Finite Group Databasebeta

← #16937836

Subgroups — #16937836

Order 4352.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533700C211yesmaximal, characteristic
2#14528911C211yesmaximal, characteristic, complemented
3#14528785C211yesmaximal, characteristic, complemented
4#14528785C211yesmaximal, characteristic, complemented
5C2×#11762536C211yesmaximal, characteristic, complemented
6C2×#11762536C211yesmaximal, characteristic, complemented
7C17×#1296C211yesmaximal, characteristic, complemented
8C2×#10587581—21no—
9C2×#10587581—21no—
10C2×C4×D68C2211yescharacteristic
11C2×C4×D68C2211yescharacteristic
12C2×#10587492—21no—
13C2×#10587492—21no—
14C2×C4×#3622C2211yescharacteristic
15#11762726—22no—
16#11762679C2211yescharacteristic
17#11762666—21no—
18#11762666—21no—
19#11762572—21no—
20#11762572—21no—
21#11762571—22no—
22#11762536—22no—
23#11762536—22no—
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C17×C4⋊C8C2211yescharacteristic
26C17×#384C2211yescharacteristic
27C22×D68—22no—
28C22×D68D411yescharacteristic
29C22×D68D411yescharacteristic
30C22×C4×D17—21no—
31C22×C4×D17—21no—
32C22×C8×C17—21no—
33C22×C8×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17D412yes—
37C2×C42×C17C2311yescharacteristic
38C2×#63227—22no—
39C2×#63227—22no—
40C2×#63227—21no—
41C2×#63227—21no—
42C2×C4⋊Dic17—21no—
43C2×C4⋊Dic17—21no—
44C2×C4⋊Dic17—21no—
45C2×C4⋊Dic17D411yescharacteristic
46C2×C4⋊Dic17D411yescharacteristic
47C22×#3622—21no—
48#10587581—42no—
49#10587581—42no—
50#10587581—42no—
51#10587581—42no—
52C4×D68—21no—
53C4×D68—21no—
54C4×D68—21no—
55C4×D68—21no—
56C4×D68—21no—
57C4×D68—21no—
58C4×D68—21no—
59C4×D68—21no—
60C17×C4⋊C8—21no—
61C17×C4⋊C8—21no—
62C17×C4⋊C8—21no—
63C17×C4⋊C8—21no—
64#10587502—22no—
65#10587492—42no—
66#10587492—42no—
67C4×#3622—21no—
68C4×#3622D412yescomplemented
69C23×D17—21no—
70C23×D17—21no—
71C22×C4×C17—22no—
72C22×C4×C17C2×D411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—41no—
78C2×D68—21no—
79C2×D68—21no—
80C2×D68—21no—
81C2×D68—21no—
82C2×D68—21no—
83C2×D68—21no—
84C2×D68—21no—
85C2×D68—21no—
86C2×D68—21no—
87C2×D68—21no—
88C2×D68—44no—
89C2×D68—44no—
90C2×D68—82no—
91C2×D68D812yes—
92C2×D68SD1612yes—
93C2×C4×D17—41no—
94C2×C4×D17—41no—
95C2×C4×D17—41no—
96C2×C4×D17—41no—
97C2×C4×D17—41no—
98C2×C4×D17—41no—
99C2×C4×D17—41no—
100C2×C4×D17—41no—
101C2×C4×D17—41no—
102C2×C4×D17—41no—
103C2×C4×D17—41no—
104C2×C4×D17—41no—
105C2×C8×C17—41no—
106C2×C8×C17—41no—
107C2×C8×C17—41no—
108C2×C8×C17—41no—
109C2×C8×C17—41no—
110C2×C8×C17—41no—
111C4⋊C4×C17—42no—
112C4⋊C4×C17—41no—
113C4⋊C4×C17—41no—
114C4⋊C4×C17—41no—
115C4⋊C4×C17—41no—
116C42×C17C2×D411yescharacteristic
117C42×C17#4111yescharacteristic
118C42×C17#4111yescharacteristic
119C42×C17#4111yescharacteristic
120#63227—44no—
121#63227—44no—
122#63227—41no—
123#63227—41no—
124#63227—41no—
125#63227—41no—
126C4⋊Dic17—21no—
127C4⋊Dic17—21no—
128C4⋊Dic17—21no—
129C4⋊Dic17—21no—
130C4⋊Dic17—42no—
131C4⋊Dic17—41no—
132C4⋊Dic17—41no—
133C4⋊Dic17—41no—
134C4⋊Dic17—41no—
135C2×#3622—22no—
136C2×#3622—41no—
137C2×#3622—41no—
138#10431—171nomaximal, Sylow
139C23×C17#12011yescharacteristic
140C22×D17—22no—
141C22×D17—22no—
142C22×D17—41no—
143C22×D17—41no—
144C22×D17—41no—
145C22×D17—41no—
146C22×D17—41no—
147C22×D17—41no—
148C22×D17—41no—
149C22×D17—41no—
150C22×D17—41no—
151C22×D17—41no—
152C22×D17—41no—
153C22×D17—41no—
154C2×C4×C17—21no—
155C2×C4×C17—21no—
156C2×C4×C17—42no—
157C2×C4×C17—42no—
158C2×C4×C17—42no—
159C2×C4×C17#12111yescharacteristic
160C2×C4×C17#12111yescharacteristic
161C2×C4×C17#12111yescharacteristic
162C2×C4×C17#12311yescharacteristic
