Finite Group Databasebeta

← #25267533

Subgroups — #25267533

Order 11008.

1992 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140304C211yesmaximal, characteristic, complemented
2#19140285C212yesmaximal, complemented
3#19140273C211yesmaximal, characteristic, complemented
4#19139863C212yesmaximal, complemented
5#19139669C211yesmaximal, characteristic
6#19139440C212yesmaximal, complemented
7#19139410C212yesmaximal, complemented
8#19138787C212yesmaximal, complemented
9#19138757C212yesmaximal, complemented
10#19137887C211yesmaximal, characteristic, complemented
11#19137884C211yesmaximal, characteristic, complemented
12#19137838C212yesmaximal, complemented
13#19137142C211yesmaximal, characteristic, complemented
14#19137136C212yesmaximal, complemented
15#19137107C212yesmaximal, complemented
16#19137089C212yesmaximal, complemented
17#19137037C212yesmaximal, complemented
18C4×#13063283C212yesmaximal, complemented
19C43×#2593C211yesmaximal, characteristic, complemented
20C2×#13063312C2211yescharacteristic
21C2×#13063311C2212yes—
22C2×#13063298C2212yes—
23C2×#13063290C2211yescharacteristic
24C2×#13063290C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×(C22⋊D43)⋊C4C2212yes—
28C2×(C22⋊D43)⋊C4C2212yes—
29C2×#13063283C2212yes—
30C2×#13063283C2212yes—
31C2×#13063281C2212yes—
32C2×C42×D43C2212yes—
33#14582837C2211yescharacteristic
34#14582833C2212yes—
35#14582833C2212yes—
36#14582830C2211yescharacteristic
37#14582828C2212yes—
38#14582827C2212yes—
39#14582822C2212yes—
40#14582821C2212yes—
41#14582820C2211yescharacteristic
42#14582819C2212yes—
43#14582819C2211yescharacteristic
44#14582817C2211yescharacteristic
45#14582816C2211yescharacteristic
46#14582815C2212yes—
47#14582814C2212yes—
48#14582812C2212yes—
49#14582807C2212yes—
50#14582805C2211yescharacteristic
51#14582803C2212yes—
52#14582799C2212yes—
53#14582799C2212yes—
54#14582794C2212yes—
55#14582793C2212yes—
56#14582793C2212yes—
57#14582792C2212yes—
58#14582792C2212yes—
59#14582790C2212yes—
60#14582790C2212yes—
61#14582789C2212yes—
62#14582787C2212yes—
63#14582787C2212yes—
64#14582787C2212yes—
65#14582786C2212yes—
66#14582783C2212yes—
67#14582783C2212yes—
68#14582781C2212yes—
69#14582781C2212yes—
70#14582780C2212yes—
71#14582777C2212yes—
72#14582775C2212yes—
73#14582775C2212yes—
74#14582775C2212yes—
75#14582773C2212yes—
76#14582770C2212yes—
77#14582764C2211yescharacteristic
78#14582763C2212yes—
79#14582758C2212yes—
80C4⋊C4×Dic43C2212yes—
81C4⋊C4×Dic43C2212yes—
82C4×C4⋊Dic43C2212yes—
83#14582750C2212yes—
84C22⋊C4×Dic43C2212yes—
85C22⋊C4×Dic43C2212yes—
86C22⋊C4×Dic43C2212yes—
87C4×(C2×D43)⋊C4C2212yes—
88C4×(C2×D43)⋊C4C2212yes—
89#14582746C2212yes—
90#14582746C2212yes—
91#14582746C2212yes—
92#14582744C2211yescharacteristic
93#14582744C2211yescharacteristic
94#14582744C2212yes—
95#14582744C2212yes—
