Finite Group Databasebeta

← C2×#19147554 #25977139

Subgroups — C2×#19147554 #25977139

Order 11008.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583608C211yesmaximal, characteristic, complemented
2C2×#14583606C211yesmaximal, characteristic, complemented
3#19147554C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583306C211yesmaximal, characteristic, complemented
6C2×#14583299C211yesmaximal, characteristic, complemented
7C2×#14583201C211yesmaximal, characteristic, complemented
8C2×#14583201C211yesmaximal, characteristic, complemented
9C2×#14583199C211yesmaximal, characteristic, complemented
10C2×#14583197C211yesmaximal, characteristic, complemented
11C2×#14583179C211yesmaximal, characteristic, complemented
12C2×#14583177C211yesmaximal, characteristic, complemented
13C2×#14583027C211yesmaximal, characteristic, complemented
14C2×#14583011C211yesmaximal, characteristic
15C2×D8×Dic43C211yesmaximal, characteristic
16C2×C43×#442C211yesmaximal, characteristic
17#14583608—24no—
18#14583608C2218yescomplemented
19#14583606—24no—
20#14583606C2218yescomplemented
21C2×#13063325C2211yescharacteristic
22C2×#13063324C2211yescharacteristic
23C2×#13063317C2211yescharacteristic
24C2×#13063316C2211yescharacteristic
25C2×#13063316C2211yescharacteristic
26C2×#13063316C2211yescharacteristic
27C2×#13063304—21no—
28C2×#13063304—21no—
29C2×#13063302—21no—
30C2×#13063302—21no—
31C2×#13063302—21no—
32C2×#13063302—21no—
33C2×C4×Dic86C2211yescharacteristic
34C2×D4×Dic43C2211yescharacteristic
35C2×D4×Dic43C2211yescharacteristic
36C2×D4×Dic43C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C22×C4⋊Dic43—21no—
39C22×Dic43⋊C4—21no—
40#14583308C2218yescomplemented
41#14583306C2218yescomplemented
42#14583299C2218yescomplemented
43#14583201C2218yescomplemented
44#14583201C2218yescomplemented
45#14583199C2218yescomplemented
46#14583197C2218yescomplemented
47#14583179C2218yescomplemented
48#14583177C2218yescomplemented
49#14583027C2218yescomplemented
50#14583011C2218yes—
51D8×Dic43C2218yes—
52C2×#13063259C2211yescharacteristic
53C2×#13063259C2211yescharacteristic
54C2×#13063258C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#442C2218yes—
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×Dic86D411yescharacteristic
80C23×Dic43—21no—
81C23×Dic43—21no—
82C23×Dic43—21no—
83C23×Dic43—21no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86#13063325—22no—
87#13063325C2314yes—
88#13063324—22no—
89#13063324C2314yes—
90#13063317—22no—
91#13063317C2314yes—
92#13063316—22no—
93#13063316—22no—
94#13063316—22no—
95#13063316C2314yes—
96#13063316C2314yes—
97#13063316C2314yes—
98#13063304—28no—
99#13063304—28no—
100#13063302—28no—
101#13063302—28no—
102#13063302—28no—
103#13063302—28no—
104C4×Dic86D414yes—
105C4×Dic86C2314yes—
106D4×Dic43—22no—
107D4×Dic43—22no—
108D4×Dic43—22no—
109D4×Dic43—22no—
110D4×Dic43C2314yes—
111D4×Dic43C2314yes—
112D4×Dic43C2314yes—
113D4×Dic43C2314yes—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43—21no—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43—28no—
119C2×C4⋊Dic43D411yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—28no—
131C2×Dic43⋊C4D411yescharacteristic
132C2×Dic43⋊C4D411yescharacteristic
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43—21no—
137C2×C4×Dic43C2311yescharacteristic
138C2×C4×Dic43C2311yescharacteristic
139#13063259C2314yes—
140#13063259C2314yes—
141#13063258C2314yes—
142#13063258C2314yes—
143#13063258C2314yes—
144#13063257C2314yes—
145#13063257C2314yes—
146#13063256C2314yes—
147C4⋊(C43⋊C8)C2314yes—
148Dic43⋊C8C2314yes—
149Dic43⋊C8C2314yes—
150#13063246C2314yes—
151#13063246C2314yes—
152#13063246C2314yes—
