Finite Group Databasebeta

← #17045665

Subgroups — #17045665

Order 4352.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762943C211yesmaximal, characteristic
2#14531477C211yesmaximal, characteristic, complemented
3#14529659C211yesmaximal, characteristic, complemented
4#14529649C211yesmaximal, characteristic, complemented
5#14529484C211yesmaximal, characteristic, complemented
6#14529470C211yesmaximal, characteristic, complemented
7#14529408C211yesmaximal, characteristic, complemented
8#14529401C211yesmaximal, characteristic, complemented
9#14529135C211yesmaximal, characteristic, complemented
10#14529135C211yesmaximal, characteristic, complemented
11#14529106C211yesmaximal, characteristic, complemented
12#14528983C211yesmaximal, characteristic, complemented
13#14528715C211yesmaximal, characteristic, complemented
14#14528550C211yesmaximal, characteristic, complemented
15C17×#2309C211yesmaximal, characteristic, complemented
16C22×#63228C2211yescharacteristic
17C22×#63228C2211yescharacteristic
18C2×#10587616C2211yescharacteristic
19C2×C4×D68C2211yescharacteristic, complemented
20#11762943C418yescomplemented
21C2×#10587478C2211yescharacteristic, complemented
22C2×#10587479C2211yescharacteristic, complemented
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×#10587503C2211yescharacteristic
29C2×#10587480C2211yescharacteristic, complemented
30C2×#10587480C2211yescharacteristic, complemented
31C2×C22⋊#3622C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33C2×#10587474C2211yescharacteristic, complemented
34C2×C4×#3622C2211yescharacteristic, complemented
35#11762711C2211yescharacteristic, complemented
36#11762709—21no—
37#11762707C2211yescharacteristic, complemented
38#11762699—21no—
39#11762685—21no—
40#11762680—21no—
41#11762669C2211yescharacteristic
42C4×C4⋊Dic17C2211yescharacteristic, complemented
43#11762571C2211yescharacteristic, complemented
44#11762571C2211yescharacteristic, complemented
45#11762571C2211yescharacteristic, complemented
46#11762571C2211yescharacteristic, complemented
47#11762564C2211yescharacteristic, complemented
48#11762564C2211yescharacteristic, complemented
49C23×D4×C17C2211yescharacteristic
50C2×C17×#117C2211yescharacteristic
51C2×C17×#117C2211yescharacteristic
52C17×#390—21no—
53C17×#390—21no—
54C17×#390C2211yescharacteristic
55C17×#390C2211yescharacteristic
56C17×#390C2211yescharacteristic
57C17×#390C2211yescharacteristic
58C17×#379—21no—
59C17×#379—21no—
60C25×C17—21no—
61C22×D4×C17—21no—
62C22×D4×C17—22no—
63C22×D4×C17—41no—
64C22×D4×C17—41no—
65C22×D4×C17—41no—
66C22×D4×C17—41no—
67C22×D4×C17C2×C414yescomplemented
68C22×D4×C17C2311yescharacteristic
69C22×D4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C22×C22⋊D17—21no—
72C22×D68C2311yescharacteristic
73C22×C4×D17—21no—
74C17×#117—41no—
75C17×#117—41no—
76C17×#117—41no—
77C17×#117—41no—
78C2×C4⋊C4×C17D411yescharacteristic
79C2×C4⋊C4×C17D411yescharacteristic
80C2×C4⋊C4×C17C2311yescharacteristic
81C2×C4⋊C4×C17C2311yescharacteristic
82C2×C22⋊C4×C17—21no—
83C2×C22⋊C4×C17—21no—
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×C17—21no—
90C2×C22⋊C4×C17—21no—
91C2×C22⋊C4×C17D411yescharacteristic
92C2×C22⋊C4×C17D411yescharacteristic
93C2×C42×C17—21no—
94C2×C42×C17C2311yescharacteristic
