Finite Group Databasebeta

← #25098362

Subgroups — #25098362

Order 11008.

1954 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×#14583411C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic, complemented
3C2×#14582917C211yesmaximal, characteristic, complemented
4C2×#14582915C211yesmaximal, characteristic, complemented
5C2×#14582862C211yesmaximal, characteristic, complemented
6#19135042C214yesmaximal, complemented
7#19135037C214yesmaximal, complemented
8#19134304C211yesmaximal, characteristic, complemented
9C43×#1733C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C23×C4×D43C2211yescharacteristic
12C22×#10621877C2211yescharacteristic
13#14583411—21no—
14#14583411—21no—
15#14583411—22no—
16#14583411C414yescomplemented
17#14583411C2212yes—
18#14583411C2212yes—
19C2×#13063309—21no—
20C2×#13063305C412yescomplemented
21C2×#13063300C412yescomplemented
22C2×#13063295—21no—
23C2×C4×D172—22no—
24C2×#13063284C2211yescharacteristic
25C2×#13063283—21no—
26C2×#13063282C2212yescomplemented
27C2×#13063281—21no—
28#117×D43—24no—
29#117×D43—24no—
30C2×C4⋊C4×D43—21no—
31C2×C22⋊C4×D43—21no—
32C2×C42×D43C2212yescomplemented
33#14582917—24no—
34#14582915—24no—
35C2×#13063253C2214yescomplemented
36C2×#13063251C2214yescomplemented
37#14582862—22no—
38#14582862C2212yescomplemented
39#14582862C2212yescomplemented
40C2×(C2×D43)⋊C8—22no—
41#14582658C2214yescomplemented
42C22×M16×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C2×#117×C43C2211yescharacteristic
45C43×#339C2214yescomplemented
46C24×D43D411yescharacteristic
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898—22no—
53C2×#10621898C2×C412yescomplemented
54C2×#10621898C2312yes—
55C22×Dic86C2×C411yescharacteristic, complemented
56C22×D172—22no—
57C22×D172C2×C411yescharacteristic, complemented
58C22×C22⋊D43—21no—
59C23×Dic43D411yescharacteristic
60C22×C4×D43—22no—
61C22×C4×D43—22no—
62C22×C4×D43—22no—
63C22×C4×D43—22no—
64C22×C4×D43—22no—
65C22×C4×D43—21no—
66C22×C4×D43C2×C412yes—
67C22×C4×D43C2×C412yes—
68C22×C4×D43D411yescharacteristic
69C22×C4×D43D411yescharacteristic
70C22×C4×D43D412yes—
71C22×C4×D43D412yes—
72C22×C4×D43C2311yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C2×#10621877—21no—
75C2×#10621877—22no—
76C2×#10621877—22no—
77C2×#10621877C2312yes—
78C22×C43⋊C8—21no—
79#13063309—24no—
80#13063309—22no—
81#13063309—22no—
82#13063305—22no—
83#13063305—22no—
84#13063305C2×C414yes—
85#13063305C2×C414yescomplemented
86#13063300—22no—
87#13063300—22no—
88#13063300C2×C414yes—
89#13063300C2×C414yescomplemented
90#13063295—24no—
91#13063295—22no—
92#13063295—22no—
93C4×D172—24no—
94C4×D172—24no—
95C4×D172—24no—
96C4×D172—24no—
97#13063284—22no—
98#13063284D414yescomplemented
99#13063283—28no—
100#13063282—24no—
101#13063282—24no—
102#13063281—28no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43—22no—
105C2×Dic43⋊C4—22no—
106C4⋊C4×D43—28no—
107C2×C22⋊Dic43—21no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C22⋊C4×D43—28no—
112C2×C4×Dic43—22no—
113C2×C4×Dic43C2312yes—
114C42×D43—24no—
115C42×D43—24no—
116#13063253—28no—
117#13063251—28no—
118(C2×D43)⋊C8—24no—
119(C2×D43)⋊C8—24no—
120C23×C4×C43C2311yescharacteristic
121C2×M16×C43—21no—
122C2×M16×C43—22no—
123C2×M16×C43—22no—
124C2×M16×C43C2312yes—
125C22×C8×C43—21no—
126#117×C43—22no—
127#117×C43—21no—
