Finite Group Databasebeta

← #16939554

Subgroups — #16939554

Order 4352.

1414 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D17C211yesmaximal, characteristic
2C2×#11762772C211yesmaximal, characteristic
3#14531163C211yesmaximal, characteristic
4C2×#11762566C211yesmaximal, characteristic, complemented
5C2×#11762565C211yesmaximal, characteristic, complemented
6C2×#11762565C211yesmaximal, characteristic, complemented
7C2×C17×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C2×#10587612C2211yescharacteristic
11C2×#10587612C2211yescharacteristic
12C2×#10587578—21no—
13C2×#10587558C412yescomplemented
14C2×#10587563—21no—
15#117×D17—22no—
16#117×D17—22no—
17#117×D17—22no—
18#117×D17—22no—
19C2×C4⋊C4×D17—21no—
20C2×C22⋊C4×D17—21no—
21C2×C42×D17C412yescomplemented
22#11762772—21no—
23#11762772—21no—
24#11762772—22no—
25C2×#10587491C414yescomplemented
26#11762670—21no—
27#11762666—22no—
28#11762664—21no—
29C4×#63227C414yescomplemented
30#11762566—22no—
31#11762565—22no—
32#11762565—22no—
33C22×M16×C17C2211yescharacteristic
34C2×C17×#117C2211yescharacteristic
35C2×C17×#117C2211yescharacteristic
36C17×H(3,ℤ/4)—22no—
37C24×D17D411yescharacteristic
38C23×C4×C17C2311yescharacteristic
39C23×Dic17D411yescharacteristic
40C22×C4×D17—21no—
41C22×C4×D17—21no—
42C22×C4×D17—21no—
43C22×C4×D17—21no—
44C22×C4×D17—21no—
45C22×C4×D17—21no—
46C22×C4×D17—21no—
47C22×C4×D17—21no—
48C22×C4×D17—22no—
49C22×C4×D17C2×C412yes—
50C22×C4×D17C2×C411yescharacteristic
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2×C412yes—
53C22×C4×D17D411yescharacteristic
54C22×C4×D17D411yescharacteristic
55C22×C4×D17D412yes—
56C22×C4×D17Q812yes—
57C2×M16×C17—21no—
58C2×M16×C17—21no—
59C2×M16×C17—21no—
60C2×M16×C17—21no—
61C2×M16×C17—21no—
62C2×M16×C17—21no—
63C22×C8×C17C2×C412yescomplemented
64C17×#117—21no—
65C17×#117—21no—
66C17×#117—21no—
67C17×#117—21no—
68C17×#117—21no—
69C17×#117—21no—
70C17×#117D412yes—
71C17×#117D412yes—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17—21no—
74C2×C22⋊C4×C17—21no—
75C2×C22⋊C4×C17—21no—
76C2×C42×C17C2×C412yes—
77C2×C42×C17C2×C412yescomplemented
78C2×C22⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80C2×#63227—22no—
81C2×#63227—24no—
82#10587612—21no—
83#10587612—21no—
84#10587612—21no—
85#10587612—21no—
86#10587612—21no—
87#10587612—21no—
88#10587612D412yes—
89#10587612D412yes—
90C2×C4⋊Dic17—21no—
91C2×C4⋊Dic17—21no—
92C2×#63225—22no—
93C2×C4×Dic17—22no—
94C2×C4×Dic17C2×C412yes—
95C2×C4×Dic17C2×C412yescomplemented
96C2×#63223—21no—
97C2×#63223—21no—
98C2×#63223—21no—
99C2×#63223—21no—
100C2×#63223—21no—
101C2×#63223—21no—
102C22×#3622C2×C412yescomplemented
103#10587578—24no—
104#10587578—24no—
105C4⋊C4×D17—24no—
106C4⋊C4×D17—24no—
107C22⋊C4×D17—24no—
108C22⋊C4×D17—24no—
109#10587563—24no—
110#10587563—24no—
111#10587558—24no—
112#10587558—24no—
113C42×D17—24no—
114C42×D17—24no—
