Finite Group Databasebeta

← #16937737

Subgroups — #16937737

Order 4352.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533780C211yesmaximal, characteristic
2#14529746C211yesmaximal, characteristic, complemented
3#14529543C211yesmaximal, characteristic, complemented
4#14528785C211yesmaximal, characteristic
5C2×#11762536C211yesmaximal, characteristic
6#14526623C211yesmaximal, characteristic, complemented
7C2×C17×#332C211yesmaximal, characteristic, complemented
8C2×#10587633—21no—
9C2×C4×D68C2211yescharacteristic
10C2×#10587489—21no—
11C2×#10587492—21no—
12C2×C4×#3622C2211yescharacteristic
13#11762735—22no—
14#11762716—21no—
15#11762679C2211yescharacteristic
16#11762666—21no—
17#11762666—21no—
18C4×C4⋊Dic17C2211yescharacteristic
19#11762572—21no—
20#11762572—21no—
21#11762571—22no—
22#11762536—22no—
23C2×C17×C4⋊Q8C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C17×C4⋊C8C2211yescharacteristic
26C17×#332—22no—
27C22×Q8×C17—21no—
28C22×D68D411yescharacteristic
29C22×C4×D17—21no—
30C22×C8×C17—21no—
31C22×C8×C17—21no—
32C17×C4⋊Q8—21no—
33C17×C4⋊Q8—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—21no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17D412yes—
38C2×C42×C17C2311yescharacteristic
39#10587633—42no—
40#10587633—42no—
41C2×#63227—22no—
42C2×#63227—22no—
43C2×#63227—21no—
44C2×C4⋊Dic17—21no—
45C2×C4⋊Dic17—21no—
46C2×C4⋊Dic17—21no—
47C2×C4⋊Dic17D411yescharacteristic
48C2×C4⋊Dic17D411yescharacteristic
49C2×C4⋊Dic17D411yescharacteristic
50C2×C4×Dic17—21no—
51C22×#3622—21no—
52C4×D68—21no—
53C4×D68—21no—
54C4×D68—21no—
55C4×D68—21no—
56C17×C4⋊C8—21no—
57C17×C4⋊C8—21no—
58C17×C4⋊C8—21no—
59C17×C4⋊C8D412yes—
60#10587502—22no—
61#10587502—22no—
62#10587502—21no—
63#10587492—42no—
64#10587489—42no—
65C4×#3622—21no—
66C4×#3622—21no—
67C23×D17—21no—
68C2×Q8×C17—41no—
69C2×Q8×C17—41no—
70C2×Q8×C17—41no—
71C2×Q8×C17—41no—
72C2×Q8×C17—41no—
73C2×Q8×C17—41no—
74C22×C4×C17—22no—
75C22×C4×C17C2×D411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×Dic17—21no—
79C22×Dic17—21no—
80C22×Dic17—21no—
81C22×Dic17—41no—
82C2×D68—21no—
83C2×D68—21no—
84C2×D68—21no—
85C2×D68—21no—
86C2×D68—21no—
87C2×D68D812yes—
88C2×C4×D17—41no—
89C2×C4×D17—41no—
90C2×C4×D17—41no—
91C2×C4×D17—41no—
92C2×C4×D17—41no—
93C2×C4×D17—41no—
94C2×C8×C17—22no—
95C2×C8×C17—41no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C2×C8×C17—41no—
99C2×C8×C17—41no—
100C4⋊C4×C17—22no—
101C4⋊C4×C17—22no—
102C4⋊C4×C17—41no—
103C4⋊C4×C17—41no—
104C42×C17C2×D411yescharacteristic
105C42×C17#4111yescharacteristic
106C42×C17#4111yescharacteristic
107C42×C17#4111yescharacteristic
108#63227—44no—
109#63227—44no—
110#63227—41no—
111#63227—41no—
112C4⋊Dic17—21no—
113C4⋊Dic17—21no—
114C4⋊Dic17—21no—
115C4⋊Dic17—21no—
116C4⋊Dic17—21no—
117C4⋊Dic17—21no—
118C4⋊Dic17—42no—
119C4⋊Dic17—41no—
120C4⋊Dic17—41no—
121C4⋊Dic17—41no—
122C4⋊Dic17—41no—
123C4×Dic17—41no—
124C4×Dic17—41no—
125C2×#3622—22no—
126C2×#3622—41no—
127C2×#3622—41no—
128#10416—171nomaximal, Sylow
129C23×C17#12011yescharacteristic
130C22×D17—22no—
131C22×D17—41no—
132C22×D17—41no—
133C22×D17—41no—
134C22×D17—41no—
135C22×D17—41no—
136C22×D17—41no—
137Q8×C17—81no—
138Q8×C17—81no—
139Q8×C17—81no—
140Q8×C17—81no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—42no—
144C2×C4×C17—42no—
145C2×C4×C17—42no—
146C2×C4×C17#12111yescharacteristic
