Finite Group Databasebeta

← C2×#19146047 #25969552

Subgroups — C2×#19146047 #25969552

Order 11008.

1754 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583510C211yesmaximal, characteristic
2C2×#14583507C211yesmaximal, characteristic
3#19146047C2116yesmaximal, direct product factor
4C2×#14583208C211yesmaximal, characteristic, complemented
5C2×#14583207C211yesmaximal, characteristic, complemented
6C2×#14583206C211yesmaximal, characteristic, complemented
7C2×#14583204C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic
9C2×#14583154C211yesmaximal, characteristic
10C2×#14583139C211yesmaximal, characteristic
11C2×#14583137C211yesmaximal, characteristic
12C2×#14583107C211yesmaximal, characteristic, complemented
13C2×#14583107C211yesmaximal, characteristic, complemented
14C2×#14583106C211yesmaximal, characteristic, complemented
15C2×#14582924C211yesmaximal, characteristic
16C2×C43×#462C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583510—24no—
22#14583510C2218yes—
23#14583507—24no—
24#14583507C2218yes—
25C2×#13063323C2211yescharacteristic
26C2×#13063320—21no—
27C2×#13063320—21no—
28C2×#13063320—21no—
29C2×#13063319—21no—
30C2×#13063317—21no—
31C2×#13063317C2211yescharacteristic
32C2×#13063316C2211yescharacteristic
33C2×#13063315—21no—
34C2×#13063315—21no—
35C2×#13063315—21no—
36C2×#13063305C2211yescharacteristic
37C2×#13063301C2211yescharacteristic
38C2×#13063301C2211yescharacteristic
39C2×#13063301C2211yescharacteristic
40C2×Q8×Dic43C2211yescharacteristic
41C2×Q8×Dic43C2211yescharacteristic
42C2×C4×Dic86C2211yescharacteristic
43C2×#13063282C2211yescharacteristic
44#14583208C2218yescomplemented
45#14583207C2218yescomplemented
46#14583206C2218yescomplemented
47#14583204C2218yescomplemented
48#14583156C2218yes—
49#14583154C2218yes—
50#14583139C2218yes—
51#14583137C2218yes—
52#14583107C2218yescomplemented
53#14583107C2218yescomplemented
54#14583106C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59#14582924C2218yes—
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063249C2211yescharacteristic
68C2×#13063249C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C2×C4⋊Q8×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#462C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C2×#10621885—42no—
80C2×#10621885—42no—
81C2×#10621885C2314yes—
82C2×#10621885C2314yes—
83C2×#10621872—42no—
84C2×#10621872C2314yes—
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C2×C8×D43—42no—
88C2×C8×D43C2314yes—
89#13063323—22no—
90#13063323C2314yes—
91#13063320—28no—
92#13063320—28no—
93#13063320—28no—
94#13063319—28no—
95#13063317—22no—
96#13063317—28no—
97#13063317C2314yes—
98#13063316—22no—
99#13063316C2314yes—
100#13063315—28no—
101#13063315—28no—
102#13063315—28no—
103#13063305—22no—
104#13063305C2314yes—
105#13063301—22no—
106#13063301—22no—
107#13063301—22no—
108#13063301C2314yes—
109#13063301C2314yes—
110#13063301C2314yes—
111Q8×Dic43—22no—
112Q8×Dic43—22no—
113Q8×Dic43C2314yes—
114Q8×Dic43C2314yes—
115C4×Dic86—22no—
116C4×Dic86C2314yes—
117#13063282D414yes—
118#13063282C2314yes—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D411yescharacteristic
