Finite Group Databasebeta

← C2×#19145596 #25967851

Subgroups — C2×#19145596 #25967851

Order 11008.

2242 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic, complemented
2C2×#124×D43C211yesmaximal, characteristic
3#19145596C2116yesmaximal, direct product factor
4C2×#14583292C211yesmaximal, characteristic, complemented
5C2×#14583290C211yesmaximal, characteristic, complemented
6C2×#14583260C211yesmaximal, characteristic, complemented
7C2×#14583257C211yesmaximal, characteristic, complemented
8C2×#14583122C211yesmaximal, characteristic, complemented
9C2×#14583121C211yesmaximal, characteristic, complemented
10C2×#14583118C211yesmaximal, characteristic, complemented
11C2×#14583056C211yesmaximal, characteristic, complemented
12C2×#14583053C211yesmaximal, characteristic, complemented
13C2×#14583051C211yesmaximal, characteristic
14C2×#14583048C211yesmaximal, characteristic
15C2×#14582955C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×Dic172C2211yescharacteristic, complemented
20C22×#10621885C2211yescharacteristic, complemented
21C22×#10621885C2211yescharacteristic, complemented
22C22×#10621873C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621884C2211yescharacteristic
25#14583453—24no—
26#14583453C2218yescomplemented
27C2×#13063324C2211yescharacteristic, complemented
28C2×#13063323C2211yescharacteristic, complemented
29C2×#13063315—21no—
30C2×#13063314C2211yescharacteristic
31C2×#13063313C2211yescharacteristic
32C2×#13063312C2211yescharacteristic
33C2×#13063311—21no—
34C2×#13063311—21no—
35#124×D43—24no—
36#124×D43C2218yes—
37C2×#13063305C2211yescharacteristic
38C2×#13063303—21no—
39C2×#13063301C2211yescharacteristic
40C2×C4×Dic86—21no—
41C2×C4×Dic86C2211yescharacteristic, complemented
42C2×#13063282—21no—
43C2×C22⋊C4×D43—21no—
44C2×C22⋊C4×D43—21no—
45C2×C42×D43C2211yescharacteristic
46#14583292C2218yescomplemented
47#14583290C2218yescomplemented
48#14583260C2218yescomplemented
49#14583257C2218yescomplemented
50#14583122C2218yescomplemented
51#14583121C2218yescomplemented
52#14583118C2218yescomplemented
53#14583056C2218yescomplemented
54#14583053C2218yescomplemented
55#14583051C2218yes—
56#14583048C2218yes—
57#14582955C2218yescomplemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063249C2211yescharacteristic, complemented
61C2×#13063248C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic, complemented
68C2×#13063235C2211yescharacteristic, complemented
69C22×Q16×C43C2211yescharacteristic, complemented
70C22×SD16×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic, complemented
73C43×#464C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C22×Dic86—21no—
79C22×Dic86—21no—
80C22×Dic86C2311yescharacteristic
81C22×Dic86C2311yescharacteristic
82C2×Q8×D43—22no—
83C2×Q8×D43—42no—
84C2×Q8×D43—42no—
85C2×Q8×D43C2314yes—
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C2×D4×D43—22no—
89C2×D4×D43—42no—
90C2×D4×D43—42no—
91C2×D4×D43C2314yes—
92C22×C4×D43—21no—
93C22×C4×D43D411yescharacteristic
94C22×C4×D43D411yescharacteristic
95C22×C4×D43C2311yescharacteristic
96C2×Dic172—42no—
97C2×Dic172C2314yescomplemented
98C2×#10621885—42no—
99C2×#10621885—42no—
100C2×#10621885C2314yescomplemented
101C2×#10621885C2314yescomplemented
102C2×#10621873—42no—
103C2×#10621873C2314yes—
104C2×#10621883—42no—
105C2×#10621883C2314yes—
106C2×#10621884—42no—
107C2×#10621884C2314yes—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110#13063324—22no—
111#13063324C2314yescomplemented
112#13063323—22no—
113#13063323C2314yescomplemented
114#13063315—28no—
115#13063314—22no—
116#13063314C2314yes—
117#13063313—22no—
118#13063313C2314yes—
