Finite Group Databasebeta

← C4×#11762723 #16956115

Subgroups — C4×#11762723 #16956115

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
1C2×#11762723C211yesmaximal, characteristic
2C2×C4×#63225C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic17C212yesmaximal, complemented
4C2×C4×C22⋊Dic17C212yesmaximal, complemented
5#14527043C211yesmaximal, characteristic, complemented
6#14527034C211yesmaximal, characteristic, complemented
7#14527031C212yesmaximal, complemented
8#14527027C212yesmaximal, complemented
9#14527025C211yesmaximal, characteristic
10C4×#10587502C211yesmaximal, characteristic, complemented
11C22×C4×D4×C17C211yesmaximal, characteristic
12C22×#63225C2211yescharacteristic
13C22×#63225C2211yescharacteristic
14C22×C22⋊Dic17C2212yes—
15C22×C22⋊Dic17C2212yes—
16C22×C22⋊Dic17C2212yes—
17C22×C22⋊Dic17C2212yes—
18C22×C4×Dic17C2212yes—
19C22×C4×Dic17C2211yescharacteristic
20C22×C4×Dic17C2211yescharacteristic
21#11762723C418yesdirect product factor
22C4×#63225—24no—
23C4×C22⋊Dic17—28no—
24C4×C22⋊Dic17—28no—
25C2×#10587502C2211yescharacteristic
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C23×D4×C17C2211yescharacteristic
35C24×C4×C17C2212yes—
36C2×C4×D4×C17—24no—
37C2×C4×D4×C17—28no—
38C22×C4⋊C4×C17C2211yescharacteristic
39C22×C22⋊C4×C17C2212yes—
40C22×C42×C17C2211yescharacteristic
41C25×C17C2312yes—
42C22×D4×C17—24no—
43C22×D4×C17—24no—
44C22×D4×C17—22no—
45C22×D4×C17—22no—
46C22×D4×C17C2×C414yes—
47C23×C4×C17—24no—
48C23×C4×C17—24no—
49C23×C4×C17—24no—
50C23×C4×C17—24no—
51C23×C4×C17—24no—
52C23×C4×C17—24no—
53C23×C4×C17D418yes—
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2312yes—
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×Dic17C2311yescharacteristic
59C23×Dic17C2312yes—
60C23×Dic17C2311yescharacteristic
61C23×Dic17C2311yescharacteristic
62C23×Dic17C2312yes—
63C23×Dic17C2311yescharacteristic
64C4×D4×C17—232no—
65C2×C4⋊C4×C17—24no—
66C2×C4⋊C4×C17—22no—
67C2×C22⋊C4×C17—24no—
68C2×C22⋊C4×C17—24no—
69C2×C22⋊C4×C17—24no—
70C2×C42×C17—24no—
71C2×C42×C17D414yes—
72C2×C22⋊Dic17—24no—
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—
82C2×C22⋊Dic17C2×C418yescomplemented
83C2×C22⋊Dic17C2×C418yescomplemented
84C2×#63225—22no—
85C2×#63225—22no—
86C2×#63225—22no—
87C2×#63225—22no—
88C2×#63225—22no—
89C2×#63225C2×C414yescomplemented
90C2×C4×Dic17—22no—
91C2×C4×Dic17—24no—
92C2×C4×Dic17—24no—
93C2×C4×Dic17—24no—
94C2×C4×Dic17—22no—
95C2×C4×Dic17—22no—
96C2×C4×Dic17—24no—
97C2×C4×Dic17D414yescomplemented
98#10587502—24no—
99#10587502—24no—
100#10587502—22no—
101#10587502—22no—
102#10587502—22no—
103#10587502—24no—
104#10587502—24no—
105#10587502—24no—
106#10587502C2×C414yescomplemented
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—22no—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—22no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—216no—
141C22×C4×C17—216no—
142C22×C4×C17—216no—
143C22×C4×C17—48no—
144C22×C4×C17—48no—
145C22×C4×C17—48no—
146C22×C4×C17—48no—
147C22×C4×C17C22×C412yes—
148C22×C4×C17C2×D412yes—
149C22×C4×C17C2×D414yes—
