Finite Group Databasebeta

← #17045432

Subgroups — #17045432

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×#11762888C211yesmaximal, characteristic, complemented
2C2×#11762771C211yesmaximal, characteristic, complemented
3C4×#10587568C211yesmaximal, characteristic
4#14529580C211yesmaximal, characteristic, complemented
5#14529577C211yesmaximal, characteristic, complemented
6#14529398C211yesmaximal, characteristic, complemented
7#14529392C211yesmaximal, characteristic, complemented
8#14529390C211yesmaximal, characteristic, complemented
9#14529080C211yesmaximal, characteristic, complemented
10#14529080C211yesmaximal, characteristic, complemented
11#14529078C211yesmaximal, characteristic, complemented
12#14528965C211yesmaximal, characteristic, complemented
13#14528693C211yesmaximal, characteristic, complemented
14#14528564C211yesmaximal, characteristic, complemented
15C17×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×#63218C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C22×#63218C2211yescharacteristic, complemented
20C2×#10587568C411yescharacteristic
21C2×C4×D68C2211yescharacteristic
22C2×C4×D68C2211yescharacteristic
23C2×C4×C22⋊D17C2211yescharacteristic
24#11762888—24no—
25C2×C4⋊#3622C2211yescharacteristic, complemented
26C2×#10587485C2211yescharacteristic, complemented
27#11762771—24no—
28C2×C22⋊#3622C2211yescharacteristic
29C2×C22⋊#3622C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33C2×#10587491C2211yescharacteristic
34C2×#10587491C2211yescharacteristic
35C2×#10587491C2211yescharacteristic
36C2×#10587491C2211yescharacteristic, complemented
37C2×#10587491C2211yescharacteristic, complemented
38C2×#10587491C2211yescharacteristic, complemented
39C2×#10587486C2211yescharacteristic, complemented
40C2×C4×#3622C2211yescharacteristic, complemented
41#11762687C411yescharacteristic
42#11762687C411yescharacteristic
43#11762686C411yescharacteristic
44#11762684C411yescharacteristic
45#11762683C411yescharacteristic
46#11762683C411yescharacteristic
47#11762664C411yescharacteristic
48C4×#63227C2211yescharacteristic
49C4×#63227C2211yescharacteristic
50#11762564C2211yescharacteristic, complemented
51#11762564C2211yescharacteristic, complemented
52#11762563C2211yescharacteristic, complemented
53#11762563C2211yescharacteristic, complemented
54C2×C17×C4⋊C8C2211yescharacteristic, complemented
55C2×C17×C22⋊C8C2211yescharacteristic
56C2×C17×C22⋊C8C2211yescharacteristic
57C2×C4×C8×C17C2211yescharacteristic, complemented
58C4×C22⋊C4×C17C2211yescharacteristic
59C17×#336C2211yescharacteristic, complemented
60C17×#336C2211yescharacteristic, complemented
61C24×D17C2×C411yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C22×C22⋊D17C2×C411yescharacteristic
64C23×Dic17C2×C411yescharacteristic
65C22×D68C2×C411yescharacteristic
66C22×D68C2×C411yescharacteristic
67C22×C4×D17—22no—
68C22×C4×D17—22no—
69C22×C4×D17—41no—
70C22×C4×D17—41no—
71C22×C4×D17—41no—
72C22×C4×D17—41no—
73C22×C4×D17C2×C411yescharacteristic
74C22×C4×D17C2×C411yescharacteristic
75C22×C4×D17C2311yescharacteristic
76C22×C4×D17C2311yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C22×C8×C17C2311yescharacteristic
