Finite Group Databasebeta

← #16937679

Subgroups — #16937679

Order 4352.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529591C211yesmaximal, characteristic, complemented
2#14529542C211yesmaximal, characteristic, complemented
3#14528784C211yesmaximal, characteristic, complemented
4C2×#11762553C211yesmaximal, characteristic, complemented
5C2×D4⋊#3622C211yesmaximal, characteristic, complemented
6#14526625C211yesmaximal, characteristic, complemented
7C17×#2541C211yesmaximal, characteristic
8C2×#10587478—21no—
9C2×C4⋊#3622C2211yescharacteristic
10C2×C4⋊#3622C2211yescharacteristic
11C2×#10587503—21no—
12C2×#10587503—22no—
13C2×C4×#3622C2211yescharacteristic
14#11762679C2211yescharacteristic
15#11762571—21no—
16#11762571—21no—
17#11762553—22no—
18D4⋊#3622—22no—
19C2×C17×#127—21no—
20C2×C17×#127C2211yescharacteristic
21C2×C17×#121—21no—
22C2×C17×#121—21no—
23C2×C4×D4×C17C2211yescharacteristic
24C17×#392—22no—
25C17×#390—21no—
26C4×C4⋊C4×C17C2211yescharacteristic
27C22×D4×C17—22no—
28C22×D4×C17—22no—
29C22×D4×C17—21no—
30C22×D4×C17—21no—
31C22×D4×C17D411yescharacteristic
32C22×D4×C17D412yes—
33C23×C4×C17—21no—
34C17×#127—21no—
35C17×#127—21no—
36C17×#127—21no—
37C17×#127—21no—
38C17×#127—42no—
39C17×#127—42no—
40C17×#121—42no—
41C17×#121—42no—
42C17×#121—42no—
43C17×#121—42no—
44C4×D4×C17—21no—
45C4×D4×C17—21no—
46C4×D4×C17—21no—
47C4×D4×C17—21no—
48C2×C4⋊C4×C17D411yescharacteristic
49C2×C4⋊C4×C17D411yescharacteristic
50C2×C4⋊C4×C17D411yescharacteristic
51C2×C22⋊C4×C17—22no—
52C2×C22⋊C4×C17—22no—
53C2×C22⋊C4×C17—21no—
54C2×C42×C17—21no—
55C2×C42×C17C2311yescharacteristic
56C2×C4⋊Dic17—21no—
57C2×C4⋊Dic17—21no—
58C2×C4⋊Dic17—21no—
59C22×#3622—21no—
60C22×#3622—21no—
61C22×#3622—21no—
62C17×#95—21no—
63#10587503—44no—
64#10587503—42no—
65#10587478—42no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68C4⋊#3622—21no—
69C4⋊#3622D412yescomplemented
70C4×#3622—21no—
71C4×#3622—21no—
72C24×C17—21no—
73C24×C17—22no—
74C2×D4×C17—21no—
75C2×D4×C17—22no—
76C2×D4×C17—21no—
77C2×D4×C17—22no—
78C2×D4×C17—21no—
79C2×D4×C17—21no—
80C2×D4×C17—21no—
81C2×D4×C17—42no—
82C2×D4×C17—42no—
83C2×D4×C17—44no—
84C2×D4×C17—44no—
85C2×D4×C17—44no—
86C2×D4×C17—44no—
87C2×D4×C17—41no—
88C2×D4×C17—41no—
89C2×D4×C17—41no—
90C2×D4×C17—41no—
91C2×D4×C17—41no—
92C2×D4×C17—41no—
93C2×D4×C17—41no—
94C2×D4×C17—41no—
95C2×D4×C17—41no—
96C2×D4×C17—41no—
97C2×D4×C17—41no—
98C2×D4×C17—41no—
99C2×D4×C17—82no—
100C2×D4×C17—82no—
101C2×D4×C17D812yes—
102C22×C4×C17—21no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—41no—
106C22×C4×C17—41no—
107C22×C4×C17—41no—
108C22×C4×C17—41no—
109C22×C4×C17—41no—
110C22×C4×C17—41no—
111C22×C4×C17C2×D411yescharacteristic
112C22×C4×C17C2×D411yescharacteristic
113C22×C4×C17C2×D411yescharacteristic
114C22×Dic17—41no—
115C4⋊C4×C17—21no—
116C4⋊C4×C17—21no—
117C4⋊C4×C17—21no—
118C4⋊C4×C17—21no—
119C4⋊C4×C17D812yes—
120C4⋊C4×C17SD1612yes—
121C22⋊C4×C17—44no—
122C22⋊C4×C17—44no—
123C22⋊C4×C17—41no—
124C22⋊C4×C17—41no—
125C42×C17—41no—
126C42×C17—41no—
127C42×C17C2×D411yescharacteristic
128C42×C17#4111yescharacteristic
129C42×C17#4111yescharacteristic
130C42×C17#4111yescharacteristic
131C4⋊Dic17—42no—
132C4⋊Dic17—41no—
133C4⋊Dic17—41no—
134C4⋊Dic17—41no—
135C4⋊Dic17—41no—
136C2×#3622—22no—
137C2×#3622—22no—
138C2×#3622—41no—
139C2×#3622—41no—
140C2×#3622—41no—
141C2×#3622—41no—
142C2×#3622—41no—
143C2×#3622—41no—
144C2×#3622—41no—
145#10408—171nomaximal, Sylow
146C23×C17—22no—
147C23×C17—41no—
148C23×C17—41no—
149C23×C17—41no—
150C23×C17—41no—
151C23×C17—41no—
152C23×C17—41no—
