Finite Group Databasebeta

← #102×C22⋊D43 #25111999

Subgroups — #102×C22⋊D43 #25111999

Order 11008.

2014 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D43C211yesmaximal, characteristic
2C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#102×D43C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D43C211yesmaximal, characteristic, complemented
5#19135520C211yesmaximal, characteristic, complemented
6#19135399C211yesmaximal, characteristic, complemented
7#19135023C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic, complemented
9#19134912C211yesmaximal, characteristic, complemented
10#19134909C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134526C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C22×#102×C43C211yesmaximal, characteristic, complemented
16C23×C22⋊D43—21no—
17C22×D4×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic, complemented
19D4×C22⋊D43—24no—
20D4×C22⋊D43C418yescomplemented
21C2×#13063321C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×#13063297—21no—
24C2×#13063296C2211yescharacteristic
25C2×#13063294—21no—
26C2×#13063293—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic, complemented
31C8×C22⋊D43—24no—
32C2×Dic43⋊C8C2211yescharacteristic, complemented
33C2×#13063247C2211yescharacteristic, complemented
34C2×#13063247C2211yescharacteristic, complemented
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic, complemented
38C2×#13063246C2211yescharacteristic, complemented
39C2×#13063245C2211yescharacteristic, complemented
40C2×#13063245C2211yescharacteristic, complemented
41#102×D43—24no—
42C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
43C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
44C2×C8×Dic43C2211yescharacteristic, complemented
45#14582794—21no—
46#14582772—21no—
47#14582770—21no—
48#14582768C2211yescharacteristic, complemented
49#14582759C2211yescharacteristic, complemented
50#14582756C2211yescharacteristic, complemented
51C4⋊C4×Dic43C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C23×D4×C43C2211yescharacteristic
57C23×C8×C43C2211yescharacteristic, complemented
58C22×C4⋊C4×C43C2211yescharacteristic, complemented
59C2×#102×C43—24no—
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic, complemented
63C2×#102×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43—28no—
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C22×C22⋊D43—21no—
72C22×C22⋊D43—44no—
73C22×C22⋊D43—44no—
74C22×C22⋊D43D411yescharacteristic
75C2×D4×D43—22no—
76C2×D4×D43—22no—
77C2×D4×D43—22no—
78C2×D4×D43—41no—
79C2×D4×D43—41no—
80C2×D4×D43C2×C414yescomplemented
81C23×Dic43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C2×C8×D43—22no—
87C2×C8×D43—22no—
88C2×C8×D43—41no—
89#13063321—22no—
90#13063321C2×C414yescomplemented
91#13063299—22no—
92#13063299C2×C414yescomplemented
93#13063297—28no—
94#13063296—22no—
95#13063296C2×C414yescomplemented
96#13063294—28no—
97#13063293—28no—
98D4×Dic43—22no—
99D4×Dic43C2×C414yescomplemented
100C4×C22⋊D43—44no—
101C4×C22⋊D43C2×C414yes—
102C4×C22⋊D43D414yes—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4D411yescharacteristic
110C4⋊C4×D43—22no—
111C4⋊C4×D43—41no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43D411yescharacteristic
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43C2311yescharacteristic
