Finite Group Databasebeta

← C2×#19147310 #25976269

Subgroups — C2×#19147310 #25976269

Order 11008.

2070 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583618C211yesmaximal, characteristic, complemented
2C2×#14583564C211yesmaximal, characteristic, complemented
3#19147310C2116yesmaximal, direct product factor
4C2×#14583257C211yesmaximal, characteristic, complemented
5C2×#14583248C211yesmaximal, characteristic, complemented
6C2×#14583192C211yesmaximal, characteristic, complemented
7C2×#14583191C211yesmaximal, characteristic, complemented
8C2×#14583177C211yesmaximal, characteristic, complemented
9C2×#14583113C211yesmaximal, characteristic
10C2×#14583111C211yesmaximal, characteristic
11C2×#14583103C211yesmaximal, characteristic, complemented
12C2×#14583027C211yesmaximal, characteristic, complemented
13C2×#14583002C211yesmaximal, characteristic, complemented
14C2×#14583001C211yesmaximal, characteristic, complemented
15C2×#14582979C211yesmaximal, characteristic
16C2×C43×#489C211yesmaximal, characteristic, complemented
17C22×Q8×D43—21no—
18C22×#10621873C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21#14583618—24no—
22#14583618C2218yescomplemented
23#14583564—24no—
24#14583564C2218yescomplemented
25C2×#13063324C2211yescharacteristic
26C2×#13063324C2211yescharacteristic
27C2×#13063323C2211yescharacteristic
28C2×#13063318—21no—
29C2×#13063318—21no—
30C2×#13063312C2211yescharacteristic
31C2×#13063303—21no—
32C2×#13063303—21no—
33C2×#13063302—21no—
34C2×#13063301—21no—
35C2×Q8×Dic43C2211yescharacteristic
36C2×C4×Dic86C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×D4×Dic43C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×#13063287C2211yescharacteristic
42C2×#13063281—21no—
43#14583257C2218yescomplemented
44#14583248C2218yescomplemented
45#14583192C2218yescomplemented
46#14583191C2218yescomplemented
47#14583177C2218yescomplemented
48#14583113C2218yes—
49#14583111C2218yes—
50#14583103C2218yescomplemented
51#14583027C2218yescomplemented
52#14583002C2218yescomplemented
53#14583001C2218yescomplemented
54#14582979C2218yes—
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×#124×C43C2211yescharacteristic
71C43×#489C2218yescomplemented
72C2×#103×C43C2211yescharacteristic
73C2×#103×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×Dic86D411yescharacteristic
80C22×Dic86C2311yescharacteristic
81C2×Q8×D43—28no—
82C2×Q8×D43—48no—
83C22×D172C2311yescharacteristic
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C2×#10621873—24no—
89C2×#10621873C2314yes—
90C2×#10621884—24no—
91C2×#10621884C2314yes—
92C2×#10621882—24no—
93C2×#10621882C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96#13063324—22no—
97#13063324—22no—
98#13063324C2314yes—
99#13063324C2314yes—
100#13063323—22no—
101#13063323C2314yes—
102#13063318—28no—
103#13063318—28no—
104#13063312—22no—
105#13063312C2314yes—
106#13063303—28no—
107#13063303—28no—
108#13063302—28no—
109#13063301—28no—
110Q8×Dic43—22no—
111Q8×Dic43C2314yes—
112C4×Dic86—22no—
113C4×Dic86D414yes—
114C4×Dic86C2314yes—
115C4×Dic86C2314yes—
116C4×D172—22no—
117C4×D172C2314yes—
118D4×Dic43—22no—
119D4×Dic43C2314yes—
120#13063287—22no—
121#13063287—22no—
122#13063287C2314yes—
123#13063287C2314yes—
124#13063281—28no—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43D411yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C2×Dic43⋊C4D411yescharacteristic
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43C2311yescharacteristic
145C2×C4×Dic43C2311yescharacteristic
146#13063259C2314yes—
147#13063258C2314yes—
148#13063258C2314yes—
149C4⋊(C43⋊C8)C2314yes—
