Finite Group Databasebeta

← #16938898

Subgroups — #16938898

Order 4352.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529710C211yesmaximal, characteristic
2#14529589C211yesmaximal, characteristic
3#14529545C211yesmaximal, characteristic, complemented
4#14529500C211yesmaximal, characteristic, complemented
5C2×#11762559C211yesmaximal, characteristic, complemented
6C2×#11762552C211yesmaximal, characteristic
7C17×#1296C211yesmaximal, characteristic, complemented
8C2×#10587560C2211yescharacteristic
9C2×#10587479—21no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×#10587485—21no—
12C2×#10587492—21no—
13C2×#10587492—21no—
14C2×#10587480—21no—
15C2×#10587480—21no—
16C2×C4×#3622C2211yescharacteristic
17C4×C4⋊Dic17C2211yescharacteristic
18#11762571—21no—
19#11762563—21no—
20#11762559—22no—
21#11762552—22no—
22C2×C17×C4⋊C8C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C17×#384C2211yescharacteristic
25C22×D68—21no—
26C22×D68—21no—
27C22×D68—21no—
28C22×C8×C17—21no—
29C22×C8×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C42×C17C2311yescharacteristic
34C2×C4⋊Dic17D411yescharacteristic
35C2×C4⋊Dic17D411yescharacteristic
36C2×C4×Dic17—21no—
37C22×#3622—21no—
38C22×#3622D411yescharacteristic
39C22×#3622D411yescharacteristic
40#10587560—21no—
41#10587560—21no—
42#10587560—21no—
43#10587560Q812yes—
44C17×C4⋊C8—21no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8—21no—
47C17×C4⋊C8—21no—
48#10587502—21no—
49#10587492—42no—
50#10587492—42no—
51#10587485—42no—
52#10587480—42no—
53#10587480—42no—
54#10587479—42no—
55C4⋊#3622—21no—
56C4⋊#3622D412yes—
57C4×#3622—21no—
58C4×#3622—21no—
59C23×D17—41no—
60C22×C4×C17—41no—
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17#4111yescharacteristic
64C22×Dic17—21no—
65C22×Dic17—21no—
66C2×D68—22no—
67C2×D68—22no—
68C2×D68—22no—
69C2×D68—41no—
70C2×D68—41no—
71C2×D68—41no—
72C2×D68—41no—
73C2×D68—41no—
74C2×D68—41no—
75C2×D68—41no—
76C2×D68—41no—
77C2×D68—41no—
78C2×D68—41no—
79C2×D68—41no—
80C2×D68—81no—
81C2×D68—81no—
82C2×C8×C17—41no—
83C2×C8×C17—41no—
84C2×C8×C17—41no—
85C2×C8×C17—41no—
86C2×C8×C17—41no—
87C2×C8×C17—41no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—41no—
90C4⋊C4×C17—41no—
91C4⋊C4×C17—41no—
92C4⋊C4×C17—81no—
93C42×C17C2×D411yescharacteristic
94C42×C17C2×Q811yescharacteristic
95C42×C17#4111yescharacteristic
96C42×C17#4111yescharacteristic
97C4⋊Dic17—21no—
98C4⋊Dic17—21no—
99C4⋊Dic17—21no—
100C4⋊Dic17SD1612yes—
101C4×Dic17—41no—
102C4×Dic17—41no—
103C2×#3622—21no—
104C2×#3622—21no—
105C2×#3622—21no—
106C2×#3622—22no—
107C2×#3622—21no—
108C2×#3622—21no—
109C2×#3622—41no—
110C2×#3622—41no—
111C2×#3622SD1612yes—
112#10595—171nomaximal, Sylow
113C23×C17#12111yescharacteristic
114C22×D17—42no—
115C22×D17—81no—
116C22×D17—81no—
117C22×D17—81no—
118C22×D17—81no—
119C22×D17—81no—
120C22×D17—81no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—81no—
124C2×C4×C17—81no—
125C2×C4×C17—81no—
126C2×C4×C17#12111yescharacteristic
127C2×C4×C17#12111yescharacteristic
128C2×C4×C17C22⋊Q811yescharacteristic
