Finite Group Databasebeta

← #16930852

Subgroups — #16930852

Order 4352.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539905C211yesmaximal, characteristic
2#14537527C211yesmaximal, characteristic
3#14529629C211yesmaximal, characteristic, complemented
4#14527459C211yesmaximal, characteristic
5#14526681C211yesmaximal, characteristic, complemented
6#14526634C211yesmaximal, characteristic, complemented
7C2×C17×#332C211yesmaximal, characteristic, complemented
8C2×#10587587—21no—
9#11763359C2211yescharacteristic
10#11763212—21no—
11#11763157—21no—
12#11763122C414yes—
13#11763086—22no—
14#11762886—21no—
15#11762879—22no—
16#11762874—21no—
17#11762862C2211yescharacteristic
18#11762833C2211yescharacteristic
19C2×#10587507—21no—
20C2×#10587507—21no—
21#11762775—21no—
22C4×#63223C2211yescharacteristic
23#11762554—21no—
24#11762552—21no—
25C2×C17×C4⋊Q8C2211yescharacteristic
26C2×C17×C4⋊C8C2211yescharacteristic
27C2×C17×C4⋊C8C2211yescharacteristic
28C17×#332—21no—
29C17×#332—21no—
30C22×Q8×C17—21no—
31C2×#63252—21no—
32C22×C8×C17—21no—
33C22×C8×C17—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—21no—
36C17×C4⋊Q8—21no—
37C17×C4⋊Q8—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17C2×C412yes—
40C2×C42×C17C2311yescharacteristic
41#10587616—21no—
42#10587616C2×C412yes—
43C2×#63223—21no—
44C2×#63223D411yescharacteristic
45C2×#63223D411yescharacteristic
46#10587587—42no—
47#10587587—42no—
48C2×#63218—22no—
49C2×C8×D17—22no—
50#10587561—21no—
51#10587560D411yescharacteristic
52C4×D68—21no—
53C4×D68D412yes—
54#10587555D411yescharacteristic
55C17×C4⋊C8—21no—
56C17×C4⋊C8—21no—
57C17×C4⋊C8—21no—
58C17×C4⋊C8D411yescharacteristic
59C17×C4⋊C8D411yescharacteristic
60#10587507—42no—
61#10587507—42no—
62C22⋊#3622C2×C412yes—
63#10587491—22no—
64#10587491—22no—
65#10587480—24no—
66#10587478—24no—
67C4⋊#3622—21no—
68C4⋊#3622—21no—
69C4⋊#3622—21no—
70#10587474—21no—
71C4×#3622—21no—
72C4×#3622—21no—
73C2×Q8×C17—41no—
74C2×Q8×C17—41no—
75C2×Q8×C17—41no—
76C2×Q8×C17—41no—
77C2×Q8×C17—41no—
78C2×Q8×C17—41no—
79C22×C4×C17—22no—
80C22×C4×C17C22×C411yescharacteristic
81C22×C4×C17C2×D411yescharacteristic
82C22×C4×C17#4111yescharacteristic
83C2×C22⋊D17—22no—
84#63252—41no—
85#63252—41no—
86#63252—41no—
87#63252—41no—
88C2×D68—21no—
89C2×D68—21no—
90C2×D68C22⋊C412yes—
91C2×C4×D17—22no—
92C2×Dic34—21no—
93C2×C8×C17—21no—
94C2×C8×C17—21no—
95C2×C8×C17—41no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C2×C8×C17—81no—
99C4⋊C4×C17—22no—
100C4⋊C4×C17—22no—
101C4⋊C4×C17—41no—
102C4⋊C4×C17—41no—
103C42×C17C2×D411yescharacteristic
104C42×C17C2×D411yescharacteristic
105C42×C17C2×D411yescharacteristic
106C42×C17#4111yescharacteristic
107#63227—22no—
108#63227—22no—
109C4⋊Dic17—21no—
110C4⋊Dic17C22⋊C412yes—
111#63223—21no—
112#63223—21no—
113#63223—21no—
114#63223—41no—
115#63223—41no—
116#63223D812yes—
117C2×#3622—21no—
118C2×#3622—22no—
119C2×#3622—21no—
120C2×#3622—41no—
121#63218—44no—
122C8×D17—44no—
123#9271—171nomaximal, Sylow
124C23×C17C4×D411yescharacteristic
125C22×D17—22no—
126Q8×C17—81no—
127Q8×C17—81no—
128Q8×C17—81no—
129Q8×C17—81no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—41no—
133C2×C4×C17—42no—
134C2×C4×C17—42no—
135C2×C4×C17—42no—
136C2×C4×C17C2×C22⋊C411yescharacteristic
137C2×C4×C17C4×D411yescharacteristic
138C2×C4×C17#12011yescharacteristic
139C2×C4×C17#12111yescharacteristic
140C2×C4×C17#12111yescharacteristic
141C2×C4×C17#12311yescharacteristic
142C2×C4×C17C2×D811yescharacteristic
143C2×C4×C17#13511yescharacteristic
144C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
146C22⋊D17—42no—
147C22⋊D17—42no—
148C2×Dic17—22no—
149D68—42no—
150D68—41no—
151D68—41no—
152D68—41no—
153D68—41no—
154C4×D17—42no—
155C4×D17—42no—
156Dic34—41no—
157Dic34—41no—
158C8×C17—41no—
159C8×C17—41no—
160C8×C17—81no—
161#3622—22no—
162#3622—42no—
163#3622—41no—
164#3622—81no—
165#3226—171no—
166#2935—171no—
167#1966—171no—
168#1547—171no—
169C2×#332D1711yescharacteristic, complemented
170#1301—171no—
171#1283—171no—
172C22×C17—21no—
173C22×C17—21no—
174C22×C17#38611yescharacteristic
175C22×C17C4×D811yescharacteristic
176C22×C17#44211yescharacteristic
177C2×D17—42no—
178C2×D17—42no—
179C2×D17—42no—
180C4×C17—21no—
181C4×C17—21no—
182C4×C17—21no—
183C4×C17—82no—
184C4×C17#44711yescharacteristic
