Finite Group Databasebeta

← #16937838

Subgroups — #16937838

Order 4352.

630 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533697C211yesmaximal, characteristic
2#14528940C211yesmaximal, characteristic, complemented
3#14528781C211yesmaximal, characteristic, complemented
4C2×D4⋊#3622C211yesmaximal, characteristic, complemented
5C2×#11762536C211yesmaximal, characteristic, complemented
6#14526668C211yesmaximal, characteristic, complemented
7C17×#1802C211yesmaximal, characteristic, complemented
8C2×#10587616—21no—
9C2×#10587624—21no—
10C2×C4×D68C2211yescharacteristic
11C2×#10587479—22no—
12C2×C4⋊#3622C2211yescharacteristic
13C2×#10587480—21no—
14C2×C4×#3622C2211yescharacteristic
15#11762725—22no—
16#11762679C2211yescharacteristic
17#11762669—21no—
18#11762666—21no—
19#11762571—21no—
20D4⋊#3622—22no—
21#11762536—22no—
22C2×C4×D4×C17C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×#102—21no—
25C17×#384C2211yescharacteristic
26C17×#340—21no—
27C22×D4×C17D411yescharacteristic
28C23×C4×C17—21no—
29C22×C22⋊D17—22no—
30C22×D68D411yescharacteristic
31C22×C4×D17—21no—
32C22×C8×C17—21no—
33C4×D4×C17—21no—
34C4×D4×C17—21no—
35C4×D4×C17—21no—
36C4×D4×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—21no—
40C2×C4⋊C4×C17D411yescharacteristic
41C2×C22⋊C4×C17—21no—
42C2×C42×C17C2311yescharacteristic
43C2×C22⋊Dic17—22no—
44#10587624—42no—
45#10587624—42no—
46#10587616—42no—
47#10587616—42no—
48C2×#63227—22no—
49C2×#63227—21no—
50C2×C4⋊Dic17—21no—
51C2×C4⋊Dic17—21no—
52C2×C4⋊Dic17D411yescharacteristic
53C2×C4⋊Dic17D412yes—
54C22×#3622—21no—
55C22×#3622—21no—
56C4×D68—21no—
57C4×D68—21no—
58C4×D68—21no—
59C4×D68—21no—
60C17×C4⋊C8—21no—
61C17×C4⋊C8—21no—
62C17×#102—42no—
63#10587502—22no—
64#10587480—42no—
65#10587479—44no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68C4×#3622—21no—
69C4×#3622D412yescomplemented
70C24×C17—21no—
71C23×D17—21no—
72C2×D4×C17—21no—
73C2×D4×C17—21no—
74C2×D4×C17—21no—
75C2×D4×C17—21no—
76C2×D4×C17—21no—
77C2×D4×C17SD1612yes—
78C22×C4×C17—21no—
79C22×C4×C17—41no—
80C22×C4×C17—41no—
81C22×C4×C17—41no—
82C22×C4×C17—41no—
83C22×C4×C17—41no—
84C22×C4×C17—41no—
85C22×C4×C17—41no—
86C22×C4×C17C2×D411yescharacteristic
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C2×C22⋊D17—44no—
90C2×C22⋊D17—44no—
91C2×C22⋊D17—82no—
92C22×Dic17—21no—
93C22×Dic17—22no—
94C2×D68—21no—
95C2×D68—21no—
96C2×D68—21no—
97C2×D68—21no—
98C2×D68—21no—
99C2×D68SD1612yes—
100C2×C4×D17—41no—
101C2×C4×D17—41no—
102C2×C4×D17—41no—
103C2×C4×D17—41no—
104C2×C4×D17—41no—
105C2×C4×D17—41no—
106C2×C8×C17—41no—
107C2×C8×C17—41no—
108C2×C8×C17—41no—
109C4⋊C4×C17—21no—
110C4⋊C4×C17—21no—
111C4⋊C4×C17—42no—
112C4⋊C4×C17—41no—
113C4⋊C4×C17—41no—
114C4⋊C4×C17—41no—
115C4⋊C4×C17—41no—
116C22⋊C4×C17—41no—
117C22⋊C4×C17—41no—
118C42×C17C2×D411yescharacteristic
119C42×C17#4111yescharacteristic
120C42×C17#4111yescharacteristic
121C42×C17#4111yescharacteristic
122C22⋊Dic17—44no—
123#63227—44no—
124#63227—41no—
125#63227—41no—
126C4⋊Dic17—21no—
127C4⋊Dic17—21no—
128C4⋊Dic17—41no—
129C4⋊Dic17—41no—
130C4⋊Dic17—41no—
131C4⋊Dic17—41no—
132C4⋊Dic17—42no—
133C2×#3622—22no—
134C2×#3622—22no—
135C2×#3622—22no—
136C2×#3622—41no—
137C2×#3622—41no—
138C2×#3622—41no—
139#10432—171nomaximal, Sylow
140C23×C17—22no—
141C23×C17—41no—
142C23×C17—41no—
143C23×C17—41no—
144C23×C17—41no—
145C23×C17—41no—
146C23×C17—41no—
147C23×C17#12011yescharacteristic
148C22×D17—22no—
149C22×D17—41no—
150C22×D17—41no—
151C22×D17—41no—
152C22×D17—41no—
153C22×D17—41no—
154C22×D17—41no—
155D4×C17—22no—
156D4×C17—22no—
157D4×C17—41no—
