Finite Group Databasebeta

← #25102348

Subgroups — #25102348

Order 11008.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583378C211yesmaximal, characteristic, complemented
2C2×#14583045C211yesmaximal, characteristic
3C2×#14583001C211yesmaximal, characteristic, complemented
4C2×C4×#10621882C211yesmaximal, characteristic, complemented
5#19137289C211yesmaximal, characteristic, complemented
6#19134951C211yesmaximal, characteristic, complemented
7#19134941C211yesmaximal, characteristic, complemented
8#19134911C211yesmaximal, characteristic, complemented
9#19134850C211yesmaximal, characteristic, complemented
10#19134844C211yesmaximal, characteristic, complemented
11#19134784C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic, complemented
13C4×#13063248C211yesmaximal, characteristic, complemented
14#19134364C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20#14583378—24no—
21#14583378—24no—
22C2×C4×Dic86C2211yescharacteristic
23C2×#13063290C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063282C2211yescharacteristic
29C2×#13063281—21no—
30C22×Dic43⋊C4—21no—
31C2×C4⋊C4×D43C2211yescharacteristic
32#14583045C418yescomplemented
33#14583001—24no—
34C4×#10621882—24no—
35C2×#13063259C2211yescharacteristic
36C2×#13063258C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46#14582801—21no—
47#14582800C2211yescharacteristic
48#14582798C2211yescharacteristic
49#14582790—21no—
50#14582777—21no—
51#14582773—21no—
52#14582756C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×D172—21no—
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C23×Dic43—21no—
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43C2311yescharacteristic
79C2×#10621873—22no—
80C2×#10621873—22no—
81C2×#10621873C2×C414yescomplemented
82C2×#10621882—22no—
83C2×#10621882—22no—
84C2×#10621882C2×C414yescomplemented
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063300—22no—
88#13063300C2×C414yescomplemented
89C4×Dic86—22no—
90C4×Dic86D414yescomplemented
91#13063290—22no—
92#13063290—22no—
93C4×D172—22no—
94C4×D172—22no—
95D4×Dic43—22no—
96D4×Dic43—22no—
97C4×C22⋊D43—28no—
98(C22⋊D43)⋊C4—28no—
99#13063282—22no—
100#13063282—22no—
101#13063281—28no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4—28no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4D411yescharacteristic
110C2×Dic43⋊C4D411yescharacteristic
111C4⋊C4×D43—22no—
112C4⋊C4×D43—22no—
113C2×C22⋊Dic43—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4D411yescharacteristic
120C2×(C2×D43)⋊C4D411yescharacteristic
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43C2311yescharacteristic
124#13063259—22no—
125#13063258—22no—
126#13063250—22no—
127#13063248—22no—
128#13063248C2×C414yescomplemented
129#13063247—22no—
130#13063246—22no—
131#13063245—22no—
132(C2×D43)⋊C8—22no—
133(C2×D43)⋊C8C2×C414yescomplemented
134C4×C43⋊C8—22no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C22×D4×C43C2311yescharacteristic
138C23×C4×C43—21no—
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×D4×C43—22no—
142C4×D4×C43D414yescomplemented
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#102×C43—22no—
150#102×C43C2×C414yescomplemented
151#97×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C23×D43—21no—
155C23×D43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43C22×C412yes—
160C2×D4×C43C2×D412yes—
161C2×D4×C43#4112yes—
162C22×C4×C43—24no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—81no—
167C22×C4×C43—81no—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—24no—
172C2×C22⋊D43—24no—
173C2×C22⋊D43—24no—
174C22×Dic43—24no—
175C22×Dic43—24no—
176C22×Dic43—24no—
177C22×Dic43—24no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—81no—
