Finite Group Databasebeta

← #17050698

Subgroups — #17050698

Order 4352.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763514C211yesmaximal, characteristic
2C2×#11762880C211yesmaximal, characteristic
3#14531709C211yesmaximal, characteristic
4#14529755C211yesmaximal, characteristic, complemented
5#14529734C211yesmaximal, characteristic, complemented
6#14529216C211yesmaximal, characteristic, complemented
7#14529207C211yesmaximal, characteristic, complemented
8#14529095C211yesmaximal, characteristic, complemented
9#14529091C211yesmaximal, characteristic, complemented
10#14528874C211yesmaximal, characteristic, complemented
11#14528869C211yesmaximal, characteristic, complemented
12#14528798C211yesmaximal, characteristic, complemented
13#14528613C211yesmaximal, characteristic, complemented
14#14528502C211yesmaximal, characteristic, complemented
15C2×C17×#340C211yesmaximal, characteristic, complemented
16C22×#63218C2211yescharacteristic
17#11763514—24no—
18#11763514C418yescomplemented
19C2×#10587574C2211yescharacteristic
20C2×#10587575—21no—
21C2×#10587583C2211yescharacteristic
22C2×#10587610—21no—
23C2×#10587610C2211yescharacteristic
24C2×#10587582—21no—
25C2×#10587573C2211yescharacteristic
26C2×C4×C22⋊D17—21no—
27C2×C4×C22⋊D17C2211yescharacteristic
28C2×#10587578C2211yescharacteristic
29C2×C4⋊C4×D17C2211yescharacteristic
30#11762880—24no—
31C2×#10587485C2211yescharacteristic
32C2×#10587487C2211yescharacteristic
33C2×#10587487C2211yescharacteristic
34C2×#10587481C2211yescharacteristic
35C2×#10587481C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37C2×#10587491C2211yescharacteristic
38C2×#10587486C2211yescharacteristic
39#11762699—21no—
40#11762690—21no—
41#11762688—21no—
42#11762674C2211yescharacteristic
43#11762669C2211yescharacteristic
44#11762666C2211yescharacteristic
45C4⋊C4×Dic17C2211yescharacteristic
46C4×C22⋊Dic17—21no—
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762571C2211yescharacteristic
54#11762571C2211yescharacteristic
55C23×C8×C17C2211yescharacteristic
56C22×C4⋊C4×C17C2211yescharacteristic
57C22×C4⋊C4×C17C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C17×#340C2211yescharacteristic
60C17×#340C2211yescharacteristic
61C17×#340C2211yescharacteristic
62C23×C4×C17—21no—
63C23×C4×C17—21no—
64C23×C4×C17C2311yescharacteristic
65C22×C22⋊D17D411yescharacteristic
66C22×C4×D17—21no—
67C22×C4×D17C2311yescharacteristic
68C22×Dic34—21no—
69C22×Dic34C2311yescharacteristic
70C22×C8×C17—22no—
71C22×C8×C17—22no—
72C22×C8×C17—41no—
73C22×C8×C17C2311yescharacteristic
74C22×C8×C17C2311yescharacteristic
75C2×C4⋊C4×C17—22no—
76C2×C4⋊C4×C17—21no—
77C2×C4⋊C4×C17—22no—
78C2×C4⋊C4×C17—21no—
79C2×C4⋊C4×C17—41no—
80C2×C4⋊C4×C17C2×C414yes—
81C2×C4⋊C4×C17C2311yescharacteristic
82C2×C4⋊C4×C17C2311yescharacteristic
83C2×C4⋊C4×C17C2311yescharacteristic
84C2×C4⋊C4×C17C2311yescharacteristic
85C2×C22⋊Dic17—21no—
86C2×C22⋊Dic17—21no—
87C2×C22⋊Dic17D411yescharacteristic
88C4×C22⋊D17—28no—
89C4×C22⋊D17C2×C414yes—
90C4×C22⋊D17D414yes—
91C2×#63227—21no—
92C2×#63227—21no—
93C2×#63227—21no—
94C2×#63227D411yescharacteristic
95C2×C4⋊Dic17—21no—
96C2×C4⋊Dic17C2311yescharacteristic
