Finite Group Databasebeta

← C2×#19147350 #25976348

Subgroups — C2×#19147350 #25976348

Order 11008.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583634C211yesmaximal, characteristic, complemented
2C2×#14583609C211yesmaximal, characteristic, complemented
3#19147350C2116yesmaximal, direct product factor
4C2×#14583264C211yesmaximal, characteristic, complemented
5C2×#14583259C211yesmaximal, characteristic, complemented
6C2×#14583254C211yesmaximal, characteristic, complemented
7C2×#14583207C211yesmaximal, characteristic, complemented
8C2×#14583200C211yesmaximal, characteristic, complemented
9C2×#14583180C211yesmaximal, characteristic, complemented
10C2×#14583115C211yesmaximal, characteristic, complemented
11C2×#14583115C211yesmaximal, characteristic, complemented
12C2×#14583095C211yesmaximal, characteristic
13C2×#14583012C211yesmaximal, characteristic, complemented
14C2×#14583001C211yesmaximal, characteristic, complemented
15C2×C4×D344C211yesmaximal, characteristic, complemented
16C2×C43×#446C211yesmaximal, characteristic, complemented
17C22×#10621873C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C22×D344C2211yescharacteristic
20#14583634—24no—
21#14583634C2218yescomplemented
22#14583609—24no—
23#14583609C2218yescomplemented
24C2×#13063325C2211yescharacteristic
25C2×#13063322C2211yescharacteristic
26C2×#13063317C2211yescharacteristic
27C2×#13063317C2211yescharacteristic
28C2×#13063314—21no—
29C2×#13063313C2211yescharacteristic
30C2×#13063313C2211yescharacteristic
31C2×#13063310—21no—
32C2×#13063310—21no—
33C2×#13063303—21no—
34C2×#13063303—21no—
35C2×#13063301—21no—
36C2×C4×Dic86C2211yescharacteristic
37C2×C4×D172C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×C4×D172C2211yescharacteristic
42C2×#13063287—21no—
43C2×C4⋊C4×D43—21no—
44#14583264C2218yescomplemented
45#14583259C2218yescomplemented
46#14583254C2218yescomplemented
47#14583207C2218yescomplemented
48#14583200C2218yescomplemented
49#14583180C2218yescomplemented
50#14583115C2218yescomplemented
51#14583115C2218yescomplemented
52#14583095C2218yes—
53#14583012C2218yescomplemented
54#14583001C2218yescomplemented
55C4×D344C2218yescomplemented
56C2×#13063259C2211yescharacteristic
57C2×#13063259C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
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×D172—21no—
80C22×D172—21no—
81C22×D172C2311yescharacteristic
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C2×#10621873—24no—
90C2×#10621873C2314yes—
91C2×D344—24no—
92C2×D344—24no—
93C2×D344C2314yes—
94C2×D344C2314yes—
95#13063325—22no—
96#13063325C2314yes—
97#13063322—22no—
98#13063322C2314yes—
99#13063317—22no—
100#13063317—22no—
101#13063317C2314yes—
102#13063317C2314yes—
103#13063314—28no—
104#13063313—22no—
105#13063313—22no—
106#13063313C2314yes—
107#13063313C2314yes—
108#13063310—28no—
109#13063310—28no—
110#13063303—28no—
111#13063303—28no—
112#13063301—28no—
113C4×Dic86—22no—
114C4×Dic86C2314yes—
115C4×D172—22no—
116C4×D172—22no—
117C4×D172—22no—
118C4×D172—22no—
119C4×D172—22no—
120C4×D172C2314yes—
121C4×D172C2314yes—
122C4×D172C2314yes—
123C4×D172C2314yes—
124C4×D172C2314yes—
125#13063287—28no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
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—
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×(C2×D43)⋊C4—21no—
146C2×C4×Dic43—21no—
147#13063259C2314yes—
148#13063259C2314yes—
149#13063257C2314yes—
150#13063250C2314yes—
151#13063250C2314yes—
