Finite Group Databasebeta

← #17039665

Subgroups — #17039665

Order 4352.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763320C211yesmaximal, characteristic
2C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
3#14529768C212yesmaximal, complemented
4#14529619C212yesmaximal, complemented
5#14529235C214yesmaximal, complemented
6C4×#10587477C214yesmaximal, complemented
7C17×#2280C211yesmaximal, characteristic, complemented
8C22×#63252C411yescharacteristic, complemented
9#11763320—21no—
10#11763320—21no—
11#11763320—21no—
12#11763320—21no—
13#11763320—21no—
14#11763320—21no—
15#11763320—21no—
16#11763320—21no—
17C2×#10587615C412yescomplemented
18C2×#10587610C411yescharacteristic, complemented
19C2×#10587610C2211yescharacteristic
20C2×#10587616C411yescharacteristic, complemented
21C2×#10587616C2211yescharacteristic
22C2×#10587639C2212yes—
23C2×C4×C22⋊D17C412yescomplemented
24C2×C4×C22⋊D17C2212yes—
25C2×#10587612C411yescharacteristic, complemented
26C22×C22⋊Dic17C2212yes—
27C22×C4×Dic17—21no—
28C2×#10587477C2218yes—
29C4×C22⋊Dic17—21no—
30C4×C22⋊Dic17—21no—
31C4×C22⋊Dic17C2212yes—
32C4×C22⋊Dic17C2212yes—
33C2×#10587502—21no—
34#11762575C2218yes—
35C24×C4×C17C2211yescharacteristic
36C2×C17×#117—21no—
37C17×#381—21no—
38C17×#380—21no—
39C17×#380C2212yes—
40C17×#379C2212yes—
41C4×C22⋊C4×C17—21no—
42C4×C22⋊C4×C17C2212yes—
43C25×C17C2311yescharacteristic
44C23×C4×C17—44no—
45C23×C4×C17C2×C411yescharacteristic
46C23×C4×C17C2×C411yescharacteristic
47C23×C4×C17C2×C411yescharacteristic
48C23×C4×C17C2×C411yescharacteristic
49C23×C4×C17D411yescharacteristic
50C23×C4×C17D411yescharacteristic
51C23×C4×C17D411yescharacteristic
52C23×C4×C17D411yescharacteristic
53C23×C4×C17D411yescharacteristic
54C23×C4×C17D411yescharacteristic
55C23×C4×C17D411yescharacteristic
56C23×C4×C17D411yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C22×C22⋊D17C2×C412yes—
60C22×C22⋊D17C2×C412yes—
61C22×C22⋊D17C2312yes—
62C23×Dic17—22no—
63C2×#63252—21no—
64C2×#63252—21no—
65C2×#63252—21no—
66C2×#63252—21no—
67C2×#63252—44no—
68C22×D68C2×C411yescharacteristic, complemented
69C22×C4×D17C2×C412yescomplemented
70C22×Dic34C2×C411yescharacteristic, complemented
71C17×#117—44no—
72C2×C4⋊C4×C17—22no—
73C2×C22⋊C4×C17—22no—
74C2×C22⋊C4×C17—22no—
75C2×C22⋊C4×C17C2314yes—
76C2×C42×C17—22no—
77#10587639—22no—
78#10587639—22no—
79#10587639—22no—
80#10587639—22no—
81C2×C22⋊Dic17—22no—
82C2×C22⋊Dic17—28no—
83C2×C22⋊Dic17C2×C412yes—
84C2×C22⋊Dic17C2×C412yes—
85C2×C22⋊Dic17C2312yes—
86C2×C22⋊Dic17C2314yes—
87#10587616—21no—
88#10587616—21no—
89#10587616—21no—
90#10587616—21no—
91#10587616—21no—
92#10587616—21no—
93#10587616—21no—
94#10587616—21no—
95#10587615—22no—
96#10587615—22no—
97#10587615—22no—
98#10587615—22no—
99C4×C22⋊D17—22no—
100C4×C22⋊D17—22no—
101C4×C22⋊D17—22no—
102C4×C22⋊D17—22no—