96C42×Dic43C2212yes—
97C42×Dic43C2211yescharacteristic
98C43×#400C2211yescharacteristic
99C43×#398C2211yescharacteristic
100C43×#394C2212yes—
101C43×#390C2211yescharacteristic
102C43×#388C2212yes—
103C43×#388C2212yes—
104C43×#388C2212yes—
105C43×#388C2212yes—
106C4×C4⋊C4×C43C2212yes—
107C22×Dic86C2311yescharacteristic
108C22×Dic86C2311yescharacteristic
109C22×D172C2311yescharacteristic
110C22×C22⋊D43C2312yes—
111C22×C22⋊D43C2312yes—
112C23×Dic43C2312yes—
113C22×C4×D43C2312yes—
114C22×C4×D43C2312yes—
115C22×C4×D43C2312yes—
116#13063312—24no—
117#13063311—28no—
118#13063298—28no—
119#13063290—42no—
120#13063290—42no—
121D4×Dic43—42no—
122#13063287—42no—
123(C22⋊D43)⋊C4—28no—
124(C22⋊D43)⋊C4—44no—
125#13063283—28no—
126#13063283—28no—
127#13063281—28no—
128C2×C4⋊Dic43C2312yes—
129C2×C4⋊Dic43C2312yes—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4C2312yes—
132C2×Dic43⋊C4C2312yes—
133C2×Dic43⋊C4C2312yes—
134C2×Dic43⋊C4C2312yes—
135C2×Dic43⋊C4C2311yescharacteristic
136C2×Dic43⋊C4C2311yescharacteristic
137C2×Dic43⋊C4C2312yes—
138C2×Dic43⋊C4C2312yes—
139C2×Dic43⋊C4C2312yes—
140C2×C22⋊Dic43C2312yes—
141C2×C22⋊Dic43C2312yes—
142C2×C22⋊Dic43C2312yes—
143C2×C22⋊Dic43C2312yes—
144C2×C22⋊Dic43C2312yes—
145C2×(C2×D43)⋊C4C2312yes—
146C2×(C2×D43)⋊C4C2312yes—
147C2×(C2×D43)⋊C4C2312yes—
148C2×(C2×D43)⋊C4C2312yes—
149C2×(C2×D43)⋊C4C2312yes—
150C2×(C2×D43)⋊C4C2312yes—
151C2×(C2×D43)⋊C4C2312yes—
152C2×(C2×D43)⋊C4C2312yes—
153C2×(C2×D43)⋊C4C2312yes—
154C2×C4×Dic43C2312yes—
155C2×C4×Dic43C2312yes—
156C2×C4×Dic43C2312yes—
157C2×C4×Dic43C2312yes—
158C2×C4×Dic43C2312yes—
159C2×C4×Dic43C2312yes—
160C2×C4×Dic43C2312yes—
161C2×C4×Dic43C2312yes—
162C2×C4×Dic43C2311yescharacteristic
163C2×C4×Dic43C2311yescharacteristic
164C2×C4×Dic43C2311yescharacteristic
165C2×C4×Dic43C2312yes—
166C2×C4×Dic43C2311yescharacteristic
167C42×D43—28no—
168C43⋊#95C2311yescharacteristic
169C43⋊#95C2312yes—
170C43⋊#95C2312yes—
171C43⋊#95C2312yes—
172C43⋊#95C2312yes—
173C43⋊#95C2312yes—
174C43⋊#95C2312yes—
175C43⋊#95C2312yes—
176C43⋊#95C2312yes—
177C43⋊#95C2312yes—
178C43⋊#95C2312yes—
179C43⋊#95C2312yes—
180C43⋊#95C2312yes—
181C43⋊#95C2312yes—
182C43⋊#95C2312yes—
183C43⋊#95C2312yes—
184C43⋊#95C2311yescharacteristic
185C43⋊#95C2312yes—
186C22×D4×C43C2311yescharacteristic
187C2×C4⋊C4×C43C2312yes—
188C2×C4⋊C4×C43C2312yes—
189C2×C4⋊C4×C43C2311yescharacteristic
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C4⋊C4×C43C2311yescharacteristic
192C2×C22⋊C4×C43C2312yes—
193C2×C22⋊C4×C43C2312yes—
194C2×C22⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2312yes—
196C2×C22⋊C4×C43C2312yes—
197C2×C22⋊C4×C43C2312yes—
198C2×C42×C43C2312yes—
199C2×C42×C43C2312yes—
200C2×C42×C43C2311yescharacteristic
201#95×C43C2312yes—
202#95×C43C2312yes—
203#95×C43C2312yes—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206#95×C43C2312yes—
