Finite Group Databasebeta

← C2×#14531639 #17193545

Subgroups — C2×#14531639 #17193545

Order 4352.

3006 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587578C211yesmaximal, characteristic
2#14531639C2116yesmaximal, direct product factor
3C2×#11762695C211yesmaximal, characteristic, complemented
4C2×#11762694C211yesmaximal, characteristic, complemented
5C2×#11762692C211yesmaximal, characteristic, complemented
6C2×#11762683C211yesmaximal, characteristic
7C2×#11762680C211yesmaximal, characteristic
8C2×#11762676C211yesmaximal, characteristic, complemented
9C2×#11762673C211yesmaximal, characteristic, complemented
10C2×#11762671C211yesmaximal, characteristic
11C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
12C2×C4×#63227C211yesmaximal, characteristic
13C2×#11762656C211yesmaximal, characteristic
14C2×#11762655C211yesmaximal, characteristic, complemented
15C2×#95×D17C211yesmaximal, characteristic
16C2×C17×#387C211yesmaximal, characteristic, complemented
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×#10587578C4116yescomplemented
21C2×#10587578C2218yes—
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762695C2218yescomplemented
36#11762694C2218yescomplemented
37#11762692C2218yescomplemented
38#11762683C2218yes—
39#11762680C2218yes—
40#11762676C2218yescomplemented
41#11762673C2218yescomplemented
42#11762671C2218yes—
43C4⋊C4×Dic17C2218yescomplemented
44C4×#63227C2218yes—
45#11762656C2218yes—
46#11762655C2218yescomplemented
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59#95×D17C2218yes—
60C22×C4⋊C4×C17C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C42×C17C2211yescharacteristic
63C17×#387C2218yescomplemented
64C2×C17×#95C2211yescharacteristic
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C24×D17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C22×C4×D17—24no—
84C22×C4×D17—24no—
85C22×C4×D17—24no—
86C22×C4×D17—24no—
87C22×C4×D17—24no—
88C22×C4×D17—24no—
89C22×C4×D17—42no—
90C22×C4×D17—42no—
91C22×C4×D17C2×C418yes—
92C22×C4×D17C2314yes—
93C22×C4×D17C2314yes—
94C22×C4×D17C2314yes—
95C2×C4⋊C4×C17—24no—
96C2×C4⋊C4×C17C2×C418yescomplemented
97C2×C4⋊C4×C17C2314yes—
98C2×C4⋊C4×C17C2314yes—
99C2×C42×C17—24no—
100C2×C42×C17C2314yes—
101C2×#63227—24no—
102C2×#63227—24no—
103C2×#63227C2×C418yes—
104C2×#63227C2×C418yes—
105C2×#63227C2314yes—
106C2×#63227C2314yes—
107C2×#63227C2314yes—
108C2×#63227C2314yes—
109C2×C4⋊Dic17—24no—
110C2×C4⋊Dic17C2×C418yescomplemented
111C2×C4⋊Dic17C2314yes—
112C2×C4⋊Dic17C2314yes—
113C2×#63225—42no—
114C2×#63225—42no—
115C2×#63225C2314yes—
116C2×#63225C2314yes—
117C2×C4×Dic17—24no—
118C2×C4×Dic17—42no—
119C2×C4×Dic17—42no—
120C2×C4×Dic17C2×C418yescomplemented
121C2×C4×Dic17C2×C418yescomplemented
122C2×C4×Dic17C2314yes—
123C2×C4×Dic17C2314yes—
124C2×C4×Dic17C2314yes—
125C2×C4×Dic17C2314yes—
126C2×C4×Dic17C2314yes—
127#10587578C2×C4164yescomplemented
128C17×#95C2314yes—
