Finite Group Databasebeta

← #17051248

Subgroups — #17051248

Order 4352.

1212 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762860C211yesmaximal, characteristic, complemented
2C2×#11762772C211yesmaximal, characteristic
3C4×C22⋊C4×D17C211yesmaximal, characteristic
4#14529397C211yesmaximal, characteristic, complemented
5#14529395C211yesmaximal, characteristic, complemented
6#14529390C211yesmaximal, characteristic, complemented
7#14529388C211yesmaximal, characteristic, complemented
8#14528967C211yesmaximal, characteristic, complemented
9#14528966C211yesmaximal, characteristic, complemented
10#14528851C211yesmaximal, characteristic, complemented
11#14528763C211yesmaximal, characteristic, complemented
12#14528693C211yesmaximal, characteristic
13#14528568C211yesmaximal, characteristic, complemented
14#14528547C211yesmaximal, characteristic, complemented
15C17×#1753C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×#63223C2211yescharacteristic
18C2×C22⋊C4×D17C411yescharacteristic
19C2×C22⋊C4×D17C411yescharacteristic
20C2×C42×D17C2211yescharacteristic
21C2×C42×D17C2211yescharacteristic
22#11762860—24no—
23C2×#10587485C2211yescharacteristic, complemented
24C2×#10587485C2211yescharacteristic, complemented
25C2×#10587485C2211yescharacteristic, complemented
26C2×#10587485C2211yescharacteristic, complemented
27#11762772—24no—
28C2×C22⋊#3622C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587491C2211yescharacteristic
31C2×#10587491C2211yescharacteristic
32C2×#10587491C2211yescharacteristic
33C2×#10587491C2211yescharacteristic
34C2×#10587491C2211yescharacteristic
35C2×#10587491C2211yescharacteristic
36C2×#10587491C2211yescharacteristic
37C2×#10587474C2211yescharacteristic, complemented
38C2×C4×#3622C2211yescharacteristic, complemented
39C22⋊C4×Dic17C411yescharacteristic
40C22⋊C4×Dic17C411yescharacteristic
41C4×#63227C2211yescharacteristic
42C4×#63227C2211yescharacteristic
43C4×C22⋊Dic17C2211yescharacteristic
44#11762656C411yescharacteristic
45#11762656C411yescharacteristic
46#95×D17C411yescharacteristic
47#95×D17C411yescharacteristic
48#11762564C2211yescharacteristic, complemented
49#11762564C2211yescharacteristic, complemented
50#11762563C2211yescharacteristic, complemented
51#11762563C2211yescharacteristic, complemented
52#11762563C2211yescharacteristic, complemented
53#11762563C2211yescharacteristic, complemented
54C22×M16×C17C2211yescharacteristic
55C2×C17×C22⋊C8C2211yescharacteristic
56C2×C17×#97C2211yescharacteristic, complemented
57C2×C4×C8×C17C2211yescharacteristic, complemented
58C4×C22⋊C4×C17C2211yescharacteristic
59C17×#336C2211yescharacteristic, complemented
60C17×#336C2211yescharacteristic, complemented
61C24×D17C2×C411yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×Dic17C2×C411yescharacteristic
64C22×C4×D17—22no—
65C22×C4×D17—22no—
66C22×C4×D17—22no—
67C22×C4×D17—22no—
68C22×C4×D17—41no—
69C22×C4×D17—41no—
70C22×C4×D17C2×C411yescharacteristic
71C22×C4×D17C2×C411yescharacteristic
72C22×C4×D17C2×C411yescharacteristic
73C22×C4×D17C2×C411yescharacteristic
74C22×C4×D17C2×C411yescharacteristic
