Finite Group Databasebeta

← #16929133

Subgroups — #16929133

Order 4352.

592 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
1C2×#11763090C211yesmaximal, characteristic
2#14531731C211yesmaximal, characteristic
3#14529745C211yesmaximal, characteristic, complemented
4#14529707C211yesmaximal, characteristic, complemented
5C2×#11762538C211yesmaximal, characteristic
6#14526668C211yesmaximal, characteristic, complemented
7C17×#1279C211yesmaximal, characteristic, complemented
8C2×#10587555C2211yescharacteristic
9C2×C4×D68C2211yescharacteristic
10C2×#10587578—21no—
11#11763090—22no—
12#11763090C414yescomplemented
13C2×#10587489—21no—
14C2×C4⋊#3622C2211yescharacteristic
15C2×#10587481—21no—
16C2×#10587481—21no—
17C2×#10587492—21no—
18#11762711—21no—
19#11762701—22no—
20#11762679C2211yescharacteristic
21#11762666—21no—
22C4×C4⋊Dic17—21no—
23#11762572—22no—
24#11762538—22no—
25C2×C17×C4⋊C8C2211yescharacteristic
26C2×C4×C8×C17C2211yescharacteristic
27C4×C4⋊C4×C17C2211yescharacteristic
28C22×D68D411yescharacteristic
29C22×C4×D17—21no—
30C22×Dic34—21no—
31C22×C8×C17—21no—
32C22×C8×C17—21no—
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C4⋊C4×C17D411yescharacteristic
35C2×C42×C17—21no—
36C2×C42×C17C2311yescharacteristic
37C2×#63227—22no—
38C2×#63227—22no—
39C2×#63227—21no—
40C2×C4⋊Dic17—21no—
41C2×C4⋊Dic17—21no—
42C2×C4⋊Dic17—21no—
43C2×C4⋊Dic17—21no—
44C2×C4⋊Dic17D411yescharacteristic
45C2×C4⋊Dic17D412yes—
46C2×C4×Dic17—22no—
47C22×#3622—21no—
48#10587578—42no—
49#10587578—42no—
50C4×D68—21no—
51C4×D68—21no—
52C4×D68C2×C412yes—
53C4×D68D412yes—
54#10587555—21no—
55#10587555—21no—
56#10587555—21no—
57#10587555C2×C412yes—
58C17×C4⋊C8—21no—
59C17×C4⋊C8C2×C412yes—
60C4×C8×C17—21no—
61C4×C8×C17—21no—
62C17×#95—21no—
63#10587502—22no—
64#10587492—24no—
65#10587489—24no—
66#10587481—42no—
67#10587481—42no—
68C4⋊#3622—21no—
69C4⋊#3622—21no—
70C23×D17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17C2×D411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C22×Dic17—21no—
77C22×Dic17—22no—
78C22×Dic17—41no—
79C2×D68—21no—
80C2×D68—21no—
81C2×D68—21no—
82C2×D68—21no—
83C2×D68—21no—
84C2×D68C22⋊C412yes—
85C2×C4×D17—22no—
86C2×C4×D17—22no—
87C2×C4×D17—41no—
88C2×C4×D17—41no—
89C2×C4×D17—41no—
90C2×C4×D17—41no—
91C2×Dic34—22no—
92C2×Dic34—41no—
93C2×Dic34—41no—
94C2×Dic34—41no—
95C2×Dic34—41no—
96C2×Dic34—41no—
97C2×C8×C17—22no—
98C2×C8×C17—22no—
99C2×C8×C17—41no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C2×C8×C17—41no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17—21no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17D812yes—
107C42×C17—41no—
108C42×C17—41no—
109C42×C17C22×C411yescharacteristic
110C42×C17C2×D411yescharacteristic
111C42×C17#4111yescharacteristic
112C42×C17#4111yescharacteristic
113#63227—22no—
114#63227—22no—
115#63227—44no—
116#63227—82no—
117C4⋊Dic17—21no—
118C4⋊Dic17—22no—
119C4⋊Dic17—22no—
120C4⋊Dic17—41no—
121C4⋊Dic17—41no—
122C4⋊Dic17—41no—
123C4⋊Dic17—41no—
124C4⋊Dic17—41no—
125C4⋊Dic17—41no—
126C4⋊Dic17—42no—
127C4⋊Dic17C22⋊C412yes—
128C4×Dic17—44no—
129C2×#3622—41no—
130C2×#3622—41no—
131C2×#3622—41no—
132#8984—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—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—22no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17C2×C22⋊C411yescharacteristic
150C2×C4×C17C4×D411yescharacteristic
