Finite Group Databasebeta

← #15757032

Subgroups — #15757032

Order 3328.

464 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123884C211yesmaximal, characteristic
2#13115139C211yesmaximal, characteristic
3#13115043C211yesmaximal, characteristic, complemented
4#13115021C211yesmaximal, characteristic, complemented
5#13112722C211yesmaximal, characteristic, complemented
6#13112682C211yesmaximal, characteristic, complemented
7C13×#1501C211yesmaximal, characteristic
8C13×#525C2211yescharacteristic
9C22×#6099C2211yescharacteristic
10C2×C13×C22⋊C8C2211yescharacteristic
11C4×C13×C22⋊C4C2211yescharacteristic
12C2×#88077—21no—
13#11718895—21no—
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2211yescharacteristic
16C2×C22⋊#1055C2211yescharacteristic
17C2×#88059—21no—
18#11718673—21no—
19#11718672—21no—
20#11718672—21no—
21D4×#1055—21no—
22#11718661—21no—
23C2×C4⋊#1055—21no—
24C13×#328C411yescharacteristic, complemented
25C13×#328C411yescharacteristic, complemented
26C13×#327C411yescharacteristic, complemented
27C13×#327C411yescharacteristic, complemented
28#11718144—21no—
29#11718124—21no—
30#11718116—21no—
31C2×C13×#41D411yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C22×C8×C13—21no—
34C13×#123—21no—
35C13×C22⋊Q8C2×C411yescharacteristic
36C13×C22⋊Q8Q811yescharacteristic
37C13×#121C2×C411yescharacteristic
38C13×#121Q811yescharacteristic
39C13×#120—21no—
40C4×D4×C13—21no—
41C4×D4×C13—21no—
42C13×#117D411yescharacteristic
43C2×C13×C22⋊C4—21no—
44C2×C42×C13—21no—
45C2×C22⋊Dic13—21no—
46C2×C4×Dic13—21no—
47C2×#6099—21no—
48C2×#6099—21no—
49C2×#6099—21no—
50C2×#6099—42no—
51C2×#6099D411yescharacteristic
52C2×#6099D411yescharacteristic
53C22×#1055—21no—
54C22×#1055—21no—
55C22×#1055D411yescharacteristic
56C22×#1055D411yescharacteristic
57C13×C22⋊C8—21no—
58C13×C22⋊C8C2×C411yescharacteristic
59C13×C22⋊C8C2×C411yescharacteristic
60C13×#95C2×C411yescharacteristic
61C13×#95C2×C411yescharacteristic
62#88077—42no—
63#88071—21no—
64C22⋊#1055—21no—
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70#88059—42no—
71C4⋊#1055—21no—
72C4⋊#1055—21no—
73C4⋊#1055—42no—
74#88043—21no—
75C4×#1055—21no—
76#8875—131nomaximal, Sylow
77C24×C13#4111yescharacteristic
78C13×#41—41no—
79C13×#41—41no—
80C2×Q8×C13C4⋊C411yescharacteristic
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13C4⋊C411yescharacteristic
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13C22×C411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×Q811yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C22×Dic13—41no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4C4⋊C411yescharacteristic
104C13×C4⋊C4C4⋊C411yescharacteristic
105C13×C22⋊C4—21no—
106C13×C22⋊C4—21no—
107C13×C22⋊C4—21no—
108C13×C22⋊C4—21no—
109C13×C22⋊C4—21no—
110C13×C22⋊C4—42no—
111C42×C13—21no—
112C42×C13—41no—
113C42×C13—41no—
114C22⋊Dic13—22no—
115C22⋊Dic13—41no—
116C4×Dic13—41no—
117C4×Dic13—41no—
118#6099—22no—
119#6099—22no—
120#6099—41no—
121#6099—41no—
122#6099—41no—
123#6099—41no—
124#6099—81no—
125C2×#1055—22no—
126C2×#1055—21no—
127C2×#1055—21no—
128C2×#1055—21no—
129C2×#1055—21no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#1055—41no—
134C2×#1055—81no—
135#2976—131no—
136#1871—131no—
137#1855—131no—
138#1851—131no—
139#1501D1311yescharacteristic
140#1297—131no—
141#1282—131no—
142C23×C13—21no—
143C23×C13—21no—
144C23×C13—21no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13C4×D411yescharacteristic
148C23×C13C22⋊Q811yescharacteristic
149C23×C13#12311yescharacteristic
150Q8×C13—41no—
151D4×C13—41no—
152D4×C13—41no—
153D4×C13—41no—
154D4×C13—81no—
155D4×C13—81no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—22no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13C2×C4⋊C411yescharacteristic
177C2×C4×C13C4×D411yescharacteristic
178C2×C4×C13#12011yescharacteristic
179C2×C4×C13C22⋊Q811yescharacteristic
180C2×Dic13—42no—
181C2×Dic13—81no—
182C2×Dic13—81no—
183C8×C13—41no—
184C8×C13—41no—
185#1055—42no—
186#1055—41no—
187#1055—41no—
188#1055—41no—
189#1055—41no—
190C22×M16—131no—
191#525C2×D1311yescharacteristic
192#436—261no—
193#435—261no—
194#435—261no—
195C8×D4—261no—
196#433—261no—
197C2×#108—261no—
198C2×C4⋊C8—261no—
199C2×#104—261no—
200#408—261no—
201#407—131no—
202C2×C22⋊C8—131no—
203C2×C22⋊C8C2×D1311yescharacteristic
204C4×C22⋊C4—131no—
205C4×C22⋊C4C2×D1311yescharacteristic
206#341—261no—
207#339—261no—
208#336—261no—