152#13063250C2314yes—
153#13063247C2314yes—
154#13063247C2314yes—
155#13063247C2314yes—
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—
181C23×D43—21no—
182C2×Q8×C43—42no—
183C2×Q8×C43C2×D414yes—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C2×D172—21no—
197C2×D172—22no—
198C2×D172—24no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—24no—
202C2×D172—22no—
203C2×D172—22no—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172—44no—
207C2×D172—82no—
208C2×D172#4114yes—
209C2×D172C2412yes—
210C2×D172C2412yes—
211C2×D172C2412yes—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—24no—
217C2×C4×D43—44no—
218C2×C4×D43—82no—
219C2×C4×D43—82no—
220C2×C4×D43—82no—
221C2×C4×D43—82no—
222C2×Dic86—22no—
223C2×Dic86—22no—
224C2×Dic86—21no—
225C2×Dic86—24no—
226C2×Dic86—82no—
227C2×Dic86C2412yes—
228C2×C8×C43—22no—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43C2412yes—
233C2×C8×C43C2412yes—
234C2×C8×C43C2412yes—
235C2×C8×C43C2412yes—
236C4⋊C4×C43C2×D414yes—
237C4⋊C4×C43C2×D414yes—
238C4⋊C4×C43C2×D414yes—
239C42×C43C2×D412yes—
240C42×C43C2×D412yes—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243C42×C43C2412yes—
244C42×C43C2412yes—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254C4⋊Dic43—24no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43C2412yes—
260C4⋊Dic43C2412yes—
261C4⋊Dic43C2412yes—
262C4⋊Dic43C2412yes—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268C4×Dic43—24no—
269D344—28no—
270D344—28no—
271#10621873—28no—
272C23×C43C22×D411yescharacteristic
273C22×D43—24no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285Q8×C43—44no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43C22×D412yes—
293C2×C4×C43C22×D412yes—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D412yes—
297C2×C4×C43C22×D412yes—
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4112yes—
300C2×C4×C432−1+412yes—
301C2×C4×C43C2511yescharacteristic
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312D172—24no—
313D172—22no—
314D172—22no—
315D172—22no—
316D172—22no—
317D172—22no—
318D172—48no—
319D172—42no—
320D172—42no—
321D172—84no—
322D172C2×#4114yes—
323C4×D43—48no—
324C4×D43—84no—
325C4×D43—84no—
326C4×D43—84no—
327C4×D43—84no—
328Dic86—22no—
329Dic86—22no—
330Dic86—42no—
331Dic86—84no—
332C8×C43—22no—
333C8×C43—22no—
334C8×C43—22no—
335C8×C43—22no—
336C2×#3370—431nomaximal, Sylow
337C22×C43#54812yes—
338C22×C43#57512yes—
339C22×C43#57612yes—
340C22×C43C23×D411yescharacteristic
341C2×D43—24no—
342C2×D43—48no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—84no—
352C2×D43—84no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—22no—
356C4×C43—22no—
357C4×C43—22no—
358C4×C43—22no—
359C4×C43#54812yes—
360C4×C43C22×#4111yescharacteristic
361C4×C43C2×2−1+411yescharacteristic
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365Dic43—42no—
366Dic43—42no—
367C2×#559—431no—
368C2×#554—431no—
369#3370—4316no—
370C2×#490—431no—
371C2×#489—431no—
372C2×#488—431no—
373C2×#479—431no—
374C2×#478—431no—
375C2×#474—431no—
376C2×#463—431no—
377C2×#463—431no—
378C2×#459—431no—
379C2×#446D4311yescharacteristic, complemented
380C2×#442—431no—
381C2×#440—431no—
382C2×C4×D8—431no—
383C2×C43#337014yescomplemented
384C2×C43C2×#54811yescharacteristic
385C2×C43C2×#57511yescharacteristic
386C2×C43C2×#57611yescharacteristic
387D43—44no—
388D43—82no—
389D43—82no—
390C22×SD16—431no—
391C22×D8—431no—
392C22×D8—431no—
393#559—438no—
394#559—864no—
395#554—438no—
396#554—864no—
