Finite Group Databasebeta

← #15773375

Subgroups — #15773375

Order 3328.

778 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718118C211yesmaximal, characteristic, complemented
2#13113163C211yesmaximal, characteristic, complemented
3#13112857C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2404C211yesmaximal, characteristic
6C22×C13×#41C411yescharacteristic, complemented
7C2×C13×#120—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic13—21no—
10C13×#393C411yescharacteristic, complemented
11C13×#393C2211yescharacteristic
12C13×#392C411yescharacteristic, complemented
13C13×#392C2211yescharacteristic
14C13×#386—21no—
15C13×#386—21no—
16C13×#386—21no—
17C13×#381C411yescharacteristic, complemented
18#11718868—21no—
19#11718118—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C2×C13×#41—41no—
25C2×C13×#41—41no—
26C2×C13×#41—44no—
27C22×Q8×C13C2×C411yescharacteristic, complemented
28C22×D4×C13—21no—
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13C2×C411yescharacteristic, complemented
32C23×C4×C13—21no—
33C23×C4×C13C2×C411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C23×Dic13—41no—
36C13×#120—44no—
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⋊C4D411yescharacteristic
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C13×C22⋊C4C2311yescharacteristic
48C2×C22⋊Dic13—24no—
49C2×C22⋊Dic13—22no—
50C2×C22⋊Dic13—41no—
51C2×C22⋊Dic13—42no—
52C2×#6099—41no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95C2×C411yescharacteristic, complemented
57C13×#95C2×C411yescharacteristic, complemented
58C22⋊#1055—22no—
59C22⋊#1055—41no—
60#11753—131nomaximal, Sylow
61C24×C13—21no—
62C24×C13—21no—
63C24×C13—22no—
64C24×C13—21no—
65C24×C13—21no—
66C24×C13—21no—
67C24×C13—42no—
68C24×C13—81no—
69C24×C13C22⋊C411yescharacteristic
70C24×C13C22⋊C411yescharacteristic
71C24×C13C2×D411yescharacteristic
72C13×#41—44no—
73C13×#41—44no—
74C13×#41—44no—
75C13×#41—44no—
76C2×Q8×C13—42no—
77C2×Q8×C13—41no—
78C2×D4×C13—24no—
79C2×D4×C13—41no—
80C2×D4×C13—42no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—42no—
84C2×D4×C13—42no—
85C2×D4×C13—42no—
86C2×D4×C13—42no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—81no—
90C2×D4×C13—81no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13—42no—
101C22×C4×C13—42no—
102C22×C4×C13—81no—
103C22×C4×C13C22⋊C411yescharacteristic
104C22×C4×C13C22⋊C411yescharacteristic
105C22×C4×C13C22×C411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×Dic13—44no—
108C22×Dic13—42no—
109C22×Dic13—82no—
110C22×Dic13—82no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—42no—
116C13×C22⋊C4—42no—
117C13×C22⋊C4—42no—
118C13×C22⋊C4—81no—
119C13×C22⋊C4—81no—
120C22⋊Dic13—24no—
121C22⋊Dic13—44no—
122C22⋊Dic13—42no—
123#6099—82no—
124C2×#1055—42no—
125#2404D1311yescharacteristic
126C2×#342—131no—
127#1462—131no—
128#1351—132no—
129#1343—132no—
130C23×C13—22no—
131C23×C13—22no—
132C23×C13—22no—
133C23×C13—22no—
134C23×C13—22no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—21no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—21no—
141C23×C13—22no—
142C23×C13—41no—
143C23×C13—42no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—42no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—81no—
156C23×C13—81no—
157C23×C13—84no—
158C23×C13—82no—
159C23×C13—82no—
160C23×C13#9911yescharacteristic
161C23×C13#9911yescharacteristic
162C23×C13#10412yes—
163C23×C13C2×C22⋊C411yescharacteristic
164C23×C13AGL(1,ℤ/8)11yescharacteristic
165C23×C13#13711yescharacteristic
166Q8×C13—42no—
167Q8×C13—42no—
168D4×C13—44no—
169D4×C13—42no—
170D4×C13—44no—
171D4×C13—42no—
172D4×C13—84no—
173D4×C13—82no—
174D4×C13—82no—
175C2×C4×C13—22no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—42no—
181C2×C4×C13—41no—
182C2×C4×C13—42no—
183C2×C4×C13—48no—
184C2×C4×C13—42no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—81no—
197C2×Dic13—44no—
198C2×Dic13—88no—
199C2×Dic13—82no—
200C2×Dic13—82no—
201#1055—82no—
202C22×#41Dic1311yescharacteristic, complemented
203C2×#120—21no—
204C22×C22⋊C4—261no—
205C22×C22⋊C4C2×D1311yescharacteristic
206#407—261no—
207#393Dic1311yescharacteristic, complemented
208#393C2×D1311yescharacteristic
209#392Dic1311yescharacteristic, complemented
210#392C2×D1311yescharacteristic
211#386—21no—
212#386—21no—
213#386—21no—
214#381Dic1311yescharacteristic, complemented
215#342—132no—
216#342—261no—
217#323—132no—
218#323—261no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—22no—
228C22×C13—21no—
229C22×C13—42no—
230C22×C13—42no—
231C22×C13—42no—
232C22×C13—41no—
233C22×C13—41no—
234C22×C13—44no—
235C22×C13—44no—
236C22×C13—42no—
237C22×C13—42no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13—41no—
242C22×C13—42no—
243C22×C13—81no—
244C22×C13—81no—
245C22×C13—81no—
246C22×C13—81no—
247C22×C13—82no—
248C22×C13—82no—
249C22×C13—81no—