209#328Dic1311yescharacteristic, complemented
210#328Dic1311yescharacteristic, complemented
211#327Dic1311yescharacteristic, complemented
212#327Dic1311yescharacteristic, complemented
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13—41no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13#38511yescharacteristic
227C22×C13#44311yescharacteristic
228C22×C13#44411yescharacteristic
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—42no—
233C4×C13—41no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—81no—
237C4×C13B(4,𝔽2)11yescharacteristic
238C4×C13#45811yescharacteristic
239Dic13—82no—
240C2×#41D5211yescharacteristic
241C23×C4C22×D1311yescharacteristic
242C2×M16—131no—
243C2×M16—131no—
244C2×M16—261no—
245C2×M16—261no—
246C2×M16—261no—
247C2×M16—522no—
248C22×C8—21no—
249C22×C8—131no—
250C22×C8—131no—
251C22×C8—261no—
252C22×C8—261no—
253#123—21no—
254C22⋊Q8Dic2611yescharacteristic
255C22⋊Q8C2×Dic1311yescharacteristic
256#121Dic2611yescharacteristic
257#121C2×Dic1311yescharacteristic
258#120—21no—
259C4×D4—21no—
260C4×D4—21no—
261#117D5211yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—261no—
264C2×C42—21no—
265C2×C42—261no—
266#108—522no—
267C4⋊C8—261no—
268C4⋊C8—261no—
269C4⋊C8—522no—
270#104—522no—
271C22⋊C8—21no—
272C22⋊C8—261no—
273C22⋊C8—261no—
274C22⋊C8—261no—
275C22⋊C8—261no—
276C22⋊C8—261no—
277C22⋊C8—261no—
278C22⋊C8C2×Dic1311yescharacteristic
279C22⋊C8C2×Dic1311yescharacteristic
280#97—261no—
281C4×C8—261no—
282#95—261no—
283#95C2×Dic1311yescharacteristic
284#95C2×Dic1311yescharacteristic
285C2×C13—21no—
286C2×C13—21no—
287C2×C13—41no—
288C2×C13—41no—
289C2×C13—81no—
290C2×C13#186111yescharacteristic
291C2×C13#186611yescharacteristic
292C2×C13#186711yescharacteristic
293C24#612911yescharacteristic
294#41—41no—
295#41—41no—
296C2×Q8C4⋊Dic1311yescharacteristic
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4C4⋊Dic1311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—521no—
307C22×C4C2×Dic2611yescharacteristic
308C22×C4C2×D5211yescharacteristic
309C22×C4D4×D1311yescharacteristic
310C22×C4D4×D1311yescharacteristic
311C22×C4#612911yescharacteristic
312C22×C4C22×Dic1311yescharacteristic
313M16—262no—
314M16—262no—
315M16—521no—
316M16—521no—
317M16—521no—
318M16—521no—
319M16—1041no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—262no—
325C2×C8—261no—
326C2×C8—261no—
327C2×C8—261no—
328C2×C8—261no—
329C2×C8—521no—
330C2×C8—521no—
331C2×C8—521no—
332C2×C8—521no—
333C2×C8—1041no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C4⋊Dic1311yescharacteristic
337C4⋊C4C4⋊Dic1311yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—42no—
344C22⋊C4—262no—
345C22⋊C4—521no—
346C42—21no—
347C42—41no—
348C42—41no—
349C42—521no—
350C42—521no—
351C13#887511yescharacteristic, complemented, Sylow
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23#8813211yescharacteristic
358C23#8814011yescharacteristic
359C23D4×Dic1311yescharacteristic
360Q8—41no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—522no—
387C2×C4—1041no—
388C2×C4—1041no—
389C2×C4#8813211yescharacteristic
390C2×C4#8813611yescharacteristic
391C2×C4C2×C4⋊Dic1311yescharacteristic
392C2×C4D4×Dic1311yescharacteristic
393C8—41no—
394C8—41no—
395C8—522no—
396C8—521no—
397C8—521no—
398C8—521no—
399C8—521no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22#1171861111yescharacteristic
414C22#1171885711yescharacteristic
415C22#1171885811yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—81no—
424C4—1042no—
425C4#1171840211yescharacteristic
426C4#1171840311yescharacteristic
427C2—21no—
428C2—21no—
429C2—41no—
430C2—41no—
431C2—81no—
432C2#1311507811yescharacteristic
433C2#1311511311yescharacteristic
434C2#1311511911yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1501C2
socleC22×C13#385
prime radicalC13×#525C22
cosocleC23×C4×C13C23
hypercenter#1501D13
hypocenterC13#8875
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
3. #13115043C2semidirect
4. #13115021C2semidirect
5. #13112722C2semidirect
6. #13112682C2semidirect
24. C13×#328C4semidirect
25. C13×#328C4semidirect
26. C13×#327C4semidirect
27. C13×#327C4semidirect
209. #328Dic13semidirect
210. #328Dic13semidirect
211. #327Dic13semidirect
212. #327Dic13semidirect
351. C13#8875semidirect

Maximal subgroups

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

subgroupindex
#131238842
#131151392
#131150432
#131150212
#131127222
#131126822
C13×#15012
#887513