Finite Group Databasebeta

← #16937369

Subgroups — #16937369

Order 4352.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533815C211yesmaximal, characteristic, complemented
2#14529711C211yesmaximal, characteristic
3#14529710C211yesmaximal, characteristic
4#14529590C211yesmaximal, characteristic
5#14526668C211yesmaximal, characteristic, complemented
6#14526624C211yesmaximal, characteristic, complemented
7C17×#1279C211yesmaximal, characteristic, complemented
8C2×#10587560C2211yescharacteristic
9C2×#10587576—21no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×#10587492—22no—
12C2×#10587492—21no—
13C2×#10587492—21no—
14C2×#10587480—21no—
15C2×#10587480—21no—
16#11762741—22no—
17#11762708—21no—
18#11762707—21no—
19#11762679—21no—
20#11762679C2211yescharacteristic
21C4×C4⋊Dic17C2211yescharacteristic
22C2×C17×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C17C2211yescharacteristic
24C4×C4⋊C4×C17C2211yescharacteristic
25C22×D68—21no—
26C22×D68—21no—
27C22×D68—21no—
28C22×C8×C17—21no—
29C22×C8×C17—21no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C42×C17—21no—
33C2×C42×C17C2311yescharacteristic
34C2×C4⋊Dic17—22no—
35C2×C4⋊Dic17—22no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17D411yescharacteristic
39C2×C4⋊Dic17D411yescharacteristic
40C2×C4⋊Dic17D412yes—
41C2×#63225—22no—
42C2×C4×Dic17—21no—
43C22×#3622—21no—
44#10587576—42no—
45#10587576—42no—
46#10587560—21no—
47#10587560—21no—
48#10587560—21no—
49#10587560Q812yes—
50C17×C4⋊C8—21no—
51C17×C4⋊C8—21no—
52C4×C8×C17—21no—
53C4×C8×C17—21no—
54C17×#95—21no—
55#10587502—22no—
56#10587502—21no—
57#10587492—44no—
58#10587492—42no—
59#10587492—42no—
60#10587480—42no—
61#10587480—42no—
62C4⋊#3622—21no—
63C4⋊#3622—21no—
64C23×D17—41no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17C2×D411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C22×Dic17—21no—
71C22×Dic17—21no—
72C22×Dic17—22no—
73C2×D68—22no—
74C2×D68—22no—
75C2×D68—22no—
76C2×D68—42no—
77C2×D68—42no—
78C2×D68—41no—
79C2×D68—41no—
80C2×D68—41no—
81C2×D68—41no—
82C2×D68—41no—
83C2×D68—41no—
84C2×D68—41no—
85C2×D68—41no—
86C2×D68—41no—
87C2×D68—41no—
88C2×D68—41no—
89C2×C8×C17—22no—
90C2×C8×C17—41no—
91C2×C8×C17—41no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17—21no—
97C4⋊C4×C17D812yes—
98C4⋊C4×C17SD1612yes—
99C42×C17—41no—
100C42×C17—41no—
101C42×C17C2×Q811yescharacteristic
102C42×C17#4111yescharacteristic
103C42×C17#4111yescharacteristic
104C42×C17#4111yescharacteristic
105C4⋊Dic17—21no—
106C4⋊Dic17—21no—
107C4⋊Dic17—21no—
108C4⋊Dic17—21no—
109C4⋊Dic17—44no—
110C4⋊Dic17—41no—
111C4⋊Dic17—41no—
112C4⋊Dic17—41no—
113C4⋊Dic17—41no—
114C4⋊Dic17—42no—
115C4⋊Dic17—82no—
116#63225—44no—
117C4×Dic17—41no—
118C4×Dic17—41no—
119C2×#3622—41no—
120C2×#3622—41no—
121C2×#3622—41no—
122#10354—171nomaximal, Sylow
123C23×C17#12011yescharacteristic
124C22×D17—42no—
125C22×D17—81no—
126C22×D17—81no—
127C22×D17—81no—
128C22×D17—81no—
129C22×D17—81no—
130C22×D17—81no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—22no—
134C2×C4×C17—22no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17C22⋊Q811yescharacteristic
140C2×C4×C17C22⋊Q811yescharacteristic
141C2×C4×C17C22⋊Q811yescharacteristic
142C2×C4×C17#12411yescharacteristic
