Finite Group Databasebeta

← C2×#19146947 #25975015

Subgroups — C2×#19146947 #25975015

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic, complemented
2C2×#14583549C211yesmaximal, characteristic
3#19146947C2116yesmaximal, direct product factor
4C2×#14583296C211yesmaximal, characteristic, complemented
5C2×#14583216C211yesmaximal, characteristic, complemented
6C2×#14583215C211yesmaximal, characteristic, complemented
7C2×#14583228C211yesmaximal, characteristic, complemented
8C2×#14583227C211yesmaximal, characteristic, complemented
9C2×#14583182C211yesmaximal, characteristic, complemented
10C2×#14583187C211yesmaximal, characteristic, complemented
11C2×#14583125C211yesmaximal, characteristic, complemented
12C2×SD16×Dic43C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
14C22×#13063257C211yesmaximal, characteristic, complemented
15C2×#106×D43C211yesmaximal, characteristic, complemented
16C2×C43×#465C211yesmaximal, characteristic, complemented
17C22×#10621900—21no—
18C22×C8×D43C2211yescharacteristic
19#14583607—24no—
20#14583607C2218yescomplemented
21#14583549—24no—
22#14583549C2218yes—
23C2×#13063324C2211yescharacteristic
24C2×#13063324C2211yescharacteristic
25C2×#13063315—21no—
26C2×#13063307—21no—
27C2×#13063306—21no—
28C2×#13063305—21no—
29C2×#13063302—21no—
30C2×#13063302—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063296C2211yescharacteristic
33C2×Q8×Dic43C2211yescharacteristic
34C2×D4×Dic43C2211yescharacteristic
35C2×C4×C22⋊D43C2211yescharacteristic
36C2×(C22⋊D43)⋊C4—21no—
37C22×C4⋊Dic43C2211yescharacteristic
38C22×C4⋊Dic43C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41#14583296C2218yescomplemented
42#14583228C2218yescomplemented
43#14583227C2218yescomplemented
44#14583216C2218yescomplemented
45#14583215C2218yescomplemented
46#14583187C2218yescomplemented
47#14583182C2218yescomplemented
48#14583125C2218yescomplemented
49SD16×Dic43C2218yescomplemented
50C8×C22⋊D43C2218yescomplemented
51C2×#13063257C2211yescharacteristic
52C2×#13063257C2211yescharacteristic
53C2×#13063257C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063257C2218yescomplemented
56C2×#13063256C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60#106×D43C2218yescomplemented
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#465C2218yescomplemented
74C2×#106×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—28no—
78C2×#10621900—48no—
79C22×Dic86—21no—
80C22×Dic86—21no—
81C22×C22⋊D43—21no—
82C22×C22⋊D43D411yescharacteristic
83C23×Dic43—21no—
84C23×Dic43—21no—
85C23×Dic43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—24no—
92C2×C8×D43C2314yes—
93#13063324—22no—
94#13063324—22no—
95#13063324C2314yes—
96#13063324C2314yes—
97#13063315—28no—
98#13063307—28no—
99#13063306—28no—
100#13063305—28no—
101#13063302—28no—
102#13063302—28no—
103#13063301—22no—
104#13063301C2314yes—
105#13063296—22no—
106#13063296C2314yes—
107Q8×Dic43—22no—
108Q8×Dic43C2314yes—
109D4×Dic43—22no—
110D4×Dic43C2314yes—
111C4×C22⋊D43D414yes—
112C4×C22⋊D43C2314yes—
113(C22⋊D43)⋊C4—28no—
114C2×C4⋊Dic43—22no—
115C2×C4⋊Dic43—21no—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—22no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2314yes—
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2314yes—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4D411yescharacteristic
131C4⋊C4×D43—22no—
132C4⋊C4×D43—22no—
133C4⋊C4×D43C2314yes—
134C4⋊C4×D43C2314yes—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43D411yescharacteristic
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4D411yescharacteristic
140C2×C4×Dic43—21no—
141C2×C4×Dic43C2311yescharacteristic
142#13063257C2314yes—
143#13063257C2314yes—
144#13063257C2314yes—
145#13063257C2314yes—
146#13063256C2314yes—
147#13063256C2314yes—
148#13063256C2314yes—
149#13063256C2314yes—
150Dic43⋊C8C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063246C2314yes—
154#13063246C2314yes—
155C22⋊(C43⋊C8)C2314yes—
156(C2×D43)⋊C8C2314yes—