150C22×C4×C17C2×D412yes—
151C22×C4×C17C2×D412yes—
152C22×C4×C17C2×D414yes—
153C22×C4×C17C2×D412yes—
154C22×C4×C17#4112yes—
155C22×C4×C17#4112yes—
156C22×C4×C17#4114yes—
157C22×Dic17—21no—
158C22×Dic17—21no—
159C22×Dic17—21no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—21no—
174C22×Dic17—22no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17C22×C414yes—
186C22×Dic17C22×C412yes—
187C22×Dic17C22×C412yes—
188C22×Dic17C2×D412yes—
189C22×Dic17C2×D412yes—
190C22×Dic17#4114yes—
191C22×Dic17#4112yes—
192C22×Dic17#4112yes—
193C4⋊C4×C17—28no—
194C22⋊C4×C17—216no—
195C42×C17—28no—
196C22⋊Dic17—216no—
197C22⋊Dic17—216no—
198C22⋊Dic17—216no—
199C22⋊Dic17—216no—
200#63225—28no—
201#63225—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×D411yescharacteristic
243C23×C17C22×D412yes—
244C23×C17C22×D411yescharacteristic
245C23×C17C2×#4112yes—
246C23×C17C2×#4111yescharacteristic
247C23×C17C2×#4111yescharacteristic
248C23×C17C2×#4112yes—
249C23×C17C2×#4111yescharacteristic
250C23×C17C2×#4111yescharacteristic
251C23×C17C2×#4112yes—
252D4×C17—232no—
253C2×C4×C17—24no—
254C2×C4×C17—22no—
255C2×C4×C17—22no—
256C2×C4×C17—24no—
257C2×C4×C17—22no—
258C2×C4×C17—24no—
259C2×C4×C17—24no—
260C2×C4×C17—24no—
261C2×C4×C17—22no—
262C2×C4×C17—22no—
263C2×C4×C17—42no—
264C2×C4×C17—42no—
265C2×C4×C17—42no—
266C2×C4×C17—42no—
267C2×C4×C17—42no—
268C2×C4×C17—42no—
269C2×C4×C17—432no—
270C2×C4×C17C4×D414yes—
271C2×C4×C17#12014yes—
272C2×C4×C17#12114yes—
273C2×C4×C17#12118yes—
274C2×C4×C17#12318yes—
275C2×C4×C17#12414yes—
276C2×Dic17—22no—
277C2×Dic17—22no—
278C2×Dic17—22no—
279C2×Dic17—22no—
280C2×Dic17—22no—
281C2×Dic17—22no—
282C2×Dic17—24no—
283C2×Dic17—24no—
284C2×Dic17—24no—
285C2×Dic17—22no—
286C2×Dic17—24no—
287C2×Dic17—22no—
288C2×Dic17—24no—
289C2×Dic17—24no—
290C2×Dic17—24no—
291C2×Dic17—24no—
292C2×Dic17—22no—
293C2×Dic17—24no—
294C2×Dic17—41no—
295C2×Dic17—41no—
296C2×Dic17—42no—
297C2×Dic17—42no—
298C2×Dic17—42no—
299C2×Dic17—42no—
300C2×Dic17—41no—
301C2×Dic17—42no—
302C2×Dic17—41no—
303C2×Dic17—42no—
304C2×Dic17—42no—
305C2×Dic17—42no—
306C2×Dic17—41no—
307C2×Dic17—42no—
308C2×Dic17—41no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17C4×D414yescomplemented
312C22×C4×D4D1711yescharacteristic
313C2×#394—171no—
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×D411yescharacteristic
339C22×C17C2×C4×D412yes—
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#52512yes—
351C22×C17#52511yescharacteristic
352C22×C17C2×#12411yescharacteristic
353C22×C17#52912yes—
354C22×C17#52912yes—
355C22×C17#52912yes—
356C22×C17#52912yes—
357C22×C17#52911yescharacteristic
358C22×C17#53211yescharacteristic
359C22×C17#53212yes—
360C22×C17#53211yescharacteristic
361C4×C17—24no—
362C4×C17—44no—
363C4×C17—42no—
364C4×C17#39418yescomplemented
365Dic17—24no—
366Dic17—42no—
367Dic17—42no—
368Dic17—44no—
369Dic17—42no—
370Dic17—44no—
371C23×D4C2×D1711yescharacteristic
372C24×C4C2×D1712yes—
373C2×C4×D4—28no—
374C2×C4×D4—24no—
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⋊C4—172no—
382C22×C22⋊C4C2×D1712yes—
