211yesmaximal, characteristic, complemented
13#19134782C211yesmaximal, characteristic, complemented
14#19134316C211yesmaximal, characteristic, complemented
15C43×#2414C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18#14583606—24no—
19#14583606—24no—
20C2×#13063325C2211yescharacteristic
21C2×#13063316—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063302—21no—
25C2×#13063302—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×D4×Dic43—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30#14583210—24no—
31#14583143—24no—
32C2×#13063258C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#121×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C43×#394—21no—
57C43×#392—21no—
58C43×#390—21no—
59C43×#390C2211yescharacteristic
60C43×#389C2211yescharacteristic
61C43×#388—21no—
62C43×#380C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063325—22no—
78#13063325—22no—
79#13063316—28no—
80#13063304—22no—
81#13063304—22no—
82#13063304—22no—
83#13063304D414yescomplemented
84#13063302—28no—
85#13063302—28no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88D4×Dic43—28no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—22no—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43D414yescomplemented
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C4×Dic43—21no—
105#13063258—22no—
106#13063258—22no—
107#13063258—22no—
108#13063248—22no—
109#13063248—22no—
110#13063248—41no—
111#13063246—22no—
112#13063246—22no—
113#13063246—22no—
114C22⋊(C43⋊C8)—22no—
115C22⋊(C43⋊C8)—22no—
116C22⋊(C43⋊C8)—41no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C22×D4×C43D411yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123#121×C43—22no—
124#121×C43—22no—
125#121×C43—22no—
126#121×C43—41no—
127C4×D4×C43—22no—
128C4×D4×C43—22no—
129#117×C43—22no—
130#117×C43—41no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43D411yescharacteristic
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C42×C43—21no—
145C2×C42×C43C2311yescharacteristic
146#95×C43—21no—
147#95×C43—21no—
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C24×C43C2×D411yescharacteristic
151C2×D4×C43—22no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
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—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—81no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C22×C4×C43—21no—
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×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43C2×D412yes—
180C22×C4×C43C2×D412yes—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C22×Dic43—24no—
187C22×Dic43—24no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—81no—
193C22×Dic43—81no—
194C22×Dic43—81no—
195C22×Dic43—81no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—24no—
202C2×Dic86—81no—
203C2×Dic86—81no—
204C2×Dic86C2×D412yes—
205C4⋊C4×C43—22no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—81no—
212C4⋊C4×C43#4112yes—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—42no—
219C22⋊C4×C43—81no—
220C22⋊C4×C43—81no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—42no—
224C22⋊Dic43—24no—
225C22⋊Dic43—24no—
226#10621883—44no—
227C4⋊Dic43—24no—
228C4⋊Dic43—24no—
229C4⋊Dic43—24no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43C2×D412yes—
234C4⋊Dic43C2×D412yes—
235C4⋊Dic43C2×D412yes—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239C4×Dic43—24no—
240#10621877—44no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8#4112yes—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43#12012yes—
273C23×C43#13712yes—
274C23×C43C22×D411yescharacteristic
275D4×C43—28no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—84no—
281D4×C43—84no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
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—22no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
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#12012yes—
310C2×C4×C43#13712yes—
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43H(5,𝔽2)11yescharacteristic
316C2×C4×C432−1+411yescharacteristic
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
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—84no—
330C2×Dic43—84no—
331Dic86—22no—
332Dic86—22no—
333Dic86—41no—
334Dic86—41no—
335Dic86—84no—
336C43⋊C8—22no—
337C43⋊C8—41no—
338C43⋊C8—41no—
339C43⋊C8—41no—
340#25559—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43C2×#12011yescharacteristic
363C22×C43#54611yescharacteristic
364C22×C43#54711yescharacteristic
365C22×C43C2×#13711yescharacteristic
366C22×C43C2×#13711yescharacteristic
367C22×C43#57611yescharacteristic
368C22×C43#57611yescharacteristic
369C4×C43—22no—
370C4×C43—22no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43—42no—
374C4×C43—81no—
375C4×C43—81no—
376C4×C43#53211yescharacteristic
377C4×C43#53711yescharacteristic
378C4×C43#54611yescharacteristic
379C4×C43#54711yescharacteristic
380Dic43—42no—
381Dic43—42no—
382Dic43—42no—
383Dic43—42no—
384C2×#554—431no—
385C2×#480—431no—
386C2×#468—431no—
387#2414D4311yescharacteristic
388#2057—431no—
389#2036—431no—
390#2023—431no—
391#2000—431no—
392#1880—431no—
393#1874—431no—
394#1873—431no—
395#1870—431no—
396#1863—431no—
397#1852—431no—
398#1736—431no—
399C2×C43—42no—
400C2×C43—42no—
401C2×C43—161no—
402C2×C43#243011yescharacteristic
403C2×C43#300411yescharacteristic
404C2×C43#300811yescharacteristic
405C2×C43#331411yescharacteristic
406C2×C43#333311yescharacteristic
407C2×C43#334611yescharacteristic
408C2×C43#335711yescharacteristic
409C22×SD16—431no—
410C22×M16—431no—
411#554—864no—
412#554—864no—
413C2×C4⋊Q8—431no—
414C2×#125—861no—