128#117×C43—21no—
129#117×C43C2×C412yescomplemented
130#117×C43D414yescomplemented
131#117×C43C2312yes—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C412yescomplemented
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C42×C43—21no—
137C2×C42×C43C2312yes—
138C24×C43C2×D411yescharacteristic
139C23×D43—22no—
140C23×D43—22no—
141C23×D43—21no—
142C23×D43—44no—
143C23×D43C22⋊C412yes—
144C23×D43C22⋊C412yes—
145C23×D43C2×D411yescharacteristic
146C23×D43C2×D411yescharacteristic
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4112yes—
157C22×C4×C43#4112yes—
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—42no—
162C2×C22⋊D43—42no—
163C22×Dic43—21no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43C22⋊C412yes—
168C22×Dic43C22⋊C412yes—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171#10621898—24no—
172#10621898—24no—
173#10621898—22no—
174#10621898—22no—
175#10621898—22no—
176#10621898—22no—
177#10621898—42no—
178#10621898—42no—
179#10621898—42no—
180#10621898—42no—
181C2×D172—21no—
182C2×D172—24no—
183C2×D172—24no—
184C2×D172—22no—
185C2×D172—22no—
186C2×D172—48no—
187C2×D172C22×C412yes—
188C2×C4×D43—24no—
189C2×C4×D43—24no—
190C2×C4×D43—24no—
191C2×C4×D43—24no—
192C2×C4×D43—22no—
193C2×C4×D43—22no—
194C2×C4×D43—24no—
195C2×C4×D43—24no—
196C2×C4×D43—24no—
197C2×C4×D43—24no—
198C2×C4×D43—22no—
199C2×C4×D43—22no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—28no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—48no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43C22⋊C412yes—
215C2×C4×D43C22⋊C412yes—
216C2×C4×D43C22⋊C412yes—
217C2×C4×D43C22⋊C412yes—
218C2×C4×D43C22×C412yes—
219C2×C4×D43C22×C412yes—
220C2×C4×D43C2×D412yes—
221C2×C4×D43C2×D412yes—
222C2×Dic86—22no—
223C2×Dic86—22no—
224C2×Dic86—21no—
225C2×Dic86C22×C412yes—
226M16×C43—22no—
227M16×C43—22no—
228M16×C43—42no—
229C2×C8×C43—22no—
230C2×C8×C43—42no—
231C4⋊C4×C43—22no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43C22×C414yes—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—22no—
237C42×C43—22no—
238C42×C43—22no—
239C42×C43—22no—
240C42×C43C2×D414yescomplemented
241C22⋊Dic43—24no—
242(C2×D43)⋊C4—28no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247C4⋊Dic43—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43—24no—
250Dic43⋊C4—28no—
251C4×Dic43—28no—
252C4×Dic43—22no—
253C4×Dic43C2×D414yescomplemented
254#10621877—22no—
255#10621877—22no—
256#10621877—42no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—42no—
259C23×C43—42no—
260C23×C43C2×C22⋊C411yescharacteristic
261C23×C43C2×C22⋊C411yescharacteristic
262C23×C43#12012yes—
263C23×C43#12312yes—
264C23×C43C22×D411yescharacteristic
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—24no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—24no—
271C22×D43—24no—
272C22×D43—24no—
273C22×D43—24no—
274C22×D43—22no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—42no—
278C22×D43—48no—
279C22×D43—48no—
280C22×D43—44no—
281C22×D43—42no—
282C22×D43C2×C22⋊C412yes—
283C22×D43C2×C22⋊C412yes—
284C2×C4×C43—24no—
285C2×C4×C43—24no—
286C2×C4×C43—44no—
287C2×C4×C43—44no—
288C2×C4×C43C2×C22⋊C411yescharacteristic
289C2×C4×C43C2×C22⋊C411yescharacteristic
290C2×C4×C43C4×D412yes—
291C2×C4×C43C4×D412yes—
292C2×C4×C43C4×D412yes—
293C2×C4×C43C4×D412yes—
294C2×C4×C43#12012yes—