79C22×C8×C17C2311yescharacteristic
80C22×C8×C17C2311yescharacteristic
81C22×C8×C17C2311yescharacteristic
82C2×C22⋊C4×C17C2×C411yescharacteristic
83C2×C22⋊C4×C17C2×C411yescharacteristic
84C2×C42×C17C2311yescharacteristic
85C2×C42×C17C2311yescharacteristic
86C2×C22⋊Dic17C2×C411yescharacteristic
87C4×C22⋊D17—41no—
88C4×C22⋊D17—41no—
89C2×#63227C2×C411yescharacteristic
90C2×#63227C2×C411yescharacteristic
91C2×#63227C2×C411yescharacteristic
92C2×#63227C2×C411yescharacteristic
93C2×#63227C2×C411yescharacteristic
94C2×#63227C2×C411yescharacteristic
95C2×#63227C2×C411yescharacteristic
96C2×#63227C2×C411yescharacteristic
97C2×#63227C2×C411yescharacteristic
98C2×C4⋊Dic17C2×C411yescharacteristic
99C2×C4⋊Dic17C2×C411yescharacteristic
100C2×#63225C2×C411yescharacteristic
101C2×C4×Dic17C2311yescharacteristic
102C22×#3622C2311yescharacteristic
103C22×#3622C2311yescharacteristic
104C22×#3622C2311yescharacteristic
105C22×#3622C2311yescharacteristic
106C2×#63218—22no—
107C2×#63218—22no—
108C2×#63218—41no—
109C2×#63218—41no—
110C2×#63218—41no—
111C2×#63218—41no—
112C2×#63218—41no—
113C2×#63218—41no—
114C2×#63218D414yescomplemented
115#10587568—24no—
116C4×D68—22no—
117C4×D68—22no—
118C4×D68—41no—
119C4×D68—41no—
120C17×C4⋊C8—41no—
121C17×C22⋊C8—22no—
122C17×C22⋊C8—41no—
123C4×C8×C17—22no—
124C17×#95C2×C411yescharacteristic
125C17×#95C2×C411yescharacteristic
126#10587502C2×C411yescharacteristic
127#10587502C2×C411yescharacteristic
128#10587502C2×C411yescharacteristic
129#10587502C2×C411yescharacteristic
130C22⋊#3622—22no—
131C22⋊#3622—41no—
132#10587491—22no—
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—
143C4⋊#3622—22no—
144C4×#3622—41no—
145C24×C17C22×C411yescharacteristic
146C23×D17—22no—
147C23×D17—22no—
148C23×D17—22no—
149C23×D17—41no—
150C23×D17—41no—
151C23×D17—41no—
152C23×D17—41no—
153C23×D17C22×C411yescharacteristic
154C23×D17C22×C411yescharacteristic
155C23×D17C22×C411yescharacteristic
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17C22×C411yescharacteristic
163C22×C4×C17C22×C411yescharacteristic
164C22×C4×C17C22×C411yescharacteristic
165C22×C4×C17C22×C411yescharacteristic
166C22×C4×C17C22×C411yescharacteristic
167C22×C4×C17C2411yescharacteristic
168C2×C22⋊D17—22no—
169C2×C22⋊D17—41no—
170C2×C22⋊D17—41no—
171C22×Dic17—22no—
172C22×Dic17—41no—
173C22×Dic17—41no—
174C22×Dic17C22×C411yescharacteristic
175C22×Dic17C22×C411yescharacteristic
176C22×Dic17C22×C411yescharacteristic
177C22×Dic17C22×C411yescharacteristic
178C22×Dic17C22×C411yescharacteristic
179C2×D68—22no—
180C2×D68—22no—
181C2×D68—22no—
182C2×D68—22no—
183C2×D68—41no—
184C2×D68—41no—
185C2×C4×D17—21no—
186C2×C4×D17—21no—
187C2×C4×D17—21no—
188C2×C4×D17—21no—
189C2×C4×D17—22no—
190C2×C4×D17—21no—
191C2×C4×D17—21no—
192C2×C4×D17—21no—
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—22no—
203C2×C4×D17—44no—
204C2×C4×D17—44no—
205C2×C4×D17—44no—
206C2×C4×D17—44no—
207C2×C4×D17—41no—
208C2×C4×D17—41no—
209C2×C4×D17—41no—
210C2×C4×D17—41no—
211C2×C4×D17C2×D412yes—
212C2×C4×D17#4112yes—
213C2×C8×C17—21no—
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×C17C2×D412yes—
225C22⋊C4×C17—41no—
