Finite Group Databasebeta

← #16930563

Subgroups — #16930563

Order 4352.

646 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762887C211yesmaximal, characteristic, complemented
2#14529591C211yesmaximal, characteristic, complemented
3#14528784C211yesmaximal, characteristic, complemented
4C2×#11762553C211yesmaximal, characteristic, complemented
5#14526668C211yesmaximal, characteristic, complemented
6#14526618C211yesmaximal, characteristic, complemented
7C2×C17×#459C211yesmaximal, characteristic
8C22×#63223—21no—
9#11762887—22no—
10#11762887—22no—
11C2×C4⋊#3622C2211yescharacteristic
12C2×C4⋊#3622C2211yescharacteristic
13C2×#10587503—21no—
14C2×#10587503—21no—
15C2×#10587503—21no—
16C2×C22⋊#3622—21no—
17C2×C4×#3622C2211yescharacteristic
18#11762679C2211yescharacteristic
19#11762571—21no—
20#11762553—22no—
21C22×D8×C17—21no—
22C2×C17×#127C2211yescharacteristic
23C2×C4×D4×C17C2211yescharacteristic
24C17×#459—22no—
25C17×#459C414yescomplemented
26C2×C17×C4⋊C8C2211yescharacteristic
27C2×C17×#102—21no—
28C22×D4×C17—21no—
29C22×D4×C17—21no—
30C22×D4×C17—21no—
31C22×D4×C17D411yescharacteristic
32C23×C4×C17—21no—
33C2×D8×C17—24no—
34C2×D8×C17—42no—
35C2×D8×C17—42no—
36C22×C8×C17—21no—
37C17×#127—21no—
38C17×#127—21no—
39C17×#127—21no—
40C17×#127C2×C412yes—
41C4×D4×C17—21no—
42C4×D4×C17—21no—
43C4×D4×C17C2×C412yes—
44C4×D4×C17D412yes—
45C2×C4⋊C4×C17D411yescharacteristic
46C2×C22⋊C4×C17—21no—
47C2×C42×C17C2311yescharacteristic
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17—21no—
51C2×#63223—24no—
52C2×#63223—42no—
53C2×#63223—42no—
54C22×#3622—21no—
55C22×#3622—21no—
56C22×#3622D411yescharacteristic
57C22×#3622D411yescharacteristic
58C17×C4⋊C8—21no—
59C17×C4⋊C8C2×C412yes—
60C17×#102—24no—
61#10587503—42no—
62#10587503—42no—
63#10587503—42no—
64C22⋊#3622—24no—
65C4⋊#3622—21no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68C4⋊#3622D412yes—
69C4×#3622—21no—
70C4×#3622—21no—
71C24×C17—21no—
72C24×C17—41no—
73C2×D4×C17—22no—
74C2×D4×C17—22no—
75C2×D4×C17—22no—
76C2×D4×C17—21no—
77C2×D4×C17—21no—
78C2×D4×C17—21no—
79C2×D4×C17—21no—
80C2×D4×C17—21no—
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—41no—
90C2×D4×C17—41no—
91C2×D4×C17—41no—
92C2×D4×C17—81no—
93C2×D4×C17—81no—
94C2×D4×C17C22⋊C412yes—
95C22×C4×C17—21no—
96C22×C4×C17—22no—
97C22×C4×C17—22no—
98C22×C4×C17—41no—
99C22×C4×C17—41no—
100C22×C4×C17—41no—
101C22×C4×C17—41no—
102C22×C4×C17C2×D411yescharacteristic
103C22×C4×C17C2×D411yescharacteristic
104C22×C4×C17#4111yescharacteristic
105C22×Dic17—41no—
106D8×C17—48no—
107C2×C8×C17—22no—
108C2×C8×C17—41no—
109C2×C8×C17—41no—
110C4⋊C4×C17—21no—
111C4⋊C4×C17C22⋊C412yes—
112C22⋊C4×C17—22no—
113C22⋊C4×C17—22no—
114C42×C17C22×C411yescharacteristic
115C42×C17C2×D411yescharacteristic
116C42×C17C2×D411yescharacteristic
117C42×C17#4111yescharacteristic
118C4⋊Dic17—41no—
119C4⋊Dic17—41no—
120C4⋊Dic17—41no—
121C4⋊Dic17—41no—
122C4⋊Dic17—81no—
123#63223—48no—
124C2×#3622—21no—
125C2×#3622—21no—
126C2×#3622—21no—
127C2×#3622—22no—
128C2×#3622—21no—
129C2×#3622—21no—
130C2×#3622—41no—
131C2×#3622—41no—
132C2×#3622—41no—
133C2×#3622—41no—
134C2×#3622—41no—
135C2×#3622D812yescomplemented
136#9229—171nomaximal, Sylow
137C23×C17—22no—
138C23×C17—41no—
139C23×C17—41no—
140C23×C17—41no—
141C23×C17—41no—
142C23×C17—41no—
143C23×C17—41no—
144C23×C17—42no—
145C23×C17—81no—
146C23×C17—81no—
147C23×C17—81no—
148C23×C17—81no—
149C23×C17—81no—
150C23×C17—81no—
151C23×C17#12111yescharacteristic
