Finite Group Databasebeta

← #16929050

Subgroups — #16929050

Order 4352.

476 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538855C211yesmaximal, characteristic
2#14529760C211yesmaximal, characteristic, complemented
3C4×#10587508C211yesmaximal, characteristic
4#14527204C211yesmaximal, characteristic, complemented
5#14526673C211yesmaximal, characteristic, complemented
6#14526616C211yesmaximal, characteristic, complemented
7C17×#2991C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763150—21no—
10#11763094C411yescharacteristic, complemented
11#11763089C411yescharacteristic, complemented
12#11763019C411yescharacteristic, complemented
13#11763014C411yescharacteristic, complemented
14#11762971—21no—
15C4×#63231—21no—
16C4×#63229—21no—
17#11762862C2211yescharacteristic
18C2×#10587508—21no—
19C4×#63223C2211yescharacteristic
20C42×Dic17C2211yescharacteristic
21#11762570—22no—
22#11762568—21no—
23#11762539—21no—
24#11762539—21no—
25C4×#41×C17C2211yescharacteristic
26C8×Q8×C17—21no—
27C17×#436—21no—
28C17×#436—22no—
29C17×#431—21no—
30C17×#431C2211yescharacteristic
31C17×#423—21no—
32C17×#423C2211yescharacteristic
33C2×#41×C17D411yescharacteristic
34C2×M16×C17—22no—
35C2×M16×C17D412yes—
36C4×Q8×C17C2×C411yescharacteristic
37C4×Q8×C17D411yescharacteristic
38C4×D4×C17—21no—
39C4×D4×C17—21no—
40C4×D4×C17C2×C411yescharacteristic
41C4×D4×C17D411yescharacteristic
42C17×#117—21no—
43C17×#117D411yescharacteristic
44C2×C42×C17—21no—
45C2×C42×C17C2311yescharacteristic
46C2×#63231—21no—
47C2×#63229—21no—
48#10587612—21no—
49#10587610—21no—
50#10587610—21no—
51C2×C4×Dic17—21no—
52C2×C4×Dic17—21no—
53C2×C4×Dic17—21no—
54C2×#63223—21no—
55#10587556—21no—
56#10587555C2×C411yescharacteristic
57#10587555C2×C411yescharacteristic
58C4×Dic34—21no—
59C4×Dic34—21no—
60C17×C4⋊C8—22no—
61C17×C4⋊C8—21no—
62C17×C4⋊C8—21no—
63C17×C4⋊C8D411yescharacteristic
64C17×C4⋊C8D411yescharacteristic
65C17×C22⋊C8—22no—
66C17×C22⋊C8—21no—
67C4×C8×C17—22no—
68C4×C8×C17—21no—
69#10587508—24no—
70#10587506—21no—
71#10587503—21no—
72C22⋊#3622—21no—
73#10587481—21no—
74#10587481—21no—
75#10587479—21no—
76#10587478—21no—
77C4⋊#3622C2×C411yescharacteristic
78C4⋊#3622C2×C411yescharacteristic
79#10587474—21no—
80C4×#3622—21no—
81C4×#3622—21no—
82#41×C17—22no—
83#41×C17—41no—
84C2×Q8×C17C22⋊C411yescharacteristic
85C2×D4×C17—21no—
86C2×D4×C17C22⋊C411yescharacteristic
87C22×C4×C17—21no—
88C22×C4×C17—21no—
89C22×C4×C17—21no—
90C22×C4×C17C2×D411yescharacteristic
91C22×C4×C17C2×D411yescharacteristic
92C22×C4×C17#4111yescharacteristic
93C22×Dic17—41no—
94C2×Dic34—21no—
95C2×Dic34—21no—
96M16×C17—42no—
97M16×C17—82no—
98C2×C8×C17—21no—
99C2×C8×C17—22no—
100C2×C8×C17—21no—
101C4⋊C4×C17—21no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17C22⋊C411yescharacteristic
104C4⋊C4×C17C22⋊C411yescharacteristic
105C22⋊C4×C17—21no—
106C22⋊C4×C17—21no—
107C22⋊C4×C17—21no—
108C42×C17—21no—
109C42×C17—21no—
110C42×C17—21no—
111C42×C17C22×C411yescharacteristic
112C42×C17C2×D411yescharacteristic
113C42×C17C2×D411yescharacteristic
114C42×C17#4111yescharacteristic
115C22⋊Dic17—41no—
116#63231—42no—
117#63229—42no—
118C4⋊Dic17—21no—
