Finite Group Databasebeta

← #16938922

Subgroups — #16938922

Order 4352.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529711C211yesmaximal, characteristic
2#14529589C211yesmaximal, characteristic
3#14529503C211yesmaximal, characteristic, complemented
4C2×#11762561C211yesmaximal, characteristic, complemented
5C2×#11762552C211yesmaximal, characteristic
6#14526667C211yesmaximal, characteristic, complemented
7C17×#1948C211yesmaximal, characteristic, complemented
8C2×#10587560C2211yescharacteristic
9C2×C4⋊#3622—21no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587480—21no—
13C2×#10587480—21no—
14C2×#10587480—21no—
15C2×#10587480—21no—
16C2×C4×#3622C2211yescharacteristic
17#11762564—21no—
18#11762561—22no—
19#11762552—22no—
20C2×C17×#106—21no—
21C2×C17×C4⋊C8C2211yescharacteristic
22C17×#384C2211yescharacteristic
23C4×C4⋊C4×C17C2211yescharacteristic
24C17×#340—21no—
25C22×D68—21no—
26C22×D68—21no—
27C22×D68—21no—
28C22×C8×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C42×C17—21no—
35C2×C42×C17C2311yescharacteristic
36C22×#3622—21no—
37C22×#3622—21no—
38C22×#3622D411yescharacteristic
39C22×#3622D411yescharacteristic
40#10587560—21no—
41#10587560—21no—
42#10587560—21no—
43#10587560Q812yes—
44C17×#106—42no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8D412yes—
47C17×#95—21no—
48#10587480—42no—
49#10587480—42no—
50#10587480—42no—
51#10587480—42no—
52C4⋊#3622—21no—
53C4⋊#3622—21no—
54C4⋊#3622—21no—
55C4⋊#3622—21no—
56C4⋊#3622—42no—
57C4×#3622—21no—
58C4×#3622—21no—
59C23×D17—41no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—41no—
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17#4111yescharacteristic
66C2×D68—22no—
67C2×D68—22no—
68C2×D68—22no—
69C2×D68—41no—
70C2×D68—41no—
71C2×D68—41no—
72C2×D68—41no—
73C2×D68—41no—
74C2×D68—41no—
75C2×D68—41no—
76C2×D68—41no—
77C2×D68—41no—
78C2×D68—41no—
79C2×D68—41no—
80C2×D68—81no—
81C2×D68—81no—
82C2×C8×C17—22no—
83C2×C8×C17—41no—
84C2×C8×C17—41no—
85C4⋊C4×C17—21no—
86C4⋊C4×C17—21no—
87C4⋊C4×C17—21no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—41no—
90C4⋊C4×C17—41no—
91C4⋊C4×C17—41no—
92C4⋊C4×C17—81no—
93C4⋊C4×C17D812yes—
94C42×C17—41no—
95C42×C17—41no—
96C42×C17C2×D411yescharacteristic
97C42×C17C2×Q811yescharacteristic
98C42×C17#4111yescharacteristic
99C42×C17#4111yescharacteristic
100C2×#3622—21no—
101C2×#3622—21no—
102C2×#3622—21no—
103C2×#3622—21no—
104C2×#3622—21no—
105C2×#3622—41no—
106C2×#3622—41no—
107C2×#3622—41no—
108C2×#3622—41no—
109C2×#3622—41no—
110C2×#3622—41no—
111C2×#3622SD1612yes—
112#10599—171nomaximal, Sylow
113C23×C17#12111yescharacteristic
114C22×D17—42no—
115C22×D17—81no—
116C22×D17—81no—
117C22×D17—81no—
118C22×D17—81no—
119C22×D17—81no—
120C22×D17—81no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—22no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—81no—
130C2×C4×C17—81no—
131C2×C4×C17—81no—
132C2×C4×C17#12111yescharacteristic
133C2×C4×C17#12111yescharacteristic
134C2×C4×C17C22⋊Q811yescharacteristic