103C4×C22⋊D17—22no—
104C4×C22⋊D17—22no—
105C4×C22⋊D17—22no—
106C4×C22⋊D17—22no—
107C2×#63227C2×C412yescomplemented
108C2×#63227C2×C412yescomplemented
109#10587612—21no—
110#10587612—21no—
111#10587612—21no—
112#10587612—21no—
113C2×C4⋊Dic17C2×C411yescharacteristic, complemented
114C2×C4⋊Dic17C2×C411yescharacteristic, complemented
115#10587610—21no—
116#10587610—21no—
117#10587610—21no—
118#10587610—21no—
119#10587610—21no—
120#10587610—21no—
121#10587610—21no—
122#10587610—21no—
123C2×#63225C2×C412yescomplemented
124C2×#63225C2×C412yescomplemented
125C2×C4×Dic17—22no—
126C2×C4×Dic17—22no—
127C2×C4×Dic17—44no—
128C2×C4×Dic17C2×C412yescomplemented
129C17×#95—22no—
130C17×#95—22no—
131#10587502—22no—
132#10587502—22no—
133#10587477—216no—
134C24×C17—24no—
135C24×C17—42no—
136C24×C17—42no—
137C24×C17C22×C411yescharacteristic
138C24×C17C22×C411yescharacteristic
139C24×C17C2×D411yescharacteristic
140C24×C17C2×D411yescharacteristic
141C24×C17C2×D411yescharacteristic
142C24×C17C2×D411yescharacteristic
143C24×C17C2411yescharacteristic
144C23×D17C22×C412yes—
145C22×C4×C17—24no—
146C22×C4×C17—24no—
147C22×C4×C17—24no—
148C22×C4×C17—24no—
149C22×C4×C17—42no—
150C22×C4×C17—42no—
151C22×C4×C17—42no—
152C22×C4×C17—42no—
153C22×C4×C17—42no—
154C22×C4×C17—42no—
155C22×C4×C17—42no—
156C22×C4×C17—42no—
157C22×C4×C17—42no—
158C22×C4×C17—42no—
159C22×C4×C17—42no—
160C22×C4×C17C22⋊C411yescharacteristic
161C22×C4×C17C22⋊C411yescharacteristic
162C22×C4×C17C22⋊C411yescharacteristic
163C22×C4×C17C22⋊C411yescharacteristic
164C22×C4×C17C22⋊C411yescharacteristic
165C22×C4×C17C22⋊C411yescharacteristic
166C22×C4×C17C22⋊C411yescharacteristic
167C22×C4×C17C22⋊C411yescharacteristic
168C22×C4×C17C22⋊C411yescharacteristic
169C22×C4×C17C22⋊C411yescharacteristic
170C22×C4×C17C22⋊C411yescharacteristic
171C22×C4×C17C22⋊C411yescharacteristic
172C22×C4×C17C22⋊C411yescharacteristic
173C22×C4×C17C22⋊C411yescharacteristic
174C22×C4×C17C22⋊C411yescharacteristic
175C22×C4×C17C22⋊C411yescharacteristic
176C22×C4×C17C22×C411yescharacteristic
177C22×C4×C17C22×C411yescharacteristic
178C22×C4×C17C22×C411yescharacteristic
179C22×C4×C17C22×C411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2×D411yescharacteristic
183C22×C4×C17C2×D411yescharacteristic
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17C2×D411yescharacteristic
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17C2×D411yescharacteristic
188C2×C22⋊D17—22no—
189C2×C22⋊D17—22no—
190C2×C22⋊D17—22no—
191C2×C22⋊D17—22no—
192C2×C22⋊D17—22no—
193C2×C22⋊D17—22no—
194C2×C22⋊D17—28no—
195C2×C22⋊D17—44no—
196C2×C22⋊D17—44no—
197C22×Dic17—28no—
198C22×Dic17—24no—
199C22×Dic17—44no—
200C22×Dic17—44no—
201C22×Dic17C22×C412yes—
202C22×Dic17C22×C412yes—
203C22×Dic17C22×C412yes—
204#63252—44no—
205#63252—44no—
206#63252—44no—
207#63252—44no—
