Finite Group Databasebeta

← #16929109

Subgroups — #16929109

Order 4352.

692 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763001C211yesmaximal, characteristic
2#14531731C211yesmaximal, characteristic, complemented
3#14529591C211yesmaximal, characteristic, complemented
4C2×#11762536C211yesmaximal, characteristic, complemented
5#14526668C211yesmaximal, characteristic, complemented
6#14526625C211yesmaximal, characteristic, complemented
7C17×#1982C211yesmaximal, characteristic, complemented
8C22×#63228—21no—
9C2×C4×D68C2211yescharacteristic
10C2×#10587578—21no—
11#11763001—22no—
12#11763001C414yescomplemented
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587503—21no—
15C2×#10587503—22no—
16C2×C4×#3622C2211yescharacteristic
17#11762711—21no—
18#11762701—22no—
19#11762679C2211yescharacteristic
20#11762666—21no—
21C4×C4⋊Dic17—21no—
22#11762536—22no—
23C2×C17×#127C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C17×#102—21no—
26C2×C17×#102—21no—
27C4×C4⋊C4×C17C2211yescharacteristic
28C22×D4×C17—21no—
29C22×D4×C17—21no—
30C22×D4×C17—21no—
31C22×D68D411yescharacteristic
32C22×C4×D17—21no—
33C22×C8×C17—21no—
34C17×#127—21no—
35C17×#127—21no—
36C17×#127—21no—
37C17×#127C2×C412yes—
38C2×C4⋊C4×C17D411yescharacteristic
39C2×C4⋊C4×C17D411yescharacteristic
40C2×C42×C17—21no—
41C2×C42×C17C2311yescharacteristic
42C2×#63228—24no—
43C2×#63228—42no—
44C2×#63228—42no—
45C2×#63227—22no—
46C2×#63227—22no—
47C2×#63227—21no—
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17D411yescharacteristic
51C2×C4⋊Dic17D412yes—
52C2×C4×Dic17—22no—
53C22×#3622—21no—
54C22×#3622—21no—
55#10587578—42no—
56#10587578—42no—
57C4×D68—21no—
58C4×D68—21no—
59C4×D68C2×C412yes—
60C4×D68D412yes—
61C17×C4⋊C8—21no—
62C17×C4⋊C8—21no—
63C17×#102—42no—
64C17×#102—42no—
65C17×#95—21no—
66#10587503—24no—
67#10587503—44no—
68#10587502—22no—
69C4⋊#3622—21no—
70C4⋊#3622C2×C412yes—
71C4×#3622—21no—
72C4×#3622—21no—
73C24×C17—41no—
74C23×D17—21no—
75C2×D4×C17—22no—
76C2×D4×C17—22no—
77C2×D4×C17—22no—
78C2×D4×C17—42no—
79C2×D4×C17—42no—
80C2×D4×C17—41no—
81C2×D4×C17—41no—
82C2×D4×C17—41no—
83C2×D4×C17—41no—
84C2×D4×C17—41no—
85C2×D4×C17—41no—
86C2×D4×C17—41no—
87C2×D4×C17—41no—
88C2×D4×C17—41no—
89C2×D4×C17—41no—
90C2×D4×C17—41no—
91C22×C4×C17—21no—
92C22×C4×C17—21no—
93C22×C4×C17C2×D411yescharacteristic
94C22×C4×C17C2×D411yescharacteristic
95C22×C4×C17C2×D411yescharacteristic
96C22×Dic17—21no—
97C22×Dic17—22no—
98C2×D68—21no—
99C2×D68—21no—
100C2×D68—21no—
101C2×D68—21no—
102C2×D68—21no—
103C2×D68C22⋊C412yes—
104C2×C4×D17—22no—
105C2×C4×D17—22no—
106C2×C4×D17—41no—
107C2×C4×D17—41no—
108C2×C4×D17—41no—
109C2×C4×D17—41no—
110C2×C8×C17—41no—
111C2×C8×C17—41no—
112C2×C8×C17—41no—
113C4⋊C4×C17—21no—
114C4⋊C4×C17—21no—
115C4⋊C4×C17—21no—
116C4⋊C4×C17D812yescomplemented
