Finite Group Databasebeta

← #16957553

Subgroups — #16957553

Order 4352.

1470 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762707C211yesmaximal, characteristic
2C2×#11762705C211yesmaximal, characteristic
3C2×#11762705C211yesmaximal, characteristic
4C2×C4⋊C4×Dic17C211yesmaximal, characteristic
5#14527039C212yesmaximal
6#14527035C212yesmaximal
7#14527019C212yesmaximal
8#14527013C211yesmaximal, characteristic
9#14527012C212yesmaximal
10C4×#10587502C211yesmaximal, characteristic
11C2×C17×#382C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×#63225C2212yes—
15C22×#63225C2212yes—
16C22×#63225C2212yes—
17C22×C4×Dic17C2211yescharacteristic
18C22×C4×Dic17C2212yes—
19C22×C4×Dic17C2211yescharacteristic
20#11762707C418yescomplemented
21#11762705—24no—
22#11762705—24no—
23C4⋊C4×Dic17—24no—
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2211yescharacteristic
26C2×#10587502C2211yescharacteristic
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C22×C4⋊C4×C17C2211yescharacteristic
35C22×C4⋊C4×C17C2211yescharacteristic
36C22×C42×C17C2211yescharacteristic
37C17×#382—24no—
38C2×C17×#95C2212yes—
39C2×C17×#95C2212yes—
40C23×C4×C17C2312yes—
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2312yes—
44C23×C4×C17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2311yescharacteristic
47C23×Dic17C2311yescharacteristic
48C23×Dic17C2311yescharacteristic
49C23×Dic17C2312yes—
50C23×Dic17C2311yescharacteristic
51C2×C4⋊C4×C17—22no—
52C2×C4⋊C4×C17—22no—
53C2×C4⋊C4×C17—22no—
54C2×C4⋊C4×C17—22no—
55C2×C4⋊C4×C17—22no—
56C2×C4⋊C4×C17D414yes—
57C2×C42×C17—22no—
58C2×C42×C17—22no—
59C2×C42×C17C2×C414yes—
60C2×C4⋊Dic17—22no—
61C2×C4⋊Dic17—22no—
62C2×C4⋊Dic17C2×C414yes—
63C2×C4⋊Dic17C2×C414yes—
64C2×C4⋊Dic17D414yes—
65C2×C4⋊Dic17Q814yes—
66C2×#63225—24no—
67C2×#63225—24no—
68C2×#63225—24no—
69C2×#63225—24no—
70C2×#63225—42no—
71C2×#63225—42no—
72C2×#63225—42no—
73C2×#63225—42no—
74C2×#63225C2×C418yes—
75C2×C4×Dic17—22no—
76C2×C4×Dic17—22no—
77C2×C4×Dic17—22no—
78C2×C4×Dic17—22no—
79C2×C4×Dic17—22no—
80C2×C4×Dic17—24no—
81C2×C4×Dic17—24no—
82C2×C4×Dic17—42no—
83C2×C4×Dic17Q814yes—
84C17×#95—24no—
85C17×#95—24no—
86#10587502—24no—
87#10587502—24no—
88#10587502—24no—
89#10587502—22no—
90#10587502—22no—
91#10587502—22no—
92#10587502—24no—
93#10587502—22no—
94#10587502—42no—
95#10587502C2×C418yes—
96C24×C17C2411yescharacteristic
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—22no—
105C22×C4×C17—22no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—22no—
109C22×C4×C17—22no—
110C22×C4×C17—21no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—21no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17C22×C412yes—
123C22×C4×C17C22×C412yes—
124C22×C4×C17C22×C412yes—
125C22×C4×C17C2×D412yes—
126C22×C4×C17C2×D414yes—
127C22×C4×C17C2×D412yes—
128C22×C4×C17C2×Q812yes—
129C22×C4×C17C2×Q812yes—
130C22×C4×C17#4112yes—
131C22×C4×C17#4112yes—