97C2×C4⋊Dic17C2311yescharacteristic
98C2×C4⋊Dic17C2311yescharacteristic
99#10587610—22no—
100#10587610—28no—
101#10587610C2×C414yes—
102C2×#63225—21no—
103C2×#63225—21no—
104C2×#63225—21no—
105C2×#63225—21no—
106C2×#63225D411yescharacteristic
107C2×C4×Dic17—21no—
108C2×C4×Dic17—21no—
109C2×C4×Dic17—21no—
110C2×C4×Dic17C2311yescharacteristic
111C22×#3622C2311yescharacteristic
112C22×#3622C2311yescharacteristic
113C2×#63218—22no—
114C2×#63218—22no—
115C2×#63218—41no—
116#10587583—22no—
117#10587583C2×C414yescomplemented
118#10587582—28no—
119#10587578—22no—
120#10587578—41no—
121C4⋊C4×D17—22no—
122C4⋊C4×D17C2×C414yescomplemented
123#10587575—28no—
124#10587574—22no—
125#10587574C2×C414yescomplemented
126#10587573—22no—
127#10587573C2×C414yescomplemented
128#10587502—21no—
129#10587502—21no—
130#10587502—21no—
131#10587502—21no—
132#10587502—21no—
133C22⋊#3622—22no—
134#10587491—22no—
135#10587487—22no—
136#10587487—41no—
137#10587486—22no—
138#10587485—22no—
139#10587481—22no—
140#10587481—41no—
141C24×C17C2×D411yescharacteristic
142C23×D17C2×D411yescharacteristic
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—24no—
151C22×C4×C17—21no—
152C22×C4×C17—42no—
153C22×C4×C17—42no—
154C22×C4×C17—81no—
155C22×C4×C17—81no—
156C22×C4×C17—81no—
157C22×C4×C17C22×C412yes—
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17C2×D412yes—
160C22×C4×C17C2411yescharacteristic
161C2×C22⋊D17—22no—
162C2×C22⋊D17—22no—
163C2×C22⋊D17C22⋊C414yes—
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17C2×D411yescharacteristic
169C22×Dic17C2×D411yescharacteristic
170C22×Dic17C2×D411yescharacteristic
171C2×C4×D17—21no—
172C2×C4×D17—21no—
173C2×C4×D17—21no—
174C2×C4×D17—21no—
175C2×C4×D17—24no—
176C2×C4×D17—81no—
177C2×C4×D17—81no—
178C2×C4×D17C22×C412yes—
179C2×C4×D17C2×D412yes—
180C2×Dic34—21no—
181C2×Dic34—21no—
182C2×Dic34—21no—
183C2×Dic34—21no—
184C2×Dic34—21no—
185C2×Dic34—24no—
186C2×Dic34—81no—
187C2×Dic34—81no—
188C2×Dic34C22×C412yes—
189C2×C8×C17—21no—
190C2×C8×C17—21no—
191C2×C8×C17—21no—
192C2×C8×C17—21no—
193C2×C8×C17—21no—
194C2×C8×C17—44no—
195C2×C8×C17#4112yes—
196C4⋊C4×C17—24no—
197C4⋊C4×C17—21no—
198C4⋊C4×C17—21no—
199C4⋊C4×C17—21no—
200C4⋊C4×C17—21no—
201C4⋊C4×C17—21no—
202C4⋊C4×C17—42no—
203C4⋊C4×C17C22×C412yes—
204C4⋊C4×C17C22×C412yes—
205C4⋊C4×C17#4112yes—
206C22⋊Dic17—24no—
207C22⋊Dic17—42no—
208C22⋊Dic17C22⋊C414yes—
209#63227—24no—
210#63227—42no—
211#63227—81no—
212#63227C22⋊C414yes—
213C4⋊Dic17—21no—
214C4⋊Dic17—24no—
215C4⋊Dic17—21no—
216C4⋊Dic17—21no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17C22×C412yes—
220#63225—24no—
221#63225—24no—
222#63225—24no—
223#63225—24no—
224#63225C22⋊C414yes—
225C4×Dic17—24no—
226C4×Dic17—42no—
227C4×Dic17—81no—
228C4×Dic17C22×C412yes—
229C4×Dic17C2×D412yes—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236#63218—44no—
237#22497—171nomaximal, Sylow
238C23×C17—21no—
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—21no—
242C23×C17C2×C22⋊C412yes—
243C23×C17#13712yes—
244C23×C17#13712yes—
245C23×C17C22×D411yescharacteristic
246C22×D17—21no—
247C22×D17—21no—
248C22×D17—21no—
249C22×D17—21no—
250C22×D17—21no—
251C22×D17—21no—
252C22×D17C2×C22⋊C412yes—
