Finite Group Databasebeta

← #16956677

Subgroups — #16956677

Order 4352.

1426 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762708C211yesmaximal, characteristic
2C2×#11762674C212yesmaximal
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic
4#14527043C212yesmaximal
5#14527040C212yesmaximal
6#14527014C211yesmaximal, characteristic
7#14527013C211yesmaximal, characteristic
8#14527013C211yesmaximal, characteristic
9#14527010C212yesmaximal
10C4×#10587502C211yesmaximal, characteristic
11C2×C17×#389C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2212yes—
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4×Dic17C2211yescharacteristic
16C22×C4×Dic17C2211yescharacteristic
17C22×C4×Dic17C2212yes—
18#11762708—24no—
19#11762674—28no—
20C4⋊C4×Dic17C418yescomplemented
21C2×#10587502C2211yescharacteristic
22C2×#10587502C2211yescharacteristic
23C2×#10587502C2211yescharacteristic
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2211yescharacteristic
33C22×C4⋊C4×C17C2211yescharacteristic
34C22×C4⋊C4×C17C2212yes—
35C22×C4⋊C4×C17C2211yescharacteristic
36C22×C42×C17C2211yescharacteristic
37C17×#389—24no—
38C2×C17×#95C2212yes—
39C23×C4×C17C2312yes—
40C23×C4×C17C2311yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2312yes—
43C23×C4×C17C2311yescharacteristic
44C23×Dic17C2312yes—
45C23×Dic17C2312yes—
46C23×Dic17C2311yescharacteristic
47C23×Dic17C2311yescharacteristic
48C23×Dic17C2311yescharacteristic
49C23×Dic17C2311yescharacteristic
50C2×C4⋊C4×C17—24no—
51C2×C4⋊C4×C17—22no—
52C2×C4⋊C4×C17—24no—
53C2×C4⋊C4×C17—22no—
54C2×C4⋊C4×C17—22no—
55C2×C4⋊C4×C17—42no—
56C2×C4⋊C4×C17C2×C414yes—
57C2×C4⋊C4×C17D414yes—
58C2×C4⋊C4×C17Q814yes—
59C2×C42×C17—22no—
60C2×C42×C17—22no—
61C2×C42×C17—22no—
62C2×C4⋊Dic17—24no—
63C2×C4⋊Dic17—22no—
64C2×C4⋊Dic17—22no—
65C2×C4⋊Dic17—22no—
66C2×C4⋊Dic17—22no—
67C2×C4⋊Dic17—22no—
68C2×C4⋊Dic17—24no—
69C2×C4⋊Dic17—42no—
70C2×C4⋊Dic17C2×C414yes—
71C2×C4×Dic17—22no—
72C2×C4×Dic17—22no—
73C2×C4×Dic17—22no—
74C2×C4×Dic17—22no—
75C2×C4×Dic17—22no—
76C2×C4×Dic17—24no—
77C2×C4×Dic17—24no—
78C2×C4×Dic17C2×C414yes—
79C2×C4×Dic17C2×C418yes—
80C17×#95—24no—
81#10587502—24no—
82#10587502—24no—
83#10587502—22no—
84#10587502—24no—
85#10587502—24no—
86#10587502—24no—
87#10587502—22no—
88#10587502—24no—
89#10587502—22no—
90#10587502—42no—
91#10587502C2×C418yes—
92#10587502D414yes—
93C24×C17C2411yescharacteristic
94C22×C4×C17—22no—
95C22×C4×C17—22no—
96C22×C4×C17—22no—
97C22×C4×C17—22no—
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—21no—
101C22×C4×C17—21no—
102C22×C4×C17—21no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17C22×C414yes—
118C22×C4×C17C22×C412yes—
119C22×C4×C17C2×D412yes—
120C22×C4×C17C2×D414yes—
121C22×C4×C17C2×D412yes—
122C22×C4×C17C2×Q814yes—
123C22×C4×C17C2×Q812yes—
124C22×C4×C17#4112yes—
125C22×C4×C17#4112yes—
126C22×C4×C17#4112yes—
127C22×C4×C17#4112yes—
128C22×C4×C17#4112yes—
129C22×Dic17—21no—
