Finite Group Databasebeta

← #394×Dic17 #16956121

Subgroups — #394×Dic17 #16956121

Order 4352.

2550 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
1C22×D4×Dic17C211yesmaximal, characteristic
2C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic17C212yesmaximal, complemented
4C2×C22⋊C4×Dic17C212yesmaximal, complemented
5#14527041C211yesmaximal, characteristic, complemented
6#14527037C211yesmaximal, characteristic, complemented
7#14527033C212yesmaximal, complemented
8#14527029C212yesmaximal, complemented
9#14527025C211yesmaximal, characteristic
10#95×Dic17C211yesmaximal, characteristic, complemented
11C2×C17×#394C211yesmaximal, characteristic
12C24×Dic17C2212yes—
13C2×D4×Dic17—24no—
14C2×D4×Dic17—28no—
15C22×C4⋊Dic17C2211yescharacteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C22⋊Dic17C2212yes—
18C22×C22⋊Dic17C2212yes—
19C22×C22⋊Dic17C2212yes—
20C22×C4×Dic17C2212yes—
21C22×C4×Dic17C2211yescharacteristic
22C22×C4×Dic17C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24C4⋊C4×Dic17—24no—
25C22⋊C4×Dic17—28no—
26C22⋊C4×Dic17—28no—
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C23×D4×C17C2211yescharacteristic
36C22×C4⋊C4×C17C2211yescharacteristic
37C22×C22⋊C4×C17C2212yes—
38C22×C22⋊C4×C17C2212yes—
39C17×#394C418yescomplemented
40C2×C17×#95C2211yescharacteristic
41C25×C17C2312yes—
42C22×D4×C17—24no—
43C22×D4×C17—24no—
44C22×D4×C17—22no—
45C22×D4×C17—22no—
46C22×D4×C17C2×C414yes—
47C23×C4×C17C2311yescharacteristic
48C23×C4×C17C2312yes—
49C23×C4×C17C2311yescharacteristic
50C23×C4×C17C2311yescharacteristic
51C23×Dic17—24no—
52C23×Dic17—24no—
53C23×Dic17—24no—
54C23×Dic17—24no—
55C23×Dic17—24no—
56C23×Dic17—24no—
57C23×Dic17D418yes—
58C23×Dic17C2311yescharacteristic
59C23×Dic17C2311yescharacteristic
60C23×Dic17C2312yes—
61C23×Dic17C2311yescharacteristic
62C23×Dic17C2312yes—
63C23×Dic17C2311yescharacteristic
64C2×C4⋊C4×C17—22no—
65C2×C4⋊C4×C17—22no—
66C2×C4⋊C4×C17C2×C414yescomplemented
67C2×C22⋊C4×C17—24no—
68C2×C22⋊C4×C17—24no—
69C2×C22⋊C4×C17—24no—
70C2×C22⋊C4×C17—24no—
71C2×C22⋊C4×C17C2×C418yescomplemented
72C2×C22⋊C4×C17C2×C418yescomplemented
73C2×C22⋊Dic17—24no—
74C2×C22⋊Dic17—24no—
75C2×C22⋊Dic17—24no—
76C2×C22⋊Dic17—24no—
77C2×C22⋊Dic17—24no—
78C2×C22⋊Dic17—24no—
79C2×C22⋊Dic17—24no—
80C2×C22⋊Dic17—24no—
81C2×C22⋊Dic17—24no—
82D4×Dic17—232no—
83C2×C4⋊Dic17—22no—
84C2×C4⋊Dic17—22no—
85C2×C4⋊Dic17—24no—
86C2×C4⋊Dic17—22no—
87C2×C4⋊Dic17—22no—
88C2×C4×Dic17—24no—
89C2×C4×Dic17—22no—
90C2×C4×Dic17—24no—
91C2×C4×Dic17—24no—
92C2×C4×Dic17—24no—
93C2×C4×Dic17—22no—
94C2×C4×Dic17—22no—
95C2×C4×Dic17—24no—
96C2×C4×Dic17D414yes—
97C2×C4×Dic17D414yescomplemented
98C17×#95C2×C414yescomplemented
99#10587502—24no—
100#10587502—22no—
101#10587502—22no—
102#10587502—24no—
103#10587502—24no—
104#10587502—24no—
105#10587502—22no—
106#10587502—24no—
107C24×C17—22no—
108C24×C17—22no—
109C24×C17—22no—
110C24×C17—22no—
111C24×C17—22no—
112C24×C17—22no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—22no—
