Finite Group Databasebeta

← #15845676

Subgroups — #15845676

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125422C211yesmaximal, characteristic, complemented
2#13124907C212yesmaximal
3#13114390C212yesmaximal, complemented
4#13114383C212yesmaximal, complemented
5#13114354C211yesmaximal, characteristic, complemented
6#13114349C211yesmaximal, characteristic, complemented
7#13114330C211yesmaximal, characteristic, complemented
8#13114325C211yesmaximal, characteristic, complemented
9#13113584C211yesmaximal, characteristic, complemented
10#13113500C212yesmaximal, complemented
11C13×#2965C211yesmaximal, characteristic
12C4×C13×#41C2211yescharacteristic
13#11719175C2212yes—
14C13×#446C2211yescharacteristic
15C13×#446C2211yescharacteristic
16C13×#436C2211yescharacteristic
17C13×#436C2211yescharacteristic
18C13×#435—21no—
19C13×#435—21no—
20C13×#431—21no—
21C13×#431C2211yescharacteristic
22C4×C13×M16—21no—
23C2×C4×C8×C13C2211yescharacteristic
24#11718900—22no—
25#11718777—21no—
26#11718777—21no—
27#11718692C2212yes—
28C4×#6107—22no—
29#11718681C2212yes—
30#11718680C2212yes—
31C4×#6105—22no—
32#11718668C2212yes—
33#11718657—22no—
34#11718586C2212yes—
35#11718360C2211yescharacteristic
36C4×Dic52—21no—
37C4×Dic52—21no—
38#11718343C2211yescharacteristic
39#11718342C2212yes—
40#11718078C2212yes—
41#11718078C2212yes—
42#11718074C2212yes—
43#11718074C2212yes—
44#11718050C2212yes—
45#11718049C2211yescharacteristic
46#11718049C2211yescharacteristic
47C2×C13×#41D411yescharacteristic
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C22×C8×C13D411yescharacteristic
51C22×C8×C13D411yescharacteristic
52C4×Q8×C13D411yescharacteristic
53C4×Q8×C13C2311yescharacteristic
54C4×D4×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13D411yescharacteristic
57C4×D4×C13C2311yescharacteristic
58C13×#117—21no—
59C13×#117D411yescharacteristic
60C2×C42×C13—21no—
61C2×C42×C13C2311yescharacteristic
62C2×#6107—22no—
63C2×#6105—22no—
64#88180—22no—
65#88178—22no—
66#88178—22no—
67C2×Dic52—21no—
68C2×Dic52—21no—
69#88124—22no—
70#88123C2312yes—
71#88123C2312yes—
72C4×Dic26—22no—
73C4×Dic26—22no—
74C13×C4⋊C8—21no—
75C13×C4⋊C8—21no—
76C13×C4⋊C8C2311yescharacteristic
77C13×C4⋊C8C2311yescharacteristic
78C13×C22⋊C8—21no—
79C13×C22⋊C8—21no—
80C13×C22⋊C8—21no—
81C13×#97—21no—
82C13×#97—21no—
83C4×C8×C13—21no—
84C4×C8×C13D411yescharacteristic
85C4×C8×C13D411yescharacteristic
86C4×C8×C13C2311yescharacteristic
87C4×C8×C13C2311yescharacteristic
88#88075—22no—
89#88072—22no—
90C22⋊#1055—22no—
91#88058—21no—
92#88058—21no—
93#88056—22no—
94#88056—22no—
95#88050—22no—
96#88050—22no—
97#88048—22no—
98#88047—22no—
99C4⋊#1055C2312yes—
100C4⋊#1055C2312yes—
101C4×#1055—22no—
102#19161—131nomaximal, Sylow
103C13×#41—42no—
104C2×Q8×C13C2×D411yescharacteristic
105C2×D4×C13—21no—
106C2×D4×C13C2×D411yescharacteristic
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13#4111yescharacteristic
113C2×Dic26—22no—
114C2×Dic26—22no—
115C13×M16—42no—
116C13×M16—42no—
117C2×C8×C13—22no—
118C2×C8×C13—21no—
119C2×C8×C13—21no—
120C2×C8×C13—41no—
121C2×C8×C13C2×D411yescharacteristic
122C2×C8×C13C2×D411yescharacteristic
123C2×C8×C13C2×D411yescharacteristic
124C2×C8×C13C2×D411yescharacteristic
