Finite Group Databasebeta

← #16939612

Subgroups — #16939612

Order 4352.

1550 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D17C211yesmaximal, characteristic
2C2×#11762772C211yesmaximal, characteristic
3C2×C4×#63227C211yesmaximal, characteristic
4C2×#11762570C211yesmaximal, characteristic, complemented
5C2×#11762569C211yesmaximal, characteristic, complemented
6C2×#11762568C211yesmaximal, characteristic, complemented
7C2×C17×#339C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C2×#10587612C2211yescharacteristic
11C2×#10587578C412yescomplemented
12C2×#10587558—21no—
13C2×#10587563—21no—
14#117×D17—22no—
15#117×D17—22no—
16#117×D17—22no—
17#117×D17—22no—
18C2×C4⋊C4×D17C412yescomplemented
19C22×#63227—21no—
20C2×C22⋊C4×D17—21no—
21C22×C4×Dic17C2211yescharacteristic
22C2×C42×D17—21no—
23#11762772—22no—
24#11762772C414yescomplemented
25C2×#10587491—21no—
26C2×#10587491—21no—
27C4×#63227—22no—
28C4×#63227C414yescomplemented
29C2×#10587502—21no—
30#11762570—22no—
31#11762569—22no—
32#11762568—22no—
33C22×M16×C17C2211yescharacteristic
34C2×C17×#117C2211yescharacteristic
35C22×C42×C17C2211yescharacteristic
36C17×#339—22no—
37C24×D17D411yescharacteristic
38C23×C4×C17—21no—
39C23×C4×C17C2311yescharacteristic
40C23×Dic17—21no—
41C23×Dic17D411yescharacteristic
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—21no—
49C22×C4×D17—21no—
50C22×C4×D17—22no—
51C22×C4×D17C2×C412yes—
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2×C412yes—
55C22×C4×D17D411yescharacteristic
56C22×C4×D17D411yescharacteristic
57C22×C4×D17D412yes—
58C22×C4×D17Q812yes—
59C2×M16×C17—21no—
60C2×M16×C17—21no—
61C2×M16×C17—21no—
62C2×M16×C17—21no—
63C2×M16×C17—21no—
64C2×M16×C17C2×C412yescomplemented
65C22×C8×C17—21no—
66C17×#117—21no—
67C17×#117—21no—
68C17×#117D412yes—
69C17×#117D412yes—
70C2×C4⋊C4×C17C2×C412yes—
71C2×C22⋊C4×C17—21no—
72C2×C42×C17—21no—
73C2×C42×C17—21no—
74C2×C42×C17—21no—
75C2×C42×C17—21no—
76C2×C42×C17—21no—
77C2×C42×C17—21no—
78C2×C42×C17C2×C412yescomplemented
79C2×C22⋊Dic17—21no—
80C2×#63227—28no—
81C2×#63227—22no—
82C2×#63227—24no—
83#10587612—21no—
84#10587612—21no—
85#10587612D412yes—
86#10587612D412yes—
87C2×C4⋊Dic17C2×C412yes—
88C2×#63225—22no—
89C2×C4×Dic17—21no—
90C2×C4×Dic17—21no—
91C2×C4×Dic17—22no—
92C2×C4×Dic17—21no—
93C2×C4×Dic17—21no—
94C2×C4×Dic17—21no—
95C2×C4×Dic17—21no—
96C2×C4×Dic17C2×C412yescomplemented
97C2×#63223—21no—
98C2×#63223—21no—
99C2×#63223—21no—
100C2×#63223—21no—
101C2×#63223—21no—
102C2×#63223C2×C412yescomplemented
103C22×#3622—21no—
104#10587578—24no—
105#10587578—24no—
106C4⋊C4×D17—24no—
107C4⋊C4×D17—24no—
108C22⋊C4×D17—24no—
109C22⋊C4×D17—24no—
110#10587563—24no—
111#10587563—24no—
112#10587558—24no—
113#10587558—24no—
114C42×D17—24no—
115C42×D17—24no—
116#10587502—24no—
117#10587491—24no—
118#10587491—24no—
119C24×C17C2×D411yescharacteristic
120C23×D17—21no—
121C23×D17—21no—
122C23×D17—21no—
123C23×D17—21no—
124C23×D17—24no—
125C23×D17—42no—
126C23×D17C22⋊C411yescharacteristic
