Finite Group Databasebeta

← #17045433

Subgroups — #17045433

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×#11762887C211yesmaximal, characteristic, complemented
2C2×#11762772C211yesmaximal, characteristic, complemented
3C4×#10587623C211yesmaximal, characteristic
4#14529580C211yesmaximal, characteristic, complemented
5#14529576C211yesmaximal, characteristic, complemented
6#14529398C211yesmaximal, characteristic, complemented
7#14529391C211yesmaximal, characteristic, complemented
8#14529388C211yesmaximal, characteristic, complemented
9#14529388C211yesmaximal, characteristic, complemented
10#14529079C211yesmaximal, characteristic, complemented
11#14529079C211yesmaximal, characteristic, complemented
12#14528967C211yesmaximal, characteristic, complemented
13#14528693C211yesmaximal, characteristic, complemented
14#14528570C211yesmaximal, characteristic, complemented
15C17×#1870C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×#63223C2211yescharacteristic
18C22×#63223C2211yescharacteristic, complemented
19C2×#10587623C411yescharacteristic
20C2×C4×C22⋊D17C2211yescharacteristic
21C2×C4×C22⋊D17C2211yescharacteristic
22#11762887—24no—
23C2×C4⋊#3622C2211yescharacteristic, complemented
24C2×#10587485C2211yescharacteristic, complemented
25C2×#10587485C2211yescharacteristic, complemented
26#11762772—24no—
27C2×C22⋊#3622C2211yescharacteristic
28C2×C22⋊#3622C2211yescharacteristic, complemented
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33C2×#10587491C2211yescharacteristic
34C2×#10587491C2211yescharacteristic
35C2×#10587491C2211yescharacteristic
36C2×#10587491C2211yescharacteristic
37C2×#10587486C2211yescharacteristic, complemented
38C2×C4×#3622C2211yescharacteristic, complemented
39C2×C8×Dic17C2211yescharacteristic, complemented
40#11762689C411yescharacteristic
41#11762685C411yescharacteristic
42#11762685C411yescharacteristic
43#11762681C411yescharacteristic
44#11762680C411yescharacteristic
45#11762680C411yescharacteristic
46#11762664C411yescharacteristic
47C4×#63227C2211yescharacteristic
48C4×#63227C2211yescharacteristic
49C4×C22⋊Dic17C2211yescharacteristic
50#11762563C2211yescharacteristic, complemented
51#11762563C2211yescharacteristic, complemented
52#11762563C2211yescharacteristic, complemented
53#11762563C2211yescharacteristic, complemented
54C22×M16×C17C2211yescharacteristic
55C2×C4×D4×C17C2211yescharacteristic
56C2×C17×C22⋊C8C2211yescharacteristic
57C2×C17×C22⋊C8C2211yescharacteristic, complemented
58C2×C17×C22⋊C8C2211yescharacteristic, complemented
59C17×#336C2211yescharacteristic, complemented
60C17×#336C2211yescharacteristic, 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—
81C22×C8×C17C2311yescharacteristic
82C22×C8×C17C2311yescharacteristic
83C22×C8×C17C2311yescharacteristic
84C22×C8×C17C2311yescharacteristic
85C4×D4×C17—22no—
86C4×D4×C17—22no—
87C2×C4⋊C4×C17C2×C411yescharacteristic
88C2×C22⋊C4×C17C2×C411yescharacteristic
89C2×C22⋊C4×C17C2×C411yescharacteristic
90C2×C42×C17C2311yescharacteristic
91C2×C22⋊Dic17C2×C411yescharacteristic
92C2×C22⋊Dic17C2×C411yescharacteristic
93C2×C22⋊Dic17C2×C411yescharacteristic
94C2×C22⋊Dic17C2×C411yescharacteristic
95#10587623—24no—
96C4×C22⋊D17—41no—
97C4×C22⋊D17—41no—
98C4×C22⋊D17—41no—
99C4×C22⋊D17—41no—
100C2×#63227C2×C411yescharacteristic
101C2×#63227C2×C411yescharacteristic
102C2×#63227C2×C411yescharacteristic
103C2×#63227C2×C411yescharacteristic
104C2×#63227C2×C411yescharacteristic
105C2×#63227C2×C411yescharacteristic
106C2×#63225C2×C411yescharacteristic
107C2×#63225C2×C411yescharacteristic
108C2×C4×Dic17C2311yescharacteristic
109C2×C4×Dic17C2311yescharacteristic
110C2×#63223—22no—
111C2×#63223—41no—
112C2×#63223—41no—
113C2×#63223—41no—
114C2×#63223—41no—
115C2×#63223D414yescomplemented
116C22×#3622C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C22×#3622C2311yescharacteristic
120C17×C22⋊C8—22no—
121C17×C22⋊C8—41no—
122C17×C22⋊C8—41no—
123#10587502C2×C411yescharacteristic
124#10587502C2×C411yescharacteristic
125#10587502C2×C411yescharacteristic
126#10587502C2×C411yescharacteristic
127#10587502C2×C411yescharacteristic
128#10587502C2×C411yescharacteristic
129C22⋊#3622—22no—
130C22⋊#3622—22no—
131#10587491—22no—
132#10587491—22no—
133#10587491—22no—
134#10587491—22no—
135#10587491—41no—
136#10587491—41no—
137#10587491—41no—
138#10587491—41no—
139#10587486—41no—
140#10587485—41no—
141#10587485—41no—
142C8×Dic17—41no—
143C4⋊#3622—22no—
144C4×#3622—22no—
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—
214C2×C8×C17—21no—
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×C17—21no—
226C4⋊C4×C17—22no—
227C22⋊C4×C17—22no—
228C22⋊C4×C17—22no—
