Finite Group Databasebeta

← #17956483

Subgroups — #17956483

Order 4352.

572 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544640C211yesmaximal, characteristic
2C4×C22⋊#3624C211yesmaximal, characteristic
3#14543622C212yesmaximal
4#14543622C212yesmaximal
5C2×#11762694C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C22⋊#3624C2212yes—
8C2×C22⋊#3624C2212yes—
9C2×C4×#3624—21no—
10#11763675—21no—
11#11763675—21no—
12C22×C4⋊Dic17C411yescharacteristic
13C22×#63225C411yescharacteristic
14C22×C4×Dic17C2211yescharacteristic
15#11762694—21no—
16#11762694—21no—
17#11762694—21no—
18#11762694—21no—
19C2×#10587502C411yescharacteristic
20C2×#10587502C2211yescharacteristic
21C2×#10587502C2211yescharacteristic
22C2×C17×#95C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×Dic17C2×C411yescharacteristic
27C23×Dic17C2×C411yescharacteristic
28C23×Dic17C2×C411yescharacteristic
29C23×Dic17C2311yescharacteristic
30C22×#3624—22no—
31C22×#3624—22no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—22no—
35C2×C4⋊Dic17C814yescomplemented
36C2×#63225—21no—
37C2×#63225—21no—
38C2×#63225—42no—
39C2×C4×Dic17—42no—
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C22⋊#3624—22no—
45C22⋊#3624—24no—
46C22⋊#3624Q814yes—
47#10587544—42no—
48C4×#3624—42no—
49C17×#95—21no—
50C17×#95—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57C24×C17C22×C411yescharacteristic
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—22no—
61C22×C4×C17—22no—
62C22×C4×C17—21no—
63C22×C4×C17—22no—
64C22×C4×C17—41no—
65C22×C4×C17—41no—
66C22×C4×C17—41no—
67C22×C4×C17—41no—
68C22×C4×C17—41no—
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C2×C812yes—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—22no—
76C22×Dic17—41no—
77C22×Dic17—41no—
78C22×Dic17—41no—
79C22×Dic17—41no—
80C22×Dic17—41no—
81C22×Dic17—41no—
82C22×Dic17—41no—
83C22×Dic17—41no—
84C22×Dic17C22⋊C411yescharacteristic
85C22×Dic17C22⋊C411yescharacteristic
86C22×Dic17C2×C812yes—
87C22×Dic17C2×C812yes—
88C22×Dic17M1612yes—
89C22×Dic17C2×D411yescharacteristic
90C22×Dic17C2×D411yescharacteristic
91C22×Dic17C2×Q812yes—
92C22×Dic17#4112yes—
93C2×#3624—24no—
94C2×#3624—42no—
95C2×#3624—42no—
96C2×#3624—42no—
97C2×#3624—42no—
98C2×#3624—42no—
99C4⋊Dic17—24no—
100C4⋊Dic17—24no—
101#63225—42no—
102#63225—42no—
103C4×Dic17—22no—
104C4×Dic17—22no—
105C4×Dic17—41no—
106C4×Dic17—41no—
107#9880—171nomaximal, Sylow
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17C2×C22⋊C411yescharacteristic
113C23×C17C4×Q812yes—
114C23×C17C22×C811yescharacteristic
115C23×C17C2×M1611yescharacteristic
116C23×C17#13112yes—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—22no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—44no—
124C2×C4×C17—42no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—42no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—82no—
132C2×C4×C17#9912yes—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—22no—
142C2×Dic17—42no—
143C2×Dic17—42no—
144C2×Dic17—42no—
145C2×Dic17—42no—
146C2×Dic17—42no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—42no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—82no—
154C2×Dic17C22⋊C812yes—
155C2×Dic17C22⋊C812yes—
156C2×Dic17C22⋊Q812yes—
157C2×Dic17#12411yescharacteristic
158C2×Dic17C4⋊Q811yescharacteristic
159#3624—44no—
160#3624—82no—
161C2×#387—171no—
162#1797—171no—
163C4×C22⋊C8—171no—
164#1280—172no—
165#1280—172no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—22no—
171C22×C17—22no—
172C22×C17—22no—
173C22×C17—22no—
174C22×C17#39111yescharacteristic
175C22×C17C2×C22⋊C811yescharacteristic
176C22×C17#40811yescharacteristic
177C22×C17C2×#9911yescharacteristic
178C22×C17#41011yescharacteristic
179C22×C17#41311yescharacteristic
180C22×C17#41311yescharacteristic
181C22×C17C8×Q812yes—
182C22×C17#44612yes—
183C4×C17—22no—
184C4×C17—42no—
185C4×C17—41no—
186C4×C17—81no—
187Dic17—22no—
188Dic17—22no—
189Dic17—22no—
190Dic17—21no—
191Dic17—21no—