253C2×C4×C17—21no—
254C2×C4×C17—21no—
255C2×C4×C17—22no—
256C2×C4×C17—22no—
257C2×C4×C17—22no—
258C2×C4×C17—22no—
259C2×C4×C17—22no—
260C2×C4×C17—22no—
261C2×C4×C17—22no—
262C2×C4×C17—41no—
263C2×C4×C17—41no—
264C2×C4×C17—41no—
265C2×C4×C17—41no—
266C2×C4×C17—41no—
267C2×C4×C17—41no—
268C2×C4×C17—41no—
269C2×C4×C17—41no—
270C2×C4×C17—41no—
271C2×C4×C17—84no—
272C2×C4×C17—84no—
273C2×C4×C17C2×C22⋊C412yes—
274C2×C4×C17C23×C411yescharacteristic
275C2×C4×C17C22×D411yescharacteristic
276C2×C4×C17C2×#4111yescharacteristic
277C2×C4×C17C2×#4111yescharacteristic
278C2×C4×C17H(5,𝔽2)11yescharacteristic
279C2×C4×C172−1+411yescharacteristic
280C22⋊D17—28no—
281C2×Dic17—21no—
282C2×Dic17—21no—
283C2×Dic17—21no—
284C2×Dic17—21no—
285C2×Dic17—21no—
286C2×Dic17—21no—
287C2×Dic17—22no—
288C2×Dic17—22no—
289C2×Dic17—41no—
290C2×Dic17—41no—
291C2×Dic17—41no—
292C2×Dic17—41no—
293C2×Dic17—41no—
294C2×Dic17—41no—
295C2×Dic17—41no—
296C2×Dic17—41no—
297C2×Dic17—41no—
298C2×Dic17—41no—
299C2×Dic17C2×C22⋊C412yes—
300C2×Dic17C2×C22⋊C412yes—
301C2×Dic17C2×C22⋊C412yes—
302C4×D17—22no—
303C4×D17—22no—
304C4×D17—22no—
305C4×D17—22no—
306C4×D17—84no—
307Dic34—22no—
308Dic34—22no—
309Dic34—41no—
310Dic34—41no—
311Dic34—84no—
312C8×C17—22no—
313C8×C17—41no—
314#3622—41no—
315#3622—41no—
316C2×#554—171no—
317C2×#435—171no—
318#2352—171no—
319#1993—171no—
320#1988—171no—
321#1894—171no—
322#1892—171no—
323#1873—171no—
324#1872—171no—
325#1824—171no—
326#1823—171no—
327#1805—171no—
328#1763—171no—
329#1736—171no—
330C2×#340D1711yescharacteristic, complemented
331C22×C17—22no—
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17#41914yes—
338C22×C17C22×C22⋊C411yescharacteristic
339C22×C17#54611yescharacteristic
340C22×C17#54711yescharacteristic
341C22×C17C2×#13711yescharacteristic
342C22×C17C2×#13711yescharacteristic
343C22×C17#57611yescharacteristic
344C22×C17#57711yescharacteristic
345C2×D17—22no—
346C2×D17—22no—
347C2×D17—22no—
348C2×D17—41no—
349C2×D17—41no—
350C2×D17—41no—
351C2×D17—41no—
352C4×C17—22no—
353C4×C17—42no—
354C4×C17—42no—
355C4×C17—42no—
356C4×C17—81no—
357C4×C17C4×#4111yescharacteristic
358C4×C17#52011yescharacteristic
359C4×C17#54611yescharacteristic
360C4×C17#54711yescharacteristic
361Dic17—22no—
362Dic17—22no—
363Dic17—22no—
364Dic17—42no—
365Dic17—42no—
366Dic17—81no—
367Dic17—81no—
368C22×M16—171no—
369C23×C8C2×D1711yescharacteristic
370#554—178no—
371#554—344no—
372C2×C4⋊Q8—171no—
373C2×#125—341no—
374C2×C22⋊Q8—171no—
375C2×C22⋊Q8—171no—
376C2×C22⋊Q8—341no—
377C2×C22⋊Q8—341no—
378C2×C4×Q8—171no—
379C2×C4×D4—171no—
380C2×C4×D4—341no—
381C2×#117—171no—
382C22×C4⋊C4—171no—
383C22×C4⋊C4C2×D1711yescharacteristic
384C22×C4⋊C4C2×D1711yescharacteristic
385#435—344no—
386C2×C4⋊C8—171no—
387C2×#103—171no—
388C2×#103—171no—
389C2×#103—171no—
390C2×#103—171no—
391C2×C22⋊C8—171no—
392C2×C22⋊C8—171no—
393C2×#97—171no—
394#388—341no—
395#387—341no—
396#386—341no—
397#382—171no—
398#380—171no—
399#380—171no—
400C4×C4⋊C4—171no—
401C4×C22⋊C4—341no—
402#340—171no—
403#340—171no—
404#340—171no—
405#340—171no—
406#340—171no—
407#340—171no—
408#340—171no—
409#340—171no—
410#340C2×D1711yescharacteristic
