Finite Group Databasebeta

← #17045436

Subgroups — #17045436

Order 4352.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762777C211yesmaximal, characteristic, complemented
2#14531999C211yesmaximal, 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#14529081C211yesmaximal, characteristic, complemented
10#14529081C211yesmaximal, characteristic, complemented
11#14529077C211yesmaximal, characteristic, complemented
12#14528961C211yesmaximal, characteristic, complemented
13#14528695C211yesmaximal, characteristic, complemented
14#14528565C211yesmaximal, characteristic, complemented
15C2×C17×#436C211yesmaximal, characteristic, complemented
16C22×#63252C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×C4×C22⋊D17C2211yescharacteristic
19C2×C4×C22⋊D17C2211yescharacteristic
20C2×#10587485C2211yescharacteristic
21C2×#10587485C2211yescharacteristic
22#11762777—24no—
23C2×C22⋊#3622C2211yescharacteristic
24C2×C22⋊#3622C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic
26C2×#10587491C2211yescharacteristic
27C2×#10587491C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33C2×#10587491C2211yescharacteristic
34C2×#10587486C2211yescharacteristic
35C2×C8×Dic17C2211yescharacteristic
36#11762729C411yescharacteristic
37#11762726C411yescharacteristic
38#11762724C411yescharacteristic
39#11762724C411yescharacteristic
40#11762721C411yescharacteristic
41#11762718C411yescharacteristic
42#11762717C411yescharacteristic
43#11762717C411yescharacteristic
44C4×#63227C2211yescharacteristic
45C4×#63227C2211yescharacteristic
46C4×C22⋊Dic17C2211yescharacteristic
47#11762564C2211yescharacteristic
48#11762564C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53C22×M16×C17C2211yescharacteristic
54C22×M16×C17C2211yescharacteristic
55C2×C4×D4×C17C2211yescharacteristic
56C17×#436—24no—
57C2×C17×C4⋊C8C2211yescharacteristic
58C2×C17×C22⋊C8C2211yescharacteristic
59C2×C17×C22⋊C8C2211yescharacteristic
60C2×C4×C8×C17C2211yescharacteristic
61C22×D4×C17C2×C411yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C22×C22⋊D17C2×C411yescharacteristic
65C22×C22⋊D17C2×C411yescharacteristic
66C22×C22⋊D17C2×C411yescharacteristic
67C22×C22⋊D17C2×C411yescharacteristic
68C2×#63252—22no—
69C2×#63252—22no—
70C2×#63252—41no—
71C2×#63252—41no—
72C2×#63252—41no—
73C2×#63252—41no—
74C22×D68C2×C411yescharacteristic
75C22×C4×D17C2311yescharacteristic
76C22×C4×D17C2311yescharacteristic
77C22×Dic34C2×C411yescharacteristic
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
98C4×C22⋊D17—41no—
99C4×C22⋊D17—41no—
100C4×C22⋊D17—41no—
101C4×C22⋊D17—41no—
102C2×#63227C2×C411yescharacteristic
103C2×#63227C2×C411yescharacteristic
104C2×#63227C2×C411yescharacteristic
105C2×#63227C2×C411yescharacteristic
106C2×#63227C2×C411yescharacteristic
107C2×#63227C2×C411yescharacteristic
108C2×#63225C2×C411yescharacteristic
109C2×#63225C2×C411yescharacteristic
110C2×C4×Dic17C2311yescharacteristic
111C2×C4×Dic17C2311yescharacteristic
112C22×#3622—22no—
113C22×#3622—41no—
114C22×#3622—41no—
115C22×#3622C2311yescharacteristic
116C22×#3622C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C22×#3622C2311yescharacteristic
119C17×C4⋊C8—22no—
120C17×C22⋊C8—22no—
