Finite Group Databasebeta

← #17045421

Subgroups — #17045421

Order 4352.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762772C211yesmaximal, characteristic, complemented
2C4×#10587623C211yesmaximal, characteristic
3#14529580C211yesmaximal, characteristic, complemented
4#14529576C211yesmaximal, characteristic, complemented
5#14529396C211yesmaximal, characteristic, complemented
6#14529390C211yesmaximal, characteristic, complemented
7#14529390C211yesmaximal, characteristic, complemented
8#14529389C211yesmaximal, characteristic, complemented
9#14529082C211yesmaximal, characteristic, complemented
10#14529081C211yesmaximal, characteristic, complemented
11#14529081C211yesmaximal, characteristic, complemented
12#14528966C211yesmaximal, characteristic, complemented
13#14528693C211yesmaximal, characteristic, complemented
14#14528565C211yesmaximal, characteristic, complemented
15C2×C17×#436C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×#63223C2211yescharacteristic
18C2×#10587623C411yescharacteristic
19C2×C4×C22⋊D17C2211yescharacteristic
20C2×C4×C22⋊D17C2211yescharacteristic
21C2×#10587485C2211yescharacteristic, complemented
22C2×#10587485C2211yescharacteristic, complemented
23#11762772—24no—
24C2×C22⋊#3622C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic, complemented
26C2×C22⋊#3622C2211yescharacteristic, complemented
27C2×#10587491C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33C2×#10587491C2211yescharacteristic
34C2×#10587491C2211yescharacteristic
35C2×#10587486C2211yescharacteristic, complemented
36C2×C8×Dic17C2211yescharacteristic, complemented
37#11762689C411yescharacteristic
38#11762685C411yescharacteristic
39#11762685C411yescharacteristic
40#11762681C411yescharacteristic
41#11762680C411yescharacteristic
42#11762680C411yescharacteristic
43#11762664C411yescharacteristic
44C4×#63227C2211yescharacteristic
45C4×#63227C2211yescharacteristic
46C4×C22⋊Dic17C2211yescharacteristic
47#11762564C2211yescharacteristic, complemented
48#11762564C2211yescharacteristic, complemented
49#11762563C2211yescharacteristic, complemented
50#11762563C2211yescharacteristic, complemented
51#11762563C2211yescharacteristic, complemented
52#11762563C2211yescharacteristic, complemented
53C22×M16×C17C2211yescharacteristic
54C22×M16×C17C2211yescharacteristic, complemented
55C2×C4×D4×C17C2211yescharacteristic
56C17×#436—24no—
57C2×C17×C4⋊C8C2211yescharacteristic, complemented
58C2×C17×C22⋊C8C2211yescharacteristic
59C2×C17×C22⋊C8C2211yescharacteristic, complemented
60C2×C4×C8×C17C2211yescharacteristic, complemented
61C24×D17C2×C411yescharacteristic
62C22×D4×C17C2×C411yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C22×C22⋊D17C2×C411yescharacteristic
66C22×C22⋊D17C2×C411yescharacteristic
