Finite Group Databasebeta

← #16950624

Subgroups — #16950624

Order 4352.

404 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17×#427C211yesmaximal, characteristic
2C2×#11762588C211yesmaximal, characteristic
3#14528819C211yesmaximal, characteristic
4#14526881C211yesmaximal, characteristic, complemented
5#14526880C211yesmaximal, characteristic, complemented
6#14526879C211yesmaximal, characteristic, complemented
7C17×#1382C211yesmaximal, characteristic, complemented
8C22×C8×D17C2211yescharacteristic
9#117×D17—21no—
10C22×#63214C2211yescharacteristic
11C2×#10587490C2211yescharacteristic
12#11762847C2211yescharacteristic
13#11762846C411yescharacteristic
14#11762846C411yescharacteristic
15#11762845—21no—
16#11762844—21no—
17#107×D17C411yescharacteristic
18#107×D17C411yescharacteristic
19#106×D17—21no—
20#11762772—21no—
21#11762588—21no—
22#11762588—21no—
23#11762573—21no—
24C22×C16×C17C2211yescharacteristic
25C2×C17×#108C2211yescharacteristic
26C17×#427C2211yescharacteristic
27C22×C4×D17D411yescharacteristic
28C2×M16×C17—21no—
29C22×C8×C17C2311yescharacteristic
30C17×#117—21no—
31#10587612—21no—
32C2×#63223—21no—
33C22×#3622D411yescharacteristic
34C2×C8×D17—21no—
35C2×C8×D17—21no—
36C2×C8×D17—21no—
37C2×C8×D17—21no—
38C2×C8×D17C2×C411yescharacteristic
39C2×C8×D17C2×C411yescharacteristic
40C2×C8×D17D411yescharacteristic
41C2×C8×D17D411yescharacteristic
42#10587578—21no—
43#10587578—21no—
44C4⋊C4×D17—21no—
45C4⋊C4×D17—21no—
46C22⋊C4×D17—41no—
47#10587563—41no—
48#10587558—41no—
49C42×D17—41no—
50C2×C16×C17—21no—
51C2×C16×C17—21no—
52C2×C16×C17—21no—
53C17×#108—21no—
54C17×#108—21no—
55C17×#107C2×C411yescharacteristic
56C17×#107C2×C411yescharacteristic
57C17×#106—21no—
58#10587491—41no—
59#10587491—41no—
60#10587490—21no—
61#10587490—21no—
62#10587489C2×C411yescharacteristic
63#10587489C2×C411yescharacteristic
64#10587488—21no—
65C2×#63214—21no—
66C2×#63214—21no—
67C2×#63214—21no—
68#10587479—21no—
69#10587479—21no—
70#10587478—21no—
71#10587478—21no—
72C23×D17SD1611yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×Dic17SD1611yescharacteristic
75C2×C4×D17—21no—
76C2×C4×D17—21no—
77C2×C4×D17—21no—
78C2×C4×D17—21no—
79C2×C4×D17—41no—
80C2×C4×D17—41no—
81C2×C4×D17C22⋊C411yescharacteristic
82C2×C4×D17C22⋊C411yescharacteristic
83C2×C4×D17D811yescharacteristic
84C2×C4×D17D811yescharacteristic
85M16×C17—41no—
86M16×C17—41no—
87C2×C8×C17—41no—
88C2×C8×C17C22×C411yescharacteristic
89C2×C8×C17C2×D411yescharacteristic
90C2×C8×C17#4111yescharacteristic
91C2×C8×C17#4111yescharacteristic
92C2×C8×C17#4111yescharacteristic
93C2×C8×C17#4111yescharacteristic
94C4⋊C4×C17—21no—
95C4⋊C4×C17—21no—
96C22⋊C4×C17—41no—
97C42×C17—41no—
98C22⋊Dic17—41no—
99#63227—41no—
100#63227—41no—
101C4⋊Dic17—21no—
102C4⋊Dic17—21no—
103#63225—41no—
104#63225—41no—
105C4×Dic17—41no—
106C4×Dic17—41no—
107C4×Dic17—41no—
108#63223—41no—
109#63223—41no—
110C2×#3622—21no—
111C2×#3622—21no—
112C2×#3622—41no—
113C2×#3622C22⋊C411yescharacteristic
114C2×#3622C22⋊C411yescharacteristic
115C8×D17—21no—
116C8×D17—21no—