226C22⋊C4×C17M1614yescomplemented
227C42×C17—21no—
228C42×C17—21no—
229C42×C17—21no—
230C42×C17—21no—
231C22⋊Dic17—41no—
232#63227—22no—
233#63227—22no—
234#63227—22no—
235#63227—22no—
236#63227—22no—
237#63227—41no—
238#63227—41no—
239#63227—41no—
240#63227—41no—
241C4⋊Dic17—22no—
242C4⋊Dic17—41no—
243#63225—41no—
244C4×Dic17—21no—
245C4×Dic17—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—21no—
255C2×#3622—21no—
256C2×#3622—21no—
257C2×#3622C2×D412yes—
258#63218—44no—
259#63218—44no—
260#63218—44no—
261#22038—171nomaximal, Sylow
262C23×C17—21no—
263C23×C17—21no—
264C23×C17—21no—
265C23×C17—21no—
266C23×C17—21no—
267C23×C17—21no—
268C23×C17C2×M1612yes—
269C23×C17C23×C411yescharacteristic
270C22×D17—21no—
271C22×D17—21no—
272C22×D17—21no—
273C22×D17—21no—
274C22×D17—21no—
275C22×D17—21no—
276C22×D17—21no—
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×D17C4×D412yes—
297C22×D17#13112yes—
298C2×C4×C17—21no—
299C2×C4×C17—21no—
300C2×C4×C17—21no—
301C2×C4×C17—21no—
302C2×C4×C17—21no—
303C2×C4×C17—21no—
304C2×C4×C17—21no—
305C2×C4×C17—21no—
306C2×C4×C17—21no—
307C2×C4×C17—21no—
308C2×C4×C17—21no—
309C2×C4×C17—21no—
310C2×C4×C17—21no—
311C2×C4×C17—41no—
312C2×C4×C17—41no—
313C2×C4×C17—41no—
314C2×C4×C17—41no—
315C2×C4×C17C2×M1612yes—
316C2×C4×C17C2×M1612yes—
317C2×C4×C17C22×D411yescharacteristic
318C2×C4×C17C2×#4111yescharacteristic
319C2×C4×C17H(5,𝔽2)11yescharacteristic
320C2×C4×C17H(5,𝔽2)11yescharacteristic
321C2×C4×C17H(5,𝔽2)11yescharacteristic
322C2×C4×C17H(5,𝔽2)11yescharacteristic
323C22⋊D17—44no—
324C2×Dic17—21no—
325C2×Dic17—21no—
326C2×Dic17—21no—
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—44no—
339C2×Dic17C4×D412yes—
340D68—44no—
341D68—44no—
342C4×D17—22no—
343C4×D17—22no—
344C4×D17—22no—
345C4×D17—22no—
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—41no—
358C8×C17—41no—
359C8×C17—41no—
360#3622—22no—
361#3622—41no—
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#1923D1711yescharacteristic, complemented
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×C17C2×C4×D411yescharacteristic
387C22×C17#51811yescharacteristic
388C22×C17#51811yescharacteristic
389C22×C17C22×M1611yescharacteristic
390C22×C17C2×#13111yescharacteristic
391C22×C17#56811yescharacteristic
392C22×C17#56811yescharacteristic
393C2×D17—22no—
394C2×D17—22no—
395C2×D17—22no—
396C2×D17—22no—
397C2×D17—22no—
398C2×D17—22no—
399C2×D17—416no—
400C2×D17—41no—
401C2×D17—41no—
402C2×D17—41no—
403C2×D17—41no—
404C2×D17—41no—
405C2×D17—41no—
406C2×D17—41no—
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—41no—
420C4×C17#53411yescharacteristic
421C4×C17#53511yescharacteristic
422C4×C17#53811yescharacteristic
423C4×C17#53811yescharacteristic
424Dic17—22no—
425Dic17—41no—
426Dic17—41no—
427Dic17—41no—
428Dic17—41no—
429C24×C4—171no—
430C22×M16—171no—
431C22×M16—171no—
432C22×M16—171no—
433C2×#120—171no—
434C2×C4×D4—171no—
435C2×C4×D4—171no—
436C2×C4×D4—171no—
437#436—344no—
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
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⋊C4C2×D1711yescharacteristic
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#232111yescharacteristic
