Finite Group Databasebeta

← #16929413

Subgroups — #16929413

Order 4352.

528 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14532052C211yesmaximal, characteristic
2#14527212C212yesmaximal, complemented
3#14527098C211yesmaximal, characteristic
4#14526685C212yesmaximal, complemented
5C17×#2905C211yesmaximal, characteristic
6C2×C4×Dic34C2211yescharacteristic
7#11762862C2212yes—
8#11762748C411yescharacteristic
9#11762745C411yescharacteristic
10#11762742—21no—
11#11762732—21no—
12#11762729C411yescharacteristic
13#11762721C411yescharacteristic
14C4×#63225—21no—
15C4×C4⋊Dic17C2211yescharacteristic
16C4×C22⋊Dic17—21no—
17#11762539—24no—
18#11762535—21no—
19#11762533—21no—
20C22×M16×C17—21no—
21C2×C17×#117C2211yescharacteristic
22C17×#424—24no—
23C17×#423—21no—
24C17×#423C2212yes—
25C23×C4×C17D411yescharacteristic
26C22×Dic34C2×C411yescharacteristic
27C2×M16×C17—22no—
28C2×M16×C17—22no—
29C2×M16×C17—42no—
30C2×M16×C17—42no—
31C22×C8×C17—22no—
32C17×#117—22no—
33C17×#117—22no—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C22⋊C4×C17C2×C411yescharacteristic
37C2×C22⋊C4×C17D411yescharacteristic
38C2×C42×C17D411yescharacteristic
39C2×C42×C17C2311yescharacteristic
40C2×C22⋊Dic17—21no—
41C2×C22⋊Dic17—21no—
42C2×C4⋊Dic17—21no—
43C2×C4⋊Dic17C2×C411yescharacteristic
44C2×#63225—21no—
45C2×#63225—21no—
46C2×#63225—21no—
47C2×C4×Dic17—21no—
48C2×C4×Dic17—21no—
49C4×Dic34—22no—
50C4×Dic34—22no—
51C17×C4⋊C8—24no—
52C17×C4⋊C8—22no—
53C17×C4⋊C8D414yes—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587502C2×C411yescharacteristic
59#10587502C2×C411yescharacteristic
60C22⋊#3622—22no—
61C4⋊#3622—22no—
62C4×#3622—22no—
63C24×C17C22⋊C411yescharacteristic
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17SD1612yes—
72C22×C4×C17Q1612yes—
73C22×C4×C17C22×C411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—21no—
79C22×Dic17—21no—
80C2×Dic34—22no—
81C2×Dic34—42no—
82M16×C17—44no—
83M16×C17—42no—
84M16×C17—42no—
85C2×C8×C17—24no—
86C2×C8×C17—44no—
87C4⋊C4×C17—22no—
88C4⋊C4×C17—22no—
89C22⋊C4×C17—22no—
90C22⋊C4×C17—22no—
91C42×C17—21no—
92C42×C17—21no—
93C42×C17C2×D412yes—
94C42×C17#4112yes—
95C22⋊Dic17—42no—
96C22⋊Dic17—42no—
97C4⋊Dic17—22no—
98C4⋊Dic17—42no—
99#63225—42no—
100#63225—42no—
101#63225—42no—
102C4×Dic17—41no—
103C4×Dic17—41no—
104C4×Dic17—41no—
105C4×Dic17—41no—
106C2×#3622—42no—
107#9033—171nomaximal, Sylow
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—41no—
111C23×C17—41no—
112C23×C17#10312yes—
113C23×C17C2×C22⋊C411yescharacteristic
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—22no—
117C2×C4×C17—22no—
118C2×C4×C17—22no—
119C2×C4×C17—22no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17#10312yes—
127C2×C4×C17C4×D412yes—
128C2×C4×C17#12011yescharacteristic
129C2×C4×C17#12112yes—
130C2×C4×C17#12311yescharacteristic
131C2×C4×C17C2×SD1611yescharacteristic
132C2×C4×C17C2×Q1611yescharacteristic
133C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C17#13711yescharacteristic
135C2×Dic17—22no—
136C2×Dic17—22no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147Dic34—24no—
148Dic34—42no—
149C8×C17—44no—
150#3622—82no—
151#2905D1711yescharacteristic
152#2396—171no—
153#1487—172no—
154#1458—171no—
155#1303—172no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—22no—
159C22×C17—42no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—81no—
163C22×C17#38611yescharacteristic
164C22×C17C2×#10311yescharacteristic
165C22×C17#41711yescharacteristic
166C4×C17—22no—
167C4×C17—22no—
168C4×C17—22no—
169C4×C17—41no—
170C4×C17—41no—
171C4×C17#45011yescharacteristic
172C4×C17#45111yescharacteristic
173C4×C17#48311yescharacteristic
174C4×C17#48411yescharacteristic
175Dic17—42no—
176Dic17—42no—
177Dic17—81no—
178Dic17—81no—
179C22×M16—21no—
180C2×C4×Q8—171no—
181C2×#117C2×D1711yescharacteristic
182#431—172no—
183#424—24no—
184#423—21no—