129C17×#95C2314yes—
130C17×#95C2314yes—
131C17×#95C2314yes—
132#10587502C2314yes—
133#10587502C2314yes—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144C24×C17C2411yescharacteristic
145C23×D17—22no—
146C23×D17—22no—
147C23×D17—22no—
148C23×D17—22no—
149C23×D17C22×C414yes—
150C23×D17#4114yes—
151C23×D17#4114yes—
152C23×D17C2412yes—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—22no—
169C22×C4×C17—22no—
170C22×C4×C17C22×C414yes—
171C22×C4×C17C22×C414yes—
172C22×C4×C17C22×C414yes—
173C22×C4×C17#4114yes—
174C22×C4×C17C2412yes—
175C22×C4×C17C2412yes—
176C22×C4×C17C2412yes—
177C22×C4×C17C2412yes—
178C22×C4×C17C2412yes—
179C22×C4×C17C2412yes—
180C22×C4×C17C2412yes—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—22no—
198C22×Dic17C22×C414yes—
199C22×Dic17C22×C414yes—
200C22×Dic17C22×C414yes—
201C22×Dic17#4114yes—
202C22×Dic17C2412yes—
203C22×Dic17C2412yes—
204C22×Dic17C2412yes—
205C22×Dic17C2412yes—
206C22×Dic17C2412yes—
207C22×Dic17C2412yes—
208C22×Dic17C2412yes—
209C2×C4×D17—232no—
210C2×C4×D17—28no—
211C2×C4×D17—28no—
212C2×C4×D17—28no—
213C2×C4×D17—28no—
214C2×C4×D17—28no—
215C2×C4×D17—28no—
216C2×C4×D17—44no—
217C2×C4×D17—44no—
218C2×C4×D17—416no—
219C2×C4×D17—416no—
220C2×C4×D17C22×C4116yes—
221C4⋊C4×C17—28no—
222C4⋊C4×C17C22×C4116yescomplemented
223C42×C17—28no—
224#63227—28no—
225#63227—28no—
226#63227C22×C4116yes—
227#63227C22×C4116yes—
228C4⋊Dic17—28no—
229C4⋊Dic17C22×C4116yescomplemented
230#63225—44no—
231#63225—44no—
232C4×Dic17—28no—
233C4×Dic17—44no—
234C4×Dic17—44no—
235C4×Dic17C22×C4116yescomplemented
236C4×Dic17C22×C4116yescomplemented
237C2×#2343—171nomaximal, Sylow
238C23×C17C23×C412yes—
239C23×C17C2×#4112yes—
240C23×C17C2×#4112yes—
241C23×C17C2×#4112yes—
242C23×C17C2×#4112yes—
243C23×C17H(5,𝔽2)12yes—
244C23×C172−1+412yes—
245C23×C17C2511yescharacteristic
246C22×D17—28no—
247C22×D17—28no—
248C22×D17—28no—
249C22×D17—28no—
250C22×D17—28no—
251C22×D17—28no—
252C22×D17—22no—
253C22×D17—22no—
254C22×D17—22no—
255C22×D17—22no—
256C22×D17#117116yes—
257C22×D17C23×C414yes—
258C22×D17C2×#4114yes—
259C22×D17C2×#4114yes—
260C2×C4×C17—28no—
261C2×C4×C17—28no—
262C2×C4×C17—28no—
263C2×C4×C17—28no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—44no—
282C2×C4×C17—44no—
283C2×C4×C17—44no—
284C2×C4×C17C23×C414yes—
285C2×C4×C17C23×C414yes—
286C2×C4×C17C23×C414yes—
287C2×C4×C17C2×#4114yes—
288C2×Dic17—28no—
289C2×Dic17—28no—
290C2×Dic17—28no—
291C2×Dic17—28no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—44no—
310C2×Dic17—44no—
311C2×Dic17—44no—
312C2×Dic17C23×C414yes—
313C2×Dic17C23×C414yes—
314C2×Dic17C23×C414yes—
315C2×Dic17C2×#4114yes—
316C4×D17—232no—
317C4×D17—416no—
318C4×D17—416no—
319C22×#117—171no—
320#2343—1716no—
321C2×#387—171no—
322C2×#387—171no—
323C2×#387—171no—
324C2×#387D1711yescharacteristic, complemented
325C2×#385—171no—
326C2×#385—171no—
327C2×#383—171no—
328C2×#382—171no—