208C2×D68—21no—
209C2×D68—21no—
210C2×D68—42no—
211C2×C4×D17—22no—
212C2×C4×D17—22no—
213C2×C4×D17—44no—
214C2×Dic34—21no—
215C2×Dic34—21no—
216C2×Dic34—42no—
217C4⋊C4×C17—44no—
218C22⋊C4×C17—28no—
219C22⋊C4×C17—44no—
220C22⋊C4×C17—44no—
221C42×C17—44no—
222C22⋊Dic17—28no—
223C22⋊Dic17—22no—
224C22⋊Dic17—22no—
225C22⋊Dic17—22no—
226C22⋊Dic17—22no—
227C22⋊Dic17—22no—
228C22⋊Dic17—22no—
229C22⋊Dic17—24no—
230C22⋊Dic17#4118yescomplemented
231#63227—22no—
232#63227—22no—
233#63227—22no—
234#63227—22no—
235C4⋊Dic17—21no—
236C4⋊Dic17—21no—
237C4⋊Dic17—21no—
238C4⋊Dic17—21no—
239#63225—22no—
240#63225—22no—
241#63225—22no—
242#63225—22no—
243C4×Dic17—22no—
244C4×Dic17—22no—
245C4×Dic17—44no—
246C4×Dic17—44no—
247#21420—171nomaximal, Sylow
248C23×C17—22no—
249C23×C17—22no—
250C23×C17—22no—
251C23×C17—22no—
252C23×C17—22no—
253C23×C17—22no—
254C23×C17—22no—
255C23×C17—22no—
256C23×C17—22no—
257C23×C17—22no—
258C23×C17—22no—
259C23×C17—22no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17—41no—
263C23×C17—41no—
264C23×C17—41no—
265C23×C17—41no—
266C23×C17—41no—
267C23×C17—41no—
268C23×C17—416no—
269C23×C17C2×C22⋊C411yescharacteristic
270C23×C17C2×C22⋊C411yescharacteristic
271C23×C17C2×C22⋊C411yescharacteristic
272C23×C17C2×C22⋊C411yescharacteristic
273C23×C17C23×C411yescharacteristic
274C23×C17C22×D411yescharacteristic
275C23×C17C22×D411yescharacteristic
276C23×C17C2×#4114yes—
277C22×D17—22no—
278C22×D17—24no—
279C22×D17—42no—
280C22×D17—42no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17—41no—
306C2×C4×C17—41no—
307C2×C4×C17—41no—
308C2×C4×C17—44no—
309C2×C4×C17—44no—
310C2×C4×C17—44no—
311C2×C4×C17#9914yescomplemented
312C2×C4×C17C2×C22⋊C411yescharacteristic
313C2×C4×C17C2×C22⋊C411yescharacteristic
314C2×C4×C17C2×C22⋊C411yescharacteristic
315C2×C4×C17C2×C22⋊C411yescharacteristic
316C2×C4×C17C2×C22⋊C411yescharacteristic
317C2×C4×C17C2×C22⋊C411yescharacteristic
318C2×C4×C17C2×C22⋊C411yescharacteristic
319C2×C4×C17C2×C22⋊C411yescharacteristic
320C22⋊D17—44no—
321C22⋊D17—44no—
322C22⋊D17—44no—
323C22⋊D17—44no—
324C22⋊D17—44no—
325C22⋊D17—44no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—24no—
330C2×Dic17—28no—
331C2×Dic17—416no—
332C2×Dic17—44no—
333C2×Dic17—44no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336D68—42no—
337D68—42no—
338C4×D17—44no—
339C4×D17—44no—
340Dic34—42no—
341Dic34—42no—
342C2×#525—171no—
343#2280D1711yescharacteristic, complemented
344C2×C4×C22⋊C4—171no—
345#1996—172no—
346#1964—172no—
347#1898—174no—
348C4×#99—174no—
349C22×C17—28no—
350C22×C17—21no—
351C22×C17—21no—
352C22×C17—21no—
353C22×C17—21no—
354C22×C17—21no—
355C22×C17—21no—
356C22×C17—21no—
357C22×C17—21no—
358C22×C17—21no—
359C22×C17—21no—
360C22×C17—21no—
361C22×C17—21no—
362C22×C17—21no—
363C22×C17—21no—
364C22×C17—21no—
365C22×C17—21no—