150Dic43⋊C8C2314yes—
151Dic43⋊C8C2314yes—
152#13063250C2314yes—
153#13063249C2314yes—
154#13063248C2314yes—
155#13063248C2314yes—
156#13063247C2314yes—
157#13063246C2314yes—
158#13063235C2314yes—
159C8×Dic43C2314yes—
160C22×Q8×C43—21no—
161C22×Q8×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C4⋊Q8×C43—22no—
166C4⋊Q8×C43C2314yes—
167#124×C43—22no—
168#124×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C42×C43C2311yescharacteristic
175#103×C43C2314yes—
176#103×C43C2314yes—
177#102×C43C2314yes—
178#102×C43C2314yes—
179#97×C43C2314yes—
180C24×C43—21no—
181C23×D43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—24no—
184C2×Q8×C43—22no—
185C2×Q8×C43—22no—
186C2×Q8×C43—44no—
187C2×Q8×C43C2412yes—
188C2×D4×C43—21no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43C2412yes—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×Dic43—24no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—44no—
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207Q8×D43—432no—
208C2×D172—21no—
209C2×D172—22no—
210C2×D172#4114yes—
211C2×D172C2412yes—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—24no—
215C2×C4×D43—44no—
216C2×C4×D43—44no—
217C2×C4×D43—44no—
218C2×Dic86—24no—
219C2×Dic86—22no—
220C2×Dic86—22no—
221C2×Dic86—21no—
222C2×Dic86—24no—
223C2×Dic86—24no—
224C2×Dic86—44no—
225C2×Dic86—44no—
226C2×Dic86C2×D414yes—
227C2×Dic86C2412yes—
228C2×C8×C43—22no—
229C2×C8×C43—22no—
230C2×C8×C43C2412yes—
231C2×C8×C43C2412yes—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—24no—
239C42×C43C2×D412yes—
240C42×C43C2412yes—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43—24no—
244#10621884—28no—
245#10621882—28no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43C2×D414yes—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4C2×D414yes—
261Dic43⋊C4C2×D414yes—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2×D412yes—
266C4×Dic43C2412yes—
267C4×Dic43C2412yes—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272#10621873—28no—
273C23×C43—22no—
274C23×C43—42no—
275C23×C43—42no—
276C23×C43—42no—
277C23×C43C22×D411yescharacteristic
278C22×D43—24no—
279C22×D43—22no—
280C22×D43—42no—
281C22×D43—42no—
282Q8×C43—22no—
283Q8×C43—22no—
284Q8×C43—48no—
285Q8×C43—42no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—42no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43C22×D412yes—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4112yes—
301C2×C4×C432−1+412yes—
302C2×C4×C43C2511yescharacteristic
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—48no—
313C2×Dic43AGL(1,ℤ/8)14yes—
314C2×Dic43C22×D412yes—
315C2×Dic43C22×D412yes—
316C2×Dic43C22×D412yes—
317C2×Dic43C22×D412yes—
318D172—24no—
319D172—22no—
320D172C2×#4114yes—
321C4×D43—48no—
322C4×D43—48no—
323C4×D43—48no—
324Dic86—28no—
325Dic86—22no—
326Dic86—22no—
327Dic86—48no—
328Dic86—42no—
329Dic86—48no—
330C8×C43—22no—
331C8×C43—22no—
332C43⋊C8—22no—
333C43⋊C8—22no—
334C2×#3367—431nomaximal, Sylow
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—84no—
339C22×C43#54812yes—
340C22×C43C2×AGL(1,ℤ/8)12yes—
341C22×C43#57812yes—
342C22×C43C23×D411yescharacteristic
343C2×D43—24no—
344C2×D43—48no—
345C2×D43—42no—
346C2×D43—42no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43#54812yes—
353C4×C43C22×#4111yescharacteristic
354C4×C43C2×2−1+411yescharacteristic
355Dic43—22no—
356Dic43—22no—
357Dic43—22no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361Dic43C2×AGL(1,ℤ/8)14yes—
362C2×#556—431no—
363C2×D4×Q8—431no—
364#3367—4316no—
365C2×#489—431no—
366C2×#489D4311yescharacteristic, complemented
367C2×#487—431no—
368C2×#477—431no—
