Finite Group Databasebeta

← #25149900

Subgroups — #25149900

Order 11008.

1206 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic, complemented
2C2×#14583257C211yesmaximal, characteristic, complemented
3C2×#14583119C211yesmaximal, characteristic, complemented
4#19139531C211yesmaximal, characteristic
5#19135604C211yesmaximal, characteristic, complemented
6#19135603C211yesmaximal, characteristic, complemented
7#19135595C211yesmaximal, characteristic, complemented
8#19135545C211yesmaximal, characteristic, complemented
9#19135391C211yesmaximal, characteristic, complemented
10#19134913C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134901C211yesmaximal, characteristic, complemented
13#19134900C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#2000C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17#14583607—24no—
18#14583607—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063312C2211yescharacteristic
22C2×#13063305—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×#13063302—21no—
26C2×#13063301C2211yescharacteristic
27C2×#13063296C2211yescharacteristic
28C2×Q8×Dic43C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×(C22⋊D43)⋊C4—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32C2×C4⋊C4×D43C2211yescharacteristic
33#14583257—24no—
34#14583119—24no—
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582835—21no—
47#14582807—21no—
48#14582802—21no—
49#14582799—21no—
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43D411yescharacteristic
67C23×Dic43—21no—
68C22×C4×D43—21no—
69C22×C4×D43C2311yescharacteristic
70C2×#10621885—22no—
71C2×#10621885—41no—
72C2×#10621885—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063324—22no—
76#13063324D414yescomplemented
77#13063315—28no—
78#13063312—22no—
79#13063312—22no—
80#13063305—28no—
81#13063305—22no—
82#13063305—41no—
83#13063304—22no—
84#13063304—41no—
85#13063302—28no—
86#13063301—22no—
87#13063301—22no—
88#13063296—22no—
89#13063296—41no—
90Q8×Dic43—22no—
91Q8×Dic43D414yescomplemented
92C4×C22⋊D43—22no—
93C4×C22⋊D43—22no—
94(C22⋊D43)⋊C4—28no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43—22no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4D411yescharacteristic
108C4⋊C4×D43—22no—
109C4⋊C4×D43—22no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43D411yescharacteristic
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4D411yescharacteristic
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43C2311yescharacteristic
121Dic43⋊C8—22no—
122#13063250—22no—
123#13063250—22no—
124#13063249—22no—
125#13063248—22no—
126#13063246—22no—
127#13063246—22no—
128C22⋊(C43⋊C8)—41no—
129(C2×D43)⋊C8—41no—
130(C2×D43)⋊C8—41no—
131#13063235—22no—
132C43⋊#95—21no—
133C22×Q8×C43C2311yescharacteristic
134C22×D4×C43—21no—
135C22×D4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C2×SD16×C43—22no—
138C2×SD16×C43—41no—
139C2×SD16×C43—41no—
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C22⋊Q8×C43—22no—
143C22⋊Q8×C43—22no—
144#121×C43—22no—
145#121×C43—41no—
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151#103×C43—22no—
152#102×C43—22no—
153C22⋊C8×C43—41no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C23×D43C2×D411yescharacteristic
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43C2×D412yes—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—81no—
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×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2411yescharacteristic
183C2×C22⋊D43—22no—
184C2×C22⋊D43—22no—
185C2×C22⋊D43—22no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—81no—
189C22×Dic43—24no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—81no—
195C22×Dic43—81no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—24no—
206C2×C4×D43—81no—
207C2×C4×D43—81no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—24no—
215C2×Dic86—81no—
216C2×Dic86—81no—
217SD16×C43—44no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43C2×D412yes—
228C4⋊C4×C43#4112yes—
229C22⋊C4×C43—24no—
230C22⋊C4×C43—42no—
231C22⋊Dic43—22no—
232C22⋊Dic43—42no—
233C22⋊Dic43—42no—
234C22⋊Dic43—42no—
235C22⋊Dic43—42no—
236#10621885—44no—
237(C2×D43)⋊C4—24no—
238(C2×D43)⋊C4—22no—
239(C2×D43)⋊C4—42no—
240C4⋊Dic43—24no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—24no—
245C4⋊Dic43—42no—
246C4⋊Dic43C2×D412yes—
247C4⋊Dic43C2×D412yes—
