Finite Group Databasebeta

← #16936772

Subgroups — #16936772

Order 4352.

524 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 105 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
1#14539925C211yesmaximal, characteristic
2#14533769C211yesmaximal, characteristic
3#14527457C211yesmaximal, characteristic
4#14527283C211yesmaximal, characteristic
5#14527179C211yesmaximal, characteristic
6#14526685C211yesmaximal, characteristic
7C17×#3078C211yesmaximal, characteristic
8C2×#10587555C2211yescharacteristic
9C2×#10587630—21no—
10#11763205—21no—
11#11763159—21no—
12#11763137—22no—
13#11763094—22no—
14#11762862C2211yescharacteristic
15#11762862C2211yescharacteristic
16#11762739—22no—
17#11762714—21no—
18#11762707—22no—
19C4×C4⋊Dic17C2211yescharacteristic
20#11762556—22no—
21#11762546—22no—
22Q8⋊#3622—22no—
23C17×#533C2211yescharacteristic
24C2×C4×Q8×C17C2211yescharacteristic
25C17×#479—22no—
26C17×#477—21no—
27C17×#475—21no—
28C17×#428—21no—
29C17×#423C2211yescharacteristic
30C17×#419—21no—
31C22×Q8×C17D411yescharacteristic
32C22×Dic34—21no—
33C2×M16×C17—21no—
34C17×C4⋊Q8D411yescharacteristic
35C17×C4⋊Q8D411yescharacteristic
36C17×#125—21no—
37C17×C22⋊Q8—21no—
38C17×C22⋊Q8—21no—
39C4×Q8×C17—21no—
40C4×Q8×C17—21no—
41C4×Q8×C17—21no—
42C4×Q8×C17—21no—
43C4×Q8×C17—21no—
44C4×Q8×C17—21no—
45C17×#117—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17D411yescharacteristic
48C2×C42×C17—21no—
49C2×C42×C17C2311yescharacteristic
50#10587630—42no—
51#10587630—42no—
52C2×C4⋊Dic17—21no—
53C2×C4⋊Dic17—21no—
54C2×C4⋊Dic17D412yes—
55C2×#63225—24no—
56C2×C4×Dic17—21no—
57#10587555—21no—
58#10587555—21no—
59#10587555—21no—
60#10587555—21no—
61C17×#107—22no—
62C17×#106—22no—
63C17×C4⋊C8—21no—
64C17×C4⋊C8D412yes—
65C17×#103—22no—
66C17×#103—22no—
67#10587506—24no—
68#10587502—24no—
69#10587502D412yes—
70C22⋊#3622—21no—
71C22⋊#3622—21no—
72#10587479—24no—
73C4⋊#3622—21no—
74C4⋊#3622D412yes—
75C4×#3622—21no—
76C4×#3622—21no—
77C2×Q8×C17—21no—
78C2×Q8×C17—21no—
79C2×Q8×C17—21no—
80C2×Q8×C17—21no—
81C2×Q8×C17—21no—
82C2×Q8×C17—21no—
83C2×Q8×C17—21no—
84C2×Q8×C17SD1612yes—
85C22×C4×C17—21no—
86C22×C4×C17—21no—
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×D411yescharacteristic
90C22×Dic17—22no—
91C22×Dic17—22no—
92C2×Dic34—41no—
93C2×Dic34—41no—
94C2×Dic34—41no—
95C2×Dic34—41no—
96C2×Dic34—41no—
97C2×Dic34—41no—
98M16×C17—41no—
99M16×C17—41no—
100C2×C8×C17—22no—
101C4⋊C4×C17—21no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17—21no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—41no—
108C4⋊C4×C17—41no—
109C4⋊C4×C17—41no—
110C4⋊C4×C17—41no—
111C22⋊C4×C17—41no—
112C42×C17—41no—
113C42×C17—41no—
114C42×C17—41no—
115C42×C17C2×D411yescharacteristic
116C42×C17C2×D411yescharacteristic
117C42×C17C2×D411yescharacteristic
118C42×C17#4111yescharacteristic
119C4⋊Dic17—24no—
120C4⋊Dic17—22no—
121C4⋊Dic17—22no—
122C4⋊Dic17—41no—
123C4⋊Dic17—41no—
124#63225—48no—
125C4×Dic17—41no—
126C4×Dic17—41no—
127C2×#3622—22no—
128C2×#3622—41no—
129#10251—171nomaximal, Sylow
130C23×C17#12011yescharacteristic
131Q8×C17—22no—
132Q8×C17—22no—
133Q8×C17—41no—
134Q8×C17—41no—
135Q8×C17—42no—
136Q8×C17—81no—
137C2×C4×C17—22no—
138C2×C4×C17—22no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—41no—
142C2×C4×C17—42no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17#12011yescharacteristic
147C2×C4×C17#12011yescharacteristic
148C2×C4×C17#12111yescharacteristic
149C2×C4×C17#12111yescharacteristic
150C2×C4×C17#12111yescharacteristic
151C2×C4×C17#12711yescharacteristic
152C2×C4×C17C2×SD1611yescharacteristic
153C2×C4×C17#13511yescharacteristic
154C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C17#13711yescharacteristic
156C2×Dic17—24no—
157C2×Dic17—42no—
158C2×Dic17—42no—
159C2×Dic17—42no—
160C2×Dic17—42no—
161C2×Dic17—42no—
162Dic34—81no—
163Dic34—81no—
164Dic34—81no—
165Dic34—81no—
166C8×C17—42no—
167#3622—42no—
168#3622—81no—
169#3229—171no—
170#3078D1711yescharacteristic
171#2546—171no—
172#1546—171no—
173#1503—171no—
174#1479—171no—
175#1303—171no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17#39211yescharacteristic