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—21no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—22no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—22no—
147C22×Dic17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—21no—
151C22×Dic17—21no—
152C22×Dic17—21no—
153C22×Dic17—21no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—21no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—21no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C22×Dic17C22×C414yes—
165C22×Dic17C22×C414yes—
166C22×Dic17C2×D414yes—
167C22×Dic17C2×Q812yes—
168C22×Dic17C2×Q814yes—
169C22×Dic17C2×Q812yes—
170C22×Dic17#4112yes—
171C22×Dic17#4112yes—
172C22×Dic17#4112yes—
173C22×Dic17#4112yes—
174C4⋊C4×C17—28no—
175C4⋊C4×C17—44no—
176C42×C17—28no—
177C4⋊Dic17—28no—
178C4⋊Dic17C4⋊C4116yescomplemented
179#63225—48no—
180#63225—48no—
181#63225—48no—
182C4×Dic17—28no—
183C4×Dic17—48no—
184C4×Dic17—44no—
185#14006—171nomaximal, Sylow
186C23×C17C23×C411yescharacteristic
187C23×C17C22×D411yescharacteristic
188C23×C17C22×D411yescharacteristic
189C23×C17C22×Q811yescharacteristic
190C23×C17C22×Q811yescharacteristic
191C23×C17C2×#4111yescharacteristic
192C23×C17C2×#4111yescharacteristic
193C23×C17C2×#4111yescharacteristic
194C23×C17C2×#4111yescharacteristic
195C23×C17C2×#4111yescharacteristic
196C23×C17C2×#4111yescharacteristic
197C23×C17H(5,𝔽2)11yescharacteristic
198C23×C17H(5,𝔽2)11yescharacteristic
199C23×C172−1+411yescharacteristic
200C23×C172−1+411yescharacteristic
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—22no—
206C2×C4×C17—22no—
207C2×C4×C17—24no—
208C2×C4×C17—24no—
209C2×C4×C17—24no—
210C2×C4×C17—42no—
211C2×C4×C17—42no—
212C2×C4×C17—41no—
213C2×C4×C17—42no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—42no—
217C2×C4×C17—41no—
218C2×C4×C17—41no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17—41no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17—42no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17C2×C4⋊C414yes—
230C2×C4×C17C4×D414yes—
231C2×C4×C17C4×Q814yes—
232C2×C4×C17#12114yes—
233C2×C4×C17C22⋊Q814yes—
234C2×C4×C17#12514yes—
235C2×C4×C17C4⋊Q814yes—
236C2×Dic17—24no—
237C2×Dic17—24no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—24no—
241C2×Dic17—24no—
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—22no—
245C2×Dic17—22no—
246C2×Dic17—24no—
247C2×Dic17—24no—
248C2×Dic17—24no—
249C2×Dic17—24no—
250C2×Dic17—24no—
251C2×Dic17—22no—
252C2×Dic17—22no—
253C2×Dic17—22no—
254C2×Dic17—22no—
255C2×Dic17—22no—
256C2×Dic17—22no—
257C2×Dic17—22no—
258C2×Dic17—22no—
259C2×Dic17—22no—
260C2×Dic17—41no—
261C2×Dic17—41no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265C2×Dic17—41no—
266C2×Dic17—42no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—42no—
271C2×Dic17—41no—
272C2×Dic17—42no—
273C2×Dic17—42no—
274C2×Dic17—41no—
275C2×Dic17—41no—
276C2×Dic17C2×C4⋊C418yes—
277C2×Dic17#12514yes—
278C2×#389—171no—
