Finite Group Databasebeta

← #16950302

Subgroups — #16950302

Order 4352.

512 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762599C212yesmaximal
2#14528776C211yesmaximal, characteristic
3#14528772C211yesmaximal, characteristic
4#14526902C212yesmaximal
5C17×#2322C211yesmaximal, characteristic
6#11762833—21no—
7C2×#10587504C2212yes—
8C2×#10587505C2212yes—
9#11762669—21no—
10#11762599—24no—
11#11762578—21no—
12#11762576—21no—
13C2×C17×#123C2211yescharacteristic
14C2×C4×D4×C17C2211yescharacteristic
15C22×C4⋊C4×C17C411yescharacteristic, complemented
16C17×#389—21no—
17C17×#388—21no—
18C17×#387—21no—
19C17×#386C2211yescharacteristic
20C17×#385—21no—
21C17×#385C411yescharacteristic, complemented
22C17×#381C411yescharacteristic, complemented
23C4×C22⋊C4×C17C411yescharacteristic, complemented
24C22×D4×C17C2311yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17C2×C411yescharacteristic
28C23×C4×C17D411yescharacteristic
29C17×#123—21no—
30C17×#123—21no—
31C17×#123D412yes—
32C17×#123Q812yes—
33C4×D4×C17—41no—
34C4×D4×C17—41no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—41no—
40C2×C4⋊C4×C17—41no—
41C2×C4⋊C4×C17D411yescharacteristic
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C22⋊C4×C17C2×C411yescharacteristic
45C2×C22⋊C4×C17C2×C411yescharacteristic
46C2×C22⋊C4×C17C2×C411yescharacteristic
47C2×C22⋊C4×C17D411yescharacteristic
48C2×C42×C17—21no—
49C2×C42×C17D411yescharacteristic
50C2×C22⋊Dic17—22no—
51C2×C4⋊Dic17—41no—
52C2×#63223—22no—
53C17×#95—21no—
54C17×#95—21no—
55C17×#95—21no—
56C17×#95—21no—
57C17×#95—21no—
58#10587505—22no—
59#10587505—22no—
60#10587504—22no—
61#10587504—22no—
62#10587502—41no—
63C4⋊#3622—41no—
64C4⋊#3622—41no—
65C24×C17C22×C411yescharacteristic
66C24×C17C2×D411yescharacteristic
67C2×D4×C17—41no—
68C2×D4×C17—41no—
69C2×D4×C17C2×D411yescharacteristic
70C2×D4×C17C2×Q811yescharacteristic
71C2×D4×C17#4111yescharacteristic
72C2×D4×C17#4111yescharacteristic
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—21no—
81C22×C4×C17—21no—
82C22×C4×C17—41no—
83C22×C4×C17—41no—
84C22×C4×C17—41no—
85C22×C4×C17—81no—
86C22×C4×C17—81no—
87C22×C4×C17—81no—
88C22×C4×C17C22⋊C411yescharacteristic
89C22×C4×C17C22⋊C411yescharacteristic
90C22×C4×C17C22⋊C411yescharacteristic
91C22×C4×C17C22⋊C411yescharacteristic
92C22×C4×C17C4⋊C412yescomplemented
93C22×C4×C17C2×D411yescharacteristic
94C22×Dic17—42no—
95C4⋊C4×C17—22no—
96C4⋊C4×C17—22no—
97C4⋊C4×C17—41no—
98C4⋊C4×C17—42no—
99C4⋊C4×C17—41no—
100C4⋊C4×C17—41no—
101C4⋊C4×C17—81no—
102C22⋊C4×C17—21no—
103C22⋊C4×C17—22no—
104C22⋊C4×C17—22no—
105C22⋊C4×C17—41no—
106C22⋊C4×C17—41no—
107C22⋊C4×C17—41no—
108C22⋊C4×C17—81no—
109C22⋊C4×C17C4⋊C412yescomplemented
110C42×C17—21no—
111C42×C17—21no—
112C42×C17—81no—
113C22⋊Dic17—42no—
114C22⋊Dic17—42no—
115C4⋊Dic17—82no—
116#63223—42no—
117#63223—42no—
118C2×#3622—42no—
119#12796—171nomaximal, Sylow
120C23×C17—21no—
121C23×C17—21no—
122C23×C17—21no—
123C23×C17—21no—