116C24×C17—22no—
117C24×C17—22no—
118C24×C17—22no—
119C24×C17C22×C414yes—
120C24×C17C2×D414yes—
121C24×C17#4114yes—
122C24×C17C2411yescharacteristic
123C2×D4×C17—28no—
124C2×D4×C17—216no—
125C2×D4×C17—28no—
126C2×D4×C17—216no—
127C2×D4×C17—28no—
128C22×C4×C17—22no—
129C22×C4×C17—21no—
130C22×C4×C17—22no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—21no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—21no—
144C22×C4×C17C22×C414yes—
145C22×C4×C17C22×C412yes—
146C22×C4×C17C22×C412yes—
147C22×C4×C17C22×C412yes—
148C22×C4×C17C2×D412yes—
149C22×C4×C17C2×D412yes—
150C22×C4×C17#4112yes—
151C22×C4×C17#4112yes—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—21no—
156C22×Dic17—21no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—22no—
160C22×Dic17—22no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—21no—
167C22×Dic17—22no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—21no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—216no—
177C22×Dic17—216no—
178C22×Dic17—216no—
179C22×Dic17—48no—
180C22×Dic17—48no—
181C22×Dic17—48no—
182C22×Dic17—48no—
183C22×Dic17C2×D414yes—
184C22×Dic17C2×D412yes—
185C22×Dic17C2×D412yes—
186C22×Dic17C2×D414yes—
187C22×Dic17C2×D412yes—
188C22×Dic17C2×D412yes—
189C22×Dic17#4114yes—
190C22×Dic17#4112yes—
191C22×Dic17#4112yes—
192C22×Dic17#4114yes—
193C4⋊C4×C17—28no—
194C22⋊C4×C17—216no—
195C22⋊C4×C17—216no—
196C22⋊Dic17—216no—
197C22⋊Dic17—216no—
198C22⋊Dic17—216no—
199C4⋊Dic17—28no—
200C4⋊Dic17—28no—
201C4×Dic17—28no—
202C4×Dic17—28no—
203C4×Dic17—44no—
204C4×Dic17—48no—
205C4×#394—171nomaximal, Sylow
206C23×C17—24no—
207C23×C17—24no—
208C23×C17—24no—
209C23×C17—24no—
210C23×C17—24no—
211C23×C17—24no—
212C23×C17—24no—
213C23×C17—24no—
214C23×C17—24no—
215C23×C17—24no—
216C23×C17—24no—
217C23×C17—24no—
218C23×C17—24no—
219C23×C17—24no—
220C23×C17—24no—
221C23×C17—24no—
222C23×C17—24no—
223C23×C17—24no—
224C23×C17—42no—
225C23×C17—42no—
226C23×C17—42no—
227C23×C17—42no—
228C23×C17—42no—
229C23×C17—42no—
230C23×C17—42no—
231C23×C17—42no—
232C23×C17—42no—
233C23×C17—42no—
234C23×C17—42no—
235C23×C17—42no—
236C23×C17—42no—
237C23×C17—42no—
238C23×C17—42no—
239C23×C17—42no—
240C23×C17C4×D418yes—
241C23×C17C23×C411yescharacteristic
242C23×C17C22×D412yes—
243C23×C17C22×D411yescharacteristic
244C23×C17C22×D411yescharacteristic
245C23×C17C2×#4112yes—
246C23×C17C2×#4111yescharacteristic
247C23×C17C2×#4111yescharacteristic
248C23×C17C2×#4111yescharacteristic
249C23×C17C2×#4112yes—
250C23×C17C2×#4111yescharacteristic
251C23×C17C2×#4112yes—
252D4×C17—232no—
253C2×C4×C17—22no—
254C2×C4×C17—24no—
255C2×C4×C17—22no—
256C2×C4×C17—22no—
257C2×C4×C17—22no—
258C2×C4×C17—22no—
259C2×C4×C17—24no—
260C2×C4×C17—22no—
261C2×C4×C17—22no—
262C2×C4×C17—22no—
263C2×C4×C17—24no—
264C2×C4×C17—24no—
265C2×C4×C17—24no—
266C2×C4×C17—22no—
267C2×C4×C17—24no—
268C2×C4×C17—41no—
269C2×C4×C17—42no—
270C2×C4×C17—42no—
271C2×C4×C17—41no—
272C2×C4×C17—42no—
273C2×C4×C17—42no—
274C2×C4×C17—42no—
275C2×C4×C17C4×D414yes—