295C2×C4×C43#12112yes—
296C2×C4×C43#12112yes—
297C2×C4×C43#12112yes—
298C2×C4×C43#12112yes—
299C2×C4×C43#12312yes—
300C2×C4×C43C23×C411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C22⋊D43—42no—
307C22⋊D43—42no—
308C22⋊D43—44no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—24no—
314C2×Dic43—24no—
315C2×Dic43—22no—
316C2×Dic43—24no—
317C2×Dic43—44no—
318C2×Dic43—42no—
319C2×Dic43C2×C22⋊C412yes—
320C2×Dic43C2×C22⋊C412yes—
321D172—22no—
322D172—22no—
323D172—48no—
324D172—48no—
325D172—42no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—24no—
335C4×D43—24no—
336C4×D43—24no—
337C4×D43—24no—
338C4×D43—416no—
339C4×D43—42no—
340C4×D43—42no—
341C4×D43—44no—
342Dic86—22no—
343Dic86—22no—
344Dic86—42no—
345C8×C43—42no—
346C43⋊C8—42no—
347#20979—431nomaximal, Sylow
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43#38612yes—
354C22×C43#38612yes—
355C22×C43C22×C22⋊C411yescharacteristic
356C22×C43C2×#12011yescharacteristic
357C22×C43C2×#12311yescharacteristic
358C2×D43—24no—
359C2×D43—24no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—48no—
366C2×D43—48no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—44no—
370C2×D43—42no—
371C2×D43—84no—
372C2×D43#42114yescomplemented
373C4×C43—44no—
374C4×C43—44no—
375C4×C43#38612yes—
376C4×C43#38612yes—
377C4×C43C2×C4×D411yescharacteristic
378C4×C43C2×C4×D411yescharacteristic
379C4×C43C2×#12111yescharacteristic
380C4×C43C2×#12111yescharacteristic
381Dic43—22no—
382Dic43—22no—
383Dic43—44no—
384Dic43—42no—
385C2×#525—431no—
386C22×#117—431no—
387C2×#421—431no—
388C2×#421—431no—
389C2×#407—431no—
390#1897—434no—
391#1896—434no—
392#1733—431no—
393#1733D4311yescharacteristic, complemented
394C2×C43—21no—
395C2×C43—21no—
396C2×C43—22no—
397C2×C43—22no—
398C2×C43C2×#38611yescharacteristic
399C2×C43C2×#42112yes—
400D43—24no—
401D43—42no—
402D43—82no—
403C22×#41—431no—
404C24×C4—431no—
405C22×M16—431no—
406C22×M16C2×D4311yescharacteristic
407#525—432no—
408#525—432no—
409#525—434no—
410#525—861no—
411#525—861no—
412#525—862no—
413C2×#123—861no—
414C2×C22⋊Q8—432no—
415C2×#121—432no—
416C2×#120—861no—
417C2×C4×D4—862no—
418C2×#117—431no—
419C2×#117—432no—
420C2×#117—861no—
421C2×#117—861no—
422C2×#117—864no—
423C2×#117—864no—
424C2×#117C2×D4311yescharacteristic
425C2×#117C2×D4311yescharacteristic
426C22×C4⋊C4—861no—
427C22×C22⋊C4—861no—
428C22×C42—432no—
429#421—864no—
430#421—864no—
431C2×#104—434no—
432C2×#104—434no—
433#407—432no—
434#407—432no—
435#407—862no—
436C2×C22⋊C8—862no—
437#339—434no—
438#339C2×D4314yescomplemented
439C43#2097911yescharacteristic, complemented, Sylow
440C25—431no—
441C2×#41—432no—
442C2×#41—432no—
443C2×#41—861no—
444C2×#41—861no—
445C2×#41—862no—
446C2×#41—862no—
447C2×#41—862no—
448C2×#41—862no—
449C22×Q8—431no—
450C22×D4—431no—
451C22×D4—862no—
452C22×D4—861no—
453C23×C4—431no—
454C23×C4—432no—
455C23×C4—432no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—432no—
459C23×C4—432no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—862no—
463C23×C4—862no—
464C23×C4—862no—
465C23×C4—862no—
466C23×C4—862no—
467C23×C4—861no—
468C23×C4C22×D4311yescharacteristic
469C2×M16—21no—
470C2×M16—22no—
471C2×M16—22no—
472C2×M16—432no—
473C2×M16—861no—
474C2×M16—862no—
475C2×M16—862no—
476C2×M16C22×D4312yes—
477C22×C8—21no—
478C22×C8—861no—
479#123—864no—
