Finite Group Databasebeta

← C2×#19146896 #25973502

Subgroups — C2×#19146896 #25973502

Order 11008.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583550C211yesmaximal, characteristic, complemented
2C2×#14583548C211yesmaximal, characteristic, complemented
3#19146896C2116yesmaximal, direct product factor
4C2×#14583248C211yesmaximal, characteristic, complemented
5C2×#14583234C211yesmaximal, characteristic, complemented
6C2×#14583233C211yesmaximal, characteristic, complemented
7C2×#14583177C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic, complemented
9C2×#14583145C211yesmaximal, characteristic, complemented
10C2×#14583103C211yesmaximal, characteristic, complemented
11C2×#14583045C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14582979C211yesmaximal, characteristic, complemented
14C2×#14582975C211yesmaximal, characteristic, complemented
15C2×#14582897C211yesmaximal, characteristic, complemented
16C2×C43×#417C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×#10621900C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23#14583550—24no—
24#14583550C2218yescomplemented
25#14583548—24no—
26#14583548C2218yescomplemented
27C2×#13063324C2211yescharacteristic
28C2×#13063323C2211yescharacteristic
29C2×#13063310—21no—
30C2×#13063308—21no—
31C2×#13063308—21no—
32C2×#13063306—21no—
33C2×#13063304C2211yescharacteristic
34C2×#13063303—21no—
35C2×#13063301C2211yescharacteristic
36C2×#13063300C2211yescharacteristic
37C2×#13063299C2211yescharacteristic
38C2×#13063297—21no—
39C2×D4×Dic43C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×C4×C22⋊D43C2211yescharacteristic
42C22×Dic43⋊C4—21no—
43C2×C4⋊C4×D43C2211yescharacteristic
44#14583248C2218yescomplemented
45#14583234C2218yescomplemented
46#14583233C2218yescomplemented
47#14583177C2218yescomplemented
48#14583148C2218yescomplemented
49#14583145C2218yescomplemented
50#14583103C2218yescomplemented
51#14583045C2218yescomplemented
52#14583044C2218yescomplemented
53#14582979C2218yescomplemented
54#14582975C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59#14582897C2218yescomplemented
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C43×#417C2218yescomplemented
73C2×#103×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C2×#10621900—24no—
80C2×#10621900—22no—
81C2×#10621900—42no—
82C2×#10621900C2314yes—
83C22×Dic86—21no—
84C22×Dic86C2311yescharacteristic
85C22×D172—21no—
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43D411yescharacteristic
90C23×Dic43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95C2×#10621873—42no—
96C2×#10621873C2314yes—
97C2×#10621884—42no—
98C2×#10621884C2314yes—
99C2×#10621882—24no—
100C2×#10621882C2314yes—
101C2×#10621872—42no—
102C2×#10621872C2314yes—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105#13063324—22no—
106#13063324C2314yes—
107#13063323—22no—
108#13063323C2314yes—
109#13063310—28no—
110#13063308—28no—
111#13063308—28no—
112#13063306—28no—
113#13063304—22no—
114#13063304C2314yes—
115#13063303—28no—
116#13063301—22no—
117#13063301C2314yes—
118#13063300—22no—
119#13063300C2314yes—
120#13063299—22no—
121#13063299C2314yes—
122#13063297—28no—
123D4×Dic43—22no—
124D4×Dic43C2314yes—
125#13063287—22no—
126#13063287C2314yes—
127C4×C22⋊D43D414yes—
128C4×C22⋊D43C2314yes—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—28no—
138C2×Dic43⋊C4D411yescharacteristic
139C4⋊C4×D43—22no—
140C4⋊C4×D43C2314yes—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43D411yescharacteristic
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4D411yescharacteristic
149C2×C4×Dic43C2311yescharacteristic
150#13063259C2314yes—
151#13063258C2314yes—
152#13063258C2314yes—
153Dic43⋊C8C2314yes—
154#13063250C2314yes—
155#13063249C2314yes—
156#13063248C2314yes—
157#13063248C2314yes—
158#13063247C2314yes—
159#13063246C2314yes—
160C22⋊(C43⋊C8)C2314yes—
161(C2×D43)⋊C8C2314yes—
162C8×Dic43C2314yes—
163C2×#41×C43—22no—
164C2×#41×C43—24no—
165C2×#41×C43—42no—
166C2×#41×C43C2314yes—
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43—21no—
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43—21no—
172C23×C4×C43C2311yescharacteristic
173C2×M16×C43—42no—
174C2×M16×C43C2314yes—
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2311yescharacteristic
