Finite Group Databasebeta

← #16937706

Subgroups — #16937706

Order 4352.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533786C211yesmaximal, characteristic
2#14529590C211yesmaximal, characteristic
3#14529542C211yesmaximal, characteristic, complemented
4#14528790C211yesmaximal, characteristic, complemented
5C2×#11762552C211yesmaximal, characteristic
6C2×#11762541C211yesmaximal, characteristic, complemented
7C17×#1279C211yesmaximal, characteristic, complemented
8C2×#10587560C2211yescharacteristic
9C2×#10587561—21no—
10C2×C4×Dic34C2211yescharacteristic
11C2×#10587478—21no—
12C2×C4⋊#3622C2211yescharacteristic
13C2×#10587487—21no—
14C2×#10587492—22no—
15#11762727—22no—
16#11762711—21no—
17#11762710—21no—
18#11762710—21no—
19#11762679C2211yescharacteristic
20#11762572—21no—
21#11762571—21no—
22#11762552—22no—
23#11762541—22no—
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C17C2211yescharacteristic
26C4×C4⋊C4×C17C2211yescharacteristic
27C22×D68—21no—
28C22×D68—21no—
29C22×D68D412yes—
30C22×Dic34D411yescharacteristic
31C22×C8×C17—21no—
32C22×C8×C17—21no—
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C4⋊C4×C17D411yescharacteristic
35C2×C42×C17—21no—
36C2×C42×C17C2311yescharacteristic
37C2×#63227—22no—
38C2×#63227—22no—
39C2×#63227—22no—
40C2×#63227—22no—
41C2×C4⋊Dic17—21no—
42C2×C4⋊Dic17—21no—
43C2×C4⋊Dic17—21no—
44C2×C4⋊Dic17D411yescharacteristic
45C2×#63225—21no—
46C2×C4×Dic17—21no—
47C22×#3622—21no—
48#10587561—42no—
49#10587561—42no—
50#10587560—21no—
51#10587560—21no—
52#10587560—21no—
53#10587560—21no—
54C4×Dic34—21no—
55C4×Dic34—21no—
56C4×Dic34—21no—
57C4×Dic34—21no—
58C17×C4⋊C8—21no—
59C17×C4⋊C8—21no—
60C4×C8×C17—21no—
61C4×C8×C17—21no—
62C17×#95—21no—
63#10587492—44no—
64#10587487—42no—
65#10587478—42no—
66C4⋊#3622—21no—
67C4⋊#3622D412yes—
68C23×D17—22no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17C2×D411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—41no—
77C2×D68—22no—
78C2×D68—22no—
79C2×D68—42no—
80C2×D68—42no—
81C2×D68—41no—
82C2×D68—41no—
83C2×D68—41no—
84C2×D68—41no—
85C2×D68—41no—
86C2×D68—41no—
87C2×D68—41no—
88C2×D68—41no—
89C2×D68—41no—
90C2×D68—41no—
91C2×D68—41no—
92C2×D68—41no—
93C2×Dic34—21no—
94C2×Dic34—21no—
95C2×Dic34—21no—
96C2×Dic34—21no—
97C2×Dic34—21no—
98C2×Dic34D812yes—
99C2×C8×C17—22no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C2×C8×C17—41no—
103C2×C8×C17—41no—
104C2×C8×C17—41no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—21no—
108C4⋊C4×C17—21no—
109C42×C17—41no—
110C42×C17—41no—
111C42×C17C2×D411yescharacteristic
112C42×C17#4111yescharacteristic
113C42×C17#4111yescharacteristic
114C42×C17#4111yescharacteristic
115#63227—44no—
116#63227—44no—
117#63227—82no—
118#63227—82no—
119C4⋊Dic17—21no—
120C4⋊Dic17—21no—
121C4⋊Dic17—42no—
122C4⋊Dic17—41no—
123C4⋊Dic17—41no—
124C4⋊Dic17—41no—
125C4⋊Dic17—41no—
126#63225—41no—
127#63225—41no—
128C4×Dic17—41no—
129C4×Dic17—41no—
130C2×#3622—22no—
131C2×#3622—41no—
132C2×#3622—41no—
133#10411—171nomaximal, Sylow
134C23×C17#12011yescharacteristic
135C22×D17—42no—
136C22×D17—42no—
137C22×D17—42no—
138C22×D17—42no—
139C22×D17—42no—
140C22×D17—42no—
141C22×D17—42no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—41no—
150C2×C4×C17#12111yescharacteristic
151C2×C4×C17#12111yescharacteristic
152C2×C4×C17#12111yescharacteristic
153C2×C4×C17#12311yescharacteristic