153C23×C17—42no—
154C23×C17—42no—
155C23×C17—42no—
156C23×C17—42no—
157C23×C17—42no—
158C23×C17—42no—
159C23×C17—42no—
160C23×C17#12011yescharacteristic
161D4×C17—22no—
162D4×C17—22no—
163D4×C17—44no—
164D4×C17—41no—
165D4×C17—41no—
166D4×C17—82no—
167D4×C17—88no—
168D4×C17—88no—
169D4×C17—81no—
170D4×C17—81no—
171D4×C17—81no—
172D4×C17—81no—
173D4×C17—81no—
174D4×C17—81no—
175D4×C17—81no—
176D4×C17—81no—
177C2×C4×C17—21no—
178C2×C4×C17—21no—
179C2×C4×C17—22no—
180C2×C4×C17—22no—
181C2×C4×C17—41no—
182C2×C4×C17—41no—
183C2×C4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—41no—
186C2×C4×C17—41no—
187C2×C4×C17—41no—
188C2×C4×C17—81no—
189C2×C4×C17—81no—
190C2×C4×C17—81no—
191C2×C4×C17—81no—
192C2×C4×C17#12111yescharacteristic
193C2×C4×C17#12111yescharacteristic
194C2×C4×C17#12111yescharacteristic
195C2×C4×C17#12311yescharacteristic
196C2×C4×C17#12311yescharacteristic
197C2×C4×C17#12411yescharacteristic
198C2×C4×C17C2×D811yescharacteristic
199C2×C4×C17C2×D811yescharacteristic
200C2×C4×C17C2×SD1611yescharacteristic
201C2×C4×C17#13511yescharacteristic
202C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C17#13711yescharacteristic
206C2×Dic17—81no—
207C2×Dic17—81no—
208C2×Dic17—81no—
209#3622—42no—
210#3622—42no—
211#3622—81no—
212#2541D1711yescharacteristic
213#1957—171no—
214#1947—171no—
215#1802—171no—
216C2×#331—171no—
217C2×D4⋊C8—171no—
218#1279—171no—
219C22×C17—42no—
220C22×C17—42no—
221C22×C17—42no—
222C22×C17—81no—
223C22×C17—81no—
224C22×C17—81no—
225C22×C17—81no—
226C22×C17—82no—
227C22×C17—82no—
228C22×C17—82no—
229C22×C17—82no—
230C22×C17—82no—
231C22×C17—82no—
232C22×C17—82no—
233C22×C17#39411yescharacteristic
234C22×C17#44711yescharacteristic
235C22×C17#44711yescharacteristic
236C22×C17#45011yescharacteristic
237C22×C17#45211yescharacteristic
238C22×C17#45311yescharacteristic
239C22×C17#45511yescharacteristic
240C4×C17—21no—
241C4×C17—21no—
242C4×C17—42no—
243C4×C17—42no—
244C4×C17—81no—
245C4×C17#45911yescharacteristic
246C4×C17#46011yescharacteristic
247C4×C17#46611yescharacteristic
248C4×C17#46811yescharacteristic
249C4×C17#48011yescharacteristic
250C4×C17#48211yescharacteristic
251C4×C17#48611yescharacteristic
252C4×C17#49011yescharacteristic
253Dic17—161no—
254C2×#127—21no—
255C2×#127C2×D1711yescharacteristic
256C2×#121—21no—
257C2×#121—21no—
258C2×C4×D4C2×D1711yescharacteristic
259C2×#107—341no—
260C2×C4⋊C8—171no—
261C2×C4⋊C8—171no—
262C2×#102—341no—
263C2×#102—342no—
264C2×C4×C8—171no—
265#392—22no—
266#390—21no—
267#384—171no—
268C4×C4⋊C4C2×D1711yescharacteristic
269#340—341no—
270#340—341no—
271#331—342no—
272D4⋊C8—342no—
273C2×C17—82no—
274C2×C17—162no—
275C2×C17#161911yescharacteristic
276C2×C17#163111yescharacteristic
277C2×C17#163911yescharacteristic
278C2×C17#164111yescharacteristic
279C2×C17#203311yescharacteristic
280C2×C17#203711yescharacteristic
281C2×C17#204111yescharacteristic
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4C22⋊D1711yescharacteristic
287C22×D4C22⋊D1712yes—
288C23×C4—21no—
289C22×C8—341no—
290C22×C8—341no—
291C22×C8—341no—
292#127—21no—
293#127—21no—
294#127—21no—
295#127—21no—
296#127—42no—
297#127—42no—
298#121—42no—
299#121—42no—
300#121—42no—
301#121—42no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C2×C4⋊C4—341no—
307C2×C4⋊C4—341no—
308C2×C4⋊C4—341no—
309C2×C4⋊C4C22⋊D1711yescharacteristic
310C2×C4⋊C4C22⋊D1711yescharacteristic
311C2×C4⋊C4C22⋊D1711yescharacteristic
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—21no—
315C2×C42—21no—
316C2×C42C22×D1711yescharacteristic
317#107—682no—
318C4⋊C8—172no—