121Dic43⋊C8—22no—
122#13063247—22no—
123#13063247—41no—
124#13063246—22no—
125#13063246—22no—
126#13063246—41no—
127#13063246—41no—
128#13063245—22no—
129#13063245—41no—
130C22⋊(C43⋊C8)—22no—
131(C2×D43)⋊C8—22no—
132C8×Dic43—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C25×C43—21no—
137C22×D4×C43—22no—
138C22×D4×C43—22no—
139C22×D4×C43—21no—
140C22×D4×C43—22no—
141C22×D4×C43—41no—
142C22×D4×C43—41no—
143C22×D4×C43C2×C414yescomplemented
144C22×D4×C43C2311yescharacteristic
145C22×D4×C43C2311yescharacteristic
146C23×C4×C43—21no—
147C23×C4×C43C2311yescharacteristic
148C22×C8×C43—22no—
149C22×C8×C43—22no—
150C22×C8×C43—41no—
151C22×C8×C43C2311yescharacteristic
152C22×C8×C43C2311yescharacteristic
153C2×C4⋊C4×C43—22no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43—41no—
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C4⋊C4×C43C2311yescharacteristic
158#102×C43—22no—
159#102×C43—22no—
160#102×C43—22no—
161#102×C43D414yescomplemented
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—24no—
165C24×C43—42no—
166C24×C43—42no—
167C24×C43—42no—
168C24×C43—42no—
169C24×C43—81no—
170C24×C43—81no—
171C24×C43C2×D411yescharacteristic
172C23×D43—21no—
173C23×D43—24no—
174C23×D43—42no—
175C23×D43—42no—
176C23×D43—42no—
177C23×D43—42no—
178C23×D43—81no—
179C23×D43—81no—
180C23×D43C2×D411yescharacteristic
181C2×D4×C43—24no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—28no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—44no—
194C2×D4×C43—44no—
195C2×D4×C43—44no—
196C2×D4×C43C22×C412yes—
197C2×D4×C43C22×C412yes—
198C2×D4×C43C2×D412yes—
199C2×D4×C43#4112yes—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—42no—
207C22×C4×C43—42no—
208C22×C4×C43—81no—
209C22×C4×C43C22×C412yes—
210C22×C4×C43C2×D412yes—
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—24no—
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—42no—
219C2×C22⋊D43—42no—
220C2×C22⋊D43—432no—
221C2×C22⋊D43—42no—
222C2×C22⋊D43—42no—
223C2×C22⋊D43—42no—
224C2×C22⋊D43—42no—
225C2×C22⋊D43—42no—
226C2×C22⋊D43—42no—
227C2×C22⋊D43—81no—
228C2×C22⋊D43—81no—
229C2×C22⋊D43C22⋊C414yes—
230C2×C22⋊D43D814yes—
231C2×C22⋊D43SD1614yes—
232C22×Dic43—24no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—42no—
237C22×Dic43—42no—
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241D4×D43—28no—
242D4×D43—44no—
243D4×D43—44no—
244D4×D43—44no—
245C2×D172—21no—
246C2×D172—21no—
247C2×D172—21no—
248C2×D172—21no—
249C2×D172—21no—
250C2×D172C22×C412yes—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—21no—
255C2×C4×D43—42no—
256C2×C4×D43—42no—
257C2×C4×D43—81no—
258C2×C4×D43C22×C412yes—
259C2×C4×D43C2×D412yes—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—44no—
266C2×C8×C43C2×D412yescomplemented
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—42no—
271C4⋊C4×C43C2×D412yescomplemented
272C22⋊Dic43—24no—
273C22⋊Dic43—24no—
274C22⋊Dic43—42no—
275C22⋊Dic43C22⋊C414yes—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—42no—
278(C2×D43)⋊C4C22⋊C414yes—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43C22×C412yes—
285Dic43⋊C4—42no—
286Dic43⋊C4—42no—
287Dic43⋊C4—81no—
288Dic43⋊C4C22⋊C414yes—
289C4×Dic43—42no—
290C4×Dic43C22×C412yes—
