Finite Group Databasebeta

← C2×#19147424 #25976364

Subgroups — C2×#19147424 #25976364

Order 11008.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583622C211yesmaximal, characteristic, complemented
2C2×#14583609C211yesmaximal, characteristic, complemented
3#19147424C2116yesmaximal, direct product factor
4C2×#14583268C211yesmaximal, characteristic, complemented
5C2×#14583259C211yesmaximal, characteristic, complemented
6C2×#14583254C211yesmaximal, characteristic, complemented
7C2×#14583207C211yesmaximal, characteristic, complemented
8C2×#14583185C211yesmaximal, characteristic, complemented
9C2×#14583200C211yesmaximal, characteristic, complemented
10C2×#14583115C211yesmaximal, characteristic
11C2×#14583115C211yesmaximal, characteristic
12C2×#14583105C211yesmaximal, characteristic, complemented
13C2×#14583012C211yesmaximal, characteristic
14C2×#14583001C211yesmaximal, characteristic, complemented
15C2×C4×#10621873C211yesmaximal, characteristic, complemented
16C2×C43×#446C211yesmaximal, characteristic, complemented
17C22×#10621873C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×D344C2211yescharacteristic
20#14583622—24no—
21#14583622C2218yescomplemented
22#14583609—24no—
23#14583609C2218yescomplemented
24C2×#13063325C2211yescharacteristic
25C2×#13063325C2211yescharacteristic
26C2×#13063320—21no—
27C2×#13063320—21no—
28C2×#13063317C2211yescharacteristic
29C2×#13063317C2211yescharacteristic
30C2×#13063313C2211yescharacteristic
31C2×#13063313C2211yescharacteristic
32C2×#13063303—21no—
33C2×#13063303—21no—
34C2×#13063301—21no—
35C2×#13063301—21no—
36C2×C4×Dic86C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×C4×D172C2211yescharacteristic
42C2×#13063283—21no—
43C2×C4⋊C4×D43—21no—
44#14583268C2218yescomplemented
45#14583259C2218yescomplemented
46#14583254C2218yescomplemented
47#14583207C2218yescomplemented
48#14583200C2218yescomplemented
49#14583185C2218yescomplemented
50#14583115C2218yes—
51#14583115C2218yes—
52#14583105C2218yescomplemented
53#14583012C2218yes—
54#14583001C2218yescomplemented
55C4×#10621873C2218yescomplemented
56C2×#13063259C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×C4×Q8×C43C2211yescharacteristic
70C43×#446C2218yescomplemented
71C2×C4⋊C8×C43C2211yescharacteristic
72C2×C4⋊C8×C43C2211yescharacteristic
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×#97×C43C2211yescharacteristic
75C2×#97×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C2×#10621873—24no—
87C2×#10621873—24no—
88C2×#10621873C2314yes—
89C2×#10621873C2314yes—
90C2×D344—24no—
91C2×D344C2314yes—
92#13063325—22no—
93#13063325—22no—
94#13063325C2314yes—
95#13063325C2314yes—
96#13063320—28no—
97#13063320—28no—
98#13063317—22no—
99#13063317—22no—
100#13063317C2314yes—
101#13063317C2314yes—
102#13063313—22no—
103#13063313—22no—
104#13063313C2314yes—
105#13063313C2314yes—
106#13063303—28no—
107#13063303—28no—
108#13063301—28no—
109#13063301—28no—
110C4×Dic86—22no—
111C4×Dic86—22no—
112C4×Dic86C2314yes—
113C4×Dic86C2314yes—
114C4×D172—22no—
115C4×D172—22no—
116C4×D172—22no—
117C4×D172—22no—
118C4×D172C2314yes—
119C4×D172C2314yes—
120C4×D172C2314yes—
121C4×D172C2314yes—
122#13063283—28no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C4⋊C4×D43—28no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147#13063259C2314yes—
148#13063257C2314yes—
149#13063257C2314yes—
150#13063250C2314yes—
151#13063250C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159#13063247C2314yes—
160C22×Q8×C43D411yescharacteristic
