Finite Group Databasebeta

← #16937941

Subgroups — #16937941

Order 4352.

408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763020C211yesmaximal, characteristic
2#14528777C211yesmaximal, characteristic
3#14527457C211yesmaximal, characteristic
4#14527455C211yesmaximal, characteristic
5#14527178C211yesmaximal, characteristic
6#14526681C211yesmaximal, characteristic
7C17×#1570C211yesmaximal, characteristic
8C22×Dic68—21no—
9C2×#10587555C2211yescharacteristic
10C2×C4×Dic34C2211yescharacteristic
11#11763020—22no—
12#11763020—22no—
13#11762862C2211yescharacteristic
14#11762833C2211yescharacteristic
15C2×#10587487—21no—
16C2×#10587495—21no—
17#11762577—21no—
18#11762556—22no—
19#11762554—22no—
20#11762539—22no—
21C17×#431C2211yescharacteristic
22C17×#423C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C17×#334—22no—
25C22×Dic34—21no—
26C22×Dic34D411yescharacteristic
27C2×M16×C17—21no—
28C22×C8×C17—21no—
29C2×C42×C17C2311yescharacteristic
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17D411yescharacteristic
33C2×#63225—21no—
34C2×C4×Dic17—21no—
35C2×#63223—21no—
36C2×Dic68—24no—
37C2×Dic68—42no—
38C2×Dic68—42no—
39#10587555—21no—
40#10587555—21no—
41#10587555—21no—
42#10587555D412yes—
43C4×Dic34—21no—
44C4×Dic34—21no—
45C4×Dic34—21no—
46C4×Dic34—21no—
47C17×C4⋊C8—21no—
48C17×C4⋊C8—21no—
49C17×C4⋊C8—21no—
50C17×C4⋊C8D412yes—
51C17×C4⋊C8D412yes—
52C17×C22⋊C8—21no—
53C4×C8×C17—21no—
54C22⋊#3622—21no—
55#10587495—42no—
56#10587487—24no—
57C4⋊#3622—21no—
58C4⋊#3622—21no—
59C4⋊#3622—21no—
60C4×#3622—21no—
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17#4111yescharacteristic
63C22×C4×C17#4111yescharacteristic
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17—41no—
67C2×Dic34—21no—
68C2×Dic34—21no—
69C2×Dic34—21no—
70C2×Dic34—21no—
71C2×Dic34—21no—
72C2×Dic34—22no—
73C2×Dic34—41no—
74C2×Dic34—41no—
75C2×Dic34—41no—
76C2×Dic34—41no—
77C2×Dic34—41no—
78C2×Dic34SD1612yes—
79M16×C17—41no—
80M16×C17—41no—
81C2×C8×C17—22no—
82C2×C8×C17—22no—
83C2×C8×C17—41no—
84C2×C8×C17—41no—
85C2×C8×C17—41no—
86C42×C17C2×D411yescharacteristic
87C42×C17C2×D411yescharacteristic
88C42×C17C2×D411yescharacteristic
89C42×C17#4111yescharacteristic
90C4⋊Dic17—21no—
91C4⋊Dic17—21no—
92C4⋊Dic17—22no—
93C4⋊Dic17—22no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96#63225—41no—
97#63225—41no—
98C4×Dic17—41no—
99C4×Dic17—41no—
100#63223—41no—
101#63223—41no—
102C2×#3622—41no—
103C2×#3622—41no—
104Dic68—48no—
105#10447—171nomaximal, Sylow
106C23×C17#12311yescharacteristic
107C2×C4×C17—22no—
108C2×C4×C17—41no—
109C2×C4×C17#12011yescharacteristic
110C2×C4×C17#12111yescharacteristic
111C2×C4×C17#12111yescharacteristic
112C2×C4×C17#12111yescharacteristic
113C2×C4×C17#12311yescharacteristic
114C2×C4×C17#12411yescharacteristic
115C2×C4×C17C2×SD1611yescharacteristic
116C2×C4×C17#13511yescharacteristic
117C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
119C2×Dic17—22no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—42no—
123C2×Dic17—41no—
124C2×Dic17—81no—
125C2×Dic17—81no—
126C2×Dic17—81no—
127Dic34—22no—
128Dic34—22no—
129Dic34—41no—
130Dic34—41no—
131Dic34—42no—
132Dic34—42no—
133Dic34—81no—
134Dic34—81no—
135C8×C17—42no—
136C8×C17—42no—
137C8×C17—81no—
138#3622—81no—
139#3622—81no—
140C2×#462—171no—
141#1801—171no—
142#1570D1711yescharacteristic
143#1546—171no—
144#1546—171no—
145#1479—171no—
146#1301—171no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17#39411yescharacteristic
150C22×C17#48111yescharacteristic
151C22×C17#48211yescharacteristic
152C4×C17—21no—
153C4×C17—21no—
154C4×C17—21no—
155C4×C17#44911yescharacteristic
156C4×C17#45011yescharacteristic
157C4×C17#46511yescharacteristic