182C22×Dic43—81no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186#10621900—28no—
187#10621900—28no—
188#10621900—28no—
189#10621900—28no—
190C2×D172—21no—
191C2×D172—24no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—81no—
197C2×D172—81no—
198C2×D172C22×C412yes—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—24no—
204C2×C4×D43—42no—
205C2×C4×D43—81no—
206C2×C4×D43—81no—
207C2×C4×D43—81no—
208C2×C4×D43—81no—
209C2×C4×D43C22×C412yes—
210C2×C4×D43#4112yes—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86C22×C412yes—
215C2×Dic86C2×D412yes—
216C2×Dic86#4112yes—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43C22×C412yes—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43C22×C412yes—
228C4⋊C4×C43C2×D412yes—
229C22⋊C4×C43—24no—
230C42×C43—81no—
231C42×C43C2×D412yes—
232C42×C43C2×D412yes—
233C22⋊Dic43—24no—
234#10621882—28no—
235(C2×D43)⋊C4—22no—
236(C2×D43)⋊C4—22no—
237(C2×D43)⋊C4—24no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—81no—
240(C2×D43)⋊C4—81no—
241(C2×D43)⋊C4—81no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—81no—
246C4⋊Dic43C2×D412yes—
247Dic43⋊C4—24no—
248Dic43⋊C4—24no—
249Dic43⋊C4—22no—
250Dic43⋊C4—24no—
251Dic43⋊C4—22no—
252C4×Dic43—24no—
253C4×Dic43—24no—
254C4×Dic43—21no—
255C4×Dic43—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8C22×C412yes—
262#10621873—28no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C22×D411yescharacteristic
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—22no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43C4×D412yes—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43C4×D414yes—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—84no—
303C2×C4×C43#12012yes—
304C2×C4×C43#12012yes—
305C2×C4×C43C23×C411yescharacteristic
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C22⋊D43—216no—
312C2×Dic43—216no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—21no—
316C2×Dic43—22no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—22no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—84no—
331C2×Dic43C4×D412yes—
332D172—22no—
333D172—22no—
334D172—41no—
335D172—41no—
336D172—84no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—84no—
342C4×D43—84no—
343Dic86—22no—
344Dic86—22no—
345Dic86—22no—
346Dic86C4×D414yes—
347C8×C43—22no—
348C8×C43—41no—
349C43⋊C8—22no—
350C43⋊C8—41no—
351#21460—431nomaximal, Sylow
352C22×C43—24no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43C2×C4×D411yescharacteristic
360C22×C43C2×#12011yescharacteristic
361C22×C43#52511yescharacteristic
362C22×C43#57611yescharacteristic
363C22×C43#57611yescharacteristic
364C22×C43#57711yescharacteristic
365C22×C43#57811yescharacteristic
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—81no—
377C2×D43—81no—
378C2×D43—81no—
379C2×D43—81no—
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—81no—
385C4×C43C2×C4×D411yescharacteristic
386C4×C43C2×C4×D411yescharacteristic
387C4×C43#52511yescharacteristic
388C4×C43#52511yescharacteristic
389Dic43—24no—
390Dic43—22no—
391Dic43—42no—
392Dic43—41no—
393Dic43—41no—
394Dic43—81no—
395C2×#520—431no—
396C2×#449—431no—
397C2×#440—431no—
398C2×C4×D8—431no—
399#2324—431no—
400#1880—431no—
401#1879—431no—
402#1874—431no—
403#1863—431no—
404#1862—431no—
405#1852—431no—
406#1788—431no—
407#1762D4311yescharacteristic, complemented
408C4×#103—431no—
409#1750—431no—
410C2×C43—44no—
411C2×C43C4×#12011yescharacteristic
412C2×C43#294611yescharacteristic
413C2×C43#295111yescharacteristic
414C2×C43#300811yescharacteristic
415C2×C43#301311yescharacteristic
416C2×C43#311911yescharacteristic
417C2×C43#312411yescharacteristic
418D43—42no—
419D43—82no—
420C22×#41—431no—