366C22×C17—44no—
367C22×C17—44no—
368C22×C17—44no—
369C22×C17—44no—
370C22×C17—44no—
371C22×C17—44no—
372C22×C17C2×#9912yes—
373C22×C17#41012yes—
374C22×C17C22×C22⋊C411yescharacteristic
375C22×C17C4×#4112yes—
376C22×C17#52512yes—
377C22×C17#53212yes—
378C2×D17—42no—
379C2×D17—42no—
380C2×D17—42no—
381C2×D17—84no—
382C4×C17—21no—
383C4×C17—21no—
384C4×C17—21no—
385C4×C17—21no—
386C4×C17—21no—
387C4×C17—21no—
388C4×C17—84no—
389C4×C17C2×#9912yes—
390C4×C17C2×#9912yes—
391Dic17—48no—
392Dic17—42no—
393Dic17—42no—
394Dic17—42no—
395C22×#41—171no—
396C24×C4C2×D1711yescharacteristic
397#525—341no—
398#525—341no—
399#525—341no—
400#525—341no—
401#525—341no—
402#525—341no—
403#525—341no—
404#525—341no—
405C2×#123—172no—
406C2×C22⋊Q8—171no—
407C2×C22⋊Q8—171no—
408C2×#121—171no—
409C2×#121—171no—
410C2×#120—172no—
411C2×C4×D4—172no—
412C2×C4×D4—172no—
413C2×#117—21no—
414C2×#117—171no—
415C22×C22⋊C4—172no—
416C22×C42—341no—
417C2×#99—178no—
418#381—21no—
419#380—21no—
420#380C2×D1712yes—
421#379C2×D1712yes—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—172no—
424C4×C22⋊C4—172no—
425C4×C22⋊C4—341no—
426C4×C22⋊C4—341no—
427C4×C22⋊C4C2×D1712yes—
428C2×#95—341no—
429#342—178no—
430C2×C17—22no—
431C2×C17—22no—
432C2×C17—22no—
433C2×C17—22no—
434C2×C17—22no—
435C2×C17—41no—
436C2×C17—41no—
437C2×C17#229711yescharacteristic
438C2×C17C22×#9911yescharacteristic
439C2×C17C2×#41011yescharacteristic
440D17—82no—
441C25C22×D1711yescharacteristic
442C2×#41—341no—
443C2×#41—341no—
444C2×#41—341no—
445C2×#41—341no—
446C2×#41—684no—
447C22×Q8—171no—
448C22×D4—172no—
449C22×D4—172no—
450C22×D4—172no—
451C22×D4—171no—
452C23×C4—44no—
453C23×C4—172no—
454C23×C4—342no—
455C23×C4C4×D1711yescharacteristic
456C23×C4C4×D1711yescharacteristic
457C23×C4C4×D1711yescharacteristic
458C23×C4C4×D1711yescharacteristic
459C23×C4D6811yescharacteristic
460C23×C4D6811yescharacteristic
461C23×C4D6811yescharacteristic
462C23×C4D6811yescharacteristic
463C23×C4C22⋊D1711yescharacteristic
464C23×C4C22⋊D1711yescharacteristic
465C23×C4C22⋊D1711yescharacteristic
466C23×C4C22⋊D1711yescharacteristic
467C23×C4C22×D1711yescharacteristic
468C23×C4C22×D1711yescharacteristic
469#123—342no—
470#123—342no—
471#123—342no—
472#123—342no—
473C22⋊Q8—341no—
474C22⋊Q8—341no—
475C22⋊Q8—341no—
476C22⋊Q8—341no—
477C22⋊Q8—341no—
478C22⋊Q8—341no—
479C22⋊Q8—341no—
480C22⋊Q8—341no—
481#121—341no—
482#121—341no—
483#121—341no—
484#121—341no—
485#121—341no—
486#121—341no—
487#121—341no—
488#121—341no—
489#120—342no—
490#120—342no—
491#120—342no—
492#120—342no—
493C4×D4—342no—
494C4×D4—342no—
495C4×D4—342no—
496C4×D4—342no—
497C4×D4—342no—
498C4×D4—342no—
499C4×D4—342no—
500C4×D4—342no—
501#117—44no—
502#117—341no—
503#117—341no—
504#117—341no—
505#117—341no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—172no—
