Finite Group Databasebeta

← #16958013

Subgroups — #16958013

Order 4352.

1442 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762707C211yesmaximal, characteristic
2C2×#11762696C212yesmaximal
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic
4C2×C4×C4⋊Dic17C211yesmaximal, characteristic
5#14527045C212yesmaximal
6#14527038C212yesmaximal
7#14527013C211yesmaximal, characteristic
8#14527013C211yesmaximal, characteristic
9#14527013C211yesmaximal, characteristic
10#14527010C212yesmaximal
11C17×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4⋊Dic17C2211yescharacteristic
16C22×#63225C2212yes—
17C22×C4×Dic17C2212yes—
18C22×C4×Dic17C2211yescharacteristic
19C22×C4×Dic17C2211yescharacteristic
20#11762707C418yescomplemented
21#11762696—28no—
22C4⋊C4×Dic17—24no—
23C4×C4⋊Dic17—24no—
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C22×C4⋊C4×C17C2211yescharacteristic
35C22×C4⋊C4×C17C2211yescharacteristic
36C22×C42×C17C2211yescharacteristic
37C2×C17×#95C2212yes—
38C2×C17×#95C2212yes—
39C23×C4×C17C2312yes—
40C23×C4×C17C2311yescharacteristic
41C23×C4×C17C2312yes—
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2311yescharacteristic
44C23×Dic17C2312yes—
45C23×Dic17C2312yes—
46C23×Dic17C2311yescharacteristic
47C23×Dic17C2311yescharacteristic
48C23×Dic17C2311yescharacteristic
49C23×Dic17C2311yescharacteristic
50C2×C4⋊C4×C17—22no—
51C2×C4⋊C4×C17—22no—
52C2×C4⋊C4×C17—22no—
53C2×C4⋊C4×C17—22no—
54C2×C4⋊C4×C17—22no—
55C2×C4⋊C4×C17Q814yes—
56C2×C42×C17—22no—
57C2×C42×C17—22no—
58C2×C42×C17C2×C414yes—
59C2×C4⋊Dic17—22no—
60C2×C4⋊Dic17—22no—
61C2×C4⋊Dic17—22no—
62C2×C4⋊Dic17—22no—
63C2×C4⋊Dic17—22no—
64C2×C4⋊Dic17—22no—
65C2×C4⋊Dic17—22no—
66C2×C4⋊Dic17—22no—
67C2×C4⋊Dic17—22no—
68C2×C4⋊Dic17C2×C414yes—
69C2×C4⋊Dic17C2×C414yes—
70C2×C4⋊Dic17D414yes—
71C2×#63225—24no—
72C2×#63225—24no—
73C2×#63225C2×C418yes—
74C2×C4×Dic17—22no—
75C2×C4×Dic17—22no—
76C2×C4×Dic17—22no—
77C2×C4×Dic17—22no—
78C2×C4×Dic17—22no—
79C2×C4×Dic17—24no—
80C2×C4×Dic17—24no—
81C2×C4×Dic17—24no—
82C2×C4×Dic17D414yes—
83C17×#95—24no—
84C17×#95—42no—
85#10587502—24no—
86#10587502—24no—
87#10587502—24no—
88#10587502—22no—
89#10587502—22no—
90#10587502—24no—
91#10587502—24no—
92#10587502—42no—
93#10587502—42no—
94#10587502C2×C418yes—
95C24×C17C2411yescharacteristic
96C22×C4×C17—21no—
97C22×C4×C17—21no—
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—21no—
101C22×C4×C17—22no—
102C22×C4×C17—22no—
103C22×C4×C17—22no—
104C22×C4×C17—21no—
105C22×C4×C17—22no—
106C22×C4×C17—22no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—21no—
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×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17C22×C412yes—
120C22×C4×C17C22×C412yes—
121C22×C4×C17C22×C412yes—
122C22×C4×C17C2×D412yes—
123C22×C4×C17C2×D412yes—
124C22×C4×C17C2×Q814yes—
125C22×C4×C17C2×Q812yes—
126C22×C4×C17#4112yes—