117C8×D17—21no—
118C8×D17—21no—
119C8×D17—21no—
120C8×D17—21no—
121C8×D17—21no—
122C8×D17—21no—
123C16×C17—41no—
124#63214—41no—
125#12869—171nomaximal, Sylow
126C23×C17C2×SD1611yescharacteristic
127C22×D17—21no—
128C22×D17—21no—
129C22×D17—22no—
130C22×D17—41no—
131C22×D17#10211yescharacteristic
132C22×D17#10211yescharacteristic
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17C2×C22⋊C411yescharacteristic
136C2×C4×C17#12311yescharacteristic
137C2×C4×C17#12311yescharacteristic
138C2×C4×C17C2×D811yescharacteristic
139C2×C4×C17#13711yescharacteristic
140C2×C4×C17#13711yescharacteristic
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17#10211yescharacteristic
146C2×Dic17#10211yescharacteristic
147C4×D17—21no—
148C4×D17—21no—
149C4×D17—21no—
150C4×D17—21no—
151C4×D17—21no—
152C4×D17—21no—
153C4×D17—21no—
154C4×D17—21no—
155C4×D17—82no—
156C4×D17—82no—
157C8×C17—81no—
158C8×C17#11711yescharacteristic
159C8×C17#11711yescharacteristic
160C8×C17#12311yescharacteristic
161C8×C17#12311yescharacteristic
162#3622—21no—
163#3622—21no—
164#3622—81no—
165C2×#427—171no—
166C2×C22⋊C16—171no—
167#1810—171no—
168#1382—171no—
169#1382—171no—
170#1382—171no—
171#1382D1711yescharacteristic, complemented
172C22×C17—21no—
173C22×C17—21no—
174C22×C17C2×#10211yescharacteristic
175C22×C17#48311yescharacteristic
176C22×C17#48311yescharacteristic
177C2×D17—21no—
178C2×D17—21no—
179C2×D17—21no—
180C2×D17—21no—
181C2×D17—21no—
182C2×D17—42no—
183C2×D17—42no—
184C2×D17#35912yes—
185C4×C17—81no—
186C4×C17—81no—
187C4×C17#38111yescharacteristic
188C4×C17#41911yescharacteristic
189C4×C17#48011yescharacteristic
190C4×C17#48011yescharacteristic
191Dic17—21no—
192Dic17—21no—
193Dic17—81no—
194Dic17—81no—
195C23×C8—171no—
196C2×#117—341no—
197C22×C16—171no—
198C22×C16C2×D1711yescharacteristic
199C2×#108—171no—
200C2×#108C2×D1711yescharacteristic
201#427—171no—
202#427—171no—
203#427—171no—
204#427—341no—
205#427—341no—
206#427C2×D1711yescharacteristic
207C2×#107—171no—
208C2×#107—171no—
209C2×#106—341no—
210#407—341no—
211C22⋊C16—341no—
212C22⋊C16—341no—
213#341—341no—
214C2×C17—21no—
215C2×C17—21no—
216C2×C17#182311yescharacteristic
217C2×C17C2×#35911yescharacteristic
218C2×C17#214311yescharacteristic
219D17—22no—
220D17—41no—
221C23×C4—171no—
222C2×M16—21no—
223C2×M16—341no—
224C22×C8—171no—
225C22×C8—171no—
226C22×C8—171no—
227C22×C8—171no—
228C22×C8—171no—
229C22×C8—341no—
230C22×C8—341no—
231C22×C8—341no—
232C22×C8—341no—
233C22×C8C22×D1711yescharacteristic
234#117—21no—
235#117—341no—
236#117—341no—
237#117—341no—
238#117—681no—
239#117—681no—
240C2×C4⋊C4—341no—
241C2×C4⋊C4—341no—
242C2×C22⋊C4—681no—
243C2×C42—681no—
244C2×C16—21no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—341no—
248C2×C16—341no—
249C2×C16—341no—
250#108—21no—
251#108—21no—
252#108—341no—
253#108—341no—
254#107—171no—
255#107—171no—
256#107—341no—
257#107—341no—
258#107C4×D1711yescharacteristic
259#107C4×D1711yescharacteristic
260#106—21no—
261#106—341no—
262#106—341no—
263#106—341no—
264C22⋊C8—681no—
265C22⋊C8—681no—