163C2×C4×C17#12311yescharacteristic
164C2×C4×C17#12411yescharacteristic
165C2×C4×C17C2×D811yescharacteristic
166C2×C4×C17C2×SD1611yescharacteristic
167C2×C4×C17#13511yescharacteristic
168C2×C4×C17#13511yescharacteristic
169C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C17#13711yescharacteristic
173C2×Dic17—41no—
174C2×Dic17—41no—
175C2×Dic17—41no—
176C2×Dic17—41no—
177C2×Dic17—41no—
178C2×Dic17—41no—
179C2×Dic17—81no—
180C2×Dic17—81no—
181C2×Dic17—81no—
182D68—22no—
183D68—22no—
184D68—22no—
185D68—22no—
186D68—41no—
187D68—41no—
188D68—41no—
189D68—41no—
190D68—88no—
191C4×D17—81no—
192C4×D17—81no—
193C4×D17—81no—
194C4×D17—81no—
195C4×D17—81no—
196C4×D17—81no—
197C4×D17—81no—
198C4×D17—81no—
199C8×C17—81no—
200C8×C17—81no—
201#3622—42no—
202#2537—171no—
203#1834—171no—
204#1802—171no—
205#1802—171no—
206C2×D4⋊C8—171no—
207C2×D4⋊C8—171no—
208#1296D1711yescharacteristic, complemented
209C22×C17#39411yescharacteristic
210C22×C17#44711yescharacteristic
211C22×C17#44911yescharacteristic
212C22×C17#45011yescharacteristic
213C22×C17#45211yescharacteristic
214C22×C17#45411yescharacteristic
215C22×C17#45511yescharacteristic
216C2×D17—42no—
217C2×D17—42no—
218C2×D17—42no—
219C2×D17—42no—
220C2×D17—42no—
221C2×D17—42no—
222C2×D17—81no—
223C2×D17—81no—
224C2×D17—81no—
225C2×D17—81no—
226C2×D17—81no—
227C2×D17—81no—
228C2×D17—81no—
229C2×D17—81no—
230C4×C17—21no—
231C4×C17—21no—
232C4×C17—82no—
233C4×C17#46511yescharacteristic
234C4×C17#46611yescharacteristic
235C4×C17#46811yescharacteristic
236C4×C17#46911yescharacteristic
237C4×C17#48011yescharacteristic
238C4×C17#48111yescharacteristic
239C4×C17#48211yescharacteristic
240C4×C17#48211yescharacteristic
241Dic17—81no—
242Dic17—81no—
243Dic17—161no—
244C2×#121—341no—
245C2×#121—341no—
246C2×C4×D4—171no—
247C2×C4×D4—171no—
248C2×C4⋊C8C2×D1711yescharacteristic
249C2×C4⋊C8C2×D1711yescharacteristic
250C2×#102—341no—
251C2×#102—341no—
252C2×C4×C8—171no—
253#394—342no—
254#384—171no—
255#384C2×D1711yescharacteristic
256#380—341no—
257#380—341no—
258#340—341no—
259#340—341no—
260#340—342no—
261D4⋊C8—342no—
262D4⋊C8—342no—
263C2×C17#162511yescharacteristic
264C2×C17#163511yescharacteristic
265C2×C17#163911yescharacteristic
266C2×C17#164611yescharacteristic
267C2×C17#203311yescharacteristic
268C2×C17#203411yescharacteristic
269C2×C17#204011yescharacteristic
270D17—82no—
271D17—82no—
272C22×D4—171no—
273C22×D4—171no—
274C22×D4—342no—
275C23×C4—341no—
276C23×C4—341no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—341no—
280#121—682no—
281#121—682no—
282#121—682no—
283#121—682no—
284C4×D4—341no—
285C4×D4—341no—
286C4×D4—341no—
287C4×D4—341no—
288C4×D4—341no—
289C4×D4—341no—
290C4×D4—341no—
291C4×D4—341no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—171no—
295C2×C4⋊C4—171no—
296C2×C4⋊C4—341no—
297C2×C4⋊C4—341no—
298C2×C4⋊C4—341no—
299C2×C4⋊C4D6812yes—
300C2×C22⋊C4—342no—
301C2×C22⋊C4—342no—
302C2×C22⋊C4—341no—
303C2×C22⋊C4—341no—
304C2×C42C22×D1711yescharacteristic
305C4⋊C8—21no—
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309#102—682no—
310#102—682no—
311C4×C8—172no—
312C4×C8—341no—
313#95—342no—
314C17#1043111yescharacteristic, complemented, Sylow
315C24—341no—
316C24—341no—
317C2×D4—172no—
318C2×D4—172no—
319C2×D4—341no—
320C2×D4—341no—
321C2×D4—341no—
322C2×D4—341no—
323C2×D4—341no—
324C2×D4—341no—
325C2×D4—341no—
326C2×D4—341no—
327C2×D4—341no—
328C2×D4—341no—
329C2×D4—684no—
330C2×D4—684no—
331C2×D4—1362no—
332C22×C4—22no—
333C22×C4—341no—
334C22×C4—341no—
335C22×C4—681no—
336C22×C4—681no—
337C22×C4—681no—
338C22×C4—681no—
339C22×C4—681no—
340C22×C4—681no—
