Finite Group Databasebeta

← #17949640

Subgroups — #17949640

Order 4352.

714 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544445C211yesmaximal, characteristic
2#14544445C211yesmaximal, characteristic
3#14543603C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5D17×#389C211yesmaximal, characteristic
6C22×#63242—21no—
7C22×#63242—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×C4⋊C4×D17—21no—
13C2×C4⋊C4×D17C411yescharacteristic
14C2×C4⋊C4×D17C411yescharacteristic
15C2×C42×D17C2211yescharacteristic
16#11762708C2211yescharacteristic
17#11762707C411yescharacteristic
18#11762706—21no—
19#11762705C2211yescharacteristic
20#11762704—21no—
21#95×D17—21no—
22C17×#389C411yescharacteristic
23C22×C4×D17—21no—
24C22×C4×D17—21no—
25C22×C4×D17C2×C411yescharacteristic
26C22×C4×D17D411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×#3624—22no—
29C22×#3624—22no—
30C2×#63242—24no—
31C2×#63242—24no—
32C2×#63242—42no—
33C2×#63242—42no—
34C2×#63242—42no—
35C2×#63242—42no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C4⋊C4×C17C2×C411yescharacteristic
39C2×C42×C17C2×C411yescharacteristic
40C2×C4⋊Dic17—21no—
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×C4⋊Dic17C2×C411yescharacteristic
43C2×#63225—21no—
44C2×#63225—21no—
45C2×#63225—21no—
46C2×#63225—21no—
47C2×C4×Dic17D411yescharacteristic
48C2×C4×Dic17D411yescharacteristic
49C2×C4×Dic17C2311yescharacteristic
50C4⋊C4×D17—22no—
51C4⋊C4×D17—42no—
52C4⋊C4×D17—42no—
53C4⋊C4×D17—42no—
54C4⋊C4×D17C814yescomplemented
55C42×D17—42no—
56C17×#95—21no—
57#10587502—21no—
58#10587502—21no—
59#10587502—21no—
60C23×D17C22⋊C411yescharacteristic
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22×C411yescharacteristic
66C22×Dic17—21no—
67C22×Dic17—21no—
68C22×Dic17C22⋊C411yescharacteristic
69C22×Dic17C2×D411yescharacteristic
70C22×Dic17C2×D411yescharacteristic
71C2×C4×D17—22no—
72C2×C4×D17—22no—
73C2×C4×D17—22no—
74C2×C4×D17—22no—
75C2×C4×D17—22no—
76C2×C4×D17—22no—
77C2×C4×D17—24no—
78C2×C4×D17—42no—
79C2×C4×D17—42no—
80C2×C4×D17—42no—
81C2×C4×D17—42no—
82C2×C4×D17—42no—
83C2×C4×D17C2×C812yes—
84C2×C4×D17M1612yes—
85C2×C4×D17D812yes—
86C2×C4×D17SD1612yes—
87C2×C4×D17SD1612yes—
88C2×C4×D17Q1612yes—
89C2×#3624—24no—
90C2×#3624—24no—
91C2×#3624—42no—
92C2×#3624—42no—
93C2×#3624—42no—
94C2×#3624—42no—
95#63242—48no—
96#63242—48no—
97C4⋊C4×C17—21no—
98C4⋊C4×C17—41no—
99C4⋊C4×C17—42no—
100C4⋊C4×C17C2×C812yescomplemented
101C42×C17—41no—
102C4⋊Dic17—21no—
103C4⋊Dic17—41no—
104C4⋊Dic17—41no—
105C4⋊Dic17—41no—
106C4⋊Dic17C2×C812yescomplemented
107#63225—24no—
108#63225—42no—
109#63225—42no—
110#63225—41no—
111#63225—41no—
112C4×Dic17—41no—
113C4×Dic17—41no—
114C4×Dic17—41no—
115C2×#1271—171nomaximal, Sylow
116C23×C17C2×C22⋊C411yescharacteristic
117C22×D17C22⋊C812yes—
118C22×D17#9912yes—
119C22×D17#10112yes—
120C22×D17#10212yes—
121C22×D17#10312yes—
122C22×D17#10412yes—