329C2×#381—171no—
330C2×C4×C4⋊C4—171no—
331C2×C4×C22⋊C4—171no—
332C2×C4×C22⋊C4—171no—
333C2×#376—171no—
334C22×#95—171no—
335C22×C17C2×#11714yes—
336C22×C17C4×#4114yes—
337C22×C17#52014yes—
338C22×C17#55114yes—
339C22×C17#55114yes—
340C22×C17#55214yes—
341C22×C17#55214yes—
342C22×C17C24×C411yescharacteristic
343C22×C17C22×#4111yescharacteristic
344C22×C17C22×#4111yescharacteristic
345C22×C17C22×#4111yescharacteristic
346C22×C17C22×#4111yescharacteristic
347C22×C17C2×H(5,𝔽2)11yescharacteristic
348C22×C17C2×2−1+411yescharacteristic
349C2×D17—232no—
350C2×D17—24no—
351C2×D17—24no—
352C2×D17—24no—
353C2×D17—24no—
354C2×D17—24no—
355C2×D17—24no—
356C2×D17C2×#11718yes—
357C4×C17—24no—
358C4×C17—24no—
359C4×C17—24no—
360C4×C17—24no—
361C4×C17—42no—
362C4×C17—42no—
363C4×C17—42no—
364Dic17—24no—
365Dic17—24no—
366Dic17—24no—
367Dic17—24no—
368Dic17—42no—
369Dic17—42no—
370Dic17—42no—
371C24×C4—171no—
372C24×C4—171no—
373C24×C4—171no—
374C2×#117—1716no—
375C2×#117—178no—
376C22×C4⋊C4—171no—
377C22×C4⋊C4—171no—
378C22×C4⋊C4—171no—
379C22×C4⋊C4—171no—
380C22×C4⋊C4C2×D1711yescharacteristic
381C22×C4⋊C4C2×D1711yescharacteristic
382C22×C22⋊C4—171no—
383C22×C22⋊C4—171no—
384C22×C22⋊C4—171no—
385C22×C22⋊C4—171no—
386C22×C42—171no—
387C22×C42—171no—
388C22×C42—171no—
389C22×C42—171no—
390C22×C42—171no—
391C22×C42C2×D1711yescharacteristic
392#387—178no—
393#387—178no—
394#387—178no—
395#387C2×D1718yescomplemented
396#385—178no—
397#385—178no—
398#383—178no—
399#382—178no—
400#381—178no—
401C4×C4⋊C4—178no—
402C4×C22⋊C4—178no—
403C4×C22⋊C4—178no—
404#376—178no—
405C2×#95—171no—
406C2×#95—171no—
407C2×#95—171no—
408C2×#95—171no—
409C2×#95—171no—
410C2×#95—171no—
411C2×#95—171no—
412C2×#95—171no—
413C2×#95—171no—
414C2×#95—171no—
415C2×#95—171no—
416C2×#95—171no—
417C2×#95—178no—
418C2×#95C2×D1711yescharacteristic
419C2×#95C2×D1711yescharacteristic
420C2×#95C2×D1711yescharacteristic
421C2×#95C2×D1711yescharacteristic
422C2×C17#234318yescomplemented
423C2×C17C22×#11711yescharacteristic
424C2×C17C2×C4×#4111yescharacteristic
425C2×C17C2×#52011yescharacteristic
426C2×C17C2×#55111yescharacteristic
427C2×C17C2×#55111yescharacteristic
428C2×C17C2×#55211yescharacteristic
429C2×C17C2×#55211yescharacteristic
430D17—28no—
431C25—171no—
432C23×C4—171no—
433C23×C4—171no—
434C23×C4—171no—
435C23×C4—171no—
436C23×C4—178no—
437C23×C4—174no—
438C23×C4—171no—
439C23×C4—171no—
440C23×C4—171no—
441C23×C4—174no—
442C23×C4—174no—
443C23×C4—344no—
444C23×C4—344no—
445C23×C4—344no—
446C23×C4—344no—
447C23×C4—344no—
448C23×C4—344no—
449C23×C4—682no—
450C23×C4—682no—
451C23×C4C22×D1711yescharacteristic
452C23×C4C22×D1711yescharacteristic
453C23×C4C22×D1711yescharacteristic
454C23×C4C22×D1711yescharacteristic
455C23×C4C22×D1711yescharacteristic
456C23×C4C22×D1711yescharacteristic
457C23×C4C22×D1711yescharacteristic
458#117—1764no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—178no—
