Finite Group Databasebeta

← C2×#19144826 #25964878

Subgroups — C2×#19144826 #25964878

Order 11008.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic
2C2×#14583376C211yesmaximal, characteristic, complemented
3#19144826C2116yesmaximal, direct product factor
4C2×#14583241C211yesmaximal, characteristic, complemented
5C2×#14583224C211yesmaximal, characteristic
6C2×#14583195C211yesmaximal, characteristic, complemented
7C2×#14583185C211yesmaximal, characteristic, complemented
8C2×#14583122C211yesmaximal, characteristic, complemented
9C2×#14583122C211yesmaximal, characteristic, complemented
10C2×#14583057C211yesmaximal, characteristic, complemented
11C2×#14583040C211yesmaximal, characteristic
12C2×#14583007C211yesmaximal, characteristic, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14C2×C4×Dic172C211yesmaximal, characteristic, complemented
15C2×C4×#10621873C211yesmaximal, characteristic, complemented
16C2×C43×#433C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×Dic172C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22#14583520—24no—
23#14583520C2218yes—
24C2×#13063325C2211yescharacteristic
25C2×#13063320—21no—
26C2×#13063313C2211yescharacteristic
27C2×#13063311—21no—
28C2×#13063307—21no—
29C2×#13063304C2211yescharacteristic
30C2×#13063303—21no—
31C2×#13063299C2211yescharacteristic
32#14583376—24no—
33#14583376C2218yescomplemented
34C2×C4×Dic86C2211yescharacteristic
35C2×C4×Dic86C2211yescharacteristic
36C2×C4×Dic86C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38C2×C4×Dic86C2211yescharacteristic
39C2×#13063290—21no—
40C2×#13063290—21no—
41C2×C4×D172C2211yescharacteristic
42C2×#13063284C2211yescharacteristic
43C2×#13063281—21no—
44C2×#13063281—21no—
45#14583241C2218yescomplemented
46#14583224C2218yes—
47#14583195C2218yescomplemented
48#14583185C2218yescomplemented
49#14583122C2218yescomplemented
50#14583122C2218yescomplemented
51#14583057C2218yescomplemented
52#14583040C2218yes—
53#14583007C2218yescomplemented
54#14583001C2218yescomplemented
55C4×Dic172C2218yescomplemented
56C4×#10621873C2218yescomplemented
57C2×#13063259C2211yescharacteristic
58C2×#13063259C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063257C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063250C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×#117×C43C2211yescharacteristic
70C43×#433C2218yescomplemented
71C2×C4⋊C8×C43C2211yescharacteristic
72C2×C4⋊C8×C43C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×#97×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—22no—
79C22×Dic86—24no—
80C22×Dic86—24no—
81C22×Dic86—21no—
82C22×Dic86C2314yes—
83C22×Dic86C2311yescharacteristic
84C22×Dic86C2311yescharacteristic
85C22×Dic86C2311yescharacteristic
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C23×Dic43—21no—
89C22×C4×D43—21no—
90C2×Dic172—24no—
91C2×Dic172—24no—
92C2×Dic172C2314yes—
93C2×Dic172C2314yes—
94C2×#10621873—24no—
95C2×#10621873—24no—
96C2×#10621873C2314yes—
97C2×#10621873C2314yes—
98#13063325—22no—
99#13063325C2314yes—
100#13063320—28no—
101#13063313—22no—
102#13063313C2314yes—
103#13063311—28no—
104#13063307—28no—
105#13063304—22no—
106#13063304C2314yes—
107#13063303—28no—
108#13063299—22no—
109#13063299C2314yes—
110C4×Dic86—22no—
111C4×Dic86—22no—
112C4×Dic86—22no—
113C4×Dic86—22no—
114C4×Dic86—22no—
115C4×Dic86C2314yes—
116C4×Dic86C2314yes—
117C4×Dic86C2314yes—
118C4×Dic86C2314yes—
119C4×Dic86C2314yes—
120#13063290—28no—
121#13063290—28no—
122C4×D172—22no—
123C4×D172C2314yes—
124#13063284—22no—
125#13063284C2314yes—
126#13063281—28no—