119C4⋊Dic17—21no—
120C4⋊Dic17—21no—
121C4⋊Dic17—21no—
122#63225—41no—
123#63225—41no—
124C4×Dic17—22no—
125C4×Dic17—22no—
126C4×Dic17—22no—
127C4×Dic17—41no—
128C4×Dic17—41no—
129C4×Dic17—41no—
130C4×Dic17—41no—
131#63223—22no—
132#63223—41no—
133C2×#3622—21no—
134C2×#3622—21no—
135C2×#3622—41no—
136#8972—171nomaximal, Sylow
137C23×C17—21no—
138C23×C17#12111yescharacteristic
139Q8×C17—21no—
140Q8×C17#10412yes—
141D4×C17—21no—
142D4×C17—21no—
143D4×C17—42no—
144C2×C4×C17—21no—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—21no—
148C2×C4×C17—21no—
149C2×C4×C17—21no—
150C2×C4×C17—21no—
151C2×C4×C17—21no—
152C2×C4×C17—21no—
153C2×C4×C17—42no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17—41no—
157C2×C4×C17—41no—
158C2×C4×C17C2×C22⋊C411yescharacteristic
159C2×C4×C17C4×D411yescharacteristic
160C2×C4×C17C4×D411yescharacteristic
161C2×C4×C17#12011yescharacteristic
162C2×C4×C17#12111yescharacteristic
163C2×C4×C17#12311yescharacteristic
164C2×Dic17—42no—
165C2×Dic17—42no—
166C2×Dic17—42no—
167C2×Dic17—41no—
168C2×Dic17—41no—
169Dic34—41no—
170Dic34—41no—
171Dic34—41no—
172Dic34—41no—
173C8×C17—42no—
174C8×C17—41no—
175C8×C17—41no—
176#3622—42no—
177#3622—41no—
178#3622—41no—
179#3107—171no—
180#2991D1711yescharacteristic
181#1994—171no—
182C4×#104—171no—
183#1485—171no—
184#1299—171no—
185#1276—171no—
186C22×C17—21no—
187C22×C17—21no—
188C22×C17—21no—
189C22×C17—41no—
190C22×C17—41no—
191C22×C17—41no—
192C22×C17#38611yescharacteristic
193C4×C17—21no—
194C4×C17—22no—
195C4×C17—21no—
196C4×C17—21no—
197C4×C17—41no—
198C4×C17—41no—
199C4×C17C2×#10411yescharacteristic
200C4×C17#42111yescharacteristic
201C4×C17#44311yescharacteristic
202C4×C17#44411yescharacteristic
203C4×C17#45511yescharacteristic
204C4×C17#45611yescharacteristic
205Dic17—44no—
206Dic17—81no—
207Dic17—81no—
208#533—171no—
209C4×#41C2×D1711yescharacteristic
210#485—341no—
211#475—171no—
212#474—171no—
213#462—171no—
214#461—171no—
215#452—341no—
216C8×Q8—21no—
217C4×Q16—341no—
218C4×SD16—341no—
219#436—22no—
220#436—21no—
221#431—21no—
222#431—171no—
223#431C2×D1711yescharacteristic
224#423—21no—
225#423C2×D1711yescharacteristic
226C2×#104—341no—
227C4×M16—171no—
228C43—171no—
229#339—342no—
230#339—341no—
231Q8⋊C8—341no—
232Q8⋊C8—341no—
233C2×C17—41no—
234C2×C17—81no—
235C2×C17#187111yescharacteristic
236C2×C17#187611yescharacteristic
237C2×C17#188211yescharacteristic
238C2×#41D6811yescharacteristic
239C2×Q16—341no—
240C2×SD16—341no—
241C2×M16—22no—
242C2×M16—341no—
243C2×M16C22⋊D1712yes—
244C4⋊Q8—171no—
245C4⋊Q8—171no—
246#125—341no—
247C22⋊Q8—341no—
248C22⋊Q8—341no—
249C4×Q8—341no—
250C4×Q8—341no—
251C4×Q8C4×D1711yescharacteristic
252C4×Q8C22⋊D1711yescharacteristic
253C4×D4—21no—
254C4×D4—21no—
255C4×D4C4×D1711yescharacteristic
256C4×D4C22⋊D1711yescharacteristic
257#117—21no—
258#117—341no—
259#117D6811yescharacteristic
260C2×C42—21no—
261C2×C42—341no—
262C2×C42—341no—
263C2×C42—341no—
264C2×C42C22×D1711yescharacteristic
265#107—341no—
266#106—341no—
267C4⋊C8—22no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—171no—
271C4⋊C8—171no—
272C4⋊C8C22⋊D1711yescharacteristic
273C4⋊C8C22⋊D1711yescharacteristic
