Finite Group Databasebeta

← #16938112

Subgroups — #16938112

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
1C2×#11763001C211yesmaximal, characteristic
2#14529591C211yesmaximal, characteristic, complemented
3#14529577C211yesmaximal, characteristic, complemented
4#14528785C211yesmaximal, characteristic, complemented
5C2×#11762561C211yesmaximal, characteristic, complemented
6#14526668C211yesmaximal, characteristic, complemented
7C2×C17×#331C211yesmaximal, characteristic, complemented
8C22×#63228—21no—
9C2×C4×D68C2211yescharacteristic
10#11763001—22no—
11#11763001—22no—
12C2×C4⋊#3622C2211yescharacteristic
13C2×#10587492—21no—
14C2×#10587503—21no—
15C2×#10587503—21no—
16C2×#10587503—21no—
17C2×#10587491—21no—
18C2×#10587491—21no—
19C2×C4×#3622C2211yescharacteristic
20#11762679C2211yescharacteristic
21#11762572—21no—
22#11762561—22no—
23C2×C17×#127C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C17×C4⋊C8C2211yescharacteristic
26C17×#331—22no—
27C22×D4×C17—21no—
28C22×D4×C17—21no—
29C22×D4×C17—21no—
30C22×D68D411yescharacteristic
31C22×C4×D17—21no—
32C22×C8×C17—21no—
33C22×C8×C17—21no—
34C17×#127—21no—
35C17×#127—21no—
36C17×#127—21no—
37C17×#127D412yes—
38C2×C42×C17C2311yescharacteristic
39C2×#63228—24no—
40C2×#63228—42no—
41C2×#63228—42no—
42C2×#63227—21no—
43C2×C4⋊Dic17—21no—
44C2×C4⋊Dic17—21no—
45C2×C4⋊Dic17—21no—
46C2×C4⋊Dic17D411yescharacteristic
47C22×#3622—21no—
48C22×#3622D411yescharacteristic
49C22×#3622D411yescharacteristic
50C4×D68—21no—
51C4×D68—21no—
52C4×D68—21no—
53C4×D68—21no—
54C17×C4⋊C8—21no—
55C17×C4⋊C8—21no—
56C17×C4⋊C8—21no—
57C17×C4⋊C8—21no—
58#10587503—24no—
59#10587503—42no—
60#10587503—42no—
61#10587492—42no—
62#10587491—42no—
63#10587491—42no—
64C4⋊#3622—21no—
65C4⋊#3622D412yes—
66C4×#3622—21no—
67C4×#3622—21no—
68C24×C17—41no—
69C23×D17—21no—
70C2×D4×C17—22no—
71C2×D4×C17—22no—
72C2×D4×C17—22no—
73C2×D4×C17—41no—
74C2×D4×C17—41no—
75C2×D4×C17—41no—
76C2×D4×C17—41no—
77C2×D4×C17—41no—
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—81no—
85C2×D4×C17—81no—
86C22×C4×C17C2×D411yescharacteristic
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17#4111yescharacteristic
89C22×Dic17—21no—
90C22×Dic17—41no—
91C2×D68—21no—
92C2×D68—21no—
93C2×D68—21no—
94C2×D68—21no—
95C2×D68—21no—
96C2×D68D812yes—
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×C8×C17—41no—
104C2×C8×C17—41no—
105C2×C8×C17—41no—
106C2×C8×C17—41no—
107C2×C8×C17—41no—
108C2×C8×C17—41no—
109C42×C17C2×D411yescharacteristic
110C42×C17C2×D411yescharacteristic
111C42×C17#4111yescharacteristic
112C42×C17#4111yescharacteristic
113#63228—48no—
114#63227—41no—
115#63227—41no—
116C4⋊Dic17—21no—
117C4⋊Dic17—21no—
118C4⋊Dic17—41no—
119C4⋊Dic17—41no—
120C4⋊Dic17—41no—
121C4⋊Dic17—41no—
122C4⋊Dic17—81no—
123C2×#3622—21no—
124C2×#3622—21no—
125C2×#3622—22no—
126C2×#3622—21no—
127C2×#3622—21no—
128C2×#3622—21no—
129C2×#3622—41no—
130C2×#3622—41no—
131C2×#3622D812yescomplemented
132#10472—171nomaximal, Sylow
133C23×C17—42no—
134C23×C17—81no—
135C23×C17—81no—
136C23×C17—81no—
137C23×C17—81no—
138C23×C17—81no—
139C23×C17—81no—
140C23×C17#12111yescharacteristic
141C22×D17—22no—
142C22×D17—41no—
143C22×D17—41no—
144C22×D17—41no—
145C22×D17—41no—
146C22×D17—41no—
147C22×D17—41no—
148D4×C17—42no—
149D4×C17—42no—
150D4×C17—42no—
151D4×C17—42no—
152D4×C17—82no—
153D4×C17—82no—
