Finite Group Databasebeta

← #16938152

Subgroups — #16938152

Order 4352.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763015C211yesmaximal, characteristic
2#14529744C211yesmaximal, characteristic, complemented
3#14529577C211yesmaximal, characteristic
4#14528781C211yesmaximal, characteristic
5C2×#11762559C211yesmaximal, characteristic, complemented
6C2×#11762554C211yesmaximal, characteristic, complemented
7C17×#1296C211yesmaximal, characteristic, complemented
8C22×#63219—21no—
9C2×#10587555C2211yescharacteristic
10C2×C4×D68C2211yescharacteristic
11#11763015—22no—
12#11763015—22no—
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587487—21no—
15C2×#10587480—21no—
16C2×#10587491—21no—
17C2×#10587491—21no—
18C2×C4×#3622C2211yescharacteristic
19#11762571—21no—
20#11762571—21no—
21#11762571—21no—
22#11762559—22no—
23#11762554—22no—
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C17×C4⋊C8C2211yescharacteristic
26C17×#384C2211yescharacteristic
27C22×D68D411yescharacteristic
28C22×C4×D17—21no—
29C22×Dic34—21no—
30C22×C8×C17—21no—
31C22×C8×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C42×C17C2311yescharacteristic
36C2×#63227—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17D411yescharacteristic
40C22×#3622—21no—
41C22×#3622D411yescharacteristic
42C22×#3622D411yescharacteristic
43C2×#63219—24no—
44C2×#63219—42no—
45C2×#63219—42no—
46C4×D68—21no—
47C4×D68—21no—
48C4×D68—21no—
49C4×D68—21no—
50#10587555—21no—
51#10587555—21no—
52#10587555—21no—
53#10587555D412yes—
54C17×C4⋊C8—21no—
55C17×C4⋊C8—21no—
56C17×C4⋊C8—21no—
57C17×C4⋊C8D412yes—
58#10587491—42no—
59#10587491—42no—
60#10587487—24no—
61#10587480—42no—
62C4⋊#3622—21no—
63C4⋊#3622—21no—
64C4×#3622—21no—
65C4×#3622—21no—
66C23×D17—21no—
67C22×C4×C17—41no—
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C22×C4×C17#4111yescharacteristic
71C22×Dic17—21no—
72C22×Dic17—41no—
73C2×D68—21no—
74C2×D68—21no—
75C2×D68—21no—
76C2×D68—21no—
77C2×D68—21no—
78C2×D68SD1612yes—
79C2×C4×D17—41no—
80C2×C4×D17—41no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17—41no—
84C2×C4×D17—41no—
85C2×Dic34—22no—
86C2×Dic34—41no—
87C2×Dic34—41no—
88C2×Dic34—41no—
89C2×Dic34—41no—
90C2×Dic34—41no—
91C2×C8×C17—22no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C2×C8×C17—41no—
97C4⋊C4×C17—41no—
98C4⋊C4×C17—41no—
99C4⋊C4×C17—41no—
100C4⋊C4×C17—41no—
101C4⋊C4×C17—81no—
102C42×C17C2×D411yescharacteristic
103C42×C17C2×D411yescharacteristic
104C42×C17#4111yescharacteristic
105C42×C17#4111yescharacteristic
106#63227—41no—
107#63227—41no—
108C4⋊Dic17—21no—
109C4⋊Dic17—22no—
110C4⋊Dic17—22no—
111C4⋊Dic17—21no—
112C4⋊Dic17—41no—
113C4⋊Dic17—41no—
114C2×#3622—21no—
115C2×#3622—21no—
116C2×#3622—21no—
117C2×#3622—21no—
118C2×#3622—21no—
119C2×#3622—41no—
120C2×#3622—41no—
121C2×#3622—41no—
122C2×#3622SD1612yescomplemented
123#63219—48no—
124#10477—171nomaximal, Sylow
125C23×C17#12111yescharacteristic
126C22×D17—22no—
127C22×D17—41no—
128C22×D17—41no—
129C22×D17—41no—
130C22×D17—41no—
131C22×D17—41no—
132C22×D17—41no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17#12011yescharacteristic
139C2×C4×C17#12111yescharacteristic
140C2×C4×C17#12111yescharacteristic
141C2×C4×C17#12311yescharacteristic