115#10587502—24no—
116#10587491—24no—
117#10587491—24no—
118C24×C17C2×D411yescharacteristic
119C23×D17—21no—
120C23×D17—21no—
121C23×D17—21no—
122C23×D17—21no—
123C23×D17—44no—
124C23×D17C22⋊C411yescharacteristic
125C23×D17C22⋊C412yes—
126C23×D17C22⋊C411yescharacteristic
127C23×D17C4⋊C412yes—
128C22×C4×C17—22no—
129C22×C4×C17—22no—
130C22×C4×C17C22×C411yescharacteristic
131C22×C4×C17C22×C411yescharacteristic
132C22×C4×C17C22×C411yescharacteristic
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17C2×D411yescharacteristic
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2×Q811yescharacteristic
140C22×C4×C17#4111yescharacteristic
141C22×C4×C17#4111yescharacteristic
142C22×C4×C17#4111yescharacteristic
143C22×C4×C17#4111yescharacteristic
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—21no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17C22⋊C412yes—
151C22×Dic17C22⋊C411yescharacteristic
152C22×Dic17C22⋊C411yescharacteristic
153C22×Dic17C4⋊C412yes—
154C2×C4×D17—21no—
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×C4×D17—21no—
159C2×C4×D17—21no—
160C2×C4×D17—21no—
161C2×C4×D17—21no—
162C2×C4×D17—22no—
163C2×C4×D17—22no—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17—22no—
167C2×C4×D17—22no—
168C2×C4×D17—22no—
169C2×C4×D17—22no—
170C2×C4×D17—21no—
171C2×C4×D17—21no—
172C2×C4×D17—21no—
173C2×C4×D17—21no—
174C2×C4×D17—22no—
175C2×C4×D17—22no—
176C2×C4×D17—22no—
177C2×C4×D17—22no—
178C2×C4×D17—22no—
179C2×C4×D17—22no—
180C2×C4×D17—22no—
181C2×C4×D17—22no—
182C2×C4×D17—21no—
183C2×C4×D17—21no—
184C2×C4×D17—21no—
185C2×C4×D17—21no—
186C2×C4×D17—28no—
187C2×C4×D17—48no—
188C2×C4×D17C4212yes—
189C2×C4×D17C4212yes—
190C2×C4×D17C22⋊C412yes—
191C2×C4×D17C22⋊C412yes—
192C2×C4×D17C4⋊C412yes—
193C2×C4×D17C4⋊C412yes—
194C2×C4×D17C4⋊C412yes—
195C2×C4×D17C4⋊C412yes—
196M16×C17—41no—
197M16×C17—41no—
198M16×C17—41no—
199M16×C17—41no—
200C2×C8×C17—22no—
201C2×C8×C17—22no—
202C2×C8×C17—22no—
203C4⋊C4×C17—22no—
204C4⋊C4×C17—22no—
205C4⋊C4×C17—41no—
206C4⋊C4×C17—41no—
207C22⋊C4×C17—22no—
208C22⋊C4×C17—22no—
209C22⋊C4×C17—41no—
210C22⋊C4×C17—41no—
211C42×C17—22no—
212C42×C17—22no—
213C42×C17—22no—
214C42×C17C22⋊C414yescomplemented
215C22⋊Dic17—22no—
216C22⋊Dic17—22no—
217C22⋊Dic17—41no—
218C22⋊Dic17—41no—
219#63227—28no—
220#63227—48no—
221C4⋊Dic17—22no—
222C4⋊Dic17—22no—
223C4⋊Dic17—41no—
224C4⋊Dic17—41no—
225#63225—28no—
226C4×Dic17—28no—
227C4×Dic17—22no—
228C4×Dic17—22no—
229C4×Dic17—22no—
230C4×Dic17C22⋊C414yescomplemented
231#63223—41no—
232#63223—41no—
233#63223—41no—
234#63223—41no—
235C2×#3622—22no—
236C2×#3622—22no—
237C2×#3622—22no—
238#10716—171nomaximal, Sylow
239C23×C17—42no—
240C23×C17C2×C22⋊C411yescharacteristic
241C23×C17C2×C22⋊C411yescharacteristic
242C23×C17C2×C4⋊C411yescharacteristic
243C23×C17#12011yescharacteristic
244C23×C17#12011yescharacteristic
245C23×C17#12311yescharacteristic