421C22×SD16—431no—
422C22×D8—431no—
423C2×#121—431no—
424#520—864no—
425#520—864no—
426C2×C4×Q8—431no—
427C2×C4×Q8—431no—
428C2×C4×D4—431no—
429C2×C4×D4—431no—
430C2×C4×D4—861no—
431C2×C4×D4—861no—
432C2×C4×D4C2×D4311yescharacteristic
433C2×#117—431no—
434C2×#117—861no—
435C22×C4⋊C4—431no—
436C22×C4⋊C4—861no—
437#449—438no—
438#440—864no—
439C4×D8—864no—
440C2×#107—431no—
441C2×#107—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102C2×D4311yescharacteristic
449C2×#102C2×D4311yescharacteristic
450C2×C22⋊C8—431no—
451C2×C22⋊C8—431no—
452C2×#97C2×D4311yescharacteristic
453C2×C4×C8—431no—
454#390—431no—
455#390—861no—
456#389—431no—
457#388—861no—
458#386—861no—
459#385—861no—
460#380—431no—
461C4×C4⋊C4C2×D4311yescharacteristic
462#340—431no—
463#340—431no—
464#340C2×D4311yescharacteristic
465#340C2×D4311yescharacteristic
466#336—431no—
467#336—431no—
468C43#2146011yescharacteristic, complemented, Sylow
469C2×#41—434no—
470C2×#41—862no—
471C2×#41—862no—
472C2×#41—862no—
473C2×#41—862no—
474C2×#41—862no—
475C22×Q8—431no—
476C22×D4—431no—
477C22×D4—861no—
478C22×D4—861no—
479C22×D4C22×D4311yescharacteristic
480C23×C4—21no—
481C23×C4—431no—
482C23×C4—861no—
483C23×C4—861no—
484C23×C4—861no—
485C23×C4—861no—
486C2×SD16—434no—
487C2×SD16—862no—
488C2×SD16—862no—
489C2×D8—434no—
490C2×D8—862no—
491C2×D8—862no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8C22×D4311yescharacteristic
495C22×C8C22×D4311yescharacteristic
496#121—434no—
497#121—862no—
498C4×Q8—434no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×Q8—862no—
502C4×D4—22no—
503C4×D4—868no—
504C4×D4—862no—
505C4×D4—868no—
506C4×D4—862no—
507C4×D4—862no—
508C4×D4—862no—
509C4×D4D17214yescomplemented
510#117—868no—
511#117—862no—
512#117—862no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—862no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—868no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—862no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—431no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C42—21no—
537C2×C42—431no—
538C2×C42—861no—
539C2×C42—861no—
540C2×C42C22×D4311yescharacteristic
541#107—862no—
542#107—862no—
543#103—434no—
544#103—862no—
545#103—862no—
546#102—22no—
547#102—862no—
548#102—862no—
549#102—862no—
550#102C4×D4314yescomplemented
551C22⋊C8—434no—
552C22⋊C8—862no—
553#97—22no—
554C4×C8—862no—
555#95—21no—
556#95—861no—
557#95—861no—
558C24—21no—
559C24—431no—
560C24—861no—
561#41—868no—
562#41—868no—
563#41—868no—
564#41—868no—
565C2×Q8—432no—
566C2×Q8—432no—
567C2×Q8—432no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—432no—
575C2×D4—864no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—864no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—3441no—
585C2×D4—3441no—
586C2×D4C2×C4×D4312yes—
587C2×D4C2×D17212yes—
588C2×D4#1062189812yes—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—21no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—431no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—864no—
601C22×C4—864no—
602C22×C4—864no—
603C22×C4—864no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—864no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—3441no—
613C22×C4—3441no—
614C22×C4—3441no—
615C22×C4—3441no—
616C22×C4—3441no—
617C22×C4—3441no—
618C22×C4—1722no—
619C22×C4D4×D4311yescharacteristic
620C22×C4D4×D4311yescharacteristic
621C22×C4C23×D4311yescharacteristic
622SD16—868no—
623D8—868no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—432no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8C2×C4×D4312yes—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—432no—
641C4⋊C4—864no—
642C4⋊C4—864no—
643C4⋊C4—862no—
644C4⋊C4—862no—
