Finite Group Databasebeta

← #17953147

Subgroups — #17953147

Order 4352.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544640C211yesmaximal, characteristic
2#14544638C211yesmaximal, characteristic
3C2×#11763655C212yesmaximal
4#14543622C212yesmaximal
5C2×#11762690C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C4⋊#3624—21no—
8C2×C22⋊#3624C2212yes—
9C2×C22⋊#3624C2212yes—
10#11763675—21no—
11#11763675—21no—
12#11763655—24no—
13C22×#63225C2211yescharacteristic
14C22×C4×Dic17C2211yescharacteristic
15#11762690—21no—
16#11762690—21no—
17#11762690—21no—
18#11762690—21no—
19C2×#10587502C411yescharacteristic
20C2×#10587502C411yescharacteristic
21C2×#10587502C411yescharacteristic
22C2×#10587502C2211yescharacteristic
23C22×C4⋊C4×C17C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×Dic17C2×C411yescharacteristic
28C23×Dic17C2×C411yescharacteristic
29C23×Dic17C2×C411yescharacteristic
30C23×Dic17C2311yescharacteristic
31C22×#3624—22no—
32C22×#3624—22no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—42no—
36C2×#63225—21no—
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×#63225D412yes—
41C2×#63225Q812yes—
42C2×C4×Dic17—42no—
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17D411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C22⋊#3624—22no—
48C22⋊#3624—22no—
49C22⋊#3624—22no—
50C22⋊#3624—22no—
51#10587544—42no—
52C4⋊#3624—42no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587502—21no—
59#10587502—21no—
60#10587502—21no—
61C24×C17C22×C411yescharacteristic
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—22no—
65C22×C4×C17—22no—
66C22×C4×C17—21no—
67C22×C4×C17—22no—
68C22×C4×C17—41no—
69C22×C4×C17—41no—
70C22×C4×C17—41no—
71C22×C4×C17—41no—
72C22×C4×C17—41no—
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C4⋊C412yes—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—22no—
79C22×Dic17—22no—
80C22×Dic17—22no—
81C22×Dic17—22no—
82C22×Dic17—21no—
83C22×Dic17—22no—
84C22×Dic17—41no—
85C22×Dic17—41no—
86C22×Dic17—41no—
87C22×Dic17—41no—
88C22×Dic17—41no—
89C22×Dic17C22⋊C411yescharacteristic
90C22×Dic17C22⋊C411yescharacteristic
91C22×Dic17C4⋊C412yes—
92C22×Dic17C2×D411yescharacteristic
93C22×Dic17C2×D411yescharacteristic
94C22×Dic17C2×D411yescharacteristic
95C22×Dic17C2×Q811yescharacteristic
96C22×Dic17#4111yescharacteristic
97C22×Dic17#4111yescharacteristic
98C2×#3624—42no—
99C2×#3624—42no—
100C2×#3624—42no—
101C2×#3624—42no—
102C2×#3624—42no—
103C2×#3624—42no—
104C4⋊C4×C17—42no—
105C4⋊C4×C17—42no—
106#63225—22no—
107#63225—22no—
108#63225—22no—
109#63225—22no—
110C4×Dic17—22no—
111C4×Dic17—22no—
112C4×Dic17—41no—
113C4×Dic17—41no—
114#8562—171nomaximal, Sylow
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17C2×C22⋊C411yescharacteristic
120C23×C17C2×C4⋊C411yescharacteristic
121C23×C17#11711yescharacteristic
122C23×C17#13112yes—
123C23×C17#13112yes—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—22no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—44no—
131C2×C4×C17—42no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—42no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—82no—
139C2×C4×C17#9912yes—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—22no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—21no—
150C2×Dic17—24no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—44no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—42no—
159C2×Dic17—41no—
160C2×Dic17—41no—
161C2×Dic17—41no—
162C2×Dic17—82no—
163C2×Dic17#10112yes—
164C2×Dic17#12111yescharacteristic
165C2×Dic17#12111yescharacteristic
166C2×Dic17C22⋊Q811yescharacteristic
167C2×Dic17C22⋊Q811yescharacteristic
168#3624—82no—
169#3624—82no—
170C2×#387—171no—
171#1797—171no—
172#1797—171no—
173C2×#324—172no—
174#1280—172no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17—22no—
180C22×C17—22no—
181C22×C17—22no—
182C22×C17—22no—
183C22×C17#38011yescharacteristic
184C22×C17#40811yescharacteristic
185C22×C17#40811yescharacteristic
186C22×C17C2×#9911yescharacteristic
187C22×C17#41011yescharacteristic
188C22×C17C2×#10111yescharacteristic
189C22×C17#41311yescharacteristic
190C22×C17#42412yes—
191C22×C17#43312yes—
192C4×C17—22no—
193C4×C17—42no—