415C2×C22⋊Q8—431no—
416C2×C22⋊Q8—431no—
417C2×C22⋊Q8—861no—
418C2×C22⋊Q8—861no—
419C2×#121C2×D4311yescharacteristic
420C2×#121C2×D4311yescharacteristic
421C2×C4×Q8—431no—
422C2×C4×D4—861no—
423C2×C4×D4C2×D4311yescharacteristic
424C2×#117C2×D4311yescharacteristic
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427#480—864no—
428#468—864no—
429C2×#107—431no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441#394—21no—
442#392—21no—
443#390—21no—
444#390C2×D4311yescharacteristic
445#389C2×D4311yescharacteristic
446#388—21no—
447#380C2×D4311yescharacteristic
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452#340—431no—
453#340—431no—
454#336—431no—
455#336—431no—
456C43#2555911yescharacteristic, complemented, Sylow
457C22×Q8—431no—
458C22×Q8—861no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C22⋊D4311yescharacteristic
462C22×D4C22×D4311yescharacteristic
463C23×C4—861no—
464C23×C4—861no—
465C23×C4C22×D4311yescharacteristic
466C23×C4C22×D4311yescharacteristic
467C2×SD16—862no—
468C2×SD16—862no—
469C2×SD16—1721no—
470C2×M16—862no—
471C2×M16—862no—
472C2×M16—1721no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8—431no—
476C22×C8—431no—
477C4⋊Q8—862no—
478C4⋊Q8—862no—
479#125—868no—
480C22⋊Q8—434no—
481C22⋊Q8—868no—
482C22⋊Q8—868no—
483C22⋊Q8—862no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490C4×Q8—862no—
491C4×Q8—862no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—868no—
495#117—22no—
496#117—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—434no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—862no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4C22⋊D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4C22⋊D4311yescharacteristic
524C2×C22⋊C4C22⋊D4311yescharacteristic
525C2×C42—21no—
526C2×C42—861no—
527C2×C42C22×D4311yescharacteristic
528#107—862no—
529#107—862no—
530#107—862no—
531#103—862no—
532#103—862no—
533#103—1721no—
534#102—862no—
535#102—862no—
536#102—862no—
537C22⋊C8—862no—
538C22⋊C8—862no—
539C22⋊C8—1721no—
540#95—21no—
541#95—21no—
542C24—21no—
543C24C2×C22⋊D4311yescharacteristic
544C24C2×C22⋊D4311yescharacteristic
545C2×Q8—432no—
546C2×Q8—864no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—3441no—
553C2×Q8—3441no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—864no—
583C22×C4—864no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—3441no—
589C22×C4—3441no—
590C22×C4—3441no—
591C22×C4—3441no—
592C22×C4D4×D4312yes—
593C22×C4D4×D4312yes—
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C2×C22⋊D4311yescharacteristic
598C22×C4C23×D4311yescharacteristic
599SD16—1724no—
600M16—1724no—
601C2×C8—432no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—81no—
620C4⋊C4—432no—
621C4⋊C4—432no—
622C4⋊C4—432no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4#1062190012yes—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—864no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#1306329312yes—
667C23#1306335512yes—
668C23C22×C22⋊D4311yescharacteristic
669Q8—862no—
670Q8—862no—
671Q8—3444no—
672Q8—1721no—
673Q8—1721no—
674D4—28no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—84no—
680D4—84no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
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—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—3444no—
713C2×C4—3444no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4#1306329312yes—
723C2×C4#1306335512yes—
724C2×C4C2×D4×D4311yescharacteristic
725C2×C4C2×D4×D4311yescharacteristic
726C2×C4#41×D4311yescharacteristic
727C2×C4C2×#1062190011yescharacteristic
728C2×C4#1306337011yescharacteristic
729C2×C4#1306337211yescharacteristic
730C8—862no—
731C8—1721no—
732C8—1721no—
733C8—1721no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
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—
755C22C2×#1306329311yescharacteristic
756C22#1458354311yescharacteristic
757C22#1458354811yescharacteristic
758C22C2×#1306335511yescharacteristic
759C22C2×#1306335511yescharacteristic
760C22#1458370211yescharacteristic
761C22#1458370211yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—42no—
766C4—41no—
767C4—81no—
768C4—81no—
769C4—1722no—
770C4—1722no—
771C4—1722no—
772C4—1722no—
773C4#1458344411yescharacteristic
774C4#1458347611yescharacteristic
775C4#1458353811yescharacteristic
776C4#1458354911yescharacteristic
777C2—42no—
778C2—42no—
779C2—161no—
780C2#1913820111yescharacteristic
781C2#1914382811yescharacteristic
782C2#1914386111yescharacteristic
783C2#1914667611yescharacteristic
784C2#1914693311yescharacteristic
785C2#1914708011yescharacteristic
786C2#1914721511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2414C2
socleC23×C43C22×D4
hypercenter#2414D43
hypocenterC43#25559
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2414

Complements

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

NH ≅ G/Ntype
1. C2×#14583606C2semidirect
2. C2×#14583210C2semidirect
3. C2×#14583143C2semidirect
4. #19135923C2semidirect
5. #19135798C2semidirect
6. #19135731C2semidirect
7. #19135598C2semidirect
8. #19134953C2semidirect
9. #19134913C2semidirect
10. #19134907C2semidirect
11. #19134893C2semidirect
12. #19134848C2semidirect
13. #19134782C2semidirect
14. #19134316C2semidirect
83. #13063304D4semidirect
95. C2×C4⋊Dic43D4semidirect
456. C43#25559semidirect

Maximal subgroups

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

subgroupindex
C2×#145836062
C2×#145832102
C2×#145831432
#191359232
#191357982
#191357312
#191355982
#191349532
#191349132
#191349072
#191348932
#191348482
#191347822
#191343162
C43×#24142
#2555943