Finite Group Databasebeta

← #17054622

Subgroups — #17054622

Order 4352.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762954C211yesmaximal, characteristic
2C2×#11762907C211yesmaximal, characteristic, complemented
3C2×#11762805C211yesmaximal, characteristic, complemented
4#14531820C211yesmaximal, characteristic, complemented
5#14529659C211yesmaximal, characteristic, complemented
6#14529484C211yesmaximal, characteristic, complemented
7#14529401C211yesmaximal, characteristic, complemented
8#14529210C211yesmaximal, characteristic, complemented
9#14529139C211yesmaximal, characteristic, complemented
10#14529135C211yesmaximal, characteristic, complemented
11#14529052C211yesmaximal, characteristic, complemented
12#14528981C211yesmaximal, characteristic, complemented
13#14528614C211yesmaximal, characteristic, complemented
14#14528562C211yesmaximal, characteristic, complemented
15C17×#2341C211yesmaximal, characteristic, complemented
16C22×#63230C2211yescharacteristic
17C22×#63228C2211yescharacteristic
18C23×#3622C2211yescharacteristic
19C2×#10587616C2211yescharacteristic
20C2×C4×D68C2211yescharacteristic
21C2×#10587612C2211yescharacteristic
22#11762954C418yescomplemented
23#11762907—24no—
24C2×#10587478C2211yescharacteristic
25C2×#10587479C2211yescharacteristic
26#11762805—24no—
27C2×#10587506C2211yescharacteristic
28C2×#10587506C2211yescharacteristic
29C2×#10587506C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
32C2×#10587503C2211yescharacteristic
33C2×#10587480C2211yescharacteristic
34C2×#10587480C2211yescharacteristic
35C2×C22⋊#3622C2211yescharacteristic
36C2×#10587474C2211yescharacteristic
37C2×#10587474C2211yescharacteristic
38#11762711C2211yescharacteristic
39#11762709—21no—
40#11762707C2211yescharacteristic
41#11762698—21no—
42#11762685—21no—
43C4×C4⋊Dic17C2211yescharacteristic
44#11762656—21no—
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762564C2211yescharacteristic
50#11762564C2211yescharacteristic
51C22×#41×C17C2211yescharacteristic
52C2×C4×Q8×C17C2211yescharacteristic
53C2×C4×Q8×C17C2211yescharacteristic
54C17×#390—21no—
55C17×#390—21no—
56C17×#390C2211yescharacteristic
57C17×#390C2211yescharacteristic
58C17×#380—21no—
59C17×#380C2211yescharacteristic
60C4×C22⋊C4×C17—21no—
61C4×C22⋊C4×C17C2211yescharacteristic
62C2×#41×C17—22no—
63C2×#41×C17—22no—
64C2×#41×C17—22no—
65C2×#41×C17—41no—
66C2×#41×C17—41no—
67C2×#41×C17C2×C414yescomplemented
68C22×Q8×C17C2311yescharacteristic
69C22×D4×C17—21no—
70C22×D4×C17C2311yescharacteristic
71C23×C4×C17—21no—
72C23×C4×C17C2311yescharacteristic
73C22×C22⋊D17—21no—
74C22×D68C2311yescharacteristic
75C22×C4×D17—21no—
76C4×Q8×C17—22no—
77C4×Q8×C17—22no—
78C4×Q8×C17—41no—
79C4×Q8×C17—41no—
80C2×C4⋊C4×C17—21no—
81C2×C4⋊C4×C17—21no—
82C2×C4⋊C4×C17C2311yescharacteristic
83C2×C4⋊C4×C17C2311yescharacteristic
84C2×C22⋊C4×C17—21no—
85C2×C22⋊C4×C17—21no—
86C2×C22⋊C4×C17—21no—
87C2×C22⋊C4×C17—21no—
88C2×C22⋊C4×C17—21no—
89C2×C22⋊C4×C17D411yescharacteristic
90C2×C22⋊C4×C17D411yescharacteristic
91C2×C42×C17—21no—
92C2×C42×C17—21no—
93C2×C42×C17C2311yescharacteristic
94C2×C42×C17C2311yescharacteristic
95C2×C22⋊Dic17—21no—
96C2×#63230—22no—