127C23×D17C22⋊C412yes—
128C23×D17C22⋊C411yescharacteristic
129C23×D17C4⋊C412yes—
130C22×C4×C17—24no—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—42no—
134C22×C4×C17—41no—
135C22×C4×C17—41no—
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C22×C411yescharacteristic
138C22×C4×C17C22×C411yescharacteristic
139C22×C4×C17C2×D411yescharacteristic
140C22×C4×C17C2×D411yescharacteristic
141C22×C4×C17C2×D411yescharacteristic
142C22×C4×C17C2×D411yescharacteristic
143C22×C4×C17C2×D411yescharacteristic
144C22×C4×C17C2×D411yescharacteristic
145C22×C4×C17C2×Q811yescharacteristic
146C22×C4×C17#4111yescharacteristic
147C22×C4×C17#4111yescharacteristic
148C22×C4×C17#4111yescharacteristic
149C22×C4×C17#4111yescharacteristic
150C22×Dic17—21no—
151C22×Dic17—21no—
152C22×Dic17—21no—
153C22×Dic17—21no—
154C22×Dic17—24no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17—42no—
158C22×Dic17—41no—
159C22×Dic17—41no—
160C22×Dic17C22⋊C412yes—
161C22×Dic17C22⋊C411yescharacteristic
162C22×Dic17C22⋊C411yescharacteristic
163C22×Dic17C4⋊C412yes—
164C2×C4×D17—21no—
165C2×C4×D17—21no—
166C2×C4×D17—21no—
167C2×C4×D17—21no—
168C2×C4×D17—21no—
169C2×C4×D17—21no—
170C2×C4×D17—21no—
171C2×C4×D17—21no—
172C2×C4×D17—22no—
173C2×C4×D17—22no—
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—21no—
181C2×C4×D17—21no—
182C2×C4×D17—21no—
183C2×C4×D17—21no—
184C2×C4×D17—22no—
185C2×C4×D17—22no—
186C2×C4×D17—22no—
187C2×C4×D17—22no—
188C2×C4×D17—22no—
189C2×C4×D17—22no—
190C2×C4×D17—22no—
191C2×C4×D17—22no—
192C2×C4×D17—21no—
193C2×C4×D17—21no—
194C2×C4×D17—21no—
195C2×C4×D17—21no—
196C2×C4×D17—28no—
197C2×C4×D17—44no—
198C2×C4×D17—44no—
199C2×C4×D17C4212yes—
200C2×C4×D17C4212yes—
201C2×C4×D17C22⋊C412yes—
202C2×C4×D17C22⋊C412yes—
203C2×C4×D17C4⋊C412yes—
204C2×C4×D17C4⋊C412yes—
205C2×C4×D17C4⋊C412yes—
206C2×C4×D17C4⋊C412yes—
207M16×C17—22no—
208M16×C17—22no—
209M16×C17—41no—
210M16×C17—41no—
211C2×C8×C17—22no—
212C2×C8×C17—41no—
213C2×C8×C17—41no—
214C4⋊C4×C17—22no—
215C4⋊C4×C17C22⋊C414yescomplemented
216C22⋊C4×C17—22no—
217C22⋊C4×C17—22no—
218C42×C17—22no—
219C42×C17—22no—
220C42×C17—22no—
221C42×C17—22no—
222C42×C17—41no—
223C42×C17—41no—
224C22⋊Dic17—22no—
225C22⋊Dic17—22no—
226#63227—28no—
227#63227—216no—
228C4⋊Dic17—22no—
229C4⋊Dic17C22⋊C414yescomplemented
230#63225—28no—
231C4×Dic17—28no—
232C4×Dic17—22no—
233C4×Dic17—22no—
234C4×Dic17—22no—
235C4×Dic17—22no—
236C4×Dic17—41no—
237C4×Dic17—41no—
238#63223—22no—
239#63223—22no—
240#63223—41no—
241#63223—41no—
242C2×#3622—22no—
243C2×#3622—41no—
244C2×#3622—41no—
245#10733—171nomaximal, Sylow
246C23×C17—22no—
247C23×C17—22no—
248C23×C17C2×C22⋊C411yescharacteristic
249C23×C17C2×C22⋊C411yescharacteristic
250C23×C17C2×C4⋊C411yescharacteristic
251C23×C17#12011yescharacteristic
252C23×C17#12011yescharacteristic
253C23×C17#12311yescharacteristic
254C23×C17#12311yescharacteristic
255C22×D17—21no—
256C22×D17—21no—
257C22×D17—22no—
258C22×D17—21no—
259C22×D17—21no—
260C22×D17—22no—
261C22×D17—22no—
