Finite Group Databasebeta

← #16938116

Subgroups — #16938116

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×#11763005C211yesmaximal, characteristic
2#14529590C211yesmaximal, characteristic, complemented
3#14529578C211yesmaximal, characteristic, complemented
4#14528785C211yesmaximal, characteristic, complemented
5C2×#11762552C211yesmaximal, characteristic, complemented
6#14526668C211yesmaximal, characteristic, complemented
7C2×C17×#335C211yesmaximal, characteristic, complemented
8C22×D136—21no—
9C2×#10587560C2211yescharacteristic
10C2×C4×D68C2211yescharacteristic
11#11763005—22no—
12#11763005—22no—
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587492—21no—
15C2×#10587492—21no—
16C2×#10587492—21no—
17C2×#10587492—21no—
18C2×#10587491—21no—
19C2×#10587491—21no—
20#11762679C2211yescharacteristic
21#11762572—21no—
22#11762552—22no—
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C17C2211yescharacteristic
26C17×#335—22no—
27C22×D68—21no—
28C22×D68—21no—
29C22×D68—21no—
30C22×D68D411yescharacteristic
31C22×C4×D17—21no—
32C22×C8×C17—21no—
33C22×C8×C17—21no—
34C22×C8×C17D411yescharacteristic
35C22×C8×C17D411yescharacteristic
36C2×C42×C17C2311yescharacteristic
37C2×#63227—21no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17—21no—
41C2×C4⋊Dic17D411yescharacteristic
42C22×#3622—21no—
43C2×D136—24no—
44C2×D136—42no—
45C2×D136—42no—
46#10587560—21no—
47#10587560—21no—
48#10587560—21no—
49#10587560D412yes—
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⋊C8D412yes—
58C4×C8×C17—21no—
59C4×C8×C17—21no—
60#10587492—24no—
61#10587492—42no—
62#10587492—42no—
63#10587492—42no—
64#10587491—42no—
65#10587491—42no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68C23×D17—21no—
69C23×D17—41no—
70C22×C4×C17C2×D411yescharacteristic
71C22×C4×C17C2×D411yescharacteristic
72C22×C4×C17#4111yescharacteristic
73C22×Dic17—21no—
74C22×Dic17—41no—
75C2×D68—21no—
76C2×D68—21no—
77C2×D68—21no—
78C2×D68—21no—
79C2×D68—22no—
80C2×D68—22no—
81C2×D68—21no—
82C2×D68—22no—
83C2×D68—41no—
84C2×D68—41no—
85C2×D68—41no—
86C2×D68—41no—
87C2×D68—41no—
88C2×D68—41no—
89C2×D68—41no—
90C2×D68—41no—
91C2×D68—41no—
92C2×D68—41no—
93C2×D68—41no—
94C2×D68—81no—
95C2×D68—81no—
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—21no—
104C2×C8×C17—21no—
105C2×C8×C17—22no—
106C2×C8×C17—21no—
107C2×C8×C17—21no—
108C2×C8×C17—21no—
109C2×C8×C17—41no—
110C2×C8×C17—41no—
111C2×C8×C17—41no—
112C2×C8×C17—41no—
113C2×C8×C17—41no—
114C2×C8×C17D812yescomplemented
115C42×C17C2×D411yescharacteristic
116C42×C17C2×D411yescharacteristic
117C42×C17#4111yescharacteristic
118C42×C17#4111yescharacteristic
119#63227—41no—
120#63227—41no—
121C4⋊Dic17—21no—
122C4⋊Dic17—21no—
123C4⋊Dic17—41no—
124C4⋊Dic17—41no—
125C4⋊Dic17—41no—
126C4⋊Dic17—41no—
127C4⋊Dic17—81no—
128C2×#3622—41no—
129C2×#3622—41no—
130C2×#3622—41no—
131D136—48no—
132#10472—171nomaximal, Sylow
133C23×C17#12111yescharacteristic
134C22×D17—22no—
135C22×D17—41no—
136C22×D17—41no—
137C22×D17—41no—
138C22×D17—41no—
139C22×D17—41no—
140C22×D17—41no—
141C22×D17—42no—
142C22×D17—81no—
143C22×D17—81no—
144C22×D17—81no—
145C22×D17—81no—