124C23×C17—41no—
125C23×C17—41no—
126C23×C17—41no—
127C23×C17—41no—
128C23×C17C2×C22⋊C411yescharacteristic
129C23×C17C2×C4⋊C411yescharacteristic
130C23×C17#11711yescharacteristic
131C23×C17#12111yescharacteristic
132C23×C17C22⋊Q811yescharacteristic
133D4×C17—41no—
134D4×C17—41no—
135D4×C17—41no—
136D4×C17—41no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—22no—
140C2×C4×C17—22no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—41no—
145C2×C4×C17—42no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—42no—
149C2×C4×C17—41no—
150C2×C4×C17—41no—
151C2×C4×C17—41no—
152C2×C4×C17—41no—
153C2×C4×C17—42no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17—41no—
157C2×C4×C17—41no—
158C2×C4×C17—41no—
159C2×C4×C17—41no—
160C2×C4×C17—41no—
161C2×C4×C17—81no—
162C2×C4×C17—81no—
163C2×C4×C17—81no—
164C2×C4×C17—82no—
165C2×C4×C17#9911yescharacteristic
166C2×C4×C17#9911yescharacteristic
167C2×C4×C17#12111yescharacteristic
168C2×C4×C17C22⋊Q811yescharacteristic
169C2×Dic17—82no—
170C2×Dic17—82no—
171C2×Dic17—82no—
172#3622—82no—
173#2322D1711yescharacteristic
174C2×#352—172no—
175#1800—171no—
176#1799—171no—
177#1390—172no—
178C22×C17—21no—
179C22×C17—21no—
180C22×C17—21no—
181C22×C17—21no—
182C22×C17—21no—
183C22×C17—21no—
184C22×C17—41no—
185C22×C17—41no—
186C22×C17—41no—
187C22×C17—41no—
188C22×C17—42no—
189C22×C17—41no—
190C22×C17—41no—
191C22×C17—41no—
192C22×C17—41no—
193C22×C17—81no—
194C22×C17#38011yescharacteristic
195C22×C17C2×#9911yescharacteristic
196C22×C17#41011yescharacteristic
197C4×C17—21no—
198C4×C17—21no—
199C4×C17—21no—
200C4×C17—21no—
201C4×C17—42no—
202C4×C17—42no—
203C4×C17—41no—
204C4×C17—41no—
205C4×C17—41no—
206C4×C17—81no—
207C4×C17—81no—
208Dic17—162no—
209C2×#123C2×D1711yescharacteristic
210C2×C4×D4C2×D1711yescharacteristic
211C22×C4⋊C4Dic1711yescharacteristic, complemented
212#423—341no—
213C2×#100—172no—
214C2×#99—172no—
215#389—21no—
216#388—21no—
217#387—21no—
218#386C2×D1711yescharacteristic
219#385—21no—
220#385Dic1711yescharacteristic, complemented
221#381Dic1711yescharacteristic, complemented
222#380—341no—
223C4×C22⋊C4Dic1711yescharacteristic, complemented
224#352—344no—
225#343—341no—
226#342—341no—
227C2×C17—21no—
228C2×C17—21no—
229C2×C17—41no—
230C2×C17—41no—
231C2×C17—41no—
232C2×C17—41no—
233C2×C17#179911yescharacteristic
234C2×C17#212111yescharacteristic
235C2×C17#212311yescharacteristic
236C22×D4C22×D1711yescharacteristic
237C23×C4C2×Dic1711yescharacteristic
238C23×C4C2×Dic1711yescharacteristic
239C23×C4C2×Dic1711yescharacteristic
240C23×C4C22⋊D1711yescharacteristic
241C2×M16—342no—
242#123—21no—
243#123—21no—
244#123Dic3412yes—
245#123D6812yes—
246C4×D4—41no—
247C4×D4—41no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4—681no—
255C2×C4⋊C4C22⋊D1711yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—342no—
259C2×C22⋊C4C2×Dic1711yescharacteristic
260C2×C22⋊C4C2×Dic1711yescharacteristic
261C2×C22⋊C4C2×Dic1711yescharacteristic
