Finite Group Databasebeta

← #17054637

Subgroups — #17054637

Order 4352.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762943C211yesmaximal, characteristic
2C2×#11762919C211yesmaximal, characteristic, complemented
3C22×#10587503C211yesmaximal, characteristic, complemented
4#14531798C211yesmaximal, characteristic, complemented
5#14529659C211yesmaximal, characteristic, complemented
6#14529484C211yesmaximal, characteristic, complemented
7#14529408C211yesmaximal, characteristic, complemented
8#14529210C211yesmaximal, characteristic, complemented
9#14529135C211yesmaximal, characteristic, complemented
10#14529132C211yesmaximal, characteristic, complemented
11#14529045C211yesmaximal, characteristic, complemented
12#14528976C211yesmaximal, characteristic, complemented
13#14528609C211yesmaximal, characteristic, complemented
14#14528562C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
16C22×#63228C2211yescharacteristic
17C22×#63228C2211yescharacteristic
18C23×#3622C2211yescharacteristic
19C2×#10587616C2211yescharacteristic
20C2×C4×D68C2211yescharacteristic, complemented
21C2×#10587567—21no—
22C22×C4⋊Dic17C2211yescharacteristic
23#11762943C418yescomplemented
24#11762919—24no—
25C2×#10587479C2211yescharacteristic, complemented
26C2×#10587479C2211yescharacteristic, complemented
27C2×#10587503—24no—
28C2×#10587503C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
32C2×#10587503C2211yescharacteristic
33C2×#10587503C2211yescharacteristic
34C2×#10587480C2211yescharacteristic, complemented
35C2×#10587480C2211yescharacteristic, complemented
36C2×C22⋊#3622C2211yescharacteristic
37C2×#10587474C2211yescharacteristic, complemented
38C2×#10587474C2211yescharacteristic, complemented
39#11762711C2211yescharacteristic, complemented
40#11762707C2211yescharacteristic, complemented
41#11762701—21no—
42#11762686—21no—
43#11762683—21no—
44C4×C4⋊Dic17C2211yescharacteristic, complemented
45#11762571C2211yescharacteristic, complemented
46#11762571C2211yescharacteristic, complemented
47#11762571C2211yescharacteristic, complemented
48#11762571C2211yescharacteristic, complemented
49#11762564C2211yescharacteristic, complemented
50#11762564C2211yescharacteristic, complemented
51C23×D4×C17C2211yescharacteristic
52C2×C4×D4×C17C2211yescharacteristic
53C2×C4×D4×C17C2211yescharacteristic
54C22×C22⋊C4×C17—21no—
55C17×#390C2211yescharacteristic
56C17×#390C2211yescharacteristic
57C17×#386—21no—
58C17×#386—21no—
59C17×#380C2211yescharacteristic
60C17×#379—21no—
61C4×C22⋊C4×C17C2211yescharacteristic
62C25×C17—21no—
63C22×D4×C17—22no—
64C22×D4×C17—22no—
65C22×D4×C17—21no—
66C22×D4×C17—22no—
67C22×D4×C17—41no—
68C22×D4×C17—41no—
69C22×D4×C17C2×C414yescomplemented
70C22×D4×C17C2311yescharacteristic
71C22×D4×C17C2311yescharacteristic
72C23×C4×C17—21no—
73C23×C4×C17—21no—
74C23×C4×C17C2311yescharacteristic
75C22×C22⋊D17—21no—
76C23×Dic17—21no—
77C22×D68C2311yescharacteristic
78C22×C4×D17—21no—
79C4×D4×C17—22no—
80C4×D4×C17—22no—