97C2×#63230—22no—
98C2×#63230C2×C414yes—
99C2×#63228—41no—
100C2×#63228—41no—
101C2×#63228C2×C414yes—
102#10587616—22no—
103#10587616C2×C414yes—
104C2×#63227—21no—
105C2×#63227—21no—
106C2×#63227—21no—
107C2×#63227—21no—
108#10587612—22no—
109#10587612—41no—
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4⋊Dic17C2311yescharacteristic
112C2×C4⋊Dic17C2311yescharacteristic
113C2×#63225—21no—
114C2×C4×Dic17—21no—
115C2×C4×Dic17—21no—
116C22×#3622—22no—
117C22×#3622—22no—
118C22×#3622—41no—
119C22×#3622C2311yescharacteristic
120C22×#3622C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122C22×#3622C2311yescharacteristic
123C4×D68—22no—
124C4×D68—41no—
125C17×#95—21no—
126C17×#95D411yescharacteristic
127C17×#95D411yescharacteristic
128#10587506—22no—
129#10587506C2×C414yescomplemented
130#10587506D414yescomplemented
131#10587503—22no—
132#10587503—22no—
133#10587503C2×C414yescomplemented
134#10587502—21no—
135#10587502—21no—
136C22⋊#3622C2×C414yescomplemented
137#10587480—22no—
138#10587480—41no—
139#10587479—41no—
140#10587478—22no—
141#10587474—22no—
142#10587474—41no—
143C24×C17—21no—
144C24×C17C2×D411yescharacteristic
145C23×D17—21no—
146#41×C17—28no—
147#41×C17—44no—
148#41×C17—44no—
149#41×C17—44no—
150C2×Q8×C17—21no—
151C2×Q8×C17—21no—
152C2×Q8×C17—21no—
153C2×Q8×C17C22×C412yes—
154C2×Q8×C17C2×D412yes—
155C2×Q8×C17#4112yes—
156C2×D4×C17—24no—
157C2×D4×C17—21no—
158C2×D4×C17—21no—
159C2×D4×C17—21no—
160C2×D4×C17—21no—
161C2×D4×C17—21no—
162C2×D4×C17—42no—
163C2×D4×C17—42no—
164C2×D4×C17C22×C412yes—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—24no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—42no—
174C22×C4×C17—42no—
175C22×C4×C17C22×C412yes—
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D411yescharacteristic
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17C2×D411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17#4112yes—
182C22×C4×C17C2411yescharacteristic
183C2×C22⋊D17—24no—
184C2×C22⋊D17—81no—
185C2×C22⋊D17—81no—
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C2×D68—21no—
190C2×D68—21no—
191C2×D68—21no—
192C2×D68—21no—
193C2×D68—21no—
194C2×D68C22×C412yes—
195C2×C4×D17—42no—
196C2×C4×D17—42no—
197C2×C4×D17—81no—
198C4⋊C4×C17—21no—
199C4⋊C4×C17—21no—
200C4⋊C4×C17—21no—
201C4⋊C4×C17—21no—
202C4⋊C4×C17—42no—
203C4⋊C4×C17—42no—
204C22⋊C4×C17—41no—
205C22⋊C4×C17—41no—
206C22⋊C4×C17—42no—
207C22⋊C4×C17—42no—
208C22⋊C4×C17—81no—
209C22⋊C4×C17—81no—
210C22⋊C4×C17—81no—
211C42×C17—21no—
212C42×C17—21no—
213C42×C17—21no—
214C42×C17—21no—
215C42×C17—42no—
216C42×C17—42no—
217C22⋊Dic17—42no—
218#63230—28no—
219#63228—44no—
220#63227—24no—
221#63227—42no—
222#63227—42no—
223#63227—81no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—21no—
228C4⋊Dic17C22×C412yes—
229C4⋊Dic17C2×D412yes—
230#63225—81no—
231C4×Dic17—42no—
232C4×Dic17—81no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—21no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—44no—
243C2×#3622C22×C412yes—
244C2×#3622C22×C412yes—
245C2×#3622C2×D412yes—
246#22857—171nomaximal, Sylow
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—21no—