510C2×C4⋊C4—172no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—174no—
514C2×C22⋊C4—172no—
515C2×C22⋊C4—172no—
516C2×C22⋊C4—172no—
517C2×C22⋊C4—172no—
518C2×C22⋊C4—172no—
519C2×C22⋊C4—348no—
520C2×C22⋊C4—342no—
521C2×C22⋊C4C22×D1714yes—
522C2×C42—22no—
523C2×C42—172no—
524C2×C42—342no—
525C2×C42—342no—
526C2×C42—684no—
527#99—3416no—
528#95—22no—
529#95—22no—
530#95—342no—
531#95—342no—
532C17#2142011yescharacteristic, complemented, Sylow
533C24—24no—
534C24—42no—
535C24—42no—
536C24—172no—
537C24C2×C4×D1711yescharacteristic
538C24C2×C4×D1711yescharacteristic
539C24C2×D6811yescharacteristic
540C24C2×D6811yescharacteristic
541C24C2×C22⋊D1711yescharacteristic
542C24C2×C22⋊D1711yescharacteristic
543C24C23×D1711yescharacteristic
544#41—684no—
545#41—684no—
546#41—684no—
547#41—684no—
548C2×Q8—341no—
549C2×Q8—341no—
550C2×Q8—682no—
551C2×D4—342no—
552C2×D4—348no—
553C2×D4—342no—
554C2×D4—342no—
555C2×D4—342no—
556C2×D4—342no—
557C2×D4—342no—
558C2×D4—341no—
559C2×D4—341no—
560C2×D4—682no—
561C2×D4—684no—
562C2×D4—684no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—172no—
579C22×C4—172no—
580C22×C4—172no—
581C22×C4—348no—
582C22×C4—344no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—684no—
586C22×C4—684no—
587C22×C4—684no—
588C22×C4#6322711yescharacteristic
589C22×C4#6322711yescharacteristic
590C22×C4#6322711yescharacteristic
591C22×C4#6322711yescharacteristic
592C22×C4#6322711yescharacteristic
593C22×C4#6322711yescharacteristic
594C22×C4#6322711yescharacteristic
595C22×C4#6322711yescharacteristic
596C22×C4#6322711yescharacteristic
597C22×C4#6322711yescharacteristic
598C22×C4#6322711yescharacteristic
599C22×C4#6322711yescharacteristic
600C22×C4#6322711yescharacteristic
601C22×C4#6322711yescharacteristic
602C22×C4#6322711yescharacteristic
603C22×C4#6322711yescharacteristic
604C22×C4C2×C4×D1711yescharacteristic
605C22×C4C2×C4×D1711yescharacteristic
606C22×C4C2×C4×D1711yescharacteristic
607C22×C4C2×C4×D1711yescharacteristic
608C22×C4C2×D6811yescharacteristic
609C22×C4C2×D6811yescharacteristic
610C22×C4C2×D6811yescharacteristic
611C22×C4C2×D6811yescharacteristic
612C22×C4C2×C22⋊D1711yescharacteristic
613C22×C4C2×C22⋊D1711yescharacteristic
614C22×C4C2×C22⋊D1711yescharacteristic
615C22×C4C2×C22⋊D1711yescharacteristic
616C4⋊C4—44no—
617C4⋊C4—341no—
618C4⋊C4—341no—
619C4⋊C4—341no—
620C4⋊C4—341no—
621C4⋊C4—342no—
622C4⋊C4—342no—
623C4⋊C4—342no—
624C4⋊C4—342no—
625C22⋊C4—28no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—178no—
629C22⋊C4—348no—
630C22⋊C4—342no—
631C22⋊C4—344no—
632C22⋊C4—342no—
633C22⋊C4—342no—
634C22⋊C4—342no—
635C22⋊C4—342no—
636C22⋊C4—342no—
637C22⋊C4—342no—
638C22⋊C4—342no—
639C22⋊C4—342no—
640C22⋊C4—342no—
641C42—44no—
642C42—342no—
643C42—342no—
644C42—684no—
645C42—684no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—416no—