154C2×C4×C17#12311yescharacteristic
155C2×C4×C17#12411yescharacteristic
156C2×C4×C17C2×D811yescharacteristic
157C2×C4×C17#13511yescharacteristic
158C2×C4×C17#13511yescharacteristic
159C2×C4×C17#13511yescharacteristic
160C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C17#13711yescharacteristic
163C2×C4×C17#13711yescharacteristic
164C2×Dic17—22no—
165C2×Dic17—41no—
166C2×Dic17—41no—
167C2×Dic17—41no—
168C2×Dic17—41no—
169C2×Dic17—41no—
170C2×Dic17—81no—
171C2×Dic17—81no—
172C2×Dic17—81no—
173D68—44no—
174D68—82no—
175D68—81no—
176D68—81no—
177D68—81no—
178D68—81no—
179D68—81no—
180D68—81no—
181D68—81no—
182D68—81no—
183Dic34—22no—
184Dic34—22no—
185Dic34—41no—
186Dic34—41no—
187C8×C17—42no—
188C8×C17—81no—
189#3622—42no—
190#2548—171no—
191#1957—171no—
192#1947—171no—
193#1803—171no—
194C2×#331—171no—
195C2×Q8⋊C8—171no—
196#1279D1711yescharacteristic, complemented
197C22×C17#39411yescharacteristic
198C22×C17#44711yescharacteristic
199C22×C17#44911yescharacteristic
200C22×C17#45211yescharacteristic
201C22×C17#45211yescharacteristic
202C22×C17#45311yescharacteristic
203C22×C17#45511yescharacteristic
204C2×D17—82no—
205C2×D17—82no—
206C2×D17—82no—
207C2×D17—82no—
208C2×D17—82no—
209C2×D17—82no—
210C2×D17—82no—
211C4×C17—21no—
212C4×C17—21no—
213C4×C17—81no—
214C4×C17—81no—
215C4×C17#46311yescharacteristic
216C4×C17#46411yescharacteristic
217C4×C17#46611yescharacteristic
218C4×C17#46811yescharacteristic
219C4×C17#48011yescharacteristic
220C4×C17#48211yescharacteristic
221C4×C17#48811yescharacteristic
222C4×C17#48911yescharacteristic
223Dic17—42no—
224Dic17—81no—
225Dic17—161no—
226C2×#127—171no—
227C2×#124—341no—
228C2×C4×Q8—171no—
229C2×#107—341no—
230C2×C4⋊C8—171no—
231C2×C4⋊C8C2×D1711yescharacteristic
232C2×#103—341no—
233C2×#102—342no—
234C2×C4×C8C2×D1711yescharacteristic
235#394—342no—
236#390—341no—
237#390—341no—
238#390—341no—
239#384—171no—
240C4×C4⋊C4C2×D1711yescharacteristic
241#340—341no—
242#340—341no—
243#331—342no—
244Q8⋊C8—342no—
245C2×C17#162111yescharacteristic
246C2×C17#163011yescharacteristic
247C2×C17#164011yescharacteristic
248C2×C17#164111yescharacteristic
249C2×C17#203311yescharacteristic
250C2×C17#203711yescharacteristic
251C2×C17#204211yescharacteristic
252D17—162no—
253C22×Q8—171no—
254C22×D4—172no—
255C22×D4—341no—
256C22×D4—341no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—341no—
260#127—341no—
261#127—341no—
262#127—341no—
263#127—341no—
264#124—682no—
265#124—682no—
266C4×Q8—341no—
267C4×Q8—341no—
268C4×Q8—341no—
269C4×Q8—341no—
270C2×C4⋊C4—171no—
271C2×C4⋊C4—341no—
272C2×C4⋊C4—341no—
273C2×C4⋊C4—341no—
274C2×C4⋊C4—341no—
275C2×C4⋊C4D6811yescharacteristic
276C2×C4⋊C4D6811yescharacteristic
277C2×C22⋊C4—342no—
278C2×C22⋊C4—342no—
279C2×C22⋊C4—342no—
280C2×C22⋊C4—342no—
281C2×C42—21no—
282C2×C42—341no—
283C2×C42C22×D1711yescharacteristic
284#107—682no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—172no—
288C4⋊C8—341no—
289#103—682no—
290#102—684no—
291C4×C8—21no—
292C4×C8—21no—
293#95—21no—
294C17#1041111yescharacteristic, complemented, Sylow
295C24—342no—
296C2×Q8—172no—
297C2×Q8—341no—
298C2×Q8—341no—
299C2×Q8—341no—
300C2×Q8—341no—
301C2×Q8—341no—
302C2×D4—342no—
303C2×D4—342no—
304C2×D4—682no—
305C2×D4—682no—
306C2×D4—681no—
307C2×D4—681no—
308C2×D4—681no—
309C2×D4—681no—
310C2×D4—681no—
311C2×D4—681no—
312C2×D4—681no—
313C2×D4—681no—