121C17×C22⋊C8—22no—
122C4×C8×C17—22no—
123#10587502C2×C411yescharacteristic
124#10587502C2×C411yescharacteristic
125#10587502C2×C411yescharacteristic
126#10587502C2×C411yescharacteristic
127#10587502C2×C411yescharacteristic
128#10587502C2×C411yescharacteristic
129C22⋊#3622—22no—
130C22⋊#3622—41no—
131C22⋊#3622—41no—
132#10587491—22no—
133#10587491—22no—
134#10587491—22no—
135#10587491—22no—
136#10587491—41no—
137#10587491—41no—
138#10587491—41no—
139#10587491—41no—
140#10587486—41no—
141#10587485—41no—
142#10587485—41no—
143C8×Dic17—41no—
144C24×C17C22×C411yescharacteristic
145C24×C17C22×C411yescharacteristic
146C23×D17C22×C411yescharacteristic
147C23×D17C22×C411yescharacteristic
148C2×D4×C17—22no—
149C2×D4×C17—22no—
150C2×D4×C17—41no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17C22×C411yescharacteristic
162C22×C4×C17C22×C411yescharacteristic
163C22×C4×C17C22×C411yescharacteristic
164C22×C4×C17C22×C411yescharacteristic
165C22×C4×C17C2×D412yes—
166C22×C4×C17#4112yes—
167C22×C4×C17C2411yescharacteristic
168C2×C22⋊D17—22no—
169C2×C22⋊D17—22no—
170C2×C22⋊D17—22no—
171C2×C22⋊D17—41no—
172C2×C22⋊D17—41no—
173C2×C22⋊D17—41no—
174C2×C22⋊D17—41no—
175C2×C22⋊D17—41no—
176C2×C22⋊D17—41no—
177C2×C22⋊D17—41no—
178C2×C22⋊D17—41no—
179C2×C22⋊D17—41no—
180C22×Dic17C22×C411yescharacteristic
181C22×Dic17C22×C411yescharacteristic
182C22×Dic17C22×C411yescharacteristic
183C22×Dic17C22×C411yescharacteristic
184C22×Dic17C22×C411yescharacteristic
185C22×Dic17C22×C411yescharacteristic
186#63252—44no—
187#63252—44no—
188#63252—44no—
189#63252—44no—
190C2×D68—22no—
191C2×D68—41no—
192C2×D68—41no—
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×Dic34—22no—
206C2×Dic34—41no—
207C2×Dic34—41no—
208M16×C17—44no—
209M16×C17—44no—
210C2×C8×C17—21no—
211C2×C8×C17—21no—
212C2×C8×C17—21no—
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×C17C2×D412yes—
221C2×C8×C17C2×D412yes—
222C4⋊C4×C17—22no—
223C22⋊C4×C17—22no—
224C22⋊C4×C17—22no—
225C42×C17—21no—
226C42×C17—21no—
227C22⋊Dic17—22no—
228C22⋊Dic17—41no—
229C22⋊Dic17—41no—
230C22⋊Dic17—41no—
231#63227—22no—
232#63227—22no—
233#63227—22no—
234#63227—41no—
235#63227—41no—
236#63227—41no—
237#63225—41no—
238#63225—41no—
239C4×Dic17—21no—
240C4×Dic17—21no—
241C4×Dic17—21no—
242C4×Dic17—21no—
243C2×#3622—21no—
244C2×#3622—21no—
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—21no—
255C2×#3622—44no—
256#22039—171nomaximal, Sylow
257C23×C17—21no—
258C23×C17—21no—
259C23×C17—21no—
260C23×C17—21no—
261C23×C17—21no—
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×C17C4×D412yes—
271C23×C17C23×C411yescharacteristic
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—
286D4×C17—44no—
287C2×C4×C17—21no—
288C2×C4×C17—21no—
289C2×C4×C17—21no—
290C2×C4×C17—21no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—21no—
296C2×C4×C17—21no—
297C2×C4×C17—21no—
298C2×C4×C17—21no—
299C2×C4×C17—21no—
300C2×C4×C17—21no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17C4×D412yes—
306C2×C4×C17#13112yes—
307C2×C4×C17C22×D411yescharacteristic
308C2×C4×C17C2×#4111yescharacteristic
309C2×C4×C17H(5,𝔽2)11yescharacteristic
310C2×C4×C17H(5,𝔽2)11yescharacteristic