95C2×C42×C17C2311yescharacteristic
96C2×C22⋊Dic17—21no—
97C2×#63228—41no—
98C2×#63228—41no—
99C2×#63228—41no—
100C2×#63228—41no—
101C2×#63228C2×C414yes—
102C2×#63228C2×C414yes—
103#10587616—22no—
104#10587616C2×C414yes—
105C2×#63227—21no—
106C2×#63227—21no—
107C2×#63227—21no—
108C2×#63227—21no—
109C2×C4⋊Dic17C2311yescharacteristic
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4⋊Dic17C2311yescharacteristic
112C2×#63225—21no—
113C2×C4×Dic17—21no—
114C22×#3622C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116C22×#3622C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C4×D68—41no—
119C4×D68—41no—
120#10587503—41no—
121#10587503—41no—
122#10587503—41no—
123#10587503—41no—
124#10587503C2×C414yescomplemented
125#10587503C2×C414yescomplemented
126#10587502—21no—
127#10587502—21no—
128#10587502—21no—
129C22⋊#3622—22no—
130C22⋊#3622C2×C414yescomplemented
131#10587480—41no—
132#10587480—41no—
133#10587479—41no—
134#10587478—41no—
135#10587474—41no—
136C4×#3622—41no—
137C24×C17—21no—
138C24×C17—21no—
139C24×C17—24no—
140C24×C17—42no—
141C24×C17—42no—
142C24×C17—81no—
143C24×C17—81no—
144C24×C17—81no—
145C24×C17—81no—
146C24×C17C2×D411yescharacteristic
147C23×D17—21no—
148C2×D4×C17—24no—
149C2×D4×C17—21no—
150C2×D4×C17—21no—
151C2×D4×C17—21no—
152C2×D4×C17—21no—
153C2×D4×C17—21no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—21no—
157C2×D4×C17—21no—
158C2×D4×C17—21no—
159C2×D4×C17—44no—
160C2×D4×C17—44no—
161C2×D4×C17—42no—
162C2×D4×C17—42no—
163C2×D4×C17—44no—
164C2×D4×C17—44no—
165C2×D4×C17C22×C412yes—
166C2×D4×C17C22×C412yes—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17C22×C412yes—
174C22×C4×C17C2×D411yescharacteristic
175C22×C4×C17C2×D411yescharacteristic
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D411yescharacteristic
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17#4112yes—
180C22×C4×C17C2411yescharacteristic
181C2×C22⋊D17—24no—
182C2×C22⋊D17—81no—
183C2×C22⋊D17—81no—
184C22×Dic17—21no—
185C22×Dic17—21no—
186C22×Dic17—21no—
187C2×D68—21no—
188C2×D68—21no—
189C2×D68—21no—
190C2×D68—21no—
191C2×D68—21no—
192C2×D68C22×C412yes—
193C2×C4×D17—42no—
194C2×C4×D17—81no—
195C2×C4×D17—81no—
196C4⋊C4×C17—21no—
197C4⋊C4×C17—21no—
198C4⋊C4×C17—21no—
199C4⋊C4×C17—21no—
200C4⋊C4×C17—41no—
201C4⋊C4×C17—41no—
202C22⋊C4×C17—41no—
203C22⋊C4×C17—41no—
204C22⋊C4×C17—42no—
205C22⋊C4×C17—81no—
206C22⋊C4×C17—81no—
207C22⋊C4×C17—81no—
208C22⋊C4×C17—81no—
209C22⋊C4×C17—81no—
210C22⋊C4×C17—81no—
211C22⋊C4×C17—81no—
212C22⋊C4×C17—81no—
213C42×C17—21no—
214C42×C17—21no—
215C42×C17—21no—
216C42×C17—21no—
217C42×C17—42no—
218C22⋊Dic17—81no—
219#63228—44no—
220#63228—44no—
221#63227—24no—
222#63227—42no—
223#63227—81no—
224#63227—81no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—21no—
228C4⋊Dic17—21no—
229C4⋊Dic17—21no—
230C4⋊Dic17C22×C412yes—
231#63225—81no—
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—21no—
243C2×#3622C22×C412yes—
244C2×#3622C22×C412yes—
245#22056—171nomaximal, Sylow
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—22no—
253C23×C17—22no—
254C23×C17—48no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17—41no—
263C23×C17—41no—
264C23×C17—41no—
265C23×C17—41no—
266C23×C17—41no—
267C23×C17—84no—
268C23×C17—84no—
269C23×C17—84no—
