Finite Group Databasebeta

← #16929131

Subgroups — #16929131

Order 4352.

592 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763086C211yesmaximal, characteristic
2#14531735C211yesmaximal, characteristic
3#14529708C211yesmaximal, characteristic, complemented
4C2×#11762538C211yesmaximal, characteristic
5#14526667C211yesmaximal, characteristic, complemented
6#14526624C211yesmaximal, characteristic, complemented
7C17×#1990C211yesmaximal, characteristic, complemented
8C2×C4×D68C2211yescharacteristic
9C2×#10587578—21no—
10#11763086—22no—
11#11763086C414yescomplemented
12C2×#10587478—21no—
13C2×C4⋊#3622C2211yescharacteristic
14C2×C4⋊#3622C2211yescharacteristic
15C2×#10587506—21no—
16C2×#10587506—21no—
17C2×#10587480—21no—
18#11762710—21no—
19#11762699—22no—
20#11762666—21no—
21C4⋊C4×Dic17—21no—
22C4×C4⋊Dic17C2211yescharacteristic
23#11762538—22no—
24C2×C17×C4⋊Q8C2211yescharacteristic
25C2×C4×C8×C17C2211yescharacteristic
26C17×#384C2211yescharacteristic
27C17×#340—22no—
28C22×Q8×C17—21no—
29C22×D68D411yescharacteristic
30C22×C4×D17—21no—
31C22×C8×C17—21no—
32C17×C4⋊Q8—21no—
33C17×C4⋊Q8—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8C2×C412yes—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—21no—
40C2×C4⋊C4×C17D412yes—
41C2×C42×C17C2311yescharacteristic
42C2×#63227—22no—
43C2×#63227—22no—
44C2×#63227—21no—
45C2×C4⋊Dic17D411yescharacteristic
46C2×C4⋊Dic17D411yescharacteristic
47C2×C4⋊Dic17D411yescharacteristic
48C2×C4×Dic17—22no—
49C2×C4×Dic17—21no—
50C22×#3622—21no—
51C22×#3622—21no—
52#10587578—42no—
53#10587578—42no—
54C4×D68—21no—
55C4×D68—21no—
56C4×D68C2×C412yes—
57C4×D68D412yes—
58C4×C8×C17—21no—
59C4×C8×C17—21no—
60#10587506—42no—
61#10587506—42no—
62#10587502—22no—
63#10587502—21no—
64#10587480—24no—
65#10587478—24no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68C4⋊#3622—21no—
69C4⋊#3622C2×C412yes—
70C23×D17—21no—
71C2×Q8×C17—22no—
72C2×Q8×C17—41no—
73C2×Q8×C17—41no—
74C2×Q8×C17—41no—
75C2×Q8×C17—41no—
76C2×Q8×C17—41no—
77C22×C4×C17—22no—
78C22×C4×C17—41no—
79C22×C4×C17C2×D411yescharacteristic
80C22×C4×C17C2×D411yescharacteristic
81C22×C4×C17C2×D411yescharacteristic
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C2×D68—21no—
86C2×D68—21no—
87C2×D68—21no—
88C2×D68—21no—
89C2×D68—21no—
90C2×D68C22⋊C412yes—
91C2×C4×D17—22no—
92C2×C4×D17—22no—
93C2×C4×D17—41no—
94C2×C4×D17—41no—
95C2×C4×D17—41no—
96C2×C4×D17—41no—
97C2×C8×C17—22no—
98C2×C8×C17—41no—
99C2×C8×C17—41no—
100C4⋊C4×C17—22no—
101C4⋊C4×C17—22no—
102C4⋊C4×C17—42no—
103C4⋊C4×C17—41no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C4⋊C4×C17—41no—
107C4⋊C4×C17—41no—
108C4⋊C4×C17—41no—
109C42×C17C22×C411yescharacteristic
110C42×C17C2×D411yescharacteristic
111C42×C17#4111yescharacteristic
112C42×C17#4111yescharacteristic
113#63227—22no—
114#63227—22no—
115#63227—44no—
116#63227—82no—
117C4⋊Dic17—21no—
118C4⋊Dic17—21no—
119C4⋊Dic17—21no—
120C4⋊Dic17—21no—
121C4⋊Dic17C22⋊C412yes—
122C4⋊Dic17D812yes—
123C4×Dic17—44no—
124C4×Dic17—41no—
125C4×Dic17—41no—
126C2×#3622—22no—
127C2×#3622—41no—
128C2×#3622—41no—
129C2×#3622—41no—
130C2×#3622—41no—
131C2×#3622—41no—
132#8984—171nomaximal, Sylow
133C23×C17#12011yescharacteristic
134C22×D17—22no—
135C22×D17—41no—
136C22×D17—41no—
137C22×D17—41no—
138C22×D17—41no—
139C22×D17—41no—
140C22×D17—41no—
141Q8×C17—42no—
142Q8×C17—42no—
143Q8×C17—81no—
144Q8×C17—81no—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—42no—