253C23×C17—22no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17C4×D412yes—
261C23×C17C22×D411yescharacteristic
262C22×D17—22no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—41no—
268C22×D17—41no—
269Q8×C17—22no—
270Q8×C17—22no—
271Q8×C17—22no—
272Q8×C17C4×D414yes—
273D4×C17—22no—
274D4×C17—22no—
275D4×C17—48no—
276D4×C17—41no—
277D4×C17—41no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—21no—
281C2×C4×C17—22no—
282C2×C4×C17—21no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—21no—
288C2×C4×C17—21no—
289C2×C4×C17—21no—
290C2×C4×C17—21no—
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—21no—
298C2×C4×C17—21no—
299C2×C4×C17—48no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17—41no—
306C2×C4×C17C4×D412yes—
307C2×C4×C17C23×C411yescharacteristic
308C2×C4×C17C22×D411yescharacteristic
309C2×C4×C17C2×#4111yescharacteristic
310C2×C4×C17C2×#4111yescharacteristic
311C2×C4×C17H(5,𝔽2)11yescharacteristic
312C2×C4×C17H(5,𝔽2)11yescharacteristic
313C22⋊D17—84no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323D68—22no—
324D68—22no—
325D68—41no—
326D68—41no—
327C4×D17—84no—
328#3622—22no—
329#3622—22no—
330#3622—22no—
331#3622—41no—
332C2×#449—171no—
333C2×#440—171no—
334C2×#416—171no—
335#2363—171no—
336#2341D1711yescharacteristic, complemented
337#1972—171no—
338#1936—171no—
339#1925—171no—
340#1893—171no—
341#1880—171no—
342#1879—171no—
343#1865—171no—
344#1854—171no—
345#1763—171no—
346#1752—171no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—41no—
351C22×C17—41no—
352C22×C17—41no—
353C22×C17—41no—
354C22×C17—42no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17—81no—
358C22×C17—81no—
359C22×C17—81no—
360C22×C17—81no—
361C22×C17C2×C4×D411yescharacteristic
362C22×C17D4211yescharacteristic
363C22×C17#54611yescharacteristic
364C22×C17#57511yescharacteristic
365C22×C17#57511yescharacteristic
366C22×C17#57611yescharacteristic
367C22×C17#57711yescharacteristic
368C2×D17—42no—
369C2×D17—42no—
370C2×D17—42no—
371C2×D17—81no—
372C2×D17—81no—
373C2×D17—81no—
374C2×D17—81no—
375C4×C17—22no—
376C4×C17—24no—
377C4×C17—41no—
378C4×C17—41no—
379C4×C17—41no—
380C4×C17—41no—
381C4×C17—81no—
382C4×C17—81no—
383C4×C17C2×C4×D411yescharacteristic
384C4×C17#51811yescharacteristic
385C4×C17#54611yescharacteristic
386C4×C17#55111yescharacteristic
387Dic17—42no—
388Dic17—42no—
389Dic17—81no—
390C22×#41C2×D1711yescharacteristic
391C22×SD16—171no—
392C22×D8—171no—
393C23×C8—171no—
394C2×#121—171no—
395C2×C4×Q8C2×D1711yescharacteristic
396C2×C4×Q8C2×D1711yescharacteristic
397C2×C4×D4—171no—
398C2×#117—171no—
399#449—178no—
400#440—344no—
401C2×#107—171no—
402C2×#106—171no—
403#416—344no—
404C2×#103—171no—
405C2×#103—171no—
406C2×#103—171no—
407C2×#102—171no—
408C2×#102—171no—
409C2×#102—171no—
410C2×#102—171no—
411C2×#102—171no—
412C2×C22⋊C8—171no—
413C2×#97—171no—
414C2×#97—171no—
415#390—21no—
416#390—21no—
417#390—171no—
418#390—341no—
419#390C2×D1711yescharacteristic
420#390C2×D1711yescharacteristic
421#389—171no—
422#388—341no—
423#386—341no—
424#380—21no—
425#380C2×D1711yescharacteristic
426C4×C4⋊C4—171no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—341no—
429C4×C22⋊C4C2×D1711yescharacteristic