461C2×C4⋊C4—174no—
462C2×C4⋊C4—174no—
463C2×C4⋊C4—174no—
464C2×C4⋊C4—174no—
465C2×C4⋊C4—344no—
466C2×C4⋊C4—682no—
467C2×C4⋊C4—682no—
468C2×C4⋊C4C4×D1718yescomplemented
469C2×C4⋊C4C22×D1714yes—
470C2×C4⋊C4C22×D1714yes—
471C2×C22⋊C4—178no—
472C2×C22⋊C4—178no—
473C2×C22⋊C4—174no—
474C2×C22⋊C4—174no—
475C2×C22⋊C4—174no—
476C2×C22⋊C4—174no—
477C2×C22⋊C4—344no—
478C2×C22⋊C4—344no—
479C2×C42—24no—
480C2×C42—178no—
481C2×C42—178no—
482C2×C42—174no—
483C2×C42—174no—
484C2×C42—174no—
485C2×C42—174no—
486C2×C42—174no—
487C2×C42—344no—
488C2×C42—682no—
489C2×C42—682no—
490C2×C42C22×D1714yes—
491#95—174no—
492#95—174no—
493#95—174no—
494#95—174no—
495#95—174no—
496#95—174no—
497#95—174no—
498#95—174no—
499#95—174no—
500#95—174no—
501#95—174no—
502#95—174no—
503#95C22×D1714yes—
504#95C22×D1714yes—
505#95C22×D1714yes—
506#95C22×D1714yes—
507C17C2×#234311yescharacteristic, complemented, Sylow
508C24—174no—
509C24—174no—
510C24—174no—
511C24—172no—
512C24—342no—
513C24—342no—
514C24—342no—
515C24—342no—
516C24C23×D1711yescharacteristic
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—174no—
535C22×C4—174no—
536C22×C4—174no—
537C22×C4—174no—
538C22×C4—172no—
539C22×C4—172no—
540C22×C4—172no—
541C22×C4—172no—
542C22×C4—1716no—
543C22×C4—172no—
544C22×C4—172no—
545C22×C4—172no—
546C22×C4—348no—
547C22×C4—3432no—
548C22×C4—348no—
549C22×C4—348no—
550C22×C4—348no—
551C22×C4—348no—
552C22×C4—342no—
553C22×C4—342no—
554C22×C4—342no—
555C22×C4—342no—
556C22×C4—342no—
557C22×C4—342no—
558C22×C4—342no—
559C22×C4—342no—
560C22×C4—342no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4—342no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—348no—
570C22×C4—684no—
571C22×C4—684no—
572C22×C4—6816no—
573C22×C4—6816no—
574C22×C4C2×C4×D1714yes—
575C22×C4C2×C4×D1714yes—
576C22×C4C2×C4×D1714yes—
577C22×C4#6325414yes—
578C22×C4C23×D1712yes—
579C22×C4C23×D1712yes—
580C22×C4C23×D1712yes—
581C22×C4C23×D1712yes—
582C22×C4C23×D1712yes—
583C22×C4C23×D1712yes—
584C22×C4C23×D1712yes—
585C4⋊C4—28no—
586C4⋊C4—1716no—
587C4⋊C4—348no—
588C4⋊C4—684no—
589C4⋊C4—684no—
590C4⋊C4C2×C4×D17116yescomplemented
591C22⋊C4—1716no—
592C22⋊C4—1716no—
593C22⋊C4—348no—
594C22⋊C4—348no—
595C42—28no—
596C42—1716no—
597C42—1716no—
598C42—348no—
599C42—684no—
600C42—684no—
601C23—1716no—
602C23—174no—
603C23—174no—
604C23—174no—
605C23—348no—
606C23—348no—
607C23—348no—
608C23—348no—
609C23—348no—
610C23—348no—
611C23—342no—
612C23—342no—
613C23—342no—
614C23—342no—
615C23C22×C4×D1712yes—
616C23C2×#6325412yes—
617C23#1058769412yes—
618C23#41×D1712yes—
619C23#41×D1712yes—
620C23#41×D1712yes—
621C23#1058769612yes—
622C23C24×D1711yescharacteristic
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—174no—
648C2×C4—174no—
649C2×C4—174no—
650C2×C4—174no—
651C2×C4—3432no—
652C2×C4—348no—
653C2×C4—348no—
654C2×C4—348no—
655C2×C4—348no—
656C2×C4—342no—
