Finite Group Databasebeta

← #15778066

Subgroups — #15778066

Order 3328.

636 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718128C212yesmaximal
2C4×#88073C211yesmaximal, characteristic, complemented
3C4×#88074C211yesmaximal, characteristic, complemented
4#13112954C212yesmaximal, complemented
5C13×#2321C211yesmaximal, characteristic
6C2×C13×#120C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C22×C13×C22⋊C4C411yescharacteristic, complemented
9C13×#390—21no—
10C13×#388—21no—
11C13×#388—21no—
12C13×#386—21no—
13C13×#386C2211yescharacteristic
14C13×#385C411yescharacteristic, complemented
15C13×#379C411yescharacteristic, complemented
16C4×C13×C22⋊C4C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88073C2212yes—
19C4×C22⋊Dic13—21no—
20C4×#6099—21no—
21#11718128C418yescomplemented
22#11718122—21no—
23#11718118—21no—
24C25×C13C2×C411yescharacteristic
25C22×D4×C13—21no—
26C22×D4×C13C2311yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C13×#120—22no—
31C13×#120C2×C414yes—
32C4×D4×C13—41no—
33C4×D4×C13—41no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—41no—
43C2×C13×C22⋊C4—41no—
44C2×C13×C22⋊C4C2×C411yescharacteristic
45C2×C13×C22⋊C4C2×C411yescharacteristic
46C2×C13×C22⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C42×C13—21no—
49C2×C42×C13D411yescharacteristic
50C2×C22⋊Dic13—22no—
51C2×C4×Dic13—41no—
52C2×#6099—22no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56#88074—22no—
57#88074C2×C414yes—
58#88073—22no—
59#88073C2×C414yes—
60#88071—41no—
61#88043—41no—
62C4×#1055—41no—
63#12622—131nomaximal, Sylow
64C24×C13—21no—
65C24×C13—21no—
66C24×C13—41no—
67C24×C13—41no—
68C24×C13—81no—
69C24×C13—81no—
70C24×C13C4212yescomplemented
71C24×C13C22×C411yescharacteristic
72C24×C13C2×D411yescharacteristic
73C2×D4×C13—24no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—81no—
77C2×D4×C13—81no—
78C2×D4×C13C22×C412yes—
79C2×D4×C13#4112yes—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—41no—
88C22×C4×C13—81no—
89C22×C4×C13—81no—
90C22×C4×C13—81no—
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C22⋊C411yescharacteristic
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×Dic13—42no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—81no—
99C13×C22⋊C4—21no—
100C13×C22⋊C4—24no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—81no—
108C13×C22⋊C4—81no—
109C13×C22⋊C4—81no—
110C13×C22⋊C4C4212yescomplemented
111C42×C13—21no—
112C42×C13—21no—
113C42×C13—81no—
114C22⋊Dic13—24no—
115C22⋊Dic13—42no—
116C4×Dic13—82no—
117#6099—24no—
118#6099—42no—
119C2×#1055—42no—
120#2321D1311yescharacteristic
121C2×AΣL(1,𝔽16)—132no—
122C4×#100—131no—
123C4×#99—131no—
124#1390—132no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—22no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—42no—
139C23×C13—42no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—82no—
143C23×C13—82no—
144C23×C13—84no—
145C23×C13—82no—
146C23×C13—82no—
147C23×C13C2×C4211yescharacteristic
148C23×C13C2×C22⋊C411yescharacteristic
149C23×C13#11711yescharacteristic
150C23×C13C4×D412yes—
151D4×C13—42no—
152D4×C13—42no—
153D4×C13—84no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—22no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—41no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
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—81no—
174C2×C4×C13—81no—
175C2×C4×C13—81no—
176C2×C4×C13—82no—
177C2×C4×C13#9911yescharacteristic
178C2×C4×C13#9911yescharacteristic
179C2×C4×C13C4×D412yes—
180C2×Dic13—44no—
181C2×Dic13—82no—
182C2×Dic13—82no—
183#1055—44no—
184C2×#120C2×D1311yescharacteristic
185C2×C4×D4C2×D1311yescharacteristic
186C22×C22⋊C4Dic1311yescharacteristic, complemented
187C2×#100—132no—
188C2×#99—132no—
189C4×M16—261no—
190#390—21no—
191#388—21no—
192#388—21no—
193#386—21no—
194#386C2×D1311yescharacteristic
195#385Dic1311yescharacteristic, complemented
196#379Dic1311yescharacteristic, complemented
197C4×C22⋊C4—261no—
198C4×C22⋊C4Dic1311yescharacteristic, complemented
199AΣL(1,𝔽16)—138no—
200#343—261no—
201#342—261no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—22no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—42no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—42no—
211C22×C13—42no—
212C22×C13—42no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—42no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—84no—
222C22×C13—84no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13C4×C22⋊C411yescharacteristic