246C23×C17#12311yescharacteristic
247C22×D17—21no—
248C22×D17—21no—
249C22×D17—24no—
250C22×D17—21no—
251C22×D17—21no—
252C22×D17—22no—
253C22×D17—22no—
254C22×D17—22no—
255C22×D17—22no—
256C22×D17—24no—
257C22×D17—24no—
258C22×D17—42no—
259C22×D17—42no—
260C22×D17—42no—
261C22×D17—44no—
262C22×D17—44no—
263C22×D17—44no—
264C22×D17—44no—
265C22×D17#9512yes—
266C22×D17#9512yes—
267C2×C4×C17—24no—
268C2×C4×C17—44no—
269C2×C4×C17—44no—
270C2×C4×C17—42no—
271C2×C4×C17C2×C4211yescharacteristic
272C2×C4×C17C2×C22⋊C411yescharacteristic
273C2×C4×C17C2×C22⋊C411yescharacteristic
274C2×C4×C17C2×C22⋊C411yescharacteristic
275C2×C4×C17C2×C4⋊C411yescharacteristic
276C2×C4×C17C2×C4⋊C411yescharacteristic
277C2×C4×C17#11711yescharacteristic
278C2×C4×C17#11711yescharacteristic
279C2×C4×C17C4×D411yescharacteristic
280C2×C4×C17C4×D411yescharacteristic
281C2×C4×C17C4×D411yescharacteristic
282C2×C4×C17C4×D411yescharacteristic
283C2×C4×C17C4×D411yescharacteristic
284C2×C4×C17C4×D411yescharacteristic
285C2×C4×C17C4×D411yescharacteristic
286C2×C4×C17C4×D411yescharacteristic
287C2×C4×C17#12011yescharacteristic
288C2×C4×C17#12011yescharacteristic
289C2×C4×C17#12111yescharacteristic
290C2×C4×C17#12111yescharacteristic
291C2×C4×C17#12111yescharacteristic
292C2×C4×C17#12111yescharacteristic
293C2×C4×C17C22⋊Q811yescharacteristic
294C2×C4×C17C22⋊Q811yescharacteristic
295C2×C4×C17C22⋊Q811yescharacteristic
296C2×C4×C17C22⋊Q811yescharacteristic
297C2×C4×C17#12311yescharacteristic
298C2×C4×C17#12311yescharacteristic
299C2×Dic17—21no—
300C2×Dic17—21no—
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—24no—
308C2×Dic17—44no—
309C2×Dic17—44no—
310C2×Dic17—42no—
311C2×Dic17#9512yes—
312C2×Dic17#9512yes—
313C4×D17—22no—
314C4×D17—22no—
315C4×D17—22no—
316C4×D17—22no—
317C4×D17—22no—
318C4×D17—22no—
319C4×D17—22no—
320C4×D17—22no—
321C4×D17—22no—
322C4×D17—22no—
323C4×D17—22no—
324C4×D17—22no—
325C4×D17—22no—
326C4×D17—22no—
327C4×D17—22no—
328C4×D17—22no—
329C4×D17—416no—
330C8×C17—42no—
331#3622—42no—
332C22×#117—171no—
333C2×#407—171no—
334#2280—171no—
335C2×H(3,ℤ/4)—171no—
336C2×H(3,ℤ/4)—171no—
337C2×H(3,ℤ/4)—171no—
338C2×H(3,ℤ/4)D1711yescharacteristic, complemented
339C22×C17—22no—
340C22×C17—22no—
341C22×C17—22no—
342C22×C17—41no—
343C22×C17—41no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17C2×#9511yescharacteristic
347C22×C17#37911yescharacteristic
348C22×C17#38111yescharacteristic
349C22×C17#38511yescharacteristic
350C22×C17#38511yescharacteristic
351C22×C17#38611yescharacteristic
352C22×C17#38611yescharacteristic
353C2×D17—24no—
354C2×D17—24no—
355C2×D17—22no—
356C2×D17—22no—
357C2×D17—22no—
358C2×D17—22no—
359C2×D17—22no—
360C2×D17—44no—
361C2×D17—44no—
362C2×D17—44no—
363C2×D17—44no—
364C2×D17—42no—
365C2×D17—42no—
366C2×D17H(3,ℤ/4)14yescomplemented
367C4×C17—44no—
368C4×C17—82no—
369C4×C17C4×C22⋊C411yescharacteristic