119#13063312—22no—
120#13063312C2314yes—
121#13063311—28no—
122#13063311—28no—
123#13063305—22no—
124#13063305C2314yes—
125#13063303—28no—
126#13063301—22no—
127#13063301C2314yes—
128C4×Dic86—22no—
129C4×Dic86—28no—
130C4×Dic86C2314yescomplemented
131#13063282—28no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C22⋊C4×D43—28no—
148C22⋊C4×D43—28no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43D411yescharacteristic
151C2×C4×Dic43D411yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153C42×D43D414yes—
154C42×D43C2314yes—
155C4⋊(C43⋊C8)C2314yescomplemented
156#13063250C2314yescomplemented
157#13063249C2314yescomplemented
158#13063248C2314yescomplemented
159#13063247C2314yes—
160#13063246C2314yes—
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164#13063235C2314yescomplemented
165#13063235C2314yescomplemented
166C22×Q8×C43C2311yescharacteristic
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C2×Q16×C43—42no—
170C2×Q16×C43C2314yescomplemented
171C2×SD16×C43—42no—
172C2×SD16×C43C2314yes—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175#124×C43—22no—
176#124×C43C2314yes—
177C4×Q8×C43—22no—
178C4×Q8×C43C2314yescomplemented
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43—21no—
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C4⋊C8×C43C2314yescomplemented
186#103×C43C2314yescomplemented
187#102×C43C2314yes—
188C24×C43—21no—
189C23×D43—21no—
190C23×D43—24no—
191C23×D43—44no—
192C23×D43—44no—
193C23×D43—44no—
194C23×D43C2×D411yescharacteristic
195C2×Q8×C43—21no—
196C2×Q8×C43—21no—
197C2×Q8×C43—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43C2412yes—
202C2×Q8×C43C2412yes—
203C2×D4×C43—21no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43C2412yes—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—44no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221Q8×D43—44no—
222Q8×D43—44no—
223Q8×D43—48no—
224D4×D43—44no—
225D4×D43—44no—
226D4×D43—48no—
227C2×D172—21no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172C2412yes—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43—24no—
234C2×C4×D43—24no—
235C2×C4×D43—42no—
236C2×C4×D43—44no—
237C2×C4×D43C2×D412yes—
238C2×C4×D43C2×D414yes—
239C2×C4×D43C2×D414yes—
240C2×C4×D43C2412yes—
241C2×Dic86—22no—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86—22no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86—24no—
248C2×Dic86—24no—
249C2×Dic86—44no—
250C2×Dic86—44no—
251C2×Dic86C2412yes—
252C2×Dic86C2412yes—
253Q16×C43—44no—
254SD16×C43—44no—
255C2×C8×C43—22no—
256C2×C8×C43—22no—
257C2×C8×C43C2412yes—
258C2×C8×C43C2412yes—
259C4⋊C4×C43—24no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C2412yes—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—24no—
264C42×C43—24no—
265C42×C43C2×D412yes—
266C42×C43C2412yes—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269#10621885—44no—
270#10621885—44no—
271#10621884—44no—
272#10621883—44no—
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—24no—
279C4⋊Dic43—21no—
280C4⋊Dic43—24no—
281C4⋊Dic43C2412yes—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287C4×Dic43—24no—
288C4×Dic43C2×D412yes—
289C4×Dic43C2×D414yes—
290C4×Dic43C2×D414yes—
291C4×Dic43C2412yes—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—22no—
294C2×C43⋊C8C2412yes—
295C2×C43⋊C8C2412yes—
296Dic172—44no—
297#10621873—44no—
298C23×C43—22no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—48no—
307C22×D43—48no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—48no—
312C22×D43—816no—
313C22×D43#13714yes—
314C22×D43C22×D412yes—
315Q8×C43—22no—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—42no—