127C22×C4×C17#4112yes—
128C22×C4×C17#4112yes—
129C22×C4×C17#4112yes—
130C22×C4×C17#4112yes—
131C22×Dic17—21no—
132C22×Dic17—21no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—21no—
139C22×Dic17—21no—
140C22×Dic17—22no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—21no—
154C22×Dic17—21no—
155C22×Dic17—21no—
156C22×Dic17—21no—
157C22×Dic17—22no—
158C22×Dic17—21no—
159C22×Dic17—21no—
160C22×Dic17—22no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C22×Dic17—21no—
165C22×Dic17C22×C414yes—
166C22×Dic17C22×C414yes—
167C22×Dic17C2×D412yes—
168C22×Dic17C2×D412yes—
169C22×Dic17C2×D412yes—
170C22×Dic17C2×D412yes—
171C22×Dic17#4112yes—
172C22×Dic17#4112yes—
173C4⋊C4×C17—28no—
174C4⋊C4×C17—44no—
175C42×C17—28no—
176C4⋊Dic17—28no—
177C4⋊Dic17—28no—
178C4⋊Dic17—28no—
179C4⋊Dic17—28no—
180#63225—216no—
181C4×Dic17—28no—
182C4×Dic17—44no—
183C4×Dic17—48no—
184#14042—171nomaximal, Sylow
185C23×C17C23×C411yescharacteristic
186C23×C17C22×D411yescharacteristic
187C23×C17C22×D411yescharacteristic
188C23×C17C22×Q811yescharacteristic
189C23×C17C2×#4111yescharacteristic
190C23×C17C2×#4111yescharacteristic
191C23×C17C2×#4111yescharacteristic
192C23×C17C2×#4111yescharacteristic
193C23×C17C2×#4111yescharacteristic
194C23×C17C2×#4111yescharacteristic
195C23×C17C2×#4111yescharacteristic
196C23×C17H(5,𝔽2)11yescharacteristic
197C23×C172−1+411yescharacteristic
198C23×C172−1+411yescharacteristic
199C23×C172−1+411yescharacteristic
200C2×C4×C17—22no—
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—22no—
208C2×C4×C17—22no—
209C2×C4×C17—24no—
210C2×C4×C17—24no—
211C2×C4×C17—24no—
212C2×C4×C17—42no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—42no—
216C2×C4×C17—41no—
217C2×C4×C17—41no—
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×C17—42no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17#11714yes—
228C2×C4×C17C4×D414yes—
229C2×C4×C17C4×D414yes—
230C2×C4×C17C4×Q814yes—
231C2×C4×C17C22⋊Q814yes—
232C2×C4×C17#12314yes—
233C2×C4×C17#12514yes—
234C2×C4×C17#12614yes—
235C2×Dic17—22no—
236C2×Dic17—22no—
237C2×Dic17—22no—
238C2×Dic17—22no—
239C2×Dic17—22no—
240C2×Dic17—22no—
241C2×Dic17—24no—
242C2×Dic17—24no—
243C2×Dic17—24no—
244C2×Dic17—24no—
245C2×Dic17—24no—
246C2×Dic17—24no—
247C2×Dic17—22no—
248C2×Dic17—22no—
249C2×Dic17—22no—
250C2×Dic17—22no—
251C2×Dic17—22no—
252C2×Dic17—22no—
253C2×Dic17—22no—
254C2×Dic17—22no—
255C2×Dic17—22no—
256C2×Dic17—42no—
257C2×Dic17—41no—
258C2×Dic17—41no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—42no—
265C2×Dic17—42no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—42no—
271C2×Dic17—41no—
272C2×Dic17—41no—
273C2×Dic17—41no—
274C2×Dic17—41no—
275C2×Dic17—42no—
276C2×Dic17#12114yes—
277C2×#389—171no—
278C2×#387—172no—
279C2×C4×C4⋊C4—171no—
280C2×C4×C4⋊C4—171no—
281#1443—172no—
282#1441—172no—
283C4⋊#95—171no—
284C4⋊#95—171no—
285C4⋊#95—171no—