157C8×Dic43C2314yes—
158C22×Q8×C43C2311yescharacteristic
159C22×D4×C43—21no—
160C22×D4×C43C2311yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C2×SD16×C43—24no—
163C2×SD16×C43C2314yes—
164C22×C8×C43—24no—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2314yes—
167C22×C8×C43C2311yescharacteristic
168C22⋊Q8×C43—22no—
169C22⋊Q8×C43C2314yes—
170#121×C43—22no—
171#121×C43C2314yes—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177#106×C43C2314yes—
178#103×C43C2314yes—
179#102×C43C2314yes—
180C24×C43—21no—
181C24×C43C2×D411yescharacteristic
182C23×D43C2×D411yescharacteristic
183C2×Q8×C43—21no—
184C2×Q8×C43—22no—
185C2×Q8×C43—22no—
186C2×Q8×C43C2412yes—
187C2×D4×C43—21no—
188C2×D4×C43—24no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—44no—
192C2×D4×C43C2412yes—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—44no—
204C2×C22⋊D43SD1618yescomplemented
205C2×C22⋊D43C2×D414yes—
206C22×Dic43—24no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—24no—
212C22×Dic43—24no—
213C22×Dic43—44no—
214C22×Dic43—44no—
215C22×Dic43—82no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219#10621900—432no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—44no—
225C2×C4×D43—82no—
226C2×C4×D43C2×D412yes—
227C2×C4×D43C2412yes—
228C2×Dic86—24no—
229C2×Dic86—24no—
230C2×Dic86—44no—
231C2×Dic86—82no—
232SD16×C43—28no—
233C2×C8×C43—22no—
234C2×C8×C43—28no—
235C2×C8×C43#4114yescomplemented
236C2×C8×C43C2412yes—
237C2×C8×C43C2412yes—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43C2412yes—
242C4⋊C4×C43C2412yes—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C22⋊Dic43—24no—
246C22⋊Dic43—24no—
247C22⋊Dic43C2×D414yes—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4C2×D414yes—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—24no—
255C4⋊Dic43—24no—
256C4⋊Dic43—24no—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259C4⋊Dic43C2412yes—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4C2×D414yes—
267C4×Dic43—24no—
268C4×Dic43C2×D412yes—
269C4×Dic43C2412yes—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8C2412yes—
273C2×C43⋊C8C2412yes—
274C8×D43—28no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43C2×SD1614yes—
282C23×C43C22×D412yes—
283C23×C43C22×D411yescharacteristic
284C22×D43—22no—
285C22×D43—22no—
286C22×D43C2×SD1614yes—
287C22×D43C22×D412yes—
288Q8×C43—22no—
289Q8×C43—22no—
290Q8×C43—42no—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—48no—
294D4×C43—42no—
295C2×C4×C43—22no—
296C2×C4×C43—24no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4112yes—
308C2×C4×C432−1+412yes—
309C2×C4×C43C2511yescharacteristic
310C22⋊D43—48no—
311C22⋊D43C2×SD16116yescomplemented
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—48no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—48no—
324C2×Dic43—84no—
325C2×Dic43C2×SD1614yes—
326C2×Dic43C22×D412yes—
327C2×Dic43C22×D412yes—
328C2×Dic43C22×D412yes—
329C4×D43—24no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—48no—
333C4×D43—84no—
334Dic86—48no—
335Dic86—84no—
336C8×C43—22no—
337C8×C43C2×#4114yescomplemented
338C43⋊C8—22no—
339C43⋊C8—22no—
340C2×#3335—431nomaximal, Sylow
341C22×C43—28no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—84no—
348C22×C43#54712yes—
349C22×C43C22×SD1614yes—
350C22×C43C22×SD1612yes—
351C22×C43#57712yes—
352C22×C43C23×D411yescharacteristic
353C2×D43—28no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43C22×SD1614yes—
357C4×C43—22no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43—42no—
361C4×C43#54712yes—
362C4×C43C22×#4111yescharacteristic
363C4×C43C2×2−1+411yescharacteristic
364Dic43—22no—
365Dic43—22no—
366Dic43—42no—
367Dic43—42no—
368Dic43—42no—
369Dic43—42no—
370Dic43C22×SD1614yes—
371C2×#554—431no—
372C2×#547—431no—
373#3335—4316no—
374C2×#498—431no—
375C2×#481—431no—
376C2×#481—431no—
377C2×#483—431no—
378C2×#483—431no—
379C2×#475—431no—
380C2×#476—431no—
381C2×#465—431no—
382C2×#465D4311yescharacteristic, complemented
