Finite Group Databasebeta

← #15778892

Subgroups — #15778892

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718128C212yesmaximal
2#13114828C211yesmaximal, characteristic, complemented
3#13114824C211yesmaximal, 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—
19#11718873—21no—
20#11718585—21no—
21#11718128—24no—
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—21no—
31C13×#120—21no—
32C13×#120D412yes—
33C13×#120Q812yes—
34C4×D4×C13—41no—
35C4×D4×C13—41no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—41no—
45C2×C13×C22⋊C4—41no—
46C2×C13×C22⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4C2×C411yescharacteristic
49C2×C13×C22⋊C4D411yescharacteristic
50C2×C42×C13—21no—
51C2×C42×C13D411yescharacteristic
52C2×C22⋊Dic13—22no—
53C2×C4⋊Dic13—41no—
54C2×#6099—22no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58#88074—22no—
59#88074—22no—
60#88073—22no—
61#88073—22no—
62#88071—41no—
63C4⋊#1055—41no—
64C4⋊#1055—41no—
65#12795—131nomaximal, Sylow
66C24×C13—21no—
67C24×C13—21no—
68C24×C13—41no—
69C24×C13—41no—
70C24×C13—81no—
71C24×C13—81no—
72C24×C13C4⋊C412yescomplemented
73C24×C13C22×C411yescharacteristic
74C24×C13C2×D411yescharacteristic
75C2×D4×C13—22no—
76C2×D4×C13—22no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—81no—
80C2×D4×C13—81no—
81C2×D4×C13C2×D411yescharacteristic
82C2×D4×C13C2×Q811yescharacteristic
83C2×D4×C13#4111yescharacteristic
84C2×D4×C13#4111yescharacteristic
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—41no—
93C22×C4×C13—81no—
94C22×C4×C13—81no—
95C22×C4×C13—81no—
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C22⋊C411yescharacteristic
99C22×C4×C13C22⋊C411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×Dic13—42no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—81no—
104C13×C22⋊C4—21no—
105C13×C22⋊C4—22no—
106C13×C22⋊C4—22no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—81no—
114C13×C22⋊C4—81no—
115C13×C22⋊C4—81no—
116C13×C22⋊C4C4⋊C412yescomplemented
117C42×C13—21no—
118C42×C13—21no—
119C42×C13—81no—
120C22⋊Dic13—42no—
121C22⋊Dic13—42no—
122C4⋊Dic13—82no—
123#6099—42no—
124#6099—42no—
125C2×#1055—42no—
126#2321D1311yescharacteristic
127C2×AΣL(1,𝔽16)—132no—
128#1800—131no—
129#1799—131no—
130#1390—132no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—22no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—42no—
145C23×C13—42no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—82no—
149C23×C13—82no—
150C23×C13—84no—
151C23×C13—82no—
152C23×C13—82no—
153C23×C13C2×C22⋊C411yescharacteristic
154C23×C13C2×C4⋊C411yescharacteristic
155C23×C13#11711yescharacteristic
156C23×C13#12111yescharacteristic
157C23×C13C22⋊Q811yescharacteristic
158D4×C13—41no—
159D4×C13—41no—
160D4×C13—41no—
161D4×C13—41no—
162D4×C13—82no—
163D4×C13—82no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—22no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—81no—
184C2×C4×C13—81no—
185C2×C4×C13—81no—
186C2×C4×C13—82no—
187C2×C4×C13#9911yescharacteristic
188C2×C4×C13#9911yescharacteristic
189C2×C4×C13#12111yescharacteristic
190C2×C4×C13C22⋊Q811yescharacteristic
191C2×Dic13—82no—
192C2×Dic13—82no—
193C2×Dic13—82no—
194#1055—82no—
195C2×#120C2×D1311yescharacteristic
196C2×C4×D4C2×D1311yescharacteristic
197C22×C22⋊C4Dic1311yescharacteristic, complemented
198#423—261no—
199C2×#100—132no—
200C2×#99—132no—
201#390—21no—
202#388—21no—
203#388—21no—
204#386—21no—
205#386C2×D1311yescharacteristic
206#385Dic1311yescharacteristic, complemented
207#380—261no—
208#379Dic1311yescharacteristic, complemented
209C4×C22⋊C4Dic1311yescharacteristic, complemented
210AΣL(1,𝔽16)—264no—
211#343—261no—
212#342—261no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13—42no—
224C22×C13—42no—
225C22×C13—42no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13—41no—
229C22×C13—41no—
230C22×C13—42no—
231C22×C13—81no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13—84no—
235C22×C13—84no—
236C22×C13—81no—
237C22×C13—81no—
238C22×C13#38011yescharacteristic
239C22×C13C2×#9911yescharacteristic
240C22×C13#41011yescharacteristic
241C4×C13—21no—
242C4×C13—21no—
243C4×C13—21no—
244C4×C13—21no—
245C4×C13—42no—
246C4×C13—41no—
247C4×C13—41no—
248C4×C13—41no—