320Q8×C43—42no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—42no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43C22×D412yes—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43H(5,𝔽2)12yes—
336C2×C4×C43H(5,𝔽2)12yes—
337C2×C4×C43C2511yescharacteristic
338C22⋊D43—48no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351D172—22no—
352D172—22no—
353D172—42no—
354C4×D43—28no—
355C4×D43—24no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—44no—
359C4×D43—48no—
360Dic86—22no—
361Dic86—22no—
362Dic86—22no—
363Dic86—22no—
364Dic86—48no—
365Dic86—48no—
366Dic86—42no—
367Dic86—42no—
368C8×C43—22no—
369C8×C43—22no—
370C43⋊C8—22no—
371C43⋊C8—22no—
372C2×#3215—431nomaximal, Sylow
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—84no—
377C22×C43#53512yes—
378C22×C43C2×#13712yes—
379C22×C43#57512yes—
380C22×C43C23×D411yescharacteristic
381C2×D43—22no—
382C2×D43—28no—
383C2×D43—22no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—816no—
388C2×D43—84no—
389C2×D43C2×#13714yes—
390C4×C43—22no—
391C4×C43—22no—
392C4×C43—42no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43#53512yes—
396C4×C43C2×H(5,𝔽2)11yescharacteristic
397C4×C43C2×H(5,𝔽2)11yescharacteristic
398Dic43—22no—
399Dic43—22no—
400Dic43—22no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C2×#533—431no—
405C22×#124—431no—
406#3215—4316no—
407C2×#497—431no—
408C2×#497—431no—
409C2×#489—431no—
410C2×#489—431no—
411C2×#464—431no—
412C2×#464—431no—
413C2×#464—431no—
414C2×#464D4311yescharacteristic, complemented
415C2×#451—431no—
416C2×#451—431no—
417C2×#450—431no—
418C2×#450—431no—
419C2×#432—431no—
420C2×C43—82no—
421C2×C43#321514yescomplemented
422C2×C43C2×#53511yescharacteristic
423C2×C43C22×#13711yescharacteristic
424C2×C43C2×#57511yescharacteristic
425D43—24no—
426D43—82no—
427C23×Q8—431no—
428C23×D4—431no—
429C22×Q16—431no—
430C22×Q16—431no—
431C22×Q16—431no—
432C22×Q16C2×D4311yescharacteristic, complemented
433C22×SD16—431no—
434C22×SD16—431no—
435C22×SD16—431no—
436C22×SD16C2×D4311yescharacteristic
437#533—438no—
438#533—864no—
439C2×C4⋊Q8—431no—
440C2×C4⋊Q8—431no—
441C2×#125—861no—
442C2×#124—431no—
443C2×#124—431no—
444C2×#124—438no—
445C2×#124—431no—
446C2×#124—861no—
447C2×#124—861no—
448C2×#124—864no—
449C2×#124C2×D4311yescharacteristic
450C2×C22⋊Q8—431no—
451C2×C22⋊Q8—431no—
452C2×C22⋊Q8—861no—
453C2×C4×Q8—431no—
454C2×C4×Q8—861no—
455C2×C4×Q8C2×D4311yescharacteristic, complemented
456C2×#117—861no—
457C22×C22⋊C4—861no—
458C22×C22⋊C4—861no—
459C22×C42—431no—
460#497—438no—
461#497—438no—
462#489—438no—
463#489—438no—
464#464—438no—
465#464—438no—
466#464—438no—
467#464C2×D4318yescomplemented
468#451—438no—
469#451—438no—
470#450—438no—
471#450—438no—
472#432—438no—
473C2×C4⋊C8—431no—
474C2×C4⋊C8C2×D4311yescharacteristic, complemented
475C2×#103—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103C2×D4311yescharacteristic, complemented
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102C2×D4311yescharacteristic
483C2×C22⋊C8—431no—
484C2×C22⋊C8—431no—
485C2×#97—431no—
486C2×#97—431no—
487C43C2×#321511yescharacteristic, complemented, Sylow
488C25—861no—
489C22×Q8—434no—
490C22×Q8—431no—
491C22×Q8—431no—
492C22×Q8—861no—
493C22×Q8—861no—
494C22×Q8—862no—
495C22×Q8—1722no—
496C22×Q8—1722no—
497C22×Q8C22×D4311yescharacteristic
498C22×Q8C22×D4311yescharacteristic
499C22×D4—434no—
500C22×D4—431no—
501C22×D4—862no—
502C22×D4—861no—
503C22×D4—1722no—
504C22×D4—1722no—
505C22×D4C22×D4311yescharacteristic
506C23×C4—431no—
507C23×C4—431no—
508C23×C4—431no—
509C23×C4—861no—
510C2×Q16—42no—
511C2×Q16—434no—
512C2×Q16—434no—