207C24×C43C2412yes—
208C23×D43C2412yes—
209C2×D4×C43—22no—
210C2×D4×C43—41no—
211C2×D4×C43—41no—
212C22×C4×C43C2412yes—
213C22×C4×C43C2412yes—
214C22×C4×C43C2411yescharacteristic
215C22×C4×C43C2411yescharacteristic
216C22×C4×C43C2412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2411yescharacteristic
219C22×C4×C43C2412yes—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—24no—
224C2×C22⋊D43—42no—
225C2×C22⋊D43—42no—
226C22×Dic43—24no—
227C22×Dic43—24no—
228C22×Dic43—24no—
229C22×Dic43C2412yes—
230C22×Dic43C2411yescharacteristic
231C22×Dic43C2411yescharacteristic
232C22×Dic43C2412yes—
233C22×Dic43C2411yescharacteristic
234C22×Dic43C2412yes—
235C22×Dic43C2412yes—
236C22×Dic43C2412yes—
237C22×Dic43C2411yescharacteristic
238C2×D172—24no—
239C2×D172—41no—
240C2×C4×D43—24no—
241C2×C4×D43—24no—
242C2×C4×D43—24no—
243C2×C4×D43—24no—
244C2×C4×D43—24no—
245C2×C4×D43—24no—
246C2×C4×D43—24no—
247C2×C4×D43—24no—
248C2×C4×D43—42no—
249C2×Dic86—22no—
250C2×Dic86—24no—
251C2×Dic86—41no—
252C2×Dic86—41no—
253C2×Dic86—41no—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—41no—
257C4⋊C4×C43—41no—
258C4⋊C4×C43—41no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—42no—
264C22⋊C4×C43—42no—
265C42×C43—24no—
266C42×C43—41no—
267C42×C43—42no—
268C22⋊Dic43—24no—
269C22⋊Dic43—24no—
270C22⋊Dic43—24no—
271C22⋊Dic43—24no—
272C22⋊Dic43—42no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—42no—
279(C2×D43)⋊C4—42no—
280(C2×D43)⋊C4—42no—
281(C2×D43)⋊C4#4118yes—
282C4⋊Dic43—24no—
283C4⋊Dic43—24no—
284C4⋊Dic43—41no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289Dic43⋊C4—42no—
290Dic43⋊C4—42no—
291Dic43⋊C4—42no—
292Dic43⋊C4—41no—
293Dic43⋊C4—41no—
294C4×Dic43—24no—
295C4×Dic43—24no—
296C4×Dic43—24no—
297C4×Dic43—24no—
298C4×Dic43—24no—
299C4×Dic43—24no—
300C4×Dic43—24no—
301C4×Dic43—24no—
302C4×Dic43—22no—
303C4×Dic43—22no—
304C4×Dic43—22no—
305C4×Dic43#4118yes—
306C4×Dic43#4114yes—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43C2511yescharacteristic
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43C2×#4114yes—
322D4×C43—44no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—21no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43C2×#4114yes—
343C2×C4×C43C2×#4114yes—
344C2×C4×C43C2×#4112yes—
345C22⋊D43—48no—
346C22⋊D43—48no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—22no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—48no—
368C2×Dic43C2×#4114yes—
369C2×Dic43C2×#4114yes—
370C2×Dic43C2×#4114yes—
371C2×Dic43C2×#4114yes—
372C2×Dic43H(5,𝔽2)12yes—
373D172—44no—
374C4×D43—216no—
375C4×D43—48no—
376C4×D43—48no—
377Dic86—44no—
378Dic86—44no—
379#34874—431nomaximal, Sylow
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43C22×#4111yescharacteristic
388C22×C43C22×#4112yes—