645C4⋊C4—864no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—3441no—
650C4⋊C4C2×C4×D4312yes—
651C4⋊C4C2×D17212yes—
652C22⋊C4—24no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—3441no—
658C22⋊C4—3441no—
659C22⋊C4—3441no—
660C22⋊C4—1722no—
661C42—81no—
662C42—864no—
663C42—864no—
664C42—861no—
665C42—861no—
666C42C2×D17212yes—
667C42D4×D4312yes—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—432no—
676C23—861no—
677C23—861no—
678C23—861no—
679C23—861no—
680C23—861no—
681C23—861no—
682C23—862no—
683C23—1721no—
684C23—1721no—
685C23—1721no—
686C23—1721no—
687C23—1721no—
688C23—1721no—
689C23C2×D4×D4311yescharacteristic
690Q8—434no—
691Q8—862no—
692Q8—862no—
693Q8—862no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—8616no—
698D4—862no—
699D4—862no—
700D4—3444no—
701D4—1721no—
702D4—1721no—
703D4C4×D17214yes—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—84no—
718C2×C4—432no—
719C2×C4—8616no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—861no—
730C2×C4—862no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—3444no—
737C2×C4—3444no—
738C2×C4—3444no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4#1306329512yes—
745C2×C4#1306329512yes—
746C2×C4C22×C4×D4311yescharacteristic
747C2×C4C2×D4×D4311yescharacteristic
748C2×C4C22×D17211yescharacteristic
749C2×C4#41×D4311yescharacteristic
750C2×C4#41×D4311yescharacteristic
751C2×C4C2×#1062189811yescharacteristic
752C8—22no—
753C8—41no—
754C8—862no—
755C8—1721no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—862no—
764C22—862no—
765C22—862no—
766C22—3441no—
767C22—3441no—
768C22—3441no—
769C22—3441no—
770C22—1722no—
771C22—1722no—
772C22—1722no—
773C22—1721no—
774C22—1721no—
775C22—1721no—
776C22—1721no—
777C22C4×D4×D4311yescharacteristic
778C22C2×#1306329511yescharacteristic
779C22#1458340811yescharacteristic
780C22#1458370311yescharacteristic
781C22#1458370311yescharacteristic
782C22#1458370911yescharacteristic
783C22#1458371511yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—81no—
789C4—862no—
790C4—864no—
791C4—3441no—
792C4—1721no—
793C4—1722no—
794C4—1721no—
795C4C4×D4×D4311yescharacteristic
796C4C2×C4×D17211yescharacteristic
797C4#1458340811yescharacteristic
798C4#1458341111yescharacteristic
799C2—44no—
800C2—3442no—
801C2—1722no—
802C2C4×#1306329511yescharacteristic
803C2#1914342411yescharacteristic
804C2#1914346711yescharacteristic
805C2#1914386411yescharacteristic
806C2#1914391211yescharacteristic
807C2#1914479811yescharacteristic
808C2#1914486111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC2×#14583045C2
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#21460
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
1. C2×#14583378C2semidirect
3. C2×#14583001C2semidirect
4. C2×C4×#10621882C2semidirect
5. #19137289C2semidirect
6. #19134951C2semidirect
7. #19134941C2semidirect
8. #19134911C2semidirect
9. #19134850C2semidirect
10. #19134844C2semidirect
11. #19134784C2semidirect
12. #19134532C2semidirect
13. C4×#13063248C2semidirect
14. #19134364C2semidirect
15. C43×#1762C2semidirect
32. #14583045C4semidirect
69. C2×#10621900C2×C4semidirect
81. C2×#10621873C2×C4semidirect
84. C2×#10621882C2×C4semidirect
88. #13063300C2×C4semidirect
90. C4×Dic86D4semidirect
128. #13063248C2×C4semidirect
133. (C2×D43)⋊C8C2×C4semidirect
142. C4×D4×C43D4semidirect
150. #102×C43C2×C4semidirect
407. #1762D43semidirect
468. C43#21460semidirect
509. C4×D4D172semidirect
550. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833782
C2×#145830452
C2×#145830012
C2×C4×#106218822
#191372892
#191349512
#191349412
#191349112
#191348502
#191348442
#191347842
#191345322
C4×#130632482
#191343642
C43×#17622
#2146043