286C4⋊#95D1711yescharacteristic
287#1434—172no—
288C22×C17C2×#11711yescharacteristic
289C22×C17C2×C4×D411yescharacteristic
290C22×C17C2×C4×D411yescharacteristic
291C22×C17C2×C4×Q811yescharacteristic
292C22×C17C4×#4111yescharacteristic
293C22×C17#51911yescharacteristic
294C22×C17#52011yescharacteristic
295C22×C17C2×#12111yescharacteristic
296C22×C17C2×C22⋊Q811yescharacteristic
297C22×C17C2×#12311yescharacteristic
298C22×C17#52511yescharacteristic
299C22×C17C2×#12511yescharacteristic
300C22×C17C2×#12611yescharacteristic
301C22×C17#52911yescharacteristic
302C22×C17#53211yescharacteristic
303C22×C17#53611yescharacteristic
304C22×C17#53711yescharacteristic
305C22×C17#54111yescharacteristic
306C22×C17#54211yescharacteristic
307C22×C17#54711yescharacteristic
308C22×C17#54711yescharacteristic
309C22×C17D4×Q811yescharacteristic
310C22×C17#55011yescharacteristic
311C22×C17#55211yescharacteristic
312C22×C17#55211yescharacteristic
313C22×C17#55211yescharacteristic
314C22×C17#55311yescharacteristic
315C22×C17#55411yescharacteristic
316C22×C17#55511yescharacteristic
317C22×C17#55611yescharacteristic
318C22×C17#55611yescharacteristic
319C22×C17#55611yescharacteristic
320C22×C17#55611yescharacteristic
321C22×C17#55711yescharacteristic
322C22×C17#55711yescharacteristic
323C4×C17—24no—
324C4×C17—42no—
325C4×C17—44no—
326C4×C17—82no—
327C4×C17#38718yescomplemented
328Dic17—24no—
329Dic17—44no—
330Dic17—42no—
331Dic17—42no—
332Dic17—42no—
333Dic17—44no—
334C22×C4⋊C4—172no—
335C22×C4⋊C4—171no—
336C22×C4⋊C4—171no—
337C22×C4⋊C4—171no—
338C22×C4⋊C4—171no—
339C22×C4⋊C4C2×D1711yescharacteristic
340C22×C4⋊C4C2×D1711yescharacteristic
341C22×C42—171no—
342C22×C42—172no—
343C22×C42—171no—
344C22×C42C2×D1711yescharacteristic
345#389—178no—
346#387—348no—
347C4×C4⋊C4—344no—
348C4×C4⋊C4—344no—
349C2×#95—172no—
350C2×#95—171no—
351C2×#95—172no—
352C2×#95—172no—
353C2×#95—172no—
354C2×#95—172no—
355C2×#95—172no—
356C2×#95—171no—
357C2×#95—172no—
358C2×#95—172no—
359C2×#95C2×D1712yes—
360C2×#95C2×D1712yes—
361C2×C17C2×#38711yescharacteristic
362C2×C17C4×#12111yescharacteristic
363C2×C17#232311yescharacteristic
364C2×C17#235411yescharacteristic
365C2×C17#235611yescharacteristic
366C2×C17#236511yescharacteristic
367C2×C17#237011yescharacteristic
368C2×C17#248511yescharacteristic
369C2×C17#248611yescharacteristic
370C2×C17#250611yescharacteristic
371C2×C17#250811yescharacteristic
372C2×C17#251211yescharacteristic
373C2×C17#251411yescharacteristic
374C2×C17#253811yescharacteristic
375C2×C17#258111yescharacteristic
376C23×C4—171no—
377C23×C4—172no—
378C23×C4—172no—
379C23×C4—171no—
380C23×C4—171no—
381C23×C4—171no—
382C23×C4C22×D1712yes—
383C23×C4C22×D1712yes—
384C23×C4C22×D1711yescharacteristic
385C23×C4C22×D1711yescharacteristic
386C23×C4C22×D1711yescharacteristic
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—178no—
393C2×C4⋊C4—174no—