383C22×C42—171no—
384C22×C42—172no—
385C22×C42—171no—
386C22×C42C2×D1711yescharacteristic
387#394—178no—
388C4×C4⋊C4—344no—
389C4×C22⋊C4—348no—
390C4×C22⋊C4—348no—
391C2×#95—171no—
392C2×#95—171no—
393C2×#95—172no—
394C2×#95—171no—
395C2×#95—172no—
396C2×#95—172no—
397C2×#95—171no—
398C2×#95—172no—
399C2×#95—172no—
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×D4C4×D1714yes—
418C23×C4—24no—
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—171no—
425C23×C4—171no—
426C23×C4—171no—
427C23×C4—172no—
428C23×C4—171no—
429C23×C4—172no—
430C23×C4C22⋊D1718yes—
431C23×C4C22×D1711yescharacteristic
432C23×C4C22×D1712yes—
433C23×C4C22×D1711yescharacteristic
434C23×C4C22×D1711yescharacteristic
435C4×D4—232no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—174no—
439C2×C4⋊C4—342no—
440C2×C4⋊C4—342no—
441C2×C4⋊C4—342no—
442C2×C4⋊C4—342no—
443C2×C4⋊C4—342no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—178no—
448C2×C22⋊C4—178no—
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⋊C4—344no—
458C2×C22⋊C4—344no—
459C2×C42—24no—
460C2×C42—174no—
461C2×C42—342no—
462C2×C42—342no—
463C2×C42—344no—
464C2×C42—344no—
465C2×C42—344no—
466C2×C42—344no—
467C2×C42—342no—
468C2×C42C22⋊D1714yes—
469#95—174no—
470#95—344no—
471#95—344no—
472#95—344no—
473#95—342no—
474#95—344no—
475#95—344no—
476#95—342no—
477#95—342no—
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—
491C24C2×C4×D1714yes—
492C24#6325214yes—
493C24C2×C22⋊D1714yes—
494C24C23×D1711yescharacteristic
495C2×D4—28no—
496C2×D4—216no—
497C2×D4—28no—
498C2×D4—216no—
499C2×D4—28no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—216no—
513C22×C4—216no—
514C22×C4—216no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—172no—
520C22×C4—172no—
521C22×C4—172no—
522C22×C4—174no—
523C22×C4—172no—
524C22×C4—172no—
525C22×C4—174no—
526C22×C4—172no—
527C22×C4—341no—
528C22×C4—341no—
529C22×C4—341no—
530C22×C4—341no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4—342no—
536C22×C4—341no—
537C22×C4—342no—
538C22×C4—342no—
539C22×C4—342no—
540C22×C4—341no—
541C22×C4—342no—
542C22×C4—342no—
543C22×C4—342no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—342no—
547C22×C4—341no—
548C22×C4—341no—
549C22×C4—342no—
550C22×C4—342no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—341no—
554C22×C4—341no—
555C22×C4C2×C4×D1712yes—
556C22×C4#6325212yes—
557C22×C4D4×D1712yes—
558C22×C4#6325412yes—
559C22×C4#6325414yes—
560C22×C4C2×C22⋊D1714yes—
561C22×C4C2×C22⋊D1712yes—
562C22×C4C2×C22⋊D1712yes—
563C22×C4C2×C22⋊D1714yes—
564C22×C4C2×C22⋊D1712yes—
565C4⋊C4—28no—
566C4⋊C4—348no—
567C4⋊C4—348no—
568C22⋊C4—216no—
569C22⋊C4—3416no—
570C22⋊C4—3416no—
571C22⋊C4—3416no—
572C22⋊C4—3416no—
573C42—28no—
574C42—348no—
575C42—688no—
576C42—684no—
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—
611C23C4×C22⋊D1718yes—
612C23C22×C4×D1711yescharacteristic
613C23C2×#6325212yes—
614C23C2×#6325211yescharacteristic
615C23C2×D4×D1711yescharacteristic
616C23C2×#6325411yescharacteristic
617C23C2×#6325412yes—
618C23#41×D1711yescharacteristic