136C2×Dic43⋊C4D411yescharacteristic
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063249C2314yes—
157#13063249C2314yes—
158#13063249C2314yes—
159#13063249C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×Q8×C43C2311yescharacteristic
162C22×Q8×C43C2311yescharacteristic
163C2×Q16×C43—42no—
164C2×Q16×C43—42no—
165C2×Q16×C43C2314yes—
166C2×Q16×C43C2314yes—
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4⋊Q8×C43—22no—
170C4⋊Q8×C43C2314yes—
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#103×C43C2314yes—
182C23×D43C2×D411yescharacteristic
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43C2412yes—
193C2×Q8×C43C2412yes—
194C2×Q8×C43C2412yes—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43C2×D412yes—
212C2×C4×D43C2412yes—
213C2×Dic86—22no—
214C2×Dic86—22no—
215C2×Dic86—21no—
216C2×Dic86C2412yes—
217Q16×C43—44no—
218Q16×C43—44no—
219C2×C8×C43—22no—
220C2×C8×C43—22no—
221C2×C8×C43C2412yes—
222C2×C8×C43C2412yes—
223C4⋊C4×C43—24no—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43C2412yes—
228C42×C43—24no—
229C42×C43C2×D412yes—
230C42×C43C2412yes—
231#10621885—44no—
232#10621885—44no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—24no—
235(C2×D43)⋊C4—24no—
236(C2×D43)⋊C4—24no—
237(C2×D43)⋊C4C2×D414yes—
238(C2×D43)⋊C4C2×D414yes—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—24no—
243C4⋊Dic43—24no—
244C4⋊Dic43—24no—
245C4⋊Dic43—24no—
246C4⋊Dic43C2412yes—
247C4⋊Dic43C2412yes—
248C4⋊Dic43C2412yes—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4C2×D414yes—
259Dic43⋊C4C2×D414yes—
260C4×Dic43—24no—
261C4×Dic43—24no—
262C4×Dic43—24no—
263C4×Dic43C2×D412yes—
264C4×Dic43C2412yes—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269#10621872—44no—
270C8×D43—44no—
271C23×C43C22×D411yescharacteristic
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43C22×D412yes—
276Q8×C43—22no—
277Q8×C43—22no—
278Q8×C43—22no—
279Q8×C43—22no—
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43—42no—
283Q8×C43—42no—
284Q8×C43—42no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D412yes—
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43H(5,𝔽2)12yes—
299C2×C4×C432−1+412yes—
300C2×C4×C43C2511yescharacteristic
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43C22×D412yes—
313C2×Dic43C22×D412yes—
314C2×Dic43C22×D412yes—
315C4×D43—24no—
316C4×D43—22no—
317C4×D43—22no—
318Dic86—22no—
319Dic86—22no—
320Dic86—42no—
321C8×C43—22no—
322C8×C43—22no—
323C43⋊C8—22no—
324C43⋊C8—22no—
325C2×#3261—431nomaximal, Sylow
326C22×C43#53712yes—
327C22×C43#57812yes—
328C22×C43#57812yes—
329C22×C43C23×D411yescharacteristic
330C2×D43—22no—
331C2×D43—22no—
332C2×D43—22no—
333C2×D43—44no—
334C4×C43—22no—
335C4×C43—22no—
336C4×C43—42no—
337C4×C43—42no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43#53712yes—
341C4×C43C2×H(5,𝔽2)11yescharacteristic
342C4×C43C2×2−1+411yescharacteristic
343Dic43—22no—
344Dic43—22no—
345Dic43—22no—
346Dic43—42no—
347Dic43—42no—
348Dic43—42no—
349Dic43—42no—
350C2×#541—431no—
351C2×#541—431no—
352#3261—4316no—
353C2×#479—431no—
354C2×#479—431no—
355C2×#479—431no—
356C2×#479—431no—
357C2×#470—431no—
358C2×#470—431no—
359C2×#467—431no—