270C23×C17—84no—
271C23×C17—84no—
272C23×C17—84no—
273C23×C17C4×D412yes—
274C23×C17C22×D411yescharacteristic
275C22×D17—22no—
276C22×D17—41no—
277C22×D17—41no—
278C22×D17—41no—
279C22×D17—41no—
280C22×D17—41no—
281C22×D17—41no—
282D4×C17—22no—
283D4×C17—22no—
284D4×C17—22no—
285D4×C17—22no—
286D4×C17—48no—
287D4×C17—41no—
288D4×C17—41no—
289D4×C17—41no—
290D4×C17—41no—
291C2×C4×C17—21no—
292C2×C4×C17—21no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—21no—
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—41no—
310C2×C4×C17—41no—
311C2×C4×C17—41no—
312C2×C4×C17—41no—
313C2×C4×C17—41no—
314C2×C4×C17—41no—
315C2×C4×C17C4×D412yes—
316C2×C4×C17C23×C411yescharacteristic
317C2×C4×C17C2×#4111yescharacteristic
318C2×C4×C17H(5,𝔽2)11yescharacteristic
319C2×C4×C17H(5,𝔽2)11yescharacteristic
320C2×C4×C17H(5,𝔽2)11yescharacteristic
321C2×C4×C17H(5,𝔽2)11yescharacteristic
322C22⋊D17—84no—
323C2×Dic17—22no—
324C2×Dic17—41no—
325C2×Dic17—41no—
326C2×Dic17—41no—
327C2×Dic17—41no—
328C2×Dic17—41no—
329C2×Dic17—41no—
330C2×Dic17—41no—
331C2×Dic17—41no—
332D68—22no—
333D68—22no—
334D68—41no—
335D68—41no—
336C4×D17—84no—
337#3622—22no—
338#3622—22no—
339#3622—41no—
340#3622—41no—
341C2×#447—171no—
342#2324—171no—
343#2309D1711yescharacteristic, complemented
344#1972—171no—
345#1970—171no—
346#1936—171no—
347#1934—171no—
348#1926—171no—
349#1925—171no—
350#1879—171no—
351#1879—171no—
352#1875—171no—
353#1854—171no—
354#1786—171no—
355#1750—171no—
356C22×C17—22no—
357C22×C17—22no—
358C22×C17—22no—
359C22×C17—41no—
360C22×C17—41no—
361C22×C17—41no—
362C22×C17—41no—
363C22×C17—42no—
364C22×C17—42no—
365C22×C17—42no—
366C22×C17—42no—
367C22×C17—42no—
368C22×C17—42no—
369C22×C17—816no—
370C22×C17—81no—
371C22×C17—81no—
372C22×C17—81no—
373C22×C17—81no—
374C22×C17—81no—
375C22×C17—81no—
376C22×C17—81no—
377C22×C17—81no—
378C22×C17C2×C4×D411yescharacteristic
379C22×C17#53411yescharacteristic
380C22×C17#53511yescharacteristic
381C22×C17#57611yescharacteristic
382C22×C17#57611yescharacteristic
383C22×C17#57611yescharacteristic
384C22×C17#57711yescharacteristic
385C2×D17—42no—
386C2×D17—42no—
387C2×D17—42no—
388C2×D17—81no—
389C2×D17—81no—
390C2×D17—81no—
391C2×D17—81no—
392C4×C17—22no—
393C4×C17—41no—
394C4×C17—41no—
395C4×C17—41no—
396C4×C17—41no—
397C4×C17—81no—
398C4×C17—81no—
399C4×C17#51811yescharacteristic
400C4×C17#51811yescharacteristic
401C4×C17#53811yescharacteristic
402C4×C17#53811yescharacteristic
403Dic17—42no—
404Dic17—81no—
405Dic17—81no—
406C23×D4C2×D1711yescharacteristic
407C22×D8—171no—
408C22×D8—171no—
409C2×#121—171no—
410C2×C4×D4—171no—
411C2×#117C2×D1711yescharacteristic
412C2×#117C2×D1711yescharacteristic
413#447—178no—
414C2×#107—171no—
415C2×#106—171no—
416C2×#102—171no—
417C2×#102—171no—
418C2×#102—171no—
419C2×#102—171no—
420C2×#102—171no—
421C2×#102—171no—
422C2×#102—171no—
423C2×#102—171no—
424C2×C22⋊C8—171no—
425C2×C22⋊C8—171no—
426C2×#97—171no—
427C2×C4×C8—171no—
428#390—21no—
429#390—21no—
430#390—171no—
431#390—341no—
432#390C2×D1711yescharacteristic
433#390C2×D1711yescharacteristic
434#390C2×D1711yescharacteristic
435#390C2×D1711yescharacteristic
436#389—171no—
437#388—341no—
438#386—341no—
439#385—341no—
440#380—171no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—171no—