152D4×C17—22no—
153D4×C17—22no—
154D4×C17—42no—
155D4×C17—42no—
156D4×C17—42no—
157D4×C17—42no—
158D4×C17—41no—
159D4×C17—41no—
160D4×C17—82no—
161D4×C17—82no—
162D4×C17—81no—
163D4×C17—81no—
164D4×C17—81no—
165D4×C17—81no—
166C2×C4×C17—21no—
167C2×C4×C17—21no—
168C2×C4×C17—22no—
169C2×C4×C17—41no—
170C2×C4×C17—41no—
171C2×C4×C17—42no—
172C2×C4×C17—42no—
173C2×C4×C17—42no—
174C2×C4×C17—42no—
175C2×C4×C17C2×C22⋊C411yescharacteristic
176C2×C4×C17C4×D411yescharacteristic
177C2×C4×C17C4×D411yescharacteristic
178C2×C4×C17#12011yescharacteristic
179C2×C4×C17#12111yescharacteristic
180C2×C4×C17#12311yescharacteristic
181C2×C4×C17C2×D811yescharacteristic
182C2×C4×C17#13511yescharacteristic
183C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C17#13711yescharacteristic
189C2×Dic17—81no—
190C2×Dic17—81no—
191C2×Dic17—81no—
192C8×C17—42no—
193#3622—22no—
194#3622—42no—
195#3622—41no—
196#3622—81no—
197C2×#459D1711yescharacteristic
198C2×#436—171no—
199#1957—171no—
200#1802—171no—
201C2×#331—171no—
202#1296—171no—
203#1277—171no—
204C22×C17—42no—
205C22×C17—42no—
206C22×C17—42no—
207C22×C17—81no—
208C22×C17—81no—
209C22×C17—81no—
210C22×C17—81no—
211C22×C17—82no—
212C22×C17—82no—
213C22×C17—82no—
214C22×C17—161no—
215C22×C17—161no—
216C22×C17—161no—
217C22×C17—161no—
218C22×C17#38611yescharacteristic
219C22×C17#45911yescharacteristic
220C22×C17#46311yescharacteristic
221C22×C17#46811yescharacteristic
222C22×C17#46911yescharacteristic
223C22×C17#47111yescharacteristic
224C22×C17#47211yescharacteristic
225C4×C17—21no—
226C4×C17—21no—
227C4×C17—42no—
228C4×C17#41711yescharacteristic
229C4×C17#41811yescharacteristic
230C4×C17C4×D811yescharacteristic
231C4×C17#44211yescharacteristic
232C4×C17#44711yescharacteristic
233C4×C17#44911yescharacteristic
234C4×C17#46811yescharacteristic
235C4×C17#46911yescharacteristic
236Dic17—161no—
237C22×D8—21no—
238C22×M16—341no—
239C2×#127C2×D1711yescharacteristic
240C2×C4×D4C2×D1711yescharacteristic
241#459—22no—
242#459Dic1714yescomplemented
243#436—342no—
244#436—342no—
245C2×C4⋊C8—171no—
246C2×C4⋊C8—171no—
247C2×C4⋊C8C2×D1711yescharacteristic
248C2×#102—21no—
249C2×#102—341no—
250C2×#102—341no—
251C2×#102—341no—
252C2×C22⋊C8—341no—
253C2×C4×C8—171no—
254#384—171no—
255#340—341no—
256#331—342no—
257C2×C17—82no—
258C2×C17—162no—
259C2×C17#168511yescharacteristic
260C2×C17#168711yescharacteristic
261C2×C17#169711yescharacteristic
262C2×C17#170111yescharacteristic
263C2×C17#187911yescharacteristic
264C2×C17#189511yescharacteristic
265C2×C17#190711yescharacteristic
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4C22⋊D1711yescharacteristic
270C23×C4—21no—
271C2×D8—24no—
272C2×D8—42no—
273C2×D8—42no—
274C2×M16—344no—
275C2×M16—682no—
276C2×M16—682no—
277C22×C8—21no—
278C22×C8—171no—
279C22×C8—171no—
280C22×C8—341no—
281C22×C8—341no—
282#127—21no—
283#127—21no—
284#127—21no—
285#127C2×Dic1712yes—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4C2×Dic1712yes—
289C4×D4C22⋊D1712yes—
290C2×C4⋊C4—341no—
291C2×C4⋊C4—341no—
292C2×C4⋊C4—341no—
293C2×C4⋊C4C22⋊D1711yescharacteristic
294C2×C22⋊C4—21no—
295C2×C42C22×D1711yescharacteristic
296C4⋊C8—21no—
297C4⋊C8—172no—
298C4⋊C8—341no—
299C4⋊C8—341no—
300C4⋊C8—341no—
301C4⋊C8C2×Dic1712yes—
302#102—24no—
303#102—682no—
304#102—682no—
305#102—682no—
306C22⋊C8—344no—
307C4×C8—341no—
308C4×C8—341no—
309C17#922911yescharacteristic, complemented, Sylow
310C24—21no—
311C24—41no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—22no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—81no—