142C2×C4×C17#12311yescharacteristic
143C2×C4×C17#12411yescharacteristic
144C2×C4×C17C2×SD1611yescharacteristic
145C2×C4×C17C2×SD1611yescharacteristic
146C2×C4×C17#13511yescharacteristic
147C2×C4×C17#13511yescharacteristic
148C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C17#13711yescharacteristic
152C2×Dic17—42no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—41no—
156C2×Dic17—81no—
157C2×Dic17—81no—
158D68—22no—
159D68—22no—
160D68—41no—
161D68—41no—
162C4×D17—81no—
163C4×D17—81no—
164C4×D17—81no—
165C4×D17—81no—
166Dic34—42no—
167Dic34—42no—
168Dic34—81no—
169Dic34—81no—
170C8×C17—42no—
171C8×C17—81no—
172#3622—22no—
173#3622—41no—
174#3622—81no—
175C2×#461—171no—
176#1990—171no—
177#1954—171no—
178#1802—171no—
179C2×#334—171no—
180C2×#332—171no—
181#1296D1711yescharacteristic, complemented
182C22×C17#39411yescharacteristic
183C22×C17#46111yescharacteristic
184C22×C17#46311yescharacteristic
185C22×C17#46511yescharacteristic
186C22×C17#46911yescharacteristic
187C22×C17#47111yescharacteristic
188C22×C17#47311yescharacteristic
189C2×D17—42no—
190C2×D17—42no—
191C2×D17—42no—
192C2×D17—81no—
193C2×D17—81no—
194C2×D17—81no—
195C2×D17—81no—
196C4×C17—21no—
197C4×C17—21no—
198C4×C17—161no—
199C4×C17#44911yescharacteristic
200C4×C17#45011yescharacteristic
201C4×C17#46011yescharacteristic
202C4×C17#46411yescharacteristic
203C4×C17#46511yescharacteristic
204C4×C17#46811yescharacteristic
205C4×C17#48111yescharacteristic
206C4×C17#48211yescharacteristic
207Dic17—81no—
208Dic17—82no—
209C22×SD16—341no—
210C2×C4⋊Q8—171no—
211C2×C4×D4—171no—
212#461—342no—
213#461—342no—
214C2×C4⋊C8—171no—
215C2×C4⋊C8C2×D1711yescharacteristic
216C2×C4⋊C8C2×D1711yescharacteristic
217C2×#103—341no—
218C2×#102—341no—
219C2×C22⋊C8—341no—
220C2×C22⋊C8—341no—
221C2×C4×C8—171no—
222#384C2×D1711yescharacteristic
223#340—341no—
224#340—341no—
225#340—341no—
226#334—342no—
227#332—342no—
228C2×C17#167111yescharacteristic
229C2×C17#167911yescharacteristic
230C2×C17#169311yescharacteristic
231C2×C17#170111yescharacteristic
232C2×C17#203411yescharacteristic
233C2×C17#205211yescharacteristic
234C2×C17#205511yescharacteristic
235D17—82no—
236C22×Q8—341no—
237C22×D4—171no—
238C23×C4—341no—
239C2×SD16—344no—
240C2×SD16—682no—
241C2×SD16—682no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—171no—
245C22×C8—171no—
246C22×C8—341no—
247C4⋊Q8—172no—
248C4⋊Q8—341no—
249C4⋊Q8—341no—
250C4⋊Q8—341no—
251C4×D4—341no—
252C4×D4—341no—
253C4×D4—341no—
254C4×D4—341no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—171no—
259C2×C4⋊C4—341no—
260C2×C4⋊C4—341no—
261C2×C22⋊C4—341no—
262C2×C42C22×D1711yescharacteristic
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—341no—
267C4⋊C8—341no—
268C4⋊C8D6812yes—
269#103—344no—
270#102—682no—
271C22⋊C8—682no—
272C22⋊C8—682no—
273C4×C8—341no—
274C4×C8—341no—
275C17#1047711yescharacteristic, complemented, Sylow
276C24—341no—
277C2×Q8—342no—
278C2×Q8—681no—
279C2×Q8—681no—
280C2×Q8—681no—
281C2×Q8—681no—
282C2×Q8—681no—
283C2×D4—172no—
284C2×D4—341no—
285C2×D4—341no—
286C2×D4—341no—
287C2×D4—341no—
288C2×D4—341no—
289C22×C4—41no—
290C22×C4—341no—
291C22×C4—681no—
292C22×C4—681no—
293C22×C4—681no—
294C22×C4—681no—
295C22×C4—681no—