129C2×C4×C17C22⋊Q811yescharacteristic
130C2×C4×C17C22⋊Q811yescharacteristic
131C2×C4×C17#12611yescharacteristic
132C2×C4×C17C2×SD1611yescharacteristic
133C2×C4×C17C2×SD1611yescharacteristic
134C2×C4×C17#13511yescharacteristic
135C2×C4×C17#13511yescharacteristic
136C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
140C2×Dic17—22no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146D68—42no—
147D68—42no—
148D68—42no—
149D68—42no—
150D68—82no—
151D68—82no—
152D68—81no—
153D68—81no—
154D68—81no—
155D68—81no—
156C8×C17—81no—
157C8×C17—81no—
158#3622—22no—
159#3622—42no—
160#3622—41no—
161#1982—171no—
162#1957—171no—
163#1948—171no—
164#1939—171no—
165C2×#334—171no—
166C2×#331—171no—
167#1296D1711yescharacteristic, complemented
168C22×C17#39611yescharacteristic
169C22×C17#46011yescharacteristic
170C22×C17#46311yescharacteristic
171C22×C17#46511yescharacteristic
172C22×C17#46911yescharacteristic
173C22×C17#47111yescharacteristic
174C22×C17#47211yescharacteristic
175C2×D17—82no—
176C2×D17—82no—
177C2×D17—82no—
178C2×D17—161no—
179C2×D17—161no—
180C2×D17—161no—
181C2×D17—161no—
182C4×C17—21no—
183C4×C17—21no—
184C4×C17—161no—
185C4×C17#46011yescharacteristic
186C4×C17#46311yescharacteristic
187C4×C17#46511yescharacteristic
188C4×C17#46911yescharacteristic
189C4×C17#47611yescharacteristic
190C4×C17#47611yescharacteristic
191C4×C17#47811yescharacteristic
192C4×C17#47811yescharacteristic
193Dic17—42no—
194Dic17—81no—
195C2×#127—171no—
196C2×#106—341no—
197C2×C4⋊C8—171no—
198C2×C4⋊C8—341no—
199C2×C4⋊C8C2×D1711yescharacteristic
200C2×C4⋊C8C2×D1711yescharacteristic
201C2×#102—341no—
202C2×#102—341no—
203C2×#102—341no—
204C2×#102—341no—
205C2×C4×C8—171no—
206#384C2×D1711yescharacteristic
207C4×C4⋊C4—171no—
208#340—341no—
209#336—341no—
210#334—342no—
211#331—342no—
212C2×C17#166611yescharacteristic
213C2×C17#167711yescharacteristic
214C2×C17#168811yescharacteristic
215C2×C17#170111yescharacteristic
216C2×C17#206311yescharacteristic
217C2×C17#206511yescharacteristic
218C2×C17#206511yescharacteristic
219D17—162no—
220C22×D4—341no—
221C22×D4—341no—
222C22×D4—341no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—171no—
226C22×C8—171no—
227C22×C8—341no—
228#127—172no—
229#127—341no—
230#127—341no—
231#127—341no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—171no—
236C2×C4⋊C4—171no—
237C2×C42—341no—
238C2×C42C22×D1711yescharacteristic
239#106—682no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—172no—
245C4⋊C8—341no—
246C4⋊C8—682no—
247#102—682no—
248#102—682no—
249#102—682no—
250#102—682no—
251C4×C8—341no—
252C4×C8—341no—
253#95—341no—
254C17#1059511yescharacteristic, complemented, Sylow
255C24—681no—
256C2×D4—342no—
257C2×D4—342no—
258C2×D4—342no—
259C2×D4—681no—
260C2×D4—681no—
261C2×D4—681no—
262C2×D4—681no—
263C2×D4—681no—
264C2×D4—681no—
265C2×D4—681no—
266C2×D4—681no—
267C2×D4—681no—
268C2×D4—681no—
269C2×D4—681no—
270C2×D4—1361no—
271C2×D4—1361no—
272C22×C4—41no—
273C22×C4—341no—
274C22×C4—341no—
275C22×C4#6325211yescharacteristic