81C4×D4×C17—41no—
82C4×D4×C17—41no—
83C2×C4⋊C4×C17C2311yescharacteristic
84C2×C4⋊C4×C17C2311yescharacteristic
85C2×C22⋊C4×C17—21no—
86C2×C22⋊C4×C17—21no—
87C2×C22⋊C4×C17—21no—
88C2×C22⋊C4×C17—21no—
89C2×C22⋊C4×C17—21no—
90C2×C22⋊C4×C17—21no—
91C2×C22⋊C4×C17—21no—
92C2×C22⋊C4×C17—44no—
93C2×C22⋊C4×C17D411yescharacteristic
94C2×C22⋊C4×C17D411yescharacteristic
95C2×C42×C17C2311yescharacteristic
96C2×C42×C17C2311yescharacteristic
97C2×#63228—22no—
98C2×#63228—22no—
99C2×#63228—41no—
100C2×#63228—41no—
101C2×#63228C2×C414yescomplemented
102C2×#63228C2×C414yescomplemented
103#10587616—22no—
104#10587616C2×C414yescomplemented
105C2×#63227—21no—
106C2×#63227—21no—
107C2×#63227—21no—
108C2×#63227—21no—
109C2×C4⋊Dic17—21no—
110C2×C4⋊Dic17—22no—
111C2×C4⋊Dic17—41no—
112C2×C4⋊Dic17C2311yescharacteristic
113C2×C4⋊Dic17C2311yescharacteristic
114C2×C4⋊Dic17C2311yescharacteristic
115C2×#63225—21no—
116C2×C4×Dic17—21no—
117C22×#3622—22no—
118C22×#3622—22no—
119C22×#3622—41no—
120C22×#3622C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122C22×#3622C2311yescharacteristic
123C22×#3622C2311yescharacteristic
124#10587567—44no—
125C4×D68—22no—
126C4×D68—41no—
127C17×#95—21no—
128C17×#95D411yescharacteristic
129C17×#95D411yescharacteristic
130#10587503—22no—
131#10587503—22no—
132#10587503—22no—
133#10587503C2×C414yescomplemented
134#10587503C2×C414yescomplemented
135#10587503D414yescomplemented
136#10587502—21no—
137#10587502—21no—
138C22⋊#3622C2×C414yescomplemented
139#10587480—22no—
140#10587480—41no—
141#10587479—22no—
142#10587479—41no—
143#10587474—22no—
144#10587474—41no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—24no—
148C24×C17—42no—
149C24×C17—42no—
150C24×C17—42no—
151C24×C17—42no—
152C24×C17—81no—
153C24×C17—81no—
154C24×C17C2×D411yescharacteristic
155C23×D17—21no—
156C2×D4×C17—28no—
157C2×D4×C17—24no—
158C2×D4×C17—21no—
159C2×D4×C17—21no—
160C2×D4×C17—21no—
161C2×D4×C17—21no—
162C2×D4×C17—21no—
163C2×D4×C17—21no—
164C2×D4×C17—21no—
165C2×D4×C17—21no—
166C2×D4×C17—44no—
167C2×D4×C17—44no—
168C2×D4×C17—44no—
169C2×D4×C17—42no—
170C2×D4×C17—42no—
171C2×D4×C17C22×C412yes—
172C2×D4×C17C22×C412yes—
173C2×D4×C17C2×D412yes—
174C2×D4×C17#4112yes—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—42no—
182C22×C4×C17—42no—
183C22×C4×C17—42no—
184C22×C4×C17—42no—
185C22×C4×C17—81no—
186C22×C4×C17—81no—
187C22×C4×C17C22×C412yes—
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17#4112yes—
194C22×C4×C17C2411yescharacteristic
195C2×C22⋊D17—24no—
196C2×C22⋊D17—42no—
197C2×C22⋊D17—42no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—42no—
202C22×Dic17—42no—
203C22×Dic17—81no—
204C2×D68—21no—
205C2×D68—21no—
206C2×D68—21no—
207C2×D68—21no—
208C2×D68—21no—
209C2×D68C22×C412yes—
210C2×C4×D17—42no—
211C2×C4×D17—42no—
212C2×C4×D17—81no—
213C4⋊C4×C17—21no—
214C4⋊C4×C17—21no—
215C4⋊C4×C17—21no—
216C4⋊C4×C17—21no—
217C22⋊C4×C17—22no—
218C22⋊C4×C17—22no—
219C22⋊C4×C17—42no—
220C22⋊C4×C17—42no—
221C22⋊C4×C17—42no—
