Finite Group Databasebeta

← C2×#14532264 #17202035

Subgroups — C2×#14532264 #17202035

Order 4352.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587580C211yesmaximal, characteristic
2C22×#10587579C211yesmaximal, characteristic
3#14532264C2116yesmaximal, direct product factor
4C2×#11762740C211yesmaximal, characteristic, complemented
5C2×#11762738C211yesmaximal, characteristic, complemented
6C2×#11762738C211yesmaximal, characteristic, complemented
7C2×#11762694C211yesmaximal, characteristic, complemented
8C2×#11762690C211yesmaximal, characteristic, complemented
9C2×#11762687C211yesmaximal, characteristic
10C2×#11762683C211yesmaximal, characteristic, complemented
11C2×#11762683C211yesmaximal, characteristic, complemented
12C2×#11762671C211yesmaximal, characteristic, complemented
13C2×#11762671C211yesmaximal, characteristic, complemented
14C2×#11762668C211yesmaximal, characteristic, complemented
15C2×#95×D17C211yesmaximal, characteristic, complemented
16C2×C17×#400C211yesmaximal, characteristic, complemented
17C23×D68C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C23×C4×D17C2211yescharacteristic
22C2×#10587580—28no—
23C2×#10587580C2218yes—
24C2×#10587579—28no—
25C2×#10587579C2218yes—
26C22×C4⋊Dic17C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×#63227C2211yescharacteristic
38C22×#63227C2211yescharacteristic
39C22×C4×Dic17C2211yescharacteristic
40#11762740C2218yescomplemented
41#11762738C2218yescomplemented
42#11762738C2218yescomplemented
43#11762694C2218yescomplemented
44#11762690C2218yescomplemented
45#11762687C2218yes—
46#11762683C2218yescomplemented
47#11762683C2218yescomplemented
48#11762671C2218yescomplemented
49#11762671C2218yescomplemented
50#11762668C2218yescomplemented
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60#95×D17C2218yescomplemented
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C17×#400C2218yescomplemented
64C2×C17×#95C2211yescharacteristic
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C24×D17C2311yescharacteristic
70C24×D17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C22×D68—24no—
85C22×D68—24no—
86C22×D68D418yes—
87C22×D68C2314yes—
88C22×C4×D17—24no—
89C22×C4×D17—24no—
90C22×C4×D17—24no—
91C22×C4×D17—24no—
92C22×C4×D17—24no—
93C22×C4×D17—24no—
94C22×C4×D17—24no—
95C22×C4×D17—24no—
96C22×C4×D17—24no—
97C22×C4×D17—42no—
98C22×C4×D17—42no—
99C22×C4×D17—42no—
100C22×C4×D17C2314yes—
101C22×C4×D17C2314yes—
102C22×C4×D17C2314yes—
103C22×C4×D17C2314yes—
104C2×C4⋊C4×C17—24no—
105C2×C4⋊C4×C17—24no—
106C2×C4⋊C4×C17C2314yes—
107C2×C4⋊C4×C17C2314yes—
108C2×#63227—24no—
109C2×#63227—24no—
110C2×#63227—24no—
111C2×#63227—24no—
112C2×#63227—24no—
113C2×#63227—24no—
114C2×#63227—24no—
115C2×#63227—42no—
116C2×#63227C2314yes—
117C2×#63227C2314yes—
118C2×#63227C2314yes—
119C2×#63227C2314yes—
120C2×#63227C2314yes—
121C2×#63227C2314yes—
122C2×#63227C2314yes—
123C2×#63227C2314yes—
124C2×C4⋊Dic17—24no—
125C2×C4⋊Dic17C2314yes—
126C2×#63225—24no—
127C2×#63225—24no—
128C2×#63225—42no—
129C2×#63225—42no—
130C2×#63225C2314yes—
131C2×#63225C2314yes—
132C2×#63225C2314yes—
133C2×#63225C2314yes—
134C2×C4×Dic17—24no—
