Finite Group Databasebeta

← #15907779

Subgroups — #15907779

Order 3328.

842 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊Dic13C211yesmaximal, characteristic
2#13116273C212yesmaximal, complemented
3#13116029C212yesmaximal, complemented
4#13115631C211yesmaximal, characteristic
5#13115597C211yesmaximal, characteristic, complemented
6#13115144C212yesmaximal, complemented
7#13114963C211yesmaximal, characteristic, complemented
8#13114920C212yesmaximal, complemented
9#13114841C211yesmaximal, characteristic, complemented
10C4×#88075C211yesmaximal, characteristic, complemented
11C13×#2538C211yesmaximal, characteristic
12C2×C13×C22⋊Q8C2212yes—
13C2×C4×Q8×C13C2211yescharacteristic
14C2×C4×D4×C13C2211yescharacteristic
15C2×D4×Dic13—21no—
16C22×C4⋊Dic13C2212yes—
17C13×#396—22no—
18C13×#390—21no—
19C13×#389—21no—
20C13×#384C2211yescharacteristic
21C13×#380C2212yes—
22C2×#88075C2211yescharacteristic
23C2×#88075C2211yescharacteristic
24C2×#88075C2212yes—
25#11718873C2212yes—
26C2×C22⋊#1055C2212yes—
27C2×C22⋊#1055C2212yes—
28#11718646—21no—
29C2×#88048C2212yes—
30#11718611—22no—
31#11718596C2211yescharacteristic
32C4×C4⋊Dic13C2211yescharacteristic
33C2×C4⋊#1055C2211yescharacteristic
34C2×C4×#1055C2211yescharacteristic
35#11718121C2212yes—
36#11718121C2212yes—
37#11718121C2211yescharacteristic
38#11718121C2211yescharacteristic
39#11718121C2212yes—
40#11718121C2212yes—
41C22×Q8×C13C2311yescharacteristic
42C22×D4×C13D411yescharacteristic
43C23×C4×C13C2312yes—
44C23×Dic13—22no—
45C13×C22⋊Q8—24no—
46C13×C22⋊Q8—42no—
47C4×Q8×C13—22no—
48C4×Q8×C13—22no—
49C4×D4×C13—22no—
50C4×D4×C13—22no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C4⋊C4C2311yescharacteristic
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4D412yes—
61C2×C42×C13—21no—
62C2×C42×C13C2311yescharacteristic
63C2×C22⋊Dic13—22no—
64D4×Dic13—44no—
65C2×C4⋊Dic13—24no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13—42no—
70C2×C4⋊Dic13C2312yes—
71C2×C4⋊Dic13C2311yescharacteristic
72C2×C4⋊Dic13C2311yescharacteristic
73C2×C4×Dic13—21no—
74C22×#1055C2311yescharacteristic
75C22×#1055C2311yescharacteristic
76C22×#1055C2312yes—
77C13×#95—22no—
78#88075—22no—
79#88075—22no—
80#88075—42no—
81#88071—21no—
82#88071—22no—
83C22⋊#1055—42no—
84C22⋊#1055—42no—
85#88048—42no—
86C4⋊#1055—22no—
87C4×#1055—22no—
88#24969—131nomaximal, Sylow
89C24×C13C2×D412yes—
90C2×Q8×C13—21no—
91C2×Q8×C13—21no—
92C2×Q8×C13—21no—
93C2×Q8×C13—21no—
94C2×Q8×C13—21no—
95C2×Q8×C13#4112yes—
96C2×D4×C13—22no—
97C2×D4×C13—22no—
98C2×D4×C13SD1614yes—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13C2×D412yes—
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2411yescharacteristic
112C22×Dic13—21no—
113C22×Dic13—21no—
114C22×Dic13—22no—
115C22×Dic13—44no—
116C22×Dic13—44no—
117C22×Dic13—82no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—44no—
124C13×C4⋊C4—42no—
125C13×C4⋊C4—42no—
126C13×C4⋊C4—81no—
127C13×C22⋊C4—24no—
128C13×C22⋊C4—44no—
129C13×C22⋊C4—82no—
130C42×C13—42no—
131C42×C13#4112yes—
132C42×C13#4112yes—
133C22⋊Dic13—44no—
134C4⋊Dic13—21no—
135C4⋊Dic13—21no—
136C4⋊Dic13—22no—
137C4⋊Dic13—22no—
138C4⋊Dic13—21no—
139C4⋊Dic13—44no—
140C4⋊Dic13—42no—
141C4⋊Dic13—81no—
142C4⋊Dic13#4112yes—
143C4×Dic13—42no—
144C2×#1055—21no—
145C2×#1055—21no—
146C2×#1055—21no—
147C2×#1055—21no—
148C2×#1055—22no—
149C2×#1055—21no—
150C2×#1055—21no—
151C2×#1055—22no—
152C2×#1055—22no—
153#2538D1311yescharacteristic