411#340C2×D1711yescharacteristic
412#340C2×D1711yescharacteristic
413#340C2×D1711yescharacteristic
414C2×C17—24no—
415C2×C17#233911yescharacteristic
416C2×C17C2×#41911yescharacteristic
417C2×C17#289711yescharacteristic
418C2×C17#331411yescharacteristic
419C2×C17#331611yescharacteristic
420C2×C17#334411yescharacteristic
421C2×C17#334611yescharacteristic
422D17—42no—
423C22×Q8—171no—
424C22×Q8—341no—
425C22×D4—171no—
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—171no—
429C23×C4—341no—
430C23×C4C22×D1711yescharacteristic
431C2×M16—342no—
432C2×M16—342no—
433C2×M16—681no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—41no—
437C22×C8—171no—
438C22×C8—171no—
439C22×C8C22×D1711yescharacteristic
440C22×C8C22×D1711yescharacteristic
441C4⋊Q8—174no—
442C4⋊Q8—342no—
443#125—348no—
444C22⋊Q8—174no—
445C22⋊Q8—174no—
446C22⋊Q8—348no—
447C22⋊Q8—348no—
448C22⋊Q8—342no—
449C22⋊Q8—342no—
450C4×Q8—174no—
451C4×Q8—342no—
452C4×D4—174no—
453C4×D4—174no—
454C4×D4—348no—
455#117—342no—
456#117—681no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—171no—
463C2×C4⋊C4—171no—
464C2×C4⋊C4—174no—
465C2×C4⋊C4—171no—
466C2×C4⋊C4—171no—
467C2×C4⋊C4—342no—
468C2×C4⋊C4—341no—
469C2×C4⋊C4—341no—
470C2×C4⋊C4—341no—
471C2×C4⋊C4—341no—
472C2×C4⋊C4—341no—
473C2×C4⋊C4C4×D1714yes—
474C2×C4⋊C4C22×D1711yescharacteristic
475C2×C4⋊C4C22×D1711yescharacteristic
476C2×C4⋊C4C22×D1711yescharacteristic
477C2×C4⋊C4C22×D1711yescharacteristic
478C2×C22⋊C4—171no—
479C2×C22⋊C4—171no—
480C2×C22⋊C4—341no—
481C2×C22⋊C4—341no—
482C2×C22⋊C4—341no—
483C2×C22⋊C4—341no—
484C2×C22⋊C4—341no—
485C2×C42—171no—
486C2×C42—341no—
487C2×C42—341no—
488C2×C42—341no—
489C4⋊C8—342no—
490#103—342no—
491#103—342no—
492#103—681no—
493#103—681no—
494C22⋊C8—342no—
495C22⋊C8—342no—
496#97—342no—
497#95—341no—
498#95—341no—
499#95—341no—
500#95—341no—
501#95—341no—
502C17#2249711yescharacteristic, complemented, Sylow
503C24—171no—
504C24D4×D1711yescharacteristic
505C2×Q8—172no—
506C2×Q8—344no—
507C2×Q8—341no—
508C2×Q8—341no—
509C2×Q8—341no—
510C2×Q8—341no—
511C2×Q8—341no—
512C2×Q8—1361no—
513C2×Q8—1361no—
514C2×D4—174no—
515C2×D4—342no—
516C2×D4—342no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—171no—
532C22×C4—171no—
533C22×C4—171no—
534C22×C4—172no—
535C22×C4—172no—
536C22×C4—344no—
537C22×C4—341no—
538C22×C4—341no—
539C22×C4—341no—
540C22×C4—341no—
541C22×C4—341no—
542C22×C4—341no—
543C22×C4—341no—
544C22×C4—341no—
545C22×C4—1361no—
546C22×C4—1361no—
547C22×C4C2×C4×D1712yes—
548C22×C4D4×D1712yes—
549C22×C4D4×D1711yescharacteristic
550C22×C4C23×D1711yescharacteristic
551M16—684no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—44no—
558C2×C8—341no—
559C2×C8—341no—
560C2×C8—341no—
561C2×C8—341no—
562C2×C8—341no—
563C2×C8—341no—
564C2×C8#6325212yes—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—24no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—174no—
573C4⋊C4—172no—
574C4⋊C4—344no—
575C4⋊C4—344no—
576C4⋊C4—344no—
577C4⋊C4—344no—
578C4⋊C4—341no—
579C4⋊C4—344no—
580C4⋊C4—341no—
581C4⋊C4—341no—
582C4⋊C4—341no—
583C4⋊C4—341no—
584C4⋊C4C2×C4×D1712yes—
585C4⋊C4C2×C4×D1712yes—
586C4⋊C4#6325212yes—
587C22⋊C4—174no—
588C22⋊C4—174no—