394C2×C4⋊C4—174no—
395C2×C4⋊C4—174no—
396C2×C4⋊C4—342no—
397C2×C4⋊C4—342no—
398C2×C4⋊C4—342no—
399C2×C4⋊C4—342no—
400C2×C4⋊C4—342no—
401C2×C4⋊C4—344no—
402C2×C4⋊C4—342no—
403C2×C4⋊C4—342no—
404C2×C4⋊C4—344no—
405C2×C4⋊C4—342no—
406C2×C4⋊C4—342no—
407C2×C4⋊C4Dic3414yes—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—174no—
411C2×C42—342no—
412C2×C42—342no—
413C2×C42—344no—
414C2×C42—344no—
415C2×C42—344no—
416C2×C42—342no—
417C2×C42—342no—
418C2×C42—342no—
419C2×C42C4×D1714yes—
420#95—24no—
421#95—42no—
422#95—178no—
423#95—344no—
424#95—342no—
425#95—342no—
426#95—344no—
427#95—344no—
428#95—344no—
429#95—344no—
430#95—682no—
431#95—682no—
432C17#1404211yescharacteristic, complemented, Sylow
433C24C23×D1711yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—172no—
458C22×C4—172no—
459C22×C4—172no—
460C22×C4—174no—
461C22×C4—174no—
462C22×C4—172no—
463C22×C4—172no—
464C22×C4—172no—
465C22×C4—341no—
466C22×C4—341no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—341no—
470C22×C4—341no—
471C22×C4—341no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—341no—
476C22×C4—341no—
477C22×C4—342no—
478C22×C4—342no—
479C22×C4—341no—
480C22×C4—342no—
481C22×C4—341no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—341no—
489C22×C4—341no—
490C22×C4—341no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—341no—
495C22×C4—341no—
496C22×C4—341no—
497C22×C4—341no—
498C22×C4—341no—
499C22×C4C2×Dic3414yes—
500C22×C4C2×Dic3412yes—
501C22×C4C2×C4×D1712yes—
502C22×C4C2×C4×D1712yes—
503C22×C4C2×C4×D1712yes—
504C22×C4#6325212yes—
505C22×C4D4×D1712yes—
506C22×C4D4×D1712yes—
507C22×C4#6325412yes—
508C22×C4#6325412yes—
509C22×C4#6325612yes—
510C22×C4#6325612yes—
511C4⋊C4—28no—
512C4⋊C4—44no—
513C4⋊C4—348no—
514C4⋊C4—348no—
515C4⋊C4—348no—
516C4⋊C4—348no—
517C4⋊C4—3416no—
518C42—28no—
519C42—348no—
520C42—688no—
521C42—684no—
522C23C22×Dic3411yescharacteristic
523C23C22×C4×D1711yescharacteristic
524C23C2×#6325211yescharacteristic
525C23C2×D4×D1711yescharacteristic
526C23C2×D4×D1711yescharacteristic
527C23C2×#6325411yescharacteristic
528C23C2×#6325411yescharacteristic
529C23#1058769111yescharacteristic
530C23C2×#6325611yescharacteristic
531C23C2×#6325611yescharacteristic
532C23#1058769411yescharacteristic
533C23#41×D1711yescharacteristic
534C23#41×D1711yescharacteristic
535C23#1058769711yescharacteristic
536C23#1058769711yescharacteristic
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—174no—
565C2×C4—342no—
566C2×C4—342no—
567C2×C4—342no—
568C2×C4—342no—
569C2×C4—342no—
570C2×C4—342no—
571C2×C4—342no—
572C2×C4—342no—
573C2×C4—342no—
574C2×C4—342no—
575C2×C4—344no—
576C2×C4—344no—
577C2×C4—344no—
578C2×C4—344no—
579C2×C4—344no—
580C2×C4—344no—
581C2×C4—342no—
582C2×C4—342no—
583C2×C4—342no—
584C2×C4—342no—
585C2×C4—342no—
586C2×C4—682no—
587C2×C4—682no—
588C2×C4—681no—
589C2×C4—681no—
590C2×C4—681no—