397C2×C4⋊Q8—431no—
398C2×#127—431no—
399C2×#125—431no—
400C2×#125—431no—
401C2×#124—431no—
402C2×#124—431no—
403C2×#124—861no—
404C2×#123—861no—
405C2×#123—861no—
406C2×C22⋊Q8—861no—
407C2×C22⋊Q8—861no—
408C2×C22⋊Q8—861no—
409C2×C4×Q8—431no—
410C2×C4×Q8C2×D4311yescharacteristic
411C2×C4×D4—431no—
412C2×C4×D4—431no—
413C2×C4×D4—431no—
414C2×C4×D4—431no—
415C2×C4×D4—431no—
416C2×C4×D4—861no—
417C22×C4⋊C4—861no—
418#490—438no—
419#489—438no—
420#488—438no—
421#479—438no—
422#478—438no—
423#474—438no—
424#463—438no—
425#463—438no—
426#459—438no—
427#446C2×D4318yescomplemented
428#442—438no—
429#440—438no—
430C4×D8—438no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#106—431no—
434C2×C4⋊C8C2×D4311yescharacteristic
435C2×C4⋊C8C2×D4311yescharacteristic
436C2×C4⋊C8C2×D4311yescharacteristic
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#97C2×D4311yescharacteristic
448C2×#97C2×D4311yescharacteristic
449C2×C4×C8C2×D4311yescharacteristic
450C43C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—431no—
452C22×Q8—861no—
453C22×Q8D17211yescharacteristic
454C22×D4—431no—
455C22×D4—431no—
456C22×D4—431no—
457C22×D4—861no—
458C22×D4—861no—
459C23×C4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C2×SD16—434no—
465C2×SD16—864no—
466C2×D8—434no—
467C2×D8—434no—
468C2×D8—864no—
469C2×D8—864no—
470C22×C8C22×D4311yescharacteristic
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C4⋊Q8—434no—
475C4⋊Q8—862no—
476#127—434no—
477#127—862no—
478#125—434no—
479#125—434no—
480#125—862no—
481#125—862no—
482#124—434no—
483#124—434no—
484#124—868no—
485#124—862no—
486#124—862no—
487#123—868no—
488#123—868no—
489C22⋊Q8—868no—
490C22⋊Q8—868no—
491C22⋊Q8—868no—
492C4×Q8—434no—
493C4×Q8—862no—
494C4×Q8D17214yes—
495C4×Q8C22×D4314yes—
496C4×D4—434no—
497C4×D4—434no—
498C4×D4—434no—
499C4×D4—434no—
500C4×D4—434no—
501C4×D4—868no—
502C4×D4—862no—
503C4×D4—862no—
504C4×D4—862no—
505C4×D4—862no—
506C4×D4—862no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—868no—
518C2×C4⋊C4D17211yescharacteristic
519C2×C4⋊C4D17211yescharacteristic
520C2×C4⋊C4D17211yescharacteristic
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C42—861no—
531C2×C42C22×D4311yescharacteristic
532C2×C42C22×D4311yescharacteristic
533C2×C42C22×D4311yescharacteristic
534#107—434no—
535#107—434no—
536#106—434no—
537C4⋊C8C22×D4314yes—
538C4⋊C8C22×D4314yes—
539C4⋊C8C22×D4314yes—
540#103—434no—
541#103—434no—
542#103—434no—
543#102—434no—
544#102—434no—
545#102—434no—
546#102—434no—
547#102—434no—
548#102—434no—
549#102—434no—
550#97C22×D4314yes—
551#97C22×D4314yes—
552C4×C8C22×D4314yes—
553C24—861no—
554C24—861no—
555C24—861no—
556C2×Q8—42no—
557C2×Q8—432no—
558C2×Q8—864no—
559C2×Q8—861no—
560C2×Q8—862no—
561C2×Q8—862no—
562C2×Q8—3442no—
563C2×Q8C2×D17214yes—
564C2×D4—434no—
565C2×D4—432no—
566C2×D4—432no—
567C2×D4—432no—
568C2×D4—861no—
569C2×D4—864no—
570C2×D4—864no—
571C2×D4—861no—
572C2×D4—861no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—3442no—
579C2×D4—1724no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—864no—
586C22×C4—864no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—864no—
590C22×C4—3442no—
591C22×C4—3442no—
592C22×C4—3442no—
593C22×C4—3442no—
594C22×C4—1724no—
595C22×C4C2×D17211yescharacteristic
596C22×C4C2×D17211yescharacteristic
597C22×C4C2×D17211yescharacteristic
598C22×C4C2×D17211yescharacteristic
599C22×C4C2×D17211yescharacteristic
600C22×C4C2×D17211yescharacteristic
601C22×C4C23×D4311yescharacteristic