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C4×Q8×C43D414yes—
166C4×Q8×C43C2314yes—
167C2×C4⋊C4×C43D411yescharacteristic
168C2×C4⋊C4×C43D411yescharacteristic
169C2×C4⋊C4×C43D411yescharacteristic
170C2×C42×C43C2311yescharacteristic
171C2×C42×C43C2311yescharacteristic
172C2×C42×C43C2311yescharacteristic
173C4⋊C8×C43C2314yes—
174C4⋊C8×C43C2314yes—
175C4⋊C8×C43C2314yes—
176#97×C43C2314yes—
177#97×C43C2314yes—
178C4×C8×C43C2314yes—
179C23×D43—21no—
180C23×D43—21no—
181C2×Q8×C43—42no—
182C2×Q8×C43C2×D414yes—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C2×D172—21no—
197C2×D172—22no—
198C2×D172—21no—
199C2×D172—22no—
200C2×D172—22no—
201C2×D172#4114yes—
202C2×D172C2412yes—
203C2×D172C2412yes—
204C2×C4×D43—24no—
205C2×C4×D43—24no—
206C2×C4×D43—24no—
207C2×C4×D43—24no—
208C2×C4×D43—44no—
209C2×C4×D43—44no—
210C2×C4×D43—82no—
211C2×C4×D43—82no—
212C2×Dic86—22no—
213C2×Dic86—22no—
214C2×Dic86—22no—
215C2×Dic86—22no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—24no—
219C2×Dic86—82no—
220C2×Dic86C2412yes—
221C2×Dic86C2412yes—
222C2×C8×C43—22no—
223C2×C8×C43—22no—
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C2×C8×C43C2412yes—
227C2×C8×C43C2412yes—
228C2×C8×C43C2412yes—
229C2×C8×C43C2412yes—
230C4⋊C4×C43C2×D414yes—
231C4⋊C4×C43C2×D414yes—
232C4⋊C4×C43C2×D414yes—
233C42×C43C2×D412yes—
234C42×C43C2×D412yes—
235C42×C43C2×D412yes—
236C42×C43C2412yes—
237C42×C43C2412yes—
238C42×C43C2412yes—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247C4⋊Dic43—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43—24no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264C4×Dic43—24no—
265C4×Dic43—24no—
266D344—28no—
267#10621873—28no—
268#10621873—28no—
269C23×C43C22×D411yescharacteristic
270C22×D43—24no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—42no—
274C22×D43—42no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—42no—
278Q8×C43—44no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43C22×D412yes—
286C2×C4×C43C22×D412yes—
287C2×C4×C43C22×D412yes—
288C2×C4×C43C22×D412yes—
289C2×C4×C43C22×D412yes—
290C2×C4×C43C22×D412yes—
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4112yes—
293C2×C4×C432−1+412yes—
294C2×C4×C43C2511yescharacteristic
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305C2×Dic43—42no—
306C2×Dic43—42no—
307D172—24no—
308D172—22no—
309D172—22no—
310D172—22no—
311D172—42no—
312D172C2×#4114yes—
313C4×D43—48no—
314C4×D43—48no—
315C4×D43—84no—
316C4×D43—84no—
317Dic86—22no—
318Dic86—22no—
319Dic86—22no—
320Dic86—22no—
321Dic86—42no—
322Dic86—42no—
323Dic86—84no—
324C8×C43—22no—
325C8×C43—22no—
326C8×C43—22no—
327C8×C43—22no—
328C2×#3376—431nomaximal, Sylow
329C22×C43#54812yes—
330C22×C43#57512yes—
331C22×C43#57712yes—
332C22×C43C23×D411yescharacteristic
333C2×D43—24no—
334C2×D43—48no—
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—84no—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43—22no—
344C4×C43—22no—
345C4×C43—22no—
346C4×C43—22no—
347C4×C43#54812yes—
348C4×C43C22×#4111yescharacteristic
349C4×C43C2×2−1+411yescharacteristic
350Dic43—42no—
351Dic43—42no—
352Dic43—42no—
353Dic43—42no—
354Dic43—42no—
355Dic43—42no—
356C2×#556—431no—
357C2×#554—431no—
358#3376—4316no—
359C2×#491—431no—
360C2×#489—431no—
361C2×#488—431no—
362C2×#479—431no—
363C2×#475—431no—
364C2×#478—431no—
365C2×#463—431no—
366C2×#463—431no—
367C2×#461—431no—
368C2×#446D4311yescharacteristic, complemented
369C2×#442—431no—
370C2×#440—431no—
371C2×C4×SD16—431no—
372C2×C43#337614yescomplemented
373C2×C43C2×#54811yescharacteristic