153#13063246C2314yes—
154#13063235C2314yes—
155C8×Dic43C2314yes—
156C22×D4×C43C2311yescharacteristic
157C22×D4×C43C2311yescharacteristic
158C23×C4×C43—21no—
159C23×C4×C43—21no—
160C2×D8×C43Q818yescomplemented
161C2×D8×C43C2314yes—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C4×D4×C43—22no—
165C4×D4×C43—22no—
166C4×D4×C43C2314yes—
167C4×D4×C43C2314yes—
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C22⋊C4×C43—21no—
171C2×C22⋊C4×C43—21no—
172C2×C42×C43C2311yescharacteristic
173#106×C43C2314yes—
174#102×C43C2314yes—
175#102×C43C2314yes—
176#97×C43C2314yes—
177C24×C43—21no—
178C24×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—22no—
182C2×D4×C43—22no—
183C2×D4×C43C2×Q814yes—
184C2×D4×C43C2×Q814yes—
185C2×D4×C43C2412yes—
186C2×D4×C43C2412yes—
187C22×C4×C43—24no—
188C22×C4×C43—24no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—44no—
192C22×C4×C43—82no—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C22×Dic43—24no—
197C22×Dic43—24no—
198C22×Dic43—24no—
199C22×Dic43—24no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—44no—
205C22×Dic43—82no—
206C22×Dic43—82no—
207C22×Dic43—82no—
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C2×Dic86—24no—
213C2×Dic86—24no—
214C2×Dic86—42no—
215C2×Dic86—82no—
216C2×Dic86—82no—
217C2×Dic86C2×D414yes—
218D8×C43C2×Q8116yescomplemented
219C2×C8×C43—22no—
220C2×C8×C43C2×Q814yes—
221C2×C8×C43C2412yes—
222C2×C8×C43C2412yes—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43C2412yes—
226C4⋊C4×C43C2412yes—
227C22⋊C4×C43—24no—
228C22⋊C4×C43—24no—
229C42×C43C2×D412yes—
230C42×C43C2412yes—
231C22⋊Dic43—24no—
232C22⋊Dic43—24no—
233C22⋊Dic43—24no—
234C22⋊Dic43—24no—
235C4⋊Dic43—24no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—24no—
241C4⋊Dic43—24no—
242C4⋊Dic43—24no—
243C4⋊Dic43C2×D414yes—
244C4⋊Dic43C2412yes—
245C4⋊Dic43C2412yes—
246C4⋊Dic43C2412yes—
247C4⋊Dic43C2412yes—
248Dic43⋊C4—24no—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4C2×D414yes—
255Dic43⋊C4C2×D414yes—
256C4×Dic43C2×D412yes—
257C4×Dic43C2×D412yes—
258C4×Dic43C2412yes—
259C4×Dic43C2412yes—
260C2×C43⋊C8—22no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8C2412yes—
263C2×C43⋊C8C2412yes—
264C23×C43—24no—
265C23×C43—24no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—42no—
269C23×C43—42no—
270C23×C43—42no—
271C23×C43—42no—
272C23×C43C22×D411yescharacteristic
273D4×C43—24no—
274D4×C43—24no—
275D4×C43—22no—
276D4×C43—22no—
277D4×C43C22×Q814yes—
278D4×C43C22×Q814yes—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—48no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—84no—
287C2×C4×C43C22×D412yes—
288C2×C4×C43C22×D412yes—
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C22×Q812yes—
291C2×C4×C432−1+412yes—
292C2×C4×C43C2511yescharacteristic
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—48no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305C2×Dic43—42no—
306C2×Dic43—84no—
307C2×Dic43—84no—
308C2×Dic43—84no—
309C2×Dic43C22×D412yes—
310C2×Dic43C22×D412yes—
311C2×Dic43C22×D412yes—
312C2×Dic43C22×D412yes—
313Dic86—44no—
314Dic86—84no—
315Dic86—84no—
316C8×C43—22no—
317C8×C43C22×Q814yes—
318C43⋊C8—22no—
319C43⋊C8—22no—
320C2×#3389—431nomaximal, Sylow
321C22×C43—24no—
322C22×C43—24no—
323C22×C43—48no—
324C22×C43—48no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43D4×Q812yes—
330C22×C43#57512yes—
331C22×C43#57612yes—
332C22×C43C23×D411yescharacteristic
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—42no—
336C4×C43—42no—
337C4×C43D4×Q812yes—
338C4×C43C23×Q811yescharacteristic
339C4×C43C2×2−1+411yescharacteristic
340Dic43—22no—
341Dic43—22no—
342Dic43—22no—
343Dic43—22no—