476C2×C17#293311yescharacteristic
477C2×C17D4×M1611yescharacteristic
478C2×C17#297411yescharacteristic
479C2×C17#297511yescharacteristic
480C2×C17#297611yescharacteristic
481C2×C17#297811yescharacteristic
482D17—42no—
483D17—42no—
484D17—81no—
485C25—171no—
486C22×D4—171no—
487C22×D4—171no—
488C22×D4—171no—
489C23×C4—171no—
490C23×C4—171no—
491C23×C4—171no—
492C23×C4—171no—
493C23×C4—171no—
494C23×C4—171no—
495C23×C4—342no—
496C23×C4—342no—
497C23×C4—681no—
498C23×C4—681no—
499C23×C4—681no—
500C23×C4—681no—
501C23×C4C22×D1711yescharacteristic
502C2×M16—174no—
503C2×M16—342no—
504C2×M16—342no—
505C2×M16—681no—
506C2×M16—681no—
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—342no—
521C4×D4—342no—
522C4×D4—681no—
523C4×D4—681no—
524C4×D4—681no—
525C4×D4—681no—
526C2×C4⋊C4—171no—
527C2×C4⋊C4—171no—
528C2×C4⋊C4—171no—
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×C42C22×D1711yescharacteristic
543C2×C42C22×D1711yescharacteristic
544C4⋊C8—41no—
545C4⋊C8—342no—
546C4⋊C8—681no—
547C22⋊C8—22no—
548C22⋊C8—41no—
549C22⋊C8—342no—
550C22⋊C8—342no—
551C22⋊C8—342no—
552C22⋊C8—342no—
553C22⋊C8—342no—
554C22⋊C8—342no—
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#95C4×D1711yescharacteristic
568#95C4×D1711yescharacteristic
569C17#2203811yescharacteristic, complemented, Sylow
570C24—171no—
571C24—171no—
572C24—171no—
573C24—342no—
574C24—342no—
575C24—342no—
576C24—681no—
577C24—681no—
578C24—681no—
579C24—681no—
580C24C2×C4×D1711yescharacteristic
581C2×D4—342no—
582C2×D4—342no—
583C2×D4—342no—
584C2×D4—342no—
585C2×D4—342no—
586C2×D4—681no—
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—171no—
597C22×C4—172no—
598C22×C4—172no—
599C22×C4—171no—
600C22×C4—171no—
601C22×C4—171no—
602C22×C4—171no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4—341no—
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—341no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—681no—
623C22×C4—681no—
624C22×C4—681no—
625C22×C4—681no—
626C22×C4—684no—
627C22×C4—684no—
628C22×C4—684no—
629C22×C4—684no—
630C22×C4—681no—
631C22×C4—681no—
632C22×C4C2×C4×D1711yescharacteristic
633C22×C4C2×C4×D1711yescharacteristic
634C22×C4C2×C4×D1711yescharacteristic
635C22×C4C2×C4×D1711yescharacteristic
636C22×C4C2×C4×D1711yescharacteristic
637C22×C4C23×D1711yescharacteristic
638M16—684no—
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—172no—
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×C8—341no—
664C2×C8D4×D1712yes—
665C4⋊C4—342no—
666C4⋊C4—681no—
667C4⋊C4—681no—
668C22⋊C4—41no—
669C22⋊C4—342no—
670C22⋊C4—342no—
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#6321814yescomplemented
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—341no—
685C42—341no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—172no—
693C23—172no—
694C23—341no—
695C23—341no—
696C23—341no—
697C23—341no—
698C23—341no—
699C23—341no—
700C23—341no—
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—
720C23C2×#6321812yes—
721C23C22×C4×D1711yescharacteristic
722D4—684no—
723D4—684no—
724D4—684no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—172no—
743C2×C4—341no—
