Finite Group Databasebeta

← #16929549

Subgroups — #16929549

Order 4352.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539339C211yesmaximal, characteristic
2#14537731C211yesmaximal, characteristic, complemented
3#14527282C211yesmaximal, characteristic, complemented
4#14527183C211yesmaximal, characteristic
5#14526625C211yesmaximal, characteristic, complemented
6#14526622C211yesmaximal, characteristic, complemented
7C17×#1980C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763205C411yescharacteristic, complemented
10#11763181C411yescharacteristic, complemented
11#11763161C411yescharacteristic, complemented
12#11763155C411yescharacteristic, complemented
13#11763036—22no—
14#11762939—21no—
15#11762937—22no—
16C8×Dic34—21no—
17C4×#63229—22no—
18#11762862C2211yescharacteristic
19#11762837—21no—
20C2×C4⋊#3622C2211yescharacteristic
21#11762767—21no—
22C2×C4×#3622C2211yescharacteristic
23#11762545—22no—
24D4⋊#3622—21no—
25D4⋊#3622—21no—
26C17×#532C2211yescharacteristic
27C2×C17×#104—21no—
28C2×C17×#104—21no—
29C4×M16×C17C2211yescharacteristic
30C4×C4⋊C4×C17C2211yescharacteristic
31C2×#41×C17—21no—
32C2×M16×C17D411yescharacteristic
33C2×M16×C17D411yescharacteristic
34C17×C4⋊Q8C2×C411yescharacteristic
35C17×#127C2×C411yescharacteristic
36C17×#124—21no—
37C17×#121—21no—
38C17×#121—21no—
39C4×D4×C17—21no—
40C4×D4×C17—21no—
41C2×C4⋊C4×C17—21no—
42C2×C42×C17—21no—
43C2×C42×C17C2311yescharacteristic
44C2×#63229—22no—
45#10587612—21no—
46#10587610—21no—
47#10587610D412yes—
48C22×#3622—21no—
49C22×#3622—21no—
50#10587556—21no—
51#10587555C2×C411yescharacteristic
52#10587555C2×C411yescharacteristic
53C4×Dic34—21no—
54C4×Dic34D412yes—
55C17×#104—42no—
56C17×#104—42no—
57C17×#97—21no—
58C4×C8×C17—21no—
59C17×#95—21no—
60#10587503—22no—
61C22⋊#3622—21no—
62#10587486—22no—
63#10587485—22no—
64#10587485—22no—
65C8×Dic17—22no—
66#10587481—22no—
67#10587479—22no—
68C4⋊#3622—21no—
69C4⋊#3622—21no—
70C4⋊#3622D411yescharacteristic
71C4⋊#3622D411yescharacteristic
72C4×#3622—21no—
73C4×#3622—21no—
74C4×#3622C2×C411yescharacteristic
75C4×#3622C2×C411yescharacteristic
76#41×C17—41no—
77#41×C17—41no—
78#41×C17—41no—
79#41×C17—41no—
80C2×Q8×C17—21no—
81C2×D4×C17—21no—
82C2×D4×C17—21no—
83C2×D4×C17—21no—
84C2×D4×C17—41no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17#4111yescharacteristic
90C2×Dic34—21no—
91C2×Dic34C22⋊C412yes—
92M16×C17—21no—
93M16×C17—21no—
94M16×C17—21no—
95M16×C17SD1612yescomplemented
96C2×C8×C17—21no—
97C2×C8×C17—21no—
98C4⋊C4×C17—22no—
99C4⋊C4×C17—21no—
100C4⋊C4×C17—21no—
101C4⋊C4×C17—41no—
102C22⋊C4×C17—41no—
103C22⋊C4×C17—41no—
104C42×C17—41no—
105C42×C17—41no—
106C42×C17C22×C411yescharacteristic
107C42×C17C2×D411yescharacteristic
108C42×C17C2×D411yescharacteristic
109C42×C17#4111yescharacteristic
110C22⋊Dic17—22no—
111#63229—44no—
112C4⋊Dic17—21no—
113C4⋊Dic17—21no—
114C4⋊Dic17—21no—
115C4⋊Dic17C22⋊C412yes—
116#63225—22no—
117#63225—22no—
118C4×Dic17—22no—
119C2×#3622—21no—
120C2×#3622—21no—
121C2×#3622—21no—