262C22×D17—22no—
263C22×D17—22no—
264C22×D17—22no—
265C22×D17—22no—
266C22×D17—24no—
267C22×D17—24no—
268C22×D17—42no—
269C22×D17—42no—
270C22×D17—44no—
271C22×D17—44no—
272C22×D17—44no—
273C22×D17—44no—
274C22×D17#9512yes—
275C22×D17#9512yes—
276C22×D17#10414yes—
277C2×C4×C17—24no—
278C2×C4×C17—24no—
279C2×C4×C17—44no—
280C2×C4×C17—42no—
281C2×C4×C17—44no—
282C2×C4×C17—42no—
283C2×C4×C17—42no—
284C2×C4×C17—42no—
285C2×C4×C17C2×C4211yescharacteristic
286C2×C4×C17C2×C22⋊C411yescharacteristic
287C2×C4×C17C2×C22⋊C411yescharacteristic
288C2×C4×C17C2×C22⋊C411yescharacteristic
289C2×C4×C17C2×C4⋊C411yescharacteristic
290C2×C4×C17C2×C4⋊C411yescharacteristic
291C2×C4×C17#11711yescharacteristic
292C2×C4×C17#11711yescharacteristic
293C2×C4×C17C4×D411yescharacteristic
294C2×C4×C17C4×D411yescharacteristic
295C2×C4×C17C4×D411yescharacteristic
296C2×C4×C17C4×D411yescharacteristic
297C2×C4×C17C4×D411yescharacteristic
298C2×C4×C17C4×D411yescharacteristic
299C2×C4×C17C4×D411yescharacteristic
300C2×C4×C17C4×D411yescharacteristic
301C2×C4×C17#12011yescharacteristic
302C2×C4×C17#12011yescharacteristic
303C2×C4×C17#12111yescharacteristic
304C2×C4×C17#12111yescharacteristic
305C2×C4×C17#12111yescharacteristic
306C2×C4×C17#12111yescharacteristic
307C2×C4×C17C22⋊Q811yescharacteristic
308C2×C4×C17C22⋊Q811yescharacteristic
309C2×C4×C17C22⋊Q811yescharacteristic
310C2×C4×C17C22⋊Q811yescharacteristic
311C2×C4×C17#12311yescharacteristic
312C2×C4×C17#12311yescharacteristic
313C2×Dic17—21no—
314C2×Dic17—21no—
315C2×Dic17—21no—
316C2×Dic17—21no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—24no—
322C2×Dic17—24no—
323C2×Dic17—44no—
324C2×Dic17—42no—
325C2×Dic17—44no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17#9512yes—
330C2×Dic17#9512yes—
331C4×D17—22no—
332C4×D17—22no—
333C4×D17—22no—
334C4×D17—22no—
335C4×D17—22no—
336C4×D17—22no—
337C4×D17—22no—
338C4×D17—22no—
339C4×D17—22no—
340C4×D17—22no—
341C4×D17—22no—
342C4×D17—22no—
343C4×D17—22no—
344C4×D17—22no—
345C4×D17—22no—
346C4×D17—22no—
347C4×D17—416no—
348C8×C17—42no—
349#3622—42no—
350C22×#117—171no—
351C2×#407—171no—
352C2×C4×C22⋊C4—171no—
353C2×#339—171no—
354C2×#339—171no—
355C2×#339—171no—
356C2×#339D1711yescharacteristic, complemented
357C22×C17—22no—
358C22×C17—22no—
359C22×C17—21no—
360C22×C17—21no—
361C22×C17—21no—
362C22×C17—21no—
363C22×C17—22no—
364C22×C17—22no—
365C22×C17C2×#9511yescharacteristic
366C22×C17#37911yescharacteristic
367C22×C17#38111yescharacteristic
368C22×C17#38511yescharacteristic
369C22×C17#38511yescharacteristic
370C22×C17#38611yescharacteristic
371C22×C17#38611yescharacteristic
372C22×C17C2×#10412yes—
373C22×C17#42112yes—
374C2×D17—24no—
375C2×D17—22no—
376C2×D17—22no—
377C2×D17—24no—
378C2×D17—22no—
379C2×D17—22no—
380C2×D17—22no—
381C2×D17—44no—
382C2×D17—44no—
383C2×D17—44no—
384C2×D17—44no—
385C2×D17—42no—
386C2×D17—42no—
387C2×D17#33914yescomplemented
388C4×C17—44no—
389C4×C17—44no—
390C4×C17C4×C22⋊C411yescharacteristic
391C4×C17C4×C22⋊C411yescharacteristic
