Finite Group Databasebeta

← #16938111

Subgroups — #16938111

Order 4352.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529591C211yesmaximal, characteristic, complemented
2#14529579C211yesmaximal, characteristic, complemented
3#14528784C211yesmaximal, characteristic, complemented
4C2×#11762561C211yesmaximal, characteristic, complemented
5C2×#11762553C211yesmaximal, characteristic, complemented
6#14526668C211yesmaximal, characteristic, complemented
7C2×C17×#459C211yesmaximal, characteristic
8C2×C4⋊#3622C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×#10587503—21no—
11C2×#10587503—21no—
12C2×#10587503—21no—
13C2×C22⋊#3622—21no—
14C2×C22⋊#3622—21no—
15C2×C4×#3622C2211yescharacteristic
16#11762679C2211yescharacteristic
17#11762571—21no—
18#11762561—22no—
19#11762553—22no—
20C22×D8×C17—21no—
21C2×C17×#127C2211yescharacteristic
22C2×C4×D4×C17C2211yescharacteristic
23C17×#459—22no—
24C17×#459—22no—
25C2×C17×C4⋊C8C2211yescharacteristic
26C2×C17×#102—21no—
27C22×D4×C17—21no—
28C22×D4×C17—21no—
29C22×D4×C17—21no—
30C22×D4×C17D411yescharacteristic
31C23×C4×C17—21no—
32C2×D8×C17—24no—
33C2×D8×C17—42no—
34C2×D8×C17—42no—
35C22×C8×C17—21no—
36C17×#127—21no—
37C17×#127—21no—
38C17×#127—21no—
39C17×#127D412yes—
40C4×D4×C17—21no—
41C4×D4×C17—21no—
42C4×D4×C17—21no—
43C4×D4×C17—21no—
44C2×C4⋊C4×C17D411yescharacteristic
45C2×C22⋊C4×C17—21no—
46C2×C42×C17C2311yescharacteristic
47C2×C4⋊Dic17—21no—
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17—21no—
50C22×#3622—21no—
51C22×#3622—21no—
52C22×#3622D411yescharacteristic
53C22×#3622D411yescharacteristic
54C17×C4⋊C8—21no—
55C17×C4⋊C8D412yes—
56C17×#102—24no—
57#10587503—42no—
58#10587503—42no—
59#10587503—42no—
60C22⋊#3622—42no—
61C22⋊#3622—42no—
62C4⋊#3622—21no—
63C4⋊#3622—21no—
64C4⋊#3622—21no—
65C4⋊#3622—21no—
66C4×#3622—21no—
67C4×#3622—21no—
68C24×C17—21no—
69C24×C17—41no—
70C2×D4×C17—21no—
71C2×D4×C17—22no—
72C2×D4×C17—22no—
73C2×D4×C17—21no—
74C2×D4×C17—22no—
75C2×D4×C17—21no—
76C2×D4×C17—21no—
77C2×D4×C17—21no—
78C2×D4×C17—41no—
79C2×D4×C17—41no—
80C2×D4×C17—41no—
81C2×D4×C17—41no—
82C2×D4×C17—41no—
83C2×D4×C17—41no—
84C2×D4×C17—41no—
85C2×D4×C17—41no—
86C2×D4×C17—41no—
87C2×D4×C17—41no—
88C2×D4×C17—41no—
89C2×D4×C17—81no—
90C2×D4×C17—81no—
91C2×D4×C17D812yes—
92C22×C4×C17—21no—
93C22×C4×C17—41no—
94C22×C4×C17—41no—
95C22×C4×C17—41no—
96C22×C4×C17—41no—
97C22×C4×C17—41no—
98C22×C4×C17—41no—
99C22×C4×C17C2×D411yescharacteristic
100C22×C4×C17C2×D411yescharacteristic
101C22×C4×C17#4111yescharacteristic
102C22×Dic17—41no—
103D8×C17—48no—
104C2×C8×C17—22no—
105C2×C8×C17—41no—
106C2×C8×C17—41no—
107C4⋊C4×C17—21no—
108C4⋊C4×C17—21no—
109C22⋊C4×C17—41no—
110C22⋊C4×C17—41no—
111C42×C17C2×D411yescharacteristic
112C42×C17C2×D411yescharacteristic
113C42×C17#4111yescharacteristic
114C42×C17#4111yescharacteristic
115C4⋊Dic17—41no—
116C4⋊Dic17—41no—
117C4⋊Dic17—41no—
118C4⋊Dic17—41no—
119C4⋊Dic17—81no—
120C2×#3622—21no—
121C2×#3622—21no—
122C2×#3622—21no—
123C2×#3622—21no—
124C2×#3622—21no—
125C2×#3622—41no—
126C2×#3622—41no—
127C2×#3622—41no—
128C2×#3622—41no—
129C2×#3622—41no—
130C2×#3622—41no—
131C2×#3622D812yescomplemented
132#10472—171nomaximal, Sylow
133C23×C17—22no—
134C23×C17—41no—
135C23×C17—41no—
136C23×C17—41no—
137C23×C17—41no—
138C23×C17—41no—
139C23×C17—41no—
140C23×C17—42no—
141C23×C17—81no—
142C23×C17—81no—