222C22⋊C4×C17—42no—
223C22⋊C4×C17—42no—
224C22⋊C4×C17—81no—
225C22⋊C4×C17—81no—
226C42×C17—21no—
227C42×C17—21no—
228C42×C17—21no—
229C42×C17—21no—
230#63228—28no—
231#63228—44no—
232#63227—24no—
233#63227—42no—
234#63227—42no—
235#63227—81no—
236C4⋊Dic17—21no—
237C4⋊Dic17—21no—
238C4⋊Dic17—21no—
239C4⋊Dic17—21no—
240C4⋊Dic17—42no—
241C4⋊Dic17C22×C412yes—
242C4⋊Dic17C2×D412yes—
243#63225—42no—
244C4×Dic17—42no—
245C2×#3622—21no—
246C2×#3622—21no—
247C2×#3622—21no—
248C2×#3622—21no—
249C2×#3622—21no—
250C2×#3622—21no—
251C2×#3622—21no—
252C2×#3622—21no—
253C2×#3622—21no—
254C2×#3622—44no—
255C2×#3622C22×C412yes—
256C2×#3622C22×C412yes—
257C2×#3622C2×D412yes—
258#22858—171nomaximal, Sylow
259C23×C17—21no—
260C23×C17—21no—
261C23×C17—21no—
262C23×C17—21no—
263C23×C17—22no—
264C23×C17—22no—
265C23×C17—22no—
266C23×C17—22no—
267C23×C17—48no—
268C23×C17—41no—
269C23×C17—41no—
270C23×C17—41no—
271C23×C17—41no—
272C23×C17—41no—
273C23×C17—41no—
274C23×C17—41no—
275C23×C17—41no—
276C23×C17—41no—
277C23×C17—41no—
278C23×C17—48no—
279C23×C17—84no—
280C23×C17—84no—
281C23×C17—84no—
282C23×C17—84no—
283C23×C17—84no—
284C23×C17C4×D412yes—
285C23×C17AGL(1,ℤ/8)12yes—
286C23×C17AGL(1,ℤ/8)12yes—
287C23×C17C22×D411yescharacteristic
288C22×D17—22no—
289C22×D17—41no—
290C22×D17—41no—
291C22×D17—41no—
292C22×D17—41no—
293C22×D17—41no—
294C22×D17—41no—
295D4×C17—22no—
296D4×C17—22no—
297D4×C17—22no—
298D4×C17—22no—
299D4×C17—22no—
300D4×C17—48no—
301D4×C17—41no—
302D4×C17—41no—
303D4×C17C4×D414yescomplemented
304C2×C4×C17—21no—
305C2×C4×C17—21no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—21no—
311C2×C4×C17—21no—
312C2×C4×C17—21no—
313C2×C4×C17—21no—
314C2×C4×C17—21no—
315C2×C4×C17—21no—
316C2×C4×C17—21no—
317C2×C4×C17—21no—
318C2×C4×C17—21no—
319C2×C4×C17—21no—
320C2×C4×C17—21no—
321C2×C4×C17—21no—
322C2×C4×C17—41no—
323C2×C4×C17—41no—
324C2×C4×C17—41no—
325C2×C4×C17—41no—
326C2×C4×C17—41no—
327C2×C4×C17—41no—
328C2×C4×C17—84no—
329C2×C4×C17—84no—
330C2×C4×C17C4×D412yes—
331C2×C4×C17C23×C411yescharacteristic
332C2×C4×C17C22×D411yescharacteristic
333C2×C4×C17C2×#4111yescharacteristic
334C2×C4×C17C2×#4111yescharacteristic
335C2×C4×C17H(5,𝔽2)11yescharacteristic
336C2×C4×C17H(5,𝔽2)11yescharacteristic
337C22⋊D17—48no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—41no—
343C2×Dic17—41no—
344C2×Dic17—41no—
345C2×Dic17—41no—
346C2×Dic17—41no—
347C2×Dic17—84no—
348D68—22no—
349D68—22no—
350D68—41no—
351D68—41no—
352C4×D17—84no—
353#3622—22no—
354#3622—22no—
355#3622—22no—
356#3622—41no—
357C2×#447—171no—
358C2×#442—171no—
359C22×#102—171no—
360#2361—171no—
361D4×C22⋊C4D1711yescharacteristic, complemented
362#1972—171no—
363#1936—171no—
364#1926—171no—
365#1893—171no—
366#1879—171no—
367#1879—171no—
368#1864—171no—
369#1853—171no—
370#1762—171no—
371#1752—171no—
372C22×C17—22no—
373C22×C17—22no—
374C22×C17—22no—
375C22×C17—22no—
376C22×C17—22no—
377C22×C17—22no—
378C22×C17—24no—
379C22×C17—42no—
380C22×C17—42no—