117C42×C17—41no—
118C42×C17—41no—
119C42×C17C22×C411yescharacteristic
120C42×C17C2×D411yescharacteristic
121C42×C17#4111yescharacteristic
122C42×C17#4111yescharacteristic
123#63228—48no—
124#63227—22no—
125#63227—22no—
126#63227—44no—
127#63227—82no—
128C4⋊Dic17—21no—
129C4⋊Dic17—41no—
130C4⋊Dic17—41no—
131C4⋊Dic17—41no—
132C4⋊Dic17—41no—
133C4⋊Dic17—42no—
134C4⋊Dic17C22⋊C412yes—
135C4×Dic17—44no—
136C2×#3622—22no—
137C2×#3622—22no—
138C2×#3622—41no—
139C2×#3622—41no—
140C2×#3622—41no—
141C2×#3622—41no—
142#8980—171nomaximal, Sylow
143C23×C17—42no—
144C23×C17—81no—
145C23×C17—81no—
146C23×C17—81no—
147C23×C17—81no—
148C23×C17—81no—
149C23×C17—81no—
150C23×C17#12011yescharacteristic
151C22×D17—22no—
152C22×D17—41no—
153C22×D17—41no—
154C22×D17—41no—
155C22×D17—41no—
156C22×D17—41no—
157C22×D17—41no—
158D4×C17—44no—
159D4×C17—42no—
160D4×C17—42no—
161D4×C17—42no—
162D4×C17—42no—
163D4×C17—82no—
164D4×C17—81no—
165D4×C17—81no—
166D4×C17—81no—
167D4×C17—81no—
168C2×C4×C17—21no—
169C2×C4×C17—21no—
170C2×C4×C17—22no—
171C2×C4×C17—41no—
172C2×C4×C17—41no—
173C2×C4×C17—41no—
174C2×C4×C17—41no—
175C2×C4×C17—41no—
176C2×C4×C17C2×C22⋊C411yescharacteristic
177C2×C4×C17C4×D411yescharacteristic
178C2×C4×C17C4×D411yescharacteristic
179C2×C4×C17#12111yescharacteristic
180C2×C4×C17#12111yescharacteristic
181C2×C4×C17#12311yescharacteristic
182C2×C4×C17C2×D811yescharacteristic
183C2×C4×C17#13511yescharacteristic
184C2×C4×C17#13511yescharacteristic
185C2×C4×C17#13511yescharacteristic
186C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
190C2×Dic17—22no—
191C2×Dic17—41no—
192C2×Dic17—41no—
193C2×Dic17—42no—
194C2×Dic17—42no—
195C2×Dic17—42no—
196D68—22no—
197D68—22no—
198D68—41no—
199D68—41no—
200C4×D17—42no—
201C4×D17—42no—
202C4×D17—42no—
203C4×D17—42no—
204C8×C17—81no—
205#3622—42no—
206#3622—42no—
207C2×#459—171no—
208#2354—171no—
209#1982D1711yescharacteristic, complemented
210#1957—171no—
211C2×D4⋊C8—171no—
212#1296—171no—
213#1279—171no—
214C22×C17—82no—
215C22×C17—82no—
216C22×C17—82no—
217C22×C17—161no—
218C22×C17—161no—
219C22×C17—161no—
220C22×C17—161no—
221C22×C17#38611yescharacteristic
222C22×C17#44711yescharacteristic
223C22×C17#44911yescharacteristic
224C22×C17#44911yescharacteristic
225C22×C17#44911yescharacteristic
226C22×C17#45311yescharacteristic
227C22×C17#45411yescharacteristic
228C2×D17—42no—
229C2×D17—42no—
230C2×D17—42no—
231C2×D17—81no—
232C2×D17—81no—
233C2×D17—81no—
234C2×D17—81no—
235C4×C17—21no—
236C4×C17—21no—
237C4×C17—42no—
238C4×C17—81no—
239C4×C17#41611yescharacteristic
240C4×C17#41811yescharacteristic
241C4×C17C4×D811yescharacteristic
242C4×C17#44211yescharacteristic
243C4×C17#45911yescharacteristic
244C4×C17#46311yescharacteristic
245C4×C17#48211yescharacteristic
246C4×C17#48211yescharacteristic