513C2×Q16—434no—
514C2×Q16—1722no—
515C2×Q16—1722no—
516C2×Q16—1722no—
517C2×Q16C22×D4314yescomplemented
518C2×SD16—42no—
519C2×SD16—434no—
520C2×SD16—434no—
521C2×SD16—434no—
522C2×SD16—1722no—
523C2×SD16—1722no—
524C2×SD16—1722no—
525C2×SD16C22×D4314yes—
526C22×C8—431no—
527C22×C8—431no—
528C22×C8C22×D4311yescharacteristic
529C22×C8C22×D4311yescharacteristic
530C4⋊Q8—434no—
531C4⋊Q8—434no—
532C4⋊Q8—862no—
533C4⋊Q8—862no—
534#125—868no—
535#124—22no—
536#124—434no—
537#124—434no—
538#124—434no—
539#124—868no—
540#124—868no—
541#124—862no—
542#124—862no—
543#124—862no—
544#124C22×D4314yes—
545C22⋊Q8—434no—
546C22⋊Q8—434no—
547C22⋊Q8—862no—
548C22⋊Q8—868no—
549C22⋊Q8—862no—
550C4×Q8—22no—
551C4×Q8—434no—
552C4×Q8—868no—
553C4×Q8—862no—
554C4×Q8C22×D4314yescomplemented
555#117—868no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4C22×D4311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—868no—
568C2×C22⋊C4—868no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C42—21no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—431no—
581C2×C42—434no—
582C2×C42—434no—
583C2×C42—861no—
584C2×C42C22×D4311yescharacteristic
585C4⋊C8—434no—
586C4⋊C8C22×D4314yescomplemented
587#103—434no—
588#103—434no—
589#103—434no—
590#103C22×D4314yescomplemented
591#102—434no—
592#102—434no—
593#102—434no—
594#102C22×D4314yes—
595C22⋊C8—434no—
596C22⋊C8—434no—
597#97—434no—
598#97—434no—
599C24—21no—
600C24—431no—
601C24—864no—
602C24—861no—
603C24—1724no—
604C24—1724no—
605C24—1724no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—432no—
613C2×Q8—432no—
614C2×Q8—864no—
615C2×Q8—864no—
616C2×Q8—861no—
617C2×Q8—861no—
618C2×Q8—862no—
619C2×Q8—862no—
620C2×Q8—862no—
621C2×Q8—862no—
622C2×Q8—1724no—
623C2×Q8—1724no—
624C2×Q8—1724no—
625C2×Q8—1724no—
626C2×Q8—1728no—
627C2×Q8C23×D4312yes—
628C2×Q8C23×D4312yes—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—432no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—862no—
636C2×D4—862no—
637C2×D4—1724no—
638C2×D4—1724no—
639C2×D4—1728no—
640C2×D4—1724no—
641C2×D4C23×D4312yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—431no—
646C22×C4—431no—
647C22×C4—431no—
648C22×C4—434no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—434no—
652C22×C4—864no—
653C22×C4—864no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—1722no—
660C22×C4—1724no—
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4C23×D4311yescharacteristic
664Q16—44no—
665Q16—1724no—
666Q16—1724no—
667Q16—1724no—
668SD16—44no—
669SD16—1724no—
670SD16—1724no—
671SD16—1724no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—432no—
675C2×C8—432no—
676C2×C8—862no—
677C2×C8—862no—
678C2×C8C23×D4312yes—
679C2×C8C23×D4312yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—432no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—861no—
689C4⋊C4—864no—
690C4⋊C4C23×D4312yes—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—864no—
694C22⋊C4—864no—
695C22⋊C4—864no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C42—24no—
702C42—434no—
703C42—434no—
704C42—432no—
705C42—432no—
706C42—864no—
707C42D4×D4312yes—
708C42C23×D4312yes—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—434no—
714C23—432no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—34416no—
719C23—1728no—
720C23—1728no—
721C23—1728no—
722C23—1722no—
723C23—1722no—
724C23—1722no—
725C23C2×D4×D4311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—862no—
733Q8—862no—
734Q8—862no—
735Q8—862no—
736Q8—1728no—
737Q8—1728no—
738Q8—1722no—
739Q8—1722no—
740D4—22no—
741D4—22no—
742D4—42no—
743D4—862no—
744D4—862no—
745D4—1728no—