311C2×C4×C17H(5,𝔽2)11yescharacteristic
312C2×C4×C17H(5,𝔽2)11yescharacteristic
313C22⋊D17—44no—
314C22⋊D17—44no—
315C22⋊D17—44no—
316C22⋊D17—44no—
317C2×Dic17—21no—
318C2×Dic17—21no—
319C2×Dic17—21no—
320C2×Dic17—21no—
321C2×Dic17—21no—
322C2×Dic17—21no—
323C2×Dic17—21no—
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#13112yes—
335D68—44no—
336C4×D17—41no—
337C4×D17—41no—
338C4×D17—41no—
339C4×D17—41no—
340C4×D17—41no—
341C4×D17—41no—
342C4×D17—41no—
343C4×D17—41no—
344Dic34—44no—
345C8×C17—22no—
346C8×C17—22no—
347C8×C17—41no—
348C8×C17—41no—
349#3622—41no—
350#3622—41no—
351#3622—41no—
352#3622—41no—
353C2×#436D1711yescharacteristic, complemented
354C2×#408—171no—
355#2388—171no—
356#1955—171no—
357#1954—171no—
358#1924—171no—
359#1923—171no—
360#1923—171no—
361#1923—171no—
362#1870—171no—
363#1870—171no—
364#1869—171no—
365#1850—171no—
366#1780—171no—
367#1753—171no—
368C22×C17—22no—
369C22×C17—22no—
370C22×C17—22no—
371C22×C17—41no—
372C22×C17—41no—
373C22×C17—41no—
374C22×C17—41no—
375C22×C17—41no—
376C22×C17—41no—
377C22×C17—41no—
378C22×C17—41no—
379C22×C17—41no—
380C22×C17—41no—
381C22×C17—41no—
382C22×C17C2×C4×D411yescharacteristic
383C22×C17#51811yescharacteristic
384C22×C17#51811yescharacteristic
385C22×C17C2×#13111yescharacteristic
386C22×C17C2×#13111yescharacteristic
387C22×C17#56811yescharacteristic
388C22×C17#56811yescharacteristic
389C2×D17—41no—
390C2×D17—41no—
391C2×D17—41no—
392C2×D17—41no—
393C2×D17—41no—
394C2×D17—41no—
395C2×D17—41no—
396C2×D17—41no—
397C2×D17—41no—
398C2×D17—41no—
399C2×D17—41no—
400C2×D17—41no—
401C2×D17—41no—
402C2×D17—41no—
403C4×C17—22no—
404C4×C17—22no—
405C4×C17—41no—
406C4×C17—41no—
407C4×C17#53411yescharacteristic
408C4×C17#53511yescharacteristic
409C4×C17#53811yescharacteristic
410C4×C17#53811yescharacteristic
411Dic17—22no—
412Dic17—41no—
413Dic17—41no—
414Dic17—41no—
415Dic17—41no—
416Dic17—41no—
417C22×#41—171no—
418C22×M16C2×D1711yescharacteristic
419C22×M16C2×D1711yescharacteristic
420C23×C8—171no—
421C2×C4×D4—171no—
422C2×C4×D4—171no—
423C2×C4×D4C2×D1711yescharacteristic
424#436—24no—
425C2×C4⋊C8—171no—
426C2×C4⋊C8—171no—
427C2×C4⋊C8C2×D1711yescharacteristic
428#408—344no—
429C2×C22⋊C8—171no—
430C2×C22⋊C8—171no—
431C2×C22⋊C8—171no—
432C2×C22⋊C8—171no—
433C2×C22⋊C8—171no—
434C2×C22⋊C8—171no—
435C2×C22⋊C8—171no—
436C2×C22⋊C8—171no—
437C2×C22⋊C8—171no—
438C2×C22⋊C8—171no—
439C2×C22⋊C8—171no—
440C2×C22⋊C8C2×D1711yescharacteristic
441C2×C22⋊C8C2×D1711yescharacteristic
442C2×#97—171no—
443C2×C4×C8—171no—
444C2×C4×C8C2×D1711yescharacteristic
445#395—171no—
446#394—171no—
447#394—171no—
448#394—171no—
449#393—171no—
450#392—171no—
451#392—171no—
452#392—171no—
453C4×C22⋊C4—171no—
454C4×C22⋊C4—171no—
455C4×C22⋊C4—171no—
456#336—171no—
457#336—171no—
458#336—171no—
459#336—171no—
460#336—171no—
461#336—171no—
462C2×C17—42no—
463C2×C17—81no—
464C2×C17#232111yescharacteristic
465C2×C17#293311yescharacteristic
466C2×C17#293511yescharacteristic
467C2×C17#297611yescharacteristic
468C2×C17#297811yescharacteristic
469C2×C17#297911yescharacteristic
470C2×C17#298111yescharacteristic
471D17—81no—
472D17—81no—
473C2×#41—342no—
474C2×#41—342no—
475C2×#41—681no—