381C22×C17—42no—
382C22×C17—42no—
383C22×C17—42no—
384C22×C17—42no—
385C22×C17—42no—
386C22×C17—42no—
387C22×C17—42no—
388C22×C17—816no—
389C22×C17—81no—
390C22×C17—81no—
391C22×C17—81no—
392C22×C17—81no—
393C22×C17#44214yescomplemented
394C22×C17C2×C4×D411yescharacteristic
395C22×C17D4211yescharacteristic
396C22×C17#54611yescharacteristic
397C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C17#57611yescharacteristic
400C22×C17#57711yescharacteristic
401C2×D17—42no—
402C2×D17—42no—
403C2×D17—42no—
404C2×D17—81no—
405C2×D17—81no—
406C2×D17—81no—
407C2×D17—81no—
408C4×C17—22no—
409C4×C17—41no—
410C4×C17—41no—
411C4×C17—41no—
412C4×C17—41no—
413C4×C17—81no—
414C4×C17—81no—
415C4×C17C2×C4×D411yescharacteristic
416C4×C17#51811yescharacteristic
417C4×C17#54611yescharacteristic
418C4×C17#55111yescharacteristic
419Dic17—42no—
420Dic17—42no—
421Dic17—81no—
422C23×D4C2×D1711yescharacteristic
423C22×D8—171no—
424C22×D8—171no—
425C23×C8—171no—
426C2×#121—171no—
427C2×C4×D4—171no—
428C2×C4×D4—341no—
429C2×C4×D4C2×D1711yescharacteristic
430C2×C4×D4C2×D1711yescharacteristic
431C22×C4⋊C4—171no—
432C22×C22⋊C4—21no—
433#447—178no—
434#442—344no—
435C2×#106—171no—
436C2×#106—171no—
437C2×#102—171no—
438C2×#102—171no—
439C2×#102—171no—
440C2×#102—171no—
441C2×#102—171no—
442C2×#102—171no—
443C2×#102—171no—
444C2×#102—171no—
445C2×#102—344no—
446C2×C22⋊C8—171no—
447C2×#97—171no—
448C2×#97—171no—
449#390—171no—
450#390C2×D1711yescharacteristic
451#390C2×D1711yescharacteristic
452#389—171no—
453#388—341no—
454#386—21no—
455#386—21no—
456#386—341no—
457#385—341no—
458#380C2×D1711yescharacteristic
459#379—21no—
460C4×C4⋊C4—171no—
461C4×C22⋊C4C2×D1711yescharacteristic
462#340—171no—
463#340—171no—
464#340—171no—
465#340—171no—
466#336—171no—
467#336—171no—
468C2×C17—24no—
469C2×C17—44no—
470C2×C17—82no—
471C2×C17#235811yescharacteristic
472C2×C17C2×#44211yescharacteristic
473C2×C17#294611yescharacteristic
474C2×C17#326411yescharacteristic
475C2×C17#326511yescharacteristic
476C2×C17#330611yescharacteristic
477C2×C17#331811yescharacteristic
478D17—82no—
479C25—21no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—41no—
485C22×D4—41no—
486C22×D4—171no—
487C22×D4—341no—
488C22×D4C4×D1714yescomplemented
489C22×D4C22×D1711yescharacteristic
490C22×D4C22×D1711yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—341no—
494C23×C4—341no—
495C23×C4C22×D1711yescharacteristic
496C2×D8—174no—
497C2×D8—174no—
498C2×D8—342no—
499C2×D8—342no—
500C2×D8—681no—
501C2×D8—681no—
502C22×C8—171no—
503C22×C8—171no—
504C22×C8—171no—
505C22×C8—171no—
506C22×C8—342no—
507C22×C8—342no—
508C22×C8—681no—
509#121—174no—
510#121—342no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—41no—
514C4×D4—41no—
515C4×D4—342no—
516C4×D4—681no—
517C4×D4—684no—
518C2×C4⋊C4—171no—
519C2×C4⋊C4—171no—
520C2×C4⋊C4—171no—
521C2×C4⋊C4—342no—
522C2×C4⋊C4—341no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4—681no—
525C2×C4⋊C4C22×D1711yescharacteristic