123C22×D17#10412yes—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—22no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17#10212yes—
137C2×C4×C17#10312yes—
138C2×C4×C17C22×C811yescharacteristic
139C2×C4×C17C2×M1611yescharacteristic
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—22no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17C22⋊C812yes—
153C2×Dic17C2×D811yescharacteristic
154C2×Dic17C2×SD1611yescharacteristic
155C2×Dic17C2×SD1611yescharacteristic
156C2×Dic17C2×Q1611yescharacteristic
157C4×D17—24no—
158C4×D17—24no—
159C4×D17—24no—
160C4×D17—24no—
161C4×D17—24no—
162C4×D17—24no—
163C4×D17—48no—
164C4×D17—84no—
165#3624—44no—
166#3624—44no—
167C2×#389—171no—
168C2×#336—171no—
169C2×#336—171no—
170#1271—172no—
171#1271—172no—
172C22×C17C2×C22⋊C811yescharacteristic
173C22×C17C2×#9911yescharacteristic
174C22×C17C2×#10111yescharacteristic
175C22×C17C2×#10211yescharacteristic
176C22×C17C2×#10311yescharacteristic
177C22×C17C2×#10411yescharacteristic
178C22×C17C2×#10411yescharacteristic
179C2×D17#32414yes—
180C2×D17D4⋊C814yes—
181C2×D17Q8⋊C814yes—
182C2×D17#32714yes—
183C2×D17#32814yes—
184C2×D17#33014yes—
185C2×D17#33214yes—
186C4×C17—21no—
187C4×C17—21no—
188C4×C17—22no—
189C4×C17—22no—
190C4×C17—42no—
191C4×C17—81no—
192Dic17—22no—
193Dic17—21no—
194Dic17—21no—
195Dic17—21no—
196Dic17—21no—
197Dic17—42no—
198Dic17—81no—
199C23×C8—341no—
200C23×C8—341no—
201C22×C4⋊C4—171no—
202C22×C4⋊C4—171no—
203C22×C4⋊C4—341no—
204C22×C42—171no—
205#389—171no—
206#389—171no—
207#389—171no—
208#389—341no—
209#389—341no—
210#389#59511yescharacteristic
211C2×#95—341no—
212#336—172no—
213#336—172no—
214#336—341no—
215#336—341no—
216C2×C17C2×#32411yescharacteristic
217C2×C17C2×D4⋊C811yescharacteristic
218C2×C17C2×Q8⋊C811yescharacteristic
219C2×C17C2×#32711yescharacteristic
220C2×C17C2×#32811yescharacteristic
221C2×C17C2×#33011yescharacteristic
222C2×C17C2×#33211yescharacteristic
223D17#127118yescomplemented
224C23×C4—171no—
225C23×C4—171no—
226C23×C4—171no—
227C23×C4—341no—
228C23×C4—341no—
229C22×C8—342no—
230C22×C8—342no—
231C22×C8—344no—
232C22×C8—344no—
233C22×C8—682no—
234C22×C8—682no—
235C22×C8—682no—
236C22×C8—682no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—171no—
239C2×C4⋊C4—174no—
240C2×C4⋊C4—171no—
241C2×C4⋊C4—342no—
242C2×C4⋊C4—341no—
243C2×C4⋊C4—341no—
244C2×C4⋊C4—341no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4—341no—
247C2×C4⋊C4—682no—
248C2×C4⋊C4—682no—
249C2×C4⋊C4—682no—
250C2×C4⋊C4C2×#59511yescharacteristic
251C2×C4⋊C4C2×#59511yescharacteristic
252C2×C42—171no—
253C2×C42—171no—
254C2×C42—171no—
255C2×C42—682no—
256C2×C42C2×#59511yescharacteristic
257#95—21no—
258#95—341no—
259#95—341no—
260#95—341no—
261C17C2×#127111yescharacteristic, complemented, Sylow
262C24—171no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—171no—
266C22×C4—171no—
267C22×C4—171no—
268C22×C4—172no—
269C22×C4—172no—