135C2×C4×Dic17C2314yes—
136#10587580—232no—
137#10587579—232no—
138C17×#95C2314yes—
139C17×#95C2314yes—
140C17×#95C2314yes—
141C17×#95C2314yes—
142C17×#95C2314yes—
143#10587502C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146#10587502C2314yes—
147#10587502C2314yes—
148#10587502C2314yes—
149#10587502C2314yes—
150#10587502C2314yes—
151#10587502C2314yes—
152C24×C17C2411yescharacteristic
153C23×D17—22no—
154C23×D17—22no—
155C23×D17—22no—
156C23×D17—22no—
157C23×D17—22no—
158C23×D17—22no—
159C23×D17—22no—
160C23×D17—22no—
161C23×D17—22no—
162C23×D17—22no—
163C23×D17C2×D414yes—
164C23×D17C2×D414yes—
165C23×D17#4114yes—
166C23×D17#4114yes—
167C23×D17C2412yes—
168C23×D17C2412yes—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17—22no—
174C22×C4×C17—22no—
175C22×C4×C17—22no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
178C22×C4×C17—22no—
179C22×C4×C17—22no—
180C22×C4×C17—22no—
181C22×C4×C17—22no—
182C22×C4×C17—22no—
183C22×C4×C17—22no—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—22no—
188C22×C4×C17—22no—
189C22×C4×C17C2×D414yes—
190C22×C4×C17C2412yes—
191C22×C4×C17C2412yes—
192C22×C4×C17C2412yes—
193C22×C4×C17C2412yes—
194C22×C4×C17C2412yes—
195C22×C4×C17C2412yes—
196C22×C4×C17C2412yes—
197C22×Dic17—22no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—22no—
213C22×Dic17#4114yes—
214C22×Dic17#4114yes—
215C22×Dic17C2412yes—
216C22×Dic17C2412yes—
217C22×Dic17C2412yes—
218C22×Dic17C2412yes—
219C22×Dic17C2412yes—
220C22×Dic17C2412yes—
221C2×D68—232no—
222C2×D68—28no—
223C2×D68—28no—
224C2×D68C2×D4116yes—
225C2×C4×D17—28no—
226C2×C4×D17—28no—
227C2×C4×D17—28no—
228C2×C4×D17—28no—
229C2×C4×D17—28no—
230C2×C4×D17—28no—
231C2×C4×D17—28no—
232C2×C4×D17—28no—
233C2×C4×D17—28no—
234C2×C4×D17—44no—
235C2×C4×D17—44no—
236C2×C4×D17—44no—
237C2×C4×D17—416no—
238C2×C4×D17—416no—
239C2×C4×D17—416no—
240C2×C4×D17—416no—
241C4⋊C4×C17—28no—
242C4⋊C4×C17—28no—
243#63227—28no—
244#63227—28no—
245#63227—28no—
246#63227—28no—
247#63227—28no—
248#63227—28no—
249#63227—28no—
250#63227—44no—
251C4⋊Dic17—28no—
252#63225—28no—
253#63225—28no—
254#63225—44no—
255#63225—44no—
256C4×Dic17—28no—
257C2×#2419—171nomaximal, Sylow
258C23×C17C22×D412yes—
259C23×C17C2×#4112yes—
260C23×C17C2×#4112yes—
261C23×C17C2×#4112yes—
262C23×C17C2×#4112yes—
263C23×C17H(5,𝔽2)12yes—
264C23×C172−1+412yes—
265C23×C17C2511yescharacteristic
266C22×D17—28no—
267C22×D17—28no—
268C22×D17—28no—
269C22×D17—28no—
270C22×D17—28no—
271C22×D17—28no—
272C22×D17—22no—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—28no—
277C22×D17—28no—
278C22×D17—28no—
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—44no—
286C22×D17—44no—
287C22×D17—44no—
288C22×D17—44no—
289C22×D17#123116yes—
290C22×D17C22×D414yes—
291C22×D17C22×D414yes—
292C22×D17C2×#4114yes—
293C22×D17C2×#4114yes—
294C2×C4×C17—28no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—44no—
316C2×C4×C17—44no—
317C2×C4×C17—44no—
318C2×C4×C17—44no—
319C2×C4×C17—44no—
320C2×C4×C17—44no—
321C2×C4×C17C22×D414yes—
322C2×Dic17—28no—
323C2×Dic17—28no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—22no—
336C2×Dic17—22no—