369C2×#477—431no—
370C2×#474—431no—
371C2×#463—431no—
372C2×#463—431no—
373C2×#461—431no—
374C2×#446—431no—
375C2×#440—431no—
376C2×#440—431no—
377C2×C4×D8—431no—
378C2×C43—82no—
379C2×C43#336714yescomplemented
380C2×C43C2×#54811yescharacteristic
381C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
382C2×C43C2×#57811yescharacteristic
383D43—44no—
384C23×Q8—861no—
385C22×SD16—431no—
386C22×SD16—431no—
387C22×D8—431no—
388#556—438no—
389#556—864no—
390D4×Q8—438no—
391D4×Q8—864no—
392C2×C4⋊Q8—431no—
393C2×C4⋊Q8—431no—
394C2×C4⋊Q8—431no—
395C2×C4⋊Q8C2×D4311yescharacteristic
396C2×#126—861no—
397C2×#126—861no—
398C2×#124—431no—
399C2×#124C2×D4311yescharacteristic
400C2×C22⋊Q8—861no—
401C2×C22⋊Q8—861no—
402C2×C22⋊Q8—861no—
403C2×C22⋊Q8—861no—
404C2×C4×Q8—431no—
405C2×C4×Q8—431no—
406C2×C4×Q8—431no—
407C2×C4×D4—431no—
408C2×C4×D4—431no—
409C2×C4×D4—431no—
410C2×C4×D4—431no—
411C2×#117—861no—
412#489—438no—
413#489C2×D4318yescomplemented
414#487—438no—
415#477—438no—
416#477—438no—
417#474—438no—
418#463—438no—
419#463—438no—
420#461—438no—
421#446—438no—
422#440—438no—
423#440—438no—
424C4×D8—438no—
425C2×#107—431no—
426C2×#107—431no—
427C2×#107—431no—
428C2×C4⋊C8—431no—
429C2×C4⋊C8—431no—
430C2×C4⋊C8—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103C2×D4311yescharacteristic
436C2×#103C2×D4311yescharacteristic
437C2×#102—431no—
438C2×#102—431no—
439C2×#102C2×D4311yescharacteristic
440C2×#102C2×D4311yescharacteristic
441C2×#97—431no—
442C2×#97C2×D4311yescharacteristic
443C2×C4×C8—431no—
444C43C2×#336711yescharacteristic, complemented, Sylow
445C22×Q8—21no—
446C22×Q8—431no—
447C22×Q8—431no—
448C22×Q8—861no—
449C22×Q8—861no—
450C22×Q8—868no—
451C22×Q8—1728no—
452C22×Q8C22×D4311yescharacteristic
453C22×D4—431no—
454C22×D4C22×D4311yescharacteristic
455C23×C4—861no—
456C23×C4—861no—
457C23×C4—861no—
458C23×C4—861no—
459C2×SD16—434no—
460C2×SD16—434no—
461C2×SD16—864no—
462C2×SD16—864no—
463C2×D8—434no—
464C2×D8—864no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C4⋊Q8—22no—
470C4⋊Q8—434no—
471C4⋊Q8—434no—
472C4⋊Q8—434no—
473C4⋊Q8—862no—
474C4⋊Q8—862no—
475C4⋊Q8—862no—
476C4⋊Q8C22×D4314yes—
477#126—868no—
478#126—868no—
479#124—22no—
480#124—434no—
481#124—862no—
482#124C22×D4314yes—
483C22⋊Q8—868no—
484C22⋊Q8—868no—
485C22⋊Q8—868no—
486C22⋊Q8—868no—
487C4×Q8—434no—
488C4×Q8—434no—
489C4×Q8—434no—
490C4×Q8—434no—
491C4×Q8—862no—
492C4×Q8—862no—
493C4×D4—434no—
494C4×D4—434no—
495C4×D4—434no—
496C4×D4—434no—
497C4×D4—862no—
498C4×D4—862no—
499C4×D4—862no—
500C4×D4—862no—
501#117—868no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C4⋊C4C22×D4311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C42—431no—
525C2×C42—431no—
526C2×C42—861no—
527C2×C42—861no—
528C2×C42C22×D4311yescharacteristic
529#107—434no—
530#107—434no—
531#107—434no—
532C4⋊C8—434no—
533C4⋊C8—434no—
534C4⋊C8—434no—
535#103—434no—
536#103—434no—
537#103—434no—
538#103—434no—
539#103C22×D4314yes—
540#103C22×D4314yes—
541#102—434no—
542#102—434no—
543#102C22×D4314yes—
544#102C22×D4314yes—
545#97—434no—
546#97C22×D4314yes—
547C4×C8—434no—
548C24—21no—
549C24—861no—
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—44no—
555C2×Q8—434no—
556C2×Q8—432no—
557C2×Q8—864no—
558C2×Q8—864no—
559C2×Q8—864no—
560C2×Q8—861no—
561C2×Q8—862no—
562C2×Q8—862no—
563C2×Q8—1724no—
564C2×Q8—1724no—
565C2×Q8—17232no—
566C2×Q8C23×D4312yes—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—434no—
571C2×D4—432no—
572C2×D4—861no—
573C2×D4—862no—
574C2×D4C23×D4312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—864no—
583C22×C4—864no—