744C2×C4—341no—
745C2×C4—342no—
746C2×C4—342no—
747C2×C4—342no—
748C2×C4—342no—
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×C4C2×#6321812yes—
773C2×C4C2×#6321812yes—
774C2×C4C2×D4×D1711yescharacteristic
775C2×C4#1058769111yescharacteristic
776C2×C4#41×D1711yescharacteristic
777C2×C4#1058769611yescharacteristic
778C2×C4#1058769611yescharacteristic
779C2×C4#1058769611yescharacteristic
780C8—22no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—342no—
785C8—681no—
786C8—681no—
787C8—681no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—342no—
796C22—342no—
797C22—342no—
798C22—342no—
799C22—342no—
800C22—342no—
801C22—6816no—
802C22—681no—
803C22—681no—
804C22—681no—
805C22—681no—
806C22—681no—
807C22—681no—
808C22—681no—
809C22—681no—
810C22—681no—
811C22—681no—
812C22—681no—
813C22—681no—
814C22—681no—
815C22—681no—
816C22—681no—
817C22C4×D4×D1711yescharacteristic
818C22#1176328111yescharacteristic
819C22#1176328311yescharacteristic
820C22C22×#6321811yescharacteristic
821C22#131×D1711yescharacteristic
822C22#1176357411yescharacteristic
823C22#1176357511yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—342no—
830C4—681no—
831C4—681no—
832C4—681no—
833C4—681no—
834C4#1176337011yescharacteristic
835C4#1176337511yescharacteristic
836C4#1176339311yescharacteristic
837C4#1176339811yescharacteristic
838C2—42no—
839C2—682no—
840C2—682no—
841C2—1361no—
842C2#1453144611yescharacteristic
843C2#1453750711yescharacteristic
844C2D4×#6321811yescharacteristic
845C2#1453781711yescharacteristic
846C2#1453782411yescharacteristic
847C2#1453783011yescharacteristic
848C2#1453784111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1923C2
prime radicalC2×#10587568C4
cosocleC22×C4×C17C24
hypercenter#1923D17
hypocenterC17#22038
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#11762888C2semidirect
2. C2×#11762771C2semidirect
4. #14529580C2semidirect
5. #14529577C2semidirect
6. #14529398C2semidirect
7. #14529392C2semidirect
8. #14529390C2semidirect
9. #14529080C2semidirect
10. #14529080C2semidirect
11. #14529078C2semidirect
12. #14528965C2semidirect
13. #14528693C2semidirect
14. #14528564C2semidirect
15. C17×#1923C2semidirect
19. C22×#63218C22semidirect
25. C2×C4⋊#3622C22semidirect
26. C2×#10587485C22semidirect
36. C2×#10587491C22semidirect
37. C2×#10587491C22semidirect
38. C2×#10587491C22semidirect
39. C2×#10587486C22semidirect
40. C2×C4×#3622C22semidirect
50. #11762564C22semidirect
51. #11762564C22semidirect
52. #11762563C22semidirect
53. #11762563C22semidirect
54. C2×C17×C4⋊C8C22semidirect
57. C2×C4×C8×C17C22semidirect
59. C17×#336C22semidirect
60. C17×#336C22semidirect
114. C2×#63218D4semidirect
226. C22⋊C4×C17M16semidirect
372. #1923D17semidirect
440. C2×C4⋊C8C2×D17semidirect
457. C2×C4×C8C2×D17semidirect
472. #336C2×D17semidirect
473. #336C2×D17semidirect
569. C17#22038semidirect
679. C22⋊C4#63218semidirect

Maximal subgroups

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

subgroupindex
C2×#117628882
C2×#117627712
C4×#105875682
#145295802
#145295772
#145293982
#145293922
#145293902
#145290802
#145290782
#145289652
#145286932
#145285642
C17×#19232
#2203817