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—44no—
341C2×Dic17—44no—
342C2×Dic17—44no—
343C2×Dic17—44no—
344C2×Dic17C2×#4114yes—
345C2×Dic17C2×#4114yes—
346D68—232no—
347C4×D17—416no—
348C4×D17—416no—
349C4×D17—416no—
350C4×D17—416no—
351C22×#123—171no—
352C22×C4×D4—171no—
353#2419—1716no—
354C2×#400D1711yescharacteristic, complemented
355C2×#398—171no—
356C2×#397—171no—
357C2×#397—171no—
358C2×#387—171no—
359C2×#387—171no—
360C2×#386—171no—
361C2×#385—171no—
362C2×#385—171no—
363C2×#381—171no—
364C2×#381—171no—
365C2×#380—171no—
366C22×#95—171no—
367C22×C17C2×#12314yes—
368C22×C17#52914yes—
369C22×C17#53914yes—
370C22×C17#54614yes—
371C22×C17#54714yes—
372C22×C17#55114yes—
373C22×C17#55214yes—
374C22×C17C23×D411yescharacteristic
375C22×C17C22×#4111yescharacteristic
376C22×C17C22×#4111yescharacteristic
377C22×C17C22×#4111yescharacteristic
378C22×C17C22×#4111yescharacteristic
379C22×C17C2×H(5,𝔽2)11yescharacteristic
380C22×C17C2×2−1+411yescharacteristic
381C2×D17—24no—
382C2×D17—232no—
383C2×D17—24no—
384C2×D17—24no—
385C2×D17—24no—
386C2×D17—24no—
387C2×D17—24no—
388C2×D17—24no—
389C2×D17—24no—
390C2×D17—24no—
391C2×D17—42no—
392C2×D17—416no—
393C2×D17—42no—
394C2×D17—42no—
395C2×D17—42no—
396C2×D17C2×#12318yes—
397C4×C17—24no—
398C4×C17—42no—
399C4×C17—42no—
400C4×C17—42no—
401C4×C17—42no—
402C4×C17—42no—
403C4×C17—42no—
404Dic17—24no—
405Dic17—24no—
406Dic17—42no—
407Dic17—42no—
408Dic17—42no—
409Dic17—42no—
410C23×D4—171no—
411C24×C4—171no—
412C24×C4—171no—
413C24×C4—171no—
414C24×C4—171no—
415C2×#123—178no—
416C2×#123—348no—
417C2×C4×D4—178no—
418C2×C4×D4—348no—
419C22×C4⋊C4—171no—
420C22×C4⋊C4—171no—
421C22×C4⋊C4—171no—
422C22×C4⋊C4—171no—
423C22×C4⋊C4—171no—
424C22×C4⋊C4C2×D1711yescharacteristic
425C22×C4⋊C4C2×D1711yescharacteristic
426C22×C22⋊C4—171no—
427C22×C22⋊C4—171no—
428C22×C22⋊C4—171no—
429C22×C22⋊C4—171no—
430C22×C22⋊C4—171no—
431C22×C22⋊C4—171no—
432C22×C22⋊C4—171no—
433C22×C22⋊C4—171no—
434C22×C42—171no—
435#400C2×D1718yescomplemented
436#398—178no—
437#397—178no—
438#397—178no—
439#387—178no—
440#387—178no—
441#386—178no—
442#385—178no—
443#385—178no—
444#381—178no—
445#381—178no—
446#380—178no—
447C2×#95—171no—
448C2×#95—171no—
449C2×#95—171no—
450C2×#95—171no—
451C2×#95—171no—
452C2×#95—171no—
453C2×#95—171no—
454C2×#95—171no—
455C2×#95—171no—
456C2×#95—178no—
457C2×#95C2×D1711yescharacteristic
458C2×#95C2×D1711yescharacteristic
459C2×#95C2×D1711yescharacteristic
460C2×#95C2×D1711yescharacteristic
461C2×#95C2×D1711yescharacteristic
462C2×C17#241918yescomplemented
463C2×C17C22×#12311yescharacteristic
464C2×C17C2×#52911yescharacteristic
465C2×C17C2×#53911yescharacteristic
466C2×C17C2×#54611yescharacteristic
467C2×C17C2×#54711yescharacteristic
468C2×C17C2×#55111yescharacteristic
469C2×C17C2×#55211yescharacteristic
470D17—28no—
471D17—44no—
472C25—171no—
473C25—171no—
474C22×D4—178no—
475C22×D4—174no—
476C22×D4—344no—
477C22×D4—344no—
478C23×C4—171no—
479C23×C4—171no—
480C23×C4—171no—
481C23×C4—171no—
482C23×C4—171no—
483C23×C4—171no—
484C23×C4—174no—
485C23×C4—174no—
486C23×C4—174no—
487C23×C4—174no—
488C23×C4—344no—
489C23×C4—344no—
490C23×C4—344no—
491C23×C4—344no—