526C2×C4⋊C4C22×D1711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—44no—
535C2×C22⋊C4—341no—
536C2×C22⋊C4—341no—
537C2×C22⋊C4—341no—
538C2×C22⋊C4—341no—
539C2×C22⋊C4C22⋊D1711yescharacteristic
540C2×C22⋊C4C22⋊D1711yescharacteristic
541C2×C42—341no—
542C2×C42C22×D1711yescharacteristic
543C2×C42C22×D1711yescharacteristic
544#106—342no—
545#106—681no—
546#102—174no—
547#102—174no—
548#102—174no—
549#102—342no—
550#102—342no—
551#102—342no—
552#102—342no—
553#102—681no—
554C22⋊C8—174no—
555#97—342no—
556#97—681no—
557#95—21no—
558#95—341no—
559#95—341no—
560#95C22⋊D1711yescharacteristic
561#95C22⋊D1711yescharacteristic
562C17#2285811yescharacteristic, complemented, Sylow
563C24—21no—
564C24—21no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24—341no—
573C24C2×C22⋊D1711yescharacteristic
574C2×D4—28no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—24no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—172no—
590C2×D4—344no—
591C2×D4—341no—
592C2×D4—341no—
593C2×D4—341no—
594C2×D4—341no—
595C2×D4—341no—
596C2×D4—682no—
597C2×D4—682no—
598C2×D4C2×C4×D1712yes—
599C2×D4C2×C4×D1712yes—
600C2×D4D4×D1712yes—
601C2×D4#6325412yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—341no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—682no—
618C22×C4—682no—
619C22×C4—682no—
620C22×C4—682no—
621C22×C4—1361no—
622C22×C4—1361no—
623C22×C4C2×C4×D1712yes—
624C22×C4#6325212yes—
625C22×C4C2×C22⋊D1711yescharacteristic
626C22×C4C2×C22⋊D1711yescharacteristic
627C22×C4C2×C22⋊D1711yescharacteristic
628C22×C4C2×C22⋊D1711yescharacteristic
629C22×C4C2×C22⋊D1711yescharacteristic
630C22×C4C23×D1711yescharacteristic
631D8—348no—
632D8—684no—
633C2×C8—172no—
634C2×C8—172no—
635C2×C8—172no—
636C2×C8—341no—
637C2×C8—341no—
638C2×C8—341no—
639C2×C8—341no—
640C2×C8—341no—
641C2×C8—341no—
642C2×C8—341no—
643C2×C8—341no—
644C2×C8—341no—
645C2×C8—684no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—172no—
651C4⋊C4—172no—
652C4⋊C4—341no—
653C4⋊C4—341no—
654C4⋊C4—341no—
655C4⋊C4—341no—
656C4⋊C4—682no—
657C4⋊C4—682no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—344no—
668C22⋊C4—682no—
669C22⋊C4—682no—
670C22⋊C4—1361no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—682no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—48no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—342no—
702C23—681no—
703C23—681no—
704C23—681no—
705C23—681no—
706C23—681no—
707C23—681no—
708C23C4×C22⋊D1712yes—
709C23#1058761812yes—
710C23#1058763512yes—
711C23C22×C22⋊D1711yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—342no—
721D4—342no—
722D4—688no—
723D4—681no—
724D4—681no—
725D4#1058756714yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—681no—
755C2×C4—681no—
756C2×C4—681no—
757C2×C4—681no—
758C2×C4—681no—
759C2×C4—681no—
760C2×C4—681no—
761C2×C4—1364no—
762C2×C4—1364no—
763C2×C4C4×C22⋊D1712yes—
764C2×C4C22×C4×D1711yescharacteristic
765C2×C4C2×#6325211yescharacteristic
766C2×C4C2×D4×D1711yescharacteristic
