Finite Group Databasebeta

← #16938136

Subgroups — #16938136

Order 4352.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763009C211yesmaximal, characteristic
2#14529590C211yesmaximal, characteristic
3#14528789C211yesmaximal, characteristic, complemented
4C2×#11762560C211yesmaximal, characteristic, complemented
5C2×#11762552C211yesmaximal, characteristic
6#14526668C211yesmaximal, characteristic, complemented
7C17×#1984C211yesmaximal, characteristic, complemented
8C22×#63230—21no—
9C2×#10587560C2211yescharacteristic
10#11763009—22no—
11#11763009—22no—
12C2×C4⋊#3622C2211yescharacteristic
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587506—21no—
15C2×#10587492—21no—
16C2×#10587492—21no—
17C2×#10587480—21no—
18#11762679C2211yescharacteristic
19#11762571—21no—
20#11762560—22no—
21#11762552—22no—
22C2×C4×Q8×C17C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C17C2211yescharacteristic
25C17×#336—21no—
26C17×#336—21no—
27C22×Q8×C17D411yescharacteristic
28C22×D68—21no—
29C22×D68—21no—
30C22×D68—21no—
31C22×C8×C17—21no—
32C22×C8×C17D411yescharacteristic
33C22×C8×C17D411yescharacteristic
34C4×Q8×C17—21no—
35C4×Q8×C17—21no—
36C4×Q8×C17—21no—
37C4×Q8×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17D411yescharacteristic
40C2×C42×C17—21no—
41C2×C42×C17C2311yescharacteristic
42C2×#63230—24no—
43C2×#63230—42no—
44C2×#63230—42no—
45C2×C4⋊Dic17—21no—
46C2×C4⋊Dic17—21no—
47C2×C4⋊Dic17—21no—
48C22×#3622—21no—
49C22×#3622—21no—
50#10587560—21no—
51#10587560—21no—
52#10587560—21no—
53#10587560D412yes—
54C17×C4⋊C8—21no—
55C17×C4⋊C8—21no—
56C4×C8×C17—21no—
57C4×C8×C17—21no—
58#10587506—42no—
59#10587492—42no—
60#10587492—42no—
61#10587480—24no—
62C4⋊#3622—21no—
63C4⋊#3622—21no—
64C4⋊#3622—21no—
65C4⋊#3622D412yes—
66C23×D17—41no—
67C2×Q8×C17—21no—
68C2×Q8×C17—21no—
69C2×Q8×C17—21no—
70C2×Q8×C17—21no—
71C2×Q8×C17—21no—
72C2×Q8×C17SD1612yes—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17C2×D411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C22×C4×C17#4111yescharacteristic
78C22×Dic17—41no—
79C2×D68—22no—
80C2×D68—22no—
81C2×D68—22no—
82C2×D68—41no—
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—81no—
94C2×D68—81no—
95C2×C8×C17—21no—
96C2×C8×C17—21no—
97C2×C8×C17—21no—
98C2×C8×C17—21no—
99C2×C8×C17—21no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C2×C8×C17—41no—
103C2×C8×C17SD1612yescomplemented
104C4⋊C4×C17—21no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17—41no—
107C4⋊C4×C17—41no—
108C42×C17—41no—
109C42×C17—41no—
110C42×C17C2×D411yescharacteristic
111C42×C17C2×D411yescharacteristic
112C42×C17#4111yescharacteristic
113C42×C17#4111yescharacteristic
114#63230—48no—
115C4⋊Dic17—41no—
116C4⋊Dic17—41no—
117C4⋊Dic17—41no—
118C4⋊Dic17—41no—
119C4⋊Dic17—81no—
120C2×#3622—22no—
121C2×#3622—41no—
122C2×#3622—41no—
123C2×#3622—41no—
124C2×#3622—41no—
125C2×#3622—41no—
126#10475—171nomaximal, Sylow
127C23×C17#12111yescharacteristic
128C22×D17—42no—
129C22×D17—81no—
130C22×D17—81no—
131C22×D17—81no—
132C22×D17—81no—
133C22×D17—81no—
134C22×D17—81no—
135Q8×C17—22no—
136Q8×C17—22no—
137Q8×C17—41no—
138Q8×C17—41no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—22no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17#12011yescharacteristic