374C2×C43C2×#57511yescharacteristic
375C2×C43C2×#57711yescharacteristic
376D43—44no—
377D43—82no—
378C22×SD16—431no—
379C22×SD16—431no—
380C22×D8—431no—
381#556—438no—
382#556—864no—
383#554—438no—
384#554—864no—
385C2×C4⋊Q8—431no—
386C2×C4⋊Q8—431no—
387C2×#126—861no—
388C2×#126—861no—
389C2×#125—431no—
390C2×#125—431no—
391C2×#124—431no—
392C2×#124—431no—
393C2×C22⋊Q8—861no—
394C2×C22⋊Q8—861no—
395C2×C22⋊Q8—861no—
396C2×C22⋊Q8—861no—
397C2×C4×Q8—431no—
398C2×C4×Q8—431no—
399C2×C4×Q8C2×D4311yescharacteristic
400C2×C4×D4—431no—
401C2×C4×D4—431no—
402C2×C4×D4—431no—
403C2×C4×D4—431no—
404C2×#117—861no—
405C22×C4⋊C4—861no—
406#491—438no—
407#489—438no—
408#488—438no—
409#479—438no—
410#478—438no—
411#475—438no—
412#463—438no—
413#463—438no—
414#461—438no—
415#446C2×D4318yescomplemented
416#442—438no—
417#440—438no—
418C4×SD16—438no—
419C2×#107—431no—
420C2×#106—431no—
421C2×#106—431no—
422C2×C4⋊C8C2×D4311yescharacteristic
423C2×C4⋊C8C2×D4311yescharacteristic
424C2×C4⋊C8C2×D4311yescharacteristic
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×#97C2×D4311yescharacteristic
436C2×#97C2×D4311yescharacteristic
437C2×C4×C8C2×D4311yescharacteristic
438C43C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—431no—
440C22×Q8—431no—
441C22×Q8—861no—
442C22×Q8D17211yescharacteristic
443C22×D4—431no—
444C22×D4—431no—
445C23×C4—861no—
446C23×C4—861no—
447C23×C4—861no—
448C23×C4—861no—
449C2×SD16—434no—
450C2×SD16—434no—
451C2×SD16—864no—
452C2×SD16—864no—
453C2×D8—434no—
454C2×D8—864no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459C4⋊Q8—434no—
460C4⋊Q8—434no—
461C4⋊Q8—862no—
462C4⋊Q8—862no—
463#126—868no—
464#126—868no—
465#125—434no—
466#125—434no—
467#125—862no—
468#125—862no—
469#124—434no—
470#124—434no—
471#124—862no—
472#124—862no—
473C22⋊Q8—868no—
474C22⋊Q8—868no—
475C22⋊Q8—868no—
476C22⋊Q8—868no—
477C4×Q8—434no—
478C4×Q8—434no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8D17214yes—
482C4×Q8C22×D4314yes—
483C4×D4—434no—
484C4×D4—434no—
485C4×D4—434no—
486C4×D4—434no—
487C4×D4—862no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—862no—
491#117—868no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
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—868no—
506C2×C4⋊C4D17211yescharacteristic
507C2×C4⋊C4D17211yescharacteristic
508C2×C4⋊C4D17211yescharacteristic
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42C22×D4311yescharacteristic
520C2×C42C22×D4311yescharacteristic
521C2×C42C22×D4311yescharacteristic
522#107—434no—
523#106—434no—
524#106—434no—
525C4⋊C8C22×D4314yes—
526C4⋊C8C22×D4314yes—
527C4⋊C8C22×D4314yes—
528#103—434no—
529#103—434no—
530#103—434no—
531#103—434no—
532#103—434no—
533#103—434no—
534#102—434no—
535#102—434no—
536#102—434no—
537#102—434no—
538#97C22×D4314yes—
539#97C22×D4314yes—
540C4×C8C22×D4314yes—
541C24—861no—
542C24—861no—
543C2×Q8—42no—
544C2×Q8—432no—
545C2×Q8—432no—
546C2×Q8—864no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×Q8—862no—
550C2×Q8—862no—
551C2×Q8—862no—
552C2×Q8—862no—
553C2×Q8—3442no—
554C2×Q8C2×D17214yes—
555C2×D4—434no—
556C2×D4—432no—
557C2×D4—432no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—862no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—864no—
570C22×C4—864no—
571C22×C4—864no—
572C22×C4—864no—
573C22×C4—3442no—
574C22×C4—3442no—
575C22×C4—1724no—
576C22×C4—1724no—
577C22×C4C2×D17211yescharacteristic
578C22×C4C2×D17211yescharacteristic
579C22×C4C2×D17211yescharacteristic
580C22×C4C2×D17211yescharacteristic
581C22×C4C2×D17211yescharacteristic