767C2×C4C2×#6325411yescharacteristic
768C2×C4#1058769111yescharacteristic
769C2×C4#1058769111yescharacteristic
770C8—342no—
771C8—342no—
772C8—342no—
773C8—681no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—816no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—682no—
796C22—682no—
797C22—682no—
798C22—1361no—
799C22—1361no—
800C22—1361no—
801C22—1361no—
802C22#1176291914yescomplemented
803C22C2×C4×C22⋊D1711yescharacteristic
804C22D4×C22⋊D1711yescharacteristic
805C22#1176345311yescharacteristic
806C22C2×#1058763511yescharacteristic
807C22C2×#1058761811yescharacteristic
808C22#1176361211yescharacteristic
809C22#1176362011yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—81no—
816C4—81no—
817C4—682no—
818C4—682no—
819C4—1361no—
820C4C2×#1058756711yescharacteristic
821C4#1176328211yescharacteristic
822C4#1176344911yescharacteristic
823C4#1176348511yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—1362no—
828C2#1453176311yescharacteristic
829C2C2×#1176291911yescharacteristic
830C2#1453761611yescharacteristic
831C2#1454026511yescharacteristic
832C2#1454027511yescharacteristic
833C2#1454074511yescharacteristic
834C2#1454092511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingD4×C22⋊C4×C17C2
socleC23×C17C22×D4
prime radicalC2×#11762943C2
cosocleC22×C4×C17C24
hypercenterD4×C22⋊C4D17
hypocenterC17#22858
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11762919C2semidirect
3. C22×#10587503C2semidirect
4. #14531798C2semidirect
5. #14529659C2semidirect
6. #14529484C2semidirect
7. #14529408C2semidirect
8. #14529210C2semidirect
9. #14529135C2semidirect
10. #14529132C2semidirect
11. #14529045C2semidirect
12. #14528976C2semidirect
13. #14528609C2semidirect
14. #14528562C2semidirect
15. D4×C22⋊C4×C17C2semidirect
20. C2×C4×D68C22semidirect
23. #11762943C4semidirect
25. C2×#10587479C22semidirect
26. C2×#10587479C22semidirect
34. C2×#10587480C22semidirect
35. C2×#10587480C22semidirect
37. C2×#10587474C22semidirect
38. C2×#10587474C22semidirect
39. #11762711C22semidirect
40. #11762707C22semidirect
44. C4×C4⋊Dic17C22semidirect
45. #11762571C22semidirect
46. #11762571C22semidirect
47. #11762571C22semidirect
48. #11762571C22semidirect
49. #11762564C22semidirect
50. #11762564C22semidirect
69. C22×D4×C17C2×C4semidirect
101. C2×#63228C2×C4semidirect
102. C2×#63228C2×C4semidirect
104. #10587616C2×C4semidirect
133. #10587503C2×C4semidirect
134. #10587503C2×C4semidirect
135. #10587503D4semidirect
138. C22⋊#3622C2×C4semidirect
303. D4×C17C4×D4semidirect
361. D4×C22⋊C4D17semidirect
393. C22×C17#442semidirect
488. C22×D4C4×D17semidirect
562. C17#22858semidirect
725. D4#10587567semidirect
802. C22#11762919semidirect

Maximal subgroups

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

subgroupindex
C2×#117629432
C2×#117629192
C22×#105875032
#145317982
#145296592
#145294842
#145294082
#145292102
#145291352
#145291322
#145290452
#145289762
#145286092
#145285622
D4×C22⋊C4×C172
#2285817