476C2×#41—681no—
477C2×#41—681no—
478C2×#41—681no—
479C22×Q8—171no—
480C22×D4—171no—
481C22×D4—171no—
482C22×D4—171no—
483C22×D4—171no—
484C22×D4—171no—
485C22×D4C4×D1711yescharacteristic
486C23×C4—171no—
487C23×C4—171no—
488C23×C4C22×D1711yescharacteristic
489C23×C4C22×D1711yescharacteristic
490C2×M16—22no—
491C2×M16—41no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—41no—
495C2×M16C22⋊D1714yescomplemented
496C22×C8—171no—
497C22×C8—171no—
498C22×C8—171no—
499C22×C8—171no—
500C22×C8—342no—
501C22×C8—681no—
502C22×C8—681no—
503C22×C8C22×D1711yescharacteristic
504C22×C8C22×D1711yescharacteristic
505C22×C8C22×D1711yescharacteristic
506C22×C8C22×D1711yescharacteristic
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—681no—
510C4×D4—681no—
511C4×D4—681no—
512C4×D4—681no—
513C2×C4⋊C4—171no—
514C2×C4⋊C4—171no—
515C2×C4⋊C4C4×D1711yescharacteristic
516C2×C22⋊C4—171no—
517C2×C22⋊C4—171no—
518C2×C22⋊C4—171no—
519C2×C22⋊C4—171no—
520C2×C22⋊C4—171no—
521C2×C22⋊C4—171no—
522C2×C22⋊C4—171no—
523C2×C22⋊C4—171no—
524C2×C22⋊C4—171no—
525C2×C22⋊C4—171no—
526C2×C22⋊C4C4×D1711yescharacteristic
527C2×C22⋊C4C4×D1711yescharacteristic
528C2×C42—171no—
529C2×C42—171no—
530C2×C42C22×D1711yescharacteristic
531C4⋊C8—22no—
532C4⋊C8—681no—
533C4⋊C8—681no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—342no—
537C22⋊C8—342no—
538C22⋊C8—342no—
539C22⋊C8—342no—
540C22⋊C8—342no—
541C22⋊C8—681no—
542C22⋊C8—681no—
543C22⋊C8—681no—
544C22⋊C8—681no—
545C22⋊C8—681no—
546C22⋊C8—681no—
547#97—681no—
548C4×C8—22no—
549C4×C8—681no—
550#95—171no—
551#95—171no—
552#95—171no—
553#95—171no—
554#95—171no—
555#95—171no—
556C17#2203911yescharacteristic, complemented, Sylow
557C24—171no—
558C24—171no—
559C24C2×C4×D1711yescharacteristic
560C24C2×C4×D1711yescharacteristic
561#41—684no—
562#41—684no—
563#41—684no—
564#41—684no—
565C2×Q8—342no—
566C2×Q8—681no—
567C2×Q8—681no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—41no—
571C2×D4—342no—
572C2×D4—342no—
573C2×D4—342no—
574C2×D4—342no—
575C2×D4—681no—
576C2×D4—681no—
577C2×D4—681no—
578C2×D4—681no—
579C2×D4—681no—
580C2×D4—681no—
581C2×D4—681no—
582C2×D4—681no—
583C2×D4—681no—
584C2×D4—681no—
585C2×D4—681no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—171no—
597C22×C4—171no—
598C22×C4—171no—
599C22×C4—171no—
600C22×C4—171no—
601C22×C4—171no—
602C22×C4—341no—
603C22×C4—341no—
604C22×C4—341no—
605C22×C4—341no—
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×C4C2×C4×D1711yescharacteristic
615C22×C4C2×C4×D1711yescharacteristic
616C22×C4C2×C4×D1711yescharacteristic
617C22×C4C2×C4×D1711yescharacteristic
618C22×C4#6325212yes—
619C22×C4C2×C22⋊D1712yes—
620C22×C4C23×D1711yescharacteristic
621M16—44no—
622M16—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—341no—
634C2×C8—341no—
635C2×C8—341no—
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—
646C2×C8C2×C22⋊D1712yes—
647C2×C8C2×C22⋊D1712yes—
648C4⋊C4—22no—
649C4⋊C4—681no—
650C4⋊C4—681no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—342no—
654C22⋊C4—342no—
655C22⋊C4—342no—
656C22⋊C4—342no—
657C22⋊C4—681no—
658C22⋊C4—681no—
659C22⋊C4—681no—
660C22⋊C4—681no—
661C22⋊C4—681no—
662C22⋊C4—681no—
663C42—21no—