314C2×D4—681no—
315C2×D4—681no—
316C2×D4—681no—
317C2×D4—681no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—341no—
321C22×C4—341no—
322C22×C4—681no—
323C22×C4C2×D6811yescharacteristic
324C22×C4D4×D1711yescharacteristic
325C22×C4D4×D1711yescharacteristic
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—342no—
333C2×C8—681no—
334C2×C8—681no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—341no—
340C4⋊C4—341no—
341C4⋊C4—682no—
342C4⋊C4—681no—
343C4⋊C4—681no—
344C4⋊C4—681no—
345C4⋊C4—681no—
346C4⋊C4—681no—
347C4⋊C4—681no—
348C22⋊C4—684no—
349C22⋊C4—684no—
350C22⋊C4—1362no—
351C22⋊C4—1362no—
352C42—41no—
353C42—41no—
354C42—681no—
355C42—681no—
356C42#6325211yescharacteristic
357C42#6325211yescharacteristic
358C42D4×D1711yescharacteristic
359C42#6325611yescharacteristic
360C23—682no—
361C23—682no—
362C23—682no—
363C23—682no—
364C23—682no—
365C23—682no—
366C23—682no—
367C23#1058756811yescharacteristic
368Q8—342no—
369Q8—342no—
370Q8—681no—
371Q8—681no—
372D4—684no—
373D4—1362no—
374D4—1361no—
375D4—1361no—
376D4—1361no—
377D4—1361no—
378D4—1361no—
379D4—1361no—
380D4—1361no—
381D4—1361no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—342no—
391C2×C4—681no—
392C2×C4—681no—
393C2×C4—681no—
394C2×C4—681no—
395C2×C4—681no—
396C2×C4—1361no—
397C2×C4—1361no—
398C2×C4—1361no—
399C2×C4#1058756111yescharacteristic
400C2×C4#1058757011yescharacteristic
401C2×C4#1058757011yescharacteristic
402C2×C4#1058758011yescharacteristic
403C2×C4#1058758011yescharacteristic
404C2×C4#1058758111yescharacteristic
405C2×C4#1058759011yescharacteristic
406C2×C4#1058759011yescharacteristic
407C2×C4#1058759411yescharacteristic
408C2×C4#1058759511yescharacteristic
409C2×C4D8×D1711yescharacteristic
410C2×C4#1058760011yescharacteristic
411C2×C4#1058760211yescharacteristic
412C2×C4#1058760411yescharacteristic
413C8—42no—
414C8—81no—
415C8—682no—
416C22—1362no—
417C22—1362no—
418C22—1362no—
419C22—1362no—
420C22—1362no—
421C22—1362no—
422C22—1362no—
423C22#1176272711yescharacteristic
424C22#1176294411yescharacteristic
425C22#1176295611yescharacteristic
426C22#1176297311yescharacteristic
427C22#1176297411yescharacteristic
428C22#1176297811yescharacteristic
429C22#1176298811yescharacteristic
430C4—21no—
431C4—21no—
432C4—81no—
433C4—81no—
434C4—2721no—
435C4—682no—
436C4—1361no—
437C4#1176302511yescharacteristic
438C4#1176303211yescharacteristic
439C4#1176304411yescharacteristic
440C4#1176305811yescharacteristic
441C4#1176312411yescharacteristic
442C4#1176313511yescharacteristic
443C4#1176316411yescharacteristic
444C4#1176316911yescharacteristic
445C2—2722no—
446C2#1452785211yescharacteristic
447C2#1452790711yescharacteristic
448C2#1452797211yescharacteristic
449C2#1452798011yescharacteristic
450C2#1452996911yescharacteristic
451C2#1452999711yescharacteristic
452C2#1453002611yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1279C2
socleC23×C17#120
prime radicalC2×#10587560C22
hypercenter#1279D17
hypocenterC17#10411
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #14529542C2semidirect
4. #14528790C2semidirect
6. C2×#11762541C2semidirect
7. C17×#1279C2semidirect
196. #1279D17semidirect
294. C17#10411semidirect

Maximal subgroups

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

subgroupindex
#145337862
#145295902
#145295422
#145287902
C2×#117625522
C2×#117625412
C17×#12792
#1041117