130C22×Dic17—21no—
131C22×Dic17—21no—
132C22×Dic17—21no—
133C22×Dic17—22no—
134C22×Dic17—21no—
135C22×Dic17—21no—
136C22×Dic17—22no—
137C22×Dic17—21no—
138C22×Dic17—21no—
139C22×Dic17—22no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—21no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—21no—
152C22×Dic17—21no—
153C22×Dic17—21no—
154C22×Dic17—21no—
155C22×Dic17—21no—
156C22×Dic17—21no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—22no—
160C22×Dic17—22no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17C22×C412yes—
165C22×Dic17C22×C414yes—
166C22×Dic17C22×C412yes—
167C22×Dic17C2×D412yes—
168C22×Dic17C2×D412yes—
169C22×Dic17#4112yes—
170C22×Dic17#4112yes—
171C4⋊C4×C17—48no—
172C4⋊C4×C17—44no—
173C4⋊C4×C17C4⋊C4116yes—
174C42×C17—44no—
175C4⋊Dic17—28no—
176C4⋊Dic17—48no—
177C4⋊Dic17—44no—
178C4×Dic17—28no—
179C4×Dic17—216no—
180C4×Dic17—44no—
181#13918—171nomaximal, Sylow
182C23×C17C23×C411yescharacteristic
183C23×C17C22×D411yescharacteristic
184C23×C17C22×D411yescharacteristic
185C23×C17C22×Q811yescharacteristic
186C23×C17C2×#4111yescharacteristic
187C23×C17C2×#4111yescharacteristic
188C23×C17C2×#4111yescharacteristic
189C23×C17C2×#4111yescharacteristic
190C23×C17C2×#4111yescharacteristic
191C23×C17C2×#4111yescharacteristic
192C23×C17C2×#4111yescharacteristic
193C23×C17H(5,𝔽2)11yescharacteristic
194C23×C172−1+411yescharacteristic
195C23×C172−1+411yescharacteristic
196C23×C172−1+411yescharacteristic
197C2×C4×C17—24no—
198C2×C4×C17—24no—
199C2×C4×C17—24no—
200C2×C4×C17—24no—
201C2×C4×C17—24no—
202C2×C4×C17—24no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—22no—
206C2×C4×C17—22no—
207C2×C4×C17—22no—
208C2×C4×C17—22no—
209C2×C4×C17—41no—
210C2×C4×C17—41no—
211C2×C4×C17—41no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17—42no—
218C2×C4×C17—42no—
219C2×C4×C17—42no—
220C2×C4×C17—42no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17C2×C4⋊C418yes—
225C2×C4×C17C2×C4⋊C414yes—
226C2×C4×C17#11714yes—
227C2×C4×C17#11714yes—
228C2×C4×C17#12414yes—
229C2×C4×C17#12414yes—
230C2×C4×C17#12514yes—
231C2×C4×C17#12514yes—
232C2×Dic17—22no—
233C2×Dic17—22no—
234C2×Dic17—22no—
235C2×Dic17—22no—
236C2×Dic17—22no—
237C2×Dic17—22no—
238C2×Dic17—22no—
239C2×Dic17—24no—
240C2×Dic17—24no—
241C2×Dic17—22no—
242C2×Dic17—24no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—22no—
246C2×Dic17—22no—
247C2×Dic17—22no—
248C2×Dic17—22no—
249C2×Dic17—22no—
250C2×Dic17—41no—
251C2×Dic17—41no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—41no—
257C2×Dic17—41no—
258C2×Dic17—41no—
259C2×Dic17—41no—
260C2×Dic17—41no—
261C2×Dic17—41no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265C2×Dic17—41no—
266C2×Dic17—42no—
267C2×Dic17—42no—
268C2×Dic17—42no—
269C2×Dic17—42no—
270C2×Dic17—42no—
271C2×Dic17—42no—
272C2×Dic17—42no—
273C2×Dic17C4×D414yes—
274C2×#389—171no—
275C2×#389D1711yescharacteristic
276C2×#382—172no—