151C2×C4×C17C4×D411yescharacteristic
152C2×C4×C17#12111yescharacteristic
153C2×C4×C17#12111yescharacteristic
154C2×C4×C17#12311yescharacteristic
155C2×C4×C17C2×D811yescharacteristic
156C2×C4×C17#13511yescharacteristic
157C2×C4×C17#13511yescharacteristic
158C2×C4×C17#13511yescharacteristic
159C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C17#13711yescharacteristic
162C2×C4×C17#13711yescharacteristic
163C2×Dic17—22no—
164C2×Dic17—41no—
165C2×Dic17—41no—
166C2×Dic17—42no—
167C2×Dic17—42no—
168C2×Dic17—42no—
169C2×Dic17—42no—
170C2×Dic17—81no—
171C2×Dic17—81no—
172D68—22no—
173D68—22no—
174D68—41no—
175D68—41no—
176C4×D17—42no—
177C4×D17—42no—
178C4×D17—42no—
179C4×D17—42no—
180Dic34—42no—
181Dic34—42no—
182Dic34—81no—
183Dic34—81no—
184C8×C17—42no—
185C8×C17—42no—
186#3622—81no—
187C2×#474—171no—
188#2354—171no—
189#1990—171no—
190#1981—171no—
191C2×D4⋊C8—171no—
192#1296—171no—
193#1279D1711yescharacteristic, complemented
194C22×C17#38611yescharacteristic
195C22×C17#44711yescharacteristic
196C22×C17#44911yescharacteristic
197C22×C17#45211yescharacteristic
198C22×C17#45211yescharacteristic
199C22×C17#45511yescharacteristic
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—42no—
211C4×C17—81no—
212C4×C17#41611yescharacteristic
213C4×C17#41911yescharacteristic
214C4×C17C4×D811yescharacteristic
215C4×C17#44211yescharacteristic
216C4×C17#45911yescharacteristic
217C4×C17#46311yescharacteristic
218C4×C17#48511yescharacteristic
219C4×C17#48511yescharacteristic
220Dic17—42no—
221Dic17—82no—
222Dic17—82no—
223C2×C4⋊Q8—171no—
224C2×C4×D4—171no—
225C2×#117—341no—
226#474—174no—
227#474—342no—
228C2×#107—341no—
229C2×C4⋊C8—171no—
230C2×C4⋊C8C2×D1711yescharacteristic
231C2×#103—341no—
232C2×#103—341no—
233C2×#102—341no—
234C2×C4×C8C2×D1711yescharacteristic
235#390—341no—
236#388—342no—
237#384—171no—
238#380—341no—
239C4×C4⋊C4—341no—
240C4×C4⋊C4C2×D1711yescharacteristic
241#340—342no—
242D4⋊C8—342no—
243C2×C17#164111yescharacteristic
244C2×C17#164611yescharacteristic
245C2×C17#164711yescharacteristic
246C2×C17#165211yescharacteristic
247C2×C17#187311yescharacteristic
248C2×C17#187911yescharacteristic
249C2×C17#188211yescharacteristic
250D17—82no—
251C22×Q8—341no—
252C22×D4—171no—
253C23×C4—341no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—341no—
257C4⋊Q8—172no—
258C4⋊Q8—341no—
259C4⋊Q8—341no—
260C4⋊Q8—341no—
261C4×D4—172no—
262C4×D4—172no—
263C4×D4—341no—
264C4×D4—341no—
265#117—682no—
266#117—682no—
267C2×C4⋊C4—171no—
268C2×C4⋊C4—172no—
269C2×C4⋊C4—341no—
270C2×C4⋊C4—341no—
271C2×C4⋊C4—341no—
272C2×C4⋊C4—341no—
273C2×C4⋊C4D6811yescharacteristic
274C2×C4⋊C4D6811yescharacteristic
275C2×C22⋊C4—341no—
276C2×C22⋊C4—342no—
277C2×C22⋊C4—342no—
278C2×C42—21no—
279C2×C42—342no—
280C2×C42C22×D1711yescharacteristic
281#107—344no—
282C4⋊C8—21no—
283C4⋊C8—341no—
284C4⋊C8—341no—
285C4⋊C8C4×D1712yes—
286#103—682no—
287#103—682no—
288#102—344no—
289C4×C8—21no—
290C4×C8—21no—
291#95—21no—
292#95—342no—
293C17#898411yescharacteristic, complemented, Sylow
294C24—341no—
295C2×Q8—342no—
296C2×Q8—681no—
297C2×Q8—681no—
298C2×Q8—681no—
299C2×Q8—681no—
300C2×Q8—681no—
301C2×D4—172no—
302C2×D4—341no—
303C2×D4—341no—
304C2×D4—341no—
305C2×D4—341no—
306C2×D4—341no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—341no—
310C22×C4—342no—
311C22×C4—342no—
312C22×C4—342no—
313C22×C4—681no—