341C22×C4—681no—
342C22×C4—681no—
343C22×C4—681no—
344C22×C4—681no—
345C22×C4—681no—
346C22×C4—681no—
347C22×C4—681no—
348C22×C4C2×D6811yescharacteristic
349C22×C4D4×D1711yescharacteristic
350C22×C4D4×D1711yescharacteristic
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—342no—
358C2×C8—681no—
359C2×C8—681no—
360C4⋊C4—42no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—341no—
366C4⋊C4—341no—
367C4⋊C4—341no—
368C4⋊C4—341no—
369C4⋊C4—682no—
370C4⋊C4—681no—
371C4⋊C4—681no—
372C4⋊C4—681no—
373C4⋊C4—681no—
374C22⋊C4—684no—
375C22⋊C4—684no—
376C22⋊C4—681no—
377C22⋊C4—681no—
378C22⋊C4—681no—
379C22⋊C4—681no—
380C42#6325211yescharacteristic
381C42#6325211yescharacteristic
382C42D4×D1711yescharacteristic
383C42#6325611yescharacteristic
384C23—342no—
385C23—342no—
386C23—681no—
387C23—681no—
388C23—681no—
389C23—681no—
390C23—681no—
391C23—681no—
392C23—681no—
393C23—681no—
394C23—681no—
395C23—681no—
396C23—681no—
397C23—681no—
398C23#1058756811yescharacteristic
399D4—342no—
400D4—342no—
401D4—342no—
402D4—342no—
403D4—681no—
404D4—681no—
405D4—681no—
406D4—681no—
407D4—1368no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—681no—
414C2×C4—681no—
415C2×C4—681no—
416C2×C4—681no—
417C2×C4—681no—
418C2×C4—681no—
419C2×C4—1361no—
420C2×C4—1361no—
421C2×C4—1361no—
422C2×C4—1361no—
423C2×C4—1361no—
424C2×C4—1361no—
425C2×C4—1361no—
426C2×C4—1361no—
427C2×C4—1361no—
428C2×C4—1361no—
429C2×C4—1361no—
430C2×C4#1058756111yescharacteristic
431C2×C4#1058757011yescharacteristic
432C2×C4#1058757011yescharacteristic
433C2×C4#1058758011yescharacteristic
434C2×C4#1058758011yescharacteristic
435C2×C4#1058758111yescharacteristic
436C2×C4D8×D1711yescharacteristic
437C2×C4#1058759711yescharacteristic
438C2×C4SD16×D1711yescharacteristic
439C2×C4#1058760011yescharacteristic
440C2×C4#1058760011yescharacteristic
441C2×C4#1058760211yescharacteristic
442C2×C4#1058760411yescharacteristic
443C2×C4#1058760511yescharacteristic
444C8—81no—
445C8—81no—
446C8—682no—
447C22—682no—
448C22—682no—
449C22—682no—
450C22—682no—
451C22—682no—
452C22—682no—
453C22—1361no—
454C22—1361no—
455C22—1361no—
456C22—1361no—
457C22—1361no—
458C22—1361no—
459C22—1361no—
460C22—1361no—
461C22#1176272711yescharacteristic
462C22#1176294411yescharacteristic
463C22#1176295711yescharacteristic
464C22#1176296111yescharacteristic
465C22#1176297411yescharacteristic
466C22#1176298411yescharacteristic
467C22#1176298911yescharacteristic
468C4—21no—
469C4—21no—
470C4—82no—
471C4—2721no—
472C4—1361no—
473C4—1361no—
474C4#1176304111yescharacteristic
475C4#1176304411yescharacteristic
476C4#1176305811yescharacteristic
477C4#1176306111yescharacteristic
478C4#1176312411yescharacteristic
479C4#1176312911yescharacteristic
480C4#1176313511yescharacteristic
481C4#1176313611yescharacteristic
482C2—1362no—
483C2—1362no—
484C2#1452787411yescharacteristic
485C2#1452793611yescharacteristic
486C2#1452796411yescharacteristic
487C2#1452801311yescharacteristic
488C2#1452996911yescharacteristic
489C2#1452997611yescharacteristic
490C2#1453001411yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socleC23×C17#120
prime radical#14533700C2
hypercenter#1296D17
hypocenterC17#10431
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #14528911C2semidirect
3. #14528785C2semidirect
4. #14528785C2semidirect
5. C2×#11762536C2semidirect
6. C2×#11762536C2semidirect
7. C17×#1296C2semidirect
68. C4×#3622D4semidirect
208. #1296D17semidirect
314. C17#10431semidirect

Maximal subgroups

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

subgroupindex
#145337002
#145289112
#145287852
C2×#117625362
C17×#12962
#1043117