Finite Group Databasebeta

← #16937765

Subgroups — #16937765

Order 4352.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533738C211yesmaximal, characteristic
2#14529746C211yesmaximal, characteristic, complemented
3#14529548C211yesmaximal, characteristic, complemented
4#14528785C211yesmaximal, characteristic
5C2×#11762536C211yesmaximal, characteristic
6#14526623C211yesmaximal, characteristic, complemented
7C2×C17×#332C211yesmaximal, characteristic, complemented
8C2×#10587632—21no—
9C2×#10587632—21no—
10C2×C4×D68C2211yescharacteristic
11C2×#10587488—21no—
12C2×#10587492—21no—
13C2×C4×#3622C2211yescharacteristic
14#11762744—22no—
15#11762710—21no—
16#11762679C2211yescharacteristic
17#11762678—21no—
18C4×C4⋊Dic17C2211yescharacteristic
19#11762572—21no—
20#11762572—21no—
21#11762571—22no—
22#11762536—22no—
23C2×C17×C4⋊Q8C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C17×C4⋊C8C2211yescharacteristic
26C17×#332—22no—
27C22×Q8×C17—21no—
28C22×D68D411yescharacteristic
29C22×C4×D17—21no—
30C22×C8×C17—21no—
31C22×C8×C17—21no—
32C17×C4⋊Q8—21no—
33C17×C4⋊Q8—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—21no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17D412yes—
38C2×C42×C17C2311yescharacteristic
39#10587632—42no—
40#10587632—42no—
41#10587632—42no—
42#10587632—42no—
43C2×#63227—22no—
44C2×#63227—22no—
45C2×#63227—21no—
46C2×C4⋊Dic17—21no—
47C2×C4⋊Dic17—21no—
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17D411yescharacteristic
50C2×C4⋊Dic17D411yescharacteristic
51C2×C4⋊Dic17D411yescharacteristic
52C2×#63225—22no—
53C2×#63225—22no—
54C2×C4×Dic17—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×C4⋊C8—21no—
63C17×C4⋊C8D412yes—
64#10587502—21no—
65#10587492—42no—
66#10587488—42no—
67C4×#3622—21no—
68C4×#3622—21no—
69C23×D17—21no—
70C2×Q8×C17—41no—
71C2×Q8×C17—41no—
72C2×Q8×C17—41no—
73C2×Q8×C17—41no—
74C2×Q8×C17—41no—
75C2×Q8×C17—41no—
76C22×C4×C17—22no—
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×Dic17—21no—
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—41no—
84C2×D68—21no—
85C2×D68—21no—
86C2×D68—21no—
87C2×D68—21no—
88C2×D68—21no—
89C2×D68SD1612yes—
90C2×C4×D17—41no—
91C2×C4×D17—41no—
92C2×C4×D17—41no—
93C2×C4×D17—41no—
94C2×C4×D17—41no—
95C2×C4×D17—41no—
96C2×C8×C17—22no—
97C2×C8×C17—41no—
98C2×C8×C17—41no—
99C2×C8×C17—41no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C4⋊C4×C17—22no—
103C4⋊C4×C17—22no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C42×C17C2×D411yescharacteristic
107C42×C17#4111yescharacteristic
108C42×C17#4111yescharacteristic
109C42×C17#4111yescharacteristic
110#63227—44no—
111#63227—44no—
112#63227—41no—
113#63227—41no—
114C4⋊Dic17—21no—
115C4⋊Dic17—21no—
116C4⋊Dic17—21no—
117C4⋊Dic17—21no—
118C4⋊Dic17—42no—
119C4⋊Dic17—41no—
120C4⋊Dic17—41no—
121C4⋊Dic17—41no—
122C4⋊Dic17—41no—
123C4⋊Dic17D812yes—
124C4⋊Dic17SD1612yes—
125#63225—44no—
126#63225—44no—
127C4×Dic17—41no—
128C4×Dic17—41no—
129C2×#3622—22no—
130C2×#3622—41no—
131C2×#3622—41no—
132#10420—171nomaximal, Sylow
133C23×C17#12011yescharacteristic
134C22×D17—22no—
135C22×D17—41no—
136C22×D17—41no—
137C22×D17—41no—
138C22×D17—41no—
139C22×D17—41no—
140C22×D17—41no—
141Q8×C17—81no—
142Q8×C17—81no—
143Q8×C17—81no—
144Q8×C17—81no—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—42no—
148C2×C4×C17—42no—
149C2×C4×C17—42no—
150C2×C4×C17#12111yescharacteristic