146C22×D17—81no—
147C22×D17—81no—
148C2×C4×C17—21no—
149C2×C4×C17—21no—
150C2×C4×C17#12011yescharacteristic
151C2×C4×C17#12111yescharacteristic
152C2×C4×C17#12111yescharacteristic
153C2×C4×C17#12311yescharacteristic
154C2×C4×C17#12311yescharacteristic
155C2×C4×C17#12411yescharacteristic
156C2×C4×C17C2×D811yescharacteristic
157C2×C4×C17C2×D811yescharacteristic
158C2×C4×C17#13511yescharacteristic
159C2×C4×C17#13511yescharacteristic
160C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C17#13711yescharacteristic
164C2×Dic17—41no—
165C2×Dic17—41no—
166C2×Dic17—41no—
167C2×Dic17—81no—
168C2×Dic17—81no—
169C2×Dic17—81no—
170D68—22no—
171D68—22no—
172D68—42no—
173D68—41no—
174D68—42no—
175D68—42no—
176D68—42no—
177D68—41no—
178D68—82no—
179D68—82no—
180D68—81no—
181D68—81no—
182D68—81no—
183D68—81no—
184C4×D17—81no—
185C4×D17—81no—
186C4×D17—81no—
187C4×D17—81no—
188C8×C17—22no—
189C8×C17—42no—
190C8×C17—41no—
191C8×C17—81no—
192#3622—81no—
193C2×#459—171no—
194#1957—171no—
195#1954—171no—
196#1802—171no—
197C2×#335D1711yescharacteristic, complemented
198C2×#331—171no—
199#1296—171no—
200C22×C17#39411yescharacteristic
201C22×C17#45911yescharacteristic
202C22×C17#46311yescharacteristic
203C22×C17#46611yescharacteristic
204C22×C17#46811yescharacteristic
205C22×C17#47111yescharacteristic
206C22×C17#47211yescharacteristic
207C2×D17—42no—
208C2×D17—42no—
209C2×D17—42no—
210C2×D17—81no—
211C2×D17—81no—
212C2×D17—81no—
213C2×D17—81no—
214C2×D17—82no—
215C2×D17—82no—
216C2×D17—82no—
217C2×D17—161no—
218C2×D17—161no—
219C2×D17—161no—
220C2×D17—161no—
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×#127—171no—
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×C8C2×D1711yescharacteristic
248#384—171no—
249#340—341no—
250#335—22no—
251#331—342no—
252C2×C17#166711yescharacteristic
253C2×C17#168111yescharacteristic
254C2×C17#168511yescharacteristic
255C2×C17#169711yescharacteristic
256C2×C17#203311yescharacteristic
257C2×C17#205111yescharacteristic
258C2×C17#205411yescharacteristic
259D17—82no—
260D17—162no—
261C22×D4—171no—
262C22×D4—341no—
263C22×D4—341no—
264C22×D4—341no—
265C23×C4—341no—
266C2×D8—344no—
267C2×D8—682no—
268C2×D8—682no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—341no—
272C22×C8D6811yescharacteristic
273C22×C8D6811yescharacteristic
274#127—172no—
275#127—341no—
276#127—341no—
277#127—341no—
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—341no—
292C4⋊C8—341no—
293C4⋊C8C22⋊D1712yes—
294#102—344no—
295#102—682no—
296#102—682no—
297#102—682no—
298C22⋊C8—682no—
299C22⋊C8—682no—
300C4×C8—21no—
301C4×C8—21no—
302C17#1047211yescharacteristic, complemented, Sylow
303C24—341no—
304C24—681no—
305C2×D4—172no—
306C2×D4—341no—
307C2×D4—342no—
308C2×D4—342no—
309C2×D4—341no—
310C2×D4—341no—
311C2×D4—341no—
312C2×D4—341no—
313C2×D4—342no—
314C2×D4—681no—
315C2×D4—681no—
316C2×D4—681no—
317C2×D4—681no—
318C2×D4—681no—
319C2×D4—681no—
320C2×D4—681no—
321C2×D4—681no—
322C2×D4—681no—
323C2×D4—681no—
324C2×D4—681no—
325C2×D4—1361no—
326C2×D4—1361no—
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×C4C2×D6811yescharacteristic
336C22×C4D4×D1711yescharacteristic