619C23#41×D1711yescharacteristic
620C23#41×D1712yes—
621C23C22×C22⋊D1711yescharacteristic
622C23C22×C22⋊D1712yes—
623D4—232no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—432no—
641C2×C4—174no—
642C2×C4—342no—
643C2×C4—342no—
644C2×C4—342no—
645C2×C4—342no—
646C2×C4—342no—
647C2×C4—342no—
648C2×C4—344no—
649C2×C4—344no—
650C2×C4—344no—
651C2×C4—342no—
652C2×C4—344no—
653C2×C4—342no—
654C2×C4—344no—
655C2×C4—344no—
656C2×C4—342no—
657C2×C4—344no—
658C2×C4—344no—
659C2×C4—344no—
660C2×C4—681no—
661C2×C4—681no—
662C2×C4—682no—
663C2×C4—682no—
664C2×C4—682no—
665C2×C4—681no—
666C2×C4—682no—
667C2×C4—681no—
668C2×C4—682no—
669C2×C4—682no—
670C2×C4—682no—
671C2×C4—682no—
672C2×C4—681no—
673C2×C4—682no—
674C2×C4—681no—
675C2×C4—682no—
676C2×C4—682no—
677C2×C4C4×C22⋊D1714yes—
678C2×C4#1058762118yes—
679C2×C4#1058762214yes—
680C2×C4#1058762414yes—
681C2×C4#1058762518yes—
682C2×C4#1058763914yes—
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—
698C22C4×D4×D1711yescharacteristic
699C22C2×C4×C22⋊D1711yescharacteristic
700C22C2×C4×C22⋊D1712yes—
701C22C4×#6325411yescharacteristic
702C22C4×#6325412yes—
703C22C2×#1058763911yescharacteristic
704C22C2×#1058762411yescharacteristic
705C22C2×#1058762512yes—
706C22C2×#1058762112yes—
707C22#1176331612yes—
708C22#1176331611yescharacteristic
709C22#1176331812yes—
710C22#1176332011yescharacteristic
711C22#1176332012yes—
712C22C2×#1058762211yescharacteristic
713C22#1176333912yes—
714C22#1176333912yes—
715C22#1176333912yes—
716C22#1176334112yes—
717C22#1176334111yescharacteristic
718C22#1176335511yescharacteristic
719C22#1176335512yes—
720C22#1176335611yescharacteristic
721C4—24no—
722C4—44no—
723C4—42no—
724C4—344no—
725C4—682no—
726C4—682no—
727C4—684no—
728C4—682no—
729C4—684no—
730C4#1176272318yesdirect product factor
731C2—48no—
732C2C4×#1058763911yescharacteristic
733C2C4×#1058762411yescharacteristic
734C2C4×#1058762512yes—
735C2C4×#1058762112yes—
736C2C4×#1058762211yescharacteristic
737C2C2×#1176272311yescharacteristic
738C2#1453199711yescharacteristic
739C2#1453202211yescharacteristic
740C2#1453202612yes—
741C2#1453204312yes—
742C2#1453206811yescharacteristic
subgroupG/H
centerC23×C4C22×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC22×C4×D4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC22×C4×D4D17
hypocenterC17C4×#394
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63225C2semidirect
3. C2×C4×C22⋊Dic17C2semidirect
4. C2×C4×C22⋊Dic17C2semidirect
5. #14527043C2semidirect
6. #14527034C2semidirect
7. #14527031C2semidirect
8. #14527027C2semidirect
10. C4×#10587502C2semidirect
21. #11762723C4direct (N × H)
82. C2×C22⋊Dic17C2×C4semidirect
83. C2×C22⋊Dic17C2×C4semidirect
89. C2×#63225C2×C4semidirect
97. C2×C4×Dic17D4semidirect
106. #10587502C2×C4semidirect
311. C2×Dic17C4×D4semidirect
364. C4×C17#394semidirect
478. C17C4×#394semidirect
730. C4#11762723direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117627232
C2×C4×#632252
C2×C4×C22⋊Dic172
#145270432
#145270342
#145270312
#145270272
#145270252
C4×#105875022
C22×C4×D4×C172
C4×#39417