276C22×C4D4×D1711yescharacteristic
277C22×C4D4×D1711yescharacteristic
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—172no—
285C2×C8—341no—
286C2×C8—341no—
287C2×C8—341no—
288C2×C8—342no—
289C2×C8—341no—
290C2×C8—341no—
291C2×C8—681no—
292C2×C8—681no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—81no—
298C4⋊C4—172no—
299C4⋊C4—341no—
300C4⋊C4—341no—
301C4⋊C4—341no—
302C42—681no—
303C42—681no—
304C42#6325211yescharacteristic
305C42#6325211yescharacteristic
306C42D4×D1711yescharacteristic
307C42Q8×D1711yescharacteristic
308C23—682no—
309C23—1361no—
310C23—1361no—
311C23—1361no—
312C23—1361no—
313C23—1361no—
314C23—1361no—
315C23#1058757011yescharacteristic
316D4—682no—
317D4—682no—
318D4—682no—
319D4—682no—
320D4—1362no—
321D4—1362no—
322D4—1361no—
323D4—1361no—
324D4—1361no—
325D4—1361no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—342no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4—681no—
336C2×C4—681no—
337C2×C4#1058756211yescharacteristic
338C2×C4#1058757011yescharacteristic
339C2×C4#1058757011yescharacteristic
340C2×C4#1058758211yescharacteristic
341C2×C4#1058758211yescharacteristic
342C2×C4#1058758211yescharacteristic
343C2×C4#1058759711yescharacteristic
344C2×C4#1058759711yescharacteristic
345C2×C4SD16×D1711yescharacteristic
346C2×C4SD16×D1711yescharacteristic
347C2×C4#1058760011yescharacteristic
348C2×C4#1058760011yescharacteristic
349C2×C4#1058760511yescharacteristic
350C2×C4#1058760511yescharacteristic
351C8—81no—
352C8—81no—
353C8—342no—
354C8—682no—
355C8—681no—
356C22—2721no—
357C22—2721no—
358C22—2721no—
359C22—2721no—
360C22—1362no—
361C22—1362no—
362C22—1362no—
363C22#1176273311yescharacteristic
364C22#1176300811yescharacteristic
365C22#1176302711yescharacteristic
366C22#1176304111yescharacteristic
367C22#1176306111yescharacteristic
368C22#1176307511yescharacteristic
369C22#1176307811yescharacteristic
370C4—21no—
371C4—21no—
372C4—161no—
373C4—682no—
374C4—1361no—
375C4#1176300811yescharacteristic
376C4#1176302711yescharacteristic
377C4#1176304111yescharacteristic
378C4#1176306111yescharacteristic
379C4#1176309811yescharacteristic
380C4#1176309811yescharacteristic
381C4#1176311211yescharacteristic
382C4#1176311211yescharacteristic
383C2—2722no—
384C2#1452813511yescharacteristic
385C2#1452819611yescharacteristic
386C2#1452826711yescharacteristic
387C2#1452834811yescharacteristic
388C2#1453014511yescharacteristic
389C2#1453015911yescharacteristic
390C2#1453015911yescharacteristic
subgroupG/H
centerC23#10587570
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socleC23×C17#121
prime radicalC2×#10587560C22
hypercenter#1296D17
hypocenterC17#10595
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #14529545C2semidirect
4. #14529500C2semidirect
5. C2×#11762559C2semidirect
7. C17×#1296C2semidirect
167. #1296D17semidirect
254. C17#10595semidirect

Maximal subgroups

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

subgroupindex
#145297102
#145295892
#145295452
#145295002
C2×#117625592
C2×#117625522
C17×#12962
#1059517