148C2×C4×C17#12111yescharacteristic
149C2×C4×C17#12111yescharacteristic
150C2×C4×C17#12311yescharacteristic
151C2×C4×C17#12311yescharacteristic
152C2×C4×C17#12411yescharacteristic
153C2×C4×C17C2×SD1611yescharacteristic
154C2×C4×C17C2×SD1611yescharacteristic
155C2×C4×C17#13511yescharacteristic
156C2×C4×C17#13511yescharacteristic
157C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C17#13711yescharacteristic
161C2×Dic17—81no—
162C2×Dic17—81no—
163C2×Dic17—81no—
164D68—42no—
165D68—42no—
166D68—42no—
167D68—42no—
168D68—82no—
169D68—82no—
170D68—81no—
171D68—81no—
172D68—81no—
173D68—81no—
174C8×C17—22no—
175C8×C17—41no—
176C8×C17—81no—
177#3622—42no—
178#3622—81no—
179C2×#460—171no—
180#1984D1711yescharacteristic, complemented
181#1957—171no—
182#1803—171no—
183C2×#334—171no—
184C2×#331—171no—
185#1296—171no—
186C22×C17#39411yescharacteristic
187C22×C17#46011yescharacteristic
188C22×C17#46411yescharacteristic
189C22×C17#46511yescharacteristic
190C22×C17#46911yescharacteristic
191C22×C17#47111yescharacteristic
192C22×C17#47211yescharacteristic
193C2×D17—82no—
194C2×D17—82no—
195C2×D17—82no—
196C2×D17—161no—
197C2×D17—161no—
198C2×D17—161no—
199C2×D17—161no—
200C4×C17—21no—
201C4×C17—21no—
202C4×C17—42no—
203C4×C17—81no—
204C4×C17#44911yescharacteristic
205C4×C17#45011yescharacteristic
206C4×C17#46111yescharacteristic
207C4×C17#46311yescharacteristic
208C4×C17#46511yescharacteristic
209C4×C17#46811yescharacteristic
210C4×C17#48111yescharacteristic
211C4×C17#48211yescharacteristic
212Dic17—161no—
213C22×SD16—341no—
214C2×#127—171no—
215C2×C4×Q8C2×D1711yescharacteristic
216#460—342no—
217#460—342no—
218C2×C4⋊C8—171no—
219C2×C4⋊C8—171no—
220C2×C4⋊C8C2×D1711yescharacteristic
221C2×#103—341no—
222C2×#102—341no—
223C2×#102—341no—
224C2×#102—341no—
225C2×C4×C8C2×D1711yescharacteristic
226#384—171no—
227#340—341no—
228#336—21no—
229#336—21no—
230#334—342no—
231#331—342no—
232C2×C17#166611yescharacteristic
233C2×C17#167811yescharacteristic
234C2×C17#168811yescharacteristic
235C2×C17#170211yescharacteristic
236C2×C17#203411yescharacteristic
237C2×C17#205111yescharacteristic
238C2×C17#205511yescharacteristic
239D17—162no—
240C22×Q8D6811yescharacteristic
241C22×D4—341no—
242C22×D4—341no—
243C22×D4—341no—
244C2×SD16—344no—
245C2×SD16—682no—
246C2×SD16—682no—
247C22×C8—21no—
248C22×C8—341no—
249C22×C8—341no—
250C22×C8C22⋊D1711yescharacteristic
251C22×C8C22⋊D1711yescharacteristic
252#127—172no—
253#127—341no—
254#127—341no—
255#127—341no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—341no—
262C2×C4⋊C4—341no—
263C2×C4⋊C4—341no—
264C2×C4⋊C4D6811yescharacteristic
265C2×C42—21no—
266C2×C42C22×D1711yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—172no—
270C4⋊C8—341no—
271C4⋊C8—341no—
272C4⋊C8—341no—
273#103—682no—
274#102—344no—
275#102—682no—
276#102—682no—
277C4×C8—21no—
278C4×C8—21no—
279C17#1047511yescharacteristic, complemented, Sylow
280C24—681no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8#6321912yes—
287C2×D4—342no—
288C2×D4—342no—
289C2×D4—342no—
290C2×D4—681no—
291C2×D4—681no—
292C2×D4—681no—
293C2×D4—681no—
294C2×D4—681no—
295C2×D4—681no—
296C2×D4—681no—
297C2×D4—681no—
298C2×D4—681no—
299C2×D4—681no—