67C23×Dic17C2×C411yescharacteristic
68C22×C4×D17—22no—
69C22×C4×D17—22no—
70C22×C4×D17—41no—
71C22×C4×D17—41no—
72C22×C4×D17—41no—
73C22×C4×D17—41no—
74C22×C4×D17C2×C411yescharacteristic
75C22×C4×D17C2×C411yescharacteristic
76C22×C4×D17C2311yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C2×M16×C17—22no—
79C2×M16×C17—41no—
80C2×M16×C17—41no—
81C2×M16×C17—41no—
82C2×M16×C17—41no—
83C2×M16×C17D414yescomplemented
84C22×C8×C17C2311yescharacteristic
85C22×C8×C17C2311yescharacteristic
86C22×C8×C17C2311yescharacteristic
87C22×C8×C17C2311yescharacteristic
88C4×D4×C17—22no—
89C4×D4×C17—22no—
90C2×C4⋊C4×C17C2×C411yescharacteristic
91C2×C22⋊C4×C17C2×C411yescharacteristic
92C2×C22⋊C4×C17C2×C411yescharacteristic
93C2×C42×C17C2311yescharacteristic
94C2×C22⋊Dic17C2×C411yescharacteristic
95C2×C22⋊Dic17C2×C411yescharacteristic
96C2×C22⋊Dic17C2×C411yescharacteristic
97C2×C22⋊Dic17C2×C411yescharacteristic
98#10587623—24no—
99C4×C22⋊D17—41no—
100C4×C22⋊D17—41no—
101C4×C22⋊D17—41no—
102C4×C22⋊D17—41no—
103C2×#63227C2×C411yescharacteristic
104C2×#63227C2×C411yescharacteristic
105C2×#63227C2×C411yescharacteristic
106C2×#63227C2×C411yescharacteristic
107C2×#63227C2×C411yescharacteristic
108C2×#63227C2×C411yescharacteristic
109C2×#63225C2×C411yescharacteristic
110C2×#63225C2×C411yescharacteristic
111C2×C4×Dic17C2311yescharacteristic
112C2×C4×Dic17C2311yescharacteristic
113C2×#63223—22no—
114C2×#63223—41no—
115C2×#63223—41no—
116C22×#3622C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C22×#3622C2311yescharacteristic
120C17×C4⋊C8—22no—
121C17×C22⋊C8—22no—
122C17×C22⋊C8—22no—
123C4×C8×C17—22no—
124#10587502C2×C411yescharacteristic
125#10587502C2×C411yescharacteristic
126#10587502C2×C411yescharacteristic
127#10587502C2×C411yescharacteristic
128#10587502C2×C411yescharacteristic
129#10587502C2×C411yescharacteristic
130C22⋊#3622—22no—
131C22⋊#3622—41no—
132C22⋊#3622—41no—
133#10587491—22no—
134#10587491—22no—
135#10587491—22no—
136#10587491—22no—
137#10587491—41no—
138#10587491—41no—
139#10587491—41no—
140#10587491—41no—
141#10587486—41no—
142#10587485—41no—
143#10587485—41no—
144C8×Dic17—41no—
145C24×C17C22×C411yescharacteristic
146C24×C17C22×C411yescharacteristic
147C23×D17—22no—
148C23×D17—22no—
149C23×D17—22no—
150C23×D17—41no—
151C23×D17—41no—
152C23×D17—41no—
153C23×D17—41no—
154C23×D17C22×C411yescharacteristic
155C23×D17C22×C411yescharacteristic
156C2×D4×C17—22no—
157C2×D4×C17—22no—
158C2×D4×C17—41no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17C22×C411yescharacteristic
170C22×C4×C17C22×C411yescharacteristic
171C22×C4×C17C22×C411yescharacteristic
172C22×C4×C17C22×C411yescharacteristic
173C22×C4×C17C2×D412yes—
174C22×C4×C17#4112yes—
175C22×C4×C17C2411yescharacteristic