492C23×C4—344no—
493C23×C4—344no—
494C23×C4—344no—
495C23×C4—344no—
496C23×C4—344no—
497C23×C4—682no—
498C23×C4—682no—
499C23×C4—682no—
500C23×C4C22×D1711yescharacteristic
501C23×C4C22×D1711yescharacteristic
502C23×C4C22×D1711yescharacteristic
503C23×C4C22×D1711yescharacteristic
504C23×C4C22×D1711yescharacteristic
505C23×C4C22×D1711yescharacteristic
506C23×C4C22×D1711yescharacteristic
507#123—3432no—
508C4×D4—3432no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—174no—
512C2×C4⋊C4—174no—
513C2×C4⋊C4—174no—
514C2×C4⋊C4—174no—
515C2×C4⋊C4—174no—
516C2×C4⋊C4—344no—
517C2×C4⋊C4—344no—
518C2×C4⋊C4—344no—
519C2×C4⋊C4—682no—
520C2×C4⋊C4—682no—
521C2×C4⋊C4C22×D1714yes—
522C2×C4⋊C4C22×D1714yes—
523C2×C22⋊C4—174no—
524C2×C22⋊C4—174no—
525C2×C22⋊C4—174no—
526C2×C22⋊C4—174no—
527C2×C22⋊C4—174no—
528C2×C22⋊C4—174no—
529C2×C22⋊C4—174no—
530C2×C22⋊C4—174no—
531C2×C22⋊C4—344no—
532C2×C22⋊C4—344no—
533C2×C22⋊C4—344no—
534C2×C22⋊C4—344no—
535C2×C22⋊C4—344no—
536C2×C22⋊C4—344no—
537C2×C22⋊C4—344no—
538C2×C22⋊C4—682no—
539C2×C42—174no—
540C2×C42—344no—
541#95—174no—
542#95—174no—
543#95—174no—
544#95—174no—
545#95—174no—
546#95—174no—
547#95—174no—
548#95—174no—
549#95—174no—
550#95C22×D1714yes—
551#95C22×D1714yes—
552#95C22×D1714yes—
553#95C22×D1714yes—
554#95C22×D1714yes—
555C17C2×#241911yescharacteristic, complemented, Sylow
556C24—174no—
557C24—174no—
558C24—174no—
559C24—172no—
560C24—174no—
561C24—172no—
562C24—342no—
563C24—342no—
564C24—342no—
565C24—342no—
566C24—342no—
567C24—342no—
568C24—342no—
569C24—342no—
570C24—342no—
571C24—342no—
572C24C23×D1711yescharacteristic
573C2×D4—1716no—
574C2×D4—3432no—
575C2×D4—348no—
576C2×D4—348no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—174no—
598C22×C4—174no—
599C22×C4—172no—
600C22×C4—172no—
601C22×C4—172no—
602C22×C4—172no—
603C22×C4—172no—
604C22×C4—172no—
605C22×C4—348no—
606C22×C4—348no—
607C22×C4—348no—
608C22×C4—348no—
609C22×C4—348no—
610C22×C4—348no—
611C22×C4—348no—
612C22×C4—348no—
613C22×C4—348no—
614C22×C4—342no—
615C22×C4—342no—
616C22×C4—342no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—342no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—342no—
626C22×C4—342no—
627C22×C4—342no—
628C22×C4—342no—
629C22×C4—342no—
630C22×C4—684no—
631C22×C4—684no—
632C22×C4—684no—
633C22×C4—6816no—
634C22×C4—6816no—
635C22×C4—6816no—
636C22×C4—6816no—
637C22×C4D4×D1714yes—
638C22×C4C23×D1712yes—
639C22×C4C23×D1712yes—
640C22×C4C23×D1712yes—
641C22×C4C23×D1712yes—
642C22×C4C23×D1712yes—
643C22×C4C23×D1712yes—
644C22×C4C23×D1712yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—348no—
648C4⋊C4—348no—
649C4⋊C4—348no—
650C4⋊C4—684no—
651C4⋊C4—684no—
652C22⋊C4—348no—
653C22⋊C4—348no—
654C22⋊C4—348no—
655C22⋊C4—348no—
656C22⋊C4—348no—
657C22⋊C4—348no—
658C22⋊C4—348no—
659C22⋊C4—684no—
660C42—348no—
661C23—1716no—
662C23—174no—
663C23—174no—
664C23—174no—
665C23—174no—
666C23—348no—
667C23—348no—
668C23—348no—
669C23—348no—
670C23—342no—
671C23—342no—
672C23—342no—
673C23—342no—
674C23—348no—
675C23—348no—
676C23—348no—
677C23—348no—
678C23—342no—
679C23—342no—
680C23—342no—
681C23—342no—
682C23—342no—