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4C2×D411yescharacteristic
128C13×C4⋊C4C2×D411yescharacteristic
129C13×C22⋊C4—21no—
130C13×C22⋊C4—21no—
131C13×C22⋊C4—21no—
132C42×C13—21no—
133C42×C13—21no—
134C42×C13—21no—
135C42×C13C2×D411yescharacteristic
136C42×C13C2×D411yescharacteristic
137C42×C13#4111yescharacteristic
138C42×C13C2411yescharacteristic
139C22⋊Dic13—42no—
140#6107—44no—
141#6105—44no—
142C4⋊Dic13—22no—
143C4⋊Dic13—22no—
144C4⋊Dic13—22no—
145C4⋊Dic13—22no—
146#6101—42no—
147#6101—42no—
148C4×Dic13—42no—
149C2×#1055—22no—
150C2×#1055—22no—
151Dic52—42no—
152Dic52—42no—
153#3170—131no—
154#3107—132no—
155#2965D1311yescharacteristic
156#1700—132no—
157#1699—132no—
158#1694—131no—
159#1693—131no—
160#1690—131no—
161#1689—131no—
162#1564—131no—
163#1544—132no—
164C23×C13—21no—
165C23×C13#12111yescharacteristic
166Q8×C13—22no—
167D4×C13—22no—
168D4×C13—42no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—22no—
172C2×C4×C13—22no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—42no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—42no—
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13C22×D411yescharacteristic
184C2×C4×C13C22×D411yescharacteristic
185C2×C4×C13C2×#4111yescharacteristic
186C2×Dic13—42no—
187C2×Dic13—42no—
188Dic26—42no—
189Dic26—42no—
190Dic26—42no—
191Dic26—42no—
192C8×C13—21no—
193C8×C13—21no—
194C8×C13—21no—
195C8×C13—41no—
196C8×C13—41no—
197C8×C13#13512yes—
198#1055—42no—
199#1055—42no—
200#533—132no—
201C4×#41C2×D1311yescharacteristic
202#500—131no—
203#494—131no—
204#487—132no—
205#485—262no—
206#475—132no—
207#474—132no—
208#467—261no—
209#467—261no—
210#462—132no—
211#461—132no—
212#452—262no—
213#446C2×D1311yescharacteristic
214#446C2×D1311yescharacteristic
215C4×Q16—262no—
216C4×Q16—261no—
217C4×Q16—261no—
218C4×SD16—262no—
219#436C2×D1311yescharacteristic
220#436C2×D1311yescharacteristic
221#435—21no—
222#435—21no—
223#431—21no—
224#431—132no—
225#431C2×D1311yescharacteristic
226C4×M16—21no—
227C2×C4×C8C2×D1311yescharacteristic
228#335—132no—
229#334—131no—
230#334—131no—
231#332—132no—
232#332—132no—
233#332—132no—
234#332—132no—
235C22×C13—21no—
236C22×C13—21no—
237C22×C13—21no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13C2×#12111yescharacteristic
242C4×C13—21no—
243C4×C13—21no—
244C4×C13—21no—
245C4×C13—41no—
246C4×C13—41no—
247C4×C13—41no—
248C4×C13#47312yes—
249C4×C13C2×#13511yescharacteristic
250C4×C13#57512yes—
251C4×C13#57511yescharacteristic
252Dic13—82no—
253Dic13—82no—
254C2×#41D5211yescharacteristic
255C2×Q16—262no—
256C2×Q16—261no—
257C2×Q16—261no—
258C2×SD16—262no—
259C2×M16—21no—
260C2×M16—21no—
261C22×C8C22⋊D1311yescharacteristic
262C22×C8C22⋊D1311yescharacteristic
263C4⋊Q8—132no—
264C4⋊Q8—132no—
265#125—262no—
266C22⋊Q8—262no—
267C22⋊Q8—262no—
268C4×Q8—262no—
269C4×Q8—262no—
270C4×Q8D5211yescharacteristic
271C4×Q8C22×D1311yescharacteristic
272C4×D4—21no—
273C4×D4—21no—
274C4×D4D5211yescharacteristic
275C4×D4C22×D1311yescharacteristic
276#117—21no—
277#117—262no—
278#117D5211yescharacteristic
279C2×C42—21no—
280C2×C42C22×D1311yescharacteristic
281#107—261no—
282#107—261no—
283#107—262no—
284#106—262no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—132no—
288C4⋊C8—132no—
289C4⋊C8C22×D1311yescharacteristic