291C4×Dic43C2×D412yes—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C8×D43—44no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—48no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—48no—
319C23×C43—84no—
320C23×C43—84no—
321C23×C43—84no—
322C23×C43—84no—
323C23×C43—84no—
324C23×C43C2×C22⋊C412yes—
325C23×C43C2×D812yes—
326C23×C43C2×SD1612yes—
327C23×C43C22×D411yescharacteristic
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—21no—
331C22×D43—21no—
332C22×D43—22no—
333C22×D43—48no—
334C22×D43—41no—
335C22×D43—41no—
336C22×D43—41no—
337C22×D43—41no—
338C22×D43—41no—
339C22×D43—41no—
340C22×D43—48no—
341C22×D43—84no—
342C22×D43—84no—
343C22×D43—84no—
344C22×D43—84no—
345C22×D43—84no—
346C22×D43C2×C22⋊C412yes—
347C22×D43C2×D812yes—
348C22×D43C2×SD1612yes—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—22no—
353D4×C43—22no—
354D4×C43—48no—
355D4×C43—41no—
356D4×C43—41no—
357D4×C43C4×D414yescomplemented
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—84no—
371C2×C4×C43C2×C22⋊C412yes—
372C2×C4×C43C23×C411yescharacteristic
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C2×#4111yescharacteristic
376C2×C4×C43H(5,𝔽2)11yescharacteristic
377C2×C4×C43H(5,𝔽2)11yescharacteristic
378C22⋊D43—48no—
379C22⋊D43—48no—
380C22⋊D43—48no—
381C22⋊D43—48no—
382C22⋊D43—84no—
383C22⋊D43#102116yesdirect product factor
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—22no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—48no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43C2×C22⋊C412yes—
399C2×Dic43C2×C22⋊C412yes—
400C2×Dic43C2×C22⋊C412yes—
401C2×Dic43C2×D812yes—
402C2×Dic43C2×SD1612yes—
403D172—22no—
404D172—22no—
405D172—41no—
406D172—41no—
407C4×D43—22no—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—22no—
411C4×D43—84no—
412C8×C43—22no—
413C8×C43—41no—
414C43⋊C8—41no—
415C43⋊C8—41no—
416D4×#102—431nomaximal, Sylow
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—22no—
421C22×C43—22no—
422C22×C43—22no—
423C22×C43—24no—
424C22×C43—42no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43—42no—
432C22×C43—42no—
433C22×C43—816no—
434C22×C43—81no—
435C22×C43—81no—
436C22×C43—81no—
437C22×C43—81no—
438C22×C43C2×#10214yescomplemented
439C22×C43C22×C22⋊C411yescharacteristic
440C22×C43D4211yescharacteristic
441C22×C43#54611yescharacteristic
442C22×C43C22×D811yescharacteristic
443C22×C43C22×SD1611yescharacteristic
444C22×C43#57611yescharacteristic
445C22×C43#57711yescharacteristic
446C2×D43—22no—
447C2×D43—22no—
448C2×D43—22no—
449C2×D43—22no—
450C2×D43—22no—
451C2×D43—22no—
452C2×D43—42no—
453C2×D43—42no—
454C2×D43—42no—
455C2×D43—816no—
456C2×D43—81no—
457C2×D43—81no—
458C2×D43—81no—
459C2×D43—81no—
460C2×D43C2×#10214yescomplemented
461C4×C43—22no—
462C4×C43—42no—
463C4×C43—81no—
464C4×C43C2×C4×D411yescharacteristic
465C4×C43#51811yescharacteristic
466C4×C43D4211yescharacteristic
467C4×C43#54611yescharacteristic
468Dic43—22no—
469Dic43—22no—
470Dic43—42no—
471Dic43—81no—
472Dic43—81no—
473Dic43C2×#10214yescomplemented
474C2×D42—431no—
475C2×C8×D4—431no—
476C22×#102—431no—
477C22×#102D4311yescharacteristic, complemented
478D4×C4⋊C4—431no—
479#1982—431no—
480#1957—431no—
481#1893—431no—
482#1893—431no—
483#1874—431no—
484#1874—431no—
485#1802—431no—
486#1786—431no—
487#1786—431no—
488C4×#102—431no—
489C2×C43—24no—
490C2×C43—44no—
491C2×C43—82no—
492C2×C43D4×C22⋊C411yescharacteristic