392C4×C17#38011yescharacteristic
393C4×C17#38011yescharacteristic
394C4×C17#38511yescharacteristic
395C4×C17#38511yescharacteristic
396C4×C17#38611yescharacteristic
397C4×C17#38611yescharacteristic
398Dic17—22no—
399Dic17—22no—
400Dic17—44no—
401Dic17—44no—
402C24×C4—171no—
403C22×M16—171no—
404C22×M16C2×D1711yescharacteristic
405C2×#117—171no—
406C2×#117—172no—
407C2×#117—341no—
408C2×#117—341no—
409C2×#117—342no—
410C2×#117—342no—
411C2×#117—342no—
412C2×#117—342no—
413C2×#117C2×D1711yescharacteristic
414C22×C4⋊C4—172no—
415C22×C22⋊C4—341no—
416C22×C22⋊C4—341no—
417C22×C42—171no—
418C22×C42—341no—
419C22×C42C2×D1711yescharacteristic
420#407—174no—
421#407—342no—
422C2×C22⋊C8—341no—
423C2×C22⋊C8—341no—
424C4×C22⋊C4—174no—
425C4×C22⋊C4—342no—
426C2×#95—341no—
427#339—22no—
428#339—342no—
429#339—342no—
430#339—342no—
431C2×C17—21no—
432C2×C17—21no—
433C2×C17—21no—
434C2×C17—21no—
435C2×C17C22⋊#9511yescharacteristic
436C2×C17C2×#33911yescharacteristic
437C2×C17#173311yescharacteristic
438C2×C17#178912yes—
439C2×C17#182612yes—
440D17—24no—
441D17—42no—
442C25—171no—
443C23×C4—21no—
444C23×C4—171no—
445C23×C4—171no—
446C23×C4—171no—
447C23×C4—172no—
448C23×C4—172no—
449C23×C4—172no—
450C23×C4—171no—
451C23×C4—171no—
452C23×C4—172no—
453C23×C4—342no—
454C23×C4—341no—
455C23×C4—341no—
456C23×C4—341no—
457C23×C4—341no—
458C23×C4—341no—
459C23×C4—341no—
460C23×C4—341no—
461C23×C4—341no—
462C23×C4—341no—
463C23×C4C22×D1711yescharacteristic
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—172no—
470C2×M16—341no—
471C2×M16—341no—
472C2×M16—341no—
473C2×M16—341no—
474C2×M16—341no—
475C2×M16C4×D1712yescomplemented
476C22×C8—21no—
477C22×C8—341no—
478#117—21no—
479#117—21no—
480#117—172no—
481#117—172no—
482#117—344no—
483#117—344no—
484#117—344no—
485#117—344no—
486#117—344no—
487#117—341no—
488#117—341no—
489#117—344no—
490#117D6812yes—
491#117C22⋊D1712yes—
492C2×C4⋊C4—172no—
493C2×C4⋊C4—344no—
494C2×C4⋊C4—342no—
495C2×C4⋊C4—344no—
496C2×C4⋊C4C4×D1712yes—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—344no—
499C2×C22⋊C4—344no—
500C2×C22⋊C4—342no—
501C2×C22⋊C4—344no—
502C2×C22⋊C4—348no—
503C2×C22⋊C4—341no—
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—172no—
511C2×C42—344no—
512C2×C42—344no—
513C2×C42—342no—
514C2×C42—341no—
515C2×C42—341no—
516C2×C42—341no—
517C2×C42—341no—
518C2×C42—341no—
519C2×C42—341no—
520C2×C42C4×D1712yescomplemented
521C22⋊C8—344no—
522C22⋊C8—344no—
523#95—344no—
524C17#1073311yescharacteristic, complemented, Sylow
525C24—171no—
526C24—171no—
527C24—172no—
528C24—172no—
529C24—344no—
530C24—341no—
531C24—341no—
532C24—341no—
533C24—341no—
534C24—682no—
535C24D4×D1711yescharacteristic
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—42no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—172no—
543C22×C4—171no—
544C22×C4—171no—
545C22×C4—172no—
546C22×C4—172no—
547C22×C4—172no—
548C22×C4—172no—
549C22×C4—172no—
550C22×C4—172no—
551C22×C4—172no—
552C22×C4—172no—
553C22×C4—172no—