248C4⋊Dic43#4112yes—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251Dic43⋊C4—24no—
252Dic43⋊C4—22no—
253Dic43⋊C4—42no—
254C4×Dic43—24no—
255C4×Dic43—81no—
256C4×Dic43C2×D412yes—
257C4×Dic43C2×D412yes—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43#13712yes—
278C23×C43C22×D411yescharacteristic
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43#13712yes—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—41no—
289Q8×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—84no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—22no—
300C2×C4×C43—21no—
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×C43C22×D411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43H(5,𝔽2)11yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C22⋊D43—28no—
318C22⋊D43—84no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—22no—
324C2×Dic43—21no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—21no—
328C2×Dic43—21no—
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—41no—
338C2×Dic43—84no—
339C2×Dic43#12012yes—
340C2×Dic43#12012yes—
341C4×D43—41no—
342C4×D43—41no—
343C4×D43—41no—
344C4×D43—41no—
345C4×D43—84no—
346Dic86—41no—
347Dic86—41no—
348Dic86—41no—
349Dic86—41no—
350Dic86—84no—
351C8×C43—41no—
352C8×C43—41no—
353C43⋊C8—41no—
354C43⋊C8—41no—
355#25579—431nomaximal, Sylow
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43C2×#12011yescharacteristic
371C22×C43#54611yescharacteristic
372C22×C43#54611yescharacteristic
373C22×C43C2×#13711yescharacteristic
374C22×C43C2×#13711yescharacteristic
375C22×C43#57611yescharacteristic
376C22×C43#57711yescharacteristic
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—41no—
384C4×C43—41no—
385C4×C43—42no—
386C4×C43—42no—
387C4×C43—42no—
388C4×C43#53211yescharacteristic
389C4×C43#53511yescharacteristic
390C4×C43#55011yescharacteristic
391C4×C43#55011yescharacteristic
392Dic43—22no—
393Dic43—22no—
394Dic43—41no—
395Dic43—42no—
396Dic43—42no—
397Dic43—42no—
398Dic43—81no—
399C2×#554—431no—
400C2×#489—431no—
401C2×#464—431no—
402#2540—431no—
403#2001—431no—
404#2001—431no—
405#2000—431no—
406#2000D4311yescharacteristic, complemented
407#1988—431no—
408#1955—431no—
409#1874—431no—
410#1874—431no—
411#1872—431no—
412#1872—431no—
413#1763—431no—
414C2×C43—42no—
415C2×C43—161no—
416C2×C43#243111yescharacteristic
417C2×C43#300411yescharacteristic
418C2×C43#301211yescharacteristic
419C2×C43#331411yescharacteristic
420C2×C43#331411yescharacteristic
421C2×C43#331611yescharacteristic
422C2×C43#331611yescharacteristic
423D43—42no—
424C22×Q16—431no—
425C22×SD16C2×D4311yescharacteristic
426#554—864no—
427#554—864no—
428C2×C4⋊Q8—431no—
429C2×#125—861no—
430C2×#124—431no—
431C2×C22⋊Q8—431no—
432C2×C22⋊Q8—431no—
433C2×C22⋊Q8—431no—
434C2×C22⋊Q8—861no—
435C2×C22⋊Q8—861no—
436C2×C22⋊Q8C2×D4311yescharacteristic
437C2×#121—431no—
438C2×#121C2×D4311yescharacteristic
439C2×C4×Q8—431no—
440C2×C4×D4—431no—
441C2×C4×D4—861no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444#489—864no—
445#464—864no—
446C2×C4⋊C8—431no—
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103C2×D4311yescharacteristic
452C2×#102—431no—
453C2×#102—431no—
454C2×#102C2×D4311yescharacteristic
455C2×C22⋊C8—431no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×C22⋊C8C2×D4311yescharacteristic
459C2×#97—431no—
460#399—861no—
461#392—861no—
462#390—861no—
463#390—861no—
464C4×C4⋊C4—431no—
465#340—431no—
466#340—431no—
467#340—431no—
468#340—431no—
469#340—431no—
470#340C2×D4311yescharacteristic
471C43#2557911yescharacteristic, complemented, Sylow
472C22×Q8—431no—
473C22×Q8—861no—
474C22×Q8C22×D4311yescharacteristic
475C22×D4—21no—
476C22×D4—431no—
477C22×D4—861no—
478C22×D4C22×D4311yescharacteristic
479C23×C4—431no—
480C23×C4—861no—
481C23×C4—861no—
482C23×C4C22×D4311yescharacteristic
483C2×Q16—862no—
484C2×Q16—1721no—
485C2×Q16—1721no—
486C2×SD16—22no—
487C2×SD16—41no—
488C2×SD16—41no—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8C22×D4311yescharacteristic
492C22×C8C22×D4311yescharacteristic
493C4⋊Q8—434no—
494C4⋊Q8—862no—
495#125—868no—
496#124—862no—
497#124—862no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—868no—
501C22⋊Q8—868no—
502C22⋊Q8—862no—
503C22⋊Q8—862no—
504C22⋊Q8—862no—
505C22⋊Q8—862no—
506C22⋊Q8—1721no—
507C22⋊Q8—1721no—
508#121—22no—
509#121—41no—
510#121—862no—
511#121—1721no—
512C4×Q8—434no—
513C4×Q8—862no—
514C4×D4—862no—
515C4×D4—862no—
