Finite Group Databasebeta

← #17039667

Subgroups — #17039667

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
2#14531167C211yesmaximal, characteristic, complemented
3#14529769C212yesmaximal, complemented
4#14529620C212yesmaximal, complemented
5#14529237C214yesmaximal, complemented
6C4×#10587477C214yesmaximal, complemented
7C2×C4×C22⋊C4×C17C211yesmaximal, 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×#10587612—21no—
26C2×#10587612C411yescharacteristic, complemented
27C2×#10587477C2218yes—
28#11762672—21no—
29#11762669—21no—
30#11762669C2212yes—
31#11762665C2212yes—
32C4×C22⋊Dic17—21no—
33C4×C22⋊Dic17C2212yes—
34#11762575C2218yes—
35C24×C4×C17C2211yescharacteristic
36C22×C22⋊C4×C17C2212yes—
37C22×C42×C17—21no—
38C4×C22⋊C4×C17—21no—
39C4×C22⋊C4×C17—21no—
40C4×C22⋊C4×C17C2212yes—
41C4×C22⋊C4×C17C2212yes—
42C2×C17×#95—21no—
43C25×C17C2311yescharacteristic
44C23×C4×C17—22no—
45C23×C4×C17—44no—
46C23×C4×C17C2×C411yescharacteristic
47C23×C4×C17C2×C411yescharacteristic
48C23×C4×C17C2×C411yescharacteristic
49C23×C4×C17C2×C411yescharacteristic
50C23×C4×C17D411yescharacteristic
51C23×C4×C17D411yescharacteristic
52C23×C4×C17D411yescharacteristic
53C23×C4×C17D411yescharacteristic
54C23×C4×C17D411yescharacteristic
55C23×C4×C17D411yescharacteristic
56C23×C4×C17D411yescharacteristic
57C23×C4×C17D411yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C22×C22⋊D17C2×C412yes—
61C22×C22⋊D17C2×C412yes—
62C22×C22⋊D17C2312yes—
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
71C2×C22⋊C4×C17—22no—
72C2×C22⋊C4×C17—28no—
73C2×C22⋊C4×C17C2314yes—
74C2×C42×C17—22no—
75C2×C42×C17—22no—
76C2×C42×C17—44no—
77#10587639—22no—
78#10587639—22no—
79#10587639—22no—
80#10587639—22no—
81C2×C22⋊Dic17—22no—
82C2×C22⋊Dic17—22no—
83C2×C22⋊Dic17C2×C412yes—
84C2×C22⋊Dic17C2×C412yes—
85C2×C22⋊Dic17C2314yes—
86C2×C22⋊Dic17C2312yes—
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—
113#10587612—44no—
114C2×C4⋊Dic17—22no—
115C2×C4⋊Dic17C2×C411yescharacteristic, complemented
116C2×C4⋊Dic17C2×C411yescharacteristic, complemented
117#10587610—21no—
118#10587610—21no—
119#10587610—21no—
120#10587610—21no—
121#10587610—21no—
122#10587610—21no—
123#10587610—21no—
124#10587610—21no—
125C2×#63225C2×C412yescomplemented
126C2×#63225C2×C412yescomplemented
127C2×C4×Dic17—22no—
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—28no—
149C22×C4×C17—24no—
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×C17—42no—
161C22×C4×C17—44no—
162C22×C4×C17—44no—
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×C17C22×C411yescharacteristic
181C22×C4×C17C22×C411yescharacteristic
182C22×C4×C17C22×C411yescharacteristic
183C22×C4×C17C2×D411yescharacteristic
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17C2×D411yescharacteristic
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D411yescharacteristic
191C2×C22⋊D17—22no—
192C2×C22⋊D17—22no—
193C2×C22⋊D17—22no—
194C2×C22⋊D17—22no—
195C2×C22⋊D17—22no—
196C2×C22⋊D17—22no—
197C2×C22⋊D17—28no—
198C2×C22⋊D17—44no—
199C2×C22⋊D17—44no—
200C22×Dic17—24no—
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—
217C22⋊C4×C17—28no—
218C22⋊C4×C17—24no—
219C22⋊C4×C17#4118yescomplemented
220C42×C17—44no—
221C42×C17—44no—
222C22⋊Dic17—22no—
223C22⋊Dic17—22no—
224C22⋊Dic17—22no—
225C22⋊Dic17—22no—
226C22⋊Dic17—22no—
227C22⋊Dic17—22no—
228C22⋊Dic17—28no—
229C22⋊Dic17—44no—
230C22⋊Dic17—44no—
231#63227—22no—
232#63227—22no—
233#63227—22no—
234#63227—22no—
235C4⋊Dic17—21no—
236C4⋊Dic17—21no—
237C4⋊Dic17—21no—
238C4⋊Dic17—21no—
239C4⋊Dic17—44no—
240#63225—22no—
241#63225—22no—
242#63225—22no—
243#63225—22no—
244C4×Dic17—22no—
245C4×Dic17—22no—
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—28no—
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—41no—
309C2×C4×C17—44no—
310C2×C4×C17—416no—
311C2×C4×C17—44no—
312C2×C4×C17#9914yescomplemented
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
320C2×C4×C17C2×C22⋊C411yescharacteristic
321C22⋊D17—44no—
322C22⋊D17—44no—
323C22⋊D17—44no—
324C22⋊D17—44no—
325C22⋊D17—44no—
326C22⋊D17—44no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—24no—
331C2×Dic17—42no—
332C2×Dic17—42no—
333C2×Dic17—44no—
334C2×Dic17—44no—
335C2×Dic17—44no—
336D68—42no—
337D68—42no—