176C2×C22⋊D17—22no—
177C2×C22⋊D17—22no—
178C2×C22⋊D17—22no—
179C2×C22⋊D17—41no—
180C2×C22⋊D17—41no—
181C2×C22⋊D17—41no—
182C22×Dic17—22no—
183C22×Dic17—41no—
184C22×Dic17—41no—
185C22×Dic17C22×C411yescharacteristic
186C22×Dic17C22×C411yescharacteristic
187C22×Dic17C22×C411yescharacteristic
188C22×Dic17C22×C411yescharacteristic
189C22×Dic17C22×C411yescharacteristic
190C22×Dic17C22×C411yescharacteristic
191C2×C4×D17—22no—
192C2×C4×D17—22no—
193C2×C4×D17—21no—
194C2×C4×D17—21no—
195C2×C4×D17—21no—
196C2×C4×D17—21no—
197C2×C4×D17—21no—
198C2×C4×D17—21no—
199C2×C4×D17—21no—
200C2×C4×D17—21no—
201C2×C4×D17—21no—
202C2×C4×D17—21no—
203C2×C4×D17—21no—
204C2×C4×D17—21no—
205C2×C4×D17—41no—
206C2×C4×D17—41no—
207C2×C4×D17—41no—
208C2×C4×D17—41no—
209C2×C4×D17—44no—
210C2×C4×D17—44no—
211C2×C4×D17—44no—
212C2×C4×D17—44no—
213M16×C17—44no—
214M16×C17—44no—
215C2×C8×C17—21no—
216C2×C8×C17—21no—
217C2×C8×C17—21no—
218C2×C8×C17—21no—
219C2×C8×C17—21no—
220C2×C8×C17—21no—
221C2×C8×C17—21no—
222C2×C8×C17—21no—
223C2×C8×C17—21no—
224C2×C8×C17—21no—
225C2×C8×C17C2×D412yes—
226C2×C8×C17C2×D412yes—
227C4⋊C4×C17—22no—
228C22⋊C4×C17—22no—
229C22⋊C4×C17—22no—
230C42×C17—21no—
231C42×C17—21no—
232C22⋊Dic17—22no—
233C22⋊Dic17—41no—
234C22⋊Dic17—41no—
235C22⋊Dic17—41no—
236#63227—22no—
237#63227—22no—
238#63227—41no—
239#63227—41no—
240#63227—41no—
241#63227M1614yescomplemented
242#63225—41no—
243#63225—41no—
244C4×Dic17—21no—
245C4×Dic17—21no—
246C4×Dic17—21no—
247C4×Dic17—21no—
248#63223—44no—
249C2×#3622—21no—
250C2×#3622—21no—
251C2×#3622—21no—
252C2×#3622—21no—
253C2×#3622—21no—
254C2×#3622—21no—
255C2×#3622—21no—
256C2×#3622—21no—
257C2×#3622—21no—
258C2×#3622—21no—
259C2×#3622—21no—
260C2×#3622—21no—
261#22038—171nomaximal, Sylow
262C23×C17—21no—
263C23×C17—21no—
264C23×C17—21no—
265C23×C17—21no—
266C23×C17—21no—
267C23×C17—21no—
268C23×C17—21no—
269C23×C17—21no—
270C23×C17—21no—
271C23×C17—21no—
272C23×C17—21no—
273C23×C17—21no—
274C23×C17—21no—
275C23×C17C4×D412yes—
276C23×C17C23×C411yescharacteristic
277C22×D17—21no—
278C22×D17—21no—
279C22×D17—21no—
280C22×D17—21no—
281C22×D17—21no—
282C22×D17—21no—
283C22×D17—21no—
284C22×D17—21no—
285C22×D17—21no—
286C22×D17—21no—
287C22×D17—21no—
288C22×D17—21no—
289C22×D17—44no—
290C22×D17—44no—
291C22×D17—44no—
292C22×D17—44no—
293C22×D17—44no—
294C22×D17—44no—
295C22×D17—44no—
296C22×D17C2×M1612yes—
297C22×D17#13112yes—
298D4×C17—44no—
299C2×C4×C17—21no—
300C2×C4×C17—21no—
301C2×C4×C17—21no—
302C2×C4×C17—21no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—21no—
308C2×C4×C17—21no—
309C2×C4×C17—21no—
310C2×C4×C17—21no—
311C2×C4×C17—21no—
312C2×C4×C17—21no—
313C2×C4×C17—41no—
314C2×C4×C17—41no—
315C2×C4×C17—41no—
316C2×C4×C17—41no—
317C2×C4×C17C4×D412yes—