154D4×C4⋊C4—131no—
155#2077—132no—
156#2035—132no—
157#1954—131no—
158#1948—131no—
159#1872—132no—
160#1834—131no—
161#1823—132no—
162#1803—131no—
163C4×#103—131no—
164C23×C13—22no—
165C23×C13—22no—
166C23×C13—22no—
167C23×C13—22no—
168C23×C13—22no—
169C23×C13—22no—
170C23×C13C2×SD1614yes—
171C23×C13C22×D411yescharacteristic
172Q8×C13—22no—
173Q8×C13—22no—
174Q8×C13—41no—
175Q8×C13—41no—
176D4×C13—28no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—22no—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—22no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—42no—
186C2×C4×C13—42no—
187C2×C4×C13—42no—
188C2×C4×C13—42no—
189C2×C4×C13—41no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—41no—
193C2×C4×C13—42no—
194C2×C4×C13—41no—
195C2×C4×C13#12312yes—
196C2×C4×C13#12312yes—
197C2×C4×C13C2×SD1612yes—
198C2×C4×C13#13712yes—
199C2×C4×C13C2×#4111yescharacteristic
200C2×C4×C13C2×#4111yescharacteristic
201C2×C4×C13C2×#4111yescharacteristic
202C2×C4×C13C2×#4111yescharacteristic
203C2×C4×C13H(5,𝔽2)11yescharacteristic
204C2×C4×C13H(5,𝔽2)11yescharacteristic
205C2×Dic13—22no—
206C2×Dic13—41no—
207C2×Dic13—41no—
208C2×Dic13—42no—
209C2×Dic13—41no—
210C2×Dic13—41no—
211C2×Dic13—42no—
212C2×Dic13—42no—
213C2×Dic13—41no—
214C2×Dic13—88no—
215#1055—42no—
216#1055—41no—
217#1055—41no—
218C2×C22⋊Q8C2×D1312yes—
219C2×C4×Q8C2×D1311yescharacteristic
220C2×C4×D4—261no—
221C2×C4×D4C2×D1311yescharacteristic
222C22×C4⋊C4—132no—
223C2×#106—132no—
224C2×C4⋊C8—131no—
225C2×#103—131no—
226C2×#103—131no—
227C2×#103—132no—
228C2×C22⋊C8—132no—
229C2×C22⋊C8—132no—
230C2×C4×C8—131no—
231#396—22no—
232#390—21no—
233#389—21no—
234#389—261no—
235#385—262no—
236#384—131no—
237#384C2×D1311yescharacteristic
238#380—132no—
239#380C2×D1312yes—
240C4×C4⋊C4—131no—
241#340—132no—
242#340—131no—
243#340—132no—
244#340—131no—
245#340—132no—
246#340—132no—
247C22×C13—24no—
248C22×C13—24no—
249C22×C13—24no—
250C22×C13—42no—
251C22×C13—42no—
252C22×C13—42no—
253C22×C13—42no—
254C22×C13C2×#12311yescharacteristic
255C22×C13#54611yescharacteristic
256C22×C13#54611yescharacteristic
257C22×C13C22×SD1611yescharacteristic
258C22×C13C2×#13711yescharacteristic
259C22×C13#57611yescharacteristic
260C22×C13#57811yescharacteristic
261C4×C13—22no—
262C4×C13—42no—
263C4×C13—42no—
264C4×C13—82no—
265C4×C13—81no—
266C4×C13#48314yes—
267C4×C13#52911yescharacteristic
268C4×C13#54011yescharacteristic
269C4×C13#55311yescharacteristic
270C4×C13#55511yescharacteristic
271Dic13—42no—
272Dic13—82no—
273Dic13—81no—
274C22×Q8C22×D1311yescharacteristic
275C22×D4C22⋊D1311yescharacteristic
276C23×C4—262no—
277C23×C4C22×D1312yes—
278C22×C8—131no—
279C22×C8—131no—
280C22×C8—132no—
281C22⋊Q8—24no—
282C22⋊Q8—42no—
283C4×Q8—22no—
284C4×Q8—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—524no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—131no—
293C2×C4⋊C4—132no—
294C2×C4⋊C4—131no—
295C2×C4⋊C4—264no—
296C2×C4⋊C4—262no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—522no—
300C2×C4⋊C4C22⋊D1311yescharacteristic
301C2×C4⋊C4C22×D1311yescharacteristic
302C2×C4⋊C4C22×D1312yes—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—262no—
306C2×C22⋊C4C22⋊D1312yes—
307C2×C42—21no—
308C2×C42—261no—
309C2×C42C22×D1311yescharacteristic
310#106—522no—
311C4⋊C8—262no—
312#103—262no—
313#103—262no—
314#103—522no—
315C22⋊C8—522no—
316C22⋊C8—522no—
317C4×C8—262no—
318#95—22no—
319#95—261no—
320#95—262no—