266C17#1286911yescharacteristic, complemented, Sylow
267C24—171no—
268C22×C4—171no—
269C22×C4—171no—
270C22×C4—171no—
271C22×C4—171no—
272C22×C4—171no—
273C22×C4—341no—
274C22×C4—341no—
275C22×C4—341no—
276C22×C4—341no—
277C22×C4—681no—
278C22×C4—681no—
279C22×C4D4×D1711yescharacteristic
280M16—41no—
281M16—41no—
282M16—681no—
283M16—681no—
284C2×C8—41no—
285C2×C8—171no—
286C2×C8—171no—
287C2×C8—341no—
288C2×C8—341no—
289C2×C8—341no—
290C2×C8—341no—
291C2×C8—341no—
292C2×C8—341no—
293C2×C8—341no—
294C2×C8—341no—
295C2×C8—341no—
296C2×C8—341no—
297C2×C8—681no—
298C2×C8C2×C4×D1711yescharacteristic
299C2×C8#6325211yescharacteristic
300C2×C8#6325211yescharacteristic
301C2×C8D4×D1711yescharacteristic
302C2×C8#6325411yescharacteristic
303C2×C8#6325611yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—341no—
307C4⋊C4—341no—
308C4⋊C4—681no—
309C4⋊C4—681no—
310C22⋊C4—41no—
311C22⋊C4—681no—
312C22⋊C4—681no—
313C22⋊C4—681no—
314C42—41no—
315C42—681no—
316C42—681no—
317C42—681no—
318C16—41no—
319C16—681no—
320C23—171no—
321C23—171no—
322C23—342no—
323C23—341no—
324C23—341no—
325C23—681no—
326C23SD16×D1711yescharacteristic
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—171no—
330C2×C4—171no—
331C2×C4—341no—
332C2×C4—341no—
333C2×C4—341no—
334C2×C4—341no—
335C2×C4—341no—
336C2×C4—341no—
337C2×C4—341no—
338C2×C4—341no—
339C2×C4—341no—
340C2×C4—341no—
341C2×C4—681no—
342C2×C4—681no—
343C2×C4—1362no—
344C2×C4—1362no—
345C2×C4C22⋊C4×D1711yescharacteristic
346C2×C4#1058756911yescharacteristic
347C2×C4#1058758011yescharacteristic
348C2×C4D8×D1711yescharacteristic
349C2×C4#1058760111yescharacteristic
350C2×C4#1058760411yescharacteristic
351C8—81no—
352C8—341no—
353C8—341no—
354C8—1361no—
355C8#1058755811yescharacteristic
356C8#1058756911yescharacteristic
357C8#1058757811yescharacteristic
358C8#1058758011yescharacteristic
359C22—21no—
360C22—21no—
361C22—172no—
362C22—341no—
363C22—341no—
364C22—341no—
365C22—341no—
366C22—341no—
367C22—682no—
368C22—682no—
369C22#102×D1711yescharacteristic
370C22#1176313811yescharacteristic
371C22#1176314111yescharacteristic
372C4—81no—
373C4—81no—
374C4—341no—
375C4—341no—
376C4—1361no—
377C4—1361no—
378C4#1176267111yescharacteristic
379C4#1176281611yescharacteristic
380C4#1176312111yescharacteristic
381C4#1176312411yescharacteristic
382C2—21no—
383C2—21no—
384C2—342no—
385C2—681no—
386C2#1452886911yescharacteristic
387C2D17×#35911yescharacteristic
388C2#1453051011yescharacteristic
subgroupG/H
centerC2×C4D8×D17
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
FittingC17×#1382C2
socleC22×C17C2×#102
prime radicalC23×D17SD16
cosocleC22×C8×C17C23
hypercenter#1382D17
hypocenterC17#12869
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
4. #14526881C2semidirect
5. #14526880C2semidirect
6. #14526879C2semidirect
7. C17×#1382C2semidirect
171. #1382D17semidirect
266. C17#12869semidirect

Maximal subgroups

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

subgroupindex
D17×#4272
C2×#117625882
#145288192
#145268812
#145268802
#145268792
C17×#13822
#1286917