589C22⋊C4—344no—
590C22⋊C4—344no—
591C22⋊C4—682no—
592C22⋊C4—682no—
593C22⋊C4—1361no—
594C42—172no—
595C42—172no—
596C42—344no—
597C42—682no—
598C42—1361no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—172no—
604C23—341no—
605C23—341no—
606C23—341no—
607C23—341no—
608C23—341no—
609C23—341no—
610C23C22⋊C4×D1712yes—
611C23#1058760112yes—
612C23#1058760412yes—
613C23C2×D4×D1711yescharacteristic
614Q8—342no—
615Q8—342no—
616Q8—681no—
617Q8—681no—
618Q8—1364no—
619D4—348no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—84no—
639C2×C4—84no—
640C2×C4—172no—
641C2×C4—172no—
642C2×C4—172no—
643C2×C4—341no—
644C2×C4—341no—
645C2×C4—341no—
646C2×C4—341no—
647C2×C4—341no—
648C2×C4—341no—
649C2×C4—342no—
650C2×C4—342no—
651C2×C4—342no—
652C2×C4—342no—
653C2×C4—342no—
654C2×C4—342no—
655C2×C4—681no—
656C2×C4—681no—
657C2×C4—681no—
658C2×C4—681no—
659C2×C4—681no—
660C2×C4—681no—
661C2×C4—681no—
662C2×C4—681no—
663C2×C4—681no—
664C2×C4—681no—
665C2×C4—1364no—
666C2×C4C22⋊C4×D1712yes—
667C2×C4C22×C4×D1711yescharacteristic
668C2×C4C2×#6325211yescharacteristic
669C2×C4C2×#6325211yescharacteristic
670C2×C4C2×D4×D1711yescharacteristic
671C2×C4#1058769111yescharacteristic
672C2×C4#1058769411yescharacteristic
673C8—22no—
674C8—41no—
675C8—681no—
676C8—681no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—342no—
684C22—342no—
685C22—342no—
686C22—681no—
687C22—681no—
688C22—681no—
689C22—681no—
690C22#1176281614yes—
691C22C2×C22⋊C4×D1711yescharacteristic
692C22#1176344911yescharacteristic
693C22#1176346011yescharacteristic
694C22C2×#1058760111yescharacteristic
695C22C2×#1058760411yescharacteristic
696C22#1176361011yescharacteristic
697C22#1176361511yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—342no—
704C4—342no—
705C4—342no—
706C4—682no—
707C4—682no—
708C4—1361no—
709C4—1361no—
710C4C4×#6325211yescharacteristic
711C4#1176329011yescharacteristic
712C4#1176344911yescharacteristic
713C4#1176346011yescharacteristic
714C2—24no—
715C2—682no—
716C2#1453161111yescharacteristic
717C2C2×#1176281611yescharacteristic
718C2#1453730511yescharacteristic
719C2#1454086111yescharacteristic
720C2#1454089111yescharacteristic
721C2#1454123511yescharacteristic
722C2#1454126511yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#340C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
cosocleC22×C4×C17C24
hypercenterC2×#340D17
hypocenterC17#22497
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #14529755C2semidirect
5. #14529734C2semidirect
6. #14529216C2semidirect
7. #14529207C2semidirect
8. #14529095C2semidirect
9. #14529091C2semidirect
10. #14528874C2semidirect
11. #14528869C2semidirect
12. #14528798C2semidirect
13. #14528613C2semidirect
14. #14528502C2semidirect
15. C2×C17×#340C2semidirect
18. #11763514C4semidirect
117. #10587583C2×C4semidirect
122. C4⋊C4×D17C2×C4semidirect
125. #10587574C2×C4semidirect
127. #10587573C2×C4semidirect
330. C2×#340D17semidirect
502. C17#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#117635142
C2×#117628802
#145317092
#145297552
#145297342
#145292162
#145292072
#145290952
#145290912
#145288742
#145288692
#145287982
#145286132
#145285022
C2×C17×#3402
#2249717