154D4×C17—81no—
155D4×C17—81no—
156D4×C17—81no—
157D4×C17—81no—
158C2×C4×C17—21no—
159C2×C4×C17—21no—
160C2×C4×C17#12011yescharacteristic
161C2×C4×C17#12111yescharacteristic
162C2×C4×C17#12111yescharacteristic
163C2×C4×C17#12311yescharacteristic
164C2×C4×C17#12311yescharacteristic
165C2×C4×C17#12411yescharacteristic
166C2×C4×C17C2×D811yescharacteristic
167C2×C4×C17C2×D811yescharacteristic
168C2×C4×C17#13511yescharacteristic
169C2×C4×C17#13511yescharacteristic
170C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C17#13711yescharacteristic
174C2×Dic17—41no—
175C2×Dic17—41no—
176C2×Dic17—41no—
177C2×Dic17—81no—
178C2×Dic17—81no—
179C2×Dic17—81no—
180D68—22no—
181D68—22no—
182D68—41no—
183D68—41no—
184C4×D17—81no—
185C4×D17—81no—
186C4×D17—81no—
187C4×D17—81no—
188C8×C17—81no—
189C8×C17—81no—
190#3622—22no—
191#3622—42no—
192#3622—41no—
193C2×#459—171no—
194#1957—171no—
195#1954—171no—
196#1802—171no—
197C2×#335—171no—
198C2×#331D1711yescharacteristic, complemented
199#1296—171no—
200C22×C17—82no—
201C22×C17—82no—
202C22×C17—82no—
203C22×C17—161no—
204C22×C17—161no—
205C22×C17—161no—
206C22×C17—161no—
207C22×C17#39411yescharacteristic
208C22×C17#45911yescharacteristic
209C22×C17#46311yescharacteristic
210C22×C17#46611yescharacteristic
211C22×C17#46811yescharacteristic
212C22×C17#47111yescharacteristic
213C22×C17#47211yescharacteristic
214C2×D17—42no—
215C2×D17—42no—
216C2×D17—42no—
217C2×D17—81no—
218C2×D17—81no—
219C2×D17—81no—
220C2×D17—81no—
221C4×C17—21no—
222C4×C17—21no—
223C4×C17#44711yescharacteristic
224C4×C17#45211yescharacteristic
225C4×C17#45911yescharacteristic
226C4×C17#46311yescharacteristic
227C4×C17#46611yescharacteristic
228C4×C17#46911yescharacteristic
229C4×C17#48011yescharacteristic
230C4×C17#48211yescharacteristic
231Dic17—81no—
232Dic17—161no—
233C22×D8—341no—
234C2×#127C2×D1711yescharacteristic
235C2×C4×D4—171no—
236#459—342no—
237#459—342no—
238C2×C4⋊C8—171no—
239C2×C4⋊C8C2×D1711yescharacteristic
240C2×C4⋊C8C2×D1711yescharacteristic
241C2×#102—341no—
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—22no—
252C2×C17—162no—
253C2×C17#166711yescharacteristic
254C2×C17#168111yescharacteristic
255C2×C17#168511yescharacteristic
256C2×C17#169711yescharacteristic
257C2×C17#203311yescharacteristic
258C2×C17#205111yescharacteristic
259C2×C17#205411yescharacteristic
260D17—82no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—171no—
265C23×C4—341no—
266C2×D8—344no—
267C2×D8—682no—
268C2×D8—682no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—171no—
272C22×C8—171no—
273C22×C8—341no—
274#127—21no—
275#127—21no—
276#127—21no—
277#127C22⋊D1712yes—
278C4×D4—341no—
279C4×D4—341no—
280C4×D4—341no—
281C4×D4—341no—
282C2×C4⋊C4—171no—
283C2×C4⋊C4—341no—
284C2×C4⋊C4—341no—
285C2×C4⋊C4—341no—
286C2×C22⋊C4—341no—
287C2×C42C22×D1711yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—172no—
293C4⋊C8—341no—
294#102—344no—
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—41no—
304C24—341no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—81no—
320C2×D4—81no—
321C2×D4—172no—
322C2×D4—341no—
323C2×D4—341no—
324C2×D4—341no—
325C2×D4—341no—
326C2×D4—341no—
327C22×C4—341no—
328C22×C4—681no—
329C22×C4—681no—
330C22×C4—681no—
331C22×C4—681no—
332C22×C4—681no—
333C22×C4—681no—
334C22×C4—681no—
335C22×C4#6325211yescharacteristic
336C22×C4D4×D1711yescharacteristic