279C2×#389—171no—
280C2×#389—171no—
281C2×#382D1711yescharacteristic
282C2×C4×C4⋊C4—171no—
283#1442—172no—
284#1441—172no—
285#1436—172no—
286C4⋊#95—172no—
287C4⋊#95—171no—
288C4×#95—171no—
289C22×C17C22×C4⋊C411yescharacteristic
290C22×C17C2×C4×D411yescharacteristic
291C22×C17C2×C4×Q811yescharacteristic
292C22×C17C4×#4111yescharacteristic
293C22×C17C4×#4111yescharacteristic
294C22×C17#51811yescharacteristic
295C22×C17#51911yescharacteristic
296C22×C17C2×#12111yescharacteristic
297C22×C17C2×C22⋊Q811yescharacteristic
298C22×C17C2×#12511yescharacteristic
299C22×C17C2×#12511yescharacteristic
300C22×C17#52911yescharacteristic
301C22×C17#52911yescharacteristic
302C22×C17C2×C4⋊Q811yescharacteristic
303C22×C17#53311yescharacteristic
304C22×C17#54211yescharacteristic
305C22×C17#54211yescharacteristic
306C22×C17#54411yescharacteristic
307C22×C17#54411yescharacteristic
308C22×C17#54611yescharacteristic
309C22×C17#54611yescharacteristic
310C22×C17#54611yescharacteristic
311C22×C17#54711yescharacteristic
312C22×C17#54811yescharacteristic
313C22×C17#54811yescharacteristic
314C22×C17#54811yescharacteristic
315C22×C17#55011yescharacteristic
316C22×C17#55211yescharacteristic
317C22×C17#55311yescharacteristic
318C22×C17#55411yescharacteristic
319C22×C17#55411yescharacteristic
320C22×C17#55511yescharacteristic
321C22×C17#55611yescharacteristic
322C22×C17#55711yescharacteristic
323C22×C17#55711yescharacteristic
324C4×C17—42no—
325C4×C17—42no—
326C4×C17—44no—
327C4×C17—82no—
328C4×C17#38918yes—
329Dic17—28no—
330Dic17—24no—
331Dic17—44no—
332Dic17—42no—
333Dic17—42no—
334Dic17—42no—
335C22×C4⋊C4—171no—
336C22×C4⋊C4—171no—
337C22×C4⋊C4—172no—
338C22×C4⋊C4—172no—
339C22×C4⋊C4—172no—
340C22×C4⋊C4C2×D1711yescharacteristic
341C22×C4⋊C4C2×D1711yescharacteristic
342C22×C42—171no—
343C22×C42—171no—
344C22×C42—172no—
345C22×C42C2×D1711yescharacteristic
346#389—178no—
347#389—344no—
348#389—344no—
349#382—24no—
350C4×C4⋊C4—344no—
351C2×#95—172no—
352C2×#95—171no—
353C2×#95—171no—
354C2×#95—171no—
355C2×#95—171no—
356C2×#95—172no—
357C2×#95—172no—
358C2×#95—172no—
359C2×#95—172no—
360C2×#95—172no—
361C2×#95C2×D1712yes—
362C2×#95C2×D1712yes—
363C2×C17C2×#38911yescharacteristic
364C2×C17C4×#12511yescharacteristic
365C2×C17#233111yescharacteristic
366C2×C17#234911yescharacteristic
367C2×C17#235111yescharacteristic
368C2×C17#236211yescharacteristic
369C2×C17#236311yescharacteristic
370C2×C17#242611yescharacteristic
371C2×C17#242711yescharacteristic
372C2×C17#243911yescharacteristic
373C2×C17#244211yescharacteristic
374C2×C17#250811yescharacteristic
375C2×C17#250911yescharacteristic
376C2×C17#255011yescharacteristic
377C2×C17#255211yescharacteristic
378C23×C4—172no—
379C23×C4—171no—
380C23×C4—172no—
381C23×C4—171no—
382C23×C4—171no—
383C23×C4—171no—
384C23×C4C22×D1712yes—
385C23×C4C22×D1711yescharacteristic
386C23×C4C22×D1711yescharacteristic
387C23×C4C22×D1712yes—