270C22×C4—172no—
271C22×C4—172no—
272C22×C4—172no—
273C22×C4—172no—
274C22×C4—342no—
275C22×C4—342no—
276C22×C4—342no—
277C22×C4—342no—
278C22×C4—342no—
279C22×C4—342no—
280C22×C4—344no—
281C22×C4—341no—
282C22×C4—341no—
283C22×C4—682no—
284C22×C4—682no—
285C22×C4—682no—
286C22×C4—682no—
287C22×C4—682no—
288C22×C4C22⋊#59511yescharacteristic
289C22×C4C22⋊#59511yescharacteristic
290C22×C4C22×#59511yescharacteristic
291C2×C8—344no—
292C2×C8—344no—
293C2×C8—682no—
294C2×C8—682no—
295C2×C8—688no—
296C2×C8—688no—
297C2×C8—682no—
298C2×C8—682no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—42no—
302C4⋊C4—172no—
303C4⋊C4—344no—
304C4⋊C4—341no—
305C4⋊C4—681no—
306C4⋊C4—681no—
307C4⋊C4—681no—
308C4⋊C4—681no—
309C4⋊C4—681no—
310C4⋊C4—682no—
311C4⋊C4—682no—
312C4⋊C4#6324212yescomplemented
313C42—41no—
314C42—681no—
315C42—681no—
316C42—681no—
317C23—172no—
318C23—172no—
319C23—172no—
320C23—172no—
321C23—172no—
322C23—172no—
323C23—172no—
324C23C2×C22⋊#59511yescharacteristic
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—172no—
338C2×C4—171no—
339C2×C4—171no—
340C2×C4—171no—
341C2×C4—171no—
342C2×C4—344no—
343C2×C4—344no—
344C2×C4—344no—
345C2×C4—344no—
346C2×C4—344no—
347C2×C4—344no—
348C2×C4—341no—
349C2×C4—341no—
350C2×C4—341no—
351C2×C4—341no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—342no—
355C2×C4—688no—
356C2×C4—681no—
357C2×C4—681no—
358C2×C4—681no—
359C2×C4—681no—
360C2×C4—681no—
361C2×C4—1364no—
362C2×C4#1058754712yes—
363C2×C4#1058754912yes—
364C2×C4C2×#6324211yescharacteristic
365C2×C4D17⋊M1611yescharacteristic
366C8—684no—
367C8—684no—
368C22—174no—
369C22—174no—
370C22—174no—
371C22—174no—
372C22—174no—
373C22—174no—
374C22—174no—
375C22#1176377711yescharacteristic
376C22D17⋊#9911yescharacteristic
377C22D17⋊#10111yescharacteristic
378C22C2×#1058754711yescharacteristic
379C22C2×#1058754911yescharacteristic
380C22D17⋊#10411yescharacteristic
381C22D17⋊#10411yescharacteristic
382C4—22no—
383C4—22no—
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—341no—
389C4—341no—
390C4—341no—
391C4—341no—
392C4—342no—
393C4—682no—
394C4—1361no—
395C2—178no—
396C2#1454401311yescharacteristic
397C2#1454407011yescharacteristic
398C2#1454407311yescharacteristic
399C2D17⋊#32711yescharacteristic
400C2D17⋊#32811yescharacteristic
401C2D17⋊#33011yescharacteristic
402C2D17⋊#33211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#389C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#389#595
hypocenterC17C2×#1271
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #14543603C2semidirect
4. #14543602C2semidirect
54. C4⋊C4×D17C8semidirect
100. C4⋊C4×C17C2×C8semidirect
106. C4⋊Dic17C2×C8semidirect
223. D17#1271semidirect
261. C17C2×#1271semidirect
312. C4⋊C4#63242semidirect

Maximal subgroups

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

subgroupindex
#145444452
#145436032
#145436022
D17×#3892
C2×#127117