554C22×C4—348no—
555C22×C4—341no—
556C22×C4—341no—
557C22×C4—341no—
558C22×C4—341no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—341no—
564C22×C4—341no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—341no—
568C22×C4—341no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—341no—
578C22×C4—341no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—342no—
583C22×C4—341no—
584C22×C4—341no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—344no—
592C22×C4—342no—
593C22×C4—342no—
594C22×C4—684no—
595C22×C4—684no—
596C22×C4—682no—
597C22×C4—681no—
598C22×C4—681no—
599C22×C4C2×C4×D1711yescharacteristic
600C22×C4C2×C4×D1711yescharacteristic
601C22×C4C2×C4×D1711yescharacteristic
602C22×C4C2×D6811yescharacteristic
603C22×C4#6325211yescharacteristic
604C22×C4#6325211yescharacteristic
605C22×C4D4×D1711yescharacteristic
606C22×C4D4×D1711yescharacteristic
607C22×C4D4×D1711yescharacteristic
608C22×C4D4×D1711yescharacteristic
609C22×C4#6325411yescharacteristic
610C22×C4Q8×D1711yescharacteristic
611C22×C4#6325611yescharacteristic
612C22×C4C2×C22⋊D1711yescharacteristic
613M16—22no—
614M16—22no—
615M16—41no—
616M16—41no—
617M16—342no—
618M16—342no—
619M16—681no—
620M16—681no—
621C2×C8—22no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—342no—
625C2×C8—681no—
626C2×C8—681no—
627C4⋊C4—22no—
628C4⋊C4—174no—
629C4⋊C4—348no—
630C4⋊C4—342no—
631C4⋊C4#6322714yescomplemented
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—348no—
635C22⋊C4—3416no—
636C22⋊C4—342no—
637C22⋊C4—342no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—41no—
643C42—41no—
644C42—348no—
645C42—342no—
646C42—342no—
647C42—342no—
648C42—342no—
649C42—681no—
650C42—681no—
651C23—22no—
652C23—22no—
653C23—174no—
654C23—172no—
655C23—172no—
656C23—344no—
657C23—344no—
658C23—342no—
659C23—341no—
660C23—341no—
661C23—342no—
662C23—342no—
663C23—341no—
664C23—341no—
665C23—342no—
666C23—342no—
667C23—342no—
668C23—342no—
669C23—682no—
670C23—682no—
671C23—684no—
672C23—684no—
673C23—684no—
674C23—684no—
675C23C22⋊C4×D1711yescharacteristic
676C23C22⋊C4×D1711yescharacteristic
677C23#1058756811yescharacteristic
678C23#1058756911yescharacteristic
679C23C4⋊C4×D1711yescharacteristic
680C23#1058758011yescharacteristic
681C23#1058762311yescharacteristic
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—172no—
691C2×C4—172no—
692C2×C4—341no—
693C2×C4—341no—
694C2×C4—341no—
695C2×C4—341no—
696C2×C4—342no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—342no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—342no—
704C2×C4—342no—
705C2×C4—342no—
706C2×C4—342no—
707C2×C4—342no—
708C2×C4—342no—
709C2×C4—342no—
710C2×C4—342no—
711C2×C4—342no—
712C2×C4—342no—
713C2×C4—342no—
714C2×C4—342no—
715C2×C4—342no—
716C2×C4—344no—
717C2×C4—344no—
718C2×C4—6816no—
719C2×C4—684no—
720C2×C4—684no—
721C2×C4—682no—
722C2×C4—682no—
723C2×C4—682no—
724C2×C4—682no—
725C2×C4C42×D1711yescharacteristic
726C2×C4#1058755811yescharacteristic
727C2×C4C4×D6811yescharacteristic