389C22×C43C22×#4112yes—
390C22×C43C2×H(5,𝔽2)11yescharacteristic
391C22×C43#58511yescharacteristic
392C2×D43—24no—
393C2×D43—24no—
394C2×D43—24no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—42no—
398C2×D43—42no—
399C4×C43—24no—
400C4×C43—22no—
401C4×C43—24no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43—41no—
406C4×C43—41no—
407Dic43—24no—
408Dic43—24no—
409Dic43—24no—
410Dic43—42no—
411Dic43—41no—
412Dic43—41no—
413Dic43—42no—
414Dic43—41no—
415Dic43#55514yes—
416#2612—431no—
417#2610—432no—
418#2609—431no—
419#2593D4311yescharacteristic, complemented
420#2574—432no—
421#2555—431no—
422#2531—432no—
423#2529—432no—
424#2476—432no—
425#2474—432no—
426#2399—431no—
427#2398—431no—
428#2392—432no—
429C4×#124—431no—
430C4×#124—432no—
431C4×#121—432no—
432#2298—432no—
433#2290—432no—
434C4×#117—432no—
435C2×C43—82no—
436C2×C43#344412yes—
437C2×C43#346011yescharacteristic
438C2×C43C2×#55511yescharacteristic
439C2×C43#347512yes—
440C2×C43#348111yescharacteristic
441D43—44no—
442C2×#124—431no—
443C2×#124—432no—
444C2×#121—432no—
445C2×C4×Q8—431no—
446C2×C4×Q8—431no—
447C2×C4×D4—431no—
448C2×C4×D4—431no—
449C2×C4×D4—432no—
450C2×C4×D4—432no—
451C2×#117—432no—
452C2×#117—432no—
453C2×#117—432no—
454C22×C42—432no—
455#400—431no—
456#400C2×D4311yescharacteristic
457#398—431no—
458#398—432no—
459#398—432no—
460#398C2×D4311yescharacteristic
461#397—432no—
462#397—432no—
463#396—432no—
464#396—432no—
465#395—432no—
466#395—431no—
467#395—431no—
468#394—431no—
469#394—432no—
470#394—432no—
471#394—431no—
472#394C2×D4312yes—
473#393—432no—
474#392—432no—
475#391—431no—
476#391—432no—
477#390—432no—
478#390—432no—
479#390C2×D4311yescharacteristic
480#389—432no—
481#388—432no—
482#388—432no—
483#388—432no—
484#388—432no—
485#388—432no—
486#388—432no—
487#388—432no—
488#388—432no—
489#388—432no—
490#388—432no—
491#388C2×D4312yes—
492#388C2×D4312yes—
493#388C2×D4312yes—
494#388C2×D4312yes—
495#387—432no—
496#387—432no—
497#387—432no—
498#387—432no—
499#387—432no—
500#387—432no—
501#386—432no—
502#386—432no—
503#386—432no—
504#386—432no—
505#385—432no—
506#385—432no—
507#382—431no—
508#382—432no—
509#380—432no—
510C4×C4⋊C4—432no—
511C4×C4⋊C4—432no—
512C4×C4⋊C4—432no—
513C4×C4⋊C4—432no—
514C4×C4⋊C4C2×D4312yes—
515C4×C22⋊C4—432no—
516C4×C22⋊C4—432no—
517C4×C22⋊C4—432no—
518C4×C22⋊C4—432no—
519C4×C22⋊C4—432no—
520C4×C22⋊C4—432no—
521C4×C22⋊C4—432no—
522C4×C22⋊C4—432no—
523#376—432no—
524#376—431no—
525#376—431no—
526#376—432no—
527C43—431no—
528C43—432no—
529C43#3487411yescharacteristic, complemented, Sylow
530C22×Q8—431no—
531C22×Q8—431no—
532C22×D4—432no—
533C22×D4—432no—
534C22×D4—431no—
535C22×D4C22×D4311yescharacteristic
536C23×C4—432no—
537C23×C4—432no—
538C23×C4—432no—
539C23×C4—432no—
540#124—864no—
541#124—868no—
542#121—868no—
