Finite Group Databasebeta

← #16938207

Subgroups — #16938207

Order 4352.

490 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
1C2×#11763090C211yesmaximal, characteristic
2#14529586C211yesmaximal, characteristic, complemented
3#14529578C211yesmaximal, characteristic
4#14528785C211yesmaximal, characteristic
5C2×#11762554C211yesmaximal, characteristic, complemented
6#14526668C211yesmaximal, characteristic, complemented
7C2×C17×#335C211yesmaximal, characteristic, complemented
8C2×#10587555C2211yescharacteristic
9C2×C4×D68C2211yescharacteristic
10#11763090—22no—
11#11763090—22no—
12C2×#10587489—21no—
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587487—21no—
15C2×#10587487—21no—
16C2×#10587492—21no—
17C2×#10587492—21no—
18C2×#10587491—21no—
19C2×#10587491—21no—
20#11762679C2211yescharacteristic
21#11762572—21no—
22#11762554—22no—
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C17C2211yescharacteristic
26C17×#335—22no—
27C22×D68D411yescharacteristic
28C22×C4×D17—21no—
29C22×Dic34—21no—
30C22×C8×C17—21no—
31C22×C8×C17—21no—
32C22×C8×C17D411yescharacteristic
33C22×C8×C17D411yescharacteristic
34C2×C42×C17C2311yescharacteristic
35C2×#63227—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17—21no—
41C2×C4⋊Dic17D411yescharacteristic
42C22×#3622—21no—
43C4×D68—21no—
44C4×D68—21no—
45C4×D68—21no—
46C4×D68—21no—
47#10587555—21no—
48#10587555—21no—
49#10587555—21no—
50#10587555D412yes—
51C17×C4⋊C8—21no—
52C17×C4⋊C8—21no—
53C17×C4⋊C8—21no—
54C17×C4⋊C8D412yes—
55C4×C8×C17—21no—
56C4×C8×C17—21no—
57#10587492—24no—
58#10587492—42no—
59#10587491—42no—
60#10587491—42no—
61#10587489—24no—
62#10587487—42no—
63#10587487—42no—
64C4⋊#3622—21no—
65C4⋊#3622—21no—
66C23×D17—21no—
67C22×C4×C17C2×D411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17#4111yescharacteristic
70C22×Dic17—21no—
71C22×Dic17—41no—
72C22×Dic17—41no—
73C2×D68—21no—
74C2×D68—21no—
75C2×D68—21no—
76C2×D68—21no—
77C2×D68—21no—
78C2×D68Q1612yes—
79C2×C4×D17—41no—
80C2×C4×D17—41no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17—41no—
84C2×C4×D17—41no—
85C2×Dic34—22no—
86C2×Dic34—41no—
87C2×Dic34—41no—
88C2×Dic34—41no—
89C2×Dic34—41no—
90C2×Dic34—41no—
91C2×C8×C17—21no—
92C2×C8×C17—21no—
93C2×C8×C17—22no—
94C2×C8×C17—21no—
95C2×C8×C17—21no—
96C2×C8×C17—21no—
97C2×C8×C17—41no—
98C2×C8×C17—41no—
99C2×C8×C17—41no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C2×C8×C17D812yes—
103C42×C17C2×D411yescharacteristic
104C42×C17C2×D411yescharacteristic
105C42×C17#4111yescharacteristic
106C42×C17#4111yescharacteristic
107#63227—41no—
108#63227—41no—
109C4⋊Dic17—21no—
110C4⋊Dic17—22no—
111C4⋊Dic17—22no—
112C4⋊Dic17—21no—
113C4⋊Dic17—41no—
114C4⋊Dic17—41no—
115C4⋊Dic17—41no—
116C4⋊Dic17—41no—
117C4⋊Dic17—41no—
118C4⋊Dic17—41no—
119C4⋊Dic17—81no—
120C2×#3622—41no—
121C2×#3622—41no—
122C2×#3622—41no—
123#10485—171nomaximal, Sylow
124C23×C17#12111yescharacteristic
125C22×D17—22no—
126C22×D17—41no—
127C22×D17—41no—
128C22×D17—41no—
129C22×D17—41no—
130C22×D17—41no—
131C22×D17—41no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17#12011yescharacteristic
135C2×C4×C17#12111yescharacteristic
136C2×C4×C17#12111yescharacteristic
137C2×C4×C17#12311yescharacteristic
138C2×C4×C17#12311yescharacteristic