290C4⋊C8C22×D1311yescharacteristic
291#103—262no—
292#103—262no—
293#103—262no—
294#103—262no—
295#103—262no—
296#102—262no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—262no—
301#97—21no—
302#97—21no—
303C4×C8—21no—
304C4×C8—262no—
305C4×C8C22⋊D1311yescharacteristic
306C4×C8C22⋊D1311yescharacteristic
307C4×C8C22×D1311yescharacteristic
308C4×C8C22×D1311yescharacteristic
309C2×C13—41no—
310C2×C13—81no—
311C2×C13#303511yescharacteristic
312C2×C13#305411yescharacteristic
313C2×C13C2×#47311yescharacteristic
314#41—42no—
315C2×Q8—262no—
316C2×Q8—262no—
317C2×Q8C2×D5211yescharacteristic
318C2×D4—21no—
319C2×D4C2×D5211yescharacteristic
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4C2×D5211yescharacteristic
324C22×C4#612711yescharacteristic
325C22×C4C2×C22⋊D1311yescharacteristic
326Q16—522no—
327Q16—524no—
328Q16—522no—
329SD16—524no—
330M16—42no—
331M16—42no—
332C2×C8—22no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—262no—
337C2×C8—262no—
338C2×C8C2×C22⋊D1311yescharacteristic
339C2×C8C2×C22⋊D1311yescharacteristic
340C2×C8C2×C22⋊D1311yescharacteristic
341C2×C8C2×C22⋊D1311yescharacteristic
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—262no—
345C4⋊C4—262no—
346C4⋊C4—262no—
347C4⋊C4—262no—
348C4⋊C4—522no—
349C4⋊C4—522no—
350C4⋊C4C2×D5211yescharacteristic
351C4⋊C4C2×D5211yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—522no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—522no—
360C42C2×D5211yescharacteristic
361C42#612711yescharacteristic
362C42C2×C22⋊D1311yescharacteristic
363C42C23×D1311yescharacteristic
364C13#1916111yescharacteristic, complemented, Sylow
365C23—21no—
366C23#8818411yescharacteristic
367Q8—22no—
368Q8—522no—
369Q8—522no—
370Q8—522no—
371Q8—522no—
372D4—22no—
373D4—42no—
374C2×C4—22no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—522no—
386C2×C4—522no—
387C2×C4#8818411yescharacteristic
388C2×C4#8818411yescharacteristic
389C2×C4#8818411yescharacteristic
390C2×C4C22×D5211yescharacteristic
391C2×C4C2×#612711yescharacteristic
392C2×C4C22×C22⋊D1311yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—41no—
397C8—41no—
398C8—522no—
399C8—522no—
400C8#8820412yes—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22C2×#8818411yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—1042no—
415C4—1042no—
416C4#1171880412yes—
417C4#1171945312yes—
418C4C2×#8820411yescharacteristic
419C4#1171952711yescharacteristic
420C2—41no—
421C2—81no—
422C2#1312429111yescharacteristic
423C2#1312444511yescharacteristic
424C2C2×#1171880411yescharacteristic
subgroupG/H
centerC2×C4#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2965C2
socleC22×C13C2×#121
prime radicalC2×C13×#41D4
hypercenter#2965D13
hypocenterC13#19161
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #13125422C2semidirect
3. #13114390C2semidirect
4. #13114383C2semidirect
5. #13114354C2semidirect
6. #13114349C2semidirect
7. #13114330C2semidirect
8. #13114325C2semidirect
9. #13113584C2semidirect
10. #13113500C2semidirect
364. C13#19161semidirect

Maximal subgroups

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

subgroupindex
#131254222
#131249072
#131143902
#131143832
#131143542
#131143492
#131143302
#131143252
#131135842
#131135002
C13×#29652
#1916113