147C2×C4×C17#12111yescharacteristic
148C2×C4×C17#12111yescharacteristic
149C2×C4×C17#12311yescharacteristic
150C2×C4×C17#12311yescharacteristic
151C2×C4×C17#12411yescharacteristic
152C2×C4×C17C2×D811yescharacteristic
153C2×C4×C17#13511yescharacteristic
154C2×C4×C17#13511yescharacteristic
155C2×C4×C17#13511yescharacteristic
156C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C17#13711yescharacteristic
159C2×C4×C17#13711yescharacteristic
160C2×Dic17—41no—
161C2×Dic17—41no—
162C2×Dic17—41no—
163C2×Dic17—41no—
164C2×Dic17—41no—
165C2×Dic17—41no—
166C2×Dic17—41no—
167C2×Dic17—41no—
168C2×Dic17—41no—
169C2×Dic17—81no—
170C2×Dic17—81no—
171C2×Dic17—81no—
172D68—22no—
173D68—22no—
174D68—41no—
175D68—41no—
176C4×D17—81no—
177C4×D17—81no—
178C4×D17—81no—
179C4×D17—81no—
180C8×C17—42no—
181C8×C17—81no—
182#3622—42no—
183#2547—171no—
184#1990—171no—
185#1947—171no—
186#1802—171no—
187C2×#332D1711yescharacteristic, complemented
188C2×D4⋊C8—171no—
189#1279—171no—
190C22×C17#39411yescharacteristic
191C22×C17#44711yescharacteristic
192C22×C17#44911yescharacteristic
193C22×C17#45211yescharacteristic
194C22×C17#45211yescharacteristic
195C22×C17#45411yescharacteristic
196C22×C17#45611yescharacteristic
197C2×D17—42no—
198C2×D17—42no—
199C2×D17—42no—
200C2×D17—81no—
201C2×D17—81no—
202C2×D17—81no—
203C2×D17—81no—
204C4×C17—21no—
205C4×C17—21no—
206C4×C17—82no—
207C4×C17#46311yescharacteristic
208C4×C17#46411yescharacteristic
209C4×C17#46611yescharacteristic
210C4×C17#46811yescharacteristic
211C4×C17#48011yescharacteristic
212C4×C17#48211yescharacteristic
213C4×C17#48811yescharacteristic
214C4×C17#48911yescharacteristic
215Dic17—81no—
216Dic17—81no—
217Dic17—81no—
218Dic17—161no—
219C2×C4⋊Q8C2×D1711yescharacteristic
220C2×#124—341no—
221C2×C4×D4—171no—
222C2×#107—341no—
223C2×C4⋊C8C2×D1711yescharacteristic
224C2×C4⋊C8C2×D1711yescharacteristic
225C2×#102—341no—
226C2×C4×C8—171no—
227#397—342no—
228#391—341no—
229#384—171no—
230#380—341no—
231#380—341no—
232C4×C4⋊C4—171no—
233#340—341no—
234#340—341no—
235#340—342no—
236#332—22no—
237D4⋊C8—342no—
238C2×C17#162511yescharacteristic
239C2×C17#163811yescharacteristic
240C2×C17#164711yescharacteristic
241C2×C17#165211yescharacteristic
242C2×C17#203311yescharacteristic
243C2×C17#203811yescharacteristic
244C2×C17#204211yescharacteristic
245D17—82no—
246C22×Q8—21no—
247C22×D4—171no—
248C23×C4—341no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—341no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256#124—682no—
257#124—682no—
258C4×D4—341no—
259C4×D4—341no—
260C4×D4—341no—
261C4×D4—341no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—171no—
264C2×C4⋊C4—171no—
265C2×C4⋊C4—171no—
266C2×C4⋊C4—341no—
267C2×C4⋊C4—341no—
268C2×C4⋊C4—341no—
269C2×C4⋊C4D6812yes—
270C2×C22⋊C4—342no—
271C2×C22⋊C4—342no—
272C2×C22⋊C4—341no—
273C2×C42—341no—
274C2×C42C22×D1711yescharacteristic
275#107—682no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8C22⋊D1712yes—
280#102—682no—
281C4×C8—341no—
282C4×C8—341no—
283#95—342no—
284#95—342no—
285#95—341no—
286C17#1041611yescharacteristic, complemented, Sylow
287C24—341no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—172no—
295C2×D4—341no—
296C2×D4—341no—
297C2×D4—341no—
298C2×D4—341no—
299C2×D4—341no—
300C22×C4—22no—
301C22×C4—341no—
302C22×C4—341no—
303C22×C4—341no—