318C2×C4×C17C2×M1612yes—
319C2×C4×C17C22×D411yescharacteristic
320C2×C4×C17C2×#4111yescharacteristic
321C2×C4×C17H(5,𝔽2)11yescharacteristic
322C2×C4×C17H(5,𝔽2)11yescharacteristic
323C2×C4×C17H(5,𝔽2)11yescharacteristic
324C2×C4×C17H(5,𝔽2)11yescharacteristic
325C22⋊D17—44no—
326C22⋊D17—44no—
327C2×Dic17—21no—
328C2×Dic17—21no—
329C2×Dic17—21no—
330C2×Dic17—21no—
331C2×Dic17—21no—
332C2×Dic17—21no—
333C2×Dic17—21no—
334C2×Dic17—21no—
335C2×Dic17—21no—
336C2×Dic17—21no—
337C2×Dic17—21no—
338C2×Dic17—21no—
339C2×Dic17—21no—
340C2×Dic17—21no—
341C2×Dic17—21no—
342C2×Dic17—21no—
343C2×Dic17—21no—
344C2×Dic17—44no—
345C2×Dic17C2×M1612yes—
346C4×D17—44no—
347C4×D17—44no—
348C4×D17—41no—
349C4×D17—41no—
350C4×D17—41no—
351C4×D17—41no—
352C4×D17—41no—
353C4×D17—41no—
354C4×D17—41no—
355C4×D17—41no—
356C8×C17—22no—
357C8×C17—22no—
358C8×C17—41no—
359C8×C17—41no—
360#3622—41no—
361#3622—41no—
362#3622—41no—
363#3622—41no—
364C2×#436D1711yescharacteristic, complemented
365C2×#407—171no—
366C4×#120—171no—
367#1955—171no—
368#1954—171no—
369#1924—171no—
370#1923—171no—
371#1923—171no—
372#1923—171no—
373#1870—171no—
374#1870—171no—
375#1870—171no—
376#1851—171no—
377#1779—171no—
378#1753—171no—
379C22×C17—22no—
380C22×C17—22no—
381C22×C17—22no—
382C22×C17—41no—
383C22×C17—41no—
384C22×C17—41no—
385C22×C17—41no—
386C22×C17—41no—
387C22×C17—41no—
388C22×C17—41no—
389C22×C17—41no—
390C22×C17—41no—
391C22×C17—41no—
392C22×C17—41no—
393C22×C17C2×C4×D411yescharacteristic
394C22×C17#51811yescharacteristic
395C22×C17#51811yescharacteristic
396C22×C17C22×M1611yescharacteristic
397C22×C17C2×#13111yescharacteristic
398C22×C17#56811yescharacteristic
399C22×C17#56811yescharacteristic
400C2×D17—22no—
401C2×D17—22no—
402C2×D17—22no—
403C2×D17—22no—
404C2×D17—22no—
405C2×D17—22no—
406C2×D17—416no—
407C2×D17—41no—
408C2×D17—41no—
409C2×D17—41no—
410C2×D17—41no—
411C2×D17—41no—
412C2×D17—41no—
413C2×D17—41no—
414C2×D17—41no—
415C4×C17—22no—
416C4×C17—22no—
417C4×C17—41no—
418C4×C17—41no—
419C4×C17#53411yescharacteristic
420C4×C17#53511yescharacteristic
421C4×C17#53811yescharacteristic
422C4×C17#53811yescharacteristic
423Dic17—22no—
424Dic17—41no—
425Dic17—41no—
426Dic17—41no—
427Dic17—41no—
428Dic17—41no—
429C24×C4—171no—
430C22×M16—171no—
431C22×M16C2×D1711yescharacteristic
432C22×M16C2×D1711yescharacteristic, complemented
433C2×#120—171no—
434C2×C4×D4—171no—
435C2×C4×D4—171no—
436C2×C4×D4C2×D1711yescharacteristic
437#436—24no—
438C2×C4⋊C8—171no—
439C2×C4⋊C8—171no—
440C2×C4⋊C8C2×D1711yescharacteristic, complemented
441#407—344no—
442C2×C22⋊C8—171no—
443C2×C22⋊C8—171no—
444C2×C22⋊C8—171no—
445C2×C22⋊C8—171no—
446C2×C22⋊C8—171no—
447C2×C22⋊C8—171no—
448C2×C22⋊C8—171no—
449C2×C22⋊C8—171no—
450C2×C22⋊C8—171no—