746D4—1722no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—432no—
756C2×C4—432no—
757C2×C4—432no—
758C2×C4—868no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—864no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—1724no—
769C2×C4—1728no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4C2×D4×D4312yes—
774C2×C4C2×D4×D4312yes—
775C2×C4C2×D4×D4311yescharacteristic
776C2×C4#1306337012yes—
777C2×C4#1306337112yes—
778C2×C4C24×D4311yescharacteristic
779C8—22no—
780C8—22no—
781C8—862no—
782C8—862no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—434no—
788C22—862no—
789C22—868no—
790C22—862no—
791C22—34416no—
792C22—3444no—
793C22—1722no—
794C22—1722no—
795C22—1722no—
796C22#1458346512yes—
797C22#137×D4312yes—
798C22#1458369612yes—
799C22C22×D4×D4311yescharacteristic
800C4—22no—
801C4—22no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—862no—
806C4—862no—
807C4—862no—
808C4—1722no—
809C4—1722no—
810C4—1722no—
811C4#1458346512yes—
812C4C2×#1306337011yescharacteristic
813C4C2×#1306337111yescharacteristic
814C2—82no—
815C2—864no—
816C2—3442no—
817C2#1914559614yesdirect product factor
818C2C2×#1458346511yescharacteristic
819C2C2×#137×D4311yescharacteristic
820C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
hypercenterC2×#464D43
hypocenterC43C2×#3215
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#14583453C2semidirect
3. #19145596C2direct (N × H)
4. C2×#14583292C2semidirect
5. C2×#14583290C2semidirect
6. C2×#14583260C2semidirect
7. C2×#14583257C2semidirect
8. C2×#14583122C2semidirect
9. C2×#14583121C2semidirect
10. C2×#14583118C2semidirect
11. C2×#14583056C2semidirect
12. C2×#14583053C2semidirect
15. C2×#14582955C2semidirect
16. C2×C43×#464C2semidirect
19. C22×Dic172C22semidirect
20. C22×#10621885C22semidirect
21. C22×#10621885C22semidirect
26. #14583453C22semidirect
27. C2×#13063324C22semidirect
28. C2×#13063323C22semidirect
41. C2×C4×Dic86C22semidirect
46. #14583292C22semidirect
47. #14583290C22semidirect
48. #14583260C22semidirect
49. #14583257C22semidirect
50. #14583122C22semidirect
51. #14583121C22semidirect
52. #14583118C22semidirect
53. #14583056C22semidirect
54. #14583053C22semidirect
57. #14582955C22semidirect
58. C2×C4⋊(C43⋊C8)C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063249C22semidirect
61. C2×#13063248C22semidirect
67. C2×#13063235C22semidirect
68. C2×#13063235C22semidirect
69. C22×Q16×C43C22semidirect
72. C2×C4×Q8×C43C22semidirect
73. C43×#464C22semidirect
74. C2×C4⋊C8×C43C22semidirect
75. C2×#103×C43C22semidirect
97. C2×Dic172C23semidirect
100. C2×#10621885C23semidirect
101. C2×#10621885C23semidirect
111. #13063324C23semidirect
113. #13063323C23semidirect
130. C4×Dic86C23semidirect
155. C4⋊(C43⋊C8)C23semidirect
156. #13063250C23semidirect
157. #13063249C23semidirect
158. #13063248C23semidirect
164. #13063235C23semidirect
165. #13063235C23semidirect
170. C2×Q16×C43C23semidirect
178. C4×Q8×C43C23semidirect
185. C4⋊C8×C43C23semidirect
186. #103×C43C23semidirect
414. C2×#464D43semidirect
421. C2×C43#3215semidirect
432. C22×Q16C2×D43semidirect
455. C2×C4×Q8C2×D43semidirect
467. #464C2×D43semidirect
474. C2×C4⋊C8C2×D43semidirect
478. C2×#103C2×D43semidirect
487. C43C2×#3215semidirect
517. C2×Q16C22×D43semidirect
554. C4×Q8C22×D43semidirect
586. C4⋊C8C22×D43semidirect
590. #103C22×D43semidirect
817. C2#19145596direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834532
C2×#124×D432
#191455962
C2×#145832922
C2×#145832902
C2×#145832602
C2×#145832572
C2×#145831222
C2×#145831212
C2×#145831182
C2×#145830562
C2×#145830532
C2×#145830512
C2×#145830482
C2×#145829552
C2×C43×#4642
C2×#321543