143C2×C4×C17#12411yescharacteristic
144C2×C4×C17#12411yescharacteristic
145C2×C4×C17C2×D811yescharacteristic
146C2×C4×C17C2×SD1611yescharacteristic
147C2×C4×C17#13511yescharacteristic
148C2×C4×C17#13511yescharacteristic
149C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C17#13711yescharacteristic
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—42no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—42no—
159C2×Dic17—42no—
160C2×Dic17—41no—
161C2×Dic17—41no—
162D68—44no—
163D68—42no—
164D68—42no—
165D68—42no—
166D68—42no—
167D68—82no—
168D68—81no—
169D68—81no—
170D68—81no—
171D68—81no—
172C8×C17—42no—
173C8×C17—81no—
174#3622—81no—
175#2552—171no—
176#1982—171no—
177#1982—171no—
178#1957—171no—
179#1296—171no—
180#1279—171no—
181#1279D1711yescharacteristic, complemented
182C22×C17#39311yescharacteristic
183C22×C17#44711yescharacteristic
184C22×C17#44811yescharacteristic
185C22×C17#44911yescharacteristic
186C22×C17#44911yescharacteristic
187C22×C17#45311yescharacteristic
188C22×C17#45411yescharacteristic
189C2×D17—82no—
190C2×D17—82no—
191C2×D17—82no—
192C2×D17—161no—
193C2×D17—161no—
194C2×D17—161no—
195C2×D17—161no—
196C4×C17—21no—
197C4×C17—21no—
198C4×C17—42no—
199C4×C17—42no—
200C4×C17#47411yescharacteristic
201C4×C17#47611yescharacteristic
202C4×C17#47811yescharacteristic
203C4×C17#47811yescharacteristic
204C4×C17#48611yescharacteristic
205C4×C17#48811yescharacteristic
206C4×C17#48911yescharacteristic
207C4×C17#49011yescharacteristic
208Dic17—81no—
209Dic17—82no—
210Dic17—81no—
211C2×#127—171no—
212C2×#125—341no—
213C2×C4⋊C8—171no—
214C2×C4⋊C8C2×D1711yescharacteristic
215C2×#102—342no—
216C2×#102—341no—
217C2×#102—341no—
218C2×#102—341no—
219C2×#102—341no—
220C2×C4×C8C2×D1711yescharacteristic
221#398—342no—
222#389—341no—
223#389—341no—
224#384—171no—
225#384—341no—
226C4×C4⋊C4—171no—
227C4×C4⋊C4C2×D1711yescharacteristic
228C2×C17#162111yescharacteristic
229C2×C17#162211yescharacteristic
230C2×C17#162511yescharacteristic
231C2×C17#162611yescharacteristic
232C2×C17#202311yescharacteristic
233C2×C17#202511yescharacteristic
234C2×C17#202711yescharacteristic
235D17—162no—
236C22×D4—341no—
237C22×D4—341no—
238C22×D4—341no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—341no—
242#127—172no—
243#127—341no—
244#127—341no—
245#127—341no—
246#125—682no—
247#125—682no—
248C2×C4⋊C4—171no—
249C2×C4⋊C4—171no—
250C2×C4⋊C4—172no—
251C2×C4⋊C4—342no—
252C2×C4⋊C4—342no—
253C2×C4⋊C4—341no—
254C2×C4⋊C4—341no—
255C2×C4⋊C4—342no—
256C2×C4⋊C4D6811yescharacteristic
257C2×C4⋊C4D6811yescharacteristic
258C2×C42—21no—
259C2×C42—341no—
260C2×C42C22×D1711yescharacteristic
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—341no—
264C4⋊C8—341no—
265#102—682no—
266#102—682no—
267#102—684no—
268#102—682no—
269#102—682no—
270C4×C8—21no—
271C4×C8—21no—
272#95—21no—
273#95—342no—
274#95—341no—
275C17#1035411yescharacteristic, complemented, Sylow
276C24—681no—
277C2×D4—342no—
278C2×D4—342no—
279C2×D4—342no—
280C2×D4—682no—
281C2×D4—682no—
282C2×D4—681no—
283C2×D4—681no—
284C2×D4—681no—
285C2×D4—681no—
286C2×D4—681no—
287C2×D4—681no—
288C2×D4—681no—
289C2×D4—681no—
290C2×D4—681no—
291C2×D4—681no—
292C2×D4—681no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—341no—