314C22×C4—681no—
315C22×C4—681no—
316C22×C4—681no—
317C22×C4—681no—
318C22×C4C2×D6811yescharacteristic
319C22×C4D4×D1711yescharacteristic
320C22×C4D4×D1711yescharacteristic
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—681no—
328C2×C8—681no—
329C2×C8—681no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—172no—
334C4⋊C4—341no—
335C4⋊C4—342no—
336C4⋊C4—342no—
337C4⋊C4—682no—
338C4⋊C4—681no—
339C4⋊C4—681no—
340C4⋊C4—681no—
341C4⋊C4—681no—
342C4⋊C4—681no—
343C4⋊C4—681no—
344C4⋊C4D13612yes—
345C22⋊C4—342no—
346C22⋊C4—342no—
347C22⋊C4—684no—
348C22⋊C4—1362no—
349C42—41no—
350C42—41no—
351C42—684no—
352C42C2×C4×D1711yescharacteristic
353C42#6325211yescharacteristic
354C42D4×D1711yescharacteristic
355C42#6325611yescharacteristic
356C23—342no—
357C23—681no—
358C23—681no—
359C23—681no—
360C23—681no—
361C23—681no—
362C23—681no—
363C23#1058756811yescharacteristic
364Q8—682no—
365Q8—682no—
366Q8—1361no—
367Q8—1361no—
368D4—342no—
369D4—342no—
370D4—681no—
371D4—681no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—342no—
381C2×C4—681no—
382C2×C4—681no—
383C2×C4—682no—
384C2×C4—682no—
385C2×C4—682no—
386C2×C4—682no—
387C2×C4—682no—
388C2×C4—682no—
389C2×C4—682no—
390C2×C4—682no—
391C2×C4—1361no—
392C2×C4—1361no—
393C2×C4C4×D6811yescharacteristic
394C2×C4C22⋊C4×D1711yescharacteristic
395C2×C4#1058757011yescharacteristic
396C2×C4#1058757911yescharacteristic
397C2×C4#1058758011yescharacteristic
398C2×C4#1058758111yescharacteristic
399C2×C4C2×D13611yescharacteristic
400C2×C4#1058759011yescharacteristic
401C2×C4#1058759411yescharacteristic
402C2×C4#1058759411yescharacteristic
403C2×C4#1058759811yescharacteristic
404C2×C4#1058760111yescharacteristic
405C2×C4#1058760211yescharacteristic
406C2×C4#1058760411yescharacteristic
407C8—42no—
408C8—42no—
409C8—1361no—
410C22—682no—
411C22—682no—
412C22—682no—
413C22—1361no—
414C22—1361no—
415C22—1361no—
416C22—1361no—
417C22#1176268711yescharacteristic
418C22#1176294511yescharacteristic
419C22#1176295611yescharacteristic
420C22#1176297211yescharacteristic
421C22#1176297411yescharacteristic
422C22#1176298811yescharacteristic
423C22#1176299311yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—81no—
428C4—682no—
429C4—1362no—
430C4—1362no—
431C4#1176280211yescharacteristic
432C4#1176281611yescharacteristic
433C4C4×D13611yescharacteristic
434C4#1176292211yescharacteristic
435C4#1176300511yescharacteristic
436C4#1176302511yescharacteristic
437C4#1176315211yescharacteristic
438C4#1176315311yescharacteristic
439C2—1362no—
440C2#1452797911yescharacteristic
441C2#1452801411yescharacteristic
442C2#1452802111yescharacteristic
443C2#1452805611yescharacteristic
444C2#1452909511yescharacteristic
445C2#1452913111yescharacteristic
446C2#1452915411yescharacteristic
subgroupG/H
centerC23#10587568
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1279C2
socleC23×C17#120
prime radicalC22×D68D4
cosocleC2×C42×C17C23
hypercenter#1279D17
hypocenterC17#8984
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #14529745C2semidirect
4. #14529707C2semidirect
6. #14526668C2semidirect
7. C17×#1279C2semidirect
12. #11763090C4semidirect
193. #1279D17semidirect
293. C17#8984semidirect

Maximal subgroups

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

subgroupindex
C2×#117630902
#145317312
#145297452
#145297072
C2×#117625382
#145266682
C17×#12792
#898417