344Dic43—42no—
345Dic43—42no—
346Dic43—42no—
347Dic43—42no—
348C2×#554—431no—
349C2×#554—431no—
350#3389—4316no—
351C2×#501—431no—
352C2×#501—431no—
353C2×#499—431no—
354C2×#478—431no—
355C2×#478—431no—
356C2×#478—431no—
357C2×#478—431no—
358C2×#474—431no—
359C2×#474—431no—
360C2×#446—431no—
361C2×#442—431no—
362C2×#442D4311yescharacteristic
363C2×C4×D8—431no—
364C2×C43—44no—
365C2×C43—44no—
366C2×C43#338914yescomplemented
367C2×C43C2×D4×Q811yescharacteristic
368C2×C43C2×#57511yescharacteristic
369C2×C43C2×#57611yescharacteristic
370C22×D8C2×D4311yescharacteristic
371#554—438no—
372#554—438no—
373#554—864no—
374#554—864no—
375C2×C4⋊Q8—431no—
376C2×C4⋊Q8—431no—
377C2×#125—431no—
378C2×#125—431no—
379C2×#125—431no—
380C2×#125—431no—
381C2×C22⋊Q8—861no—
382C2×C22⋊Q8—861no—
383C2×C22⋊Q8—861no—
384C2×C22⋊Q8—861no—
385C2×C22⋊Q8—861no—
386C2×C22⋊Q8—861no—
387C2×C4×Q8—431no—
388C2×C4×D4—431no—
389C2×C4×D4—431no—
390C2×C4×D4—431no—
391C2×C4×D4—431no—
392C2×C4×D4C2×D4311yescharacteristic
393C2×C4×D4C2×D4311yescharacteristic
394C22×C4⋊C4—861no—
395C22×C4⋊C4—861no—
396#501—438no—
397#501—438no—
398#499—438no—
399#478—438no—
400#478—438no—
401#478—438no—
402#478—438no—
403#474—438no—
404#474—438no—
405#446—438no—
406#442—438no—
407#442C2×D4318yes—
408C4×D8—438no—
409C2×#107—431no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×#107—431no—
414C2×#106—431no—
415C2×#106—431no—
416C2×#106—431no—
417C2×#106C2×D4311yescharacteristic
418C2×C4⋊C8—431no—
419C2×C4⋊C8—431no—
420C2×C4⋊C8—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102C2×D4311yescharacteristic
426C2×#102C2×D4311yescharacteristic
427C2×#97—431no—
428C2×#97C2×D4311yescharacteristic
429C2×C4×C8—431no—
430C43C2×#338911yescharacteristic, complemented, Sylow
431C22×Q8—431no—
432C22×Q8—861no—
433C22×Q8—861no—
434C22×D4C22×D4311yescharacteristic
435C22×D4C22×D4311yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—861no—
439C23×C4—861no—
440C23×C4—861no—
441C23×C4—861no—
442C2×D8Dic8618yescomplemented
443C2×D8C22×D4314yes—
444C22×C8—431no—
445C22×C8—431no—
446C22×C8C22×D4311yescharacteristic
447C22×C8C22×D4311yescharacteristic
448C4⋊Q8—434no—
449C4⋊Q8—434no—
450C4⋊Q8—862no—
451C4⋊Q8—862no—
452#125—434no—
453#125—434no—
454#125—434no—
455#125—434no—
456#125—862no—
457#125—862no—
458#125—862no—
459#125—862no—
460C22⋊Q8—868no—
461C22⋊Q8—868no—
462C22⋊Q8—868no—
463C22⋊Q8—868no—
464C22⋊Q8—868no—
465C22⋊Q8—868no—
466C4×Q8—434no—
467C4×Q8—434no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—434no—
471C4×D4—434no—
472C4×D4—434no—
473C4×D4—434no—
474C4×D4—862no—
475C4×D4—862no—
476C4×D4—862no—
477C4×D4—862no—
478C4×D4C22×D4314yes—
479C4×D4C22×D4314yes—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—868no—
488C2×C4⋊C4—868no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C42—431no—
508C2×C42—431no—
509C2×C42C22×D4311yescharacteristic
510#107—434no—
511#107—434no—
512#107—434no—
513#107—434no—
514#107—434no—
515#106—434no—
516#106—434no—
517#106—434no—
518#106C22×D4314yes—
519C4⋊C8—434no—
520C4⋊C8—434no—
521C4⋊C8—434no—
522#102—434no—
523#102—434no—
524#102—434no—
525#102—434no—
526#102C22×D4314yes—
527#102C22×D4314yes—
528#97—434no—
529#97C22×D4314yes—
530C4×C8—434no—
531C24—21no—
532C24—21no—
533C2×Q8—434no—
534C2×Q8—864no—
535C2×Q8—864no—
536C2×Q8—3442no—
537C2×Q8—3442no—
538C2×Q8—1722no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4C2×Dic8614yes—
544C2×D4C2×Dic8614yes—
545C2×D4C23×D4312yes—
546C2×D4C23×D4312yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—44no—
552C22×C4—82no—
553C22×C4—431no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—864no—
558C22×C4—864no—
559C22×C4—864no—