249C4×C13—81no—
250C4×C13—81no—
251Dic13—162no—
252C25C2×Dic1311yescharacteristic
253C22×D4—21no—
254C22×D4C22×D1311yescharacteristic
255C23×C4C2×Dic1311yescharacteristic
256C23×C4C2×Dic1311yescharacteristic
257C23×C4C22⋊D1311yescharacteristic
258C2×M16—262no—
259#120—21no—
260#120—21no—
261#120Dic2612yes—
262#120D5212yes—
263C4×D4—41no—
264C4×D4—41no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—521no—
267C2×C4⋊C4C22⋊D1311yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—41no—
275C2×C22⋊C4—41no—
276C2×C22⋊C4—262no—
277C2×C22⋊C4C2×Dic1311yescharacteristic
278C2×C22⋊C4C2×Dic1311yescharacteristic
279C2×C22⋊C4C2×Dic1311yescharacteristic
280C2×C22⋊C4C22⋊D1311yescharacteristic
281C2×C42—21no—
282C2×C42C22⋊D1311yescharacteristic
283C4⋊C8—521no—
284C4⋊C8—521no—
285#100—262no—
286#100—262no—
287#99—262no—
288#99—262no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—521no—
293C2×C13—21no—
294C2×C13—21no—
295C2×C13—41no—
296C2×C13—41no—
297C2×C13—41no—
298C2×C13—41no—
299C2×C13—82no—
300C2×C13#179911yescharacteristic
301C2×C13#212111yescharacteristic
302C2×C13#212211yescharacteristic
303C24—21no—
304C24—21no—
305C24—41no—
306C24—41no—
307C24—81no—
308C24—81no—
309C24C4⋊Dic1312yescomplemented
310C24C22×Dic1311yescharacteristic
311C24C2×C22⋊D1311yescharacteristic
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—81no—
317C2×D4—81no—
318C2×D4C2×Dic2611yescharacteristic
319C2×D4C2×D5211yescharacteristic
320C2×D4#612711yescharacteristic
321C2×D4#612711yescharacteristic
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—81no—
331C22×C4—81no—
332C22×C4—81no—
333C22×C4—522no—
334C22×C4C22⋊Dic1311yescharacteristic
335C22×C4C22⋊Dic1311yescharacteristic
336C22×C4C22⋊Dic1311yescharacteristic
337C22×C4C22⋊Dic1311yescharacteristic
338C22×C4C2×C22⋊D1311yescharacteristic
339M16—522no—
340M16—522no—
341C2×C8—522no—
342C4⋊C4—41no—
343C4⋊C4—81no—
344C4⋊C4—1042no—
345C22⋊C4—21no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—42no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—81no—
355C22⋊C4—81no—
356C22⋊C4—81no—
357C22⋊C4—522no—
358C22⋊C4—522no—
359C22⋊C4C4⋊Dic1312yescomplemented
360C42—21no—
361C42—21no—
362C42—81no—
363C13#1279511yescharacteristic, complemented, Sylow
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—22no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23—82no—
385C23—84no—
386C23#8817811yescharacteristic
387C23C2×C4⋊Dic1311yescharacteristic
388C23#8818011yescharacteristic
389C23#8818411yescharacteristic
390C23C2×C22⋊Dic1311yescharacteristic
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—82no—
396D4—82no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—82no—
420C2×C4—1042no—
421C2×C4—1042no—
422C2×C4—1042no—
423C2×C4#8807411yescharacteristic
424C2×C4#8807411yescharacteristic
425C2×C4#8817811yescharacteristic
426C2×C4#8818411yescharacteristic
427C8—1042no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—42no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—84no—
450C22—84no—
451C22—81no—
452C22—81no—
453C22#1171887311yescharacteristic
454C22C2×#8807411yescharacteristic
455C22#1171890111yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—81no—
465C4—81no—
466C4—2082no—
467C2—21no—
468C2—21no—
469C2—41no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—82no—
474C2#1311482411yescharacteristic
475C2#1311648211yescharacteristic
476C2#1311648611yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2321C2
socleC22×C13C2×#99
prime radicalC2×C13×#120C22
cosocleC22×D4×C13C23
hypercenter#2321D13
hypocenterC13#12795
LCSG ▷ C24×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. #13114828C2semidirect
3. #13114824C2semidirect
4. #13112954C2semidirect
8. C22×C13×C22⋊C4C4semidirect
14. C13×#385C4semidirect
15. C13×#379C4semidirect
16. C4×C13×C22⋊C4C4semidirect
72. C24×C13C4⋊C4semidirect
116. C13×C22⋊C4C4⋊C4semidirect
197. C22×C22⋊C4Dic13semidirect
206. #385Dic13semidirect
208. #379Dic13semidirect
209. C4×C22⋊C4Dic13semidirect
309. C24C4⋊Dic13semidirect
359. C22⋊C4C4⋊Dic13semidirect
363. C13#12795semidirect

Maximal subgroups

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

subgroupindex
C2×#117181282
#131148282
#131148242
#131129542
C13×#23212
#1279513