276C2×C4×C17C4×D414yescomplemented
277C2×Dic17—22no—
278C2×Dic17—24no—
279C2×Dic17—24no—
280C2×Dic17—22no—
281C2×Dic17—24no—
282C2×Dic17—24no—
283C2×Dic17—24no—
284C2×Dic17—24no—
285C2×Dic17—24no—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—24no—
289C2×Dic17—22no—
290C2×Dic17—41no—
291C2×Dic17—42no—
292C2×Dic17—42no—
293C2×Dic17—42no—
294C2×Dic17—42no—
295C2×Dic17—42no—
296C2×Dic17—41no—
297C2×Dic17—42no—
298C2×Dic17—42no—
299C2×Dic17—42no—
300C2×Dic17—42no—
301C2×Dic17—42no—
302C2×Dic17—42no—
303C2×Dic17—42no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—432no—
307C2×Dic17#12014yes—
308C2×Dic17#12118yes—
309C2×Dic17#12114yes—
310C2×Dic17#12318yes—
311C2×Dic17#12414yes—
312C22×C4×D4—171no—
313C2×#394D1711yescharacteristic
314C2×C4×C4⋊C4—171no—
315C2×C4×C22⋊C4—172no—
316C2×C4×C22⋊C4—172no—
317#1442—171no—
318#1441—171no—
319#1440—172no—
320#1439—172no—
321#1438—171no—
322C4×#95—171no—
323C22×C17—28no—
324C22×C17—28no—
325C22×C17—28no—
326C22×C17—44no—
327C22×C17—44no—
328C22×C17—44no—
329C22×C17—44no—
330C22×C17—44no—
331C22×C17—44no—
332C22×C17—44no—
333C22×C17—44no—
334C22×C17—44no—
335C22×C17—44no—
336C22×C17—44no—
337C22×C17—44no—
338C22×C17C2×C4×D412yes—
339C22×C17C2×C4×D411yescharacteristic
340C22×C17C2×C4×D411yescharacteristic
341C22×C17C4×#4111yescharacteristic
342C22×C17C4×#4112yes—
343C22×C17C2×#12011yescharacteristic
344C22×C17C2×#12111yescharacteristic
345C22×C17C2×#12112yes—
346C22×C17C2×#12312yes—
347C22×C17#52512yes—
348C22×C17#52511yescharacteristic
349C22×C17#52512yes—
350C22×C17#52511yescharacteristic
351C22×C17#52512yes—
352C22×C17C2×#12411yescharacteristic
353C22×C17#52912yes—
354C22×C17#52912yes—
355C22×C17#52912yes—
356C22×C17#52911yescharacteristic
357C22×C17#52912yes—
358C22×C17#53212yes—
359C22×C17#53211yescharacteristic
360C22×C17#53211yescharacteristic
361C4×C17—24no—
362C4×C17—24no—
363C4×C17—42no—
364C4×C17—44no—
365Dic17—44no—
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369Dic17—44no—
370Dic17#39418yesdirect product factor
371C23×D4C2×D1711yescharacteristic
372C24×C4—172no—
373C2×C4×D4—344no—
374C2×C4×D4—348no—
375C22×C4⋊C4—171no—
376C22×C4⋊C4—171no—
377C22×C4⋊C4C2×D1711yescharacteristic
378C22×C22⋊C4—172no—
379C22×C22⋊C4—172no—
380C22×C22⋊C4—172no—
381C22×C22⋊C4C2×D1712yes—
382C22×C22⋊C4C2×D1712yes—
383C22×C42—171no—
384C22×C42—171no—
385C22×C42—172no—
386C22×C42—171no—
387#394Dic1718yesdirect product factor
388C4×C4⋊C4—344no—
389C4×C22⋊C4—348no—
390C4×C22⋊C4—348no—
391C2×#95—171no—
392C2×#95—172no—
393C2×#95—171no—
394C2×#95—172no—
395C2×#95—172no—
396C2×#95—171no—
397C2×#95—172no—
398C2×#95—172no—
399C2×#95C2×D1711yescharacteristic
400C2×C17—48no—
401C2×C17C4×#12011yescharacteristic
402C2×C17C4×#12111yescharacteristic
403C2×C17C4×#12112yes—
404C2×C17C4×#12312yes—
405C2×C17C4×#12411yescharacteristic
406C2×C17C2×#39411yescharacteristic
407C2×C17#238811yescharacteristic
408C2×C17#239211yescharacteristic
409C2×C17#239212yes—
410C2×C17#239512yes—
411C2×C17#239811yescharacteristic