158D4×C17—41no—
159C2×C4×C17—21no—
160C2×C4×C17—21no—
161C2×C4×C17—41no—
162C2×C4×C17—41no—
163C2×C4×C17—41no—
164C2×C4×C17—81no—
165C2×C4×C17—81no—
166C2×C4×C17—81no—
167C2×C4×C17—81no—
168C2×C4×C17—81no—
169C2×C4×C17—81no—
170C2×C4×C17—81no—
171C2×C4×C17#12111yescharacteristic
172C2×C4×C17#12111yescharacteristic
173C2×C4×C17#12111yescharacteristic
174C2×C4×C17#12311yescharacteristic
175C2×C4×C17#12311yescharacteristic
176C2×C4×C17#12411yescharacteristic
177C2×C4×C17C2×SD1611yescharacteristic
178C2×C4×C17C2×SD1611yescharacteristic
179C2×C4×C17#13511yescharacteristic
180C2×C4×C17#13511yescharacteristic
181C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
185C22⋊D17—88no—
186C2×Dic17—41no—
187C2×Dic17—41no—
188C2×Dic17—41no—
189C2×Dic17—42no—
190C2×Dic17—42no—
191C2×Dic17—42no—
192D68—22no—
193D68—22no—
194D68—41no—
195D68—41no—
196C4×D17—81no—
197C4×D17—81no—
198C4×D17—81no—
199C4×D17—81no—
200C8×C17—81no—
201#3622—24no—
202#3622—81no—
203#2537—171no—
204#1844—171no—
205#1802—171no—
206#1802D1711yescharacteristic, complemented
207C2×D4⋊C8—171no—
208C2×D4⋊C8—171no—
209#1296—171no—
210C22×C17—42no—
211C22×C17—42no—
212C22×C17—42no—
213C22×C17—81no—
214C22×C17—81no—
215C22×C17—81no—
216C22×C17—81no—
217C22×C17#39411yescharacteristic
218C22×C17#44911yescharacteristic
219C22×C17#44911yescharacteristic
220C22×C17#45011yescharacteristic
221C22×C17#45011yescharacteristic
222C22×C17#45311yescharacteristic
223C22×C17#45611yescharacteristic
224C2×D17—42no—
225C2×D17—42no—
226C2×D17—42no—
227C2×D17—81no—
228C2×D17—81no—
229C2×D17—81no—
230C2×D17—81no—
231C4×C17—21no—
232C4×C17—21no—
233C4×C17—81no—
234C4×C17—161no—
235C4×C17#46511yescharacteristic
236C4×C17#46511yescharacteristic
237C4×C17#46911yescharacteristic
238C4×C17#46911yescharacteristic
239C4×C17#48111yescharacteristic
240C4×C17#48111yescharacteristic
241C4×C17#48211yescharacteristic
242C4×C17#48211yescharacteristic
243Dic17—82no—
244Dic17—81no—
245C2×#121—341no—
246C2×#121—341no—
247C2×C4×D4—171no—
248C2×C4×D4C2×D1711yescharacteristic
249C2×#106—342no—
250C2×C4⋊C8—171no—
251C2×C4⋊C8C2×D1711yescharacteristic
252C2×#102—21no—
253C2×#102—341no—
254C2×C4×C8—171no—
255#394—342no—
256#384—171no—
257#384C2×D1711yescharacteristic
258#380—341no—
259#380—341no—
260#340—21no—
261#340—341no—
262D4⋊C8—342no—
263D4⋊C8—342no—
264C2×C17—82no—
265C2×C17#162411yescharacteristic
266C2×C17#162911yescharacteristic
267C2×C17#165411yescharacteristic
268C2×C17#165411yescharacteristic
269C2×C17#203411yescharacteristic
270C2×C17#203411yescharacteristic
271C2×C17#203911yescharacteristic
272D17—82no—
273C22×D4—171no—
274C22×D4—342no—
275C22×D4C22⋊D1711yescharacteristic
276C23×C4—21no—
277C23×C4—341no—
278C22×C8—21no—
279C22×C8—341no—
280C22×C8—341no—
281#121—682no—
282#121—682no—
283#121—682no—
284#121—682no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—341no—
290C4×D4—341no—
291C4×D4—341no—
292C4×D4—341no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—171no—
297C2×C4⋊C4—172no—
298C2×C4⋊C4—341no—
299C2×C4⋊C4—341no—
300C2×C4⋊C4C22⋊D1711yescharacteristic
301C2×C22⋊C4—21no—
302C2×C22⋊C4—342no—
303C2×C22⋊C4—342no—
304C2×C22⋊C4—341no—
305C2×C42C22×D1711yescharacteristic
306#106—684no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—341no—
310C4⋊C8—341no—
311#102—42no—
312#102—682no—
313C4×C8—172no—
314C4×C8—341no—
315#95—342no—
316C17#1043211yescharacteristic, complemented, Sylow
317C24—21no—
318C24—341no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—172no—
325C2×D4—341no—
326C2×D4—341no—
327C2×D4—341no—
328C2×D4—341no—
329C2×D4—341no—
330C2×D4—684no—