319C4⋊C8—341no—
320C4⋊C8—341no—
321C4⋊C8—341no—
322#102—684no—
323#102—682no—
324C4×C8—341no—
325C4×C8—341no—
326#95—21no—
327C17#1040811yescharacteristic, complemented, Sylow
328C24—21no—
329C24—22no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—22no—
333C2×D4—21no—
334C2×D4—22no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4—44no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—82no—
356C2×D4—82no—
357C2×D4#6322812yes—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—681no—
368C22×C4C2×C22⋊D1711yescharacteristic
369C22×C4C2×C22⋊D1711yescharacteristic
370C22×C4C2×C22⋊D1711yescharacteristic
371C2×C8—342no—
372C2×C8—342no—
373C2×C8—681no—
374C2×C8—681no—
375C2×C8—681no—
376C2×C8—681no—
377C2×C8—681no—
378C2×C8—681no—
379C2×C8—681no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—682no—
385C4⋊C4—681no—
386C4⋊C4—681no—
387C4⋊C4—681no—
388C4⋊C4—681no—
389C4⋊C4#6322812yes—
390C4⋊C4#6322912yes—
391C22⋊C4—44no—
392C22⋊C4—44no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—41no—
396C42—41no—
397C42D4×D1711yescharacteristic
398C42#6325411yescharacteristic
399C42#6325411yescharacteristic
400C42#6325411yescharacteristic
401C23—22no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23#1058763911yescharacteristic
416D4—22no—
417D4—22no—
418D4—44no—
419D4—41no—
420D4—41no—
421D4—82no—
422D4—88no—
423D4—88no—
424D4—81no—
425D4—81no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4—81no—
431D4—81no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—1361no—
448C2×C4—1361no—
449C2×C4—1361no—
450C2×C4C2×#6322811yescharacteristic
451C2×C4C2×#6322811yescharacteristic
452C2×C4#1058761811yescharacteristic
453C2×C4#1058761811yescharacteristic
454C2×C4#1058761811yescharacteristic
455C2×C4C2×#6322911yescharacteristic
456C2×C4#1058762111yescharacteristic
457C2×C4#1058762111yescharacteristic
458C2×C4#1058762211yescharacteristic
459C2×C4#1058762411yescharacteristic
460C2×C4#1058762511yescharacteristic
461C2×C4#1058762511yescharacteristic
462C2×C4#1058763611yescharacteristic
463C2×C4#1058763711yescharacteristic
464C8—682no—
465C8—682no—
466C8—1361no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22#1176272311yescharacteristic
482C22#1176294311yescharacteristic
483C22#1176294311yescharacteristic
484C22#1176296011yescharacteristic
485C22#1176297111yescharacteristic
486C22#1176297711yescharacteristic
487C22#1176298711yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—81no—
493C4—2721no—
494C4#1176300111yescharacteristic
495C4#1176300611yescharacteristic
496C4#1176304311yescharacteristic
497C4#1176305311yescharacteristic
498C4#1176312011yescharacteristic
499C4#1176313011yescharacteristic
500C4#1176315511yescharacteristic
501C4#1176317311yescharacteristic
502C2—82no—
503C2—162no—
504C2#1452783811yescharacteristic
505C2#1452791111yescharacteristic
506C2#1452796311yescharacteristic
507C2#1452797711yescharacteristic
508C2#1452996311yescharacteristic
509C2#1452999111yescharacteristic
510C2#1453001511yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
Fitting, prime radicalC17×#2541C2
socleC23×C17#120
hypercenter#2541D17
hypocenterC17#10408
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #14529591C2semidirect
2. #14529542C2semidirect
3. #14528784C2semidirect
4. C2×#11762553C2semidirect
5. C2×D4⋊#3622C2semidirect
6. #14526625C2semidirect
69. C4⋊#3622D4semidirect
327. C17#10408semidirect

Maximal subgroups

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

subgroupindex
#145295912
#145295422
#145287842
C2×#117625532
C2×D4⋊#36222
#145266252
C17×#25412
#1040817