127#13063281—28no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—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—
147C2×C4×Dic43—21no—
148C2×C4×Dic43—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151#13063259C2314yes—
152#13063259C2314yes—
153#13063257C2314yes—
154#13063257C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158#13063250C2314yes—
159#13063250C2314yes—
160#13063250C2314yes—
161#13063247C2314yes—
162#13063247C2314yes—
163C23×C4×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168#117×C43D414yes—
169#117×C43C2314yes—
170C2×C4⋊C4×C43D411yescharacteristic
171C2×C4⋊C4×C43D411yescharacteristic
172C2×C22⋊C4×C43D411yescharacteristic
173C2×C22⋊C4×C43D411yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43C2314yes—
177C4⋊C8×C43C2314yes—
178C22⋊C8×C43C2314yes—
179C22⋊C8×C43C2314yes—
180#97×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—24no—
195C2×C22⋊D43—82no—
196C22×Dic43—28no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—24no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C2×D172—21no—
206C2×D172—22no—
207C2×D172—22no—
208C2×D172C2412yes—
209C2×C4×D43—24no—
210C2×C4×D43—82no—
211C2×Dic86—28no—
212C2×Dic86—216no—
213C2×Dic86—24no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—22no—
217C2×Dic86—22no—
218C2×Dic86—28no—
219C2×Dic86—28no—
220C2×Dic86—22no—
221C2×Dic86—22no—
222C2×Dic86—21no—
223C2×Dic86—24no—
224C2×Dic86—82no—
225C2×Dic86#4114yes—
226C2×Dic86#4114yes—
227C2×Dic86C2412yes—
228C2×Dic86C2412yes—
229C2×Dic86C2412yes—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43—22no—
233C2×C8×C43—22no—
234C2×C8×C43C2412yes—
235C2×C8×C43C2412yes—
236C2×C8×C43C2412yes—
237C2×C8×C43C2412yes—
238C4⋊C4×C43C2×D414yes—
239C4⋊C4×C43C2×D414yes—
240C22⋊C4×C43C2×D414yes—
241C22⋊C4×C43C2×D414yes—
242C42×C43C2×D412yes—
243C42×C43C2×D412yes—
244C42×C43C2412yes—
245C42×C43C2412yes—
246C22⋊Dic43—24no—
247C22⋊Dic43—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259C4⋊Dic43C2412yes—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43—24no—
270C4×Dic43—24no—
271C4×Dic43—24no—
272C4×Dic43—24no—
273Dic172—28no—
274Dic172—28no—
275#10621873—28no—
276#10621873—28no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43C22×D412yes—
281C23×C43C22×D411yescharacteristic
282C22×D43—22no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—24no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D412yes—
297C2×C4×C43C22×D412yes—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4112yes—
301C2×C4×C43C2×#4112yes—
302C2×C4×C43C2511yescharacteristic
303C22⋊D43—84no—
304C2×Dic43—216no—
305C2×Dic43—24no—
306C2×Dic43—24no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319D172—22no—
320D172—22no—
321D172—42no—
322C4×D43—84no—
323Dic86—216no—
324Dic86—24no—
325Dic86—24no—
326Dic86—22no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—42no—
331Dic86—84no—
332Dic86C2×#4114yes—
333Dic86C2×#4114yes—
334C8×C43—22no—
335C8×C43—22no—
336C8×C43—22no—
337C8×C43—22no—
338C2×#3121—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—44no—
343C22×C43#52512yes—
344C22×C43#57712yes—
345C22×C43#57812yes—
346C22×C43C23×D411yescharacteristic
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—84no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—22no—
356C4×C43#52512yes—
357C4×C43C22×#4111yescharacteristic
358C4×C43C22×#4111yescharacteristic
359Dic43—24no—
360Dic43—24no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365Dic43—42no—
366C2×#542—431no—
367C2×#519—431no—
368#3121—4316no—
369C2×#485—431no—
370C2×#482—431no—
371C2×#477—431no—
372C2×#475—431no—
373C2×#464—431no—
374C2×#464—431no—