300C2×D4—681no—
301C2×D4—1361no—
302C2×D4—1361no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—681no—
306C22×C4C2×D6811yescharacteristic
307C22×C4#6325211yescharacteristic
308C22×C4C2×C22⋊D1711yescharacteristic
309SD16—688no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—342no—
319C2×C8—681no—
320C2×C8—681no—
321C2×C8—681no—
322C2×C8—681no—
323C2×C8—681no—
324C2×C8#6323012yescomplemented
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—681no—
330C4⋊C4—681no—
331C4⋊C4—681no—
332C4⋊C4—681no—
333C4⋊C4—1361no—
334C42—41no—
335C42—41no—
336C42D4×D1711yescharacteristic
337C42D4×D1711yescharacteristic
338C42#6325411yescharacteristic
339C42#6325411yescharacteristic
340C23—682no—
341C23—1361no—
342C23—1361no—
343C23—1361no—
344C23—1361no—
345C23—1361no—
346C23—1361no—
347C23#1058761611yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—682no—
353D4—682no—
354D4—682no—
355D4—682no—
356D4—1362no—
357D4—1362no—
358D4—1361no—
359D4—1361no—
360D4—1361no—
361D4—1361no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—1361no—
371C2×C4—1361no—
372C2×C4—1361no—
373C2×C4#1058756811yescharacteristic
374C2×C4#1058756911yescharacteristic
375C2×C4#1058757111yescharacteristic
376C2×C4#1058757211yescharacteristic
377C2×C4C2×#6321911yescharacteristic
378C2×C4#1058759011yescharacteristic
379C2×C4#1058759411yescharacteristic
380C2×C4#1058759411yescharacteristic
381C2×C4#1058762411yescharacteristic
382C2×C4#1058762511yescharacteristic
383C2×C4C2×#6323011yescharacteristic
384C2×C4#1058762811yescharacteristic
385C2×C4#1058763511yescharacteristic
386C2×C4#1058763611yescharacteristic
387C8—22no—
388C8—41no—
389C8—81no—
390C8—682no—
391C8—1361no—
392C22—2721no—
393C22—2721no—
394C22—2721no—
395C22—2721no—
396C22—1362no—
397C22—1362no—
398C22—1362no—
399C22#1176272511yescharacteristic
400C22#1176300911yescharacteristic
401C22#1176303111yescharacteristic
402C22#1176303811yescharacteristic
403C22#1176306211yescharacteristic
404C22#1176307211yescharacteristic
405C22#1176307911yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—2721no—
411C4#1176295611yescharacteristic
412C4#1176296211yescharacteristic
413C4#1176301111yescharacteristic
414C4#1176302111yescharacteristic
415C4#1176304011yescharacteristic
416C4#1176305711yescharacteristic
417C4#1176312811yescharacteristic
418C4#1176313411yescharacteristic
419C2—2722no—
420C2#1452813211yescharacteristic
421C2#1452820011yescharacteristic
422C2#1452826811yescharacteristic
423C2#1452835211yescharacteristic
424C2#1452997411yescharacteristic
425C2#1453007511yescharacteristic
426C2#1453009911yescharacteristic
subgroupG/H
centerC23#10587616
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1984C2
socleC23×C17#121
prime radicalC2×#10587560C22
hypercenter#1984D17
hypocenterC17#10475
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
3. #14528789C2semidirect
4. C2×#11762560C2semidirect
6. #14526668C2semidirect
7. C17×#1984C2semidirect
103. C2×C8×C17SD16semidirect
180. #1984D17semidirect
279. C17#10475semidirect
324. C2×C8#63230semidirect

Maximal subgroups

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

subgroupindex
C2×#117630092
#145295902
#145287892
C2×#117625602
C2×#117625522
#145266682
C17×#19842
#1047517