135C2×C4×C17C22⋊Q811yescharacteristic
136C2×C4×C17C22⋊Q811yescharacteristic
137C2×C4×C17#12611yescharacteristic
138C2×C4×C17C2×D811yescharacteristic
139C2×C4×C17C2×SD1611yescharacteristic
140C2×C4×C17#13511yescharacteristic
141C2×C4×C17#13511yescharacteristic
142C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C17#13711yescharacteristic
146D68—42no—
147D68—42no—
148D68—42no—
149D68—42no—
150D68—82no—
151D68—82no—
152D68—81no—
153D68—81no—
154D68—81no—
155D68—81no—
156C8×C17—42no—
157#3622—22no—
158#3622—41no—
159#3622—81no—
160#3622—81no—
161#1982—171no—
162#1957—171no—
163#1948D1711yescharacteristic, complemented
164#1939—171no—
165C2×#335—171no—
166C2×#331—171no—
167#1296—171no—
168C22×C17#39611yescharacteristic
169C22×C17#46011yescharacteristic
170C22×C17#46311yescharacteristic
171C22×C17#46611yescharacteristic
172C22×C17#46811yescharacteristic
173C22×C17#47111yescharacteristic
174C22×C17#47211yescharacteristic
175C2×D17—82no—
176C2×D17—82no—
177C2×D17—82no—
178C2×D17—161no—
179C2×D17—161no—
180C2×D17—161no—
181C2×D17—161no—
182C4×C17—21no—
183C4×C17—21no—
184C4×C17—42no—
185C4×C17—81no—
186C4×C17—161no—
187C4×C17#45911yescharacteristic
188C4×C17#46411yescharacteristic
189C4×C17#46511yescharacteristic
190C4×C17#46911yescharacteristic
191C4×C17#47411yescharacteristic
192C4×C17#47611yescharacteristic
193C4×C17#47811yescharacteristic
194C4×C17#47811yescharacteristic
195C2×#127—171no—
196C2×#106—21no—
197C2×C4⋊C8—171no—
198C2×C4⋊C8—171no—
199C2×C4⋊C8—341no—
200C2×C4⋊C8C2×D1711yescharacteristic
201C2×#102—341no—
202C2×#102—341no—
203C2×#102—341no—
204C2×#102—341no—
205C2×C4×C8—171no—
206#384C2×D1711yescharacteristic
207C4×C4⋊C4C2×D1711yescharacteristic
208#340—21no—
209#336—341no—
210#335—342no—
211#331—342no—
212C2×C17#166811yescharacteristic
213C2×C17#168111yescharacteristic
214C2×C17#168611yescharacteristic
215C2×C17#169711yescharacteristic
216C2×C17#206311yescharacteristic
217C2×C17#206511yescharacteristic
218C2×C17#206711yescharacteristic
219D17—162no—
220C22×D4—341no—
221C22×D4—341no—
222C22×D4—341no—
223C22×C8—21no—
224C22×C8—171no—
225C22×C8—171no—
226C22×C8—341no—
227C22×C8—341no—
228#127—172no—
229#127—341no—
230#127—341no—
231#127—341no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C22⋊D1711yescharacteristic
236C2×C4⋊C4C22⋊D1711yescharacteristic
237C2×C42—21no—
238C2×C42C22×D1711yescharacteristic
239#106—42no—
240C4⋊C8—21no—
241C4⋊C8—341no—
242C4⋊C8—341no—
243C4⋊C8—341no—
244C4⋊C8—341no—
245C4⋊C8—682no—
246C4⋊C8D6812yes—
247#102—682no—
248#102—682no—
249#102—682no—
250#102—682no—
251C4×C8—341no—
252C4×C8—341no—
253#95—21no—
254C17#1059911yescharacteristic, complemented, Sylow
255C24—681no—
256C2×D4—342no—
257C2×D4—342no—
258C2×D4—342no—
259C2×D4—681no—
260C2×D4—681no—
261C2×D4—681no—
262C2×D4—681no—
263C2×D4—681no—
264C2×D4—681no—
265C2×D4—681no—
266C2×D4—681no—
267C2×D4—681no—
268C2×D4—681no—
269C2×D4—681no—
270C2×D4—1361no—