148C2×C4×C17—42no—
149C2×C4×C17—42no—
150C2×C4×C17—42no—
151C2×C4×C17—81no—
152C2×C4×C17—81no—
153C2×C4×C17C2×C22⋊C411yescharacteristic
154C2×C4×C17C4×D411yescharacteristic
155C2×C4×C17C4×D411yescharacteristic
156C2×C4×C17#12111yescharacteristic
157C2×C4×C17#12111yescharacteristic
158C2×C4×C17#12311yescharacteristic
159C2×C4×C17C2×D811yescharacteristic
160C2×C4×C17#13511yescharacteristic
161C2×C4×C17#13511yescharacteristic
162C2×C4×C17#13511yescharacteristic
163C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C17#13711yescharacteristic
166C2×C4×C17#13711yescharacteristic
167C2×Dic17—22no—
168C2×Dic17—22no—
169C2×Dic17—41no—
170C2×Dic17—41no—
171C2×Dic17—41no—
172C2×Dic17—41no—
173C2×Dic17—41no—
174C2×Dic17—41no—
175C2×Dic17—41no—
176D68—22no—
177D68—22no—
178D68—41no—
179D68—41no—
180C4×D17—42no—
181C4×D17—42no—
182C4×D17—42no—
183C4×D17—42no—
184C8×C17—42no—
185#3622—42no—
186#3622—81no—
187C2×#474—171no—
188#2354—171no—
189#1990D1711yescharacteristic, complemented
190#1981—171no—
191C2×D4⋊C8—171no—
192#1296—171no—
193#1279—171no—
194C22×C17#38611yescharacteristic
195C22×C17#44711yescharacteristic
196C22×C17#44911yescharacteristic
197C22×C17#45211yescharacteristic
198C22×C17#45211yescharacteristic
199C22×C17#45511yescharacteristic
200C22×C17#45611yescharacteristic
201C2×D17—42no—
202C2×D17—42no—
203C2×D17—42no—
204C2×D17—81no—
205C2×D17—81no—
206C2×D17—81no—
207C2×D17—81no—
208C4×C17—21no—
209C4×C17—21no—
210C4×C17—82no—
211C4×C17—82no—
212C4×C17#41611yescharacteristic
213C4×C17#41911yescharacteristic
214C4×C17C4×D811yescharacteristic
215C4×C17#44211yescharacteristic
216C4×C17#45911yescharacteristic
217C4×C17#46311yescharacteristic
218C4×C17#48511yescharacteristic
219C4×C17#48511yescharacteristic
220Dic17—42no—
221Dic17—42no—
222Dic17—81no—
223C2×C4⋊Q8C2×D1711yescharacteristic
224C2×C4×D4—171no—
225C2×#117—341no—
226#474—174no—
227#474—342no—
228C2×#107—341no—
229C2×C4⋊C8—171no—
230C2×C4⋊C8—171no—
231C2×#103—341no—
232C2×#103—341no—
233C2×#102—341no—
234C2×C4×C8C2×D1711yescharacteristic
235#390—341no—
236#388—342no—
237#384C2×D1711yescharacteristic
238#380—341no—
239C4×C4⋊C4—171no—
240C4×C4⋊C4—341no—
241#340—22no—
242D4⋊C8—342no—
243C2×C17#164111yescharacteristic
244C2×C17#164611yescharacteristic
245C2×C17#164711yescharacteristic
246C2×C17#165211yescharacteristic
247C2×C17#187311yescharacteristic
248C2×C17#187911yescharacteristic
249C2×C17#188211yescharacteristic
250D17—82no—
251C22×Q8—21no—
252C22×D4—171no—
253C23×C4—341no—
254C22×C8—21no—
255C22×C8—341no—
256C22×C8—341no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8C4×D1712yes—
261C4×D4—172no—
262C4×D4—172no—
263C4×D4—341no—
264C4×D4—341no—
265#117—682no—
266#117—682no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—171no—
272C2×C4⋊C4—171no—
273C2×C4⋊C4—171no—
274C2×C4⋊C4C22⋊D1712yes—
275C2×C22⋊C4—341no—
276C2×C22⋊C4—342no—
277C2×C22⋊C4—342no—
278C2×C42—342no—
279C2×C42—341no—
280C2×C42C22×D1711yescharacteristic
281#107—344no—
282C4⋊C8—172no—
283C4⋊C8—341no—
284C4⋊C8—341no—
285C4⋊C8—341no—
286#103—682no—
287#103—682no—
288#102—344no—
289C4×C8—21no—
290C4×C8—21no—
291#95—342no—
292#95—341no—
293C17#898411yescharacteristic, complemented, Sylow
294C24—341no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×D4—172no—
302C2×D4—341no—
303C2×D4—341no—
304C2×D4—341no—
305C2×D4—341no—
306C2×D4—341no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—341no—
310C22×C4—341no—