375C2×#451—431no—
376C2×#448—431no—
377C2×#441—431no—
378C2×#440—431no—
379C2×C4×Q16—431no—
380C2×C4×SD16—431no—
381C2×#433D4311yescharacteristic, complemented
382C2×C43—42no—
383C2×C43#312114yescomplemented
384C2×C43C2×#52511yescharacteristic
385C2×C43C2×#57711yescharacteristic
386C2×C43C2×#57811yescharacteristic
387D43—82no—
388C23×Q8—431no—
389C22×Q16—431no—
390C22×Q16—431no—
391C22×SD16—431no—
392C22×SD16—431no—
393#542—438no—
394#542—864no—
395C2×C4⋊Q8—431no—
396C2×#126—861no—
397C2×#124—431no—
398C2×#124—861no—
399C2×#123—861no—
400C2×C22⋊Q8—431no—
401C2×C22⋊Q8—861no—
402C2×#121—431no—
403#519—438no—
404#519—864no—
405C2×C4×Q8—431no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—861no—
411C2×C4×Q8—861no—
412C2×C4×D4—431no—
413C2×#117—431no—
414C2×#117—861no—
415C2×#117—861no—
416C2×#117C2×D4311yescharacteristic
417#485—438no—
418#482—438no—
419#477—438no—
420#475—438no—
421#464—438no—
422#464—438no—
423#451—438no—
424#448—438no—
425#441—438no—
426#440—438no—
427C4×Q16—438no—
428C4×SD16—438no—
429#433C2×D4318yescomplemented
430C2×#107—431no—
431C2×#107—431no—
432C2×#106—431no—
433C2×#106—431no—
434C2×C4⋊C8C2×D4311yescharacteristic
435C2×C4⋊C8C2×D4311yescharacteristic
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×C22⋊C8C2×D4311yescharacteristic
445C2×C22⋊C8C2×D4311yescharacteristic
446C2×#97C2×D4311yescharacteristic
447C2×C4×C8C2×D4311yescharacteristic
448C43C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—431no—
450C22×Q8—431no—
451C22×Q8—431no—
452C22×Q8—434no—
453C22×Q8—864no—
454C22×Q8—864no—
455C22×Q8—861no—
456C22×Q8—862no—
457C22×Q8—861no—
458C22×D4—431no—
459C22×D4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C2×Q16—434no—
464C2×Q16—434no—
465C2×Q16—864no—
466C2×Q16—864no—
467C2×SD16—434no—
468C2×SD16—434no—
469C2×SD16—864no—
470C2×SD16—864no—
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477#126—868no—
478#124—434no—
479#124—868no—
480#124—862no—
481#123—868no—
482C22⋊Q8—434no—
483C22⋊Q8—862no—
484C22⋊Q8—868no—
485#121—434no—
486#121—862no—
487C4×Q8—434no—
488C4×Q8—434no—
489C4×Q8—434no—
490C4×Q8—434no—
491C4×Q8—434no—
492C4×Q8—868no—
493C4×Q8—868no—
494C4×Q8—862no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8—862no—
498C4×Q8—862no—
499C4×D4—434no—
500C4×D4—862no—
501#117—434no—
502#117—862no—
503#117—868no—
504#117—868no—
505#117D17214yes—
506#117C22×D4314yes—
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—861no—
518C2×C4⋊C4D17211yescharacteristic
519C2×C4⋊C4D17211yescharacteristic
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4D17211yescharacteristic
527C2×C22⋊C4D17211yescharacteristic
528C2×C42—861no—
529C2×C42—861no—
530C2×C42—861no—
531C2×C42—861no—
532C2×C42—861no—
533C2×C42—861no—
534C2×C42C22×D4311yescharacteristic
535C2×C42C22×D4311yescharacteristic
536#107—434no—
537#107—434no—
538#106—434no—
539#106—434no—
540C4⋊C8C22×D4314yes—
541C4⋊C8C22×D4314yes—
542#103—434no—
543#103—434no—
544#103—434no—
545#103—434no—
546#103—434no—
547#103—434no—
548#102—434no—
549#102—434no—
550C22⋊C8C22×D4314yes—
551C22⋊C8C22×D4314yes—
552#97C22×D4314yes—
553C4×C8C22×D4314yes—
554C24—861no—
555C24C2×D17211yescharacteristic
556C2×Q8—434no—
557C2×Q8—434no—
558C2×Q8—432no—
559C2×Q8—432no—
560C2×Q8—432no—
561C2×Q8—868no—
562C2×Q8—868no—
563C2×Q8—868no—
564C2×Q8—8616no—
565C2×Q8—864no—
566C2×Q8—861no—
567C2×Q8—861no—
568C2×Q8—864no—
569C2×Q8—861no—
570C2×Q8—862no—
571C2×Q8—862no—
572C2×Q8—862no—
573C2×Q8—862no—
574C2×Q8—3442no—
575C2×D4—432no—
576C2×D4—864no—
577C2×D4—861no—
578C2×D4—862no—
579C2×D4—862no—
