Finite Group Databasebeta

← #16930838

Subgroups — #16930838

Order 4352.

480 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539912C211yesmaximal, characteristic
2#14537527C211yesmaximal, characteristic
3#14529774C211yesmaximal, characteristic, complemented
4#14527459C211yesmaximal, characteristic
5#14526681C211yesmaximal, characteristic, complemented
6#14526634C211yesmaximal, characteristic, complemented
7C2×C17×#332C211yesmaximal, characteristic, complemented
8C2×#10587587—21no—
9#11763359C2211yescharacteristic
10#11763205—21no—
11#11763157—21no—
12#11763127C414yes—
13#11763096—22no—
14#11762886—21no—
15#11762879—22no—
16#11762874—21no—
17#11762862C2211yescharacteristic
18#11762833C2211yescharacteristic
19#11762775—21no—
20C4×#63223C2211yescharacteristic
21#11762578—21no—
22#11762578—21no—
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
60C22⋊#3622C2×C412yes—
61#10587491—22no—
62#10587491—22no—
63#10587480—24no—
64#10587479—24no—
65C4⋊#3622—21no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68#10587474—21no—
69C4×#3622—21no—
70C4×#3622—21no—
71C2×Q8×C17—41no—
72C2×Q8×C17—41no—
73C2×Q8×C17—81no—
74C2×Q8×C17—81no—
75C22×C4×C17—22no—
76C22×C4×C17C22×C411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17#4111yescharacteristic
79C2×C22⋊D17—22no—
80#63252—41no—
81#63252—41no—
82#63252—41no—
83#63252—41no—
84C2×D68—21no—
85C2×D68—21no—
86C2×D68C22⋊C412yes—
87C2×C4×D17—22no—
88C2×Dic34—21no—
89C2×C8×C17—21no—
90C2×C8×C17—21no—
91C2×C8×C17—41no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17—81no—
95C4⋊C4×C17—22no—
96C4⋊C4×C17—22no—
97C4⋊C4×C17—41no—
98C4⋊C4×C17—41no—
99C42×C17C2×D411yescharacteristic
100C42×C17C2×D411yescharacteristic
101C42×C17C2×D411yescharacteristic
102C42×C17#4111yescharacteristic
103#63227—22no—
104#63227—22no—
105C4⋊Dic17—21no—
106C4⋊Dic17C22⋊C412yes—
107#63223—21no—
108#63223—21no—
109#63223—21no—
110#63223—41no—
111#63223—41no—
112#63223SD1612yes—
113C2×#3622—21no—
114C2×#3622—22no—
115C2×#3622—21no—
116C2×#3622—41no—
117#63218—44no—
118C8×D17—44no—
119#9269—171nomaximal, Sylow
120C23×C17C4×D411yescharacteristic
121C22×D17—22no—
122Q8×C17—82no—
123Q8×C17—81no—
124Q8×C17—81no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—41no—
128C2×C4×C17—42no—
129C2×C4×C17—82no—
130C2×C4×C17C2×C22⋊C411yescharacteristic
131C2×C4×C17C4×D411yescharacteristic
132C2×C4×C17#12011yescharacteristic
133C2×C4×C17#12111yescharacteristic
134C2×C4×C17#12111yescharacteristic
135C2×C4×C17#12311yescharacteristic
136C2×C4×C17C2×SD1611yescharacteristic
137C2×C4×C17#13511yescharacteristic
138C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C17#13711yescharacteristic
140C22⋊D17—42no—
141C22⋊D17—42no—
142C2×Dic17—22no—
143D68—42no—
144D68—41no—
145D68—41no—
146D68—41no—
147D68—41no—
148C4×D17—42no—
149C4×D17—42no—
150Dic34—41no—
151Dic34—41no—
152C8×C17—41no—
153C8×C17—41no—
154C8×C17—81no—
155#3622—22no—
156#3622—42no—
157#3622—41no—
158#3622—81no—
159#3227—171no—
160#2935—171no—
161#1997—171no—
162#1547—171no—
163C2×#332D1711yescharacteristic, complemented
164#1301—171no—
165#1283—171no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17#38611yescharacteristic
169C22×C17C4×SD1611yescharacteristic
170C22×C17#44011yescharacteristic
171C2×D17—42no—
172C2×D17—42no—
173C2×D17—42no—
174C4×C17—21no—
175C4×C17—21no—
176C4×C17—21no—
177C4×C17—82no—
178C4×C17#45011yescharacteristic
179C4×C17#45211yescharacteristic
180C4×C17#46111yescharacteristic
181C4×C17#46311yescharacteristic
182C4×C17#47111yescharacteristic
183C4×C17#47211yescharacteristic
184Dic17—42no—
185C2×#131—341no—
186#532—171no—
187C2×C4⋊Q8C2×D1711yescharacteristic
188#498—341no—
189#486—341no—
190#481—174no—
191#476—342no—
192#436—341no—
193#435—342no—
194C8×D4—341no—