360C2×#467—431no—
361C2×#462—431no—
362C2×#462—431no—
363C2×#462—431no—
364C2×#462D4311yescharacteristic, complemented
365C2×#424—431no—
366C2×C43#326114yescomplemented
367C2×C43C2×#53711yescharacteristic
368C2×C43C2×#57811yescharacteristic
369C2×C43C2×#57811yescharacteristic
370D43—42no—
371C22×Q16—431no—
372C22×Q16—431no—
373C22×Q16C2×D4311yescharacteristic
374C22×Q16C2×D4311yescharacteristic
375C22×M16—431no—
376C23×C8—431no—
377#541—438no—
378#541—438no—
379#541—864no—
380#541—864no—
381C2×C4⋊Q8—431no—
382C2×C4⋊Q8C2×D4311yescharacteristic
383C2×#126—861no—
384C2×#126—861no—
385C2×#126—861no—
386C2×#126—861no—
387C2×#125—431no—
388C2×#125—431no—
389C2×#125—861no—
390C2×#125—861no—
391C2×#125—861no—
392C2×#125—861no—
393C2×C22⋊Q8—431no—
394C2×C22⋊Q8—431no—
395C2×C22⋊Q8—431no—
396C2×C22⋊Q8—431no—
397C2×C4×Q8—431no—
398C2×C4×Q8—431no—
399C2×C4×Q8—431no—
400C2×C4×Q8C2×D4311yescharacteristic
401C2×#117—431no—
402#479—438no—
403#479—438no—
404#479—438no—
405#479—438no—
406#470—438no—
407#470—438no—
408#467—438no—
409#467—438no—
410#462—438no—
411#462—438no—
412#462—438no—
413#462C2×D4318yescomplemented
414C2×#107—431no—
415C2×#107—431no—
416C2×#106—431no—
417C2×#106—431no—
418#424—438no—
419C2×C4⋊C8—431no—
420C2×C4⋊C8—431no—
421C2×C4⋊C8—431no—
422C2×C4⋊C8C2×D4311yescharacteristic
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103C2×D4311yescharacteristic
430C2×#103C2×D4311yescharacteristic
431C43C2×#326111yescharacteristic, complemented, Sylow
432C22×Q8—431no—
433C22×Q8C22×D4311yescharacteristic
434C22×Q8C22×D4311yescharacteristic
435C22×Q8C22×D4311yescharacteristic
436C23×C4—431no—
437C2×Q16—42no—
438C2×Q16—42no—
439C2×Q16—434no—
440C2×Q16—434no—
441C2×Q16—1722no—
442C2×Q16—1722no—
443C2×Q16C22×D4314yes—
444C2×Q16C22×D4314yes—
445C2×M16—434no—
446C2×M16—1722no—
447C22×C8—431no—
448C22×C8—431no—
449C22×C8—434no—
450C22×C8—1722no—
451C22×C8C22×D4311yescharacteristic
452C22×C8C22×D4311yescharacteristic
453C4⋊Q8—22no—
454C4⋊Q8—434no—
455C4⋊Q8—862no—
456C4⋊Q8C22×D4314yes—
457#126—868no—
458#126—868no—
459#126—868no—
460#126—868no—
461#125—434no—
462#125—434no—
463#125—868no—
464#125—862no—
465#125—868no—
466#125—868no—
467#125—868no—
468#125—862no—
469C22⋊Q8—434no—
470C22⋊Q8—434no—
471C22⋊Q8—434no—
472C22⋊Q8—434no—
473C22⋊Q8—862no—
474C22⋊Q8—862no—
475C22⋊Q8—862no—
476C22⋊Q8—862no—
477C4×Q8—22no—
478C4×Q8—434no—
479C4×Q8—434no—
480C4×Q8—434no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×Q8C22×D4314yes—
485#117—434no—
486#117—434no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C42—21no—
516C2×C42—431no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42C22×D4311yescharacteristic
521#107—434no—
522#107—434no—
523#106—434no—
524#106—434no—
525C4⋊C8—434no—
526C4⋊C8—434no—
527C4⋊C8—434no—
528C4⋊C8C22×D4314yes—
529#103—434no—
530#103—434no—
531#103—434no—
532#103—434no—
533#103—434no—
534#103—434no—
535#103C22×D4314yes—
536#103C22×D4314yes—
537C24—431no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—432no—
548C2×Q8—861no—
549C2×Q8—862no—
550C2×Q8—862no—
551C2×Q8C23×D4312yes—
552C2×Q8C23×D4312yes—
553C2×Q8C23×D4312yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4D4×D4311yescharacteristic