122C2×#3622—21no—
123C2×#3622—42no—
124C2×#3622—41no—
125C2×#3622—41no—
126C2×#3622—41no—
127#9054—171nomaximal, Sylow
128C23×C17—41no—
129C23×C17#12111yescharacteristic
130Q8×C17—41no—
131Q8×C17—41no—
132D4×C17—42no—
133D4×C17—41no—
134D4×C17—41no—
135D4×C17—41no—
136D4×C17—41no—
137D4×C17—81no—
138D4×C17—81no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—41no—
142C2×C4×C17—42no—
143C2×C4×C17—41no—
144C2×C4×C17—81no—
145C2×C4×C17—81no—
146C2×C4×C17—81no—
147C2×C4×C17—81no—
148C2×C4×C17C2×C22⋊C411yescharacteristic
149C2×C4×C17C4×D411yescharacteristic
150C2×C4×C17C4×D411yescharacteristic
151C2×C4×C17#12011yescharacteristic
152C2×C4×C17#12111yescharacteristic
153C2×C4×C17#12311yescharacteristic
154C2×C4×C17C2×SD1611yescharacteristic
155C2×C4×C17#13511yescharacteristic
156C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C17#13711yescharacteristic
158C2×Dic17—22no—
159C2×Dic17—22no—
160Dic34—41no—
161Dic34—41no—
162Dic34—42no—
163C8×C17—22no—
164C8×C17—41no—
165#3622—22no—
166#3622—41no—
167#3622—41no—
168#3622—41no—
169#3622—81no—
170#3167—171no—
171#2962—171no—
172#1980D1711yescharacteristic
173#1503—171no—
174#1480—171no—
175#1279—171no—
176#1278—171no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17—81no—
180C22×C17—81no—
181C22×C17—81no—
182C22×C17#38611yescharacteristic
183C22×C17#46011yescharacteristic
184C22×C17#46411yescharacteristic
185C4×C17—21no—
186C4×C17—21no—
187C4×C17—21no—
188C4×C17—82no—
189C4×C17—81no—
190C4×C17C4×SD1611yescharacteristic
191C4×C17#44011yescharacteristic
192C4×C17#44311yescharacteristic
193C4×C17#44411yescharacteristic
194C4×C17#44811yescharacteristic
195C4×C17#44911yescharacteristic
196Dic17—42no—
197Dic17—42no—
198#533—171no—
199#532C2×D1711yescharacteristic
200#498—171no—
201#492—171no—
202#487—171no—
203#486—171no—
204#465—342no—
205#446—341no—
206#446—342no—
207C8×Q8—341no—
208C4×SD16—342no—
209#431—171no—
210#424—341no—
211C2×C4⋊C8—171no—
212C2×#104—21no—
213C2×#104—21no—
214#405—341no—
215C4×M16C2×D1711yescharacteristic
216C2×C4×C8—171no—
217C4×C4⋊C4C2×D1711yescharacteristic
218#328—342no—
219D4⋊C8—341no—
220D4⋊C8—341no—
221C2×C17—21no—
222C2×C17—21no—
223C2×C17—161no—
224C2×C17#187611yescharacteristic
225C2×C17#188011yescharacteristic
226C2×C17#188411yescharacteristic
227C2×#41—21no—
228C2×SD16—342no—
229C2×M16C22⋊D1711yescharacteristic
230C2×M16C22⋊D1711yescharacteristic
231C22×C8—341no—
232C22×C8—341no—
233C4⋊Q8—171no—
234C4⋊Q8—171no—
235C4⋊Q8C4×D1711yescharacteristic
236#127C4×D1711yescharacteristic
237#125—341no—
238#124—21no—
239C22⋊Q8—172no—
240C22⋊Q8—341no—
241#121—21no—
242#121—21no—
243C4×Q8—172no—
244C4×Q8—341no—
245C4×D4—21no—
246C4×D4—21no—
247#117—341no—
248C2×C4⋊C4—21no—
249C2×C42—21no—
250C2×C42C22×D1711yescharacteristic
251#106—342no—
252C4⋊C8—171no—
253C4⋊C8—171no—
254C4⋊C8—342no—
255C4⋊C8—342no—
256C4⋊C8—341no—
257C4⋊C8—341no—
258#104—42no—
259#104—42no—
260#103—342no—
261#102—342no—
262C22⋊C8—341no—
263#97—21no—
264#97—342no—
265C4×C8—21no—
266C4×C8—171no—