370C4×C17C4×C22⋊C411yescharacteristic
371C4×C17#38011yescharacteristic
372C4×C17#38011yescharacteristic
373C4×C17#38511yescharacteristic
374C4×C17#38511yescharacteristic
375C4×C17#38611yescharacteristic
376C4×C17#38611yescharacteristic
377Dic17—22no—
378Dic17—22no—
379Dic17—44no—
380Dic17—82no—
381C24×C4—171no—
382C22×M16—171no—
383C22×M16C2×D1711yescharacteristic
384C2×#117—171no—
385C2×#117—171no—
386C2×#117—172no—
387C2×#117—341no—
388C2×#117—341no—
389C2×#117—342no—
390C2×#117—342no—
391C2×#117—342no—
392C2×#117—342no—
393C2×#117C2×D1711yescharacteristic
394C2×#117C2×D1711yescharacteristic
395C22×C4⋊C4—341no—
396C22×C22⋊C4—341no—
397C22×C42—172no—
398#407—341no—
399#407—341no—
400#407—342no—
401C2×C22⋊C8—174no—
402#381—341no—
403#380—342no—
404#379—341no—
405C4×C22⋊C4—174no—
406H(3,ℤ/4)—22no—
407H(3,ℤ/4)—342no—
408H(3,ℤ/4)—342no—
409H(3,ℤ/4)—342no—
410C2×C17—21no—
411C2×C17—21no—
412C2×C17—21no—
413C2×C17—21no—
414C2×C17—21no—
415C2×C17—21no—
416C2×C17C22⋊#9511yescharacteristic
417C2×C17C2×H(3,ℤ/4)12yes—
418D17—24no—
419D17—42no—
420C25—171no—
421C23×C4—171no—
422C23×C4—171no—
423C23×C4—172no—
424C23×C4—172no—
425C23×C4—171no—
426C23×C4—171no—
427C23×C4—171no—
428C23×C4—172no—
429C23×C4—172no—
430C23×C4—342no—
431C23×C4—341no—
432C23×C4—341no—
433C23×C4—341no—
434C23×C4—341no—
435C23×C4—341no—
436C23×C4—341no—
437C23×C4—341no—
438C23×C4—341no—
439C23×C4C22×D1711yescharacteristic
440C2×M16—21no—
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—341no—
447C2×M16—341no—
448C2×M16—341no—
449C2×M16—341no—
450C2×M16—341no—
451C2×M16—341no—
452C22×C8—172no—
453C22×C8C4×D1712yescomplemented
454#117—21no—
455#117—21no—
456#117—21no—
457#117—21no—
458#117—21no—
459#117—21no—
460#117—172no—
461#117—172no—
462#117—344no—
463#117—344no—
464#117—344no—
465#117—344no—
466#117—344no—
467#117—341no—
468#117—341no—
469#117—341no—
470#117—341no—
471#117—341no—
472#117—341no—
473#117—344no—
474#117D6812yes—
475#117C22⋊D1712yes—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—344no—
479C2×C4⋊C4—344no—
480C2×C4⋊C4—342no—
481C2×C4⋊C4—341no—
482C2×C4⋊C4—341no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—344no—
486C2×C22⋊C4—344no—
487C2×C22⋊C4—342no—
488C2×C22⋊C4—341no—
489C2×C22⋊C4—344no—
490C2×C22⋊C4—341no—
491C2×C42—172no—
492C2×C42—172no—
493C2×C42—344no—
494C2×C42—342no—
495C2×C42—344no—
496C2×C42C4×D1712yes—
497C2×C42C4×D1712yescomplemented
498C22⋊C8—344no—
499C22⋊C8—344no—
500#95—344no—
501C17#1071611yescharacteristic, complemented, Sylow
502C24—171no—
503C24—172no—
504C24—172no—
505C24—171no—
506C24—341no—
507C24—341no—
508C24—341no—
509C24—341no—
510C24—684no—
511C24D4×D1711yescharacteristic
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—172no—
515C22×C4—171no—
516C22×C4—171no—
517C22×C4—172no—
518C22×C4—172no—
519C22×C4—172no—
520C22×C4—172no—
521C22×C4—172no—
522C22×C4—172no—