321C2×C13—44no—
322C2×C13#242011yescharacteristic
323C2×C13C2×#48311yescharacteristic
324C2×C13#309811yescharacteristic
325C2×C13#329511yescharacteristic
326C2×C13#329811yescharacteristic
327C2×C13#332811yescharacteristic
328C2×C13#333311yescharacteristic
329C24C2×C22⋊D1312yes—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8#612912yes—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4#610614yes—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—261no—
349C22×C4—261no—
350C22×C4—262no—
351C22×C4—524no—
352C22×C4—524no—
353C22×C4—1042no—
354C22×C4C2×C22⋊D1312yes—
355C22×C4C2×C22⋊D1311yescharacteristic
356C22×C4C2×C22⋊D1311yescharacteristic
357C22×C4C23×D1311yescharacteristic
358C2×C8—261no—
359C2×C8—261no—
360C2×C8—261no—
361C2×C8—262no—
362C2×C8—261no—
363C2×C8—262no—
364C2×C8—261no—
365C2×C8—261no—
366C2×C8—262no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—44no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—81no—
376C4⋊C4—132no—
377C4⋊C4—261no—
378C4⋊C4—261no—
379C4⋊C4—261no—
380C4⋊C4—262no—
381C4⋊C4—262no—
382C4⋊C4—524no—
383C4⋊C4—522no—
384C4⋊C4—1041no—
385C22⋊C4—24no—
386C22⋊C4—44no—
387C22⋊C4—82no—
388C22⋊C4—524no—
389C42—42no—
390C42—522no—
391C42#612912yes—
392C42#612912yes—
393C13#2496911yescharacteristic, complemented, Sylow
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23C2×#610614yes—
401C23C22×C22⋊D1311yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—41no—
405Q8—41no—
406D4—28no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—262no—
426C2×C4—521no—
427C2×C4—521no—
428C2×C4—521no—
429C2×C4—521no—
430C2×C4—522no—
431C2×C4—522no—
432C2×C4—522no—
433C2×C4—521no—
434C2×C4—1048no—
435C2×C4#8818912yes—
436C2×C4#8818912yes—
437C2×C4C2×#610612yes—
438C2×C4#8820512yes—
439C2×C4C2×#612911yescharacteristic
440C2×C4C2×#612911yescharacteristic
441C2×C4C2×#612911yescharacteristic
442C2×C4#8825111yescharacteristic
443C2×C4#41×D1311yescharacteristic
444C2×C4#8825611yescharacteristic
445C8—521no—
446C8—521no—
447C8—522no—
448C22—24no—
449C22—24no—
450C22—24no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22C2×#8818911yescharacteristic
456C22#1171951111yescharacteristic
457C22C22×#610611yescharacteristic
458C22C2×#8820511yescharacteristic
459C22#1171953411yescharacteristic
460C22#1171954011yescharacteristic
461C22#1171954311yescharacteristic
462C4—22no—
463C4—42no—
464C4—42no—
465C4—82no—
466C4—81no—
467C4—522no—
468C4—1041no—
469C4—1042no—
470C4#1171870414yes—
471C4#1171930511yescharacteristic
472C4#1171932111yescharacteristic
473C4#1171932311yescharacteristic
474C4#1171932411yescharacteristic
475C2—44no—
476C2#1311832411yescharacteristic
477C2C2×#1171870411yescharacteristic
478C2#1312481011yescharacteristic
479C2#1312665411yescharacteristic
480C2#1312670111yescharacteristic
481C2#1312711311yescharacteristic
482C2#1312717411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2538C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2538D13
hypocenterC13#24969
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. #13116273C2semidirect
3. #13116029C2semidirect
5. #13115597C2semidirect
6. #13115144C2semidirect
7. #13114963C2semidirect
8. #13114920C2semidirect
9. #13114841C2semidirect
10. C4×#88075C2semidirect
393. C13#24969semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊Dic132
#131162732
#131160292
#131156312
#131155972
#131151442
#131149632
#131149202
#131148412
C4×#880752
C13×#25382
#2496913