151C2×C4×C17#12111yescharacteristic
152C2×C4×C17#12111yescharacteristic
153C2×C4×C17#12311yescharacteristic
154C2×C4×C17#12311yescharacteristic
155C2×C4×C17#12411yescharacteristic
156C2×C4×C17C2×D811yescharacteristic
157C2×C4×C17C2×SD1611yescharacteristic
158C2×C4×C17C2×SD1611yescharacteristic
159C2×C4×C17#13511yescharacteristic
160C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C17#13711yescharacteristic
163C2×C4×C17#13711yescharacteristic
164C2×Dic17—22no—
165C2×Dic17—22no—
166C2×Dic17—41no—
167C2×Dic17—41no—
168C2×Dic17—41no—
169C2×Dic17—41no—
170C2×Dic17—41no—
171C2×Dic17—41no—
172C2×Dic17—41no—
173C2×Dic17—81no—
174C2×Dic17—81no—
175C2×Dic17—81no—
176D68—22no—
177D68—22no—
178D68—41no—
179D68—41no—
180C4×D17—81no—
181C4×D17—81no—
182C4×D17—81no—
183C4×D17—81no—
184C8×C17—42no—
185C8×C17—81no—
186#3622—42no—
187#2542—171no—
188#1990—171no—
189#1948—171no—
190#1802—171no—
191C2×#332D1711yescharacteristic, complemented
192C2×D4⋊C8—171no—
193#1279—171no—
194C22×C17#39411yescharacteristic
195C22×C17#44711yescharacteristic
196C22×C17#44811yescharacteristic
197C22×C17#45011yescharacteristic
198C22×C17#45211yescharacteristic
199C22×C17#45411yescharacteristic
200C22×C17#45611yescharacteristic
201C2×D17—42no—
202C2×D17—42no—
203C2×D17—42no—
204C2×D17—81no—
205C2×D17—81no—
206C2×D17—81no—
207C2×D17—81no—
208C4×C17—21no—
209C4×C17—21no—
210C4×C17—82no—
211C4×C17#45911yescharacteristic
212C4×C17#46011yescharacteristic
213C4×C17#46511yescharacteristic
214C4×C17#47011yescharacteristic
215C4×C17#48311yescharacteristic
216C4×C17#48511yescharacteristic
217C4×C17#48611yescharacteristic
218C4×C17#49011yescharacteristic
219Dic17—42no—
220Dic17—42no—
221Dic17—81no—
222Dic17—161no—
223C2×C4⋊Q8C2×D1711yescharacteristic
224C2×C22⋊Q8—341no—
225C2×C22⋊Q8—341no—
226C2×C4×D4—171no—
227C2×#106—341no—
228C2×C4⋊C8C2×D1711yescharacteristic
229C2×C4⋊C8C2×D1711yescharacteristic
230C2×#102—341no—
231C2×C4×C8—171no—
232#399—342no—
233#390—341no—
234#384—171no—
235#384—341no—
236C4×C4⋊C4—171no—
237#340—341no—
238#340—341no—
239#340—342no—
240#332—22no—
241D4⋊C8—342no—
242C2×C17#162711yescharacteristic
243C2×C17#163511yescharacteristic
244C2×C17#164711yescharacteristic
245C2×C17#165111yescharacteristic
246C2×C17#203511yescharacteristic
247C2×C17#203811yescharacteristic
248C2×C17#204111yescharacteristic
249D17—82no—
250C22×Q8—21no—
251C22×D4—171no—
252C23×C4—341no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—341no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C22⋊Q8—682no—
261C22⋊Q8—682no—
262C22⋊Q8—682no—
263C22⋊Q8—682no—
264C4×D4—341no—
265C4×D4—341no—
266C4×D4—341no—
267C4×D4—341no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—171no—
270C2×C4⋊C4—171no—
271C2×C4⋊C4—171no—
272C2×C4⋊C4—342no—
273C2×C4⋊C4—342no—
274C2×C4⋊C4—341no—
275C2×C4⋊C4—341no—
276C2×C4⋊C4—341no—
277C2×C4⋊C4D6812yes—
278C2×C22⋊C4—342no—
279C2×C22⋊C4—342no—
280C2×C22⋊C4—341no—
281C2×C42—341no—
282C2×C42C22×D1711yescharacteristic
283#106—682no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8C22⋊D1712yes—
288#102—682no—
289C4×C8—341no—
290C4×C8—341no—
291#95—341no—
292C17#1042011yescharacteristic, complemented, Sylow
293C24—341no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×D4—172no—
301C2×D4—341no—
302C2×D4—341no—
303C2×D4—341no—
304C2×D4—341no—
305C2×D4—341no—
306C22×C4—22no—
307C22×C4—341no—
308C22×C4—341no—
309C22×C4—341no—
