Finite Group Databasebeta

← #16930423

Subgroups — #16930423

Order 4352.

456 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537751C211yesmaximal, characteristic
2#14528804C211yesmaximal, characteristic
3#14527283C211yesmaximal, characteristic, complemented
4#14527239C211yesmaximal, characteristic, complemented
5#14526681C211yesmaximal, characteristic, complemented
6#14526623C211yesmaximal, characteristic, complemented
7C17×#3076C211yesmaximal, characteristic
8#11762940—21no—
9#11762887—21no—
10#11762881—22no—
11#11762862—21no—
12#11762862C2211yescharacteristic
13#11762833C2211yescharacteristic
14C2×#10587508—21no—
15C4×#63223—21no—
16C2×C4×#3622C2211yescharacteristic
17C4×C4⋊Dic17C2211yescharacteristic
18#11762568—21no—
19#11762546—22no—
20Q8⋊#3622—21no—
21Q8⋊#3622—21no—
22C17×#533C2211yescharacteristic
23C4×#41×C17C2211yescharacteristic
24C17×#479—21no—
25C17×#478—21no—
26C17×#477C411yescharacteristic, complemented
27C17×#476C411yescharacteristic, complemented
28C17×#475C411yescharacteristic, complemented
29C17×#474C411yescharacteristic, complemented
30C17×#427—21no—
31C2×C17×C4⋊C8C2211yescharacteristic
32C17×#416—21no—
33C2×#41×C17D411yescharacteristic
34C22×C8×C17—21no—
35C17×C4⋊Q8C2×C411yescharacteristic
36C17×C4⋊Q8C2×C411yescharacteristic
37C17×#125—21no—
38C17×C22⋊Q8—21no—
39C17×C22⋊Q8—21no—
40C4×Q8×C17—21no—
41C4×Q8×C17—21no—
42C4×Q8×C17C2×C411yescharacteristic
43C4×Q8×C17D411yescharacteristic
44C4×D4×C17—21no—
45C4×D4×C17—21no—
46C4×D4×C17C2×C411yescharacteristic
47C4×D4×C17D411yescharacteristic
48C17×#117—21no—
49C17×#117—21no—
50C17×#117D411yescharacteristic
51C2×C42×C17—21no—
52C2×C42×C17C2311yescharacteristic
53C2×C4⋊Dic17—21no—
54C2×C4×Dic17—21no—
55C2×#63223—22no—
56C2×#63223—21no—
57C22×#3622—21no—
58C17×#107—21no—
59C17×#107—21no—
60C17×#106—21no—
61C17×#106—21no—
62C17×C4⋊C8—21no—
63C17×C4⋊C8C2×C411yescharacteristic
64C17×C4⋊C8C2×C411yescharacteristic
65C17×#103—21no—
66C17×#103—21no—
67C17×#102—21no—
68C17×#102—21no—
69#10587508—42no—
70#10587502—21no—
71C22⋊#3622—22no—
72C22⋊#3622D412yes—
73C4⋊#3622—22no—
74C4⋊#3622—21no—
75C4⋊#3622—21no—
76C4⋊#3622—21no—
77#10587474—22no—
78C4×#3622—21no—
79C4×#3622—21no—
80C4×#3622D411yescharacteristic
81C4×#3622D411yescharacteristic
82#41×C17—21no—
83#41×C17—21no—
84#41×C17—21no—
85#41×C17—21no—
86C2×Q8×C17—21no—
87C2×Q8×C17—21no—
88C2×Q8×C17C22⋊C411yescharacteristic
89C2×D4×C17—21no—
90C2×D4×C17C22⋊C411yescharacteristic
91C22×C4×C17—21no—
92C22×C4×C17—21no—
93C22×C4×C17—21no—
94C22×C4×C17C2×D411yescharacteristic
95C22×C4×C17C2×D411yescharacteristic
96C22×C4×C17#4111yescharacteristic
97C22×Dic17—41no—
98C2×C8×C17—21no—
99C2×C8×C17—21no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17—21no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—21no—
108C4⋊C4×C17—41no—
109C4⋊C4×C17—41no—
110C4⋊C4×C17C22⋊C411yescharacteristic
111C4⋊C4×C17C22⋊C411yescharacteristic
112C22⋊C4×C17—21no—
113C22⋊C4×C17—21no—
114C22⋊C4×C17—21no—
115C22⋊C4×C17—41no—
116C42×C17—21no—
117C42×C17—21no—
118C42×C17—21no—
119C42×C17—41no—
120C42×C17C22×C411yescharacteristic
121C42×C17C2×D411yescharacteristic
122C42×C17C2×D411yescharacteristic
123C42×C17#4111yescharacteristic