543C4×Q8—1722no—
544C4×Q8—1722no—
545C4×D4—868no—
546C4×D4—1724no—
547C4×D4—1722no—
548C4×D4—1722no—
549#117—868no—
550#117—868no—
551#117—868no—
552C2×C4⋊C4—432no—
553C2×C4⋊C4—432no—
554C2×C4⋊C4—432no—
555C2×C4⋊C4—432no—
556C2×C4⋊C4—432no—
557C2×C4⋊C4—432no—
558C2×C4⋊C4—432no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—432no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—432no—
564C2×C4⋊C4C22×D4312yes—
565C2×C4⋊C4C22×D4312yes—
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—432no—
570C2×C22⋊C4—432no—
571C2×C22⋊C4—432no—
572C2×C22⋊C4—432no—
573C2×C22⋊C4—432no—
574C2×C22⋊C4—432no—
575C2×C22⋊C4—432no—
576C2×C22⋊C4—432no—
577C2×C22⋊C4—432no—
578C2×C22⋊C4—432no—
579C2×C22⋊C4—432no—
580C2×C22⋊C4—432no—
581C2×C22⋊C4—432no—
582C2×C22⋊C4—432no—
583C2×C22⋊C4C22×D4312yes—
584C2×C22⋊C4C22×D4312yes—
585C2×C22⋊C4C22×D4312yes—
586C2×C22⋊C4C22×D4312yes—
587C2×C22⋊C4C22×D4312yes—
588C2×C22⋊C4C22×D4312yes—
589C2×C42—431no—
590C2×C42—432no—
591C2×C42—432no—
592C2×C42—432no—
593C2×C42—432no—
594C2×C42—432no—
595C2×C42—432no—
596C2×C42—431no—
597C2×C42—431no—
598C2×C42—431no—
599C2×C42—432no—
600C2×C42—432no—
601C2×C42—432no—
602C2×C42—868no—
603C2×C42C22×D4312yes—
604C2×C42C22×D4311yescharacteristic
605C2×C42C22×D4312yes—
606#95—432no—
607#95—432no—
608#95—432no—
609#95—432no—
610#95—432no—
611#95—432no—
612#95—432no—
613#95—431no—
614#95—432no—
615#95—431no—
616#95—432no—
617#95—432no—
618#95—432no—
619#95—432no—
620#95—432no—
621#95—432no—
622#95—432no—
623#95—432no—
624#95C22×D4312yes—
625#95C22×D4312yes—
626#95C22×D4311yescharacteristic
627#95C22×D4311yescharacteristic
628#95C22×D4312yes—
629#95C22×D4312yes—
630C24—432no—
631C24C23×D4312yes—
632C2×Q8—864no—
633C2×Q8—862no—
634C2×Q8—1721no—
635C2×Q8—1721no—
636C2×Q8—1721no—
637C2×D4—22no—
638C2×D4—41no—
639C2×D4—41no—
640C2×D4—864no—
641C2×D4—864no—
642C2×D4—864no—
643C2×D4—864no—
644C2×D4—864no—
645C2×D4—1721no—
646C2×D4—1722no—
647C2×D4—1722no—
648C22×C4—431no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—432no—
652C22×C4—432no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—432no—
656C22×C4—431no—
657C22×C4—864no—
658C22×C4—864no—
659C22×C4—864no—
660C22×C4—864no—
661C22×C4—864no—
662C22×C4—864no—
663C22×C4—864no—
664C22×C4—864no—
665C22×C4—864no—
666C22×C4—864no—
667C22×C4—864no—
668C22×C4—1722no—
669C22×C4C23×D4312yes—
670C22×C4C23×D4312yes—
671C22×C4C23×D4311yescharacteristic
672C22×C4C23×D4311yescharacteristic
673C22×C4C23×D4312yes—
674C22×C4C23×D4312yes—
675C22×C4C23×D4311yescharacteristic
676C22×C4C23×D4312yes—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—864no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—1722no—
689C4⋊C4—1721no—
690C4⋊C4—1722no—
691C4⋊C4—1721no—
692C4⋊C4—1721no—
693C4⋊C4—1722no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—438no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—1722no—