296C22×C4—681no—
297C22×C4—681no—
298C22×C4#6325211yescharacteristic
299C22×C4D4×D1711yescharacteristic
300C22×C4D4×D1711yescharacteristic
301SD16—688no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—172no—
309C2×C8—341no—
310C2×C8—341no—
311C2×C8—341no—
312C2×C8—341no—
313C2×C8—341no—
314C2×C8—681no—
315C2×C8—681no—
316C2×C8—681no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—81no—
322C4⋊C4—341no—
323C4⋊C4—342no—
324C4⋊C4—341no—
325C4⋊C4—342no—
326C4⋊C4—681no—
327C4⋊C4—681no—
328C22⋊C4—681no—
329C22⋊C4—681no—
330C42C2×D6811yescharacteristic
331C42#6325211yescharacteristic
332C42D4×D1711yescharacteristic
333C42#6325611yescharacteristic
334C23—342no—
335C23—681no—
336C23—681no—
337C23—681no—
338C23—681no—
339C23—681no—
340C23—681no—
341C23#1058757011yescharacteristic
342Q8—682no—
343Q8—682no—
344Q8—1361no—
345Q8—1361no—
346D4—342no—
347D4—342no—
348D4—681no—
349D4—681no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—681no—
356C2×C4—682no—
357C2×C4—681no—
358C2×C4—681no—
359C2×C4—1361no—
360C2×C4—1361no—
361C2×C4—1361no—
362C2×C4—1361no—
363C2×C4—1361no—
364C2×C4—1361no—
365C2×C4#1058756111yescharacteristic
366C2×C4#1058756811yescharacteristic
367C2×C4#1058757011yescharacteristic
368C2×C4#1058758011yescharacteristic
369C2×C4#1058758011yescharacteristic
370C2×C4#1058758111yescharacteristic
371C2×C4#1058759711yescharacteristic
372C2×C4#1058759711yescharacteristic
373C2×C4SD16×D1711yescharacteristic
374C2×C4SD16×D1711yescharacteristic
375C2×C4#1058760011yescharacteristic
376C2×C4#1058760211yescharacteristic
377C2×C4#1058760411yescharacteristic
378C2×C4#1058760511yescharacteristic
379C8—42no—
380C8—81no—
381C8—342no—
382C8—681no—
383C8—1361no—
384C22—682no—
385C22—682no—
386C22—682no—
387C22—1361no—
388C22—1361no—
389C22—1361no—
390C22—1361no—
391C22#1176272711yescharacteristic
392C22#1176301311yescharacteristic
393C22#1176302311yescharacteristic
394C22#1176304111yescharacteristic
395C22#1176306111yescharacteristic
396C22#1176307111yescharacteristic
397C22#1176308311yescharacteristic
398C4—21no—
399C4—21no—
400C4—161no—
401C4—1361no—
402C4—1362no—
403C4#1176295711yescharacteristic
404C4#1176296111yescharacteristic
405C4#1176300811yescharacteristic
406C4#1176303411yescharacteristic
407C4#1176303911yescharacteristic
408C4#1176305611yescharacteristic
409C4#1176312911yescharacteristic
410C4#1176313611yescharacteristic
411C2—1362no—
412C2#1452816211yescharacteristic
413C2#1452820611yescharacteristic
414C2#1452829611yescharacteristic
415C2#1452834411yescharacteristic
416C2#1452997611yescharacteristic
417C2#1453008611yescharacteristic
418C2#1453010311yescharacteristic
subgroupG/H
centerC23#10587570
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socleC23×C17#121
prime radicalC22×D68D4
hypercenter#1296D17
hypocenterC17#10477
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #14529744C2semidirect
5. C2×#11762559C2semidirect
6. C2×#11762554C2semidirect
7. C17×#1296C2semidirect
122. C2×#3622SD16semidirect
181. #1296D17semidirect
275. C17#10477semidirect

Maximal subgroups

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

subgroupindex
C2×#117630152
#145297442
#145295772
#145287812
C2×#117625592
C2×#117625542
C17×#12962
#1047717