194C4×C17—41no—
195C4×C17—81no—
196Dic17—21no—
197Dic17—21no—
198Dic17—21no—
199Dic17—21no—
200Dic17—22no—
201Dic17—42no—
202Dic17—41no—
203Dic17—81no—
204C22×C4⋊C4—171no—
205C22×C4⋊C4#59511yescharacteristic
206C22×C42—171no—
207C2×C4⋊C8—341no—
208C2×C4⋊C8—341no—
209C2×C22⋊C8—172no—
210C2×C22⋊C8—172no—
211#387—341no—
212#387—341no—
213#387—341no—
214#387—341no—
215C2×#95—171no—
216C2×#95—171no—
217C2×#95—171no—
218C2×#95—171no—
219#336—341no—
220#336—341no—
221#324—344no—
222C2×C17—22no—
223C2×C17—22no—
224C2×C17#146811yescharacteristic
225C2×C17#147011yescharacteristic
226C2×C17#147211yescharacteristic
227C2×C17#147311yescharacteristic
228C2×C17#179811yescharacteristic
229C2×C17#179911yescharacteristic
230C2×C17#180111yescharacteristic
231C23×C4—171no—
232C23×C4—171no—
233C23×C4—171no—
234C23×C4—171no—
235C23×C4C2×#59511yescharacteristic
236C23×C4C2×#59511yescharacteristic
237C23×C4C2×#59511yescharacteristic
238C22×C8—342no—
239C22×C8—342no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—172no—
244C2×C4⋊C4—172no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4—341no—
247C2×C4⋊C4—341no—
248C2×C4⋊C4—341no—
249C2×C42—171no—
250C2×C42—171no—
251C2×C42—171no—
252C2×C42—171no—
253C2×C42—682no—
254C4⋊C8—682no—
255C4⋊C8—682no—
256C22⋊C8—342no—
257C22⋊C8—342no—
258C22⋊C8—342no—
259C22⋊C8—342no—
260#95—341no—
261#95—341no—
262#95—341no—
263#95—341no—
264#95—341no—
265#95—341no—
266#95—341no—
267#95—341no—
268C17#856211yescharacteristic, complemented, Sylow
269C24C22×#59511yescharacteristic
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—171no—
282C22×C4—171no—
283C22×C4—171no—
284C22×C4—171no—
285C22×C4—171no—
286C22×C4—171no—
287C22×C4—171no—
288C22×C4—172no—
289C22×C4—171no—
290C22×C4—342no—
291C22×C4—341no—
292C22×C4—342no—
293C22×C4—342no—
294C22×C4—342no—
295C22×C4—341no—
296C22×C4—341no—
297C22×C4—342no—
298C22×C4—681no—
299C22×C4—681no—
300C22×C4—681no—
301C22×C4—681no—
302C22×C4—681no—
303C22×C4C4⋊#59512yes—
304C22×C4C22⋊#59511yescharacteristic
305C22×C4C22⋊#59511yescharacteristic
306C2×C8—682no—
307C2×C8—682no—
308C2×C8—682no—
309C2×C8—682no—
310C2×C8—682no—
311C2×C8—682no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—342no—
315C4⋊C4—342no—
316C4⋊C4—342no—
317C4⋊C4—342no—
318C42—342no—
319C42—342no—
320C42—681no—
321C42—681no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23C2×C4⋊#59511yescharacteristic
327C23#1058767711yescharacteristic
328C23#1058767812yes—
329C23#1058768012yes—
330C23C2×C22⋊#59511yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—82no—
346C2×C4—171no—
347C2×C4—171no—
348C2×C4—171no—
349C2×C4—171no—
350C2×C4—172no—
351C2×C4—341no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—341no—
355C2×C4—341no—
356C2×C4—341no—
357C2×C4—342no—
358C2×C4—341no—
359C2×C4—341no—
360C2×C4—341no—
361C2×C4—344no—
362C2×C4—681no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—684no—
367C2×C4—681no—
368C2×C4—681no—
369C2×C4—682no—
370C2×C4—681no—
371C2×C4—681no—
372C2×C4—681no—
373C2×C4—1362no—
374C2×C4#1058755112yes—
375C8—1362no—
376C8—1362no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22#1176375111yescharacteristic
386C22#1176378211yescharacteristic
387C22#1176378411yescharacteristic
388C22C2×#1058755111yescharacteristic
389C22#1176378811yescharacteristic
390C22D17⋊#10111yescharacteristic
391C22#1176379611yescharacteristic
392C22#1176381612yes—
393C22#1176383412yes—
394C4—22no—
395C4—42no—
396C4—41no—
397C4—81no—
398C4—341no—
399C4—341no—
400C4—341no—
401C4—341no—
402C4—342no—
403C4—682no—
404C4—681no—
405C4—1361no—
406C2—22no—
407C2—22no—
408C2#1454404911yescharacteristic
409C2#1454405611yescharacteristic
410C2#1454406411yescharacteristic
411C2#1454406711yescharacteristic
412C2#1454464311yescharacteristic
413C2#1454464411yescharacteristic
414C2#1454465111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
cosocleC23×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#8562
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
268. C17#8562semidirect

Maximal subgroups

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

subgroupindex
#145446402
#145446382
C2×#117636552
#145436222
C2×#117626902
#856217