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43—22no—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C4⋊C4×C43C2314yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184#102×C43C2314yes—
185#102×C43C2314yes—
186C24×C43—21no—
187C24×C43C2×D411yescharacteristic
188C23×D43—21no—
189C23×D43C2×D411yescharacteristic
190#41×C43—28no—
191#41×C43—44no—
192#41×C43—48no—
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43C2412yes—
197C2×D4×C43—21no—
198C2×D4×C43—22no—
199C2×D4×C43—24no—
200C2×D4×C43—44no—
201C2×D4×C43#4114yescomplemented
202C2×D4×C43C2412yes—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—24no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—24no—
209C22×C4×C43—21no—
210C22×C4×C43—44no—
211C22×C4×C43—44no—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2412yes—
215C22×C4×C43C2411yescharacteristic
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—44no—
220C2×C22⋊D43—44no—
221C2×C22⋊D43C2×D414yes—
222C22×Dic43—24no—
223C22×Dic43—24no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—44no—
228C22×Dic43—44no—
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232#10621900—28no—
233#10621900—44no—
234#10621900—48no—
235#10621898—432no—
236C2×D172—21no—
237C2×D172—24no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172—44no—
241C2×D172C2412yes—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—24no—
245C2×C4×D43—24no—
246C2×C4×D43—44no—
247C2×C4×D43—44no—
248C2×C4×D43C2×D412yes—
249C2×C4×D43C2412yes—
250C2×Dic86—22no—
251C2×Dic86—22no—
252C2×Dic86—21no—
253C2×Dic86—24no—
254C2×Dic86—44no—
255C2×Dic86C2412yes—
256M16×C43—44no—
257C2×C8×C43—22no—
258C2×C8×C43—22no—
259C2×C8×C43C2412yes—
260C2×C8×C43C2412yes—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—24no—
264C4⋊C4×C43C2412yes—
265C4⋊C4×C43C2412yes—
266C22⋊Dic43—24no—
267C22⋊Dic43—24no—
268C22⋊Dic43C2×D414yes—
269#10621884—44no—
270#10621882—28no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4C2×D414yes—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43C2412yes—
279C4⋊Dic43C2412yes—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4C2×D414yes—
287C4×Dic43C2×D412yes—
288C4×Dic43C2412yes—
289C2×C43⋊C8—22no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8C2412yes—
292C2×C43⋊C8C2412yes—
293#10621873—44no—
294#10621872—44no—
295C23×C43—24no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43C22×D412yes—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43C22×D412yes—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—42no—
315D4×C43—24no—
316D4×C43—22no—
317D4×C43—48no—
318D4×C43C2×#4114yescomplemented
319C2×C4×C43—22no—
320C2×C4×C43—24no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—48no—
327C2×C4×C43—48no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43C22×D412yes—
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C2×#4112yes—
334C2×C4×C43H(5,𝔽2)12yes—
335C2×C4×C43C2511yescharacteristic
336C22⋊D43—28no—
337C22⋊D43—48no—
338C22⋊D43—48no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—48no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43—48no—
349C2×Dic43AGL(1,ℤ/8)14yes—
350C2×Dic43C22×D412yes—
351C2×Dic43C22×D412yes—
352C2×Dic43C22×D412yes—
353D172—22no—
354D172—22no—
355D172—48no—
356D172—42no—
357C4×D43—24no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—48no—
361C4×D43—48no—
362Dic86—22no—
363Dic86—22no—
364Dic86—42no—
365Dic86—48no—
366C8×C43—22no—
367C8×C43—22no—
368C43⋊C8—22no—
369C43⋊C8—22no—
370C2×#3330—431nomaximal, Sylow
371C22×C43—24no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—44no—
376C22×C43—48no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43#54612yes—
380C22×C43C2×AGL(1,ℤ/8)12yes—
381C22×C43#57812yes—
382C22×C43C23×D411yescharacteristic
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—44no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—84no—
391C4×C43—22no—
392C4×C43—42no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43#54612yes—
396C4×C43C22×#4111yescharacteristic
397C4×C43C2×H(5,𝔽2)11yescharacteristic
398Dic43—22no—
399Dic43—22no—
400Dic43—42no—
401Dic43—42no—
402Dic43—42no—
403Dic43C2×AGL(1,ℤ/8)14yes—
404C2×#547—431no—
405C2×#547—431no—
406#3330—4316no—
407C2×#487—431no—
408C2×#484—431no—
409C2×#484—431no—
410C2×#474—431no—
411C2×#468—431no—
412C2×#468—431no—
413C2×#461—431no—