480#123—862no—
481#123—862no—
482C22⋊Q8—434no—
483C22⋊Q8—434no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486#121—434no—
487#121—434no—
488#121—862no—
489#121—862no—
490#120—864no—
491#120—862no—
492#120—862no—
493C4×D4—864no—
494C4×D4—864no—
495C4×D4—864no—
496C4×D4—864no—
497#117—22no—
498#117—21no—
499#117—21no—
500#117—434no—
501#117—864no—
502#117—868no—
503#117—868no—
504#117—862no—
505#117—864no—
506#117C4×D4312yescomplemented
507#117D17214yescomplemented
508#117C22×D4312yes—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—868no—
511C2×C4⋊C4—862no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4C4×D4312yescomplemented
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—868no—
518C2×C22⋊C4—862no—
519C2×C22⋊C4—862no—
520C2×C22⋊C4—862no—
521C2×C22⋊C4—861no—
522C2×C42—21no—
523C2×C42—432no—
524C2×C42—864no—
525C2×C42—862no—
526C2×C42—864no—
527C2×C42C22×D4312yes—
528#104—868no—
529#104—868no—
530C22⋊C8—864no—
531C22⋊C8—864no—
532C24—431no—
533C24—432no—
534C24—432no—
535C24—431no—
536C24—862no—
537C24—862no—
538C24—861no—
539C24—1724no—
540C24D4×D4311yescharacteristic
541#41—864no—
542#41—864no—
543#41—862no—
544#41—862no—
545#41—862no—
546#41—862no—
547#41—1722no—
548#41—1722no—
549#41—1722no—
550#41—1722no—
551C2×Q8—432no—
552C2×Q8—861no—
553C2×Q8—862no—
554C2×Q8—862no—
555C2×D4—432no—
556C2×D4—864no—
557C2×D4—864no—
558C2×D4—862no—
559C2×D4—862no—
560C2×D4—861no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—1728no—
564C2×D4—1722no—
565C2×D4—1722no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—432no—
576C22×C4—432no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—432no—
580C22×C4—868no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—864no—
584C22×C4—864no—
585C22×C4—864no—
586C22×C4—864no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—864no—
590C22×C4—864no—
591C22×C4—864no—
592C22×C4—864no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—1728no—
608C22×C4—1722no—
609C22×C4—1722no—
610C22×C4C2×C4×D4311yescharacteristic
611C22×C4C2×C4×D4311yescharacteristic
612C22×C4C2×D17212yes—
613C22×C4#1062189812yes—
614C22×C4D4×D4311yescharacteristic
615C22×C4D4×D4311yescharacteristic
616C22×C4D4×D4311yescharacteristic
617C22×C4D4×D4312yes—
618C22×C4#1062190212yes—
619C22×C4C23×D4311yescharacteristic
620M16—22no—
621M16—22no—
622M16—42no—
623M16—862no—
624M16—862no—
625M16—1722no—
626C2×C8—22no—
627C2×C8—42no—
628C2×C8—862no—
629C2×C8—1722no—
630C4⋊C4—22no—
631C4⋊C4—24no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—868no—
635C4⋊C4—864no—
636C4⋊C4C2×C4×D4314yes—
637C22⋊C4—22no—
638C22⋊C4—24no—
639C22⋊C4—22no—
640C22⋊C4—864no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—868no—
645C22⋊C4—864no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—434no—
650C42—868no—
651C42—862no—
652C42C2×D17214yescomplemented
653C23—42no—
654C23—432no—
655C23—432no—
656C23—864no—
657C23—864no—
658C23—864no—
659C23—861no—
660C23—861no—
661C23—861no—
662C23—861no—
663C23—864no—
664C23—864no—
665C23—862no—
666C23—1722no—
667C23—1722no—
668C23—1722no—
669C23—1724no—
670C23—1728no—
671C23—1728no—
672C23—1722no—
673C23C22⋊C4×D4311yescharacteristic
674C23C22⋊C4×D4311yescharacteristic
675C23#1306329512yes—
676C23#1306331012yes—
677C23C2×D4×D4311yescharacteristic
678Q8—862no—
679Q8—862no—