591C2×C4—681no—
592C2×C4—682no—
593C2×C4—681no—
594C2×C4—681no—
595C2×C4—681no—
596C2×C4—681no—
597C2×C4—682no—
598C2×C4—682no—
599C2×C4—681no—
600C2×C4—681no—
601C2×C4—682no—
602C2×C4—682no—
603C2×C4—682no—
604C2×C4—681no—
605C2×C4—681no—
606C2×C4C4×Dic3414yes—
607C2×C4#1058756414yes—
608C2×C4#1058756514yes—
609C2×C4#1058756714yes—
610C2×C4#1058757614yes—
611C2×C4#1058757814yes—
612C2×C4#1058757914yes—
613C2×C4#1058758014yes—
614C22C2×#1058757811yescharacteristic
615C22C2×#1058756711yescharacteristic
616C22C2×#1058757911yescharacteristic
617C22C2×C4×Dic3411yescharacteristic
618C22#1176327711yescharacteristic
619C22#1176328611yescharacteristic
620C22#1176329011yescharacteristic
621C22#121×D1711yescharacteristic
622C22C2×#1058756411yescharacteristic
623C22C2×#1058758011yescharacteristic
624C22#1176332211yescharacteristic
625C22C2×#1058757611yescharacteristic
626C22C2×#1058756511yescharacteristic
627C22#1176334511yescharacteristic
628C22#1176335411yescharacteristic
629C22#1176338211yescharacteristic
630C22#1176338811yescharacteristic
631C22#1176341911yescharacteristic
632C22#1176342611yescharacteristic
633C22#1176346211yescharacteristic
634C22#1176346411yescharacteristic
635C22D4×Dic3411yescharacteristic
636C22#1176347911yescharacteristic
637C22#1176349711yescharacteristic
638C22#1176349711yescharacteristic
639C22#1176350011yescharacteristic
640C22#1176350911yescharacteristic
641C22#1176351811yescharacteristic
642C22#1176352511yescharacteristic
643C22#1176352811yescharacteristic
644C22#1176352811yescharacteristic
645C22#1176353211yescharacteristic
646C22#1176353311yescharacteristic
647C22#1176353511yescharacteristic
648C22#1176353811yescharacteristic
649C4—24no—
650C4—44no—
651C4—42no—
652C4—82no—
653C4—344no—
654C4—684no—
655C4—684no—
656C4—682no—
657C4—682no—
658C4—682no—
659C4#1176269618yescomplemented
660C2C2×#1176269611yescharacteristic
661C2#1453129011yescharacteristic
662C2#1453146211yescharacteristic
663C2#1453173511yescharacteristic
664C2#1453175111yescharacteristic
665C2#1453184011yescharacteristic
666C2#1453188011yescharacteristic
667C2#1453308411yescharacteristic
668C2#1453309011yescharacteristic
669C2#1453330311yescharacteristic
670C2#1453332511yescharacteristic
671C2#1453336811yescharacteristic
672C2#1453339011yescharacteristic
673C2#1453370411yescharacteristic
674C2#1453414811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C4⋊#95C2
socle, prime radical, cosocleC24×C17C24
hypercenterC4⋊#95D17
hypocenterC17#14042
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
20. #11762707C4semidirect
327. C4×C17#387semidirect
432. C17#14042semidirect
659. C4#11762696semidirect

Maximal subgroups

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

subgroupindex
C2×#117627072
C2×#117626962
C2×C4⋊C4×Dic172
C2×C4×C4⋊Dic172
#145270452
#145270382
#145270132
#145270102
C17×C4⋊#952
#1404217