75C22×C4×D17C2×C411yescharacteristic
76C22×C4×D17C2311yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C2×M16×C17—22no—
79C2×M16×C17—22no—
80C2×M16×C17—41no—
81C22×C8×C17C2311yescharacteristic
82C22×C8×C17C2311yescharacteristic
83C22×C8×C17C2311yescharacteristic
84C22×C8×C17C2311yescharacteristic
85C2×C22⋊C4×C17C2×C411yescharacteristic
86C2×C22⋊C4×C17C2×C411yescharacteristic
87C2×C42×C17C2311yescharacteristic
88C2×C42×C17C2311yescharacteristic
89C2×C22⋊Dic17C2×C411yescharacteristic
90C2×C22⋊Dic17C2×C411yescharacteristic
91C2×#63227C2×C411yescharacteristic
92C2×#63227C2×C411yescharacteristic
93C2×#63227C2×C411yescharacteristic
94C2×#63227C2×C411yescharacteristic
95C2×C4×Dic17C2×C411yescharacteristic
96C2×C4×Dic17C2×C411yescharacteristic
97C2×C4×Dic17C2×C411yescharacteristic
98C2×C4×Dic17C2×C411yescharacteristic
99C2×C4×Dic17C2311yescharacteristic
100C2×C4×Dic17C2311yescharacteristic
101C2×#63223—22no—
102C2×#63223—22no—
103C2×#63223—41no—
104C22×#3622C2311yescharacteristic
105C22×#3622C2311yescharacteristic
106C22×#3622C2311yescharacteristic
107C22×#3622C2311yescharacteristic
108C22⋊C4×D17—24no—
109C22⋊C4×D17—24no—
110C42×D17—22no—
111C42×D17—22no—
112C42×D17—41no—
113C42×D17—41no—
114C17×C22⋊C8—22no—
115C17×#97—41no—
116C4×C8×C17—22no—
117C17×#95C2×C411yescharacteristic
118C17×#95C2×C411yescharacteristic
119#10587502C2×C411yescharacteristic
120#10587502C2×C411yescharacteristic
121#10587502C2×C411yescharacteristic
122#10587502C2×C411yescharacteristic
123#10587502C2×C411yescharacteristic
124#10587502C2×C411yescharacteristic
125C22⋊#3622—22no—
126#10587491—22no—
127#10587491—22no—
128#10587491—22no—
129#10587491—22no—
130#10587491—22no—
131#10587491—41no—
132#10587491—41no—
133#10587491D414yes—
134#10587485—22no—
135#10587485—22no—
136#10587485—41no—
137#10587485—41no—
138#10587474—41no—
139C4×#3622—22no—
140C24×C17C22×C411yescharacteristic
141C23×D17—22no—
142C23×D17—22no—
143C23×D17—22no—
144C23×D17—22no—
145C23×D17—22no—
146C23×D17—41no—
147C23×D17—41no—
148C23×D17C22×C411yescharacteristic
149C23×D17C22×C411yescharacteristic
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17C22×C411yescharacteristic
155C22×C4×C17C22×C411yescharacteristic
156C22×C4×C17C22×C411yescharacteristic
157C22×C4×C17C22×C411yescharacteristic
158C22×C4×C17C22×C411yescharacteristic
159C22×C4×C17#4112yes—
160C22×C4×C17#4112yes—
161C22×C4×C17C2411yescharacteristic
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17—41no—
165C22×Dic17C22×C411yescharacteristic
166C22×Dic17C22×C411yescharacteristic
167C22×Dic17C22×C411yescharacteristic
168C22×Dic17C22×C411yescharacteristic
169C22×Dic17C22×C411yescharacteristic
170C22×Dic17C22×C411yescharacteristic
171C2×C4×D17—22no—
172C2×C4×D17—22no—
173C2×C4×D17—21no—
174C2×C4×D17—21no—
175C2×C4×D17—21no—
176C2×C4×D17—21no—
177C2×C4×D17—22no—
178C2×C4×D17—22no—
179C2×C4×D17—22no—
180C2×C4×D17—22no—
181C2×C4×D17—22no—
182C2×C4×D17—22no—
183C2×C4×D17—22no—
184C2×C4×D17—21no—
185C2×C4×D17—21no—
186C2×C4×D17—21no—
187C2×C4×D17—21no—
188C2×C4×D17—21no—
189C2×C4×D17—21no—
190C2×C4×D17—22no—
191C2×C4×D17—22no—