584C22×C4—864no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—864no—
589C22×C4—1724no—
590C22×C4—1724no—
591C22×C4—1724no—
592C22×C4—1724no—
593C22×C4D4×D4311yescharacteristic
594C22×C4D4×D4311yescharacteristic
595C22×C4C23×D4311yescharacteristic
596SD16—868no—
597SD16—868no—
598D8—868no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—432no—
602C2×C8—432no—
603C2×C8—862no—
604C2×C8—862no—
605C2×C8C23×D4312yes—
606C2×C8C23×D4312yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—434no—
611C4⋊C4—434no—
612C4⋊C4—434no—
613C4⋊C4—432no—
614C4⋊C4—432no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—864no—
623C4⋊C4C23×D4312yes—
624C4⋊C4C23×D4312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C42—432no—
634C42—432no—
635C42—432no—
636C42—432no—
637C42—864no—
638C42—864no—
639C42D4×D4312yes—
640C42C23×D4312yes—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—864no—
646C23—862no—
647C23—1722no—
648C23—1722no—
649C23C2×D4×D4311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—48no—
653Q8—42no—
654Q8—868no—
655Q8—862no—
656Q8—862no—
657Q8—1728no—
658Q8—1728no—
659Q8—1722no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—434no—
664D4—864no—
665D4—862no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—434no—
675C2×C4—432no—
676C2×C4—432no—
677C2×C4—432no—
678C2×C4—432no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—1728no—
686C2×C4—1728no—
687C2×C4—1728no—
688C2×C4—1728no—
689C2×C4—1722no—
690C2×C4—1722no—
691C2×C4—1722no—
692C2×C4C2×D4×D4312yes—
693C2×C4C2×D4×D4312yes—
694C2×C4C2×D4×D4311yescharacteristic
695C2×C4#41×D4312yes—
696C2×C4#1306337212yes—
697C2×C4C24×D4311yescharacteristic
698C8—22no—
699C8—22no—
700C8—862no—
701C8—862no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—864no—
707C22—1722no—
708C22—1728no—
709C22—1722no—
710C22#1458355712yes—
711C22AGL(1,ℤ/8)×D4312yes—
712C22#1458371512yes—
713C22C22×D4×D4311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—434no—
720C4—862no—
721C4—862no—
722C4—862no—
723C4—1722no—
724C4—1722no—
725C4—1722no—
726C4#1458355712yes—
727C4C2×#41×D4311yescharacteristic
728C4C2×#1306337211yescharacteristic
729C2—82no—
730C2—1724no—
731C2#1914731014yesdirect product factor
732C2C2×#1458355711yescharacteristic
733C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
734C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#489C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterC2×#489D43
hypocenterC43C2×#3367
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#14583618C2semidirect
2. C2×#14583564C2semidirect
3. #19147310C2direct (N × H)
4. C2×#14583257C2semidirect
5. C2×#14583248C2semidirect
6. C2×#14583192C2semidirect
7. C2×#14583191C2semidirect
8. C2×#14583177C2semidirect
11. C2×#14583103C2semidirect
12. C2×#14583027C2semidirect
13. C2×#14583002C2semidirect
14. C2×#14583001C2semidirect
16. C2×C43×#489C2semidirect
22. #14583618C22semidirect
24. #14583564C22semidirect
43. #14583257C22semidirect
44. #14583248C22semidirect
45. #14583192C22semidirect
46. #14583191C22semidirect
47. #14583177C22semidirect
50. #14583103C22semidirect
51. #14583027C22semidirect
52. #14583002C22semidirect
53. #14583001C22semidirect
71. C43×#489C22semidirect
366. C2×#489D43semidirect
379. C2×C43#3367semidirect
413. #489C2×D43semidirect
444. C43C2×#3367semidirect
731. C2#19147310direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836182
C2×#145835642
#191473102
C2×#145832572
C2×#145832482
C2×#145831922
C2×#145831912
C2×#145831772
C2×#145831132
C2×#145831112
C2×#145831032
C2×#145830272
C2×#145830022
C2×#145830012
C2×#145829792
C2×C43×#4892
C2×#336743