451C2×C22⋊C8—171no—
452C2×C22⋊C8—171no—
453C2×C22⋊C8C2×D1711yescharacteristic
454C2×C22⋊C8C2×D1711yescharacteristic, complemented
455C2×#97—171no—
456C2×C4×C8—171no—
457C2×C4×C8C2×D1711yescharacteristic, complemented
458#386—171no—
459#386—171no—
460#386—171no—
461#385—171no—
462#385—171no—
463#385—171no—
464#379—171no—
465C4×C22⋊C4—171no—
466C4×C22⋊C4—171no—
467C4×C22⋊C4—171no—
468#336—171no—
469#336—171no—
470#336—171no—
471#336—171no—
472#336—171no—
473#336—171no—
474C2×C17—42no—
475C2×C17—81no—
476C2×C17#232111yescharacteristic
477C2×C17#293311yescharacteristic
478C2×C17D4×M1611yescharacteristic
479C2×C17#297411yescharacteristic
480C2×C17#297511yescharacteristic
481C2×C17#297611yescharacteristic
482C2×C17#297811yescharacteristic
483D17—42no—
484D17—42no—
485C25—171no—
486C22×D4—171no—
487C22×D4—171no—
488C22×D4C4×D1711yescharacteristic
489C23×C4—171no—
490C23×C4—171no—
491C23×C4—171no—
492C23×C4—171no—
493C23×C4—171no—
494C23×C4—342no—
495C23×C4—342no—
496C23×C4—681no—
497C23×C4—681no—
498C23×C4—681no—
499C23×C4—681no—
500C23×C4C22×D1711yescharacteristic
501C23×C4C22×D1711yescharacteristic
502C2×M16—22no—
503C2×M16—41no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—342no—
508C2×M16—681no—
509C2×M16—681no—
510C2×M16C22⋊D1714yescomplemented
511C22×C8—171no—
512C22×C8—171no—
513C22×C8—171no—
514C22×C8—171no—
515C22×C8C22×D1711yescharacteristic
516C22×C8C22×D1711yescharacteristic
517C22×C8C22×D1711yescharacteristic
518C22×C8C22×D1711yescharacteristic
519#120—344no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—681no—
523C4×D4—681no—
524C4×D4—681no—
525C4×D4—681no—
526C2×C4⋊C4—171no—
527C2×C4⋊C4—171no—
528C2×C4⋊C4C4×D1711yescharacteristic
529C2×C22⋊C4—171no—
530C2×C22⋊C4—171no—
531C2×C22⋊C4—171no—
532C2×C22⋊C4—171no—
533C2×C22⋊C4—171no—
534C2×C22⋊C4—171no—
535C2×C22⋊C4—171no—
536C2×C22⋊C4—171no—
537C2×C22⋊C4—171no—
538C2×C22⋊C4—171no—
539C2×C22⋊C4C4×D1711yescharacteristic
540C2×C22⋊C4C4×D1711yescharacteristic
541C2×C42—171no—
542C2×C42—171no—
543C2×C42C22×D1711yescharacteristic
544C4⋊C8—22no—
545C4⋊C8—681no—
546C4⋊C8—681no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—342no—
550C22⋊C8—342no—
551C22⋊C8—342no—
552C22⋊C8—342no—
553C22⋊C8—342no—
554C22⋊C8—681no—
555C22⋊C8—681no—
556C22⋊C8—681no—
557C22⋊C8—681no—
558C22⋊C8—681no—
559C22⋊C8—681no—
560#97—681no—
561C4×C8—22no—
562C4×C8—681no—
563#95—171no—
564#95—171no—
565#95—171no—
566#95—171no—
567#95—171no—
568#95—171no—
569C17#2203811yescharacteristic, complemented, Sylow
570C24—171no—
571C24—171no—
572C24—342no—
573C24—342no—
574C24—342no—
575C24—681no—
576C24—681no—
577C24—681no—
578C24—681no—
579C24C2×C4×D1711yescharacteristic
580C24C2×C4×D1711yescharacteristic
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—41no—