444#340—171no—
445#340—171no—
446#340—171no—
447#340—171no—
448#336—171no—
449#336—171no—
450C2×C17—42no—
451C2×C17—82no—
452C2×C17—82no—
453C2×C17#232111yescharacteristic
454C2×C17#294611yescharacteristic
455C2×C17#294811yescharacteristic
456C2×C17#319811yescharacteristic
457C2×C17#319911yescharacteristic
458C2×C17#322011yescharacteristic
459C2×C17#322411yescharacteristic
460D17—82no—
461C25—21no—
462C22×D4—22no—
463C22×D4—21no—
464C22×D4—41no—
465C22×D4—41no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—171no—
469C22×D4—341no—
470C22×D4C4×D1714yescomplemented
471C22×D4C22×D1711yescharacteristic
472C22×D4C22×D1711yescharacteristic
473C23×C4—341no—
474C23×C4C22×D1711yescharacteristic
475C2×D8—174no—
476C2×D8—174no—
477C2×D8—681no—
478C2×D8—681no—
479C2×D8—681no—
480C2×D8—681no—
481C22×C8—171no—
482C22×C8—171no—
483C22×C8—171no—
484C22×C8—171no—
485#121—174no—
486#121—342no—
487C4×D4—681no—
488C4×D4—681no—
489#117—41no—
490#117—41no—
491#117—41no—
492#117—41no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—171no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—341no—
497C2×C4⋊C4C22⋊D1711yescharacteristic
498C2×C4⋊C4C22⋊D1711yescharacteristic
499C2×C4⋊C4C22×D1711yescharacteristic
500C2×C4⋊C4C22×D1711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4—341no—
512C2×C22⋊C4—341no—
513C2×C22⋊C4—341no—
514C2×C22⋊C4—341no—
515C2×C22⋊C4C22⋊D1711yescharacteristic
516C2×C22⋊C4C22⋊D1711yescharacteristic
517C2×C42—21no—
518C2×C42—341no—
519C2×C42C22×D1711yescharacteristic
520C2×C42C22×D1711yescharacteristic
521#107—681no—
522#106—681no—
523#102—174no—
524#102—174no—
525#102—681no—
526#102—681no—
527#102—681no—
528#102—681no—
529#102—681no—
530#102—681no—
531C22⋊C8—174no—
532C22⋊C8—342no—
533#97—681no—
534C4×C8—681no—
535#95—341no—
536#95—341no—
537#95—341no—
538C17#2205611yescharacteristic, complemented, Sylow
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—341no—
549C24C2×C22⋊D1711yescharacteristic
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—24no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—172no—
568C2×D4—344no—
569C2×D4—341no—
570C2×D4—341no—
571C2×D4—341no—
572C2×D4—341no—
573C2×D4—341no—
574C2×D4—1361no—
575C2×D4—1361no—
576C2×D4C2×C4×D1712yes—
577C2×D4C2×C4×D1712yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—341no—
585C22×C4—341no—
586C22×C4—341no—
587C22×C4—682no—
588C22×C4—1361no—
589C22×C4—1361no—
590C22×C4C2×C4×D1712yes—
591C22×C4#6325212yes—
592C22×C4C2×C22⋊D1711yescharacteristic
593C22×C4C2×C22⋊D1711yescharacteristic
594C22×C4C2×C22⋊D1711yescharacteristic
595C22×C4C2×C22⋊D1711yescharacteristic
596C22×C4C2×C22⋊D1711yescharacteristic
597C22×C4C23×D1711yescharacteristic
598D8—684no—
599D8—684no—
600C2×C8—172no—
601C2×C8—172no—
602C2×C8—341no—
603C2×C8—341no—
604C2×C8—341no—
605C2×C8—341no—
606C2×C8—341no—
607C2×C8—341no—
608C2×C8—341no—
609C2×C8—341no—
610C2×C8—341no—
611C2×C8—341no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—172no—
619C4⋊C4—341no—
620C4⋊C4—341no—
621C4⋊C4—341no—
622C4⋊C4—341no—
623C4⋊C4—341no—
624C4⋊C4—1361no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—344no—
637C22⋊C4—682no—
638C22⋊C4—1361no—
639C22⋊C4—1361no—
640C22⋊C4—1361no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—1361no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—342no—