493C2×C43C22×#10211yescharacteristic
494C2×C43#289711yescharacteristic
495C2×C43D4×D811yescharacteristic
496C2×C43D4×SD1611yescharacteristic
497C2×C43#329411yescharacteristic
498C2×C43#329511yescharacteristic
499D43—24no—
500D43—82no—
501C23×D4—431no—
502C23×D4—861no—
503C23×D4C2×D4311yescharacteristic
504C23×C8—431no—
505C23×C8C2×D4311yescharacteristic, complemented
506D42—438no—
507D42—864no—
508C2×#127—431no—
509C2×#121—431no—
510C2×#121—431no—
511C2×#121—861no—
512C2×#120—861no—
513C2×#120—861no—
514C2×C4×D4—431no—
515C2×C4×D4—431no—
516C2×C4×D4—861no—
517C22×C4⋊C4—431no—
518C22×C4⋊C4C2×D4311yescharacteristic, complemented
519C8×D4—864no—
520C2×C4⋊C8—431no—
521C2×#102—24no—
522C2×#102—431no—
523C2×#102—431no—
524C2×#102—431no—
525C2×#102—431no—
526C2×#102—431no—
527C2×#102—431no—
528C2×#102—431no—
529C2×#102—431no—
530C2×#102—864no—
531C2×#102C2×D4311yescharacteristic
532C2×#102C2×D4311yescharacteristic
533C2×#102C2×D4311yescharacteristic, complemented
534C2×#102C2×D4311yescharacteristic, complemented
535C2×C22⋊C8—431no—
536C2×C22⋊C8—431no—
537C2×C4×C8—431no—
538#389—861no—
539#385—861no—
540#385—861no—
541#384—431no—
542#380—431no—
543#380—431no—
544C4×C4⋊C4—431no—
545#340—431no—
546#340—431no—
547#340—431no—
548#340—431no—
549C43D4×#10211yescharacteristic, complemented, Sylow
550C25—21no—
551C25—861no—
552C22×D4—22no—
553C22×D4—22no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—41no—
557C22×D4—41no—
558C22×D4—431no—
559C22×D4—434no—
560C22×D4—431no—
561C22×D4—862no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—861no—
565C22×D4—868no—
566C22×D4—862no—
567C22×D4—862no—
568C22×D4—861no—
569C22×D4—861no—
570C22×D4—1721no—
571C22×D4—1721no—
572C22×D4—1724no—
573C22×D4—1724no—
574C22×D4C4×D4314yescomplemented
575C22×D4C22×D4311yescharacteristic
576C22×D4C22×D4311yescharacteristic
577C23×C4—21no—
578C23×C4—431no—
579C23×C4—861no—
580C23×C4—861no—
581C23×C4C22×D4311yescharacteristic
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—41no—
585C22×C8—431no—
586C22×C8—431no—
587C22×C8—862no—
588C22×C8—862no—
589C22×C8—1721no—
590C22×C8C22×D4311yescharacteristic
591C22×C8C22×D4311yescharacteristic
592#127—434no—
593#127—862no—
594#121—434no—
595#121—434no—
596#121—868no—
597#121—862no—
598#121—862no—
599#120—868no—
600#120—868no—
601C4×D4—434no—
602C4×D4—434no—
603C4×D4—434no—
604C4×D4—862no—
605C4×D4—1724no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—431no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—862no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—1721no—
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C4⋊C4C22×D4311yescharacteristic
620C2×C22⋊C4—431no—
621C2×C22⋊C4—431no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C42—431no—
628C2×C42—861no—
629C4⋊C8—862no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—862no—
634#102—862no—
635#102—862no—
636#102—862no—
637#102—1721no—
638#102—1721no—
639#102—1721no—
640#102—1721no—
641#102C22⋊D4314yesdirect product factor
642C22⋊C8—862no—
643C22⋊C8—862no—
644C4×C8—862no—
645#95—861no—
646#95—861no—
647#95—861no—
648C24—21no—
649C24—21no—
650C24—24no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—431no—
658C24—864no—
659C24—861no—
660C24—3441no—
661C24—3441no—
662C24—1722no—
663C24—1722no—
664C24—1722no—
665C24—1722no—