195#431—171no—
196#423—171no—
197C2×C4⋊C8C2×D1711yescharacteristic
198C2×C4⋊C8C2×D1711yescharacteristic
199#408—341no—
200C4×M16—171no—
201#343—341no—
202#343—341no—
203#332—21no—
204#332—21no—
205#332—341no—
206#331—341no—
207C2×C17—21no—
208C2×C17—21no—
209C2×C17#187711yescharacteristic
210C2×C17#190711yescharacteristic
211C2×C17#191511yescharacteristic
212D17—82no—
213C2×#41—341no—
214C22×Q8—21no—
215#131—682no—
216#131—682no—
217C2×M16—171no—
218C2×M16—171no—
219C2×M16—342no—
220C2×M16—341no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—342no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—171no—
229#127—171no—
230#124—341no—
231#121—172no—
232#121—341no—
233C4×D4—172no—
234C4×D4—341no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C4×D1712yes—
237C2×C42C22×D1711yescharacteristic
238#106—344no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—341no—
243C4⋊C8—341no—
244C4⋊C8—341no—
245C4⋊C8C22⋊D1711yescharacteristic
246C4⋊C8C22⋊D1711yescharacteristic
247#102—344no—
248C22⋊C8—172no—
249C22⋊C8—342no—
250C22⋊C8—342no—
251#97—341no—
252C4×C8—341no—
253C4×C8—341no—
254C17#926911yescharacteristic, complemented, Sylow
255#41—681no—
256#41—681no—
257#41—681no—
258#41—681no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—81no—
262C2×Q8—81no—
263C2×Q8—341no—
264C2×D4—172no—
265C2×D4—342no—
266C2×D4—341no—
267C2×D4—341no—
268C22×C4—22no—
269C22×C4—342no—
270C22×C4C2×C4×D1711yescharacteristic
271C22×C4D4×D1711yescharacteristic
272C22×C4#6325411yescharacteristic
273M16—172no—
274M16—341no—
275M16—341no—
276M16—341no—
277M16—684no—
278M16—681no—
279M16—681no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—81no—
286C2×C8—341no—
287C2×C8—342no—
288C2×C8—341no—
289C2×C8—684no—
290C2×C8—681no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—172no—
296C4⋊C4—341no—
297C22⋊C4—342no—
298C22⋊C4—342no—
299C42#6325211yescharacteristic
300C42D4×D1711yescharacteristic
301C42D4×D1711yescharacteristic
302C42C2×C22⋊D1711yescharacteristic
303C23—342no—
304C23#1058756711yescharacteristic
305Q8—82no—
306Q8—81no—
307Q8—81no—
308Q8—681no—
309Q8—681no—
310D4—682no—
311D4—682no—
312D4—682no—
313D4—681no—
314D4—681no—
315D4—681no—
316D4—681no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—82no—
322C2×C4—342no—
323C2×C4—682no—
324C2×C4—682no—
325C2×C4C22⋊C4×D1711yescharacteristic
326C2×C4#1058756911yescharacteristic
327C2×C4#1058757011yescharacteristic
328C2×C4SD16×D1711yescharacteristic
329C2×C4#1058760011yescharacteristic
330C2×C4#1058760411yescharacteristic
331C2×C4#1058760511yescharacteristic
332C2×C4C4×C22⋊D1711yescharacteristic
333C2×C4#1058762311yescharacteristic
334C2×C4#1058762411yescharacteristic
335C8—41no—
336C8—41no—
337C8—81no—
338C8—342no—
339C8—682no—
340C8—681no—
341C8—1361no—
342C22—21no—
343C22—21no—
344C22—682no—
345C22—682no—
346C22—682no—
347C22#1176268511yescharacteristic
348C22#1176289411yescharacteristic
349C22#1176291211yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—682no—
355C4#1176295811yescharacteristic
356C4#1176297011yescharacteristic
357C4#1176301311yescharacteristic
358C4#1176302711yescharacteristic
359C4#1176306911yescharacteristic
360C4#1176307611yescharacteristic
361C2—21no—
362C2—21no—
363C2—1362no—
364C2#1452911511yescharacteristic
365C2#1452929511yescharacteristic
366C2#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#9269
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. #14529774C2semidirect
5. #14526681C2semidirect
6. #14526634C2semidirect
7. C2×C17×#332C2semidirect
163. C2×#332D17semidirect
254. C17#9269semidirect

Maximal subgroups

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

subgroupindex
#145399122
#145375272
#145297742
#145274592
#145266812
#145266342
C2×C17×#3322
#926917