412C25C22×D1712yes—
413C22×D4—24no—
414C22×D4—24no—
415C22×D4—22no—
416C22×D4—22no—
417C22×D4C2×Dic1714yes—
418C23×C4—171no—
419C23×C4—178no—
420C23×C4—171no—
421C23×C4—171no—
422C23×C4—171no—
423C23×C4—172no—
424C23×C4—172no—
425C23×C4—344no—
426C23×C4—344no—
427C23×C4—344no—
428C23×C4—344no—
429C23×C4—344no—
430C23×C4—344no—
431C23×C4C22×D1711yescharacteristic
432C23×C4C22×D1712yes—
433C23×C4C22×D1711yescharacteristic
434C23×C4C22×D1711yescharacteristic
435C4×D4—3432no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—344no—
439C2×C4⋊C4—342no—
440C2×C4⋊C4—342no—
441C2×C4⋊C4—342no—
442C2×C4⋊C4—342no—
443C2×C4⋊C4C2×Dic1714yescomplemented
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—344no—
449C2×C22⋊C4—344no—
450C2×C22⋊C4—344no—
451C2×C22⋊C4—344no—
452C2×C22⋊C4—344no—
453C2×C22⋊C4—344no—
454C2×C22⋊C4—344no—
455C2×C22⋊C4—344no—
456C2×C22⋊C4—344no—
457C2×C22⋊C4C2×Dic1718yescomplemented
458C2×C22⋊C4C2×Dic1718yescomplemented
459C2×C42—174no—
460C2×C42—174no—
461C2×C42—344no—
462C2×C42—342no—
463C2×C42—342no—
464C2×C42—344no—
465C2×C42—344no—
466C2×C42—344no—
467C2×C42—342no—
468C2×C42—344no—
469#95—344no—
470#95—344no—
471#95—344no—
472#95—344no—
473#95—342no—
474#95—344no—
475#95—342no—
476#95—342no—
477#95C2×Dic1714yescomplemented
478C17C4×#39411yescharacteristic, complemented, Sylow
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24D4×D1714yes—
492C24#6325414yes—
493C24C22×Dic1714yes—
494C24C23×D1711yescharacteristic
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—216no—
498C2×D4—216no—
499C2×D4—28no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—172no—
517C22×C4—172no—
518C22×C4—174no—
519C22×C4—172no—
520C22×C4—174no—
521C22×C4—172no—
522C22×C4—174no—
523C22×C4—172no—
524C22×C4—174no—
525C22×C4—172no—
526C22×C4—3416no—
527C22×C4—3416no—
528C22×C4—3416no—
529C22×C4—341no—
530C22×C4—342no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—341no—
535C22×C4—342no—
536C22×C4—342no—
537C22×C4—342no—
538C22×C4—342no—
539C22×C4—342no—
540C22×C4—342no—
541C22×C4—341no—
542C22×C4—341no—
543C22×C4—342no—
544C22×C4—341no—
545C22×C4—342no—
546C22×C4—342no—
547C22×C4—342no—
548C22×C4—342no—
549C22×C4—341no—
550C22×C4—342no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—688no—
554C22×C4—688no—
555C22×C4—688no—
556C22×C4—688no—
557C22×C4D4×D1712yes—
558C22×C4D4×D1712yes—
559C22×C4#6325412yes—
560C22×C4#6325412yes—
561C22×C4C22×Dic1714yes—
562C22×C4C22×Dic1712yes—
563C22×C4C22×Dic1712yes—
564C22×C4C22×Dic1712yes—
565C4⋊C4—28no—
566C4⋊C4—348no—
567C4⋊C4—348no—
568C22⋊C4—216no—
569C22⋊C4—216no—
570C22⋊C4—3416no—
571C22⋊C4—3416no—
572C22⋊C4—3416no—
573C42—348no—
574C42—348no—
575C42—684no—
576C42—688no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23D4×Dic1718yes—
612C23C2×D4×D1712yes—
613C23C2×D4×D1711yescharacteristic
614C23C2×D4×D1711yescharacteristic
615C23C2×#6325412yes—
616C23C2×#6325411yescharacteristic
617C23C2×#6325411yescharacteristic
618C23#41×D1711yescharacteristic
619C23#41×D1712yes—