139C2×C4×C17#12411yescharacteristic
140C2×C4×C17C2×D811yescharacteristic
141C2×C4×C17C2×Q1611yescharacteristic
142C2×C4×C17#13511yescharacteristic
143C2×C4×C17#13511yescharacteristic
144C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C17#13711yescharacteristic
148C2×Dic17—42no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—81no—
153C2×Dic17—81no—
154C2×Dic17—81no—
155C2×Dic17—81no—
156C2×Dic17—81no—
157D68—22no—
158D68—22no—
159D68—41no—
160D68—41no—
161C4×D17—81no—
162C4×D17—81no—
163C4×D17—81no—
164C4×D17—81no—
165Dic34—42no—
166Dic34—42no—
167Dic34—81no—
168Dic34—81no—
169C8×C17—22no—
170C8×C17—42no—
171C8×C17—41no—
172C8×C17—81no—
173#3622—81no—
174C2×#474—171no—
175#1956—171no—
176#1954—171no—
177#1802—171no—
178C2×#335D1711yescharacteristic, complemented
179C2×#332—171no—
180#1296—171no—
181C22×C17#39411yescharacteristic
182C22×C17#45911yescharacteristic
183C22×C17#46311yescharacteristic
184C22×C17#46711yescharacteristic
185C22×C17#46811yescharacteristic
186C22×C17#47111yescharacteristic
187C22×C17#47311yescharacteristic
188C2×D17—42no—
189C2×D17—42no—
190C2×D17—42no—
191C2×D17—81no—
192C2×D17—81no—
193C2×D17—81no—
194C2×D17—81no—
195C4×C17—21no—
196C4×C17—21no—
197C4×C17#44911yescharacteristic
198C4×C17#45111yescharacteristic
199C4×C17#45911yescharacteristic
200C4×C17#46311yescharacteristic
201C4×C17#46611yescharacteristic
202C4×C17#46911yescharacteristic
203C4×C17#48411yescharacteristic
204C4×C17#48511yescharacteristic
205Dic17—82no—
206Dic17—81no—
207Dic17—161no—
208C2×C4⋊Q8—171no—
209C2×C4×D4—171no—
210#474—342no—
211#474—342no—
212C2×#107—341no—
213C2×C4⋊C8—171no—
214C2×C4⋊C8C2×D1711yescharacteristic
215C2×C4⋊C8C2×D1711yescharacteristic
216C2×#103—341no—
217C2×#103—341no—
218C2×#102—341no—
219C2×#102—341no—
220C2×C22⋊C8—341no—
221C2×C22⋊C8—341no—
222C2×C4×C8C2×D1711yescharacteristic
223#384—171no—
224#340—341no—
225#335—22no—
226#332—342no—
227C2×C17#166911yescharacteristic
228C2×C17#168311yescharacteristic
229C2×C17#168511yescharacteristic
230C2×C17#169911yescharacteristic
231C2×C17#203611yescharacteristic
232C2×C17#205211yescharacteristic
233C2×C17#205411yescharacteristic
234D17—82no—
235C22×Q8—341no—
236C22×D4—171no—
237C23×C4—341no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—341no—
241C22×C8D6811yescharacteristic
242C22×C8D6811yescharacteristic
243C4⋊Q8—172no—
244C4⋊Q8—341no—
245C4⋊Q8—341no—
246C4⋊Q8—341no—
247C4×D4—341no—
248C4×D4—341no—
249C4×D4—341no—
250C4×D4—341no—
251C2×C4⋊C4—171no—
252C2×C4⋊C4—341no—
253C2×C4⋊C4—341no—
254C2×C4⋊C4—341no—
255C2×C4⋊C4—341no—
256C2×C4⋊C4—341no—
257C2×C22⋊C4—341no—
258C2×C42C22×D1711yescharacteristic
259#107—344no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—341no—
264C4⋊C8—341no—
265C4⋊C8C22⋊D1712yes—
266#103—682no—
267#103—682no—
268#102—344no—
269#102—682no—
270C22⋊C8—682no—
271C22⋊C8—682no—
272C4×C8—21no—
273C4×C8—21no—
274C17#1048511yescharacteristic, complemented, Sylow
275C24—341no—
276C2×Q8—342no—
277C2×Q8—681no—
278C2×Q8—681no—
279C2×Q8—681no—
280C2×Q8—681no—
281C2×Q8—681no—
282C2×D4—172no—
283C2×D4—341no—
284C2×D4—341no—
285C2×D4—341no—
286C2×D4—341no—
287C2×D4—341no—
288C22×C4—341no—
289C22×C4—681no—
290C22×C4—681no—
291C22×C4—681no—
292C22×C4—681no—