388C23×C4C22×D1711yescharacteristic
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—174no—
395C2×C4⋊C4—174no—
396C2×C4⋊C4—174no—
397C2×C4⋊C4—174no—
398C2×C4⋊C4—178no—
399C2×C4⋊C4—342no—
400C2×C4⋊C4—342no—
401C2×C4⋊C4—344no—
402C2×C4⋊C4—344no—
403C2×C4⋊C4—344no—
404C2×C4⋊C4—344no—
405C2×C4⋊C4—682no—
406C2×C4⋊C4—682no—
407C2×C4⋊C4—682no—
408C2×C4⋊C4—682no—
409C2×C4⋊C4C22⋊D1714yes—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—174no—
413C2×C42—342no—
414C2×C42—342no—
415C2×C42—344no—
416C2×C42—344no—
417C2×C42—342no—
418C2×C42—342no—
419C2×C42—342no—
420C2×C42—682no—
421C2×C42C4×D1714yes—
422#95—24no—
423#95—24no—
424#95—178no—
425#95—342no—
426#95—342no—
427#95—342no—
428#95—342no—
429#95—344no—
430#95—344no—
431#95—344no—
432#95—344no—
433#95—682no—
434C17#1400611yescharacteristic, complemented, Sylow
435C24C23×D1711yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—174no—
462C22×C4—174no—
463C22×C4—172no—
464C22×C4—174no—
465C22×C4—172no—
466C22×C4—172no—
467C22×C4—174no—
468C22×C4—172no—
469C22×C4—172no—
470C22×C4—172no—
471C22×C4—341no—
472C22×C4—341no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—341no—
476C22×C4—342no—
477C22×C4—342no—
478C22×C4—341no—
479C22×C4—341no—
480C22×C4—342no—
481C22×C4—341no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4—341no—
486C22×C4—342no—
487C22×C4—341no—
488C22×C4—341no—
489C22×C4—341no—
490C22×C4—341no—
491C22×C4—342no—
492C22×C4—341no—
493C22×C4—342no—
494C22×C4—342no—
495C22×C4—341no—
496C22×C4—341no—
497C22×C4—341no—
498C22×C4—341no—
499C22×C4—341no—
500C22×C4—341no—
501C22×C4—342no—
502C22×C4—341no—
503C22×C4C2×C4×D1712yes—
504C22×C4C2×C4×D1712yes—
505C22×C4C2×C4×D1712yes—
506C22×C4#6325212yes—
507C22×C4D4×D1712yes—
508C22×C4#6325412yes—
509C22×C4Q8×D1712yes—
510C22×C4Q8×D1712yes—
511C22×C4C2×C22⋊D1714yes—
512C22×C4C2×C22⋊D1712yes—
513C4⋊C4—28no—
514C4⋊C4—44no—
515C4⋊C4—1716no—
516C4⋊C4—348no—
517C4⋊C4—688no—
518C4⋊C4—688no—
519C4⋊C4—688no—
520C42—28no—
521C42—348no—
522C42—688no—
523C42—684no—
524C23C22×C4×D1711yescharacteristic
525C23C2×#6325211yescharacteristic
526C23C2×D4×D1711yescharacteristic
527C23C2×#6325411yescharacteristic
528C23C2×Q8×D1711yescharacteristic
529C23C2×Q8×D1711yescharacteristic
530C23#41×D1711yescharacteristic
531C23#41×D1711yescharacteristic
532C23#41×D1711yescharacteristic
533C23#41×D1711yescharacteristic
534C23#1058769611yescharacteristic
535C23#1058769611yescharacteristic
536C23#1058769711yescharacteristic
537C23#1058769711yescharacteristic
538C23C22×C22⋊D1711yescharacteristic
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—178no—
568C2×C4—174no—
569C2×C4—342no—
570C2×C4—342no—
571C2×C4—342no—
572C2×C4—344no—
573C2×C4—344no—
574C2×C4—344no—
575C2×C4—344no—
576C2×C4—342no—
577C2×C4—342no—
578C2×C4—342no—
579C2×C4—344no—
580C2×C4—344no—
581C2×C4—342no—
582C2×C4—342no—
583C2×C4—344no—
584C2×C4—344no—
585C2×C4—344no—
586C2×C4—342no—
587C2×C4—342no—