185#423C2×D1712yes—
186#400—171no—
187#399—171no—
188#398—341no—
189#396—341no—
190#395—171no—
191#393—171no—
192C4×C4⋊C4—171no—
193C4×C4⋊C4—341no—
194C4×C22⋊C4—341no—
195Q8⋊C8—344no—
196#324—341no—
197#323—341no—
198C2×C17—21no—
199C2×C17—21no—
200C2×C17—42no—
201C2×C17#187211yescharacteristic
202C2×C17#188411yescharacteristic
203C2×C17#189111yescharacteristic
204C22×Q8—171no—
205C23×C4C22⋊D1711yescharacteristic
206C2×M16—22no—
207C2×M16—22no—
208C2×M16—42no—
209C2×M16—42no—
210C22×C8—22no—
211C4×Q8—342no—
212C4×Q8—342no—
213#117—22no—
214#117—22no—
215C2×C4⋊C4—171no—
216C2×C4⋊C4—341no—
217C2×C4⋊C4—341no—
218C2×C4⋊C4—341no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4C4×D1711yescharacteristic
221C2×C4⋊C4D6811yescharacteristic
222C2×C22⋊C4—341no—
223C2×C22⋊C4—341no—
224C2×C22⋊C4C4×D1711yescharacteristic
225C2×C22⋊C4D6811yescharacteristic
226C2×C42—341no—
227C2×C42—341no—
228C2×C42C22⋊D1711yescharacteristic
229C2×C42C22×D1711yescharacteristic
230C4⋊C8—24no—
231C4⋊C8—22no—
232C4⋊C8—342no—
233C4⋊C8C22⋊D1714yes—
234C22⋊C8—342no—
235C4×C8—342no—
236#95—171no—
237#95—171no—
238#95—341no—
239#95—341no—
240#95—341no—
241#95—341no—
242C17#903311yescharacteristic, complemented, Sylow
243C24#6322711yescharacteristic
244C2×Q8—342no—
245C2×Q8—682no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—341no—
251C22×C4—341no—
252C22×C4—341no—
253C22×C4—341no—
254C22×C4#6322711yescharacteristic
255C22×C4#6322711yescharacteristic
256C22×C4#6322711yescharacteristic
257C22×C4#6322912yes—
258C22×C4#6323112yes—
259C22×C4C2×C4×D1711yescharacteristic
260C22×C4C2×D6811yescharacteristic
261C22×C4C2×C22⋊D1711yescharacteristic
262M16—44no—
263M16—42no—
264M16—42no—
265C2×C8—24no—
266C2×C8—44no—
267C2×C8—682no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—342no—
271C4⋊C4—682no—
272C4⋊C4—682no—
273C4⋊C4—682no—
274C4⋊C4—682no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—682no—
278C22⋊C4—682no—
279C42—21no—
280C42—21no—
281C42—681no—
282C42—681no—
283C42—681no—
284C42—681no—
285C42#6325212yes—
286C42C2×C22⋊D1712yes—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23#1058748112yes—
292C23C2×#6322711yescharacteristic
293Q8—344no—
294Q8—682no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—342no—
308C2×C4—342no—
309C2×C4—681no—
310C2×C4—681no—
311C2×C4—681no—
312C2×C4—681no—
313C2×C4—681no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4—681no—
319C2×C4#1058748112yes—
320C2×C4C4×C22⋊D1712yes—
321C2×C4#1058761511yescharacteristic
322C2×C4#1058761612yes—
323C2×C4#1058761811yescharacteristic
324C2×C4C2×#6322911yescharacteristic
325C2×C4#1058762811yescharacteristic
326C2×C4C2×#6323111yescharacteristic
327C2×C4#1058763911yescharacteristic
328C8—44no—
329C8—1362no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—81no—
337C22#1176268811yescharacteristic
338C22C2×#1058748111yescharacteristic
339C22#1176280811yescharacteristic
340C4—22no—
341C4—22no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—682no—
346C4—682no—
347C4—1361no—
348C4—1361no—
349C4#1176296011yescharacteristic
350C4#1176296511yescharacteristic
351C4#1176313911yescharacteristic
352C4#1176314411yescharacteristic
353C2—21no—
354C2—21no—
355C2—42no—
356C2#1452909111yescharacteristic
357C2#1452916711yescharacteristic
358C2#1452920211yescharacteristic
subgroupG/H
centerC2×C4#10587639
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2905C2
socleC22×C17#386
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2905D17
hypocenterC17#9033
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2905

Complements

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

NH ≅ G/Ntype
2. #14527212C2semidirect
4. #14526685C2semidirect
242. C17#9033semidirect

Maximal subgroups

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

subgroupindex
#145320522
#145272122
#145270982
#145266852
C17×#29052
#903317