430#340—171no—
431#340—171no—
432#340—171no—
433#340—171no—
434#336—171no—
435#336—171no—
436C2×C17—42no—
437C2×C17—82no—
438C2×C17#235811yescharacteristic
439C2×C17#294311yescharacteristic
440C2×C17#294611yescharacteristic
441C2×C17#326811yescharacteristic
442C2×C17#327111yescharacteristic
443C2×C17#330911yescharacteristic
444C2×C17#332111yescharacteristic
445D17—82no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—41no—
450C2×#41—41no—
451C2×#41C4×D1714yescomplemented
452C22×Q8C22×D1711yescharacteristic
453C22×D4—21no—
454C22×D4—171no—
455C22×D4—341no—
456C22×D4C22×D1711yescharacteristic
457C23×C4—21no—
458C23×C4—341no—
459C23×C4C22×D1711yescharacteristic
460C2×SD16—174no—
461C2×SD16—342no—
462C2×SD16—342no—
463C2×D8—174no—
464C2×D8—681no—
465C2×D8—681no—
466C22×C8—171no—
467C22×C8—171no—
468C22×C8—171no—
469C22×C8—171no—
470C22×C8—342no—
471C22×C8—342no—
472C22×C8—681no—
473#121—174no—
474#121—342no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×Q8—41no—
479C4×D4—342no—
480C4×D4—681no—
481#117—342no—
482#117—681no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—171no—
486C2×C4⋊C4—171no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—341no—
489C2×C4⋊C4C22×D1711yescharacteristic
490C2×C4⋊C4C22×D1711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—341no—
497C2×C22⋊C4—341no—
498C2×C22⋊C4—341no—
499C2×C22⋊C4—341no—
500C2×C22⋊C4—341no—
501C2×C22⋊C4C22⋊D1711yescharacteristic
502C2×C22⋊C4C22⋊D1711yescharacteristic
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—341no—
506C2×C42—341no—
507C2×C42C22×D1711yescharacteristic
508C2×C42C22×D1711yescharacteristic
509#107—342no—
510#106—681no—
511#103—174no—
512#103—174no—
513#103—342no—
514#102—174no—
515#102—342no—
516#102—342no—
517#102—342no—
518#102—681no—
519C22⋊C8—174no—
520#97—342no—
521#97—681no—
522#95—21no—
523#95—341no—
524#95—341no—
525#95C22⋊D1711yescharacteristic
526#95C22⋊D1711yescharacteristic
527C17#2285711yescharacteristic, complemented, Sylow
528C24—21no—
529C24—341no—
530C24C2×C22⋊D1711yescharacteristic
531#41—28no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C2×C4×D1712yes—
539C2×Q8D4×D1712yes—
540C2×Q8#6325412yes—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—172no—
550C2×D4—344no—
551C2×D4—341no—
552C2×D4—341no—
553C2×D4—341no—
554C2×D4—341no—
555C2×D4—341no—
556C2×D4—1361no—
557C2×D4—1361no—
558C2×D4C2×C4×D1712yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—682no—
573C22×C4—682no—
574C22×C4—1361no—
575C22×C4C2×C4×D1712yes—
576C22×C4#6325212yes—
577C22×C4C2×C22⋊D1711yescharacteristic
578C22×C4C2×C22⋊D1711yescharacteristic
579C22×C4C2×C22⋊D1711yescharacteristic
580C22×C4C2×C22⋊D1711yescharacteristic
581C22×C4C2×C22⋊D1711yescharacteristic
582C22×C4C23×D1711yescharacteristic
583SD16—348no—
584D8—684no—
585C2×C8—172no—
586C2×C8—172no—
587C2×C8—172no—
588C2×C8—341no—
589C2×C8—341no—
590C2×C8—341no—
591C2×C8—341no—
592C2×C8—341no—
593C2×C8—341no—
594C2×C8—341no—
595C2×C8—341no—
596C2×C8—341no—
597C2×C8—684no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—172no—
605C4⋊C4—172no—
606C4⋊C4—341no—
607C4⋊C4—341no—
608C4⋊C4—341no—
609C4⋊C4—341no—