192C2×C4×D17—44no—
193C2×C4×D17—44no—
194C2×C4×D17—44no—
195C2×C4×D17—44no—
196C2×C4×D17—41no—
197C2×C4×D17—41no—
198C2×C4×D17—41no—
199C2×C4×D17—41no—
200C2×C4×D17—41no—
201C2×C4×D17—41no—
202C2×C4×D17M1614yescomplemented
203C2×C4×D17C2×D412yes—
204C2×C4×D17#4112yes—
205M16×C17—44no—
206C2×C8×C17—21no—
207C2×C8×C17—21no—
208C2×C8×C17—21no—
209C2×C8×C17—21no—
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×C17C2×D412yes—
218C22⋊C4×C17—22no—
219C22⋊C4×C17—22no—
220C42×C17—21no—
221C42×C17—21no—
222C42×C17—21no—
223C42×C17—21no—
224C22⋊Dic17—22no—
225C22⋊Dic17—22no—
226#63227—22no—
227#63227—22no—
228#63227—22no—
229#63227M1614yescomplemented
230C4×Dic17—21no—
231C4×Dic17—21no—
232C4×Dic17—21no—
233C4×Dic17—21no—
234C4×Dic17—22no—
235C4×Dic17—22no—
236C4×Dic17—41no—
237C4×Dic17—41no—
238#63223—44no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—21no—
243C2×#3622—21no—
244C2×#3622—21no—
245C2×#3622—21no—
246C2×#3622—21no—
247C2×#3622—21no—
248C2×#3622—21no—
249C2×#3622—21no—
250C2×#3622C2×D412yes—
251#22553—171nomaximal, Sylow
252C23×C17—21no—
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—21no—
256C23×C17—21no—
257C23×C17—21no—
258C23×C17#11712yes—
259C23×C17C23×C411yescharacteristic
260C22×D17—21no—
261C22×D17—21no—
262C22×D17—21no—
263C22×D17—21no—
264C22×D17—28no—
265C22×D17—21no—
266C22×D17—21no—
267C22×D17—21no—
268C22×D17—21no—
269C22×D17—21no—
270C22×D17—21no—
271C22×D17—44no—
272C22×D17—44no—
273C22×D17—44no—
274C22×D17—44no—
275C22×D17—44no—
276C22×D17—44no—
277C22×D17C4×D412yes—
278C22×D17C2×M1612yes—
279C22×D17C2×M1612yes—
280C22×D17#13112yes—
281C2×C4×C17—21no—
282C2×C4×C17—21no—
283C2×C4×C17—21no—
284C2×C4×C17—21no—
285C2×C4×C17—21no—
286C2×C4×C17—21no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—21no—
292C2×C4×C17—21no—
293C2×C4×C17—21no—
294C2×C4×C17—21no—
295C2×C4×C17—21no—
296C2×C4×C17—21no—
297C2×C4×C17#11712yes—
298C2×C4×C17C2×M1612yes—
299C2×C4×C17C2×M1612yes—
300C2×C4×C17C22×D411yescharacteristic
301C2×C4×C17C2×#4111yescharacteristic
302C2×C4×C17C2×#4111yescharacteristic
303C2×C4×C17C2×#4111yescharacteristic
304C2×C4×C17H(5,𝔽2)11yescharacteristic
305C2×C4×C17H(5,𝔽2)11yescharacteristic
306C2×Dic17—21no—
307C2×Dic17—21no—
308C2×Dic17—21no—
309C2×Dic17—21no—
310C2×Dic17—21no—
311C2×Dic17—21no—
312C2×Dic17—21no—
313C2×Dic17—21no—
314C2×Dic17—21no—
315C2×Dic17—21no—
316C2×Dic17—21no—
317C2×Dic17—21no—
318C2×Dic17—21no—
319C2×Dic17—21no—
320C2×Dic17—21no—
321C2×Dic17—44no—
322C2×Dic17C4×D412yes—
323C2×Dic17C2×M1612yes—
324C2×Dic17C2×M1612yes—
325C4×D17—28no—
326C4×D17—22no—
327C4×D17—22no—
328C4×D17—22no—
329C4×D17—22no—
330C4×D17—44no—
331C4×D17—44no—
332C4×D17—44no—
333C4×D17—44no—
334C4×D17—44no—
335C4×D17—41no—
336C4×D17—41no—
337C4×D17—41no—
338C4×D17—41no—
339C8×C17—22no—
340C8×C17—41no—
341C8×C17—41no—
342C8×C17—41no—
343#3622—22no—
344#3622—41no—
345#3622—41no—
346#3622—41no—
347C2×#431—171no—
348C2×#407—171no—
349C2×C4×C22⋊C4—171no—
350#1924—171no—
351#1924—171no—
352#1923—171no—
353#1923—171no—
354#1851—171no—
355#1851—171no—
356#1817—171no—
357#1797—171no—
358#1779—171no—