580C2×D4—3442no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—868no—
584C22×C4—864no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—864no—
593C22×C4—3442no—
594C22×C4C2×D17212yes—
595C22×C4C2×D17211yescharacteristic
596C22×C4C2×D17211yescharacteristic
597C22×C4C2×D17211yescharacteristic
598C22×C4C2×D17211yescharacteristic
599C22×C4C2×D17211yescharacteristic
600C22×C4C23×D4312yes—
601C22×C4C23×D4311yescharacteristic
602Q16—868no—
603Q16—868no—
604SD16—868no—
605SD16—868no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C23×D4312yes—
611C2×C8C23×D4312yes—
612C2×C8C23×D4312yes—
613C2×C8C23×D4312yes—
614C4⋊C4—432no—
615C4⋊C4—432no—
616C4⋊C4—432no—
617C4⋊C4—432no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4C2×D17214yes—
630C4⋊C4C2×D17214yes—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4C2×D17214yes—
638C22⋊C4C2×D17214yes—
639C42—864no—
640C42—864no—
641C42—864no—
642C42—864no—
643C42—864no—
644C42—864no—
645C42C2×D17212yes—
646C42C2×D17212yes—
647C42C23×D4312yes—
648C42C23×D4312yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—862no—
653C23—1722no—
654C23—1722no—
655C23—1722no—
656C23C22×D17212yes—
657C23C22×D17211yescharacteristic
658Q8—434no—
659Q8—434no—
660Q8—8616no—
661Q8—864no—
662Q8—864no—
663Q8—862no—
664Q8—862no—
665Q8—862no—
666Q8—862no—
667Q8—3444no—
668Q8—1722no—
669D4—862no—
670D4—862no—
671D4—3444no—
672D4—1722no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—8616no—
682C2×C4—864no—
683C2×C4—864no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—3444no—
692C2×C4—1722no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4C22×D17212yes—
698C2×C4C22×D17212yes—
699C2×C4C22×D17212yes—
700C2×C4C22×D17212yes—
701C2×C4C22×D17212yes—
702C2×C4C22×D17211yescharacteristic
703C2×C4#41×D4312yes—
704C2×C4#41×D4312yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—3444no—
715C22—1722no—
716C22—1722no—
717C22—1722no—
718C22#1458341112yes—
719C22#1458371112yes—
720C22#1458371612yes—
721C22C23×D17211yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—864no—
728C4—864no—
729C4—1722no—
730C4—1722no—
731C4—1722no—
732C4—1722no—
733C4—1722no—
734C4#1458341112yes—
735C4C2×#41×D4311yescharacteristic
736C4C2×#41×D4311yescharacteristic
737C2—42no—
738C2—3442no—
739C2#1914482614yesdirect product factor
740C2C2×#1458341111yescharacteristic
741C2C2×#1458371111yescharacteristic
742C2C2×#1458371611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×#433D43
hypocenterC43C2×#3121
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. C2×#14583376C2semidirect
3. #19144826C2direct (N × H)
4. C2×#14583241C2semidirect
6. C2×#14583195C2semidirect
7. C2×#14583185C2semidirect
8. C2×#14583122C2semidirect
9. C2×#14583122C2semidirect
10. C2×#14583057C2semidirect
12. C2×#14583007C2semidirect
13. C2×#14583001C2semidirect
14. C2×C4×Dic172C2semidirect
15. C2×C4×#10621873C2semidirect
16. C2×C43×#433C2semidirect
33. #14583376C22semidirect
45. #14583241C22semidirect
47. #14583195C22semidirect
48. #14583185C22semidirect
49. #14583122C22semidirect
50. #14583122C22semidirect
51. #14583057C22semidirect
53. #14583007C22semidirect
54. #14583001C22semidirect
55. C4×Dic172C22semidirect
56. C4×#10621873C22semidirect
70. C43×#433C22semidirect
381. C2×#433D43semidirect
383. C2×C43#3121semidirect
429. #433C2×D43semidirect
448. C43C2×#3121semidirect
739. C2#19144826direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145833762
#191448262
C2×#145832412
C2×#145832242
C2×#145831952
C2×#145831852
C2×#145831222
C2×#145830572
C2×#145830402
C2×#145830072
C2×#145830012
C2×C4×Dic1722
C2×C4×#106218732
C2×C43×#4332
C2×#312143