271C2×D4—1361no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4D4×D1711yescharacteristic
276C22×C4#6325411yescharacteristic
277C22×C4C2×C22⋊D1711yescharacteristic
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—172no—
282C2×C8—341no—
283C2×C8—341no—
284C2×C8—341no—
285C2×C8—341no—
286C2×C8—341no—
287C2×C8—681no—
288C2×C8—681no—
289C2×C8—681no—
290C2×C8—681no—
291C2×C8—681no—
292C2×C8—681no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4#6322812yes—
302C42—41no—
303C42—41no—
304C42C2×D6811yescharacteristic
305C42#6325211yescharacteristic
306C42Q8×D1711yescharacteristic
307C42#6325611yescharacteristic
308C23—682no—
309C23—1361no—
310C23—1361no—
311C23—1361no—
312C23—1361no—
313C23—1361no—
314C23—1361no—
315C23#1058762511yescharacteristic
316D4—682no—
317D4—682no—
318D4—682no—
319D4—682no—
320D4—1362no—
321D4—1362no—
322D4—1361no—
323D4—1361no—
324D4—1361no—
325D4—1361no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#1058758111yescharacteristic
338C2×C4#1058758211yescharacteristic
339C2×C4#1058758311yescharacteristic
340C2×C4#1058758411yescharacteristic
341C2×C4SD16×D1711yescharacteristic
342C2×C4#1058760011yescharacteristic
343C2×C4#1058760011yescharacteristic
344C2×C4#1058760211yescharacteristic
345C2×C4#1058761611yescharacteristic
346C2×C4C2×#6322811yescharacteristic
347C2×C4#1058762811yescharacteristic
348C2×C4#1058763211yescharacteristic
349C2×C4#1058763511yescharacteristic
350C2×C4#1058763611yescharacteristic
351C8—42no—
352C8—342no—
353C8—681no—
354C8—1361no—
355C8—1361no—
356C22—2721no—
357C22—2721no—
358C22—2721no—
359C22—2721no—
360C22—1362no—
361C22—1362no—
362C22—1362no—
363C22#1176273111yescharacteristic
364C22#1176300711yescharacteristic
365C22#1176302611yescharacteristic
366C22#1176304311yescharacteristic
367C22#1176305711yescharacteristic
368C22#1176307411yescharacteristic
369C22#1176307711yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4#1176300411yescharacteristic
376C4#1176303111yescharacteristic
377C4#1176303911yescharacteristic
378C4#1176306311yescharacteristic
379C4#1176308611yescharacteristic
380C4#1176309811yescharacteristic
381C4#1176310611yescharacteristic
382C4#1176310811yescharacteristic
383C2—2722no—
384C2#1452814211yescharacteristic
385C2#1452822311yescharacteristic
386C2#1452825811yescharacteristic
387C2#1452831911yescharacteristic
388C2#1453014111yescharacteristic
389C2#1453015311yescharacteristic
390C2#1453016911yescharacteristic
subgroupG/H
centerC23#10587625
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1948C2
socleC23×C17#121
prime radicalC2×#10587560C22
hypercenter#1948D17
hypocenterC17#10599
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #14529503C2semidirect
4. C2×#11762561C2semidirect
6. #14526667C2semidirect
7. C17×#1948C2semidirect
163. #1948D17semidirect
254. C17#10599semidirect

Maximal subgroups

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

subgroupindex
#145297112
#145295892
#145295032
C2×#117625612
C2×#117625522
#145266672
C17×#19482
#1059917