523C22×C4—172no—
524C22×C4—172no—
525C22×C4—172no—
526C22×C4—348no—
527C22×C4—341no—
528C22×C4—341no—
529C22×C4—341no—
530C22×C4—341no—
531C22×C4—341no—
532C22×C4—341no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4—341no—
536C22×C4—341no—
537C22×C4—342no—
538C22×C4—342no—
539C22×C4—341no—
540C22×C4—341no—
541C22×C4—341no—
542C22×C4—341no—
543C22×C4—342no—
544C22×C4—342no—
545C22×C4—341no—
546C22×C4—341no—
547C22×C4—342no—
548C22×C4—342no—
549C22×C4—341no—
550C22×C4—341no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—342no—
554C22×C4—342no—
555C22×C4—341no—
556C22×C4—341no—
557C22×C4—342no—
558C22×C4—342no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4—342no—
565C22×C4—688no—
566C22×C4C2×C4×D1711yescharacteristic
567C22×C4C2×C4×D1711yescharacteristic
568C22×C4C2×C4×D1711yescharacteristic
569C22×C4C2×D6811yescharacteristic
570C22×C4#6325211yescharacteristic
571C22×C4#6325211yescharacteristic
572C22×C4D4×D1711yescharacteristic
573C22×C4D4×D1711yescharacteristic
574C22×C4D4×D1711yescharacteristic
575C22×C4D4×D1711yescharacteristic
576C22×C4#6325411yescharacteristic
577C22×C4Q8×D1711yescharacteristic
578C22×C4#6325611yescharacteristic
579C22×C4C2×C22⋊D1711yescharacteristic
580M16—41no—
581M16—41no—
582M16—41no—
583M16—41no—
584M16—681no—
585M16—681no—
586M16—681no—
587M16—681no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—342no—
592C2×C8—342no—
593C2×C8—342no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—348no—
599C4⋊C4—342no—
600C4⋊C4—342no—
601C4⋊C4—681no—
602C4⋊C4—681no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—348no—
608C22⋊C4—342no—
609C22⋊C4—342no—
610C22⋊C4—688no—
611C22⋊C4—681no—
612C22⋊C4—681no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—174no—
617C42—348no—
618C42—342no—
619C42—342no—
620C42—342no—
621C42#6322714yescomplemented
622C23—42no—
623C23—172no—
624C23—172no—
625C23—344no—
626C23—344no—
627C23—344no—
628C23—341no—
629C23—341no—
630C23—341no—
631C23—341no—
632C23—342no—
633C23—342no—
634C23—342no—
635C23—342no—
636C23—682no—
637C23—682no—
638C23—682no—
639C23—684no—
640C23—684no—
641C23—684no—
642C23—684no—
643C23C22⋊C4×D1711yescharacteristic
644C23C22⋊C4×D1711yescharacteristic
645C23#1058756811yescharacteristic
646C23#1058756911yescharacteristic
647C23C4⋊C4×D1711yescharacteristic
648C23#1058758011yescharacteristic
649C23#1058762311yescharacteristic
650C2×C4—24no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—42no—
654C2×C4—172no—
655C2×C4—172no—
656C2×C4—341no—
657C2×C4—341no—
658C2×C4—341no—
659C2×C4—341no—
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—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—344no—
681C2×C4—6816no—
682C2×C4—684no—
683C2×C4—684no—
684C2×C4—682no—
685C2×C4C42×D1711yescharacteristic
686C2×C4#1058755811yescharacteristic
687C2×C4C4×D6811yescharacteristic
688C2×C4C4×D6811yescharacteristic