383C2×C4×SD16—431no—
384C2×C8×D4—431no—
385C22×#106—431no—
386C22×#106—431no—
387C2×C43—24no—
388C2×C43—82no—
389C2×C43#333514yescomplemented
390C2×C43C2×#54711yescharacteristic
391C2×C43C23×SD1611yescharacteristic
392C2×C43C2×#57711yescharacteristic
393D43—24no—
394C22×#41—861no—
395C22×SD16C2×D4311yescharacteristic
396C23×C8—431no—
397C23×C8C2×D4311yescharacteristic
398#554—438no—
399#554—864no—
400#547—438no—
401#547—864no—
402C2×C4⋊Q8—431no—
403C2×C4⋊Q8—431no—
404C2×#125—861no—
405C2×#123—861no—
406C2×#123—861no—
407C2×C22⋊Q8—431no—
408C2×C22⋊Q8—861no—
409C2×C22⋊Q8—861no—
410C2×C22⋊Q8—861no—
411C2×C22⋊Q8C2×D4311yescharacteristic
412C2×#121—431no—
413C2×#121C2×D4311yescharacteristic
414C2×C4×Q8—431no—
415C2×C4×D4—431no—
416C2×C4×D4—431no—
417C2×C4×D4—861no—
418C22×C4⋊C4—431no—
419C22×C4⋊C4—431no—
420C22×C4⋊C4—431no—
421C22×C4⋊C4—431no—
422#498—438no—
423#483—438no—
424#483—438no—
425#481—438no—
426#481—438no—
427#476—438no—
428#475—438no—
429#465—438no—
430#465C2×D4318yescomplemented
431C4×SD16—438no—
432C8×D4—438no—
433C2×#106—431no—
434C2×#106—438no—
435C2×#106—431no—
436C2×#106—431no—
437C2×#106—431no—
438C2×#106—431no—
439C2×#106—431no—
440C2×#106—431no—
441C2×#106—431no—
442C2×#106—438no—
443C2×#106C2×D4311yescharacteristic
444C2×C4⋊C8—431no—
445C2×#103—431no—
446C2×#103—431no—
447C2×#103C2×D4311yescharacteristic
448C2×#102—431no—
449C2×#102—431no—
450C2×#102C2×D4311yescharacteristic
451C2×C22⋊C8—431no—
452C2×C22⋊C8—431no—
453C2×C4×C8—431no—
454C43C2×#333511yescharacteristic, complemented, Sylow
455C2×#41—868no—
456C2×#41—1728no—
457C22×Q8—861no—
458C22×Q8—861no—
459C22×Q8C22×D4311yescharacteristic
460C22×D4—21no—
461C22×D4—431no—
462C22×D4—861no—
463C22×D4C22×D4311yescharacteristic
464C23×C4—431no—
465C23×C4—861no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4—861no—
470C23×C4C22×D4311yescharacteristic
471C2×SD16—24no—
472C2×SD16C22×D4314yes—
473C22×C8—24no—
474C22×C8—431no—
475C22×C8—431no—
476C22×C8—434no—
477C22×C8—864no—
478C22×C8C22×D4311yescharacteristic
479C22×C8C22×D4314yes—
480C22×C8C22×D4311yescharacteristic
481C4⋊Q8—434no—
482C4⋊Q8—434no—
483C4⋊Q8—862no—
484C4⋊Q8—862no—
485#125—868no—
486#123—868no—
487#123—868no—
488C22⋊Q8—22no—
489C22⋊Q8—434no—
490C22⋊Q8—868no—
491C22⋊Q8—868no—
492C22⋊Q8—868no—
493C22⋊Q8—862no—
494C22⋊Q8C22×D4314yes—
495#121—22no—
496#121—434no—
497#121—862no—
498#121C22×D4314yes—
499C4×Q8—434no—
500C4×Q8—862no—
501C4×D4—434no—
502C4×D4—434no—
503C4×D4—434no—
504C4×D4—862no—
505C4×D4—868no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—434no—
513C2×C4⋊C4—434no—
514C2×C4⋊C4—434no—
515C2×C4⋊C4—434no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4—862no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—862no—
527C2×C4⋊C4—862no—
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C4⋊C4C22×D4311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—431no—
533C2×C22⋊C4—431no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C42—431no—
538C2×C42—861no—
539#106—434no—
540#106—434no—
541#106—434no—
542#106—434no—
543#106—434no—
544#106—434no—
545#106—434no—
546#106—434no—
547#106C22×D4314yes—
548C4⋊C8—434no—
549#103—434no—
550#103—434no—
551#103C22×D4314yes—
552#102—434no—
553#102—434no—
554#102C22×D4314yes—
555C22⋊C8—434no—
556C22⋊C8—434no—
557C4×C8—434no—
558C24—21no—
559C24—431no—
560C24D4×D4311yescharacteristic
561#41—17232no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—864no—
566C2×Q8—864no—
567C2×Q8—3442no—
568C2×Q8—1724no—
569C2×Q8C23×D4312yes—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—44no—
575C2×D4—438no—
576C2×D4—434no—
577C2×D4—864no—
578C2×D4—1724no—
579C2×D4C23×D4312yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—864no—
591C22×C4—864no—
592C22×C4—864no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—864no—
596C22×C4—864no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—3442no—
602C22×C4—3442no—
603C22×C4—1724no—
604C22×C4—1724no—
605C22×C4—1724no—
606C22×C4D4×D4312yes—