226C22×C13C2×#9911yescharacteristic
227C22×C13#41011yescharacteristic
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—22no—
231C4×C13—42no—
232C4×C13—41no—
233C4×C13—41no—
234C4×C13—41no—
235C4×C13—81no—
236C4×C13—81no—
237Dic13—84no—
238C25C2×Dic1311yescharacteristic
239C22×D4—21no—
240C22×D4C22×D1311yescharacteristic
241C23×C4C2×Dic1311yescharacteristic
242C23×C4C2×Dic1311yescharacteristic
243C23×C4C22⋊D1311yescharacteristic
244C2×M16—262no—
245#120—22no—
246#120C4×D1314yes—
247C4×D4—41no—
248C4×D4—41no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4C22⋊D1311yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—41no—
258C2×C22⋊C4—41no—
259C2×C22⋊C4—262no—
260C2×C22⋊C4C2×Dic1311yescharacteristic
261C2×C22⋊C4C2×Dic1311yescharacteristic
262C2×C22⋊C4C2×Dic1311yescharacteristic
263C2×C22⋊C4C22⋊D1311yescharacteristic
264C2×C42—21no—
265C2×C42—521no—
266C2×C42C22⋊D1311yescharacteristic
267#100—134no—
268#100—262no—
269#99—134no—
270#99—262no—
271#97—521no—
272C4×C8—521no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—521no—
277C2×C13—21no—
278C2×C13—21no—
279C2×C13—42no—
280C2×C13—41no—
281C2×C13—41no—
282C2×C13—82no—
283C2×C13C4×#9911yescharacteristic
284C2×C13#212111yescharacteristic
285C2×C13#212211yescharacteristic
286C24—21no—
287C24—21no—
288C24—41no—
289C24—41no—
290C24—81no—
291C24—81no—
292C24C4×Dic1312yescomplemented
293C24C22×Dic1311yescharacteristic
294C24C2×C22⋊D1311yescharacteristic
295C2×D4—24no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4C2×C4×D1312yes—
301C2×D4#612712yes—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—81no—
311C22×C4—81no—
312C22×C4—81no—
313C22×C4—522no—
314C22×C4C22⋊Dic1311yescharacteristic
315C22×C4C22⋊Dic1311yescharacteristic
316C22×C4C22⋊Dic1311yescharacteristic
317C22×C4C22⋊Dic1311yescharacteristic
318C22×C4C2×C22⋊D1311yescharacteristic
319M16—264no—
320M16—522no—
321C2×C8—522no—
322C4⋊C4—41no—
323C4⋊C4—81no—
324C22⋊C4—21no—
325C22⋊C4—24no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—42no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C22⋊C4—264no—
336C22⋊C4—522no—
337C22⋊C4C4×Dic1312yescomplemented
338C42—21no—
339C42—21no—
340C42—81no—
341C42—1042no—
342C13#1262211yescharacteristic, complemented, Sylow
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—22no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—82no—
361C23—82no—
362C23—82no—
363C23—82no—
364C23—84no—
365C23C2×C4×Dic1311yescharacteristic
366C23#8818011yescharacteristic
367C23C4×C22⋊D1312yes—
368C23C2×C22⋊Dic1311yescharacteristic
369D4—42no—
370D4—42no—
371D4—84no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—82no—
395C2×C4—524no—
396C2×C4—1042no—
397C2×C4—1042no—
398C2×C4#8807411yescharacteristic
399C2×C4#8807411yescharacteristic
400C2×C4C4×C22⋊D1312yes—
401C8—524no—
402C22—21no—
403C22—21no—
404C22—22no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—41no—
409C22—41no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—42no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—84no—
422C22—84no—
423C22—81no—
424C22—81no—
425C22C4×C22⋊Dic1311yescharacteristic
426C22C2×#8807411yescharacteristic
427C22#1171890111yescharacteristic
428C4—22no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—81no—
436C4—81no—
437C4—1044no—
438C2—21no—
439C2—21no—
440C2—42no—
441C2—41no—
442C2—41no—
443C2—82no—
444C2C4×#8807411yescharacteristic
445C2#1311648211yescharacteristic
446C2#1311648611yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC23×C13C2×C42
FrattiniC22×D4C22×D13
FittingC13×#2321C2
socleC22×C13C2×#99
prime radicalC2×C13×#120C22
cosocleC22×D4×C13C23
hypercenter#2321D13
hypocenterC13#12622
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2321

Complements

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

NH ≅ G/Ntype
2. C4×#88073C2semidirect
3. C4×#88074C2semidirect
4. #13112954C2semidirect
8. C22×C13×C22⋊C4C4semidirect
14. C13×#385C4semidirect
15. C13×#379C4semidirect
16. C4×C13×C22⋊C4C4semidirect
21. #11718128C4semidirect
70. C24×C13C42semidirect
110. C13×C22⋊C4C42semidirect
186. C22×C22⋊C4Dic13semidirect
195. #385Dic13semidirect
196. #379Dic13semidirect
198. C4×C22⋊C4Dic13semidirect
292. C24C4×Dic13semidirect
337. C22⋊C4C4×Dic13semidirect
342. C13#12622semidirect

Maximal subgroups

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

subgroupindex
C2×#117181282
C4×#880732
C4×#880742
#131129542
C13×#23212
#1262213