192Dic17—42no—
193Dic17—81no—
194C22×C4⋊C4—171no—
195C22×C4⋊C4—171no—
196C22×C42—171no—
197C2×C4⋊C8—341no—
198C2×C22⋊C8—172no—
199C2×C22⋊C8—172no—
200C2×C4×C8—341no—
201#387—341no—
202#387—341no—
203#387—341no—
204#387—341no—
205C2×#95—171no—
206C2×#95—171no—
207C2×#95—171no—
208C2×#95#59511yescharacteristic
209#336—341no—
210#336—341no—
211C2×C17—22no—
212C2×C17—22no—
213C2×C17#145811yescharacteristic
214C2×C17#145911yescharacteristic
215C2×C17#146811yescharacteristic
216C2×C17#147311yescharacteristic
217C2×C17#198411yescharacteristic
218C2×C17#199611yescharacteristic
219C2×C17#199811yescharacteristic
220C23×C4—171no—
221C23×C4—171no—
222C23×C4—171no—
223C23×C4—171no—
224C23×C4C2×#59511yescharacteristic
225C23×C4C2×#59511yescharacteristic
226C23×C4C2×#59511yescharacteristic
227C22×C8—342no—
228C22×C8—342no—
229C2×C4⋊C4—174no—
230C2×C4⋊C4—341no—
231C2×C4⋊C4—341no—
232C2×C4⋊C4—342no—
233C2×C4⋊C4—341no—
234C2×C4⋊C4—341no—
235C2×C4⋊C4—682no—
236C2×C42—171no—
237C2×C42—171no—
238C2×C42—171no—
239C2×C42—171no—
240C2×C42—682no—
241C4⋊C8—682no—
242C22⋊C8—174no—
243C22⋊C8—342no—
244C22⋊C8—344no—
245C4×C8—682no—
246#95—21no—
247#95—21no—
248#95—341no—
249#95—341no—
250#95—341no—
251#95—341no—
252#95—341no—
253#95—341no—
254C17#988011yescharacteristic, complemented, Sylow
255C24C22×#59511yescharacteristic
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—171no—
268C22×C4—171no—
269C22×C4—171no—
270C22×C4—171no—
271C22×C4—172no—
272C22×C4—172no—
273C22×C4—172no—
274C22×C4—172no—
275C22×C4—172no—
276C22×C4—341no—
277C22×C4—341no—
278C22×C4—341no—
279C22×C4—342no—
280C22×C4—681no—
281C22×C4—681no—
282C22×C4—681no—
283C22×C4—681no—
284C22×C4—681no—
285C22×C4—681no—
286C22×C4—681no—
287C22×C4—681no—
288C22×C4#6324212yes—
289C22×C4C22⋊#59511yescharacteristic
290C22×C4C22⋊#59511yescharacteristic
291C2×C8—344no—
292C2×C8—682no—
293C2×C8—682no—
294C2×C8—682no—
295C2×C8—682no—
296C2×C8—682no—
297C4⋊C4—344no—
298C4⋊C4—344no—
299C4⋊C4—682no—
300C4⋊C4—682no—
301C42—342no—
302C42—342no—
303C42—681no—
304C42—681no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×#6324211yescharacteristic
310C23D17⋊M1611yescharacteristic
311C23#1058767812yes—
312C23Q8×#59512yes—
313C23C2×C22⋊#59511yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—82no—
329C2×C4—172no—
330C2×C4—171no—
331C2×C4—171no—
332C2×C4—172no—
333C2×C4—172no—
334C2×C4—341no—
335C2×C4—341no—
336C2×C4—341no—
337C2×C4—341no—
338C2×C4—341no—
339C2×C4—341no—
340C2×C4—341no—
341C2×C4—341no—
342C2×C4—342no—
343C2×C4—682no—
344C2×C4—682no—
345C2×C4—682no—
346C2×C4—682no—
347C2×C4—682no—
348C2×C4—681no—
349C2×C4—681no—
350C2×C4—682no—
351C2×C4—681no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4—1362no—
355C2×C4#1058753912yes—
356C8—684no—
357C8—1362no—
358C22—22no—
359C22—22no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22(C2×#595)⋊Q811yescharacteristic
367C22#1176377711yescharacteristic
368C22#1176378211yescharacteristic
369C22C2×#1058753911yescharacteristic
370C22#1176378911yescharacteristic
371C22#1176379511yescharacteristic
372C22#1176379611yescharacteristic
373C22#1176385812yes—
374C22#1176386112yes—
375C4—22no—
376C4—42no—
377C4—41no—
378C4—81no—
379C4—342no—
380C4—341no—
381C4—341no—
382C4—342no—
383C4—342no—
384C4—682no—
385C4—1361no—
386C2—22no—
387C2—22no—
388C2#1454401611yescharacteristic
389C2#1454402111yescharacteristic
390C2#1454405111yescharacteristic
391C2#1454406611yescharacteristic
392C2#1454495511yescharacteristic
393C2#1454497411yescharacteristic
394C2#1454497811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC2×C17×#95C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22×C4
cosocleC23×Dic17C23
hypercenterC2×#95#595
hypocenterC17#9880
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
35. C2×C4⋊Dic17C8semidirect
254. C17#9880semidirect

Maximal subgroups

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

subgroupindex
#145446402
C4×C22⋊#36242
#145436222
C2×#117626942
#988017