359#1753—171no—
360#1753D1711yescharacteristic, complemented
361#1749—171no—
362C22×C17—22no—
363C22×C17—22no—
364C22×C17—22no—
365C22×C17—41no—
366C22×C17—41no—
367C22×C17—41no—
368C22×C17—41no—
369C22×C17C2×#11711yescharacteristic
370C22×C17C2×C4×D411yescharacteristic
371C22×C17#51811yescharacteristic
372C22×C17C22×M1611yescharacteristic
373C22×C17C22×M1611yescharacteristic
374C22×C17C2×#13111yescharacteristic
375C22×C17#56811yescharacteristic
376C2×D17—22no—
377C2×D17—22no—
378C2×D17—22no—
379C2×D17—22no—
380C2×D17—22no—
381C2×D17—22no—
382C2×D17—22no—
383C2×D17—22no—
384C2×D17—22no—
385C2×D17—416no—
386C2×D17—41no—
387C2×D17—41no—
388C2×D17—41no—
389C2×D17—41no—
390C2×D17#43514yes—
391C4×C17—22no—
392C4×C17—22no—
393C4×C17—22no—
394C4×C17—41no—
395C4×C17—41no—
396C4×C17#54611yescharacteristic
397C4×C17#54611yescharacteristic
398C4×C17#55111yescharacteristic
399C4×C17#55111yescharacteristic
400Dic17—22no—
401Dic17—22no—
402Dic17—22no—
403Dic17—41no—
404Dic17—41no—
405Dic17—41no—
406C24×C4—171no—
407C22×M16—171no—
408C22×M16C2×D1711yescharacteristic
409C22×C22⋊C4—171no—
410C22×C22⋊C4—171no—
411C22×C42—171no—
412C22×C42—171no—
413#431—344no—
414C2×C4⋊C8—171no—
415C2×C4⋊C8—171no—
416C2×C4⋊C8—171no—
417C2×C4⋊C8—171no—
418#407—344no—
419C2×C22⋊C8—171no—
420C2×C22⋊C8—171no—
421C2×C22⋊C8—171no—
422C2×C22⋊C8—171no—
423C2×C22⋊C8—171no—
424C2×C22⋊C8—171no—
425C2×C22⋊C8—171no—
426C2×C22⋊C8—171no—
427C2×C22⋊C8—171no—
428C2×C22⋊C8C2×D1711yescharacteristic
429C2×#97—171no—
430C2×#97C2×D1711yescharacteristic, complemented
431C2×C4×C8—171no—
432C2×C4×C8C2×D1711yescharacteristic, complemented
433C4×C22⋊C4—171no—
434C4×C22⋊C4—171no—
435C4×C22⋊C4—171no—
436C4×C22⋊C4—171no—
437C4×C22⋊C4—171no—
438C4×C22⋊C4—171no—
439C4×C22⋊C4—171no—
440C4×C22⋊C4C2×D1711yescharacteristic
441C2×#95—171no—
442C2×#95—171no—
443#336—171no—
444#336—171no—
445#336—171no—
446#336—171no—
447#336—171no—
448#336—171no—
449#336C2×D1711yescharacteristic, complemented
450#336C2×D1711yescharacteristic, complemented
451C2×C17—42no—
452C2×C17#234211yescharacteristic
453C2×C17#292011yescharacteristic
454C2×C17#292411yescharacteristic
455C2×C17C2×#43511yescharacteristic
456C2×C17D4×M1611yescharacteristic
457C2×C17#297411yescharacteristic
458C2×C17#297511yescharacteristic
459D17—24no—
460D17—42no—
461C25—171no—
462C23×C4—171no—
463C23×C4—171no—
464C23×C4—171no—
465C23×C4—171no—
466C23×C4—171no—
467C23×C4—171no—
468C23×C4—171no—
469C23×C4—171no—
470C23×C4—171no—
471C23×C4—342no—
472C23×C4—342no—
473C23×C4—342no—
474C23×C4—342no—
475C23×C4—681no—
476C23×C4—681no—
477C23×C4C22×D1711yescharacteristic
478C2×M16—22no—
479C2×M16—22no—
480C2×M16—41no—
481C2×M16—342no—
482C2×M16—342no—
483C2×M16—681no—
484C22×C8—171no—
485C22×C8—171no—
486C22×C8—171no—
487C22×C8—171no—
488C22×C8C22×D1711yescharacteristic
489C22×C8C22×D1711yescharacteristic
490C22×C8C22×D1711yescharacteristic
491C22×C8C22×D1711yescharacteristic
492C2×C22⋊C4—171no—
493C2×C22⋊C4—171no—
494C2×C22⋊C4—171no—
495C2×C22⋊C4—171no—
496C2×C22⋊C4—171no—
497C2×C22⋊C4—171no—
498C2×C22⋊C4—344no—
499C2×C22⋊C4—344no—