179C22×C17#45011yescharacteristic
180C22×C17#45211yescharacteristic
181C4×C17—21no—
182C4×C17—21no—
183C4×C17—21no—
184C4×C17—42no—
185C4×C17—81no—
186C4×C17—81no—
187C4×C17—81no—
188C4×C17#44811yescharacteristic
189C4×C17#44911yescharacteristic
190C4×C17#45612yes—
191C4×C17#46511yescharacteristic
192C4×C17#46811yescharacteristic
193Dic17—44no—
194Dic17—82no—
195#533C2×D1711yescharacteristic
196C2×C4⋊Q8—171no—
197C2×C4⋊Q8—341no—
198C2×C4×Q8C2×D1711yescharacteristic
199#498—341no—
200#487—341no—
201#483—342no—
202#479—22no—
203#477—21no—
204#475—21no—
205#475—342no—
206#431—171no—
207#431—171no—
208#428—21no—
209#423C2×D1711yescharacteristic
210#419—21no—
211#398—342no—
212#391—341no—
213#389—342no—
214C4×C4⋊C4—171no—
215#332—342no—
216#328—342no—
217Q8⋊C8—342no—
218C2×C17—21no—
219C2×C17—21no—
220C2×C17#200011yescharacteristic
221C2×C17#200511yescharacteristic
222C2×C17#200911yescharacteristic
223C22×Q8—341no—
224C22×Q8C22⋊D1711yescharacteristic
225C2×M16—21no—
226C4⋊Q8—341no—
227C4⋊Q8—341no—
228C4⋊Q8—341no—
229C4⋊Q8—341no—
230C4⋊Q8—682no—
231C4⋊Q8—682no—
232C4⋊Q8C22⋊D1711yescharacteristic
233C4⋊Q8C22⋊D1711yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—172no—
246C2×C4⋊C4—341no—
247C2×C4⋊C4—344no—
248C2×C4⋊C4—341no—
249C2×C4⋊C4C22⋊D1711yescharacteristic
250C2×C42—21no—
251C2×C42—341no—
252C2×C42C22×D1711yescharacteristic
253#107—22no—
254#106—22no—
255#106—344no—
256C4⋊C8—21no—
257C4⋊C8—172no—
258C4⋊C8—341no—
259C4⋊C8C22⋊D1712yes—
260#103—22no—
261#103—22no—
262#103—344no—
263C22⋊C8—341no—
264C22⋊C8—341no—
265C4×C8—341no—
266C4×C8—341no—
267#95—172no—
268#95—344no—
269C17#1025111yescharacteristic, complemented, Sylow
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—681no—
278C2×Q8—681no—
279C2×Q8—681no—
280C2×Q8—681no—
281C2×Q8—681no—
282C2×Q8—681no—
283C2×Q8#6323012yes—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—342no—
287C22×C4—342no—
288C22×C4D4×D1711yescharacteristic
289C22×C4D4×D1711yescharacteristic
290C22×C4C2×C22⋊D1711yescharacteristic
291M16—41no—
292M16—41no—
293C2×C8—22no—
294C2×C8—342no—
295C2×C8—681no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—344no—
307C4⋊C4—342no—
308C4⋊C4—342no—
309C4⋊C4—688no—
310C4⋊C4—681no—
311C4⋊C4—681no—
312C22⋊C4—41no—
313C42—41no—
314C42—41no—
315C42—41no—
316C42—681no—
317C42—681no—
318C42D4×D1711yescharacteristic
319C42#6325411yescharacteristic
320C42C2×C22⋊D1711yescharacteristic
321C42C2×C22⋊D1711yescharacteristic
322C23#1058762311yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—42no—
328Q8—81no—
329Q8—1361no—
330Q8—1361no—
331Q8—1361no—
332Q8—1361no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—344no—
343C2×C4—682no—
344C2×C4—682no—
345C2×C4—682no—
346C2×C4—682no—
347C2×C4—682no—
348C2×C4#1058762311yescharacteristic
349C2×C4#1058762411yescharacteristic
350C2×C4#1058762511yescharacteristic
351C2×C4#1058762511yescharacteristic
352C2×C4#1058762611yescharacteristic
353C2×C4C2×#6323011yescharacteristic
354C2×C4#1058762811yescharacteristic
355C2×C4#1058763511yescharacteristic
356C2×C4#1058763611yescharacteristic
357C2×C4#1058763911yescharacteristic
358C8—42no—
359C8—682no—
360C8—1361no—
361C22—21no—
362C22—21no—
363C22#1176271711yescharacteristic
364C22#1176295911yescharacteristic
365C22#1176296911yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—684no—
374C4—1362no—
375C4#1176294811yescharacteristic
376C4#1176295411yescharacteristic
377C4#1176299012yes—
378C4#1176304011yescharacteristic
379C4#1176305711yescharacteristic
380C2—21no—
381C2—21no—
382C2#1452978511yescharacteristic
383C2#1452981711yescharacteristic
384C2#1452984111yescharacteristic
subgroupG/H
centerC22#11762717
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#3078C2
socleC22×C17#392
prime radicalC23×C17#120
hypercenter#3078D17
hypocenterC17#10251
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
269. C17#10251semidirect

Maximal subgroups

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

subgroupindex
#145399252
#145337692
#145274572
#145272832
#145271792
#145266852
C17×#30782
#1025117