Finite Group Databasebeta

← #15760499

Subgroups — #15760499

Order 3328.

436 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123832C211yesmaximal, characteristic, complemented
2#13113447C211yesmaximal, characteristic, complemented
3#13113396C211yesmaximal, characteristic, complemented
4#13113374C211yesmaximal, characteristic, complemented
5#13112735C211yesmaximal, characteristic, complemented
6#13112718C211yesmaximal, characteristic, complemented
7C13×#3180C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#501C411yescharacteristic, complemented
11C13×#496C411yescharacteristic, complemented
12C13×#490C411yescharacteristic, complemented
13C13×#489C411yescharacteristic, complemented
14C13×#466—21no—
15C13×#465—21no—
16C13×#442—21no—
17C13×#440—21no—
18C2×C13×#97C2211yescharacteristic
19#11718685—21no—
20#11718672—21no—
21#11718672—21no—
22D4×#1055—21no—
23#11718661—21no—
24#11718658—21no—
25#11718597C2211yescharacteristic
26#11718587C2211yescharacteristic
27#11718586C2211yescharacteristic
28C2×#88043C2211yescharacteristic
29#11718132—21no—
30#11718132—21no—
31#11718130—21no—
32#11718129—21no—
33#11718129—21no—
34#11718129—21no—
35C2×C13×#41—21no—
36C2×C13×SD16—21no—
37C2×C13×D8—21no—
38C22×C8×C13—21no—
39C13×C4⋊Q8C2×C411yescharacteristic
40C13×#127C2×C411yescharacteristic
41C13×#126—21no—
42C13×#125C2×C411yescharacteristic
43C13×#124—21no—
44C13×#124C2×C411yescharacteristic
45C13×#123—21no—
46C13×C22⋊Q8D411yescharacteristic
47C13×#121—21no—
48C13×#121—21no—
49C13×#121D411yescharacteristic
50C4×Q8×C13D411yescharacteristic
51C4×D4×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13D411yescharacteristic
55C13×#117—21no—
56C2×C42×C13C2311yescharacteristic
57C2×C4⋊Dic13—21no—
58C2×#6099—21no—
59C22×#1055—21no—
60C22×#1055—21no—
61C13×#107—21no—
62C13×#106—21no—
63C13×#103—21no—
64C13×#102—21no—
65C13×#102—21no—
66C13×#102—21no—
67C13×#97—21no—
68C13×#97C2×C411yescharacteristic
69C13×#97C2×C411yescharacteristic
70#88071—21no—
71#88071—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055—21no—
75C22⋊#1055D411yescharacteristic
76C22⋊#1055D411yescharacteristic
77C4⋊#1055—21no—
78C4⋊#1055—21no—
79C4⋊#1055—21no—
80C4⋊#1055—21no—
81#88043—21no—
82#88043—21no—
83#88043—21no—
84#88043D411yescharacteristic
85#88043D411yescharacteristic
86C4×#1055—21no—
87C4×#1055—21no—
88#9432—131nomaximal, Sylow
89C13×#41—81no—
90C13×#41—81no—
91C2×Q8×C13—21no—
92C2×Q8×C13C22⋊C411yescharacteristic
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—41no—
98C2×D4×C13C22⋊C411yescharacteristic
99C22×C4×C13—21no—
100C22×C4×C13—41no—
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C22×Dic13—41no—
105C13×SD16—42no—
106C13×D8—42no—
107C2×C8×C13—21no—
108C2×C8×C13—21no—
109C2×C8×C13—42no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4C22⋊C411yescharacteristic
117C13×C4⋊C4C22⋊C411yescharacteristic
118C13×C22⋊C4—21no—
119C13×C22⋊C4—21no—
120C13×C22⋊C4—21no—
121C13×C22⋊C4—21no—
122C13×C22⋊C4—21no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C42×C13—21no—
126C42×C13C22×C411yescharacteristic
127C42×C13C2×D411yescharacteristic
128C42×C13C2×D411yescharacteristic
129C42×C13#4111yescharacteristic
130C4⋊Dic13—81no—
131#6099—42no—
132C2×#1055—21no—
133C2×#1055—21no—
134C2×#1055—21no—
135C2×#1055—21no—
136C2×#1055—42no—
137C2×#1055—42no—
138C2×#1055—41no—
139#3180D1311yescharacteristic
140#2968—131no—
141#1530—131no—
142#1517—131no—
143#1512—131no—
144#1302—131no—
145#1295—131no—
146C23×C13—21no—
147C23×C13—41no—
148C23×C13#12111yescharacteristic
149Q8×C13—41no—
150Q8×C13—81no—
151D4×C13—41no—
152D4×C13—41no—
153D4×C13—41no—
154D4×C13—41no—
155D4×C13—41no—
156D4×C13—81no—
157D4×C13—81no—
158D4×C13—81no—
159D4×C13—81no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—82no—
171C2×C4×C13C2×C22⋊C411yescharacteristic
172C2×C4×C13C4×D411yescharacteristic
173C2×C4×C13C4×D411yescharacteristic
174C2×C4×C13#12011yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12311yescharacteristic
177C2×Dic13—81no—
178C2×Dic13—81no—
179C2×Dic13—81no—
180C8×C13—22no—
181C8×C13—41no—
182#1055—22no—
183#1055—41no—
184#1055—41no—
185#1055—41no—
186#1055—81no—
187#532C2×D1311yescharacteristic
188#529C2×D1311yescharacteristic
189#501Dic1311yescharacteristic, complemented
190#496Dic1311yescharacteristic, complemented
191#490Dic1311yescharacteristic, complemented
192#489Dic1311yescharacteristic, complemented
