Finite Group Databasebeta

← #16937613

Subgroups — #16937613

Order 4352.

632 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534526C211yesmaximal, characteristic
2#14529101C211yesmaximal, characteristic
3#14528972C211yesmaximal, characteristic, complemented
4C2×#11762542C211yesmaximal, characteristic
5C2×#11762535C211yesmaximal, characteristic, complemented
6#14526663C211yesmaximal, characteristic, complemented
7C17×#1441C211yesmaximal, characteristic, complemented
8C2×#10587615—21no—
9C2×#10587616C2211yescharacteristic
10C2×#10587478—21no—
11C2×#10587480—21no—
12C2×C22⋊#3622C2211yescharacteristic
13C2×C22⋊#3622C2211yescharacteristic
14#11762739—21no—
15#11762731—21no—
16#11762731—21no—
17#11762726—21no—
18#11762688—21no—
19#11762669C2211yescharacteristic
20#11762571—21no—
21#11762571—21no—
22#11762542—22no—
23#11762535—22no—
24C22×C4⋊C4×C17C2211yescharacteristic
25C22×C4⋊C4×C17C2211yescharacteristic
26C2×C17×#95—21no—
27C2×C17×#95—21no—
28C2×C17×#95C2211yescharacteristic
29C23×C4×C17—21no—
30C23×C4×C17—21no—
31C23×C4×C17D411yescharacteristic
32C23×C4×C17D411yescharacteristic
33C23×C4×C17C2311yescharacteristic
34C22×C22⋊D17—21no—
35C22×D68D411yescharacteristic
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—21no—
40C2×C4⋊C4×C17—21no—
41C2×C4⋊C4×C17—21no—
42C2×C4⋊C4×C17—21no—
43C2×C4⋊C4×C17—21no—
44C2×C4⋊C4×C17—42no—
45C2×C22⋊Dic17—21no—
46#10587616—21no—
47#10587616—21no—
48#10587616—21no—
49#10587616—21no—
50#10587615—42no—
51#10587615—42no—
52C2×#63227—21no—
53C2×#63227—21no—
54C2×#63227—21no—
55C2×#63227—21no—
56C2×#63227—21no—
57C2×C4⋊Dic17D411yescharacteristic
58C2×C4⋊Dic17D411yescharacteristic
59C2×C4⋊Dic17D411yescharacteristic
60C2×#63225—21no—
61C2×#63225—21no—
62C22×#3622—21no—
63C22×#3622—21no—
64C17×#95—21no—
65C17×#95—21no—
66C17×#95—42no—
67C17×#95—42no—
68#10587502—21no—
69#10587502—21no—
70#10587502—21no—
71C22⋊#3622—21no—
72C22⋊#3622—21no—
73C22⋊#3622—21no—
74C22⋊#3622D412yes—
75#10587480—42no—
76#10587478—42no—
77C24×C17C2×D411yescharacteristic
78C23×D17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—21no—
81C22×C4×C17—21no—
82C22×C4×C17—21no—
83C22×C4×C17—21no—
84C22×C4×C17—21no—
85C22×C4×C17—22no—
86C22×C4×C17—22no—
87C22×C4×C17—21no—
88C22×C4×C17—21no—
89C22×C4×C17—21no—
90C22×C4×C17—41no—
91C22×C4×C17—41no—
92C22×C4×C17—41no—
93C22×C4×C17—41no—
94C22×C4×C17—41no—
95C22×C4×C17—41no—
96C22×C4×C17—41no—
97C22×C4×C17—41no—
98C22×C4×C17—41no—
99C22×C4×C17—41no—
100C22×C4×C17—41no—
101C22×C4×C17—41no—
102C22×C4×C17—41no—
103C22×C4×C17—41no—
104C22×C4×C17—41no—
105C22×C4×C17—41no—
106C22×C4×C17D812yes—
107C22×C4×C17C2×D411yescharacteristic
108C22×C4×C17C2×D411yescharacteristic
109C22×C4×C17C2×D411yescharacteristic