124C4⋊Dic17—22no—
125C4⋊Dic17—41no—
126C4×Dic17—41no—
127C4×Dic17—41no—
128#63223—44no—
129#63223—41no—
130#63223—41no—
131C2×#3622—21no—
132C2×#3622—21no—
133C2×#3622—22no—
134C2×#3622—42no—
135C2×#3622—41no—
136#9209—171nomaximal, Sylow
137C23×C17—21no—
138C23×C17#12111yescharacteristic
139Q8×C17—21no—
140Q8×C17—21no—
141Q8×C17—41no—
142Q8×C17—41no—
143Q8×C17—81no—
144D4×C17—21no—
145D4×C17—21no—
146D4×C17—41no—
147D4×C17—41no—
148C2×C4×C17—21no—
149C2×C4×C17—21no—
150C2×C4×C17—21no—
151C2×C4×C17—21no—
152C2×C4×C17—21no—
153C2×C4×C17—41no—
154C2×C4×C17—42no—
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×C17C2×C22⋊C411yescharacteristic
162C2×C4×C17C4×D411yescharacteristic
163C2×C4×C17C4×D411yescharacteristic
164C2×C4×C17#12011yescharacteristic
165C2×C4×C17#12111yescharacteristic
166C2×C4×C17#12311yescharacteristic
167C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C17#13711yescharacteristic
169C2×C4×C17#13711yescharacteristic
170C2×C4×C17#13711yescharacteristic
171C2×Dic17—42no—
172C2×Dic17—81no—
173C2×Dic17—81no—
174C8×C17—41no—
175C8×C17—41no—
176#3622—22no—
177#3622—41no—
178#3622—42no—
179#3622—81no—
180#3076D1711yescharacteristic
181#2965—171no—
182#1806—171no—
183#1503—171no—
184#1493—171no—
185#1301—171no—
186#1279—171no—
187C22×C17—21no—
188C22×C17—21no—
189C22×C17—41no—
190C22×C17—41no—
191C22×C17—41no—
192C22×C17#38611yescharacteristic
193C22×C17#46811yescharacteristic
194C22×C17#47011yescharacteristic
195C4×C17—21no—
196C4×C17—21no—
197C4×C17—21no—
198C4×C17—41no—
199C4×C17—41no—
200C4×C17—41no—
201C4×C17—81no—
202C4×C17—81no—
203C4×C17#41711yescharacteristic
204C4×C17#41911yescharacteristic
205C4×C17#44311yescharacteristic
206C4×C17#44411yescharacteristic
207C4×C17#46811yescharacteristic
208C4×C17#47011yescharacteristic
209Dic17—82no—
210#533C2×D1711yescharacteristic
211C4×#41C2×D1711yescharacteristic
212#479—21no—
213#478—21no—
214#477Dic1711yescharacteristic, complemented
215#476Dic1711yescharacteristic, complemented
216#475Dic1711yescharacteristic, complemented
217#474Dic1711yescharacteristic, complemented
218#446—341no—
219#436—341no—
220#435—342no—
221#431—171no—
222#431—341no—
223#427—21no—
224#423—171no—
225C2×C4⋊C8C2×D1711yescharacteristic
226C2×#104—341no—
227#416—21no—
228C4×M16—341no—
229C2×C4×C8—171no—
230C4×C4⋊C4—171no—
231#339—341no—
232#328—342no—
233Q8⋊C8—341no—
234Q8⋊C8—341no—
235C2×C17—21no—
236C2×C17—21no—
237C2×C17—81no—
238C2×C17#187611yescharacteristic
239C2×C17#189411yescharacteristic
240C2×C17#190611yescharacteristic
241C2×#41C22⋊D1711yescharacteristic
242C2×M16—342no—
243C2×M16—341no—
244C22×C8—21no—
245C22×C8—341no—
246C4⋊Q8C2×Dic1711yescharacteristic
247C4⋊Q8C2×Dic1711yescharacteristic
248#125—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8C2×Dic1711yescharacteristic
254C4×Q8C22⋊D1711yescharacteristic
255C4×D4—21no—
256C4×D4—21no—
257C4×D4C2×Dic1711yescharacteristic
258C4×D4C22⋊D1711yescharacteristic
259#117—21no—
260#117—21no—
261#117C22⋊D1711yescharacteristic
262C2×C4⋊C4—341no—
263C2×C42—21no—
264C2×C42—341no—
265C2×C42C22×D1711yescharacteristic
266#107—21no—
267#107—21no—
268#106—21no—
269#106—21no—
270C4⋊C8—21no—
271C4⋊C8—342no—
272C4⋊C8—341no—
273C4⋊C8—341no—
