Finite Group Databasebeta

← #16937493

Subgroups — #16937493

Order 4352.

422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 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#14534003C211yesmaximal, characteristic
2#14527356C211yesmaximal, characteristic
3C2×#11762546C211yesmaximal, characteristic
4#14526662C211yesmaximal, characteristic
5#14526651C211yesmaximal, characteristic
6#14526632C211yesmaximal, characteristic
7C17×#1996C211yesmaximal, characteristic
8C2×C22⋊#3622C2211yescharacteristic
9C2×C22⋊#3622C2211yescharacteristic
10#11762751—21no—
11#11762743—21no—
12#11762693—21no—
13#11762693—21no—
14#11762681—21no—
15#11762669C2211yescharacteristic
16#11762667—21no—
17C2×#10587502C2211yescharacteristic
18#11762546—21no—
19#11762546—21no—
20#11762546—21no—
21#11762546—21no—
22C2×C17×C22⋊Q8C2211yescharacteristic
23C17×#380C2211yescharacteristic
24C4×C22⋊C4×C17C2211yescharacteristic
25C17×#342—21no—
26C17×#342—21no—
27C22×Q8×C17Q811yescharacteristic
28C23×C4×C17C2311yescharacteristic
29C23×Dic17—21no—
30C17×C22⋊Q8—21no—
31C17×C22⋊Q8—21no—
32C17×C22⋊Q8—21no—
33C17×C22⋊Q8—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17Q811yescharacteristic
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17D411yescharacteristic
40C2×C22⋊C4×C17D411yescharacteristic
41C2×C42×C17—21no—
42C2×C22⋊Dic17—21no—
43C2×C4⋊Dic17—21no—
44C2×#63225—21no—
45C2×#63225—21no—
46C2×#63225—21no—
47C2×#63225—21no—
48C22×#3622—21no—
49C22×#3622—21no—
50C17×#95—21no—
51C17×#95—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502D411yescharacteristic
58#10587502D411yescharacteristic
59#10587502D411yescharacteristic
60#10587502D411yescharacteristic
61C22⋊#3622—21no—
62C22⋊#3622—21no—
63C22⋊#3622—21no—
64C22⋊#3622—21no—
65C24×C17C2×D411yescharacteristic
66C2×Q8×C17—21no—
67C2×Q8×C17—21no—
68C2×Q8×C17—81no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—41no—
74C22×C4×C17—81no—
75C22×C4×C17C2×D411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C22×C4×C17C2×Q811yescharacteristic
78C22×C4×C17#4111yescharacteristic
79C22×C4×C17#4111yescharacteristic
80C22×C4×C17#4111yescharacteristic
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C22×Dic17—42no—
86C22×Dic17—41no—
87C22×Dic17—41no—
88C22×Dic17—81no—
89C4⋊C4×C17—21no—
90C4⋊C4×C17—21no—
91C4⋊C4×C17—41no—
92C4⋊C4×C17—41no—
93C4⋊C4×C17—81no—
94C22⋊C4×C17—21no—
95C22⋊C4×C17—21no—
96C22⋊C4×C17—21no—
97C22⋊C4×C17—21no—
98C22⋊C4×C17—41no—
99C22⋊C4×C17—41no—
100C22⋊C4×C17—41no—
101C22⋊C4×C17—41no—
102C42×C17—81no—
103C22⋊Dic17—41no—
104C22⋊Dic17—41no—
105C4⋊Dic17—81no—
106#63225—42no—
107#63225—42no—
108#63225—81no—
109#63225—81no—
110C2×#3622—41no—
111C2×#3622—41no—
112C2×#3622—81no—
113C2×#3622—81no—
114#10377—171nomaximal, Sylow
115C23×C17—41no—
116C23×C17—41no—
117C23×C17#12011yescharacteristic
118C23×C17C22⋊Q811yescharacteristic
119C23×C17#12411yescharacteristic
120C23×C17#13511yescharacteristic
121C23×C17#13511yescharacteristic
122C23×C17#13711yescharacteristic
123C23×C17#13711yescharacteristic
124Q8×C17—81no—
125Q8×C17—81no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—81no—
141C2×C4×C17—81no—
142C2×C4×C17—81no—
143C2×C4×C17—81no—
144C2×C4×C17—81no—
145C2×C4×C17C22⋊Q811yescharacteristic
146C2×C4×C17C22⋊Q811yescharacteristic
147C2×C4×C17#12411yescharacteristic
148C2×C4×C17#12411yescharacteristic
149C2×Dic17—22no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159C2×Dic17—41no—
160C2×Dic17—41no—
161C2×Dic17—82no—
162C2×Dic17—82no—
163#3622—81no—
164#3622—81no—
165#2569—171no—
166#1996D1711yescharacteristic
167#1520—171no—
168C2×#328—171no—
169#1294—171no—
170#1289—171no—
171#1282—171no—
172C22×C17—21no—
173C22×C17—21no—
174C22×C17—21no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17—41no—
179C22×C17—41no—
180C22×C17—41no—
181C22×C17—41no—
182C22×C17#39311yescharacteristic
183C22×C17#45211yescharacteristic
184C22×C17#45211yescharacteristic
185C22×C17#47911yescharacteristic
186C22×C17#47911yescharacteristic
187C22×C17#48811yescharacteristic
188C22×C17#49111yescharacteristic