500C2×C22⋊C4C4×D1711yescharacteristic
501C2×C22⋊C4C4×D1711yescharacteristic
502C2×C42—171no—
503C2×C42—171no—
504C2×C42—171no—
505C2×C42—171no—
506C2×C42—171no—
507C2×C42—171no—
508C2×C42—342no—
509C2×C42—342no—
510C2×C42—681no—
511C2×C42—681no—
512C2×C42C22×D1711yescharacteristic
513C2×C42C22×D1711yescharacteristic
514C4⋊C8—342no—
515C4⋊C8—342no—
516C4⋊C8—681no—
517C4⋊C8—681no—
518C22⋊C8—22no—
519C22⋊C8—174no—
520C22⋊C8—342no—
521C22⋊C8—342no—
522C22⋊C8—342no—
523C22⋊C8—342no—
524C22⋊C8—342no—
525C22⋊C8—342no—
526C22⋊C8—681no—
527C22⋊C8—681no—
528#97—41no—
529#97—681no—
530C4×C8—22no—
531C4×C8—342no—
532#95—171no—
533#95—171no—
534#95—171no—
535#95—171no—
536#95—171no—
537#95—171no—
538#95C4×D1711yescharacteristic
539#95C4×D1711yescharacteristic
540C17#2255311yescharacteristic, complemented, Sylow
541C24—171no—
542C24—171no—
543C24—342no—
544C24—342no—
545C24—342no—
546C24—342no—
547C24—342no—
548C24—681no—
549C24—681no—
550C24C2×C4×D1711yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—171no—
556C22×C4—171no—
557C22×C4—171no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—174no—
561C22×C4—171no—
562C22×C4—171no—
563C22×C4—171no—
564C22×C4—342no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—341no—
577C22×C4—342no—
578C22×C4—341no—
579C22×C4—341no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—681no—
588C22×C4—681no—
589C22×C4—681no—
590C22×C4—681no—
591C22×C4—681no—
592C22×C4—681no—
593C22×C4—684no—
594C22×C4—684no—
595C22×C4—684no—
596C22×C4—684no—
597C22×C4—681no—
598C22×C4C2×C4×D1711yescharacteristic
599C22×C4C2×C4×D1711yescharacteristic
600C22×C4C2×C4×D1711yescharacteristic
601C22×C4C2×C4×D1711yescharacteristic
602C22×C4C2×C4×D1711yescharacteristic
603C22×C4#6325212yes—
604C22×C4#6325212yes—
605C22×C4C23×D1711yescharacteristic
606M16—44no—
607M16—684no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—172no—
620C2×C8—341no—
621C2×C8—341no—
622C2×C8—341no—
623C2×C8—341no—
624C2×C8—341no—
625C2×C8—341no—
626C2×C8—341no—
627C2×C8—341no—
628C2×C8—341no—
629C2×C8—341no—
630C2×C8—341no—
631C2×C8D4×D1712yes—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—174no—
635C22⋊C4—342no—
636C22⋊C4—342no—
637C22⋊C4—342no—
638C22⋊C4—342no—
639C22⋊C4—342no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—342no—
645C42—342no—
646C42—341no—
647C42—341no—
648C42—341no—
649C42—341no—
650C42—681no—
651C42—681no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—172no—
659C23—172no—
660C23—172no—
661C23—172no—
662C23—348no—
663C23—341no—
664C23—341no—
665C23—341no—
666C23—341no—
667C23—341no—
668C23—341no—
669C23—341no—
670C23—341no—
671C23—341no—
672C23—341no—
673C23—684no—
674C23—684no—
675C23—684no—
676C23—684no—
677C23—684no—
678C23—684no—
679C23#1058755812yes—
680C23C22×C4×D1711yescharacteristic
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—172no—
698C2×C4—172no—
699C2×C4—172no—
700C2×C4—348no—
701C2×C4—341no—
702C2×C4—341no—
703C2×C4—341no—
704C2×C4—341no—
705C2×C4—341no—
706C2×C4—341no—
707C2×C4—342no—
708C2×C4—342no—
709C2×C4—342no—
710C2×C4—342no—
711C2×C4—341no—
712C2×C4—341no—
713C2×C4—341no—
714C2×C4—341no—