277C2×C4×C4⋊C4—171no—
278#1442—172no—
279#1442—172no—
280C4⋊#95—171no—
281C4⋊#95—171no—
282C4⋊#95—171no—
283#1434—172no—
284C4×#95—171no—
285C22×C17C22×C4⋊C411yescharacteristic
286C22×C17C2×#11711yescharacteristic
287C22×C17C2×#11711yescharacteristic
288C22×C17C2×C4×D411yescharacteristic
289C22×C17C4×#4111yescharacteristic
290C22×C17#51911yescharacteristic
291C22×C17#52011yescharacteristic
292C22×C17C2×#12411yescharacteristic
293C22×C17C2×#12411yescharacteristic
294C22×C17C2×#12511yescharacteristic
295C22×C17C2×#12511yescharacteristic
296C22×C17#52911yescharacteristic
297C22×C17#52911yescharacteristic
298C22×C17#53211yescharacteristic
299C22×C17#53211yescharacteristic
300C22×C17#54111yescharacteristic
301C22×C17#54111yescharacteristic
302C22×C17#54211yescharacteristic
303C22×C17#54211yescharacteristic
304C22×C17D4211yescharacteristic
305C22×C17#54711yescharacteristic
306C22×C17#54711yescharacteristic
307C22×C17#54711yescharacteristic
308C22×C17#54811yescharacteristic
309C22×C17#54811yescharacteristic
310C22×C17D4×Q811yescharacteristic
311C22×C17#55211yescharacteristic
312C22×C17#55211yescharacteristic
313C22×C17#55211yescharacteristic
314C22×C17#55211yescharacteristic
315C22×C17#55411yescharacteristic
316C22×C17#55511yescharacteristic
317C22×C17#55511yescharacteristic
318C22×C17#55711yescharacteristic
319C22×C17#55711yescharacteristic
320C4×C17—28no—
321C4×C17—42no—
322C4×C17—42no—
323C4×C17—82no—
324C4×C17#38218yescomplemented
325Dic17—24no—
326Dic17—42no—
327Dic17—42no—
328Dic17—42no—
329Dic17—44no—
330Dic17—82no—
331C22×C4⋊C4—171no—
332C22×C4⋊C4—171no—
333C22×C4⋊C4—172no—
334C22×C4⋊C4C2×D1711yescharacteristic
335C22×C4⋊C4C2×D1712yes—
336C22×C4⋊C4C2×D1711yescharacteristic
337C22×C42—171no—
338C22×C42—172no—
339C22×C42—171no—
340C22×C42C2×D1711yescharacteristic
341#389—24no—
342#389—344no—
343#382—348no—
344C4×C4⋊C4—178no—
345C2×#95—171no—
346C2×#95—172no—
347C2×#95—171no—
348C2×#95—171no—
349C2×#95—171no—
350C2×#95—172no—
351C2×#95—172no—
352C2×#95—172no—
353C2×#95—172no—
354C2×#95—172no—
355C2×#95—172no—
356C2×#95—172no—
357C2×#95C2×D1712yes—
358C2×C17C2×#38211yescharacteristic
359C2×C17#229311yescharacteristic
360C2×C17#232011yescharacteristic
361C2×C17#234411yescharacteristic
362C2×C17#234611yescharacteristic
363C2×C17D4×C4⋊C411yescharacteristic
364C2×C17#235111yescharacteristic
365C2×C17#248911yescharacteristic
366C2×C17#248911yescharacteristic
367C2×C17#249111yescharacteristic
368C2×C17#249111yescharacteristic
369C2×C17#250611yescharacteristic
370C2×C17#250611yescharacteristic
371C2×C17#250811yescharacteristic
372C2×C17#250811yescharacteristic
373C23×C4—171no—
374C23×C4—171no—
375C23×C4—172no—
376C23×C4—171no—
377C23×C4—171no—
378C23×C4—172no—
379C23×C4C22×D1712yes—
380C23×C4C22×D1711yescharacteristic
381C23×C4C22×D1711yescharacteristic
382C23×C4C22×D1712yes—
383C23×C4C22×D1711yescharacteristic
384C2×C4⋊C4—24no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—174no—