293C22×C4—681no—
294C22×C4—681no—
295C22×C4—681no—
296C22×C4—681no—
297C22×C4C2×D6811yescharacteristic
298C22×C4D4×D1711yescharacteristic
299C22×C4#6325611yescharacteristic
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—681no—
312C2×C8—681no—
313C2×C8—681no—
314C2×C8D13612yes—
315C4⋊C4—341no—
316C4⋊C4—342no—
317C4⋊C4—342no—
318C4⋊C4—341no—
319C4⋊C4—681no—
320C4⋊C4—681no—
321C4⋊C4—681no—
322C4⋊C4—681no—
323C4⋊C4—681no—
324C4⋊C4—681no—
325C4⋊C4—1361no—
326C22⋊C4—681no—
327C22⋊C4—681no—
328C42#6325211yescharacteristic
329C42D4×D1711yescharacteristic
330C42#6325611yescharacteristic
331C42C2×C22⋊D1711yescharacteristic
332C23—342no—
333C23—681no—
334C23—681no—
335C23—681no—
336C23—681no—
337C23—681no—
338C23—681no—
339C23#1058758111yescharacteristic
340Q8—682no—
341Q8—682no—
342Q8—1361no—
343Q8—1361no—
344D4—342no—
345D4—342no—
346D4—681no—
347D4—681no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—681no—
351C2×C4—682no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4—1361no—
355C2×C4—1361no—
356C2×C4—1361no—
357C2×C4—1361no—
358C2×C4—1361no—
359C2×C4—1361no—
360C2×C4—1361no—
361C2×C4—1361no—
362C2×C4—1361no—
363C2×C4#1058758011yescharacteristic
364C2×C4#1058758011yescharacteristic
365C2×C4#1058758111yescharacteristic
366C2×C4C2×D13611yescharacteristic
367C2×C4#1058759011yescharacteristic
368C2×C4#1058759411yescharacteristic
369C2×C4#1058759411yescharacteristic
370C2×C4#1058759711yescharacteristic
371C2×C4#1058759811yescharacteristic
372C2×C4Q16×D1711yescharacteristic
373C2×C4#1058760411yescharacteristic
374C2×C4#1058761611yescharacteristic
375C2×C4#1058762311yescharacteristic
376C2×C4#1058763311yescharacteristic
377C8—22no—
378C8—42no—
379C8—41no—
380C8—81no—
381C8—1361no—
382C22—682no—
383C22—682no—
384C22—682no—
385C22—1361no—
386C22—1361no—
387C22—1361no—
388C22—1361no—
389C22#1176272611yescharacteristic
390C22#1176300511yescharacteristic
391C22#1176302511yescharacteristic
392C22#1176305111yescharacteristic
393C22#1176305611yescharacteristic
394C22#1176307311yescharacteristic
395C22#1176308511yescharacteristic
396C4—21no—
397C4—21no—
398C4—2721no—
399C4—1361no—
400C4—1362no—
401C4#1176295111yescharacteristic
402C4#1176296311yescharacteristic
403C4#1176300511yescharacteristic
404C4#1176302511yescharacteristic
405C4#1176304511yescharacteristic
406C4#1176306211yescharacteristic
407C4#1176314611yescharacteristic
408C4#1176315211yescharacteristic
409C2—1362no—
410C2#1452815011yescharacteristic
411C2#1452823611yescharacteristic
412C2#1452825011yescharacteristic
413C2#1452833211yescharacteristic
414C2#1452998911yescharacteristic
415C2#1453008511yescharacteristic
416C2#1453009511yescharacteristic
subgroupG/H
centerC23#10587581
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#335C2
socleC23×C17#121
prime radicalC22×D68D4
hypercenterC2×#335D17
hypocenterC17#10485
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #14529586C2semidirect
5. C2×#11762554C2semidirect
6. #14526668C2semidirect
7. C2×C17×#335C2semidirect
178. C2×#335D17semidirect
274. C17#10485semidirect

Maximal subgroups

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

subgroupindex
C2×#117630902
#145295862
#145295782
#145287852
C2×#117625542
#145266682
C2×C17×#3352
#1048517