680Q8—1722no—
681D4—862no—
682D4—862no—
683D4—1728no—
684D4—1728no—
685D4—1722no—
686D4—1722no—
687D4—1724no—
688D4—1722no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—864no—
700C2×C4—864no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—864no—
710C2×C4—864no—
711C2×C4—864no—
712C2×C4—864no—
713C2×C4—862no—
714C2×C4—864no—
715C2×C4—17216no—
716C2×C4—1724no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1724no—
721C2×C4C22⋊C4×D4311yescharacteristic
722C2×C4C22⋊C4×D4311yescharacteristic
723C2×C4#1306328712yes—
724C2×C4#1306328712yes—
725C2×C4C4×D17212yes—
726C2×C4C4×D17212yes—
727C2×C4#1306329512yes—
728C2×C4#1306329812yes—
729C2×C4#1306329812yes—
730C2×C4#1306330012yes—
731C2×C4#1306330012yes—
732C2×C4#1306331012yes—
733C2×C4C22×C4×D4311yescharacteristic
734C2×C4C2×D4×D4311yescharacteristic
735C2×C4C2×D4×D4311yescharacteristic
736C2×C4C22×D17211yescharacteristic
737C2×C4C2×#1062189811yescharacteristic
738C2×C4C2×#1062190211yescharacteristic
739C8—42no—
740C8—1722no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—42no—
745C22—42no—
746C22—434no—
747C22—864no—
748C22—864no—
749C22—862no—
750C22—862no—
751C22—862no—
752C22—862no—
753C22—862no—
754C22—3444no—
755C22—1728no—
756C22—1728no—
757C22—1722no—
758C22—1722no—
759C22—1724no—
760C22—1722no—
761C22#1458277712yes—
762C22#1458277712yes—
763C22C2×C22⋊C4×D4311yescharacteristic
764C22C2×#1306329511yescharacteristic
765C22C2×#1306331011yescharacteristic
766C4—44no—
767C4—44no—
768C4—862no—
769C4—862no—
770C4—1724no—
771C4—1722no—
772C4#1458277712yes—
773C4#1458277712yes—
774C4C2×#1306328711yescharacteristic
775C4C2×C4×D17211yescharacteristic
776C4C2×#1306329811yescharacteristic
777C4C2×#1306330011yescharacteristic
778C2—21no—
779C2—21no—
780C2—22no—
781C2—22no—
782C2—864no—
783C2—3442no—
784C2—1722no—
785C2C2×#1458277711yescharacteristic
786C2#421×D4312yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1733C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583411C2
cosocleC22×C4×C43C24
hypercenter#1733D43
hypocenterC43#20979
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
2. C2×#117×D43C2semidirect
3. C2×#14582917C2semidirect
4. C2×#14582915C2semidirect
5. C2×#14582862C2semidirect
6. #19135042C2semidirect
7. #19135037C2semidirect
8. #19134304C2semidirect
9. C43×#1733C2semidirect
16. #14583411C4semidirect
20. C2×#13063305C4semidirect
21. C2×#13063300C4semidirect
26. C2×#13063282C22semidirect
32. C2×C42×D43C22semidirect
35. C2×#13063253C22semidirect
36. C2×#13063251C22semidirect
38. #14582862C22semidirect
39. #14582862C22semidirect
41. #14582658C22semidirect
45. C43×#339C22semidirect
53. C2×#10621898C2×C4semidirect
55. C22×Dic86C2×C4semidirect
57. C22×D172C2×C4semidirect
85. #13063305C2×C4semidirect
89. #13063300C2×C4semidirect
98. #13063284D4semidirect
129. #117×C43C2×C4semidirect
130. #117×C43D4semidirect
133. C2×C4⋊C4×C43C2×C4semidirect
240. C42×C43C2×D4semidirect
253. C4×Dic43C2×D4semidirect
372. C2×D43#421semidirect
393. #1733D43semidirect
438. #339C2×D43semidirect
439. C43#20979semidirect
506. #117C4×D43semidirect
507. #117D172semidirect
514. C2×C4⋊C4C4×D43semidirect
652. C42C2×D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145834112
C2×#117×D432
C2×#145829172
C2×#145829152
C2×#145828622
#191350422
#191350372
#191343042
C43×#17332
#2097943