110C22×C4×C17#4111yescharacteristic
111C22×C4×C17#4111yescharacteristic
112C22×C4×C17#4111yescharacteristic
113C2×C22⋊D17—41no—
114C2×C22⋊D17—41no—
115C2×C22⋊D17—41no—
116C2×C22⋊D17—41no—
117C2×C22⋊D17—41no—
118C2×C22⋊D17—41no—
119C22×Dic17—21no—
120C22×Dic17—21no—
121C22×Dic17—21no—
122C2×D68—21no—
123C2×D68—21no—
124C2×D68—41no—
125C2×D68—41no—
126C4⋊C4×C17—22no—
127C4⋊C4×C17—22no—
128C4⋊C4×C17—41no—
129C4⋊C4×C17—41no—
130C4⋊C4×C17—41no—
131C4⋊C4×C17—41no—
132C4⋊C4×C17—41no—
133C4⋊C4×C17—41no—
134C22⋊Dic17—41no—
135C22⋊Dic17—41no—
136#63227—42no—
137#63227—42no—
138#63227—41no—
139#63227—41no—
140#63227—81no—
141#63227—81no—
142C4⋊Dic17—21no—
143C4⋊Dic17—21no—
144C4⋊Dic17—41no—
145C4⋊Dic17—41no—
146#63225—42no—
147#63225—42no—
148C2×#3622—22no—
149C2×#3622—41no—
150C2×#3622—41no—
151C2×#3622—41no—
152C2×#3622—41no—
153C2×#3622—41no—
154#10397—171nomaximal, Sylow
155C23×C17—21no—
156C23×C17—21no—
157C23×C17—21no—
158C23×C17—21no—
159C23×C17#12011yescharacteristic
160C23×C17#12111yescharacteristic
161C23×C17#12311yescharacteristic
162C23×C17C2×D811yescharacteristic
163C23×C17#13511yescharacteristic
164C23×C17AGL(1,ℤ/8)11yescharacteristic
165C23×C17#13711yescharacteristic
166C22×D17—41no—
167C22×D17—41no—
168C22×D17—41no—
169C22×D17—41no—
170C22×D17—41no—
171C22×D17—41no—
172C22×D17—41no—
173C2×C4×C17—21no—
174C2×C4×C17—21no—
175C2×C4×C17—21no—
176C2×C4×C17—21no—
177C2×C4×C17—22no—
178C2×C4×C17—22no—
179C2×C4×C17—22no—
180C2×C4×C17—41no—
181C2×C4×C17—41no—
182C2×C4×C17—41no—
183C2×C4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—41no—
186C2×C4×C17—41no—
187C2×C4×C17—41no—
188C2×C4×C17—42no—
189C2×C4×C17—42no—
190C2×C4×C17—42no—
191C2×C4×C17—42no—
192C2×C4×C17—42no—
193C2×C4×C17—42no—
194C2×C4×C17—41no—
195C2×C4×C17—42no—
196C2×C4×C17—41no—
197C2×C4×C17—41no—
198C2×C4×C17—81no—
199C2×C4×C17—81no—
200C2×C4×C17—81no—
201C2×C4×C17—81no—
202C2×C4×C17—81no—
203C2×C4×C17—81no—
204C2×C4×C17—81no—
205C2×C4×C17—81no—
206C2×C4×C17—81no—
207C2×C4×C17#12111yescharacteristic
208C2×C4×C17#12111yescharacteristic
209C2×C4×C17#12311yescharacteristic
210C2×C4×C17#12411yescharacteristic
211C22⋊D17—81no—
212C22⋊D17—81no—
213C22⋊D17—81no—
214C22⋊D17—81no—
215C2×Dic17—41no—
216C2×Dic17—41no—
217C2×Dic17—41no—
218C2×Dic17—41no—
219C2×Dic17—41no—
220C2×Dic17—41no—
221C2×Dic17—41no—
222C2×Dic17—41no—
223C2×Dic17—41no—
224D68—42no—
225D68—81no—
226#3622—42no—
227#3622—81no—
228#2618—171no—
229#1874—171no—
230#1852—171no—
231C2×#327—171no—
232C2×#324—171no—
233#1441D1711yescharacteristic, complemented
234#1294—171no—
235C22×C17—21no—
236C22×C17—21no—
237C22×C17—21no—
238C22×C17—21no—
239C22×C17—21no—
240C22×C17—21no—
241C22×C17—21no—
242C22×C17—21no—
243C22×C17—21no—
244C22×C17—21no—