715C2×C4—341no—
716C2×C4—341no—
717C2×C4—341no—
718C2×C4—341no—
719C2×C4—341no—
720C2×C4—684no—
721C2×C4—684no—
722C2×C4—684no—
723C2×C4—684no—
724C2×C4—684no—
725C2×C4—684no—
726C2×C4—681no—
727C2×C4—681no—
728C2×C4—681no—
729C2×C4—681no—
730C2×C4#1058755812yes—
731C2×C4M16×D1712yes—
732C2×C4M16×D1712yes—
733C2×C4C2×#6325211yescharacteristic
734C2×C4C2×#6325211yescharacteristic
735C2×C4C2×D4×D1711yescharacteristic
736C2×C4#1058769111yescharacteristic
737C2×C4#41×D1711yescharacteristic
738C2×C4#1058769611yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—342no—
744C8—681no—
745C8—681no—
746C8—681no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—174no—
755C22—342no—
756C22—342no—
757C22—342no—
758C22—342no—
759C22—342no—
760C22—342no—
761C22—342no—
762C22—342no—
763C22—342no—
764C22—6816no—
765C22—681no—
766C22—681no—
767C22—681no—
768C22—681no—
769C22C2×#1058755811yescharacteristic
770C22C4×D4×D1711yescharacteristic
771C22#1176328111yescharacteristic
772C22C2×M16×D1711yescharacteristic
773C22C2×M16×D1711yescharacteristic
774C22#131×D1711yescharacteristic
775C22#1176357411yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—41no—
781C4—342no—
782C4—342no—
783C4—342no—
784C4—681no—
785C4—681no—
786C4—681no—
787C4#1176344911yescharacteristic
788C4#1176345511yescharacteristic
789C4#1176348311yescharacteristic
790C4#1176348811yescharacteristic
791C2—42no—
792C2—344no—
793C2—682no—
794C2#1453162711yescharacteristic
795C2#1453741511yescharacteristic
796C2#1453743911yescharacteristic
797C2D17×#43511yescharacteristic
798C2#1453751711yescharacteristic
799C2#1453781611yescharacteristic
800C2#1453782211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1753C2
prime radicalC24×D17C2×C4
cosocleC22×C4×C17C24
hypercenter#1753D17
hypocenterC17#22553
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#11762860C2semidirect
4. #14529397C2semidirect
5. #14529395C2semidirect
6. #14529390C2semidirect
7. #14529388C2semidirect
8. #14528967C2semidirect
9. #14528966C2semidirect
10. #14528851C2semidirect
11. #14528763C2semidirect
13. #14528568C2semidirect
14. #14528547C2semidirect
15. C17×#1753C2semidirect
23. C2×#10587485C22semidirect
24. C2×#10587485C22semidirect
25. C2×#10587485C22semidirect
26. C2×#10587485C22semidirect
37. C2×#10587474C22semidirect
38. C2×C4×#3622C22semidirect
48. #11762564C22semidirect
49. #11762564C22semidirect
50. #11762563C22semidirect
51. #11762563C22semidirect
52. #11762563C22semidirect
53. #11762563C22semidirect
56. C2×C17×#97C22semidirect
57. C2×C4×C8×C17C22semidirect
59. C17×#336C22semidirect
60. C17×#336C22semidirect
202. C2×C4×D17M16semidirect
229. #63227M16semidirect
360. #1753D17semidirect
430. C2×#97C2×D17semidirect
432. C2×C4×C8C2×D17semidirect
449. #336C2×D17semidirect
450. #336C2×D17semidirect
540. C17#22553semidirect

Maximal subgroups

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

subgroupindex
C2×#117628602
C2×#117627722
C4×C22⋊C4×D172
#145293972
#145293952
#145293902
#145293882
#145289672
#145289662
#145288512
#145287632
#145286932
#145285682
#145285472
C17×#17532
#2255317