337C22×C4D4×D1711yescharacteristic
338D8—688no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—172no—
346C2×C8—341no—
347C2×C8—341no—
348C2×C8—341no—
349C2×C8—341no—
350C2×C8—341no—
351C2×C8—342no—
352C2×C8—681no—
353C2×C8—681no—
354C4⋊C4—341no—
355C4⋊C4—341no—
356C4⋊C4—681no—
357C4⋊C4—681no—
358C4⋊C4—681no—
359C4⋊C4—681no—
360C4⋊C4—1361no—
361C22⋊C4—681no—
362C22⋊C4—681no—
363C42#6325211yescharacteristic
364C42D4×D1711yescharacteristic
365C42#6325411yescharacteristic
366C42C2×C22⋊D1711yescharacteristic
367C23—42no—
368C23—81no—
369C23—81no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23—81no—
374C23—342no—
375C23—681no—
376C23—681no—
377C23—681no—
378C23—681no—
379C23—681no—
380C23—681no—
381C23#1058757011yescharacteristic
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392D4—342no—
393D4—342no—
394D4—681no—
395D4—681no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—681no—
399C2×C4—681no—
400C2×C4—681no—
401C2×C4—1361no—
402C2×C4—1361no—
403C2×C4—1361no—
404C2×C4—1361no—
405C2×C4—1361no—
406C2×C4—1361no—
407C2×C4—1361no—
408C2×C4#1058756911yescharacteristic
409C2×C4#1058757011yescharacteristic
410C2×C4#1058757111yescharacteristic
411C2×C4D8×D1711yescharacteristic
412C2×C4D8×D1711yescharacteristic
413C2×C4#1058759711yescharacteristic
414C2×C4#1058759711yescharacteristic
415C2×C4#1058760011yescharacteristic
416C2×C4#1058760111yescharacteristic
417C2×C4#1058760211yescharacteristic
418C2×C4#1058760211yescharacteristic
419C2×C4#1058761511yescharacteristic
420C2×C4#1058762311yescharacteristic
421C2×C4#1058762511yescharacteristic
422C8—81no—
423C8—81no—
424C8—342no—
425C8—681no—
426C8—682no—
427C22—82no—
428C22—82no—
429C22—82no—
430C22—161no—
431C22—161no—
432C22—161no—
433C22—161no—
434C22—682no—
435C22—682no—
436C22—682no—
437C22—1361no—
438C22—1361no—
439C22—1361no—
440C22—1361no—
441C22#1176272411yescharacteristic
442C22#1176300311yescharacteristic
443C22#1176302311yescharacteristic
444C22#1176304411yescharacteristic
445C22#1176305411yescharacteristic
446C22#1176307111yescharacteristic
447C22#1176307811yescharacteristic
448C4—21no—
449C4—21no—
450C4—2721no—
451C4—1361no—
452C4#1176294111yescharacteristic
453C4#1176296811yescharacteristic
454C4#1176300211yescharacteristic
455C4#1176302611yescharacteristic
456C4#1176304411yescharacteristic
457C4#1176306111yescharacteristic
458C4#1176312111yescharacteristic
459C4#1176313211yescharacteristic
460C2—162no—
461C2—1362no—
462C2#1452813811yescharacteristic
463C2#1452822011yescharacteristic
464C2#1452824811yescharacteristic
465C2#1452831611yescharacteristic
466C2#1452996411yescharacteristic
467C2#1453007611yescharacteristic
468C2#1453009311yescharacteristic
subgroupG/H
centerC23#10587570
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#331C2
socleC23×C17#121
prime radicalC2×#11763001C2
hypercenterC2×#331D17
hypocenterC17#10472
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #14529591C2semidirect
3. #14529577C2semidirect
4. #14528785C2semidirect
5. C2×#11762561C2semidirect
6. #14526668C2semidirect
7. C2×C17×#331C2semidirect
131. C2×#3622D8semidirect
198. C2×#331D17semidirect
302. C17#10472semidirect

Maximal subgroups

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

subgroupindex
C2×#117630012
#145295912
#145295772
#145287852
C2×#117625612
#145266682
C2×C17×#3312
#1047217