143C23×C17—81no—
144C23×C17—81no—
145C23×C17—81no—
146C23×C17—81no—
147C23×C17#12111yescharacteristic
148D4×C17—22no—
149D4×C17—22no—
150D4×C17—42no—
151D4×C17—41no—
152D4×C17—42no—
153D4×C17—42no—
154D4×C17—42no—
155D4×C17—41no—
156D4×C17—82no—
157D4×C17—82no—
158D4×C17—81no—
159D4×C17—81no—
160D4×C17—81no—
161D4×C17—81no—
162C2×C4×C17—21no—
163C2×C4×C17—21no—
164C2×C4×C17—41no—
165C2×C4×C17—41no—
166C2×C4×C17—41no—
167C2×C4×C17—81no—
168C2×C4×C17—81no—
169C2×C4×C17—81no—
170C2×C4×C17—81no—
171C2×C4×C17#12011yescharacteristic
172C2×C4×C17#12111yescharacteristic
173C2×C4×C17#12111yescharacteristic
174C2×C4×C17#12311yescharacteristic
175C2×C4×C17#12311yescharacteristic
176C2×C4×C17#12411yescharacteristic
177C2×C4×C17C2×D811yescharacteristic
178C2×C4×C17C2×D811yescharacteristic
179C2×C4×C17#13511yescharacteristic
180C2×C4×C17#13511yescharacteristic
181C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C17#13711yescharacteristic
185C2×Dic17—81no—
186C2×Dic17—81no—
187C2×Dic17—81no—
188C8×C17—42no—
189#3622—22no—
190#3622—41no—
191#3622—81no—
192#3622—81no—
193C2×#459D1711yescharacteristic
194#1957—171no—
195#1954—171no—
196#1802—171no—
197C2×#335—171no—
198C2×#331—171no—
199#1296—171no—
200C22×C17—42no—
201C22×C17—42no—
202C22×C17—42no—
203C22×C17—81no—
204C22×C17—81no—
205C22×C17—81no—
206C22×C17—81no—
207C22×C17—82no—
208C22×C17—82no—
209C22×C17—82no—
210C22×C17—161no—
211C22×C17—161no—
212C22×C17—161no—
213C22×C17—161no—
214C22×C17#39411yescharacteristic
215C22×C17#45911yescharacteristic
216C22×C17#46311yescharacteristic
217C22×C17#46611yescharacteristic
218C22×C17#46811yescharacteristic
219C22×C17#47111yescharacteristic
220C22×C17#47211yescharacteristic
221C4×C17—21no—
222C4×C17—21no—
223C4×C17—81no—
224C4×C17#44711yescharacteristic
225C4×C17#45211yescharacteristic
226C4×C17#45911yescharacteristic
227C4×C17#46311yescharacteristic
228C4×C17#46611yescharacteristic
229C4×C17#46911yescharacteristic
230C4×C17#48011yescharacteristic
231C4×C17#48211yescharacteristic
232Dic17—161no—
233C22×D8—21no—
234C2×#127C2×D1711yescharacteristic
235C2×C4×D4C2×D1711yescharacteristic
236#459—22no—
237#459—22no—
238C2×C4⋊C8—171no—
239C2×C4⋊C8—171no—
240C2×C4⋊C8C2×D1711yescharacteristic
241C2×#102—21no—
242C2×#102—341no—
243C2×#102—341no—
244C2×#102—341no—
245C2×C22⋊C8—341no—
246C2×C22⋊C8—341no—
247C2×C4×C8—171no—
248#384—171no—
249#340—341no—
250#335—342no—
251#331—342no—
252C2×C17—82no—
253C2×C17—162no—
254C2×C17#166711yescharacteristic
255C2×C17#168111yescharacteristic
256C2×C17#168511yescharacteristic
257C2×C17#169711yescharacteristic
258C2×C17#203311yescharacteristic
259C2×C17#205111yescharacteristic
260C2×C17#205411yescharacteristic
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4C22⋊D1711yescharacteristic
265C23×C4—21no—
266C2×D8—24no—
267C2×D8—42no—
268C2×D8—42no—
269C22×C8—21no—
270C22×C8—171no—
271C22×C8—171no—
272C22×C8—341no—
273C22×C8—341no—
274#127—21no—
275#127—21no—
276#127—21no—
277#127C22⋊D1712yes—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C2×C4⋊C4—341no—
283C2×C4⋊C4—341no—
284C2×C4⋊C4—341no—
285C2×C4⋊C4C22⋊D1711yescharacteristic
286C2×C22⋊C4—21no—
287C2×C42C22×D1711yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—341no—
290C4⋊C8—341no—
291C4⋊C8—341no—
292C4⋊C8—341no—
293C4⋊C8C22⋊D1712yes—
294#102—24no—
295#102—682no—
296#102—682no—