657C2×C4—342no—
658C2×C4—342no—
659C2×C4—342no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—342no—
664C2×C4—342no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—342no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—6816no—
674C2×C4—6816no—
675C2×C4—684no—
676C2×C4—684no—
677C2×C4—684no—
678C2×C4C22×C4×D1714yes—
679C2×C4C22×C4×D1714yes—
680C2×C4C22×C4×D1714yes—
681C2×C4C2×#6325414yes—
682C22—178no—
683C22—3432no—
684C22—344no—
685C22—344no—
686C22—344no—
687C22—344no—
688C22—344no—
689C22—344no—
690C22#117×D1714yes—
691C22C4×#6325414yes—
692C22#1176329114yes—
693C22#1176348214yes—
694C22#1176348414yes—
695C22#1176349114yes—
696C22#1176349314yes—
697C22C23×C4×D1711yescharacteristic
698C22C2×#41×D1711yescharacteristic
699C22C2×#41×D1711yescharacteristic
700C22C2×#41×D1711yescharacteristic
701C22C22×#6325411yescharacteristic
702C22C2×#1058769611yescharacteristic
703C22C2×#1058769411yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—24no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—344no—
712C4—344no—
713C4—344no—
714C4—344no—
715C4—682no—
716C4—682no—
717C4—682no—
718C2—348no—
719C2#1453163918yesdirect product factor
720C2C2×#117×D1711yescharacteristic
721C2C2×C4×#6325411yescharacteristic
722C2C2×#1176329111yescharacteristic
723C2C2×#1176348211yescharacteristic
724C2C2×#1176348411yescharacteristic
725C2C2×#1176349111yescharacteristic
726C2C2×#1176349311yescharacteristic
subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#387C2
socleC24×C17C24
prime radicalC24×D17C23
cosocleC23×C17C25
hypercenterC2×#387D17
hypocenterC17C2×#2343
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #14531639C2direct (N × H)
3. C2×#11762695C2semidirect
4. C2×#11762694C2semidirect
5. C2×#11762692C2semidirect
8. C2×#11762676C2semidirect
9. C2×#11762673C2semidirect
11. C2×C4⋊C4×Dic17C2semidirect
14. C2×#11762655C2semidirect
16. C2×C17×#387C2semidirect
20. C2×#10587578C4semidirect
35. #11762695C22semidirect
36. #11762694C22semidirect
37. #11762692C22semidirect
40. #11762676C22semidirect
41. #11762673C22semidirect
43. C4⋊C4×Dic17C22semidirect
46. #11762655C22semidirect
63. C17×#387C22semidirect
96. C2×C4⋊C4×C17C2×C4semidirect
110. C2×C4⋊Dic17C2×C4semidirect
120. C2×C4×Dic17C2×C4semidirect
121. C2×C4×Dic17C2×C4semidirect
127. #10587578C2×C4semidirect
222. C4⋊C4×C17C22×C4semidirect
229. C4⋊Dic17C22×C4semidirect
235. C4×Dic17C22×C4semidirect
236. C4×Dic17C22×C4semidirect
324. C2×#387D17semidirect
395. #387C2×D17semidirect
422. C2×C17#2343semidirect
468. C2×C4⋊C4C4×D17semidirect
507. C17C2×#2343semidirect
590. C4⋊C4C2×C4×D17semidirect
719. C2#14531639direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875782
#145316392
C2×#117626952
C2×#117626942
C2×#117626922
C2×#117626832
C2×#117626802
C2×#117626762
C2×#117626732
C2×#117626712
C2×C4⋊C4×Dic172
C2×C4×#632272
C2×#117626562
C2×#117626552
C2×#95×D172
C2×C17×#3872
C2×#234317