582C22×C4C2×D17211yescharacteristic
583C22×C4C23×D4311yescharacteristic
584SD16—868no—
585SD16—868no—
586D8—868no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8C23×D4312yes—
592C2×C8C23×D4312yes—
593C2×C8C23×D4312yes—
594C2×C8C23×D4312yes—
595C4⋊C4—432no—
596C4⋊C4—432no—
597C4⋊C4—432no—
598C4⋊C4—432no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—864no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—864no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4C2×D17214yes—
613C4⋊C4C2×D17214yes—
614C4⋊C4C2×D17214yes—
615C22⋊C4—864no—
616C22⋊C4—864no—
617C22⋊C4—864no—
618C22⋊C4—864no—
619C22⋊C4—864no—
620C22⋊C4—864no—
621C22⋊C4—864no—
622C22⋊C4—864no—
623C42—864no—
624C42—864no—
625C42C2×D17212yes—
626C42C2×D17212yes—
627C42C2×D17212yes—
628C42C23×D4312yes—
629C42C23×D4312yes—
630C42C23×D4312yes—
631C23—864no—
632C23—862no—
633C23—862no—
634C23—1722no—
635C23—1722no—
636C23—1722no—
637C23—1722no—
638C23—1722no—
639C23C22×D17211yescharacteristic
640Q8—44no—
641Q8—862no—
642Q8—862no—
643Q8—862no—
644Q8—862no—
645Q8—3444no—
646Q8—1722no—
647Q8—1722no—
648D4—434no—
649D4—864no—
650D4—862no—
651D4—862no—
652D4—862no—
653D4—1722no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—3444no—
667C2×C4—3444no—
668C2×C4—1728no—
669C2×C4—1728no—
670C2×C4—1722no—
671C2×C4—1722no—
672C2×C4—1722no—
673C2×C4—1722no—
674C2×C4—1722no—
675C2×C4—1722no—
676C2×C4C22×D17212yes—
677C2×C4C22×D17212yes—
678C2×C4C22×D17212yes—
679C2×C4C22×D17212yes—
680C2×C4C22×D17212yes—
681C2×C4C22×D17212yes—
682C2×C4C22×D17211yescharacteristic
683C2×C4#41×D4312yes—
684C2×C4#1306337312yes—
685C2×C4C24×D4311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C22—864no—
691C22—3444no—
692C22—1722no—
693C22—1722no—
694C22—1722no—
695C22—1722no—
696C22—1722no—
697C22—1728no—
698C22#1458356112yes—
699C22#1458369912yes—
700C22#1458371112yes—
701C22C23×D17211yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—1722no—
709C4—1722no—
710C4—1722no—
711C4—1722no—
712C4—1722no—
713C4—1722no—
714C4#1458356112yes—
715C4C2×#41×D4311yescharacteristic
716C4C2×#1306337311yescharacteristic
717C2—3442no—
718C2—1724no—
719C2#1914742414yesdirect product factor
720C2C2×#1458356111yescharacteristic
721C2C2×#1458369911yescharacteristic
722C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#446C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenterC2×#446D43
hypocenterC43C2×#3376
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#14583622C2semidirect
2. C2×#14583609C2semidirect
3. #19147424C2direct (N × H)
4. C2×#14583268C2semidirect
5. C2×#14583259C2semidirect
6. C2×#14583254C2semidirect
7. C2×#14583207C2semidirect
8. C2×#14583185C2semidirect
9. C2×#14583200C2semidirect
12. C2×#14583105C2semidirect
14. C2×#14583001C2semidirect
15. C2×C4×#10621873C2semidirect
16. C2×C43×#446C2semidirect
21. #14583622C22semidirect
23. #14583609C22semidirect
44. #14583268C22semidirect
45. #14583259C22semidirect
46. #14583254C22semidirect
47. #14583207C22semidirect
48. #14583200C22semidirect
49. #14583185C22semidirect
52. #14583105C22semidirect
54. #14583001C22semidirect
55. C4×#10621873C22semidirect
70. C43×#446C22semidirect
368. C2×#446D43semidirect
372. C2×C43#3376semidirect
415. #446C2×D43semidirect
438. C43C2×#3376semidirect
719. C2#19147424direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836222
C2×#145836092
#191474242
C2×#145832682
C2×#145832592
C2×#145832542
C2×#145832072
C2×#145831852
C2×#145832002
C2×#145831152
C2×#145831052
C2×#145830122
C2×#145830012
C2×C4×#106218732
C2×C43×#4462
C2×#337643