Finite Group Databasebeta

← #16938135

Subgroups — #16938135

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#14529721C211yesmaximal, characteristic, complemented
3#14529589C211yesmaximal, characteristic
4C2×#11762559C211yesmaximal, characteristic, complemented
5C2×#11762552C211yesmaximal, characteristic
6#14526667C211yesmaximal, characteristic, complemented
7C17×#1803C211yesmaximal, characteristic, complemented
8C22×#63230—21no—
9C2×#10587560C2211yescharacteristic
10#11763009—22no—
11#11763009—22no—
12C2×C4⋊#3622C2211yescharacteristic
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587480—21no—
15C2×#10587480—21no—
16C2×#10587480—21no—
17C2×C4×#3622C2211yescharacteristic
18#11762564—21no—
19#11762564—21no—
20#11762559—22no—
21#11762552—22no—
22C2×C4×Q8×C17C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×#103—21no—
25C17×#384C2211yescharacteristic
26C17×#340—21no—
27C22×Q8×C17D411yescharacteristic
28C22×D68—21no—
29C22×D68—21no—
30C22×D68—21no—
31C22×C8×C17—21no—
32C4×Q8×C17—21no—
33C4×Q8×C17—21no—
34C4×Q8×C17—21no—
35C4×Q8×C17—21no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—21no—
40C2×C4⋊C4×C17D411yescharacteristic
41C2×C42×C17—21no—
42C2×C42×C17C2311yescharacteristic
43C2×#63230—24no—
44C2×#63230—42no—
45C2×#63230—42no—
46C22×#3622—21no—
47C22×#3622—21no—
48C22×#3622D411yescharacteristic
49C22×#3622D411yescharacteristic
50#10587560—21no—
51#10587560—21no—
52#10587560—21no—
53#10587560D412yes—
54C17×C4⋊C8—21no—
55C17×C4⋊C8—21no—
56C17×#103—42no—
57#10587480—24no—
58#10587480—42no—
59#10587480—42no—
60C4⋊#3622—21no—
61C4⋊#3622—21no—
62C4⋊#3622—21no—
63C4⋊#3622D412yes—
64C4×#3622—21no—
65C4×#3622—21no—
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×C17—41no—
76C22×C4×C17C2×D411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17#4111yescharacteristic
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—41no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C4⋊C4×C17—21no—
99C4⋊C4×C17—21no—
100C4⋊C4×C17—41no—
101C4⋊C4×C17—41no—
102C4⋊C4×C17—41no—
103C4⋊C4×C17—41no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C4⋊C4×C17—81no—
107C42×C17—41no—
108C42×C17—41no—
109C42×C17C2×D411yescharacteristic
110C42×C17C2×D411yescharacteristic
111C42×C17#4111yescharacteristic
112C42×C17#4111yescharacteristic
113#63230—48no—
114C2×#3622—21no—
115C2×#3622—21no—
116C2×#3622—22no—
117C2×#3622—21no—
118C2×#3622—21no—
119C2×#3622—21no—
120C2×#3622—41no—
121C2×#3622—41no—
122C2×#3622—41no—
123C2×#3622—41no—
124C2×#3622—41no—
125C2×#3622SD1612yescomplemented
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—81no—
148C2×C4×C17—81no—
149C2×C4×C17—81no—
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×SD1611yescharacteristic
157C2×C4×C17C2×SD1611yescharacteristic
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
164D68—42no—
165D68—42no—
166D68—42no—
167D68—42no—
168D68—82no—
169D68—82no—
170D68—81no—
171D68—81no—
172D68—81no—
173D68—81no—
174C8×C17—81no—
175#3622—22no—
176#3622—42no—
177#3622—41no—
178#3622—81no—
179C2×#460—171no—
180#1984—171no—
181#1957—171no—
182#1803D1711yescharacteristic, complemented
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—161no—
205C4×C17#44911yescharacteristic
206C4×C17#45011yescharacteristic
207C4×C17#46111yescharacteristic
208C4×C17#46311yescharacteristic
209C4×C17#46511yescharacteristic
210C4×C17#46811yescharacteristic
211C4×C17#48111yescharacteristic
212C4×C17#48211yescharacteristic
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—21no—
222C2×#102—341no—
223C2×#102—341no—
224C2×#102—341no—
225C2×C4×C8—171no—
226#384C2×D1711yescharacteristic
227#340—21no—
228#336—341no—
229#336—341no—