337C22×C4#6325611yescharacteristic
338D8—688no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—22no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—681no—
351C2×C8—681no—
352C2×C8—681no—
353C2×C8D13612yescomplemented
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#6325611yescharacteristic
366C42C2×C22⋊D1711yescharacteristic
367C23—342no—
368C23—681no—
369C23—681no—
370C23—681no—
371C23—681no—
372C23—681no—
373C23—681no—
374C23—682no—
375C23—1361no—
376C23—1361no—
377C23—1361no—
378C23—1361no—
379C23—1361no—
380C23—1361no—
381C23#1058758111yescharacteristic
382D4—342no—
383D4—342no—
384D4—681no—
385D4—682no—
386D4—682no—
387D4—682no—
388D4—681no—
389D4—682no—
390D4—1362no—
391D4—1362no—
392D4—1361no—
393D4—1361no—
394D4—1361no—
395D4—1361no—
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#1058758011yescharacteristic
409C2×C4#1058758011yescharacteristic
410C2×C4#1058758111yescharacteristic
411C2×C4C2×D13611yescharacteristic
412C2×C4#1058759011yescharacteristic
413C2×C4#1058759411yescharacteristic
414C2×C4#1058759411yescharacteristic
415C2×C4D8×D1711yescharacteristic
416C2×C4#1058759711yescharacteristic
417C2×C4#1058760411yescharacteristic
418C2×C4#1058760511yescharacteristic
419C2×C4#1058761611yescharacteristic
420C2×C4#1058762311yescharacteristic
421C2×C4#1058763311yescharacteristic
422C8—22no—
423C8—41no—
424C8—42no—
425C8—81no—
426C8—1361no—
427C22—2721no—
428C22—2721no—
429C22—2721no—
430C22—2721no—
431C22—682no—
432C22—682no—
433C22—682no—
434C22—1362no—
435C22—1362no—
436C22—1362no—
437C22—1361no—
438C22—1361no—
439C22—1361no—
440C22—1361no—
441C22#1176272611yescharacteristic
442C22#1176300511yescharacteristic
443C22#1176302511yescharacteristic
444C22#1176304611yescharacteristic
445C22#1176305611yescharacteristic
446C22#1176307311yescharacteristic
447C22#1176308011yescharacteristic
448C4—21no—
449C4—21no—
450C4—2721no—
451C4—1361no—
452C4#1176294111yescharacteristic
453C4#1176297011yescharacteristic
454C4#1176300511yescharacteristic
455C4#1176302511yescharacteristic
456C4#1176304511yescharacteristic
457C4#1176306211yescharacteristic
458C4#1176312411yescharacteristic
459C4#1176313611yescharacteristic
460C2—2722no—
461C2—1362no—
462C2#1452814011yescharacteristic
463C2#1452822211yescharacteristic
464C2#1452825011yescharacteristic
465C2#1452831811yescharacteristic
466C2#1452996811yescharacteristic
467C2#1453007811yescharacteristic
468C2#1453009511yescharacteristic
subgroupG/H
centerC23#10587581
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#335C2
socleC23×C17#121
prime radicalC2×#11763005C2
hypercenterC2×#335D17
hypocenterC17#10472
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #14529590C2semidirect
3. #14529578C2semidirect
4. #14528785C2semidirect
5. C2×#11762552C2semidirect
6. #14526668C2semidirect
7. C2×C17×#335C2semidirect
114. C2×C8×C17D8semidirect
197. C2×#335D17semidirect
302. C17#10472semidirect
353. C2×C8D136semidirect

Maximal subgroups

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

subgroupindex
C2×#117630052
#145295902
#145295782
#145287852
C2×#117625522
#145266682
C2×C17×#3352
#1047217