274C4⋊C8—341no—
275C4⋊C8C2×Dic1711yescharacteristic
276C4⋊C8C2×Dic1711yescharacteristic
277#104—682no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282C22⋊C8—172no—
283C22⋊C8—342no—
284#97—342no—
285C4×C8—171no—
286C4×C8—171no—
287C4×C8—341no—
288C4×C8—341no—
289#95—341no—
290C17#920911yescharacteristic, complemented, Sylow
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8C22⋊Dic1711yescharacteristic
298C2×D4—21no—
299C2×D4C22⋊Dic1711yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—681no—
304C22×C4D4×D1711yescharacteristic
305C22×C4#6325411yescharacteristic
306C22×C4C2×C22⋊D1711yescharacteristic
307M16—684no—
308M16—681no—
309M16—681no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—341no—
315C2×C8—341no—
316C2×C8—342no—
317C2×C8—682no—
318C2×C8—681no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—342no—
328C4⋊C4—681no—
329C4⋊C4C22⋊Dic1711yescharacteristic
330C4⋊C4C22⋊Dic1711yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—41no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—41no—
339C42—681no—
340C42—681no—
341C42D4×D1711yescharacteristic
342C42#6325411yescharacteristic
343C42C22×Dic1711yescharacteristic
344C42C2×C22⋊D1711yescharacteristic
345C23—21no—
346C23#1058762511yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—41no—
350Q8—41no—
351Q8—81no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—682no—
370C2×C4—1361no—
371C2×C4—1361no—
372C2×C4D4×Dic1711yescharacteristic
373C2×C4D4×Dic1711yescharacteristic
374C2×C4#1058762111yescharacteristic
375C2×C4#1058762311yescharacteristic
376C2×C4#1058762511yescharacteristic
377C2×C4#1058762811yescharacteristic
378C2×C4#1058762811yescharacteristic
379C2×C4#1058763511yescharacteristic
380C2×C4#1058763711yescharacteristic
381C2×C4C2×C22⋊Dic1711yescharacteristic
382C8—41no—
383C8—41no—
384C8—342no—
385C8—681no—
386C8—682no—
387C8—1361no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22#1176268911yescharacteristic
394C22#1176305711yescharacteristic
395C22#1176306511yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—81no—
403C4—81no—
404C4—1362no—
405C4#1176281011yescharacteristic
406C4#1176281811yescharacteristic
407C4#1176292611yescharacteristic
408C4#1176293111yescharacteristic
409C4#1176305711yescharacteristic
410C4#1176306511yescharacteristic
411C2—21no—
412C2—21no—
413C2—81no—
414C2#1452911311yescharacteristic
415C2#1452921811yescharacteristic
416C2#1452928711yescharacteristic
subgroupG/H
centerC2×C4#10587625
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#3076C2
socleC22×C17#386
prime radicalC2×#41×C17D4
cosocleC2×C42×C17C23
hypercenter#3076D17
hypocenterC17#9209
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
3. #14527283C2semidirect
4. #14527239C2semidirect
5. #14526681C2semidirect
6. #14526623C2semidirect
26. C17×#477C4semidirect
27. C17×#476C4semidirect
28. C17×#475C4semidirect
29. C17×#474C4semidirect
214. #477Dic17semidirect
215. #476Dic17semidirect
216. #475Dic17semidirect
217. #474Dic17semidirect
290. C17#9209semidirect

Maximal subgroups

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

subgroupindex
#145377512
#145288042
#145272832
#145272392
#145266812
#145266232
C17×#30762
#920917