310C22×C4—681no—
311C22×C4—681no—
312C22×C4—681no—
313C22×C4—681no—
314C22×C4—681no—
315C22×C4—681no—
316C22×C4—681no—
317C22×C4C2×D6811yescharacteristic
318C22×C4D4×D1711yescharacteristic
319C22×C4D4×D1711yescharacteristic
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—342no—
327C2×C8—681no—
328C2×C8—681no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—172no—
334C4⋊C4—172no—
335C4⋊C4—341no—
336C4⋊C4—341no—
337C4⋊C4—341no—
338C4⋊C4—341no—
339C4⋊C4—682no—
340C4⋊C4—684no—
341C4⋊C4—684no—
342C4⋊C4—681no—
343C4⋊C4—681no—
344C4⋊C4—681no—
345C4⋊C4—681no—
346C22⋊C4—684no—
347C22⋊C4—684no—
348C22⋊C4—681no—
349C22⋊C4—681no—
350C42—681no—
351C42—681no—
352C42#6325211yescharacteristic
353C42#6325411yescharacteristic
354C42#6325411yescharacteristic
355C42C2×C22⋊D1711yescharacteristic
356C23—342no—
357C23—681no—
358C23—681no—
359C23—681no—
360C23—681no—
361C23—681no—
362C23—681no—
363C23#1058756811yescharacteristic
364Q8—81no—
365Q8—81no—
366Q8—81no—
367Q8—81no—
368D4—342no—
369D4—342no—
370D4—681no—
371D4—681no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—342no—
378C2×C4—342no—
379C2×C4—681no—
380C2×C4—681no—
381C2×C4—681no—
382C2×C4—681no—
383C2×C4—681no—
384C2×C4—681no—
385C2×C4—681no—
386C2×C4—1361no—
387C2×C4—1361no—
388C2×C4—1361no—
389C2×C4—1361no—
390C2×C4—1361no—
391C2×C4—1361no—
392C2×C4—1361no—
393C2×C4#1058756911yescharacteristic
394C2×C4#1058757111yescharacteristic
395C2×C4#1058757211yescharacteristic
396C2×C4D8×D1711yescharacteristic
397C2×C4#1058759711yescharacteristic
398C2×C4SD16×D1711yescharacteristic
399C2×C4SD16×D1711yescharacteristic
400C2×C4#1058760011yescharacteristic
401C2×C4#1058760211yescharacteristic
402C2×C4#1058760411yescharacteristic
403C2×C4#1058760411yescharacteristic
404C2×C4#1058761611yescharacteristic
405C2×C4#1058762411yescharacteristic
406C2×C4#1058762511yescharacteristic
407C8—42no—
408C8—81no—
409C8—682no—
410C22—682no—
411C22—682no—
412C22—682no—
413C22—1361no—
414C22—1361no—
415C22—1361no—
416C22—1361no—
417C22#1176272511yescharacteristic
418C22#1176294411yescharacteristic
419C22#1176294911yescharacteristic
420C22#1176296111yescharacteristic
421C22#1176297411yescharacteristic
422C22#1176298411yescharacteristic
423C22#1176299411yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—2721no—
428C4—682no—
429C4—682no—
430C4—1361no—
431C4#1176300211yescharacteristic
432C4#1176300711yescharacteristic
433C4#1176303511yescharacteristic
434C4#1176306411yescharacteristic
435C4#1176313811yescharacteristic
436C4#1176314811yescharacteristic
437C4#1176315411yescharacteristic
438C4#1176317211yescharacteristic
439C2—1362no—
440C2#1452788811yescharacteristic
441C2#1452793611yescharacteristic
442C2#1452802011yescharacteristic
443C2#1452804811yescharacteristic
444C2#1452997911yescharacteristic
445C2#1453000211yescharacteristic
446C2#1453001711yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#332C2
socleC23×C17#120
prime radicalC22×D68D4
hypercenterC2×#332D17
hypocenterC17#10420
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #14529746C2semidirect
3. #14529548C2semidirect
6. #14526623C2semidirect
7. C2×C17×#332C2semidirect
191. C2×#332D17semidirect
292. C17#10420semidirect

Maximal subgroups

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

subgroupindex
#145337382
#145297462
#145295482
#145287852
C2×#117625362
#145266232
C2×C17×#3322
#1042017