711C22⋊C4—1722no—
712C22⋊C4—1722no—
713C22⋊C4—1722no—
714C42—24no—
715C42—41no—
716C42—42no—
717C42—438no—
718C42—434no—
719C42—864no—
720C42—864no—
721C42—864no—
722C42—864no—
723C42—864no—
724C42—862no—
725C42—864no—
726C42—862no—
727C42—862no—
728C42—864no—
729C42—864no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—434no—
738C23—862no—
739C23—862no—
740C23—862no—
741C23—862no—
742C23—862no—
743C23—862no—
744C23C24×D4311yescharacteristic
745Q8—1724no—
746Q8—1724no—
747D4—44no—
748D4—1724no—
749D4—1728no—
750D4—1728no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—434no—
771C2×C4—432no—
772C2×C4—434no—
773C2×C4—434no—
774C2×C4—434no—
775C2×C4—8616no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—862no—
789C2×C4—862no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—862no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—1728no—
797C2×C4—1728no—
798C2×C4—1728no—
799C2×C4#41×D4314yes—
800C2×C4#41×D4312yes—
801C2×C4#41×D4314yes—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—864no—
810C22—864no—
811C22—864no—
812C22—1722no—
813C22—1722no—
814C22—1722no—
815C22—1722no—
816C22C2×#41×D4312yes—
817C22C2×#41×D4311yescharacteristic
818C22C2×#41×D4312yes—
819C22H(5,𝔽2)×D4311yescharacteristic
820C22#1458373411yescharacteristic
821C4—24no—
822C4—24no—
823C4—22no—
824C4—42no—
825C4—42no—
826C4—41no—
827C4—41no—
828C4—42no—
829C4—434no—
830C4—864no—
831C4—864no—
832C4—864no—
833C4—1722no—
834C4—1722no—
835C4—1721no—
836C4—1721no—
837C4—1721no—
838C2—82no—
839C2—1724no—
840C2#1914788912yes—
841C2#1914801411yescharacteristic
842C2#555×D4311yescharacteristic
843C2#1914815412yes—
844C2#1914820411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2593C2
prime radical#19139669C2
hypercenter#2593D43
hypocenterC43#34874
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2593

Complements

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

NH ≅ G/Ntype
1. #19140304C2semidirect
2. #19140285C2semidirect
3. #19140273C2semidirect
4. #19139863C2semidirect
6. #19139440C2semidirect
7. #19139410C2semidirect
8. #19138787C2semidirect
9. #19138757C2semidirect
10. #19137887C2semidirect
11. #19137884C2semidirect
12. #19137838C2semidirect
13. #19137142C2semidirect
14. #19137136C2semidirect
15. #19137107C2semidirect
16. #19137089C2semidirect
17. #19137037C2semidirect
18. C4×#13063283C2semidirect
19. C43×#2593C2semidirect
419. #2593D43semidirect
529. C43#34874semidirect

Maximal subgroups

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

subgroupindex
#191403042
#191402852
#191402732
#191398632
#191396692
#191394402
#191394102
#191387872
#191387572
#191378872
#191378842
#191378382
#191371422
#191371362
#191371072
#191370892
#191370372
C4×#130632832
C43×#25932
#3487443