683C23—342no—
684C23—348no—
685C23—684no—
686C23—684no—
687C23—684no—
688C23—684no—
689C23C2×D4×D1712yes—
690C23#1058769412yes—
691C23#41×D1712yes—
692C23#41×D1712yes—
693C23#41×D1712yes—
694C23#41×D1712yes—
695C23#1058769612yes—
696C23C24×D1711yescharacteristic
697D4—3432no—
698C2×C4—28no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—174no—
726C2×C4—174no—
727C2×C4—348no—
728C2×C4—342no—
729C2×C4—342no—
730C2×C4—342no—
731C2×C4—342no—
732C2×C4—348no—
733C2×C4—342no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—342no—
737C2×C4—342no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—342no—
744C2×C4—342no—
745C2×C4—6816no—
746C2×C4—6816no—
747C2×C4—6816no—
748C2×C4—6816no—
749C2×C4—684no—
750C2×C4—684no—
751C2×C4—684no—
752C2×C4—684no—
753C2×C4C2×D4×D1714yes—
754C22—178no—
755C22—344no—
756C22—344no—
757C22—344no—
758C22—3432no—
759C22—344no—
760C22—344no—
761C22—344no—
762C22—344no—
763C22—344no—
764C22—344no—
765C22—682no—
766C22—6816no—
767C22—682no—
768C22—682no—
769C22—682no—
770C22#123×D1714yes—
771C22#1176334214yes—
772C22#1176340714yes—
773C22#1176345214yes—
774C22#1176346114yes—
775C22#1176348414yes—
776C22#1176349114yes—
777C22C22×D4×D1711yescharacteristic
778C22C2×#41×D1711yescharacteristic
779C22C2×#41×D1711yescharacteristic
780C22C2×#41×D1711yescharacteristic
781C22C2×#41×D1711yescharacteristic
782C22C2×#1058769611yescharacteristic
783C22C2×#1058769411yescharacteristic
784C4—24no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—344no—
792C4—344no—
793C4—682no—
794C4—682no—
795C4—682no—
796C4—682no—
797C2—348no—
798C2—684no—
799C2#1453226418yesdirect product factor
800C2C2×#123×D1711yescharacteristic
801C2C2×#1176334211yescharacteristic
802C2C2×#1176340711yescharacteristic
803C2C2×#1176345211yescharacteristic
804C2C2×#1176346111yescharacteristic
805C2C2×#1176348411yescharacteristic
806C2C2×#1176349111yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#400C2
socleC24×C17C24
prime radicalC23×D68C22
hypercenterC2×#400D17
hypocenterC17C2×#2419
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
3. #14532264C2direct (N × H)
4. C2×#11762740C2semidirect
5. C2×#11762738C2semidirect
6. C2×#11762738C2semidirect
7. C2×#11762694C2semidirect
8. C2×#11762690C2semidirect
10. C2×#11762683C2semidirect
11. C2×#11762683C2semidirect
12. C2×#11762671C2semidirect
13. C2×#11762671C2semidirect
14. C2×#11762668C2semidirect
15. C2×#95×D17C2semidirect
16. C2×C17×#400C2semidirect
40. #11762740C22semidirect
41. #11762738C22semidirect
42. #11762738C22semidirect
43. #11762694C22semidirect
44. #11762690C22semidirect
46. #11762683C22semidirect
47. #11762683C22semidirect
48. #11762671C22semidirect
49. #11762671C22semidirect
50. #11762668C22semidirect
60. #95×D17C22semidirect
63. C17×#400C22semidirect
354. C2×#400D17semidirect
435. #400C2×D17semidirect
462. C2×C17#2419semidirect
555. C17C2×#2419semidirect
799. C2#14532264direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875802
C22×#105875792
#145322642
C2×#117627402
C2×#117627382
C2×#117626942
C2×#117626902
C2×#117626872
C2×#117626832
C2×#117626712
C2×#117626682
C2×#95×D172
C2×C17×#4002
C2×#241917