311C22×C4—342no—
312C22×C4—342no—
313C22×C4—341no—
314C22×C4—681no—
315C22×C4—681no—
316C22×C4—681no—
317C22×C4—681no—
318C22×C4D4×D1711yescharacteristic
319C22×C4D4×D1711yescharacteristic
320C22×C4C2×C22⋊D1711yescharacteristic
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—342no—
325C2×C8—681no—
326C2×C8—681no—
327C2×C8—681no—
328C2×C8—681no—
329C2×C8—681no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—42no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—172no—
340C4⋊C4—172no—
341C4⋊C4—341no—
342C4⋊C4—341no—
343C4⋊C4—341no—
344C4⋊C4—341no—
345C22⋊C4—342no—
346C22⋊C4—342no—
347C22⋊C4—684no—
348C22⋊C4—1362no—
349C42—684no—
350C42—681no—
351C42—681no—
352C42C2×C4×D1711yescharacteristic
353C42#6325211yescharacteristic
354C42D4×D1711yescharacteristic
355C42#6325411yescharacteristic
356C23—342no—
357C23—681no—
358C23—681no—
359C23—681no—
360C23—681no—
361C23—681no—
362C23—681no—
363C23#1058762311yescharacteristic
364Q8—42no—
365Q8—42no—
366Q8—81no—
367Q8—81no—
368D4—342no—
369D4—342no—
370D4—681no—
371D4—681no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—342no—
381C2×C4—342no—
382C2×C4—681no—
383C2×C4—681no—
384C2×C4—681no—
385C2×C4—681no—
386C2×C4—682no—
387C2×C4—682no—
388C2×C4—682no—
389C2×C4—682no—
390C2×C4—681no—
391C2×C4—681no—
392C2×C4—681no—
393C2×C4C22⋊C4×D1711yescharacteristic
394C2×C4#1058756711yescharacteristic
395C2×C4#1058756911yescharacteristic
396C2×C4#1058757011yescharacteristic
397C2×C4D8×D1711yescharacteristic
398C2×C4#1058759711yescharacteristic
399C2×C4#1058760011yescharacteristic
400C2×C4#1058760111yescharacteristic
401C2×C4#1058760211yescharacteristic
402C2×C4#1058760211yescharacteristic
403C2×C4#1058760411yescharacteristic
404C2×C4#1058760511yescharacteristic
405C2×C4C4×C22⋊D1711yescharacteristic
406C2×C4#1058762411yescharacteristic
407C8—42no—
408C8—682no—
409C8—1361no—
410C22—682no—
411C22—682no—
412C22—682no—
413C22—1361no—
414C22—1361no—
415C22—1361no—
416C22—1361no—
417C22#1176268511yescharacteristic
418C22#1176294111yescharacteristic
419C22#1176295311yescharacteristic
420C22#1176296811yescharacteristic
421C22#1176297011yescharacteristic
422C22#1176298611yescharacteristic
423C22#1176299111yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—82no—
428C4—682no—
429C4—682no—
430C4—1361no—
431C4#1176280411yescharacteristic
432C4#1176281611yescharacteristic
433C4#1176288911yescharacteristic
434C4#1176291811yescharacteristic
435C4#1176300311yescharacteristic
436C4#1176302311yescharacteristic
437C4#1176314811yescharacteristic
438C4#1176314911yescharacteristic
439C2—1362no—
440C2#1452797411yescharacteristic
441C2#1452800911yescharacteristic
442C2#1452801611yescharacteristic
443C2#1452805111yescharacteristic
444C2#1452909311yescharacteristic
445C2#1452912911yescharacteristic
446C2#1452915611yescharacteristic
subgroupG/H
centerC23#10587623
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1990C2
socleC23×C17#120
prime radicalC22×D68D4
cosocleC2×C42×C17C23
hypercenter#1990D17
hypocenterC17#8984
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
3. #14529708C2semidirect
5. #14526667C2semidirect
6. #14526624C2semidirect
7. C17×#1990C2semidirect
11. #11763086C4semidirect
189. #1990D17semidirect
293. C17#8984semidirect

Maximal subgroups

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

subgroupindex
C2×#117630862
#145317352
#145297082
C2×#117625382
#145266672
#145266242
C17×#19902
#898417