588C2×C4—342no—
589C2×C4—342no—
590C2×C4—342no—
591C2×C4—342no—
592C2×C4—342no—
593C2×C4—681no—
594C2×C4—681no—
595C2×C4—681no—
596C2×C4—681no—
597C2×C4—682no—
598C2×C4—682no—
599C2×C4—681no—
600C2×C4—682no—
601C2×C4—681no—
602C2×C4—681no—
603C2×C4—681no—
604C2×C4—681no—
605C2×C4—681no—
606C2×C4—682no—
607C2×C4—681no—
608C2×C4—681no—
609C2×C4#1058757314yes—
610C2×C4#1058757514yes—
611C2×C4C4⋊C4×D1714yes—
612C2×C4#1058758214yes—
613C2×C4C4×C22⋊D1714yes—
614C2×C4#1058762514yes—
615C2×C4#1058763014yes—
616C22C2×C4⋊C4×D1711yescharacteristic
617C22C2×C4×C22⋊D1711yescharacteristic
618C22C2×#1058757311yescharacteristic
619C22#1176327711yescharacteristic
620C22#1176327711yescharacteristic
621C22#1176328311yescharacteristic
622C22#1176328611yescharacteristic
623C22C2×#1058762511yescharacteristic
624C22C2×#1058758211yescharacteristic
625C22#125×D1711yescharacteristic
626C22C2×#1058757511yescharacteristic
627C22#1176333811yescharacteristic
628C22#1176333811yescharacteristic
629C22C2×#1058763011yescharacteristic
630C22#1176336511yescharacteristic
631C22#1176342811yescharacteristic
632C22#1176342811yescharacteristic
633C22#1176343911yescharacteristic
634C22#1176343911yescharacteristic
635C22#1176344711yescharacteristic
636C22#1176345211yescharacteristic
637C22#1176345211yescharacteristic
638C22#1176345811yescharacteristic
639C22#1176346611yescharacteristic
640C22#1176346711yescharacteristic
641C22#1176346711yescharacteristic
642C22#1176347811yescharacteristic
643C22#1176349811yescharacteristic
644C22#1176350311yescharacteristic
645C22#1176351511yescharacteristic
646C22#1176351511yescharacteristic
647C22#1176352211yescharacteristic
648C22#1176352711yescharacteristic
649C22#1176353611yescharacteristic
650C22#1176353611yescharacteristic
651C4—44no—
652C4—42no—
653C4—42no—
654C4—82no—
655C4—348no—
656C4—344no—
657C4—682no—
658C4—682no—
659C4—682no—
660C4—684no—
661C4#1176270418yes—
662C2C2×#1176270411yescharacteristic
663C2#1453133911yescharacteristic
664C2#1453153011yescharacteristic
665C2#1453169211yescharacteristic
666C2#1453170111yescharacteristic
667C2#1453181111yescharacteristic
668C2#1453182211yescharacteristic
669C2#1453235311yescharacteristic
670C2#1453236411yescharacteristic
671C2#1453247811yescharacteristic
672C2#1453251111yescharacteristic
673C2#1453331811yescharacteristic
674C2#1453332911yescharacteristic
675C2#1453380311yescharacteristic
676C2#1453381611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#382C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×#382D17
hypocenterC17#14006
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
20. #11762707C4semidirect
178. C4⋊Dic17C4⋊C4semidirect
434. C17#14006semidirect

Maximal subgroups

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

subgroupindex
C2×#117627072
C2×#117627052
C2×C4⋊C4×Dic172
#145270392
#145270352
#145270192
#145270132
#145270122
C4×#105875022
C2×C17×#3822
#1400617