297#102—682no—
298C22⋊C8—682no—
299C22⋊C8—682no—
300C4×C8—341no—
301C4×C8—341no—
302C17#1047211yescharacteristic, complemented, Sylow
303C24—21no—
304C24—41no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4#6322812yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—681no—
335C22×C4D4×D1711yescharacteristic
336C22×C4#6325411yescharacteristic
337C22×C4C2×C22⋊D1711yescharacteristic
338D8—48no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—172no—
343C2×C8—341no—
344C2×C8—341no—
345C2×C8—341no—
346C2×C8—341no—
347C2×C8—341no—
348C2×C8—681no—
349C2×C8—681no—
350C2×C8—681no—
351C2×C8—681no—
352C2×C8—681no—
353C2×C8—681no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—681no—
357C4⋊C4—681no—
358C4⋊C4—681no—
359C4⋊C4—681no—
360C4⋊C4—1361no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42#6325411yescharacteristic
364C42#6325411yescharacteristic
365C42C2×C22⋊D1711yescharacteristic
366C42C2×C22⋊D1711yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23#1058762511yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—41no—
389D4—42no—
390D4—82no—
391D4—82no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—1361no—
406C2×C4—1361no—
407C2×C4—1361no—
408C2×C4D8×D1711yescharacteristic
409C2×C4#1058759711yescharacteristic
410C2×C4#1058759711yescharacteristic
411C2×C4#1058759811yescharacteristic
412C2×C4C2×#6322811yescharacteristic
413C2×C4#1058761811yescharacteristic
414C2×C4#1058762111yescharacteristic
415C2×C4#1058762111yescharacteristic
416C2×C4#1058762211yescharacteristic
417C2×C4#1058762411yescharacteristic
418C2×C4#1058762511yescharacteristic
419C2×C4#1058763611yescharacteristic
420C2×C4#1058763711yescharacteristic
421C2×C4#1058763911yescharacteristic
422C8—42no—
423C8—342no—
424C8—681no—
425C8—1361no—
426C8—1361no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—161no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22#1176272311yescharacteristic
442C22#1176300211yescharacteristic
443C22#1176302211yescharacteristic
444C22#1176304311yescharacteristic
445C22#1176305311yescharacteristic
446C22#1176307011yescharacteristic
447C22#1176307711yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—2721no—
452C4#1176294311yescharacteristic
453C4#1176297111yescharacteristic
454C4#1176300211yescharacteristic
455C4#1176302211yescharacteristic
456C4#1176304211yescharacteristic
457C4#1176305911yescharacteristic
458C4#1176312011yescharacteristic
459C4#1176313011yescharacteristic
460C2—82no—
461C2—162no—
462C2#1452813711yescharacteristic
463C2#1452821911yescharacteristic
464C2#1452824711yescharacteristic
465C2#1452831511yescharacteristic
466C2#1452996311yescharacteristic
467C2#1453007311yescharacteristic
468C2#1453009211yescharacteristic
subgroupG/H
centerC23#10587625
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
Fitting, prime radicalC2×C17×#459C2
socleC23×C17#121
hypercenterC2×#459D17
hypocenterC17#10472
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #14529591C2semidirect
2. #14529579C2semidirect
3. #14528784C2semidirect
4. C2×#11762561C2semidirect
5. C2×#11762553C2semidirect
6. #14526668C2semidirect
131. C2×#3622D8semidirect
302. C17#10472semidirect

Maximal subgroups

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

subgroupindex
#145295912
#145295792
#145287842
C2×#117625612
C2×#117625532
#145266682
C2×C17×#4592
#1047217