516C4×D4—868no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—862no—
523C2×C4⋊C4—862no—
524C2×C4⋊C4—862no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—862no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C42—431no—
546C2×C42—861no—
547C2×C42—861no—
548C4⋊C8—862no—
549#103—22no—
550#103—862no—
551#103—862no—
552#103—862no—
553#103—862no—
554#102—22no—
555#102—862no—
556#102—862no—
557C22⋊C8—41no—
558C22⋊C8—1721no—
559C22⋊C8—1721no—
560C22⋊C8—1721no—
561#97—862no—
562#95—861no—
563C24—21no—
564C24—431no—
565C24D4×D4311yescharacteristic
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—864no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8—861no—
576C2×Q8—861no—
577C2×Q8—861no—
578C2×Q8—3441no—
579C2×Q8—3441no—
580C2×Q8D4×D4312yes—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—862no—
593C2×D4—3441no—
594C2×D4—1722no—
595C2×D4—1722no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—864no—
609C22×C4—864no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—3441no—
621C22×C4—3441no—
622C22×C4—3441no—
623C22×C4—3441no—
624C22×C4D4×D4311yescharacteristic
625C22×C4C23×D4311yescharacteristic
626Q16—1724no—
627SD16—44no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—432no—
644C4⋊C4—432no—
645C4⋊C4—432no—
646C4⋊C4—862no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—1722no—
656C4⋊C4—1722no—
657C4⋊C4D4×D4312yes—
658C4⋊C4#1062190012yes—
659C22⋊C4—24no—
660C22⋊C4—42no—
661C22⋊C4—862no—
662C22⋊C4—864no—
663C22⋊C4—862no—
664C22⋊C4—1722no—
665C22⋊C4—1722no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C42—432no—
670C42—432no—
671C42—864no—
672C42—3441no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—432no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—861no—
693C23#1306335412yes—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—41no—
698Q8—41no—
699Q8—3444no—
700Q8—1721no—
701Q8—1721no—
702Q8—1721no—
703Q8—1721no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—84no—
709D4—868no—
710D4—3444no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
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—432no—
728C2×C4—432no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—862no—
738C2×C4—861no—
739C2×C4—3444no—
740C2×C4—3444no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4C2×D4×D4311yescharacteristic
755C2×C4C2×D4×D4311yescharacteristic
756C2×C4#41×D4311yescharacteristic
757C2×C4C2×#1062190011yescharacteristic
758C2×C4#1306337011yescharacteristic
759C2×C4#1306337011yescharacteristic
760C8—41no—
761C8—41no—
762C8—1721no—
763C8—1721no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—862no—
779C22—862no—
780C22—862no—
781C22—1721no—
782C22—1721no—
783C22—1721no—
784C22—1721no—
785C22#120×D4311yescharacteristic
786C22#1458353611yescharacteristic
787C22#1458353811yescharacteristic
788C22#137×D4311yescharacteristic
789C22C2×#1306335411yescharacteristic
790C22#1458370311yescharacteristic
791C22#1458370611yescharacteristic
792C4—41no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—862no—
797C4—862no—
798C4—3441no—
799C4—1721no—
800C4—1722no—
801C4—1722no—
802C4—1722no—
803C4#1458344411yescharacteristic
804C4#1458346411yescharacteristic
805C4#1458356711yescharacteristic
806C4#1458356911yescharacteristic
807C2—42no—
808C2—161no—
809C2—1722no—
810C2#1913820911yescharacteristic
811C2#1914382611yescharacteristic
812C2#1914389711yescharacteristic
813C2#1914667111yescharacteristic
814C2#1914668011yescharacteristic
815C2#1914669911yescharacteristic
816C2#1914671211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2000C2
socleC23×C43C22×D4
prime radical#19139531C2
hypercenter#2000D43
hypocenterC43#25579
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#14583607C2semidirect
2. C2×#14583257C2semidirect
3. C2×#14583119C2semidirect
5. #19135604C2semidirect
6. #19135603C2semidirect
7. #19135595C2semidirect
8. #19135545C2semidirect
9. #19135391C2semidirect
10. #19134913C2semidirect
11. #19134909C2semidirect
12. #19134901C2semidirect
13. #19134900C2semidirect
14. #19134427C2semidirect
15. C43×#2000C2semidirect
76. #13063324D4semidirect
91. Q8×Dic43D4semidirect
406. #2000D43semidirect
471. C43#25579semidirect

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145832572
C2×#145831192
#191395312
#191356042
#191356032
#191355952
#191355452
#191353912
#191349132
#191349092
#191349012
#191349002
#191344272
C43×#20002
#2557943