247Dic17—42no—
248Dic17—82no—
249C22×D8—341no—
250C2×#127C2×D1711yescharacteristic
251C2×C4×D4—171no—
252C2×#117—341no—
253#459—174no—
254#459—342no—
255C2×C4⋊C8—171no—
256C2×C4⋊C8C2×D1711yescharacteristic
257C2×#102—21no—
258C2×#102—21no—
259C2×#102—341no—
260C2×#102—342no—
261C2×C4×C8—171no—
262#390—341no—
263#388—342no—
264#384—171no—
265#380—341no—
266C4×C4⋊C4—341no—
267C4×C4⋊C4C2×D1711yescharacteristic
268D4⋊C8—342no—
269C2×C17—162no—
270C2×C17#162111yescharacteristic
271C2×C17#162411yescharacteristic
272C2×C17#162511yescharacteristic
273C2×C17#162811yescharacteristic
274C2×C17#187511yescharacteristic
275C2×C17#187911yescharacteristic
276C2×C17#188311yescharacteristic
277D17—82no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—171no—
282C23×C4—341no—
283C2×D8—344no—
284C2×D8—682no—
285C2×D8—682no—
286C22×C8—21no—
287C22×C8—341no—
288C22×C8—341no—
289#127—21no—
290#127—21no—
291#127—21no—
292#127C4×D1712yes—
293C4×D4—172no—
294C4×D4—172no—
295C4×D4—341no—
296C4×D4—341no—
297#117—682no—
298#117—682no—
299C2×C4⋊C4—171no—
300C2×C4⋊C4—172no—
301C2×C4⋊C4—341no—
302C2×C4⋊C4—341no—
303C2×C4⋊C4C22⋊D1711yescharacteristic
304C2×C4⋊C4C22⋊D1711yescharacteristic
305C2×C22⋊C4—341no—
306C2×C22⋊C4—342no—
307C2×C22⋊C4—342no—
308C2×C42—21no—
309C2×C42—342no—
310C2×C42C22×D1711yescharacteristic
311C4⋊C8—21no—
312C4⋊C8—21no—
313C4⋊C8—172no—
314C4⋊C8—341no—
315#102—42no—
316#102—42no—
317#102—344no—
318#102—684no—
319C4×C8—341no—
320C4×C8—341no—
321#95—21no—
322#95—342no—
323C17#898011yescharacteristic, complemented, Sylow
324C24—41no—
325C24—341no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—42no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—172no—
343C2×D4—341no—
344C2×D4—341no—
345C2×D4—341no—
346C2×D4—341no—
347C2×D4—341no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—341no—
351C22×C4—342no—
352C22×C4—342no—
353C22×C4—342no—
354C22×C4—681no—
355C22×C4—681no—
356C22×C4—681no—
357C22×C4—681no—
358C22×C4D4×D1711yescharacteristic
359C22×C4D4×D1711yescharacteristic
360C22×C4C2×C22⋊D1711yescharacteristic
361D8—688no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—342no—
366C2×C8—342no—
367C2×C8—681no—
368C2×C8—681no—
369C2×C8—681no—
370C2×C8—681no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—172no—
375C4⋊C4—341no—
376C4⋊C4—682no—
377C4⋊C4—681no—
378C4⋊C4—681no—
379C4⋊C4—681no—
380C4⋊C4—681no—
381C4⋊C4#6322812yescomplemented
382C22⋊C4—342no—
383C22⋊C4—342no—
384C22⋊C4—684no—
385C22⋊C4—1362no—
386C42—41no—
387C42—41no—
388C42—684no—
389C42C2×C4×D1711yescharacteristic
390C42#6325211yescharacteristic
391C42D4×D1711yescharacteristic
392C42#6325411yescharacteristic
393C23—42no—
394C23—81no—
395C23—81no—
396C23—81no—
397C23—81no—
398C23—81no—
399C23—81no—
400C23—342no—
401C23—681no—
402C23—681no—
403C23—681no—