267C4×C8—171no—
268C4×C8—342no—
269C4×C8—341no—
270C4×C8—341no—
271#95—21no—
272C17#905411yescharacteristic, complemented, Sylow
273#41—41no—
274#41—41no—
275#41—41no—
276#41—41no—
277C2×Q8—21no—
278C2×Q8—172no—
279C2×Q8—341no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4D4×D1711yescharacteristic
287C22×C4#6325411yescharacteristic
288C22×C4C2×C22⋊D1711yescharacteristic
289SD16—684no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16#6322912yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—341no—
297C2×C8—341no—
298C2×C8—341no—
299C2×C8—341no—
300C2×C8—682no—
301C2×C8—681no—
302C2×C8—681no—
303C2×C8—681no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—172no—
309C4⋊C4—341no—
310C4⋊C4—342no—
311C4⋊C4—342no—
312C4⋊C4—341no—
313C4⋊C4—341no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—342no—
317C42—41no—
318C42—41no—
319C42—342no—
320C42C2×C4×D1711yescharacteristic
321C42#6325211yescharacteristic
322C42D4×D1711yescharacteristic
323C42D4×D1711yescharacteristic
324C23—41no—
325C23#1058762411yescharacteristic
326Q8—41no—
327Q8—41no—
328Q8—682no—
329Q8—681no—
330Q8—681no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—81no—
337D4—81no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—342no—
348C2×C4—342no—
349C2×C4C22⋊C4×D1711yescharacteristic
350C2×C4#1058756711yescharacteristic
351C2×C4#1058756911yescharacteristic
352C2×C4#1058757011yescharacteristic
353C2×C4C4×C22⋊D1711yescharacteristic
354C2×C4#1058761811yescharacteristic
355C2×C4C2×#6322911yescharacteristic
356C2×C4#1058762311yescharacteristic
357C2×C4#1058763611yescharacteristic
358C2×C4#1058763711yescharacteristic
359C8—22no—
360C8—41no—
361C8—342no—
362C8—681no—
363C8—681no—
364C8—681no—
365C8—1361no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22#1176268511yescharacteristic
372C22#1176300611yescharacteristic
373C22#1176302811yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—81no—
379C4—682no—
380C4—682no—
381C4C4×#6322911yescharacteristic
382C4#1176290911yescharacteristic
383C4#1176292311yescharacteristic
384C4#1176292811yescharacteristic
385C4#1176294711yescharacteristic
386C4#1176295211yescharacteristic
387C2—21no—
388C2—21no—
389C2—161no—
390C2#1452910811yescharacteristic
391C2#1452914211yescharacteristic
392C2#1452916411yescharacteristic
subgroupG/H
centerC2×C4#10587623
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1980C2
socleC22×C17#386
prime radicalC17×#532C22
cosocleC2×C42×C17C23
hypercenter#1980D17
hypocenterC17#9054
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #14537731C2semidirect
3. #14527282C2semidirect
5. #14526625C2semidirect
6. #14526622C2semidirect
9. #11763205C4semidirect
10. #11763181C4semidirect
11. #11763161C4semidirect
12. #11763155C4semidirect
95. M16×C17SD16semidirect
272. C17#9054semidirect
293. M16#63229semidirect

Maximal subgroups

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

subgroupindex
#145393392
#145377312
#145272822
#145271832
#145266252
#145266222
C17×#19802
#905417