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×Q8C22⋊D1711yescharacteristic
241C22×D4—341no—
242C22×D4—341no—
243C22×D4—341no—
244C2×SD16—344no—
245C2×SD16—682no—
246C2×SD16—682no—
247C22×C8—21no—
248C22×C8—171no—
249C22×C8—171no—
250C22×C8—341no—
251C22×C8—341no—
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—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C22⋊D1711yescharacteristic
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—42no—
274#102—344no—
275#102—682no—
276#102—682no—
277C4×C8—341no—
278C4×C8—341no—
279C17#1047511yescharacteristic, complemented, Sylow
280C24—681no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8#6323012yes—
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—41no—
306C22×C4D4×D1711yescharacteristic
307C22×C4#6325411yescharacteristic
308C22×C4C2×C22⋊D1711yescharacteristic
309SD16—688no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—172no—
314C2×C8—341no—
315C2×C8—341no—
316C2×C8—341no—
317C2×C8—341no—
318C2×C8—341no—
319C2×C8—342no—
320C2×C8—681no—
321C2×C8—681no—
322C2×C8—681no—
323C2×C8—681no—
324C2×C8—681no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C42—41no—
335C42—41no—
336C42#6325211yescharacteristic
337C42#6325211yescharacteristic
338C42D4×D1711yescharacteristic
339C42D4×D1711yescharacteristic
340C23—682no—
341C23—1361no—
342C23—1361no—
343C23—1361no—
344C23—1361no—
345C23—1361no—
346C23—1361no—
347C23#1058762511yescharacteristic
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—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4#1058756911yescharacteristic
374C2×C4#1058757011yescharacteristic
375C2×C4#1058757011yescharacteristic
376C2×C4#1058757111yescharacteristic
377C2×C4SD16×D1711yescharacteristic
378C2×C4#1058760011yescharacteristic
379C2×C4#1058760411yescharacteristic
380C2×C4#1058760511yescharacteristic
381C2×C4#1058761511yescharacteristic
382C2×C4#1058761811yescharacteristic
383C2×C4#1058762311yescharacteristic
384C2×C4C2×#6323011yescharacteristic
385C2×C4#1058763511yescharacteristic
386C2×C4#1058763611yescharacteristic
387C8—81no—
388C8—342no—
389C8—682no—
390C8—681no—
391C8—1361no—
392C22—2721no—
393C22—2721no—
394C22—2721no—
395C22—2721no—
396C22—1362no—
397C22—1362no—
398C22—1362no—
399C22#1176272411yescharacteristic
400C22#1176300711yescharacteristic
401C22#1176303311yescharacteristic
402C22#1176304011yescharacteristic
403C22#1176306011yescharacteristic
404C22#1176307411yescharacteristic
405C22#1176307711yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—161no—
411C4#1176295211yescharacteristic
412C4#1176295911yescharacteristic
413C4#1176301311yescharacteristic
414C4#1176302711yescharacteristic
415C4#1176304111yescharacteristic
416C4#1176305811yescharacteristic
417C4#1176312711yescharacteristic
418C4#1176313311yescharacteristic
419C2—2722no—
420C2#1452813411yescharacteristic
421C2#1452820211yescharacteristic
422C2#1452826611yescharacteristic
423C2#1452835411yescharacteristic
424C2#1452997311yescharacteristic
425C2#1453007411yescharacteristic
426C2#1453009811yescharacteristic
subgroupG/H
centerC23#10587625
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1803C2
socleC23×C17#121
prime radicalC2×#10587560C22
hypercenter#1803D17
hypocenterC17#10475
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #14529721C2semidirect
4. C2×#11762559C2semidirect
6. #14526667C2semidirect
7. C17×#1803C2semidirect
125. C2×#3622SD16semidirect
182. #1803D17semidirect
279. C17#10475semidirect

Maximal subgroups

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

subgroupindex
C2×#117630092
#145297212
#145295892
C2×#117625592
C2×#117625522
#145266672
C17×#18032
#1047517