620C23#41×D1711yescharacteristic
621C23#41×D1712yes—
622C23C23×Dic1711yescharacteristic
623D4—232no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—174no—
647C2×C4—174no—
648C2×C4—178no—
649C2×C4—178no—
650C2×C4—174no—
651C2×C4—342no—
652C2×C4—344no—
653C2×C4—342no—
654C2×C4—344no—
655C2×C4—344no—
656C2×C4—344no—
657C2×C4—344no—
658C2×C4—344no—
659C2×C4—344no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—344no—
663C2×C4—342no—
664C2×C4—6832no—
665C2×C4—681no—
666C2×C4—682no—
667C2×C4—682no—
668C2×C4—682no—
669C2×C4—682no—
670C2×C4—681no—
671C2×C4—682no—
672C2×C4—682no—
673C2×C4—682no—
674C2×C4—682no—
675C2×C4—682no—
676C2×C4—682no—
677C2×C4—682no—
678C2×C4—682no—
679C2×C4—681no—
680C2×C4—681no—
681C2×C4D4×Dic1714yes—
682C2×C4D4×Dic1714yescomplemented
683C22—28no—
684C22—28no—
685C22—28no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22C2×D4×Dic1711yescharacteristic
699C22C2×D4×Dic1712yes—
700C22C2×D4×Dic1711yescharacteristic
701C22#41×Dic1712yes—
702C22#41×Dic1711yescharacteristic
703C22#120×D1711yescharacteristic
704C22#121×D1711yescharacteristic
705C22#121×D1712yes—
706C22#123×D1712yes—
707C22#1176331511yescharacteristic
708C22#1176331512yes—
709C22#1176331712yes—
710C22#1176331911yescharacteristic
711C22#1176331912yes—
712C22#124×D1711yescharacteristic
713C22#1176333612yes—
714C22#1176333612yes—
715C22#1176333812yes—
716C22#1176334011yescharacteristic
717C22#1176334012yes—
718C22#1176335412yes—
719C22#1176335411yescharacteristic
720C22#1176335811yescharacteristic
721C4—24no—
722C4—24no—
723C4—42no—
724C4—44no—
725C4—178no—
726C4—684no—
727C4—682no—
728C4—682no—
729C4—682no—
730C4—684no—
731C2—48no—
732C2#120×Dic1711yescharacteristic
733C2#121×Dic1711yescharacteristic
734C2#121×Dic1712yes—
735C2#123×Dic1712yes—
736C2#124×Dic1711yescharacteristic
737C2D17×#39411yescharacteristic
738C2#1453199811yescharacteristic
739C2#1453202311yescharacteristic
740C2#1453202712yes—
741C2#1453204012yes—
742C2#1453207211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#394C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#394D17
hypocenterC17C4×#394
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic17C2semidirect
3. C2×C22⋊C4×Dic17C2semidirect
4. C2×C22⋊C4×Dic17C2semidirect
5. #14527041C2semidirect
6. #14527037C2semidirect
7. #14527033C2semidirect
8. #14527029C2semidirect
10. #95×Dic17C2semidirect
39. C17×#394C4semidirect
66. C2×C4⋊C4×C17C2×C4semidirect
71. C2×C22⋊C4×C17C2×C4semidirect
72. C2×C22⋊C4×C17C2×C4semidirect
97. C2×C4×Dic17D4semidirect
98. C17×#95C2×C4semidirect
276. C2×C4×C17C4×D4semidirect
370. Dic17#394direct (N × H)
387. #394Dic17direct (N × H)
443. C2×C4⋊C4C2×Dic17semidirect
457. C2×C22⋊C4C2×Dic17semidirect
458. C2×C22⋊C4C2×Dic17semidirect
477. #95C2×Dic17semidirect
478. C17C4×#394semidirect
682. C2×C4D4×Dic17semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic172
C2×C4⋊C4×Dic172
C2×C22⋊C4×Dic172
#145270412
#145270372
#145270332
#145270292
#145270252
#95×Dic172
C2×C17×#3942
C4×#39417