185C4×C17#44911yescharacteristic
186C4×C17#45911yescharacteristic
187C4×C17#46311yescharacteristic
188C4×C17#47111yescharacteristic
189C4×C17#47311yescharacteristic
190Dic17—42no—
191C2×#131—341no—
192#532—171no—
193C2×C4⋊Q8C2×D1711yescharacteristic
194#500—341no—
195#486—341no—
196#480—174no—
197#474—342no—
198#436—341no—
199#435—342no—
200C8×D4—341no—
201#431—171no—
202#423—171no—
203C2×C4⋊C8C2×D1711yescharacteristic
204C2×C4⋊C8C2×D1711yescharacteristic
205C2×#101—341no—
206C2×#101—341no—
207#408—341no—
208C4×M16—171no—
209#332—21no—
210#332—21no—
211#332—341no—
212#331—341no—
213C2×C17—21no—
214C2×C17—21no—
215C2×C17#187911yescharacteristic
216C2×C17#190811yescharacteristic
217C2×C17#191511yescharacteristic
218D17—82no—
219C2×#41—341no—
220C22×Q8—21no—
221#131—682no—
222#131—682no—
223C2×M16—171no—
224C2×M16—171no—
225C2×M16—342no—
226C2×M16—341no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—342no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—171no—
235#127—171no—
236#124—341no—
237#121—172no—
238#121—341no—
239C4×D4—172no—
240C4×D4—341no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4C4×D1712yes—
243C2×C42C22×D1711yescharacteristic
244#107—344no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—341no—
249C4⋊C8—341no—
250C4⋊C8—341no—
251C4⋊C8C22⋊D1711yescharacteristic
252C4⋊C8C22⋊D1711yescharacteristic
253#102—344no—
254#101—682no—
255#101—682no—
256C22⋊C8—172no—
257C22⋊C8—342no—
258C22⋊C8—342no—
259#97—341no—
260C4×C8—341no—
261C4×C8—341no—
262C17#927111yescharacteristic, complemented, Sylow
263#41—681no—
264#41—681no—
265#41—681no—
266#41—681no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—341no—
274C2×D4—172no—
275C2×D4—342no—
276C2×D4—341no—
277C2×D4—341no—
278C22×C4—22no—
279C22×C4—342no—
280C22×C4C2×C4×D1711yescharacteristic
281C22×C4D4×D1711yescharacteristic
282C22×C4#6325411yescharacteristic
283M16—172no—
284M16—341no—
285M16—341no—
286M16—341no—
287M16—684no—
288M16—681no—
289M16—681no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—81no—
296C2×C8—341no—
297C2×C8—342no—
298C2×C8—341no—
299C2×C8—684no—
300C2×C8—681no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—172no—
306C4⋊C4—341no—
307C22⋊C4—342no—
308C22⋊C4—342no—
309C42#6325211yescharacteristic
310C42D4×D1711yescharacteristic
311C42D4×D1711yescharacteristic
312C42C2×C22⋊D1711yescharacteristic
313C23—342no—
314C23#1058756711yescharacteristic
315Q8—81no—
316Q8—81no—
317Q8—81no—
318Q8—81no—
319Q8—681no—
320Q8—681no—
321D4—682no—
322D4—682no—
323D4—682no—
324D4—681no—
325D4—681no—
326D4—681no—
327D4—681no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—342no—
335C2×C4—682no—
336C2×C4—682no—
337C2×C4C22⋊C4×D1711yescharacteristic
338C2×C4#1058756911yescharacteristic
339C2×C4#1058757011yescharacteristic
340C2×C4D8×D1711yescharacteristic
341C2×C4#1058759711yescharacteristic
342C2×C4#1058760011yescharacteristic
343C2×C4#1058760211yescharacteristic
344C2×C4C4×C22⋊D1711yescharacteristic
345C2×C4#1058762311yescharacteristic
346C2×C4#1058762411yescharacteristic
347C8—41no—
348C8—41no—
349C8—81no—
350C8—342no—
351C8—682no—
352C8—681no—
353C8—1361no—
354C22—21no—
355C22—21no—
356C22—682no—
357C22—682no—
358C22—682no—
359C22#1176268511yescharacteristic
360C22#1176288911yescharacteristic
361C22#1176291811yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—682no—
367C4#1176294111yescharacteristic
368C4#1176295311yescharacteristic
369C4#1176300311yescharacteristic
370C4#1176302311yescharacteristic
371C4#1176306911yescharacteristic
372C4#1176308111yescharacteristic
373C2—21no—
374C2—21no—
375C2—1362no—
376C2#1452912911yescharacteristic
377C2#1452930211yescharacteristic
378C2#1452933311yescharacteristic
subgroupG/H
centerC22#11762685
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC2×C17×#332C2
socleC22×C17#386
prime radical#11763359C22
cosocleC2×C42×C17C23
hypercenterC2×#332D17
hypocenterC17#9271
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #14529629C2semidirect
5. #14526681C2semidirect
6. #14526634C2semidirect
7. C2×C17×#332C2semidirect
169. C2×#332D17semidirect
262. C17#9271semidirect

Maximal subgroups

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

subgroupindex
#145399052
#145375272
#145296292
#145274592
#145266812
#145266342
C2×C17×#3322
#927117