229C42×C17—21no—
230C42×C17—21no—
231C22⋊Dic17—22no—
232C22⋊Dic17—41no—
233C22⋊Dic17—41no—
234C22⋊Dic17—41no—
235#63227—22no—
236#63227—22no—
237#63227—41no—
238#63227—41no—
239#63227—41no—
240#63227M1614yescomplemented
241#63225—41no—
242#63225—41no—
243C4×Dic17—21no—
244C4×Dic17—21no—
245C4×Dic17—21no—
246C4×Dic17—21no—
247#63223—44no—
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×#3622C2×D412yes—
260C2×#3622C2×D412yes—
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—41no—
357C8×C17—41no—
358C8×C17—41no—
359C8×C17—41no—
360#3622—22no—
361#3622—22no—
362#3622—41no—
363#3622—41no—
364C2×#436—171no—
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#1870D1711yescharacteristic, complemented
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×M16—171no—
432C22×M16C2×D1711yescharacteristic
433C2×#120—171no—
434C2×C4×D4—171no—
435C2×C4×D4—171no—
436C2×C4×D4C2×D1711yescharacteristic
437#436—344no—
438C2×C4⋊C8—171no—
439C2×C4⋊C8—171no—
440C2×C4⋊C8—171no—
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⋊C8C2×D1711yescharacteristic
453C2×C22⋊C8C2×D1711yescharacteristic, complemented
454C2×C22⋊C8C2×D1711yescharacteristic, complemented
455C2×#97—171no—
456C2×C4×C8—171no—
457C2×C4×C8—171no—
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#336C2×D1711yescharacteristic, complemented
473#336C2×D1711yescharacteristic, complemented
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—174no—
506C2×M16—342no—
507C2×M16—681no—
508C2×M16—681no—
509C2×M16—681no—
510C2×M16—681no—
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—342no—
545C4⋊C8—681no—
546C4⋊C8—681no—
547C22⋊C8—22no—
548C22⋊C8—41no—
549C22⋊C8—41no—
550C22⋊C8—342no—
551C22⋊C8—342no—
552C22⋊C8—342no—
553C22⋊C8—342no—
554C22⋊C8—342no—
555C22⋊C8—342no—
556C22⋊C8—681no—
557C22⋊C8—681no—
558C22⋊C8—681no—
559C22⋊C8—681no—
560#97—681no—
561C4×C8—342no—
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×C4D4×D1712yes—
636C22×C4#6325412yes—
637C22×C4C23×D1711yescharacteristic
638M16—44no—
639M16—684no—
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—21no—
652C2×C8—21no—
653C2×C8—172no—
654C2×C8—172no—
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×C8—341no—
664C2×C8—341no—
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—
720C23#1058756712yes—
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×C4#1058756712yes—
773C2×C4M16×D1712yes—
774C2×C4C2×D4×D1711yescharacteristic
775C2×C4C2×#6325411yescharacteristic
776C2×C4#1058769111yescharacteristic
777C2×C4#1058769111yescharacteristic
778C2×C4#1058769611yescharacteristic
779C2×C4#1058769611yescharacteristic
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—342no—
785C8—342no—
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×#1058756711yescharacteristic
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#1176337011yescharacteristic
835C4#1176337411yescharacteristic
836C4#1176339611yescharacteristic
837C4#1176339611yescharacteristic
838C2—42no—
839C2—81no—
840C2—682no—
841C2—682no—
842C2#1453144711yescharacteristic
843C2#1453751411yescharacteristic
844C2#1453751611yescharacteristic
845C2#1453781611yescharacteristic
846C2#1453782211yescharacteristic
847C2#1453783111yescharacteristic
848C2#1453784311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1870C2
prime radicalC2×#10587623C4
cosocleC22×C4×C17C24
hypercenter#1870D17
hypocenterC17#22038
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#11762887C2semidirect
2. C2×#11762772C2semidirect
4. #14529580C2semidirect
5. #14529576C2semidirect
6. #14529398C2semidirect
7. #14529391C2semidirect
8. #14529388C2semidirect
9. #14529388C2semidirect
10. #14529079C2semidirect
11. #14529079C2semidirect
12. #14528967C2semidirect
13. #14528693C2semidirect
14. #14528570C2semidirect
15. C17×#1870C2semidirect
18. C22×#63223C22semidirect
23. C2×C4⋊#3622C22semidirect
24. C2×#10587485C22semidirect
25. C2×#10587485C22semidirect
28. C2×C22⋊#3622C22semidirect
37. C2×#10587486C22semidirect
38. C2×C4×#3622C22semidirect
39. C2×C8×Dic17C22semidirect
50. #11762563C22semidirect
51. #11762563C22semidirect
52. #11762563C22semidirect
53. #11762563C22semidirect
57. C2×C17×C22⋊C8C22semidirect
58. C2×C17×C22⋊C8C22semidirect
59. C17×#336C22semidirect
60. C17×#336C22semidirect
115. C2×#63223D4semidirect
240. #63227M16semidirect
375. #1870D17semidirect
453. C2×C22⋊C8C2×D17semidirect
454. C2×C22⋊C8C2×D17semidirect
472. #336C2×D17semidirect
473. #336C2×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×#117628872
C2×#117627722
C4×#105876232
#145295802
#145295762
#145293982
#145293912
#145293882
#145290792
#145289672
#145286932
#145285702
C17×#18702
#2203817