602SD16—868no—
603D8—868no—
604D8—868no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8C23×D4312yes—
610C2×C8C23×D4312yes—
611C2×C8C23×D4312yes—
612C2×C8C23×D4312yes—
613C4⋊C4—432no—
614C4⋊C4—432no—
615C4⋊C4—432no—
616C4⋊C4—432no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4C2×D17214yes—
628C4⋊C4C2×D17214yes—
629C4⋊C4C2×D17214yes—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C42—864no—
640C42C2×D17212yes—
641C42C2×D17212yes—
642C42C2×D17212yes—
643C42C23×D4312yes—
644C42C23×D4312yes—
645C42C23×D4312yes—
646C23—864no—
647C23—862no—
648C23—862no—
649C23—862no—
650C23—1722no—
651C23—1722no—
652C23—1722no—
653C23—1722no—
654C23—1722no—
655C23—1722no—
656C23—1722no—
657C23—1722no—
658C23C22×D17211yescharacteristic
659Q8—44no—
660Q8—862no—
661Q8—862no—
662Q8—3444no—
663Q8—1722no—
664D4—434no—
665D4—864no—
666D4—862no—
667D4—862no—
668D4—862no—
669D4—862no—
670D4—862no—
671D4—3444no—
672D4—1728no—
673D4—1722no—
674D4—1722no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—3444no—
687C2×C4—3444no—
688C2×C4—3444no—
689C2×C4—3444no—
690C2×C4—1728no—
691C2×C4—1722no—
692C2×C4—1722no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4C22×D17212yes—
697C2×C4C22×D17212yes—
698C2×C4C22×D17212yes—
699C2×C4C22×D17212yes—
700C2×C4C22×D17212yes—
701C2×C4C22×D17212yes—
702C2×C4C22×D17211yescharacteristic
703C2×C4#41×D4312yes—
704C2×C4#1306337312yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—864no—
711C22—3444no—
712C22—3444no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22—1722no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22—1728no—
722C22#1458356112yes—
723C22#1458369912yes—
724C22#1458370412yes—
725C22C23×D17211yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—1722no—
733C4—1722no—
734C4—1722no—
735C4—1722no—
736C4—1722no—
737C4#1458356112yes—
738C4C2×#41×D4311yescharacteristic
739C4C2×#1306337311yescharacteristic
740C2—3442no—
741C2—3442no—
742C2—1724no—
743C2#1914735014yesdirect product factor
744C2C2×#1458356111yescharacteristic
745C2C2×#1458369911yescharacteristic
746C2C2×#1458370411yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#446C2
socleC23×C43C22×D4
prime radicalC2×#14583095C2
hypercenterC2×#446D43
hypocenterC43C2×#3370
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×#14583634C2semidirect
2. C2×#14583609C2semidirect
3. #19147350C2direct (N × H)
4. C2×#14583264C2semidirect
5. C2×#14583259C2semidirect
6. C2×#14583254C2semidirect
7. C2×#14583207C2semidirect
8. C2×#14583200C2semidirect
9. C2×#14583180C2semidirect
10. C2×#14583115C2semidirect
11. C2×#14583115C2semidirect
13. C2×#14583012C2semidirect
14. C2×#14583001C2semidirect
15. C2×C4×D344C2semidirect
16. C2×C43×#446C2semidirect
21. #14583634C22semidirect
23. #14583609C22semidirect
44. #14583264C22semidirect
45. #14583259C22semidirect
46. #14583254C22semidirect
47. #14583207C22semidirect
48. #14583200C22semidirect
49. #14583180C22semidirect
50. #14583115C22semidirect
51. #14583115C22semidirect
53. #14583012C22semidirect
54. #14583001C22semidirect
55. C4×D344C22semidirect
70. C43×#446C22semidirect
379. C2×#446D43semidirect
383. C2×C43#3370semidirect
427. #446C2×D43semidirect
450. C43C2×#3370semidirect
743. C2#19147350direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836342
C2×#145836092
#191473502
C2×#145832642
C2×#145832592
C2×#145832542
C2×#145832072
C2×#145832002
C2×#145831802
C2×#145831152
C2×#145830952
C2×#145830122
C2×#145830012
C2×C4×D3442
C2×C43×#4462
C2×#337043