664C42—21no—
665C42—341no—
666C42—341no—
667C42—341no—
668C42—341no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—341no—
683C23—341no—
684C23—341no—
685C23—341no—
686C23—341no—
687C23—341no—
688C23—341no—
689C23—341no—
690C23—341no—
691C23—341no—
692C23—341no—
693C23—341no—
694C23—341no—
695C23—341no—
696C23C4×C22⋊D1712yes—
697C23C22×C4×D1711yescharacteristic
698Q8—684no—
699D4—44no—
700D4—684no—
701D4—684no—
702D4—684no—
703D4—684no—
704D4—684no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—172no—
724C2×C4—341no—
725C2×C4—341no—
726C2×C4—341no—
727C2×C4—341no—
728C2×C4—341no—
729C2×C4—341no—
730C2×C4—341no—
731C2×C4—341no—
732C2×C4—341no—
733C2×C4—341no—
734C2×C4—341no—
735C2×C4—341no—
736C2×C4—341no—
737C2×C4—341no—
738C2×C4—341no—
739C2×C4—341no—
740C2×C4—341no—
741C2×C4—681no—
742C2×C4—681no—
743C2×C4—681no—
744C2×C4—681no—
745C2×C4—681no—
746C2×C4—681no—
747C2×C4—681no—
748C2×C4—681no—
749C2×C4#1058759312yes—
750C2×C4C4×C22⋊D1712yes—
751C2×C4C2×#6325211yescharacteristic
752C2×C4#1058769111yescharacteristic
753C2×C4#1058769111yescharacteristic
754C2×C4#1058769611yescharacteristic
755C2×C4#1058769611yescharacteristic
756C2×C4C22×C22⋊D1711yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—681no—
762C8—681no—
763C8—681no—
764C8—681no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—681no—
780C22—681no—
781C22—681no—
782C22—681no—
783C22—681no—
784C22—681no—
785C22—681no—
786C22—681no—
787C22—681no—
788C22—681no—
789C22—681no—
790C22—681no—
791C22—681no—
792C22—681no—
793C22C2×C4×C22⋊D1711yescharacteristic
794C22#1176328111yescharacteristic
795C22#1176328111yescharacteristic
796C22#131×D1711yescharacteristic
797C22C2×#1058759311yescharacteristic
798C22#1176357411yescharacteristic
799C22#1176357511yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—342no—
805C4—681no—
806C4—681no—
807C4—681no—
808C4—681no—
809C4—681no—
810C4#1176336811yescharacteristic
811C4#1176337311yescharacteristic
812C4#1176339211yescharacteristic
813C4#1176339211yescharacteristic
814C2—42no—
815C2—81no—
816C2—1361no—
817C2—1361no—
818C2#1453143811yescharacteristic
819C2#1453750911yescharacteristic
820C2#1453752611yescharacteristic
821C2#1453782811yescharacteristic
822C2#1453784111yescharacteristic
823C2#1453784911yescharacteristic
824C2#1453786111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC2×C17×#436C2
prime radical#14531999C2
cosocleC22×C4×C17C24
hypercenterC2×#436D17
hypocenterC17#22039
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×#11762777C2semidirect
3. #14529580C2semidirect
4. #14529576C2semidirect
5. #14529396C2semidirect
6. #14529390C2semidirect
7. #14529390C2semidirect
8. #14529389C2semidirect
9. #14529081C2semidirect
10. #14529081C2semidirect
11. #14529077C2semidirect
12. #14528961C2semidirect
13. #14528695C2semidirect
14. #14528565C2semidirect
15. C2×C17×#436C2semidirect
83. C2×M16×C17D4semidirect
353. C2×#436D17semidirect
495. C2×M16C22⋊D17semidirect
556. C17#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#117627772
#145319992
#145295802
#145295762
#145293962
#145293902
#145293892
#145290812
#145290772
#145289612
#145286952
#145285652
C2×C17×#4362
#2203917