245C22×C17—21no—
246C22×C17—21no—
247C22×C17#39411yescharacteristic
248C22×C17#44711yescharacteristic
249C22×C17#45211yescharacteristic
250C22×C17#45411yescharacteristic
251C22×C17#45611yescharacteristic
252C22×C17B(4,𝔽2)11yescharacteristic
253C22×C17#45811yescharacteristic
254C22×C17#46611yescharacteristic
255C22×C17#46811yescharacteristic
256C22×C17#48011yescharacteristic
257C22×C17#48211yescharacteristic
258C2×D17—81no—
259C2×D17—81no—
260C2×D17—81no—
261C2×D17—81no—
262C2×D17—81no—
263C2×D17—81no—
264C2×D17—81no—
265C4×C17—21no—
266C4×C17—21no—
267C4×C17—21no—
268C4×C17—21no—
269C4×C17—42no—
270C4×C17—82no—
271C4×C17—82no—
272C4×C17—81no—
273Dic17—81no—
274Dic17—81no—
275Dic17—81no—
276C2×#123—341no—
277C2×#121—171no—
278C22×C4⋊C4C2×D1711yescharacteristic
279C22×C4⋊C4C2×D1711yescharacteristic
280C2×#107—341no—
281C2×#102—341no—
282C2×C22⋊C8—171no—
283C2×C22⋊C8—171no—
284#398—341no—
285#396—341no—
286#396—341no—
287#394—341no—
288#386—341no—
289#380—171no—
290C2×#95—21no—
291C2×#95—21no—
292C2×#95C2×D1711yescharacteristic
293#340—341no—
294#340—341no—
295#327—342no—
296#324—342no—
297C2×C17—21no—
298C2×C17—21no—
299C2×C17—21no—
300C2×C17—21no—
301C2×C17#159811yescharacteristic
302C2×C17#160311yescharacteristic
303C2×C17#161011yescharacteristic
304C2×C17#161511yescharacteristic
305C2×C17#203311yescharacteristic
306C2×C17#203811yescharacteristic
307C2×C17#204411yescharacteristic
308D17—161no—
309C22×D4—171no—
310C22×D4—341no—
311C23×C4—21no—
312C23×C4—21no—
313C23×C4C22⋊D1711yescharacteristic
314C23×C4C22⋊D1711yescharacteristic
315C23×C4C22×D1711yescharacteristic
316C22×C8—341no—
317C22×C8—341no—
318#123—682no—
319#123—682no—
320#121—341no—
321#121—341no—
322#121—341no—
323#121—341no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—171no—
334C2×C4⋊C4—171no—
335C2×C4⋊C4—171no—
336C2×C4⋊C4—341no—
337C2×C4⋊C4—341no—
338C2×C22⋊C4—341no—
339C2×C22⋊C4—341no—
340C2×C22⋊C4—341no—
341C2×C22⋊C4—341no—
342C2×C22⋊C4—341no—
343C2×C22⋊C4—341no—
344#107—682no—
345#102—682no—
346C22⋊C8—172no—
347C22⋊C8—341no—
348C22⋊C8—341no—
349C22⋊C8—341no—
350#95—21no—
351#95—21no—
352#95—42no—
353#95—42no—
354#95—341no—
355#95—341no—
356#95—341no—
357C17#1039711yescharacteristic, complemented, Sylow
358C24—341no—
359C24C2×C22⋊D1711yescharacteristic
360C2×D4—341no—
361C2×D4—341no—
362C2×D4—681no—
363C2×D4—681no—
364C2×D4—681no—
365C2×D4—681no—
366C2×D4—681no—
367C2×D4—681no—
368C2×D4—681no—
369C2×D4—681no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—341no—
398C22×C4—341no—
399C22×C4—341no—
400C22×C4#6322812yes—
401C22×C4#6325211yescharacteristic
402C22×C4#6325211yescharacteristic
403C22×C4D4×D1711yescharacteristic
404C22×C4D4×D1711yescharacteristic
405C22×C4D4×D1711yescharacteristic