560C22×C4—864no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—3442no—
566C22×C4—3442no—
567C22×C4—3442no—
568C22×C4—1724no—
569C22×C4D4×D4311yescharacteristic
570C22×C4D4×D4311yescharacteristic
571C22×C4C23×D4311yescharacteristic
572D8C2×Dic86116yescomplemented
573C2×C8—22no—
574C2×C8—432no—
575C2×C8—432no—
576C2×C8—862no—
577C2×C8—862no—
578C2×C8C2×Dic8614yes—
579C2×C8C23×D4312yes—
580C2×C8C23×D4312yes—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—434no—
584C4⋊C4—434no—
585C4⋊C4—434no—
586C4⋊C4—432no—
587C4⋊C4—432no—
588C4⋊C4—432no—
589C4⋊C4—432no—
590C4⋊C4—864no—
591C4⋊C4—864no—
592C4⋊C4—864no—
593C4⋊C4—864no—
594C4⋊C4—864no—
595C4⋊C4—864no—
596C4⋊C4—864no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4C23×D4312yes—
605C4⋊C4C23×D4312yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—864no—
609C22⋊C4—864no—
610C22⋊C4—864no—
611C22⋊C4—864no—
612C42—432no—
613C42—432no—
614C42—432no—
615C42—432no—
616C42D4×D4312yes—
617C42C23×D4312yes—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23C2×D4×D4311yescharacteristic
627Q8—3444no—
628Q8—3444no—
629Q8—1724no—
630D4—24no—
631D4—24no—
632D4—22no—
633D4—22no—
634D4C22×Dic8614yes—
635D4C22×Dic8614yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—48no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—84no—
644C2×C4—432no—
645C2×C4—432no—
646C2×C4—432no—
647C2×C4—432no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—3444no—
657C2×C4—3444no—
658C2×C4—3444no—
659C2×C4—1728no—
660C2×C4—1722no—
661C2×C4—1722no—
662C2×C4—1722no—
663C2×C4—1722no—
664C2×C4C2×D4×D4312yes—
665C2×C4C2×D4×D4312yes—
666C2×C4C2×D4×D4311yescharacteristic
667C2×C4C22×Dic8612yes—
668C2×C4#1306337212yes—
669C2×C4C24×D4311yescharacteristic
670C8—22no—
671C8—862no—
672C8—862no—
673C8C22×Dic8614yes—
674C22—24no—
675C22—24no—
676C22—42no—
677C22—42no—
678C22—48no—
679C22—48no—
680C22—42no—
681C22—42no—
682C22D4×Dic8612yes—
683C22#1458369512yes—
684C22#1458370312yes—
685C22C22×D4×D4311yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—862no—
691C4—862no—
692C4—862no—
693C4—862no—
694C4—1722no—
695C4—1722no—
696C4—1722no—
697C4—1722no—
698C4D4×Dic8612yes—
699C4C23×Dic8611yescharacteristic
700C4C2×#1306337211yescharacteristic
701C2—44no—
702C2—44no—
703C2#1914755414yesdirect product factor
704C2C2×D4×Dic8611yescharacteristic
705C2C2×#1458369511yescharacteristic
706C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenterC2×#442D43
hypocenterC43C2×#3389
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#14583608C2semidirect
2. C2×#14583606C2semidirect
3. #19147554C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583306C2semidirect
6. C2×#14583299C2semidirect
7. C2×#14583201C2semidirect
8. C2×#14583201C2semidirect
9. C2×#14583199C2semidirect
10. C2×#14583197C2semidirect
11. C2×#14583179C2semidirect
12. C2×#14583177C2semidirect
13. C2×#14583027C2semidirect
18. #14583608C22semidirect
20. #14583606C22semidirect
40. #14583308C22semidirect
41. #14583306C22semidirect
42. #14583299C22semidirect
43. #14583201C22semidirect
44. #14583201C22semidirect
45. #14583199C22semidirect
46. #14583197C22semidirect
47. #14583179C22semidirect
48. #14583177C22semidirect
49. #14583027C22semidirect
160. C2×D8×C43Q8semidirect
218. D8×C43C2×Q8semidirect
366. C2×C43#3389semidirect
430. C43C2×#3389semidirect
442. C2×D8Dic86semidirect
572. D8C2×Dic86semidirect
703. C2#19147554direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836082
C2×#145836062
#191475542
C2×#145833082
C2×#145833062
C2×#145832992
C2×#145832012
C2×#145831992
C2×#145831972
C2×#145831792
C2×#145831772
C2×#145830272
C2×#145830112
C2×D8×Dic432
C2×C43×#4422
C2×#338943