296C22×C4—341no—
297C22×C4—342no—
298C22×C4C2×D6811yescharacteristic
299C22×C4D4×D1711yescharacteristic
300C22×C4D4×D1711yescharacteristic
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—681no—
308C2×C8—681no—
309C2×C8—681no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—341no—
313C4⋊C4—341no—
314C4⋊C4—341no—
315C4⋊C4—341no—
316C4⋊C4—682no—
317C4⋊C4—684no—
318C4⋊C4—684no—
319C4⋊C4—681no—
320C4⋊C4—681no—
321C4⋊C4—681no—
322C4⋊C4—681no—
323C4⋊C4—1362no—
324C4⋊C4#6321912yes—
325C4⋊C4D13612yes—
326C42—41no—
327C42—41no—
328C42—681no—
329C42—681no—
330C42#6325211yescharacteristic
331C42#6325211yescharacteristic
332C42#6325411yescharacteristic
333C42Q8×D1711yescharacteristic
334C23—682no—
335C23—1361no—
336C23—1361no—
337C23—1361no—
338C23—1361no—
339C23—1361no—
340C23—1361no—
341C23#1058756811yescharacteristic
342D4—684no—
343D4—682no—
344D4—682no—
345D4—682no—
346D4—682no—
347D4—1362no—
348D4—1361no—
349D4—1361no—
350D4—1361no—
351D4—1361no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—681no—
361C2×C4—681no—
362C2×C4—682no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4—682no—
366C2×C4—682no—
367C2×C4—681no—
368C2×C4—681no—
369C2×C4#1058756111yescharacteristic
370C2×C4#1058757111yescharacteristic
371C2×C4#1058757111yescharacteristic
372C2×C4#1058758211yescharacteristic
373C2×C4#1058758211yescharacteristic
374C2×C4#1058758311yescharacteristic
375C2×C4C2×#6321911yescharacteristic
376C2×C4C2×D13611yescharacteristic
377C2×C4#1058759411yescharacteristic
378C2×C4#1058759511yescharacteristic
379C2×C4#1058759711yescharacteristic
380C2×C4#1058760011yescharacteristic
381C2×C4#1058760211yescharacteristic
382C2×C4#1058760511yescharacteristic
383C8—42no—
384C8—81no—
385C8—1361no—
386C22—2721no—
387C22—2721no—
388C22—2721no—
389C22—2721no—
390C22—1362no—
391C22—1362no—
392C22—1362no—
393C22#1176272211yescharacteristic
394C22#1176294511yescharacteristic
395C22#1176295011yescharacteristic
396C22#1176295511yescharacteristic
397C22#1176295711yescharacteristic
398C22#1176297811yescharacteristic
399C22#1176298311yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—1361no—
405C4—1362no—
406C4—1361no—
407C4#1176309011yescharacteristic
408C4#1176310011yescharacteristic
409C4#1176310811yescharacteristic
410C4#1176311211yescharacteristic
411C4#1176315611yescharacteristic
412C4#1176316511yescharacteristic
413C4#1176316911yescharacteristic
414C4#1176317211yescharacteristic
415C2—2722no—
416C2#1452785111yescharacteristic
417C2#1452785811yescharacteristic
418C2#1452787511yescharacteristic
419C2#1452788311yescharacteristic
420C2#1452992111yescharacteristic
421C2#1452992911yescharacteristic
422C2#1452993911yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1279C2
socleC23×C17#120
prime radicalC2×#10587560C22
hypercenter#1279D17
hypocenterC17#10354
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #14533815C2semidirect
5. #14526668C2semidirect
6. #14526624C2semidirect
7. C17×#1279C2semidirect
181. #1279D17semidirect
275. C17#10354semidirect

Maximal subgroups

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

subgroupindex
#145338152
#145297112
#145297102
#145295902
#145266682
#145266242
C17×#12792
#1035417