250C22×C13—81no—
251C22×C13AΣL(1,𝔽16)12yes—
252C22×C13C2×#9911yescharacteristic
253C22×C13#41711yescharacteristic
254C22×C13C2×#10411yescharacteristic
255C4×C13—41no—
256C4×C13—42no—
257C4×C13—41no—
258C4×C13—41no—
259C4×C13—41no—
260C4×C13—81no—
261C4×C13—81no—
262Dic13—84no—
263C25C22⋊D1311yescharacteristic
264C2×#41—41no—
265C2×#41—41no—
266C2×#41—44no—
267C22×Q8C2×Dic1311yescharacteristic, complemented
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4C2×Dic1311yescharacteristic, complemented
272C23×C4—21no—
273C23×C4—521no—
274C23×C4C2×Dic1311yescharacteristic
275C23×C4C22⋊D1311yescharacteristic
276C2×M16—521no—
277#120—44no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—41no—
284C2×C22⋊C4—41no—
285C2×C22⋊C4—264no—
286C2×C22⋊C4—262no—
287C2×C22⋊C4—521no—
288C2×C22⋊C4—522no—
289C2×C22⋊C4C2×Dic1311yescharacteristic
290C2×C22⋊C4C22⋊D1311yescharacteristic
291C2×C22⋊C4C22⋊D1311yescharacteristic
292C2×C22⋊C4C22×D1311yescharacteristic
293C22⋊C8—262no—
294C22⋊C8—521no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95C2×Dic1311yescharacteristic, complemented
299#95C2×Dic1311yescharacteristic, complemented
300C2×C13—21no—
301C2×C13—21no—
302C2×C13—22no—
303C2×C13—41no—
304C2×C13—41no—
305C2×C13—42no—
306C2×C13—41no—
307C2×C13—82no—
308C2×C13#150411yescharacteristic
309C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
310C2×C13#212711yescharacteristic
311C24—21no—
312C24—21no—
313C24—22no—
314C24—21no—
315C24—21no—
316C24—21no—
317C24—42no—
318C24—81no—
319C24C22⋊Dic1311yescharacteristic
320C24C22⋊Dic1311yescharacteristic
321C24C2×C22⋊D1311yescharacteristic
322#41—44no—
323#41—44no—
324#41—44no—
325#41—44no—
326C2×Q8—42no—
327C2×Q8—41no—
328C2×D4—24no—
329C2×D4—41no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—81no—
340C2×D4—81no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—81no—
353C22×C4—524no—
354C22×C4—522no—
355C22×C4—1042no—
356C22×C4—1042no—
357C22×C4C22⋊Dic1311yescharacteristic
358C22×C4C22⋊Dic1311yescharacteristic
359C22×C4C22×Dic1311yescharacteristic
360C22×C4C2×C22⋊D1311yescharacteristic
361M16—1042no—
362C2×C8—522no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—42no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—81no—
371C22⋊C4—81no—
372C22⋊C4—264no—
373C22⋊C4—524no—
374C22⋊C4—522no—
375C13#1175311yescharacteristic, complemented, Sylow
376C23—22no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—22no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—22no—
388C23—41no—
389C23—42no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—42no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23—84no—
404C23—82no—
405C23—82no—
406C23#8807411yescharacteristic
407C23#8807411yescharacteristic
408C23#8807712yes—
409C23#8820311yescharacteristic
410C23#8820511yescharacteristic
411C23C2×C22⋊Dic1311yescharacteristic
412Q8—42no—
413Q8—42no—
414D4—44no—
415D4—42no—
416D4—42no—
417D4—44no—
418D4—84no—
419D4—82no—
420D4—82no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—48no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—524no—
444C2×C4—1048no—
445C2×C4—1042no—
446C2×C4—1042no—
447C8—1042no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—22no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—41no—
462C22—41no—
463C22—44no—
464C22—44no—
465C22—42no—
466C22—42no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—42no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—82no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22#1171812812yes—
481C22C2×#8807411yescharacteristic
482C22#1171889311yescharacteristic
483C22C2×#8807711yescharacteristic
484C4—41no—
485C4—42no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—81no—
490C4—81no—
491C4—1044no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—41no—
496C2—41no—
497C2—42no—
498C2—41no—
499C2—82no—
500C2#1311334011yescharacteristic
501C2C2×#1171812811yescharacteristic
502C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2404C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2404D13
hypocenterC13#11753
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. C2×#11718118C2semidirect
2. #13113163C2semidirect
3. #13112857C2semidirect
4. #13112833C2semidirect
6. C22×C13×#41C4semidirect
10. C13×#393C4semidirect
12. C13×#392C4semidirect
17. C13×#381C4semidirect
27. C22×Q8×C13C2×C4semidirect
31. C22×D4×C13C2×C4semidirect
56. C13×#95C2×C4semidirect
57. C13×#95C2×C4semidirect
202. C22×#41Dic13semidirect
207. #393Dic13semidirect
209. #392Dic13semidirect
214. #381Dic13semidirect
267. C22×Q8C2×Dic13semidirect
271. C22×D4C2×Dic13semidirect
298. #95C2×Dic13semidirect
299. #95C2×Dic13semidirect
375. C13#11753semidirect

Maximal subgroups

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

subgroupindex
C2×#117181182
#131131632
#131128572
#131128332
C13×#24042
#1175313