Finite Group Databasebeta

← #17949666

Subgroups — #17949666

Order 4352.

596 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10587543C211yesmaximal, characteristic
2#14544445C211yesmaximal, characteristic
3#14543604C212yesmaximal, complemented
4#14543603C212yesmaximal, complemented
5C4×#10587632C211yesmaximal, characteristic
6C22×#63242—21no—
7C2×#10587543—21no—
8C2×C4×#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587632C411yescharacteristic
13C2×C42×D17C2211yescharacteristic
14#11762716C2211yescharacteristic
15#11762705C2211yescharacteristic
16#11762690—21no—
17#11762680—21no—
18#11762666C411yescharacteristic
19C4×#63225—21no—
20C4×C4⋊Dic17C411yescharacteristic
21C4×#63227—21no—
22C2×C4×Q8×C17C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C22×C4×D17C2×C411yescharacteristic
25C22×C4×D17D411yescharacteristic
26C22×C4×D17D411yescharacteristic
27C22×#3624—22no—
28C22×#3624—22no—
29C2×#63242—24no—
30C2×#63242—42no—
31C2×#63242—42no—
32C4×Q8×C17—42no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C42×C17—21no—
36C2×C42×C17C2×C411yescharacteristic
37#10587632—22no—
38#10587632C814yescomplemented
39C2×#63227—21no—
40C2×#63227—21no—
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×C4⋊Dic17C2×C411yescharacteristic
43C2×#63225—21no—
44C2×#63225—21no—
45C2×C4×Dic17—21no—
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17D411yescharacteristic
48C2×C4×Dic17C2311yescharacteristic
49C42×D17—42no—
50#10587543—24no—
51C4×#3624—42no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57C23×D17C22⋊C411yescharacteristic
58C2×Q8×C17—21no—
59C2×Q8×C17—41no—
60C2×Q8×C17—41no—
61C2×Q8×C17C2×C812yescomplemented
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22×C411yescharacteristic
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17C22⋊C411yescharacteristic
70C22×Dic17C2×D411yescharacteristic
71C22×Dic17C2×D411yescharacteristic
72C2×C4×D17—22no—
73C2×C4×D17—22no—
74C2×C4×D17—22no—
75C2×C4×D17—22no—
76C2×C4×D17—41no—
77C2×C4×D17—41no—
78C2×C4×D17—41no—
79C2×C4×D17C2×C812yes—
80C2×C4×D17M1612yes—
81C2×C4×D17SD1612yes—
82C2×C4×D17Q1612yes—
83C2×#3624—24no—
84C2×#3624—24no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C2×#3624—42no—
89#63242—48no—
90C4⋊C4×C17—41no—
91C4⋊C4×C17—42no—
92C42×C17—22no—
93C42×C17—42no—
94#63227—24no—
95#63227—42no—
96C4⋊Dic17—21no—
97C4⋊Dic17—41no—
98C4⋊Dic17C2×C812yescomplemented
99#63225—24no—
100#63225—42no—
101C4×Dic17—22no—
102C4×Dic17—41no—
103C4×Dic17—41no—
104C4×Dic17—42no—
105#7566—171nomaximal, Sylow
106C23×C17C2×C22⋊C411yescharacteristic
107C22×D17—21no—
108C22×D17—21no—
109C22×D17—21no—
110C22×D17—21no—
111C22×D17C22⋊C812yes—
112C22×D17#10312yes—
113C22×D17#10412yes—
114Q8×C17—42no—
115Q8×C17—42no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—22no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17#9912yes—
128C2×C4×C17#10312yes—
129C2×C4×C17#10412yes—
130C2×C4×C17C22×C811yescharacteristic
131C2×C4×C17C2×M1611yescharacteristic
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—22no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17C22⋊C812yes—
145C2×Dic17C2×SD1611yescharacteristic
146C2×Dic17C2×Q1611yescharacteristic
147C2×Dic17#13512yes—
148C4×D17—24no—
149C4×D17—24no—
150C4×D17—42no—
151C4×D17—42no—
152C4×D17—44no—
153#3624—44no—
154#3624—44no—
155C4×C22⋊Q8—171no—
156C4×C22⋊C8—171no—
157C2×#336—171no—
158#1272—172no—
159#1271—172no—
160C22×C17C2×C22⋊C811yescharacteristic
161C22×C17C2×#9911yescharacteristic
162C22×C17#41311yescharacteristic
163C22×C17C2×#10311yescharacteristic
164C22×C17#41611yescharacteristic
165C22×C17C2×#10411yescharacteristic
166C22×C17C2×#10411yescharacteristic
167C2×D17—22no—
168C2×D17—22no—
169C2×D17—22no—
170C2×D17—22no—
171C2×D17—22no—
172C2×D17—22no—
173C2×D17Q8⋊C814yes—
174C4×C17—21no—
175C4×C17—21no—
176C4×C17—42no—
177C4×C17—41no—
178C4×C17—81no—
179C4×C17#32814yes—
180Dic17—22no—
181Dic17—21no—
182Dic17—21no—
183Dic17—22no—
184Dic17—42no—
185Dic17—81no—
186C23×C8—341no—
187C2×C22⋊Q8—171no—
188C2×C4×Q8#59511yescharacteristic
189C22×C42—171no—