193#466—21no—
194#465—21no—
195#446—261no—
196#442—21no—
197#440—21no—
198#435—261no—
199#435—261no—
200C8×D4—261no—
201#433—261no—
202#432—131no—
203#431—131no—
204#405—261no—
205C2×#97—131no—
206C2×#97C2×D1311yescharacteristic
207#382—131no—
208#329—261no—
209#329—261no—
210#328—261no—
211#327—261no—
212#327—261no—
213#327—261no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13#38611yescharacteristic
223C22×C13#47111yescharacteristic
224C22×C13#47211yescharacteristic
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—41no—
232C4×C13—41no—
233C4×C13—41no—
234C4×C13—81no—
235Dic13—161no—
236C2×#41—21no—
237C2×SD16—21no—
238C2×D8—21no—
239C2×M16—261no—
240C22×C8—21no—
241C22×C8—261no—
242C22×C8—261no—
243C4⋊Q8C2×Dic1311yescharacteristic
244#127C2×Dic1311yescharacteristic
245#126—21no—
246#125C2×Dic1311yescharacteristic
247#124—21no—
248#124C2×Dic1311yescharacteristic
249#123—21no—
250C22⋊Q8C22⋊D1311yescharacteristic
251#121—21no—
252#121—21no—
253#121C22⋊D1311yescharacteristic
254C4×Q8C22⋊D1311yescharacteristic
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C22⋊D1311yescharacteristic
259#117—21no—
260C2×C4⋊C4—261no—
261C2×C42C22×D1311yescharacteristic
262#107—21no—
263#106—21no—
264C4⋊C8—261no—
265C4⋊C8—261no—
266C4⋊C8—261no—
267C4⋊C8—261no—
268#103—21no—
269#102—21no—
270#102—21no—
271#102—21no—
272C22⋊C8—131no—
273C22⋊C8—131no—
274C22⋊C8—261no—
275C22⋊C8—261no—
276C22⋊C8—261no—
277#97—21no—
278#97—131no—
279#97—131no—
280#97—261no—
281#97—261no—
282#97—261no—
283#97C2×Dic1311yescharacteristic
284#97C2×Dic1311yescharacteristic
285C4×C8—261no—
286C4×C8—261no—
287#95—261no—
288#95—261no—
289C2×C13—21no—
290C2×C13—21no—
291C2×C13—81no—
292C2×C13—161no—
293C2×C13#188411yescharacteristic
294C2×C13#190611yescharacteristic
295C2×C13#190711yescharacteristic
296#41—81no—
297#41—81no—
298C2×Q8—21no—
299C2×Q8C22⋊Dic1311yescharacteristic
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4C22⋊Dic1311yescharacteristic
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—521no—
309C22×C4D4×D1311yescharacteristic
310C22×C4#612911yescharacteristic
311C22×C4C2×C22⋊D1311yescharacteristic
312SD16—42no—
313D8—42no—
314M16—522no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—42no—
318C2×C8—261no—
319C2×C8—261no—
320C2×C8—261no—
321C2×C8—261no—
322C2×C8—522no—
323C2×C8—522no—
324C2×C8—521no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—1041no—
332C4⋊C4C22⋊Dic1311yescharacteristic
333C4⋊C4C22⋊Dic1311yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C42—21no—
342C42D4×D1311yescharacteristic
343C42#612911yescharacteristic
344C42C22×Dic1311yescharacteristic
345C42C2×C22⋊D1311yescharacteristic
346C13#943211yescharacteristic, complemented, Sylow
347C23—21no—
348C23—41no—
349C23#8819311yescharacteristic
350Q8—41no—
351Q8—81no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—82no—
372C2×C4—1041no—
373C2×C4—1041no—
374C2×C4—1041no—
375C2×C4D4×Dic1311yescharacteristic
376C2×C4D4×Dic1311yescharacteristic
377C2×C4#8818911yescharacteristic
378C2×C4#8819111yescharacteristic
379C2×C4#8819311yescharacteristic
380C2×C4C2×C22⋊Dic1311yescharacteristic
381C8—22no—
382C8—41no—
383C8—262no—
384C8—521no—
385C8—521no—
386C8—521no—
387C8—1041no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22#1171886011yescharacteristic
397C22#1171886111yescharacteristic
398C22#1171888111yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—81no—
409C4—2081no—
410C2—21no—
411C2—21no—
412C2—81no—
413C2—161no—
414C2#1311522011yescharacteristic
415C2#1311533911yescharacteristic
416C2#1311534611yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3180C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#3180D13
hypocenterC13#9432
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3180

Complements

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

NH ≅ G/Ntype
1. #13123832C2semidirect
2. #13113447C2semidirect
3. #13113396C2semidirect
4. #13113374C2semidirect
5. #13112735C2semidirect
6. #13112718C2semidirect
10. C13×#501C4semidirect
11. C13×#496C4semidirect
12. C13×#490C4semidirect
13. C13×#489C4semidirect
189. #501Dic13semidirect
190. #496Dic13semidirect
191. #490Dic13semidirect
192. #489Dic13semidirect
346. C13#9432semidirect

Maximal subgroups

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

subgroupindex
#131238322
#131134472
#131133962
#131133742
#131127352
#131127182
C13×#31802
#943213