304C22×C4—681no—
305C22×C4—681no—
306C22×C4—681no—
307C22×C4—681no—
308C22×C4—681no—
309C22×C4—681no—
310C22×C4—681no—
311C22×C4C2×D6811yescharacteristic
312C22×C4D4×D1711yescharacteristic
313C22×C4D4×D1711yescharacteristic
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—342no—
321C2×C8—681no—
322C2×C8—681no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—341no—
328C4⋊C4—341no—
329C4⋊C4—341no—
330C4⋊C4—341no—
331C4⋊C4—341no—
332C4⋊C4—341no—
333C4⋊C4—682no—
334C4⋊C4—681no—
335C4⋊C4—681no—
336C4⋊C4—681no—
337C4⋊C4—681no—
338C22⋊C4—684no—
339C22⋊C4—684no—
340C22⋊C4—681no—
341C22⋊C4—681no—
342C42—681no—
343C42—681no—
344C42#6325211yescharacteristic
345C42#6325411yescharacteristic
346C42#6325411yescharacteristic
347C42C2×C22⋊D1711yescharacteristic
348C23—342no—
349C23—681no—
350C23—681no—
351C23—681no—
352C23—681no—
353C23—681no—
354C23—681no—
355C23#1058756811yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—342no—
361D4—342no—
362D4—681no—
363D4—681no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—681no—
370C2×C4—681no—
371C2×C4—681no—
372C2×C4—681no—
373C2×C4—681no—
374C2×C4—681no—
375C2×C4—681no—
376C2×C4—681no—
377C2×C4—681no—
378C2×C4—1361no—
379C2×C4—1361no—
380C2×C4—1361no—
381C2×C4—1361no—
382C2×C4—1361no—
383C2×C4—1361no—
384C2×C4—1361no—
385C2×C4#1058756911yescharacteristic
386C2×C4#1058757111yescharacteristic
387C2×C4#1058757211yescharacteristic
388C2×C4D8×D1711yescharacteristic
389C2×C4#1058759811yescharacteristic
390C2×C4#1058760011yescharacteristic
391C2×C4#1058760011yescharacteristic
392C2×C4#1058760111yescharacteristic
393C2×C4#1058760211yescharacteristic
394C2×C4#1058760411yescharacteristic
395C2×C4#1058760511yescharacteristic
396C2×C4#1058761611yescharacteristic
397C2×C4#1058762411yescharacteristic
398C2×C4#1058762511yescharacteristic
399C8—42no—
400C8—81no—
401C8—682no—
402C22—682no—
403C22—682no—
404C22—682no—
405C22—1361no—
406C22—1361no—
407C22—1361no—
408C22—1361no—
409C22#1176272511yescharacteristic
410C22#1176294411yescharacteristic
411C22#1176295711yescharacteristic
412C22#1176297211yescharacteristic
413C22#1176297411yescharacteristic
414C22#1176298411yescharacteristic
415C22#1176299411yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—2721no—
420C4—1361no—
421C4—1361no—
422C4—1361no—
423C4#1176302611yescharacteristic
424C4#1176303311yescharacteristic
425C4#1176304211yescharacteristic
426C4#1176305211yescharacteristic
427C4#1176312111yescharacteristic
428C4#1176313111yescharacteristic
429C4#1176316511yescharacteristic
430C4#1176317011yescharacteristic
431C2—1362no—
432C2#1452787411yescharacteristic
433C2#1452795711yescharacteristic
434C2#1452802011yescharacteristic
435C2#1452805511yescharacteristic
436C2#1452996511yescharacteristic
437C2#1453000211yescharacteristic
438C2#1453002211yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#332C2
socleC23×C17#120
prime radicalC22×D68D4
hypercenterC2×#332D17
hypocenterC17#10416
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #14529746C2semidirect
3. #14529543C2semidirect
6. #14526623C2semidirect
7. C2×C17×#332C2semidirect
187. C2×#332D17semidirect
286. C17#10416semidirect

Maximal subgroups

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

subgroupindex
#145337802
#145297462
#145295432
#145287852
C2×#117625362
#145266232
C2×C17×#3322
#1041617