607C22×C4D4×D4311yescharacteristic
608C22×C4C23×D4312yes—
609C22×C4C23×D4311yescharacteristic
610SD16—28no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—432no—
614C2×C8—432no—
615C2×C8—862no—
616C2×C8—862no—
617C2×C8—868no—
618C2×C8#1062190014yescomplemented
619C2×C8C23×D4312yes—
620C2×C8C23×D4312yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—434no—
625C4⋊C4—432no—
626C4⋊C4—432no—
627C4⋊C4—432no—
628C4⋊C4—432no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—864no—
635C4⋊C4—861no—
636C4⋊C4—861no—
637C4⋊C4—861no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—861no—
641C4⋊C4C23×D4312yes—
642C4⋊C4C23×D4312yes—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—434no—
646C22⋊C4—434no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C42—432no—
651C42—432no—
652C42—864no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—434no—
660C23—432no—
661C23—862no—
662C23—862no—
663C23SD16×D4314yes—
664C23C2×D4×D4312yes—
665C23C2×D4×D4311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—3444no—
670Q8—1728no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—4316no—
676D4—1728no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—434no—
688C2×C4—432no—
689C2×C4—432no—
690C2×C4—432no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—864no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—3444no—
701C2×C4—3444no—
702C2×C4—1728no—
703C2×C4—1728no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4—1728no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4C2×D4×D4312yes—
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4C2×#1062190012yes—
712C2×C4#1306337212yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—862no—
716C8—862no—
717C8C2×#1062190014yescomplemented
718C22—22no—
719C22—22no—
720C22—28no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—434no—
726C22—862no—
727C22—862no—
728C22—868no—
729C22#1458354912yes—
730C22C2×SD16×D4314yes—
731C22C2×SD16×D4312yes—
732C22#1458370612yes—
733C22C22×D4×D4311yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—434no—
739C4—862no—
740C4—862no—
741C4—1722no—
742C4—1722no—
743C4—1722no—
744C4—1722no—
745C4#1458354912yes—
746C4C22×#1062190011yescharacteristic
747C4C2×#1306337211yescharacteristic
748C2—24no—
749C2—82no—
750C2—864no—
751C2#1914694714yesdirect product factor
752C2C2×#1458354911yescharacteristic
753C2C22×SD16×D4311yescharacteristic
754C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#465C2
socleC23×C43C22×D4
prime radicalC2×#14583549C2
hypercenterC2×#465D43
hypocenterC43C2×#3335
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#14583607C2semidirect
3. #19146947C2direct (N × H)
4. C2×#14583296C2semidirect
5. C2×#14583216C2semidirect
6. C2×#14583215C2semidirect
7. C2×#14583228C2semidirect
8. C2×#14583227C2semidirect
9. C2×#14583182C2semidirect
10. C2×#14583187C2semidirect
11. C2×#14583125C2semidirect
12. C2×SD16×Dic43C2semidirect
13. C2×C8×C22⋊D43C2semidirect
14. C22×#13063257C2semidirect
15. C2×#106×D43C2semidirect
16. C2×C43×#465C2semidirect
20. #14583607C22semidirect
41. #14583296C22semidirect
42. #14583228C22semidirect
43. #14583227C22semidirect
44. #14583216C22semidirect
45. #14583215C22semidirect
46. #14583187C22semidirect
47. #14583182C22semidirect
48. #14583125C22semidirect
49. SD16×Dic43C22semidirect
50. C8×C22⋊D43C22semidirect
55. C2×#13063257C22semidirect
60. #106×D43C22semidirect
73. C43×#465C22semidirect
204. C2×C22⋊D43SD16semidirect
235. C2×C8×C43#41semidirect
311. C22⋊D43C2×SD16semidirect
337. C8×C43C2×#41semidirect
382. C2×#465D43semidirect
389. C2×C43#3335semidirect
430. #465C2×D43semidirect
454. C43C2×#3335semidirect
618. C2×C8#10621900semidirect
717. C8C2×#10621900semidirect
751. C2#19146947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145835492
#191469472
C2×#145832962
C2×#145832162
C2×#145832152
C2×#145832282
C2×#145832272
C2×#145831822
C2×#145831872
C2×#145831252
C2×SD16×Dic432
C2×C8×C22⋊D432
C22×#130632572
C2×#106×D432
C2×C43×#4652
C2×#333543