584C2×D4—342no—
585C2×D4—342no—
586C2×D4—342no—
587C2×D4—681no—
588C2×D4—681no—
589C2×D4—681no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—171no—
601C22×C4—171no—
602C22×C4—171no—
603C22×C4—171no—
604C22×C4—171no—
605C22×C4—171no—
606C22×C4—342no—
607C22×C4—341no—
608C22×C4—341no—
609C22×C4—341no—
610C22×C4—341no—
611C22×C4—341no—
612C22×C4—341no—
613C22×C4—341no—
614C22×C4—341no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—341no—
618C22×C4—341no—
619C22×C4—342no—
620C22×C4—342no—
621C22×C4—681no—
622C22×C4—681no—
623C22×C4—681no—
624C22×C4—681no—
625C22×C4—684no—
626C22×C4—684no—
627C22×C4—684no—
628C22×C4—684no—
629C22×C4—681no—
630C22×C4—681no—
631C22×C4C2×C4×D1711yescharacteristic
632C22×C4C2×C4×D1711yescharacteristic
633C22×C4C2×C4×D1711yescharacteristic
634C22×C4C2×C4×D1711yescharacteristic
635C22×C4#6325212yes—
636C22×C4C2×C22⋊D1712yes—
637C22×C4C23×D1711yescharacteristic
638M16—44no—
639M16—44no—
640M16—684no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—341no—
652C2×C8—341no—
653C2×C8—341no—
654C2×C8—341no—
655C2×C8—341no—
656C2×C8—341no—
657C2×C8—341no—
658C2×C8—341no—
659C2×C8—341no—
660C2×C8—341no—
661C2×C8—341no—
662C2×C8—341no—
663C2×C8C2×C22⋊D1712yes—
664C2×C8C2×C22⋊D1712yes—
665C4⋊C4—22no—
666C4⋊C4—681no—
667C4⋊C4—681no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—174no—
671C22⋊C4—342no—
672C22⋊C4—342no—
673C22⋊C4—342no—
674C22⋊C4—681no—
675C22⋊C4—681no—
676C22⋊C4—681no—
677C22⋊C4—681no—
678C22⋊C4—681no—
679C22⋊C4—681no—
680C42—21no—
681C42—21no—
682C42—341no—
683C42—341no—
684C42—341no—
685C42—341no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—172no—
700C23—172no—
701C23—341no—
702C23—341no—
703C23—341no—
704C23—341no—
705C23—341no—
706C23—341no—
707C23—341no—
708C23—341no—
709C23—341no—
710C23—341no—
711C23—341no—
712C23—341no—
713C23—684no—
714C23—684no—
715C23—684no—
716C23—684no—
717C23—684no—
718C23—684no—
719C23—684no—
720C23C4×C22⋊D1712yes—
721C23C22×C4×D1711yescharacteristic
722D4—44no—
723D4—684no—
724D4—684no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—172no—
744C2×C4—341no—
745C2×C4—341no—
746C2×C4—341no—
747C2×C4—341no—
748C2×C4—341no—
749C2×C4—341no—
750C2×C4—341no—
751C2×C4—341no—
752C2×C4—341no—
753C2×C4—341no—
754C2×C4—341no—
755C2×C4—341no—
756C2×C4—341no—
757C2×C4—341no—
758C2×C4—341no—
759C2×C4—341no—
760C2×C4—341no—
761C2×C4—684no—
762C2×C4—684no—
763C2×C4—684no—
764C2×C4—681no—
765C2×C4—681no—
766C2×C4—681no—
767C2×C4—681no—
768C2×C4—681no—
769C2×C4—681no—
770C2×C4—681no—
771C2×C4—681no—
772C2×C4M16×D1712yes—
773C2×C4C4×C22⋊D1712yes—
774C2×C4C2×#6325211yescharacteristic
775C2×C4#1058769111yescharacteristic
776C2×C4#1058769111yescharacteristic
777C2×C4#1058769611yescharacteristic