666C24D4×D4311yescharacteristic
667C2×D4—28no—
668C2×D4—24no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—434no—
683C2×D4—434no—
684C2×D4—434no—
685C2×D4—432no—
686C2×D4—864no—
687C2×D4—864no—
688C2×D4—864no—
689C2×D4—868no—
690C2×D4—864no—
691C2×D4—864no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—861no—
697C2×D4—3441no—
698C2×D4—3441no—
699C2×D4—1722no—
700C2×D4—1722no—
701C2×D4—1724no—
702C2×D4—1724no—
703C2×D4—1724no—
704C2×D4—1722no—
705C2×D4—1722no—
706C2×D4—17232no—
707C2×D4—1722no—
708C2×D4—1722no—
709C2×D4—1722no—
710C2×D4—1722no—
711C2×D4C2×C4×D4312yes—
712C2×D4C2×C4×D4312yes—
713C2×D4#1062189812yes—
714C2×D4C2×C22⋊D4312yes—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—81no—
724C22×C4—431no—
725C22×C4—431no—
726C22×C4—431no—
727C22×C4—432no—
728C22×C4—432no—
729C22×C4—864no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—3441no—
738C22×C4—1722no—
739C22×C4—1722no—
740C22×C4—1722no—
741C22×C4—1722no—
742C22×C4C2×C4×D4312yes—
743C22×C4D4×D4311yescharacteristic
744C22×C4D4×D4312yes—
745C22×C4C23×D4311yescharacteristic
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8—861no—
753C2×C8—861no—
754C2×C8—861no—
755C2×C8—861no—
756C2×C8—861no—
757C2×C8—861no—
758C2×C8—1724no—
759C2×C8C2×C22⋊D4312yescomplemented
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—42no—
764C4⋊C4—434no—
765C4⋊C4—432no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C4⋊C4—3441no—
772C4⋊C4—1722no—
773C4⋊C4—1722no—
774C4⋊C4C2×C22⋊D4312yescomplemented
775C22⋊C4—434no—
776C22⋊C4—434no—
777C22⋊C4—864no—
778C22⋊C4—864no—
779C22⋊C4—864no—
780C22⋊C4—1722no—
781C22⋊C4—1722no—
782C42—432no—
783C42—432no—
784C42—1722no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—48no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—48no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—432no—
811C23—432no—
812C23—432no—
813C23—861no—
814C23—861no—
815C23—861no—
816C23—861no—
817C23—862no—
818C23—3444no—
819C23—3444no—
820C23—3444no—
821C23—3444no—
822C23—3444no—
823C23—1728no—
824C23—1728no—
825C23—1721no—
826C23—1721no—
827C23—1721no—
828C23—1721no—
829C23—1721no—
830C23—1721no—
831C23C22⋊C4×D4312yes—
832C23D8×D4312yes—
833C23SD16×D4312yes—
834C23C2×D4×D4311yescharacteristic
835D4—22no—
836D4—22no—
837D4—22no—
838D4—22no—
839D4—22no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—4316no—
844D4—862no—
845D4—862no—
846D4—3444no—
847D4—1728no—
848D4—1728no—
849D4—1728no—
850D4—1728no—
851D4—1721no—
852D4—1721no—
853D4C4×C22⋊D4314yescomplemented
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—84no—
867C2×C4—432no—
868C2×C4—432no—
869C2×C4—432no—
870C2×C4—432no—
871C2×C4—432no—
872C2×C4—861no—
873C2×C4—861no—
874C2×C4—861no—
875C2×C4—861no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—3444no—
882C2×C4—1728no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4—1721no—
887C2×C4—1721no—
888C2×C4—1721no—
889C2×C4—1721no—
890C2×C4—1721no—
891C2×C4C22⋊C4×D4312yes—
892C2×C4C22×C4×D4311yescharacteristic
893C2×C4C2×D4×D4311yescharacteristic
894C2×C4C22×C22⋊D4311yescharacteristic
895C2×C4C2×#1062189811yescharacteristic
896C2×C4#1306337011yescharacteristic
897C2×C4#1306337011yescharacteristic
898C8—22no—
899C8—41no—
900C8—1721no—
901C8—1721no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—24no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—434no—