338C4×D17—44no—
339C4×D17—44no—
340Dic34—42no—
341Dic34—42no—
342C2×#525—171no—
343#2280—171no—
344C2×C4×C22⋊C4D1711yescharacteristic, complemented
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—48no—
389C4×C17C2×#9912yes—
390C4×C17C2×#9912yes—
391Dic17—42no—
392Dic17—42no—
393Dic17—42no—
394Dic17—84no—
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—171no—
414C2×#117—341no—
415C22×C22⋊C4C2×D1712yes—
416C22×C42—21no—
417C2×#99—178no—
418#381—341no—
419#380—172no—
420#380—341no—
421#379—172no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—172no—
425C4×C22⋊C4—341no—
426C4×C22⋊C4C2×D1712yes—
427C4×C22⋊C4C2×D1712yes—
428C2×#95—21no—
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—22no—
453C23×C4—44no—
454C23×C4—172no—
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—341no—
502#117—341no—
503#117—341no—
504#117—341no—
505#117—684no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—172no—
509C2×C4⋊C4—172no—
510C2×C4⋊C4—342no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—28no—
513C2×C22⋊C4—172no—
514C2×C22⋊C4—172no—
515C2×C22⋊C4—172no—
516C2×C22⋊C4—172no—
517C2×C22⋊C4—172no—
518C2×C22⋊C4—174no—
519C2×C22⋊C4—342no—
520C2×C22⋊C4—342no—
521C2×C22⋊C4C22×D1714yes—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—44no—
525C2×C42—172no—
526C2×C42—342no—
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—28no—
567C22×C4—24no—
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—42no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—172no—
582C22×C4—172no—
583C22×C4—172no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—344no—
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—341no—
617C4⋊C4—341no—
618C4⋊C4—341no—
619C4⋊C4—341no—
620C4⋊C4—342no—
621C4⋊C4—342no—
622C4⋊C4—342no—
623C4⋊C4—342no—
624C4⋊C4—684no—
625C22⋊C4—28no—
626C22⋊C4—24no—
627C22⋊C4—342no—
628C22⋊C4—342no—
629C22⋊C4—342no—
630C22⋊C4—342no—
631C22⋊C4—342no—
632C22⋊C4—342no—
633C22⋊C4—342no—
634C22⋊C4—342no—
635C22⋊C4—342no—
636C22⋊C4—342no—
637C22⋊C4—348no—
638C22⋊C4—684no—
639C22⋊C4—684no—
640C22⋊C4#6325218yescomplemented
641C42—44no—
642C42—44no—
643C42—342no—
644C42—342no—
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
677C23C2×#6325214yes—
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—28no—
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—41no—
717C2×C4—44no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—342no—
721C2×C4—342no—
722C2×C4—342no—
723C2×C4—344no—
724C2×C4—684no—
725C2×C4—684no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4—684no—
729C2×C4—684no—
730C2×C4—684no—
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
770C22C4×#6325212yes—
771C22#1176332012yes—
772C22#1176335912yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—682no—
781C4—682no—
782C4—682no—
783C4—1364no—
784C4C2×#1058747712yes—
785C4C2×#1058747712yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—1362no—
794C2#1453127411yescharacteristic
795C2C22×#1058747711yescharacteristic
796C2C2×#1176278211yescharacteristic
subgroupG/H
centerC2×C4C2×#63227
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C4×C22⋊C4×C17C2
socleC22×C17C22×C22⋊C4
prime radicalC2×#11763320C2
cosocleC24×C17C24
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#21420
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14531167C2semidirect
3. #14529769C2semidirect
4. #14529620C2semidirect
5. #14529237C2semidirect
6. C4×#10587477C2semidirect
7. C2×C4×C22⋊C4×C17C2semidirect
8. C22×#63252C4semidirect
17. C2×#10587615C4semidirect
18. C2×#10587610C4semidirect
20. C2×#10587616C4semidirect
23. C2×C4×C22⋊D17C4semidirect
26. C2×#10587612C4semidirect
68. C22×D68C2×C4semidirect
69. C22×C4×D17C2×C4semidirect
70. C22×Dic34C2×C4semidirect
107. C2×#63227C2×C4semidirect
108. C2×#63227C2×C4semidirect
115. C2×C4⋊Dic17C2×C4semidirect
116. C2×C4⋊Dic17C2×C4semidirect
125. C2×#63225C2×C4semidirect
126. C2×#63225C2×C4semidirect
128. C2×C4×Dic17C2×C4semidirect
219. C22⋊C4×C17#41semidirect
312. C2×C4×C17#99semidirect
344. C2×C4×C22⋊C4D17semidirect
532. C17#21420semidirect
640. C22⋊C4#63252semidirect
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
#145311672
#145297692
#145296202
#145292372
C4×#105874772
C2×C4×C22⋊C4×C172
#2142017