189C4×C17—21no—
190C4×C17—21no—
191C4×C17—21no—
192C4×C17—21no—
193C4×C17—81no—
194C4×C17—81no—
195C4×C17—81no—
196C4×C17—81no—
197C4×C17—161no—
198Dic17—42no—
199Dic17—81no—
200Dic17—81no—
201Dic17—81no—
202C2×C22⋊Q8C2×D1711yescharacteristic
203C2×C22⋊C8—171no—
204C2×C22⋊C8—171no—
205#400—341no—
206#398—341no—
207#387—341no—
208#387—341no—
209#385—341no—
210#380—171no—
211#380—341no—
212#380C2×D1711yescharacteristic
213C4×C22⋊C4C2×D1711yescharacteristic
214C2×#95—171no—
215#342—21no—
216#342—21no—
217#328—341no—
218#328—341no—
219#328—341no—
220#328—341no—
221C2×C17—21no—
222C2×C17—21no—
223C2×C17—21no—
224C2×C17—21no—
225C2×C17—21no—
226C2×C17—21no—
227C2×C17#202611yescharacteristic
228C2×C17#203111yescharacteristic
229C2×C17#203211yescharacteristic
230C22×Q8Dic3411yescharacteristic
231C23×C4—341no—
232C23×C4C22×D1711yescharacteristic
233C22×C8—341no—
234C22×C8—341no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—341no—
242C2×C4⋊C4—341no—
243C2×C4⋊C4—341no—
244C2×C4⋊C4—341no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4Dic3411yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—341no—
250C2×C22⋊C4C22⋊D1711yescharacteristic
251C2×C22⋊C4C22⋊D1711yescharacteristic
252C2×C42—21no—
253C22⋊C8—341no—
254C22⋊C8—341no—
255C22⋊C8—341no—
256C22⋊C8—341no—
257#95—21no—
258#95—21no—
259#95—171no—
260#95—171no—
261#95—171no—
262#95—171no—
263#95—341no—
264#95—341no—
265#95—341no—
266#95—341no—
267#95—341no—
268C17#1037711yescharacteristic, complemented, Sylow
269C24C2×C22⋊D1711yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—81no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—81no—
279C22×C4—341no—
280C22×C4—341no—
281C22×C4—341no—
282C22×C4—341no—
283C22×C4—682no—
284C22×C4—681no—
285C22×C4—681no—
286C22×C4—1361no—
287C22×C4C2×Dic3411yescharacteristic
288C22×C4#6325211yescharacteristic
289C22×C4D4×D1711yescharacteristic
290C22×C4D4×D1711yescharacteristic
291C22×C4#6325411yescharacteristic
292C22×C4#6325411yescharacteristic
293C2×C8—681no—
294C2×C8—681no—
295C2×C8—1361no—
296C2×C8—1361no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—81no—
302C4⋊C4—682no—
303C4⋊C4—682no—
304C4⋊C4—1361no—
305C4⋊C4—1361no—
306C4⋊C4—1361no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—681no—
316C22⋊C4—681no—
317C42—81no—
318C23—41no—
319C23—41no—
320C23#1058761011yescharacteristic
321C23#1058762211yescharacteristic
322C23#1058762311yescharacteristic
323C23#1058762811yescharacteristic
324C23#1058762811yescharacteristic
325C23#1058763611yescharacteristic
326C23#1058763611yescharacteristic
327Q8—81no—
328Q8—81no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—342no—
349C2×C4—681no—
350C2×C4—681no—
351C2×C4—681no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4—681no—
355C2×C4—681no—
356C2×C4—681no—
357C2×C4—681no—
358C2×C4—681no—
359C2×C4—681no—
360C2×C4—1362no—
361C2×C4—1362no—
362C2×C4#1058756411yescharacteristic
363C2×C4#1058756411yescharacteristic
364C2×C4#1058757111yescharacteristic
365C2×C4#1058757111yescharacteristic
366C8—1361no—
367C8—1361no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1176272111yescharacteristic
379C22#1176296911yescharacteristic
380C22#1176296911yescharacteristic
381C22#1176311611yescharacteristic
382C22#1176311611yescharacteristic
383C22#1176316311yescharacteristic
384C22#1176317711yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—161no—
394C4—682no—
395C4—1361no—
396C4—1361no—
397C4—1361no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#1452993511yescharacteristic
405C2#1452995811yescharacteristic
406C2#1452996111yescharacteristic
subgroupG/H
centerC22#11762721
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1996C2
socleC22×C17#393
prime radicalC24×C17C2×D4
hypercenter#1996D17
hypocenterC17#10377
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
268. C17#10377semidirect

Maximal subgroups

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

subgroupindex
#145340032
#145273562
C2×#117625462
#145266622
#145266512
#145266322
C17×#19962
#1037717