414C2×#449—431no—
415C2×#449—431no—
416C2×C4×D8—431no—
417C2×#436—431no—
418C2×#417—431no—
419C2×#417D4311yescharacteristic, complemented
420C2×C43—42no—
421C2×C43—44no—
422C2×C43#333014yescomplemented
423C2×C43C2×#54611yescharacteristic
424C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C43C2×#57811yescharacteristic
426D43—42no—
427D43—82no—
428C22×#41—431no—
429C22×#41—861no—
430C22×#41C2×D4311yescharacteristic
431C22×SD16—431no—
432C22×SD16—431no—
433C22×D8—431no—
434C22×M16—431no—
435C22×M16C2×D4311yescharacteristic
436#547—438no—
437#547—438no—
438#547—864no—
439#547—864no—
440C2×C4⋊Q8—431no—
441C2×C4⋊Q8—431no—
442C2×#123—861no—
443C2×#123—861no—
444C2×#123—861no—
445C2×#123—861no—
446C2×C22⋊Q8—431no—
447C2×C22⋊Q8—431no—
448C2×C22⋊Q8—861no—
449C2×#121—431no—
450C2×#121—431no—
451C2×#121—861no—
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C2×C4×D4—431no—
455C22×C4⋊C4—431no—
456C22×C4⋊C4—861no—
457C22×C4⋊C4C2×D4311yescharacteristic
458#487—438no—
459#484—438no—
460#484—438no—
461#474—438no—
462#468—438no—
463#468—438no—
464#461—438no—
465#449—438no—
466#449—438no—
467C4×D8—438no—
468#436—438no—
469C2×#107—431no—
470C2×#107—431no—
471C2×#107—431no—
472C2×C4⋊C8—431no—
473#417—438no—
474#417C2×D4318yescomplemented
475C2×#103—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103C2×D4311yescharacteristic
480C2×#103C2×D4311yescharacteristic
481C2×#102—431no—
482C2×#102—431no—
483C2×#102C2×D4311yescharacteristic
484C2×#102C2×D4311yescharacteristic
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×C4×C8—431no—
488C43C2×#333011yescharacteristic, complemented, Sylow
489C2×#41—22no—
490C2×#41—24no—
491C2×#41—42no—
492C2×#41—434no—
493C2×#41—868no—
494C2×#41—862no—
495C2×#41—864no—
496C2×#41—1728no—
497C2×#41—1722no—
498C2×#41C22×D4314yes—
499C22×Q8—431no—
500C22×Q8—861no—
501C22×Q8C22×D4311yescharacteristic
502C22×D4—21no—
503C22×D4—431no—
504C22×D4—431no—
505C22×D4—861no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4C22×D4311yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—431no—
512C23×C4—861no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4—861no—
516C23×C4C22×D4311yescharacteristic
517C2×SD16—434no—
518C2×SD16—434no—
519C2×SD16—1722no—
520C2×SD16—1722no—
521C2×D8—434no—
522C2×D8—864no—
523C2×M16—42no—
524C2×M16—434no—
525C2×M16—1722no—
526C2×M16C22×D4314yes—
527C22×C8—431no—
528C22×C8—431no—
529C22×C8C22×D4311yescharacteristic
530C22×C8C22×D4311yescharacteristic
531C4⋊Q8—434no—
532C4⋊Q8—434no—
533C4⋊Q8—862no—
534C4⋊Q8—862no—
535#123—868no—
536#123—868no—
537#123—868no—
538#123—868no—
539C22⋊Q8—434no—
540C22⋊Q8—434no—
541C22⋊Q8—868no—
542C22⋊Q8—862no—
543C22⋊Q8—862no—
544#121—434no—
545#121—434no—
546#121—862no—
547#121—868no—
548#121—862no—
549C4×D4—434no—
550C4×D4—434no—
551C4×D4—434no—
552C4×D4—434no—
553C4×D4—862no—
554C4×D4—862no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—434no—
561C2×C4⋊C4—862no—
562C2×C4⋊C4—868no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C4⋊C4C22×D4311yescharacteristic
571C2×C4⋊C4C22×D4314yes—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—431no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C42—431no—
581#107—434no—
582#107—434no—
583#107—434no—
584C4⋊C8—434no—
585#103—434no—
586#103—434no—
587#103—434no—
588#103—434no—
589#103C22×D4314yes—
590#103C22×D4314yes—
591#102—434no—
592#102—434no—
593#102C22×D4314yes—
594#102C22×D4314yes—
595C22⋊C8—434no—
596C22⋊C8—434no—
597C4×C8—434no—
598C24—21no—
599C24—431no—
600C24—861no—
601C24D4×D4311yescharacteristic
602#41—28no—
603#41—44no—
604#41—48no—
605#41—868no—
606#41—17232no—
607#41—1724no—
608#41—1728no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—432no—
613C2×Q8—864no—
614C2×Q8—861no—
615C2×Q8—862no—
616C2×Q8—862no—
617C2×Q8—1724no—
618C2×Q8C23×D4312yes—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—434no—
624C2×D4—432no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—864no—
628C2×D4—864no—
629C2×D4—861no—
630C2×D4—862no—
631C2×D4—862no—
632C2×D4—1724no—
633C2×D4—1724no—
634C2×D4—1724no—
635C2×D4#1062189814yescomplemented
636C2×D4C23×D4312yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—431no—
647C22×C4—431no—
648C22×C4—431no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—864no—
652C22×C4—864no—