262C2×C22⋊C4C22⋊D1711yescharacteristic
263C2×C42—21no—
264C2×C42C22⋊D1711yescharacteristic
265C4⋊C8—681no—
266C4⋊C8—681no—
267#100—342no—
268#100—342no—
269#99—342no—
270#99—342no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—681no—
277C17#1279611yescharacteristic, complemented, Sylow
278C24C22×Dic1711yescharacteristic
279C24C2×C22⋊D1711yescharacteristic
280C2×D4—41no—
281C2×D4—41no—
282C2×D4C2×Dic3411yescharacteristic
283C2×D4C2×D6811yescharacteristic
284C2×D4#6325211yescharacteristic
285C2×D4#6325211yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—81no—
299C22×C4—81no—
300C22×C4—81no—
301C22×C4—682no—
302C22×C4C4⋊Dic1712yescomplemented
303C22×C4C22⋊Dic1711yescharacteristic
304C22×C4C22⋊Dic1711yescharacteristic
305C22×C4C22⋊Dic1711yescharacteristic
306C22×C4C22⋊Dic1711yescharacteristic
307C22×C4C2×C22⋊D1711yescharacteristic
308M16—682no—
309M16—682no—
310C2×C8—682no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—81no—
318C4⋊C4—1362no—
319C22⋊C4—22no—
320C22⋊C4—21no—
321C22⋊C4—22no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—81no—
326C22⋊C4—682no—
327C22⋊C4—682no—
328C22⋊C4C4⋊Dic1712yescomplemented
329C42—21no—
330C42—21no—
331C42—81no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23#1058761011yescharacteristic
341C23C2×C4⋊Dic1711yescharacteristic
342C23#1058761211yescharacteristic
343C23#1058761611yescharacteristic
344C23C2×C22⋊Dic1711yescharacteristic
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—1362no—
378C2×C4—1362no—
379C2×C4—1362no—
380C2×C4#1058750511yescharacteristic
381C2×C4#1058750511yescharacteristic
382C2×C4#1058761011yescharacteristic
383C2×C4#1058761611yescharacteristic
384C8—1362no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22#1176266911yescharacteristic
402C22C2×#1058750511yescharacteristic
403C22#1176278311yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—42no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—81no—
414C4—81no—
415C4—2722no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2—41no—
421C2—41no—
422C2#1452877211yescharacteristic
423C2#1453043011yescharacteristic
424C2#1453043811yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC24×C17C22×C4
FrattiniC22×D4C22×D17
FittingC17×#2322C2
socleC22×C17C2×#99
prime radical, cosocleC22×D4×C17C23
hypercenter#2322D17
hypocenterC17#12796
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2322

Complements

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

NH ≅ G/Ntype
15. C22×C4⋊C4×C17C4semidirect
21. C17×#385C4semidirect
22. C17×#381C4semidirect
23. C4×C22⋊C4×C17C4semidirect
92. C22×C4×C17C4⋊C4semidirect
109. C22⋊C4×C17C4⋊C4semidirect
211. C22×C4⋊C4Dic17semidirect
220. #385Dic17semidirect
221. #381Dic17semidirect
223. C4×C22⋊C4Dic17semidirect
277. C17#12796semidirect
302. C22×C4C4⋊Dic17semidirect
328. C22⋊C4C4⋊Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117625992
#145287762
#145287722
#145269022
C17×#23222
#1279617