274#104—344no—
275#103—341no—
276#103—341no—
277#103—341no—
278#102—341no—
279C22⋊C8—22no—
280C22⋊C8—21no—
281C22⋊C8—341no—
282#97—341no—
283C4×C8—22no—
284C4×C8—21no—
285C4×C8—341no—
286C4×C8—341no—
287C17#897211yescharacteristic, complemented, Sylow
288#41—22no—
289#41—41no—
290C2×Q8—341no—
291C2×Q8—341no—
292C2×Q8#6322711yescharacteristic
293C2×D4—21no—
294C2×D4#6322711yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—681no—
299C22×C4C2×D6811yescharacteristic
300C22×C4#6325211yescharacteristic
301C22×C4C2×C22⋊D1711yescharacteristic
302Q16—682no—
303SD16—682no—
304M16—42no—
305M16—82no—
306M16—342no—
307M16—681no—
308C2×C8—21no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—341no—
312C2×C8—341no—
313C2×C8—681no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—341no—
317C4⋊C4—341no—
318C4⋊C4—341no—
319C4⋊C4—341no—
320C4⋊C4—681no—
321C4⋊C4—681no—
322C4⋊C4#6322711yescharacteristic
323C4⋊C4#6322711yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—681no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—342no—
332C42—342no—
333C42—342no—
334C42—681no—
335C42—681no—
336C42—681no—
337C42—681no—
338C42C2×C4×D1711yescharacteristic
339C42#6325211yescharacteristic
340C42C2×C22⋊D1711yescharacteristic
341C42C2×C22⋊D1711yescharacteristic
342C23—21no—
343C23#1058761611yescharacteristic
344Q8—21no—
345Q8—681no—
346Q8—681no—
347Q8—681no—
348Q8—681no—
349Q8#1058749612yes—
350D4—21no—
351D4—21no—
352D4—42no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—682no—
368C2×C4—682no—
369C2×C4—682no—
370C2×C4—681no—
371C2×C4—681no—
372C2×C4C2×#6322711yescharacteristic
373C2×C4C4×C22⋊D1711yescharacteristic
374C2×C4C4×C22⋊D1711yescharacteristic
375C2×C4#1058761511yescharacteristic
376C2×C4#1058761611yescharacteristic
377C2×C4#1058763911yescharacteristic
378C8—42no—
379C8—41no—
380C8—41no—
381C8—682no—
382C8—681no—
383C8—681no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22#1176268811yescharacteristic
391C4—21no—
392C4—22no—
393C4—21no—
394C4—21no—
395C4—41no—
396C4—41no—
397C4—684no—
398C4—1361no—
399C4—1361no—
400C4C2×#1058749611yescharacteristic
401C4#1176282511yescharacteristic
402C4#1176292411yescharacteristic
403C4#1176292911yescharacteristic
404C4#1176298711yescharacteristic
405C4#1176299211yescharacteristic
406C2—41no—
407C2—81no—
408C2#1452908611yescharacteristic
409C2#1452911111yescharacteristic
410C2#1452915311yescharacteristic
subgroupG/H
centerC2×C4#10587639
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2991C2
socleC22×C17#386
prime radicalC2×#41×C17D4
cosocleC2×C42×C17C23
hypercenter#2991D17
hypocenterC17#8972
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2991

Complements

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

NH ≅ G/Ntype
2. #14529760C2semidirect
4. #14527204C2semidirect
5. #14526673C2semidirect
6. #14526616C2semidirect
10. #11763094C4semidirect
11. #11763089C4semidirect
12. #11763019C4semidirect
13. #11763014C4semidirect
287. C17#8972semidirect

Maximal subgroups

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

subgroupindex
#145388552
#145297602
C4×#105875082
#145272042
#145266732
#145266162
C17×#29912
#897217