404C23—681no—
405C23—681no—
406C23—681no—
407C23#1058762311yescharacteristic
408D4—44no—
409D4—42no—
410D4—42no—
411D4—42no—
412D4—42no—
413D4—82no—
414D4—81no—
415D4—81no—
416D4—81no—
417D4—81no—
418D4—342no—
419D4—342no—
420D4—681no—
421D4—681no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—342no—
431C2×C4—681no—
432C2×C4—681no—
433C2×C4—682no—
434C2×C4—682no—
435C2×C4—682no—
436C2×C4—682no—
437C2×C4—682no—
438C2×C4—682no—
439C2×C4—682no—
440C2×C4C22⋊C4×D1711yescharacteristic
441C2×C4#1058756711yescharacteristic
442C2×C4#1058756911yescharacteristic
443C2×C4#1058757011yescharacteristic
444C2×C4#1058759711yescharacteristic
445C2×C4#1058759811yescharacteristic
446C2×C4#1058760011yescharacteristic
447C2×C4#1058760211yescharacteristic
448C2×C4C4×C22⋊D1711yescharacteristic
449C2×C4C2×#6322811yescharacteristic
450C2×C4#1058761811yescharacteristic
451C2×C4#1058762411yescharacteristic
452C2×C4#1058763511yescharacteristic
453C2×C4#1058763611yescharacteristic
454C8—81no—
455C8—682no—
456C8—682no—
457C22—82no—
458C22—82no—
459C22—82no—
460C22—161no—
461C22—161no—
462C22—161no—
463C22—161no—
464C22—682no—
465C22—682no—
466C22—682no—
467C22—1361no—
468C22—1361no—
469C22—1361no—
470C22—1361no—
471C22#1176268511yescharacteristic
472C22#1176294211yescharacteristic
473C22#1176295111yescharacteristic
474C22#1176295211yescharacteristic
475C22#1176295311yescharacteristic
476C22#1176297511yescharacteristic
477C22#1176298011yescharacteristic
478C4—21no—
479C4—21no—
480C4—42no—
481C4—81no—
482C4—682no—
483C4—1362no—
484C4#1176280211yescharacteristic
485C4#1176281211yescharacteristic
486C4C4×#6322811yescharacteristic
487C4#1176291911yescharacteristic
488C4#1176300111yescharacteristic
489C4#1176302111yescharacteristic
490C4#1176313111yescharacteristic
491C4#1176313211yescharacteristic
492C2—162no—
493C2—1362no—
494C2#1452784711yescharacteristic
495C2#1452786611yescharacteristic
496C2#1452787111yescharacteristic
497C2#1452789311yescharacteristic
498C2#1452910311yescharacteristic
499C2#1452913511yescharacteristic
500C2#1452915711yescharacteristic
subgroupG/H
centerC23#10587623
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1982C2
socleC23×C17#120
prime radicalC2×#11763001C2
cosocleC2×C42×C17C23
hypercenter#1982D17
hypocenterC17#8980
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. #14531731C2semidirect
3. #14529591C2semidirect
4. C2×#11762536C2semidirect
5. #14526668C2semidirect
6. #14526625C2semidirect
7. C17×#1982C2semidirect
12. #11763001C4semidirect
116. C4⋊C4×C17D8semidirect
209. #1982D17semidirect
323. C17#8980semidirect
381. C4⋊C4#63228semidirect

Maximal subgroups

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

subgroupindex
C2×#117630012
#145317312
#145295912
C2×#117625362
#145266682
#145266252
C17×#19822
#898017