332C2×D4—81no—
333C2×D4C22⋊Dic1712yes—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—681no—
342C22×C4D4×D1711yescharacteristic
343C22×C4#6325411yescharacteristic
344C22×C4C2×C22⋊D1711yescharacteristic
345D8—48no—
346M16—688no—
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—172no—
351C2×C8—341no—
352C2×C8—341no—
353C2×C8—341no—
354C2×C8—341no—
355C2×C8—341no—
356C2×C8—342no—
357C2×C8—681no—
358C2×C8—681no—
359C2×C8—681no—
360C2×C8—681no—
361C2×C8—681no—
362C4⋊C4—21no—
363C4⋊C4—681no—
364C4⋊C4—681no—
365C4⋊C4—681no—
366C4⋊C4—681no—
367C4⋊C4—1361no—
368C4⋊C4C22⋊Dic1712yes—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C42D4×D1711yescharacteristic
372C42#6325411yescharacteristic
373C42C22×Dic1711yescharacteristic
374C42C2×C22⋊D1711yescharacteristic
375C23—22no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—81no—
386C23—81no—
387C23—81no—
388C23—81no—
389C23#1058762511yescharacteristic
390D4—22no—
391D4—22no—
392D4—41no—
393D4—41no—
394D4—42no—
395D4—42no—
396D4—42no—
397D4—42no—
398D4—82no—
399D4—82no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—81no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—1361no—
414C2×C4—1361no—
415C2×C4—1361no—
416C2×C4D8×D1711yescharacteristic
417C2×C4#1058759711yescharacteristic
418C2×C4#1058759711yescharacteristic
419C2×C4#1058759811yescharacteristic
420C2×C4#1058761811yescharacteristic
421C2×C4#1058761811yescharacteristic
422C2×C4D4×Dic1711yescharacteristic
423C2×C4D4×Dic1711yescharacteristic
424C2×C4#1058762111yescharacteristic
425C2×C4#1058762311yescharacteristic
426C2×C4#1058762511yescharacteristic
427C2×C4#1058763511yescharacteristic
428C2×C4#1058763711yescharacteristic
429C2×C4C2×C22⋊Dic1711yescharacteristic
430C8—42no—
431C8—342no—
432C8—681no—
433C8—682no—
434C8—1361no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—161no—
446C22—161no—
447C22—161no—
448C22—161no—
449C22#1176268911yescharacteristic
450C22#1176300211yescharacteristic
451C22#1176302211yescharacteristic
452C22#1176305311yescharacteristic
453C22#1176306011yescharacteristic
454C22#1176307011yescharacteristic
455C22#1176307711yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—2721no—
460C4#1176281011yescharacteristic
461C4#1176281411yescharacteristic
462C4D8×Dic1711yescharacteristic
463C4#1176292111yescharacteristic
464C4#1176294111yescharacteristic
465C4#1176295111yescharacteristic
466C4#1176305311yescharacteristic
467C4#1176306011yescharacteristic
468C2—82no—
469C2—162no—
470C2#1452824711yescharacteristic
471C2#1452826111yescharacteristic
472C2#1452831511yescharacteristic
473C2#1452834311yescharacteristic
474C2#1452913411yescharacteristic
475C2#1452922311yescharacteristic
476C2#1452929411yescharacteristic
subgroupG/H
centerC23#10587625
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
Fitting, prime radicalC2×C17×#459C2
socleC23×C17#121
cosocleC2×C42×C17C23
hypercenterC2×#459D17
hypocenterC17#9229
LCSG ▷ 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. C2×#11762887C2semidirect
2. #14529591C2semidirect
3. #14528784C2semidirect
4. C2×#11762553C2semidirect
5. #14526668C2semidirect
6. #14526618C2semidirect
25. C17×#459C4semidirect
135. C2×#3622D8semidirect
242. #459Dic17semidirect
309. C17#9229semidirect

Maximal subgroups

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

subgroupindex
C2×#117628872
#145295912
#145287842
C2×#117625532
#145266682
#145266182
C2×C17×#4592
#922917