728C2×C4C4×D6811yescharacteristic
729C2×C4C22⋊C4×D1711yescharacteristic
730C2×C4C22⋊C4×D1711yescharacteristic
731C2×C4#1058756711yescharacteristic
732C2×C4#1058756711yescharacteristic
733C2×C4#1058756811yescharacteristic
734C2×C4#1058756911yescharacteristic
735C2×C4#1058757011yescharacteristic
736C2×C4#1058757011yescharacteristic
737C2×C4C4⋊C4×D1711yescharacteristic
738C2×C4C4⋊C4×D1711yescharacteristic
739C2×C4#1058757811yescharacteristic
740C2×C4#1058757911yescharacteristic
741C2×C4#1058757911yescharacteristic
742C2×C4#1058758011yescharacteristic
743C2×C4#1058758111yescharacteristic
744C2×C4#1058758211yescharacteristic
745C2×C4#1058758211yescharacteristic
746C2×C4#1058758311yescharacteristic
747C2×C4C2×#6322711yescharacteristic
748C2×C4C4×C22⋊D1711yescharacteristic
749C2×C4C4×C22⋊D1711yescharacteristic
750C2×C4#1058762311yescharacteristic
751C2×C4#1058762411yescharacteristic
752C2×C4#1058763211yescharacteristic
753C8—42no—
754C8—682no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—174no—
764C22—342no—
765C22—344no—
766C22—344no—
767C22—342no—
768C22—342no—
769C22—342no—
770C22—342no—
771C22—684no—
772C22—684no—
773C22—684no—
774C22—684no—
775C22—682no—
776C22—682no—
777C22#95×D1711yescharacteristic
778C22#1176266411yescharacteristic
779C22#1176267111yescharacteristic
780C22#1176268011yescharacteristic
781C22#1176268311yescharacteristic
782C22#1176268511yescharacteristic
783C22#1176268711yescharacteristic
784C22#104×D1712yes—
785C22#1176282412yes—
786C4—44no—
787C4—44no—
788C4—342no—
789C4—342no—
790C4—684no—
791C4—684no—
792C4#1176265611yescharacteristic
793C4C4×#6322711yescharacteristic
794C4#1176266611yescharacteristic
795C4#1176266811yescharacteristic
796C4#1176268011yescharacteristic
797C4#1176268311yescharacteristic
798C4#1176268511yescharacteristic
799C4#1176268711yescharacteristic
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—344no—
805C2—682no—
806C2#1452700511yescharacteristic
807C2D17×#33911yescharacteristic
808C2#1452849211yescharacteristic
809C2#1452872612yes—
810C2#1452888212yes—
subgroupG/H
centerC22×C4D4×D17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#339C2
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC23×C4×C17C23
hypercenterC2×#339D17
hypocenterC17#10733
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#11762570C2semidirect
5. C2×#11762569C2semidirect
6. C2×#11762568C2semidirect
7. C2×C17×#339C2semidirect
11. C2×#10587578C4semidirect
18. C2×C4⋊C4×D17C4semidirect
24. #11762772C4semidirect
28. C4×#63227C4semidirect
64. C2×M16×C17C2×C4semidirect
78. C2×C42×C17C2×C4semidirect
96. C2×C4×Dic17C2×C4semidirect
102. C2×#63223C2×C4semidirect
215. C4⋊C4×C17C22⋊C4semidirect
229. C4⋊Dic17C22⋊C4semidirect
356. C2×#339D17semidirect
387. C2×D17#339semidirect
475. C2×M16C4×D17semidirect
520. C2×C42C4×D17semidirect
524. C17#10733semidirect
631. C4⋊C4#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
C2×C4×#632272
C2×#117625702
C2×#117625692
C2×#117625682
C2×C17×#3392
#1073317