689C2×C4C22⋊C4×D1711yescharacteristic
690C2×C4C22⋊C4×D1711yescharacteristic
691C2×C4#1058756711yescharacteristic
692C2×C4#1058756711yescharacteristic
693C2×C4#1058756811yescharacteristic
694C2×C4#1058756911yescharacteristic
695C2×C4#1058757011yescharacteristic
696C2×C4#1058757011yescharacteristic
697C2×C4C4⋊C4×D1711yescharacteristic
698C2×C4C4⋊C4×D1711yescharacteristic
699C2×C4#1058757811yescharacteristic
700C2×C4#1058757911yescharacteristic
701C2×C4#1058757911yescharacteristic
702C2×C4#1058758011yescharacteristic
703C2×C4#1058758111yescharacteristic
704C2×C4#1058758211yescharacteristic
705C2×C4#1058758211yescharacteristic
706C2×C4#1058758311yescharacteristic
707C2×C4C2×#6322711yescharacteristic
708C2×C4C4×C22⋊D1711yescharacteristic
709C2×C4C4×C22⋊D1711yescharacteristic
710C2×C4#1058762311yescharacteristic
711C2×C4#1058762411yescharacteristic
712C2×C4#1058763211yescharacteristic
713C8—42no—
714C8—682no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—174no—
723C22—344no—
724C22—344no—
725C22—342no—
726C22—342no—
727C22—342no—
728C22—342no—
729C22—342no—
730C22—684no—
731C22—684no—
732C22—684no—
733C22—684no—
734C22—682no—
735C22—682no—
736C22#95×D1711yescharacteristic
737C22#1176266411yescharacteristic
738C22#1176267111yescharacteristic
739C22#1176268011yescharacteristic
740C22#1176268311yescharacteristic
741C22#1176268511yescharacteristic
742C22#1176268711yescharacteristic
743C4—44no—
744C4—82no—
745C4—342no—
746C4—342no—
747C4—684no—
748C4—1362no—
749C4#1176265611yescharacteristic
750C4C4×#6322711yescharacteristic
751C4#1176266611yescharacteristic
752C4#1176266811yescharacteristic
753C4#1176268011yescharacteristic
754C4#1176268311yescharacteristic
755C4#1176268511yescharacteristic
756C4#1176268711yescharacteristic
757C2—21no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—344no—
764C2—682no—
765C2#1452700511yescharacteristic
766C2D17×H(3,ℤ/4)12yes—
subgroupG/H
centerC2×C4C42×D17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×H(3,ℤ/4)C2
socleC22×C17C2×#95
prime radicalC24×D17D4
cosocleC23×C4×C17C23
hypercenterC2×H(3,ℤ/4)D17
hypocenterC17#10716
LCSG ▷ C2×C4×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. C2×#11762566C2semidirect
5. C2×#11762565C2semidirect
6. C2×#11762565C2semidirect
7. C2×C17×H(3,ℤ/4)C2semidirect
13. C2×#10587558C4semidirect
21. C2×C42×D17C4semidirect
25. C2×#10587491C4semidirect
29. C4×#63227C4semidirect
63. C22×C8×C17C2×C4semidirect
77. C2×C42×C17C2×C4semidirect
95. C2×C4×Dic17C2×C4semidirect
102. C22×#3622C2×C4semidirect
214. C42×C17C22⋊C4semidirect
230. C4×Dic17C22⋊C4semidirect
338. C2×H(3,ℤ/4)D17semidirect
366. C2×D17H(3,ℤ/4)semidirect
453. C22×C8C4×D17semidirect
497. C2×C42C4×D17semidirect
501. C17#10716semidirect
621. C42#63227semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D172
C2×#117627722
#145311632
C2×#117625662
C2×#117625652
C2×C17×H(3,ℤ/4)2
#1071617