924C22—862no—
925C22—862no—
926C22—862no—
927C22—862no—
928C22—862no—
929C22—862no—
930C22—34416no—
931C22—3441no—
932C22—3441no—
933C22—3441no—
934C22—3441no—
935C22—1722no—
936C22—1722no—
937C22—1722no—
938C22#102×D4314yescomplemented
939C22C2×C22⋊C4×D4311yescharacteristic
940C22D4×C22⋊D4311yescharacteristic
941C22#1458353911yescharacteristic
942C22C2×D8×D4311yescharacteristic
943C22C2×SD16×D4311yescharacteristic
944C22#1458370011yescharacteristic
945C22#1458370511yescharacteristic
946C4—22no—
947C4—42no—
948C4—81no—
949C4—434no—
950C4—862no—
951C4—862no—
952C4—3441no—
953C4—3441no—
954C4—1722no—
955C4C2×C4×C22⋊D4311yescharacteristic
956C4#1458337211yescharacteristic
957C4D4×C22⋊D4311yescharacteristic
958C4#1458353911yescharacteristic
959C2—24no—
960C2—44no—
961C2—82no—
962C2—864no—
963C2—3442no—
964C2C22⋊C4×C22⋊D4311yescharacteristic
965C2C2×#102×D4311yescharacteristic
966C2#1914311611yescharacteristic
967C2D8×C22⋊D4311yescharacteristic
968C2SD16×C22⋊D4311yescharacteristic
969C2#1914640411yescharacteristic
970C2#1914641511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×D4×C22⋊D43C2
cosocleC22×C4×C43C24
hypercenterC22×#102D43
hypocenterC43D4×#102
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D43C2semidirect
3. C2×#102×D43C2semidirect
4. C4⋊C4×C22⋊D43C2semidirect
5. #19135520C2semidirect
6. #19135399C2semidirect
7. #19135023C2semidirect
8. #19135020C2semidirect
9. #19134912C2semidirect
10. #19134909C2semidirect
11. #19134593C2semidirect
12. #19134526C2semidirect
13. #19134524C2semidirect
14. #102×Dic43C2semidirect
15. C22×#102×C43C2semidirect
18. C22×C8×D43C22semidirect
20. D4×C22⋊D43C4semidirect
30. C2×C4⋊C4×D43C22semidirect
32. C2×Dic43⋊C8C22semidirect
33. C2×#13063247C22semidirect
34. C2×#13063247C22semidirect
37. C2×#13063246C22semidirect
38. C2×#13063246C22semidirect
39. C2×#13063245C22semidirect
40. C2×#13063245C22semidirect
42. C2×C22⋊(C43⋊C8)C22semidirect
43. C2×(C2×D43)⋊C8C22semidirect
44. C2×C8×Dic43C22semidirect
48. #14582768C22semidirect
49. #14582759C22semidirect
50. #14582756C22semidirect
51. C4⋊C4×Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
57. C23×C8×C43C22semidirect
58. C22×C4⋊C4×C43C22semidirect
62. C2×#102×C43C22semidirect
63. C2×#102×C43C22semidirect
80. C2×D4×D43C2×C4semidirect
90. #13063321C2×C4semidirect
92. #13063299C2×C4semidirect
95. #13063296C2×C4semidirect
99. D4×Dic43C2×C4semidirect
143. C22×D4×C43C2×C4semidirect
161. #102×C43D4semidirect
266. C2×C8×C43C2×D4semidirect
271. C4⋊C4×C43C2×D4semidirect
357. D4×C43C4×D4semidirect
383. C22⋊D43#102direct (N × H)
438. C22×C43C2×#102semidirect
460. C2×D43C2×#102semidirect
473. Dic43C2×#102semidirect
477. C22×#102D43semidirect
505. C23×C8C2×D43semidirect
518. C22×C4⋊C4C2×D43semidirect
533. C2×#102C2×D43semidirect
534. C2×#102C2×D43semidirect
549. C43D4×#102semidirect
574. C22×D4C4×D43semidirect
641. #102C22⋊D43direct (N × H)
759. C2×C8C2×C22⋊D43semidirect
774. C4⋊C4C2×C22⋊D43semidirect
853. D4C4×C22⋊D43semidirect
938. C22#102×D43semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D432
C2×C8×C22⋊D432
C2×#102×D432
C4⋊C4×C22⋊D432
#191355202
#191353992
#191350232
#191350202
#191349122
#191349092
#191345932
#191345262
#191345242
#102×Dic432
C22×#102×C432
D4×#10243