331C2×D4—684no—
332C2×D4—1362no—
333C2×D4#6323012yes—
334C22×C4—21no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—341no—
343C22×C4—342no—
344C22×C4—681no—
345C22×C4—681no—
346C22×C4—681no—
347C22×C4—681no—
348C22×C4—681no—
349C22×C4—681no—
350C22×C4D4×D1711yescharacteristic
351C22×C4D4×D1711yescharacteristic
352C22×C4C2×C22⋊D1711yescharacteristic
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—342no—
357C2×C8—342no—
358C2×C8—342no—
359C2×C8—681no—
360C2×C8—681no—
361C2×C8—681no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—341no—
370C4⋊C4—341no—
371C4⋊C4—682no—
372C4⋊C4—681no—
373C4⋊C4—681no—
374C4⋊C4—681no—
375C4⋊C4—681no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—684no—
379C22⋊C4—684no—
380C22⋊C4—681no—
381C22⋊C4—681no—
382C42#6325211yescharacteristic
383C42#6325211yescharacteristic
384C42D4×D1711yescharacteristic
385C42#6325411yescharacteristic
386C23—22no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—342no—
394C23—681no—
395C23—681no—
396C23—681no—
397C23—681no—
398C23—681no—
399C23—681no—
400C23#1058762311yescharacteristic
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—342no—
406D4—342no—
407D4—681no—
408D4—681no—
409D4—1368no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—681no—
423C2×C4—682no—
424C2×C4—681no—
425C2×C4—682no—
426C2×C4—682no—
427C2×C4—681no—
428C2×C4—1361no—
429C2×C4—1361no—
430C2×C4—1361no—
431C2×C4—1361no—
432C2×C4#1058756911yescharacteristic
433C2×C4#1058757011yescharacteristic
434C2×C4#1058757011yescharacteristic
435C2×C4#1058757111yescharacteristic
436C2×C4#1058759711yescharacteristic
437C2×C4#1058759811yescharacteristic
438C2×C4SD16×D1711yescharacteristic
439C2×C4#1058760011yescharacteristic
440C2×C4#1058761511yescharacteristic
441C2×C4#1058761811yescharacteristic
442C2×C4#1058762511yescharacteristic
443C2×C4C2×#6323011yescharacteristic
444C2×C4#1058763511yescharacteristic
445C2×C4#1058763611yescharacteristic
446C8—81no—
447C8—344no—
448C8—1361no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—682no—
457C22—682no—
458C22—682no—
459C22—1361no—
460C22—1361no—
461C22—1361no—
462C22—1361no—
463C22#1176272411yescharacteristic
464C22#1176295111yescharacteristic
465C22#1176295211yescharacteristic
466C22#1176295811yescharacteristic
467C22#1176295911yescharacteristic
468C22#1176297511yescharacteristic
469C22#1176299011yescharacteristic
470C4—21no—
471C4—21no—
472C4—81no—
473C4—161no—
474C4—1362no—
475C4—1361no—
476C4#1176303711yescharacteristic
477C4#1176304011yescharacteristic
478C4#1176306011yescharacteristic
479C4#1176306111yescharacteristic
480C4#1176312611yescharacteristic
481C4#1176312711yescharacteristic
482C4#1176313111yescharacteristic
483C4#1176313311yescharacteristic
484C2—82no—
485C2—1362no—
486C2#1452786611yescharacteristic
487C2#1452789911yescharacteristic
488C2#1452806611yescharacteristic
489C2#1452806711yescharacteristic
490C2#1452997111yescharacteristic
491C2#1452997311yescharacteristic
492C2#1453000611yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1802C2
socleC23×C17#120
prime radical#14533697C2
hypercenter#1802D17
hypocenterC17#10432
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #14528940C2semidirect
3. #14528781C2semidirect
4. C2×D4⋊#3622C2semidirect
5. C2×#11762536C2semidirect
6. #14526668C2semidirect
7. C17×#1802C2semidirect
69. C4×#3622D4semidirect
206. #1802D17semidirect
316. C17#10432semidirect

Maximal subgroups

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

subgroupindex
#145336972
#145289402
#145287812
C2×D4⋊#36222
C2×#117625362
#145266682
C17×#18022
#1043217