653C22×C4—864no—
654C22×C4—864no—
655C22×C4—862no—
656C22×C4—862no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—1724no—
661C22×C4—1724no—
662C22×C4—1724no—
663C22×C4—1724no—
664C22×C4D4×D4312yes—
665C22×C4D4×D4311yescharacteristic
666C22×C4C23×D4312yes—
667C22×C4C23×D4311yescharacteristic
668SD16—1724no—
669SD16—1724no—
670D8—868no—
671M16—44no—
672M16—1724no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—432no—
676C2×C8—432no—
677C2×C8—862no—
678C2×C8—862no—
679C2×C8C23×D4312yes—
680C2×C8C23×D4312yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—434no—
685C4⋊C4—432no—
686C4⋊C4—432no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—864no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—864no—
695C4⋊C4C23×D4312yes—
696C4⋊C4C23×D4312yes—
697C22⋊C4—434no—
698C22⋊C4—434no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C42—432no—
706C42—432no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—42no—
713C23—42no—
714C23—432no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—862no—
719C23—1722no—
720C23—1722no—
721C23—1722no—
722C23C2×D4×D4312yes—
723C23C2×D4×D4311yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—42no—
727Q8—862no—
728Q8—862no—
729Q8—1728no—
730Q8—1722no—
731D4—22no—
732D4—24no—
733D4—48no—
734D4—868no—
735D4—862no—
736D4—862no—
737D4—1728no—
738D4—1728no—
739D4—1728no—
740D4—1722no—
741D4C2×#1062189814yescomplemented
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—48no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—434no—
755C2×C4—432no—
756C2×C4—432no—
757C2×C4—432no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—864no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—1728no—
767C2×C4—1728no—
768C2×C4—1728no—
769C2×C4—1728no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4C2×D4×D4312yes—
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C2×#1062189812yes—
776C2×C4#1306337012yes—
777C2×C4C24×D4311yescharacteristic
778C8—22no—
779C8—22no—
780C8—862no—
781C8—862no—
782C22—22no—
783C22—24no—
784C22—22no—
785C22—22no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—48no—
790C22—862no—
791C22—862no—
792C22—862no—
793C22—3444no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22—1724no—
798C22#1458353912yes—
799C22AGL(1,ℤ/8)×D4312yes—
800C22#1458371512yes—
801C22C22×D4×D4311yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—434no—
807C4—862no—
808C4—862no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4#1458353912yes—
813C4C22×#1062189811yescharacteristic
814C4C2×#1306337011yescharacteristic
815C2—42no—
816C2—44no—
817C2—3442no—
818C2—1722no—
819C2#1914689614yesdirect product factor
820C2C2×#1458353911yescharacteristic
821C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
822C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
hypercenterC2×#417D43
hypocenterC43C2×#3330
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#14583550C2semidirect
2. C2×#14583548C2semidirect
3. #19146896C2direct (N × H)
4. C2×#14583248C2semidirect
5. C2×#14583234C2semidirect
6. C2×#14583233C2semidirect
7. C2×#14583177C2semidirect
8. C2×#14583148C2semidirect
9. C2×#14583145C2semidirect
10. C2×#14583103C2semidirect
11. C2×#14583045C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14582979C2semidirect
14. C2×#14582975C2semidirect
15. C2×#14582897C2semidirect
16. C2×C43×#417C2semidirect
24. #14583550C22semidirect
26. #14583548C22semidirect
44. #14583248C22semidirect
45. #14583234C22semidirect
46. #14583233C22semidirect
47. #14583177C22semidirect
48. #14583148C22semidirect
49. #14583145C22semidirect
50. #14583103C22semidirect
51. #14583045C22semidirect
52. #14583044C22semidirect
53. #14582979C22semidirect
54. #14582975C22semidirect
59. #14582897C22semidirect
72. C43×#417C22semidirect
201. C2×D4×C43#41semidirect
318. D4×C43C2×#41semidirect
419. C2×#417D43semidirect
422. C2×C43#3330semidirect
474. #417C2×D43semidirect
488. C43C2×#3330semidirect
635. C2×D4#10621898semidirect
741. D4C2×#10621898semidirect
819. C2#19146896direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835502
C2×#145835482
#191468962
C2×#145832482
C2×#145832342
C2×#145832332
C2×#145831772
C2×#145831482
C2×#145831452
C2×#145831032
C2×#145830452
C2×#145830442
C2×#145829792
C2×#145829752
C2×#145828972
C2×C43×#4172
C2×#333043