391C2×C4⋊C4—342no—
392C2×C4⋊C4—342no—
393C2×C4⋊C4—344no—
394C2×C4⋊C4—342no—
395C2×C4⋊C4—342no—
396C2×C4⋊C4—344no—
397C2×C4⋊C4—342no—
398C2×C4⋊C4—682no—
399C2×C4⋊C4Dic3414yes—
400C2×C4⋊C4C4×D1714yes—
401C2×C4⋊C4C22⋊D1714yes—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—178no—
406C2×C42—174no—
407C2×C42—344no—
408C2×C42—344no—
409C2×C42—342no—
410C2×C42—342no—
411C2×C42—342no—
412C2×C42—342no—
413C2×C42—342no—
414#95—24no—
415#95—178no—
416#95—174no—
417#95—342no—
418#95—342no—
419#95—344no—
420#95—344no—
421#95—344no—
422#95—344no—
423#95—342no—
424#95—344no—
425#95—344no—
426#95—682no—
427C17#1391811yescharacteristic, complemented, Sylow
428C24C23×D1711yescharacteristic
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—172no—
453C22×C4—172no—
454C22×C4—172no—
455C22×C4—172no—
456C22×C4—174no—
457C22×C4—172no—
458C22×C4—172no—
459C22×C4—341no—
460C22×C4—341no—
461C22×C4—341no—
462C22×C4—341no—
463C22×C4—342no—
464C22×C4—341no—
465C22×C4—342no—
466C22×C4—341no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—342no—
470C22×C4—341no—
471C22×C4—341no—
472C22×C4—341no—
473C22×C4—341no—
474C22×C4—341no—
475C22×C4—341no—
476C22×C4—342no—
477C22×C4—341no—
478C22×C4—341no—
479C22×C4—342no—
480C22×C4—341no—
481C22×C4—342no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4—341no—
486C22×C4—341no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—342no—
490C22×C4—342no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4C2×Dic3414yes—
495C22×C4C2×Dic3412yes—
496C22×C4C2×C4×D1714yes—
497C22×C4C2×C4×D1712yes—
498C22×C4D4×D1712yes—
499C22×C4#6325412yes—
500C22×C4#6325412yes—
501C22×C4#6325612yes—
502C22×C4#6325612yes—
503C22×C4#6325612yes—
504C22×C4C2×C22⋊D1714yes—
505C22×C4C2×C22⋊D1712yes—
506C4⋊C4—48no—
507C4⋊C4—44no—
508C4⋊C4—348no—
509C4⋊C4—688no—
510C4⋊C4—684no—
511C4⋊C4#63225116yes—
512C42—44no—
513C42—3416no—
514C42—348no—
515C42—684no—
516C23C22×Dic3411yescharacteristic
517C23C22×C4×D1711yescharacteristic
518C23C2×D4×D1711yescharacteristic
519C23C2×#6325411yescharacteristic
520C23C2×#6325411yescharacteristic
521C23#1058769111yescharacteristic
522C23C2×#6325611yescharacteristic
523C23C2×#6325611yescharacteristic
524C23C2×#6325611yescharacteristic
525C23#1058769411yescharacteristic
526C23#41×D1711yescharacteristic
527C23#41×D1711yescharacteristic
528C23#1058769711yescharacteristic
529C23#1058769711yescharacteristic
530C23C22×C22⋊D1711yescharacteristic
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—174no—
559C2×C4—342no—
560C2×C4—342no—
561C2×C4—342no—
562C2×C4—342no—
563C2×C4—342no—
564C2×C4—342no—
565C2×C4—342no—
566C2×C4—342no—
567C2×C4—342no—
568C2×C4—342no—
569C2×C4—344no—
570C2×C4—344no—
571C2×C4—342no—
572C2×C4—344no—
573C2×C4—342no—
574C2×C4—342no—
575C2×C4—342no—
576C2×C4—342no—
577C2×C4—681no—
578C2×C4—681no—
579C2×C4—681no—
580C2×C4—681no—
581C2×C4—681no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—681no—