158C4×C17#46911yescharacteristic
159C4×C17#47312yes—
160Dic17—42no—
161Dic17—81no—
162Dic17—82no—
163C22×Q16—341no—
164C2×C4⋊Q8—171no—
165C2×C4×Q8—171no—
166#462—342no—
167#462—342no—
168#431—171no—
169#431C2×D1711yescharacteristic
170#423—171no—
171#423C2×D1711yescharacteristic
172C2×C4⋊C8C2×D1711yescharacteristic
173C2×#103—341no—
174C2×#101—341no—
175#343—341no—
176#334—22no—
177#332—342no—
178#332—342no—
179Q8⋊C8—342no—
180C2×C17—21no—
181C2×C17—21no—
182C2×C17#203411yescharacteristic
183C2×C17#204711yescharacteristic
184C2×C17#204911yescharacteristic
185C22×Q8—171no—
186C22×Q8—341no—
187C2×Q16—344no—
188C2×Q16—682no—
189C2×Q16—682no—
190C2×M16—21no—
191C2×M16—341no—
192C22×C8—21no—
193C4⋊Q8—172no—
194C4⋊Q8—341no—
195C4⋊Q8—341no—
196C4⋊Q8—341no—
197C4×Q8—341no—
198C4×Q8—341no—
199C4×Q8—341no—
200C4×Q8—341no—
201C2×C4⋊C4—171no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4—341no—
205C2×C42—341no—
206C2×C42C22×D1711yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—341no—
211C4⋊C8—341no—
212C4⋊C8—341no—
213C4⋊C8D6812yes—
214C4⋊C8C22⋊D1712yes—
215#103—344no—
216#101—682no—
217C22⋊C8—21no—
218C22⋊C8—341no—
219C4×C8—21no—
220C4×C8—341no—
221C17#1044711yescharacteristic, complemented, Sylow
222C2×Q8—172no—
223C2×Q8—341no—
224C2×Q8—341no—
225C2×Q8—341no—
226C2×Q8—341no—
227C2×Q8—341no—
228C2×Q8—342no—
229C2×Q8—681no—
230C2×Q8—681no—
231C2×Q8—681no—
232C2×Q8—681no—
233C2×Q8—681no—
234C22×C4—341no—
235C22×C4—341no—
236C22×C4—681no—
237C22×C4#6325211yescharacteristic
238C22×C4D4×D1711yescharacteristic
239C22×C4#6325611yescharacteristic
240Q16—688no—
241M16—41no—
242M16—41no—
243M16—681no—
244M16—681no—
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—681no—
251C2×C8—681no—
252C4⋊C4—342no—
253C4⋊C4—341no—
254C4⋊C4—342no—
255C4⋊C4—341no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C42—681no—
261C42—681no—
262C42C2×D6811yescharacteristic
263C42D4×D1711yescharacteristic
264C42#6325611yescharacteristic
265C42C2×C22⋊D1711yescharacteristic
266C23#1058758011yescharacteristic
267Q8—342no—
268Q8—342no—
269Q8—681no—
270Q8—681no—
271Q8—682no—
272Q8—682no—
273Q8—1361no—
274Q8—1361no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—342no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4—682no—
282C2×C4—1361no—
283C2×C4—1361no—
284C2×C4—1361no—
285C2×C4#1058758011yescharacteristic
286C2×C4#1058758111yescharacteristic
287C2×C4#1058758111yescharacteristic
288C2×C4SD16×D1711yescharacteristic
289C2×C4#1058760011yescharacteristic
290C2×C4#1058760011yescharacteristic
291C2×C4#1058760211yescharacteristic
292C2×C4#1058761611yescharacteristic
293C2×C4#1058762311yescharacteristic
294C2×C4#1058763311yescharacteristic
295C8—42no—
296C8—42no—
297C8—81no—
298C8—1361no—
299C8—1361no—
300C22—21no—
301C22—21no—
302C22#1176272611yescharacteristic
303C22#1176312911yescharacteristic
304C22#1176313511yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—682no—
309C4—1361no—
310C4—1362no—
311C4#1176295311yescharacteristic
312C4#1176295811yescharacteristic
313C4#1176303911yescharacteristic
314C4#1176306311yescharacteristic
315C4#1176308412yes—
316C2—21no—
317C2—21no—
318C2#1452997511yescharacteristic
319C2#1453005211yescharacteristic
320C2#1453006611yescharacteristic
subgroupG/H
centerC22#11762726
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1570C2
socleC22×C17#394
prime radicalC23×C17#123
hypercenter#1570D17
hypocenterC17#10447
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
221. C17#10447semidirect

Maximal subgroups

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

subgroupindex
C2×#117630202
#145287772
#145274572
#145274552
#145271782
#145266812
C17×#15702
#1044717