190C2×C22⋊C8—341no—
191C2×C4×C8—341no—
192#391—171no—
193#389—171no—
194#387—341no—
195#385—341no—
196#380—171no—
197C4×C4⋊C4—171no—
198C4×C4⋊C4—341no—
199C4×C22⋊C4—341no—
200#336—172no—
201#336—172no—
202#336—341no—
203C2×C17#145911yescharacteristic
204C2×C17C2×Q8⋊C811yescharacteristic
205C2×C17#147611yescharacteristic
206C2×C17C2×#32811yescharacteristic
207C2×C17#150111yescharacteristic
208C2×C17#152411yescharacteristic
209C2×C17#154211yescharacteristic
210D17—24no—
211C22×Q8C2×#59511yescharacteristic
212C23×C4—171no—
213C23×C4—171no—
214C23×C4—171no—
215C22×C8—342no—
216C22×C8—342no—
217C22×C8—344no—
218C22×C8—682no—
219C22×C8—682no—
220C22⋊Q8—174no—
221C22⋊Q8—342no—
222C4×Q8—42no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—171no—
225C2×C4⋊C4—171no—
226C2×C4⋊C4—341no—
227C2×C4⋊C4—341no—
228C2×C4⋊C4C2×#59511yescharacteristic
229C2×C22⋊C4—341no—
230C2×C22⋊C4—341no—
231C2×C42—21no—
232C2×C42—171no—
233C2×C42—171no—
234C2×C42—171no—
235C2×C42—341no—
236C2×C42—682no—
237C2×C42C2×#59511yescharacteristic
238C22⋊C8—344no—
239C4×C8—682no—
240#95—341no—
241#95—341no—
242#95—341no—
243#95—341no—
244#95—341no—
245C17#756611yescharacteristic, complemented, Sylow
246C24—171no—
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8#6324212yescomplemented
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—171no—
254C22×C4—171no—
255C22×C4—171no—
256C22×C4—172no—
257C22×C4—172no—
258C22×C4—172no—
259C22×C4—172no—
260C22×C4—342no—
261C22×C4—342no—
262C22×C4—342no—
263C22×C4—342no—
264C22×C4—341no—
265C22×C4—341no—
266C22×C4—681no—
267C22×C4—681no—
268C22×C4—681no—
269C22×C4C22⋊#59511yescharacteristic
270C22×C4C22⋊#59511yescharacteristic
271C22×C4C22×#59511yescharacteristic
272C2×C8—344no—
273C2×C8—344no—
274C2×C8—682no—
275C2×C8—682no—
276C2×C8—688no—
277C2×C8—682no—
278C2×C8—682no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—172no—
282C4⋊C4—344no—
283C4⋊C4—341no—
284C4⋊C4—681no—
285C4⋊C4—682no—
286C22⋊C4—344no—
287C22⋊C4—682no—
288C42—22no—
289C42—42no—
290C42—342no—
291C42—681no—
292C42—681no—
293C42—682no—
294C23—172no—
295C23—172no—
296C23—172no—
297C23—341no—
298C23—341no—
299C23—341no—
300C23—341no—
301C23C2×C22⋊#59511yescharacteristic
302Q8—42no—
303Q8—42no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—172no—
316C2×C4—171no—
317C2×C4—171no—
318C2×C4—172no—
319C2×C4—341no—
320C2×C4—341no—
321C2×C4—341no—
322C2×C4—341no—
323C2×C4—341no—
324C2×C4—341no—
325C2×C4—344no—
326C2×C4—344no—
327C2×C4—342no—
328C2×C4—682no—
329C2×C4—682no—
330C2×C4—684no—
331C2×C4—681no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4—681no—
336C2×C4#1058754912yes—
337C2×C4#1058755012yes—
338C2×C4#1058755112yes—
339C2×C4C2×#6324211yescharacteristic
340C2×C4D17⋊M1611yescharacteristic
341C8—684no—
342C8—684no—
343C22—174no—
344C22—342no—
345C22—342no—
346C22—342no—
347C22—342no—
348C22—342no—
349C22—342no—
350C22#1176377711yescharacteristic
351C22C2×#1058755111yescharacteristic
352C22#1176379511yescharacteristic
353C22C2×#1058754911yescharacteristic
354C22#1176379911yescharacteristic
355C22D17⋊#10411yescharacteristic
356C22C2×#1058755011yescharacteristic
357C4—21no—
358C4—21no—
359C4—41no—
360C4—42no—
361C4—81no—
362C4—341no—
363C4—341no—
364C4—342no—
365C4—342no—
366C4—682no—
367C4—1361no—
368C4#1176366314yes—
369C2—344no—
370C2#1454401911yescharacteristic
371C2#1454407311yescharacteristic
372C2#1454407811yescharacteristic
373C2C2×#1176366311yescharacteristic
374C2#1454415911yescharacteristic
375C2#1454423611yescharacteristic
376C2#1454428511yescharacteristic
subgroupG/H
centerC22×C4C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×Q8#595
hypocenterC17#7566
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #14543604C2semidirect
4. #14543603C2semidirect
38. #10587632C8semidirect
61. C2×Q8×C17C2×C8semidirect
98. C4⋊Dic17C2×C8semidirect
245. C17#7566semidirect
250. C2×Q8#63242semidirect

Maximal subgroups

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

subgroupindex
C4×#105875432
#145444452
#145436042
#145436032
C4×#105876322
#756617