585C2×C4—681no—
586C2×C4—681no—
587C2×C4—682no—
588C2×C4—682no—
589C2×C4—682no—
590C2×C4—682no—
591C2×C4—681no—
592C2×C4—681no—
593C2×C4—682no—
594C2×C4—682no—
595C2×C4—682no—
596C2×C4—682no—
597C2×C4—682no—
598C2×C4—682no—
599C2×C4—682no—
600C2×C4#1058757614yes—
601C2×C4#1058757614yes—
602C2×C4#1058757814yes—
603C2×C4#1058757814yes—
604C2×C4C2×#6322518yes—
605C2×C4C2×#6322514yes—
606C2×C4#1058762214yes—
607C2×C4#1058763314yes—
608C22C22×#6322511yescharacteristic
609C22C2×#1058757811yescharacteristic
610C22C2×#1058757811yescharacteristic
611C22C4×D4×D1711yescharacteristic
612C22C4×#6325611yescharacteristic
613C22#1176328511yescharacteristic
614C22#1176328811yescharacteristic
615C22C2×#1058762211yescharacteristic
616C22C2×#1058763311yescharacteristic
617C22C2×#1058757611yescharacteristic
618C22C2×#1058757611yescharacteristic
619C22#1176334411yescharacteristic
620C22#1176334511yescharacteristic
621C22#1176335411yescharacteristic
622C22#1176336011yescharacteristic
623C22#1176341911yescharacteristic
624C22#1176342211yescharacteristic
625C22#1176342611yescharacteristic
626C22#1176343311yescharacteristic
627C22D4×C22⋊D1711yescharacteristic
628C22#1176345811yescharacteristic
629C22#1176345911yescharacteristic
630C22#1176346211yescharacteristic
631C22#1176346611yescharacteristic
632C22#1176347011yescharacteristic
633C22D4×Dic3411yescharacteristic
634C22#1176349311yescharacteristic
635C22#1176349711yescharacteristic
636C22#1176349711yescharacteristic
637C22#1176350111yescharacteristic
638C22#1176351811yescharacteristic
639C22#1176352311yescharacteristic
640C22#1176352511yescharacteristic
641C22#1176353511yescharacteristic
642C22#1176353811yescharacteristic
643C4—28no—
644C4—42no—
645C4—42no—
646C4—82no—
647C4—344no—
648C4—682no—
649C4—682no—
650C4—682no—
651C4—684no—
652C4—1362no—
653C4#1176267418yescomplemented
654C2C2×#1176267411yescharacteristic
655C2#1453124211yescharacteristic
656C2#1453143111yescharacteristic
657C2#1453165211yescharacteristic
658C2#1453166811yescharacteristic
659C2D4×#6322511yescharacteristic
660C2#1453170211yescharacteristic
661C2#1453312711yescharacteristic
662C2#1453312811yescharacteristic
663C2#1453314911yescharacteristic
664C2#1453315011yescharacteristic
665C2#1453330211yescharacteristic
666C2#1453330311yescharacteristic
667C2#1453332411yescharacteristic
668C2#1453332511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#389C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×#389D17
hypocenterC17#13918
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
20. C4⋊C4×Dic17C4semidirect
324. C4×C17#382semidirect
427. C17#13918semidirect
653. C4#11762674semidirect

Maximal subgroups

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

subgroupindex
C2×#117627082
C2×#117626742
C2×C4⋊C4×Dic172
#145270432
#145270402
#145270142
#145270132
#145270102
C4×#105875022
C2×C17×#3892
#1391817