570C22×C4D4×D4311yescharacteristic
571C22×C4C23×D4311yescharacteristic
572Q16—44no—
573Q16—44no—
574Q16—1724no—
575Q16—1724no—
576M16—1724no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—432no—
580C2×C8—432no—
581C2×C8—862no—
582C2×C8—862no—
583C2×C8—1724no—
584C2×C8C23×D4312yes—
585C2×C8C23×D4312yes—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—434no—
591C4⋊C4—434no—
592C4⋊C4—432no—
593C4⋊C4—432no—
594C4⋊C4—432no—
595C4⋊C4—864no—
596C4⋊C4—864no—
597C4⋊C4—864no—
598C4⋊C4—864no—
599C4⋊C4—864no—
600C4⋊C4—864no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4—864no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4C23×D4312yes—
612C22⋊C4—434no—
613C22⋊C4—434no—
614C22⋊C4—864no—
615C22⋊C4—864no—
616C22⋊C4—864no—
617C22⋊C4—864no—
618C42—24no—
619C42—432no—
620C42—432no—
621C42—864no—
622C42—864no—
623C42—864no—
624C42D4×D4312yes—
625C42C23×D4312yes—
626C23—432no—
627C23—862no—
628C23—862no—
629C23—862no—
630C23C2×D4×D4311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—862no—
641Q8—862no—
642Q8—1722no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—432no—
654C2×C4—432no—
655C2×C4—432no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—864no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—1722no—
667C2×C4—1722no—
668C2×C4—1722no—
669C2×C4—1722no—
670C2×C4C2×D4×D4312yes—
671C2×C4C2×D4×D4312yes—
672C2×C4C2×D4×D4311yescharacteristic
673C2×C4#1306337012yes—
674C2×C4#1306337212yes—
675C2×C4C24×D4311yescharacteristic
676C8—22no—
677C8—22no—
678C8—862no—
679C8—862no—
680C22—862no—
681C22—862no—
682C22—862no—
683C22—1724no—
684C22#1458347812yes—
685C22#1458371212yes—
686C22#1458371512yes—
687C22C22×D4×D4311yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—862no—
695C4—862no—
696C4—862no—
697C4—1722no—
698C4—1722no—
699C4—1722no—
700C4—1722no—
701C4#1458347812yes—
702C4C2×#1306337011yescharacteristic
703C4C2×#1306337211yescharacteristic
704C2—1722no—
705C2#1914604714yesdirect product factor
706C2C2×#1458347811yescharacteristic
707C2C2×#1458371211yescharacteristic
708C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#462C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×#462D43
hypocenterC43C2×#3261
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #19146047C2direct (N × H)
4. C2×#14583208C2semidirect
5. C2×#14583207C2semidirect
6. C2×#14583206C2semidirect
7. C2×#14583204C2semidirect
12. C2×#14583107C2semidirect
13. C2×#14583107C2semidirect
14. C2×#14583106C2semidirect
16. C2×C43×#462C2semidirect
44. #14583208C22semidirect
45. #14583207C22semidirect
46. #14583206C22semidirect
47. #14583204C22semidirect
52. #14583107C22semidirect
53. #14583107C22semidirect
54. #14583106C22semidirect
73. C43×#462C22semidirect
364. C2×#462D43semidirect
366. C2×C43#3261semidirect
413. #462C2×D43semidirect
431. C43C2×#3261semidirect
705. C2#19146047direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835102
C2×#145835072
#191460472
C2×#145832082
C2×#145832072
C2×#145832062
C2×#145832042
C2×#145831562
C2×#145831542
C2×#145831392
C2×#145831372
C2×#145831072
C2×#145831062
C2×#145829242
C2×C43×#4622
C2×#326143