675C23—681no—
676C23—681no—
677C23—681no—
678C23—681no—
679C23—681no—
680C23—681no—
681C23C4×C22⋊D1712yes—
682C23C22×C22⋊D1711yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—342no—
693D4—342no—
694D4—681no—
695D4—681no—
696D4—1364no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—342no—
722C2×C4—681no—
723C2×C4—681no—
724C2×C4—681no—
725C2×C4—681no—
726C2×C4—681no—
727C2×C4—681no—
728C2×C4—681no—
729C2×C4—681no—
730C2×C4—1364no—
731C2×C4C4×C22⋊D1712yes—
732C2×C4C22×C4×D1711yescharacteristic
733C2×C4C2×#6325211yescharacteristic
734C2×C4#1058769111yescharacteristic
735C2×C4#1058769111yescharacteristic
736C2×C4#1058769111yescharacteristic
737C2×C4#1058769111yescharacteristic
738C8—342no—
739C8—342no—
740C8—681no—
741C8—681no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—816no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—682no—
765C22—682no—
766C22—682no—
767C22—1361no—
768C22—1361no—
769C22—1361no—
770C22—1361no—
771C22C2×C4×C22⋊D1711yescharacteristic
772C22#1176336811yescharacteristic
773C22#1176337611yescharacteristic
774C22#1176361211yescharacteristic
775C22#1176361211yescharacteristic
776C22#1176361211yescharacteristic
777C22#1176362011yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—682no—
786C4—1361no—
787C4—1361no—
788C4#1176328211yescharacteristic
789C4#1176328211yescharacteristic
790C4#1176339711yescharacteristic
791C4#1176339711yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—1362no—
796C2#1453144211yescharacteristic
797C2#1453761611yescharacteristic
798C2#1453763411yescharacteristic
799C2#1453963611yescharacteristic
800C2#1453964511yescharacteristic
801C2#1453983411yescharacteristic
802C2#1453987811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2309C2
socleC23×C17C22×D4
prime radicalC2×#11762943C2
cosocleC22×C4×C17C24
hypercenter#2309D17
hypocenterC17#22056
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #14531477C2semidirect
3. #14529659C2semidirect
4. #14529649C2semidirect
5. #14529484C2semidirect
6. #14529470C2semidirect
7. #14529408C2semidirect
8. #14529401C2semidirect
9. #14529135C2semidirect
10. #14529135C2semidirect
11. #14529106C2semidirect
12. #14528983C2semidirect
13. #14528715C2semidirect
14. #14528550C2semidirect
15. C17×#2309C2semidirect
19. C2×C4×D68C22semidirect
20. #11762943C4semidirect
21. C2×#10587478C22semidirect
22. C2×#10587479C22semidirect
29. C2×#10587480C22semidirect
30. C2×#10587480C22semidirect
33. C2×#10587474C22semidirect
34. C2×C4×#3622C22semidirect
35. #11762711C22semidirect
37. #11762707C22semidirect
42. C4×C4⋊Dic17C22semidirect
43. #11762571C22semidirect
44. #11762571C22semidirect
45. #11762571C22semidirect
46. #11762571C22semidirect
47. #11762564C22semidirect
48. #11762564C22semidirect
67. C22×D4×C17C2×C4semidirect
124. #10587503C2×C4semidirect
125. #10587503C2×C4semidirect
130. C22⋊#3622C2×C4semidirect
343. #2309D17semidirect
470. C22×D4C4×D17semidirect
538. C17#22056semidirect

Maximal subgroups

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

subgroupindex
C2×#117629432
#145314772
#145296592
#145296492
#145294842
#145294702
#145294082
#145294012
#145291352
#145291062
#145289832
#145287152
#145285502
C17×#23092
#2205617