406C22×C4#6325411yescharacteristic
407C2×C8—342no—
408C2×C8—681no—
409C2×C8—681no—
410C2×C8—681no—
411C2×C8—681no—
412C2×C8—681no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—341no—
422C4⋊C4—341no—
423C4⋊C4—681no—
424C4⋊C4—681no—
425C4⋊C4—682no—
426C4⋊C4—682no—
427C22⋊C4—682no—
428C22⋊C4—682no—
429C22⋊C4—681no—
430C22⋊C4—681no—
431C22⋊C4—681no—
432C22⋊C4—681no—
433C22⋊C4—1361no—
434C22⋊C4—1361no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—681no—
440C23—681no—
441C23—681no—
442C23—681no—
443C23—681no—
444C23—681no—
445C23—681no—
446C23#1058761511yescharacteristic
447C23C2×#6322811yescharacteristic
448C23#1058762311yescharacteristic
449C23#1058762511yescharacteristic
450C23#1058762811yescharacteristic
451C23#1058763511yescharacteristic
452C23#1058763611yescharacteristic
453D4—682no—
454D4—1361no—
455D4—1361no—
456D4—1361no—
457D4—1361no—
458D4—1361no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—681no—
494C2×C4—681no—
495C2×C4—681no—
496C2×C4—681no—
497C2×C4—681no—
498C2×C4—681no—
499C2×C4—681no—
500C2×C4—681no—
501C2×C4—681no—
502C2×C4#1058756911yescharacteristic
503C2×C4#1058757011yescharacteristic
504C2×C4#1058757011yescharacteristic
505C2×C4#1058757111yescharacteristic
506C8—682no—
507C8—1361no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—1361no—
521C22—1361no—
522C22—1361no—
523C22—1361no—
524C22—1361no—
525C22—1361no—
526C22—1361no—
527C22#1176272411yescharacteristic
528C22#1176294211yescharacteristic
529C22#1176296911yescharacteristic
530C22#1176298111yescharacteristic
531C22#1176299111yescharacteristic
532C22#1176299511yescharacteristic
533C22#1176299811yescharacteristic
534C22#1176304311yescharacteristic
535C22#1176305711yescharacteristic
536C22#1176312211yescharacteristic
537C22#1176313311yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—82no—
544C4—82no—
545C4—81no—
546C4—1361no—
547C4—1361no—
548C4—1361no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—2721no—
554C2#1452771811yescharacteristic
555C2#1452774511yescharacteristic
556C2#1452778611yescharacteristic
557C2#1452781311yescharacteristic
558C2#1452996611yescharacteristic
559C2#1453000111yescharacteristic
560C2#1453003311yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1441C2
socleC23×C17#120
prime radicalC2×#10587616C22
hypercenter#1441D17
hypocenterC17#10397
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. #14528972C2semidirect
5. C2×#11762535C2semidirect
6. #14526663C2semidirect
7. C17×#1441C2semidirect
233. #1441D17semidirect
357. C17#10397semidirect

Maximal subgroups

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

subgroupindex
#145345262
#145291012
#145289722
C2×#117625422
C2×#117625352
#145266632
C17×#14412
#1039717