610C4⋊C4—1361no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C22⋊C4—344no—
619C22⋊C4—682no—
620C22⋊C4—682no—
621C22⋊C4—682no—
622C22⋊C4—1361no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—42no—
628C42—42no—
629C42—682no—
630C42—1361no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—342no—
645C23—681no—
646C23—681no—
647C23—681no—
648C23—681no—
649C23—681no—
650C23—681no—
651C23C4×C22⋊D1712yes—
652C23C22×C22⋊D1711yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8#1058756714yes—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—342no—
663D4—342no—
664D4—681no—
665D4—681no—
666D4—1364no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—48no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—681no—
698C2×C4—681no—
699C2×C4—681no—
700C2×C4—681no—
701C2×C4—681no—
702C2×C4—681no—
703C2×C4—681no—
704C2×C4—1364no—
705C2×C4C4×C22⋊D1712yes—
706C2×C4C22×C4×D1711yescharacteristic
707C2×C4C2×#6325211yescharacteristic
708C2×C4C2×D4×D1711yescharacteristic
709C2×C4C2×#6325411yescharacteristic
710C2×C4#1058769111yescharacteristic
711C2×C4#1058769111yescharacteristic
712C8—342no—
713C8—342no—
714C8—342no—
715C8—681no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—682no—
731C22—682no—
732C22—682no—
733C22—1361no—
734C22—1361no—
735C22—1361no—
736C22—1361no—
737C22C2×C4×C22⋊D1711yescharacteristic
738C22D4×C22⋊D1711yescharacteristic
739C22#1176345311yescharacteristic
740C22#1176360711yescharacteristic
741C22#1176360711yescharacteristic
742C22#1176361211yescharacteristic
743C22#1176361711yescharacteristic
744C4—22no—
745C4—24no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—81no—
751C4—81no—
752C4—682no—
753C4—682no—
754C4—1361no—
755C4C2×#1058756711yescharacteristic
756C4#1176328211yescharacteristic
757C4#1176344911yescharacteristic
758C4#1176348511yescharacteristic
759C2—42no—
760C2—82no—
761C2—1362no—
762C2#1453176311yescharacteristic
763C2#1453758211yescharacteristic
764C2#1453761211yescharacteristic
765C2#1454032511yescharacteristic
766C2#1454037011yescharacteristic
767C2#1454079011yescharacteristic
768C2#1454097011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2341C2
socleC23×C17C22×D4
prime radicalC2×#11762954C2
cosocleC22×C4×C17C24
hypercenter#2341D17
hypocenterC17#22857
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#11762907C2semidirect
3. C2×#11762805C2semidirect
4. #14531820C2semidirect
5. #14529659C2semidirect
6. #14529484C2semidirect
7. #14529401C2semidirect
8. #14529210C2semidirect
9. #14529139C2semidirect
10. #14529135C2semidirect
11. #14529052C2semidirect
12. #14528981C2semidirect
13. #14528614C2semidirect
14. #14528562C2semidirect
15. C17×#2341C2semidirect
22. #11762954C4semidirect
67. C2×#41×C17C2×C4semidirect
129. #10587506C2×C4semidirect
130. #10587506D4semidirect
133. #10587503C2×C4semidirect
136. C22⋊#3622C2×C4semidirect
336. #2341D17semidirect
451. C2×#41C4×D17semidirect
527. C17#22857semidirect

Maximal subgroups

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

subgroupindex
C2×#117629542
C2×#117629072
C2×#117628052
#145318202
#145296592
#145294842
#145294012
#145292102
#145291392
#145291352
#145290522
#145289812
#145286142
#145285622
C17×#23412
#2285717