667C23—342no—
668C23—344no—
669C23—682no—
670C23—682no—
671C23C2×#6322711yescharacteristic
672C23C2×#6322711yescharacteristic
673C23C2×#6322711yescharacteristic
674C23C2×#6322711yescharacteristic
675C23C22×C4×D1711yescharacteristic
676C23C22×D6811yescharacteristic
677C23#41×D1714yes—
678C23C22×C22⋊D1711yescharacteristic
679Q8—682no—
680Q8—682no—
681D4—682no—
682D4—684no—
683D4—684no—
684D4—684no—
685D4—684no—
686D4—684no—
687D4—684no—
688D4—682no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—342no—
720C2×C4—342no—
721C2×C4—342no—
722C2×C4—344no—
723C2×C4—348no—
724C2×C4—684no—
725C2×C4—684no—
726C2×C4—6816no—
727C2×C4—684no—
728C2×C4—684no—
729C2×C4—682no—
730C2×C4—682no—
731C2×C4#1058747714yescomplemented
732C2×C4C2×#6322711yescharacteristic
733C2×C4C2×#6322711yescharacteristic
734C2×C4C2×#6322711yescharacteristic
735C2×C4C2×#6322711yescharacteristic
736C2×C4C2×#6322711yescharacteristic
737C2×C4C2×#6322711yescharacteristic
738C2×C4C2×#6322711yescharacteristic
739C2×C4C2×#6322711yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—682no—
764C22—682no—
765C22—682no—
766C22—1364no—
767C22C2×#1058747712yes—
768C22#1176278212yes—
769C22C22×#6322711yescharacteristic
770C22#1176327712yes—
771C22#1176332112yes—
772C22#1176335512yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—84no—
780C4—688no—
781C4—682no—
782C4—682no—
783C4—682no—
784C4C2×#1058747712yes—
785C4C2×#1058747712yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—1362no—
794C2#1453127211yescharacteristic
795C2C22×#1058747711yescharacteristic
796C2C2×#1176278211yescharacteristic
subgroupG/H
centerC2×C4C2×#63227
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC17×#2280C2
socleC22×C17C22×C22⋊C4
prime radicalC2×#11763320C2
cosocleC24×C17C24
hypercenter#2280D17
hypocenterC17#21420
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic17C2semidirect
3. #14529768C2semidirect
4. #14529619C2semidirect
5. #14529235C2semidirect
6. C4×#10587477C2semidirect
7. C17×#2280C2semidirect
8. C22×#63252C4semidirect
17. C2×#10587615C4semidirect
18. C2×#10587610C4semidirect
20. C2×#10587616C4semidirect
23. C2×C4×C22⋊D17C4semidirect
25. C2×#10587612C4semidirect
68. C22×D68C2×C4semidirect
69. C22×C4×D17C2×C4semidirect
70. C22×Dic34C2×C4semidirect
107. C2×#63227C2×C4semidirect
108. C2×#63227C2×C4semidirect
113. C2×C4⋊Dic17C2×C4semidirect
114. C2×C4⋊Dic17C2×C4semidirect
123. C2×#63225C2×C4semidirect
124. C2×#63225C2×C4semidirect
128. C2×C4×Dic17C2×C4semidirect
230. C22⋊Dic17#41semidirect
311. C2×C4×C17#99semidirect
343. #2280D17semidirect
532. C17#21420semidirect
731. C2×C4#10587477semidirect

Maximal subgroups

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

subgroupindex
C2×#117633202
C2×C4×C22⋊Dic172
#145297682
#145296192
#145292352
C4×#105874772
C17×#22802
#2142017