778C2×C4#1058769611yescharacteristic
779C2×C4C22×C22⋊D1711yescharacteristic
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C8—681no—
785C8—681no—
786C8—681no—
787C8—681no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—342no—
803C22—342no—
804C22—342no—
805C22—342no—
806C22—342no—
807C22—342no—
808C22—6816no—
809C22—681no—
810C22—681no—
811C22—681no—
812C22—681no—
813C22—681no—
814C22—681no—
815C22—681no—
816C22—681no—
817C22C2×C4×C22⋊D1711yescharacteristic
818C22#1176328111yescharacteristic
819C22#1176328111yescharacteristic
820C22C2×M16×D1711yescharacteristic
821C22#131×D1711yescharacteristic
822C22#1176357411yescharacteristic
823C22#1176357511yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—342no—
829C4—681no—
830C4—681no—
831C4—681no—
832C4—681no—
833C4—681no—
834C4#1176336811yescharacteristic
835C4#1176337311yescharacteristic
836C4#1176339211yescharacteristic
837C4#1176339211yescharacteristic
838C2—42no—
839C2—81no—
840C2—682no—
841C2—682no—
842C2#1453143811yescharacteristic
843C2#1453750611yescharacteristic
844C2M16×C22⋊D1711yescharacteristic
845C2#1453781611yescharacteristic
846C2#1453782211yescharacteristic
847C2#1453782811yescharacteristic
848C2#1453784111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC2×C17×#436C2
prime radicalC2×#10587623C4
cosocleC22×C4×C17C24
hypercenterC2×#436D17
hypocenterC17#22038
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#11762772C2semidirect
3. #14529580C2semidirect
4. #14529576C2semidirect
5. #14529396C2semidirect
6. #14529390C2semidirect
7. #14529390C2semidirect
8. #14529389C2semidirect
9. #14529082C2semidirect
10. #14529081C2semidirect
11. #14529081C2semidirect
12. #14528966C2semidirect
13. #14528693C2semidirect
14. #14528565C2semidirect
15. C2×C17×#436C2semidirect
21. C2×#10587485C22semidirect
22. C2×#10587485C22semidirect
25. C2×C22⋊#3622C22semidirect
26. C2×C22⋊#3622C22semidirect
35. C2×#10587486C22semidirect
36. C2×C8×Dic17C22semidirect
47. #11762564C22semidirect
48. #11762564C22semidirect
49. #11762563C22semidirect
50. #11762563C22semidirect
51. #11762563C22semidirect
52. #11762563C22semidirect
54. C22×M16×C17C22semidirect
57. C2×C17×C4⋊C8C22semidirect
59. C2×C17×C22⋊C8C22semidirect
60. C2×C4×C8×C17C22semidirect
83. C2×M16×C17D4semidirect
241. #63227M16semidirect
364. C2×#436D17semidirect
432. C22×M16C2×D17semidirect
440. C2×C4⋊C8C2×D17semidirect
454. C2×C22⋊C8C2×D17semidirect
457. C2×C4×C8C2×D17semidirect
510. C2×M16C22⋊D17semidirect
569. C17#22038semidirect

Maximal subgroups

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

subgroupindex
C2×#117627722
C4×#105876232
#145295802
#145295762
#145293962
#145293902
#145293892
#145290822
#145290812
#145289662
#145286932
#145285652
C2×C17×#4362
#2203817