Finite Group Databasebeta

← #15761882

Subgroups — #15761882

Order 3328.

584 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88201C211yesmaximal, characteristic
2#13114691C211yesmaximal, characteristic, complemented
3C4×#88054C211yesmaximal, characteristic, complemented
4C2×Q8⋊#1055C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6C2×#11718075C211yesmaximal, characteristic
7C2×C13×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C13C2211yescharacteristic
9C2×#88201C411yescharacteristic
10C2×C4×D52C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13#11718891C411yescharacteristic
14C2×#88055—21no—
15C2×#88054—21no—
16#11718651—21no—
17#11718651—21no—
18#11718649C411yescharacteristic
19#11718638C411yescharacteristic
20C4×#6103—21no—
21C4×#6103—21no—
22C42×Dic13C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24C2×C4×#1055C2211yescharacteristic
25C13×Q8⋊C8—22no—
26#11718142—21no—
27#11718142—21no—
28Q8⋊#1055—22no—
29#11718075—22no—
30#11718051—22no—
31C22×Q8×C13C2×C411yescharacteristic
32C22×D52C2×C411yescharacteristic
33C22×C4×D13—21no—
34C22×C8×C13—21no—
35C22×C8×C13—21no—
36C4×Q8×C13—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C4×Q8×C13—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13C2311yescharacteristic
44#88201—22no—
45#88201—22no—
46C2×#6103—21no—
47C2×#6103—21no—
48C2×#6103—21no—
49C2×#6103—21no—
50C2×#6103—21no—
51C2×C4⋊Dic13C2×C411yescharacteristic
52C2×C4×Dic13C2×C411yescharacteristic
53C2×C4×Dic13C2×C411yescharacteristic
54C2×C4×Dic13D411yescharacteristic
55C2×C4×Dic13D411yescharacteristic
56C2×C4×Dic13D411yescharacteristic
57C2×C4×Dic13D411yescharacteristic
58C22×#1055—21no—
59C22×#1055—21no—
60C4×D52—21no—
61C4×D52—21no—
62C4×D52—21no—
63C4×D52—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8D412yes—
66C4×C8×C13—21no—
67C4×C8×C13—21no—
68#88071—21no—
69#88071—21no—
70#88071—21no—
71#88071—21no—
72#88055—42no—
73#88054—24no—
74C4⋊#1055—21no—
75C4⋊#1055D412yes—
76C4×#1055—21no—
77C4×#1055—21no—
78#9676—131nomaximal, Sylow
79C23×D13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—21no—
84C2×Q8×C13—21no—
85C2×Q8×C13M1612yes—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13C22×C411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×Dic13—21no—
92C22×Dic13C22⋊C411yescharacteristic
93C22×Dic13C22⋊C411yescharacteristic
94C22×Dic13C22⋊C411yescharacteristic
95C22×Dic13C22⋊C411yescharacteristic
96C2×D52—21no—
97C2×D52—21no—
98C2×D52—21no—
99C2×D52—21no—
100C2×D52—21no—
101C2×D52M1612yes—
102C2×C4×D13—41no—
103C2×C4×D13—41no—
104C2×C4×D13—41no—
105C2×C4×D13—41no—
106C2×C4×D13—41no—
107C2×C4×D13—41no—
108C2×C8×C13—22no—
109C2×C8×C13—22no—
110C2×C8×C13—41no—
111C2×C8×C13—41no—
112C2×C8×C13—41no—
113C2×C8×C13—41no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C42×C13—41no—
119C42×C13—41no—
120C42×C13C2×D411yescharacteristic
121C42×C13C2×D411yescharacteristic
122C42×C13#4111yescharacteristic
123C42×C13#4111yescharacteristic
124#6103—24no—
125#6103—24no—
126#6103—42no—
127#6103—41no—
128#6103—41no—
129#6103—42no—
130C4⋊Dic13—21no—
131C4⋊Dic13—21no—
132C4×Dic13—21no—
133C4×Dic13—21no—
134C4×Dic13—21no—
135C4×Dic13—21no—
136C4×Dic13—21no—
137C4×Dic13—21no—
138C4×Dic13—21no—
139C4×Dic13—21no—
140C4×Dic13—22no—
141C4×Dic13—41no—
142C2×#1055—22no—
143C2×#1055—22no—
144C2×#1055—41no—
145C2×#1055—41no—
146C2×#1055—41no—
147C2×#1055—41no—
148C4×#124—131no—
149#1767—131no—
150C4×C4⋊C8—131no—
151C2×Q8⋊C8—131no—
152C2×Q8⋊C8D1311yescharacteristic, complemented
153C2×D4⋊C8—131no—
154C2×D4⋊C8—131no—
155C23×C13C2×C22⋊C411yescharacteristic
156C22×D13—22no—
157C22×D13—41no—
158C22×D13—41no—
159C22×D13—41no—
160C22×D13—41no—
161C22×D13—41no—
162C22×D13—41no—
163Q8×C13—22no—
164Q8×C13—22no—
165Q8×C13—41no—
166Q8×C13—41no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—22no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13C4×D411yescharacteristic
176C2×C4×C13C4×D411yescharacteristic
177C2×C4×C13#12111yescharacteristic
178C2×C4×C13#12111yescharacteristic
179C2×C4×C13#12411yescharacteristic
180C2×C4×C13#12711yescharacteristic
181C2×C4×C13C2×M1611yescharacteristic
182C2×C4×C13C2×M1611yescharacteristic
183C2×C4×C13#13111yescharacteristic
184C2×C4×C13#13111yescharacteristic
185C2×C4×C13#13511yescharacteristic
186C2×C4×C13#13511yescharacteristic
187C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C13#13711yescharacteristic
189C2×Dic13—21no—
190C2×Dic13—21no—
191C2×Dic13—21no—
192C2×Dic13—21no—
193C2×Dic13—21no—
194C2×Dic13—21no—
195C2×Dic13—21no—
196C2×Dic13—21no—
197C2×Dic13—21no—
198C2×Dic13—21no—
199C2×Dic13—21no—
200C2×Dic13—41no—
201C2×Dic13—41no—
202C2×Dic13—41no—
203C2×Dic13#10412yes—
204D52—22no—
205D52—22no—
206D52—41no—
207D52—41no—
208C4×D13—81no—
209C4×D13—81no—
210C4×D13—81no—
211C4×D13—81no—
212C8×C13—42no—
213C8×C13—42no—
214#1055—42no—
215#1055—42no—
216C2×#124—131no—
217C2×C4×Q8C2×D1311yescharacteristic
218C2×C4×D4—131no—
219C2×C4⋊C8—131no—
220C2×C4⋊C8—261no—
221C2×C4⋊C8C2×D1311yescharacteristic
222C2×#97—261no—
223C2×C4×C8—131no—
224C2×C4×C8C2×D1311yescharacteristic
225#391—131no—
226#390—131no—
227#388—261no—
228#388—261no—
229#382—131no—
230C4×C22⋊C4—261no—
231C4×C22⋊C4—261no—
232C43—131no—
233#336—261no—
234#336—261no—
235Q8⋊C8—22no—
236Q8⋊C8—262no—
237D4⋊C8—262no—
238D4⋊C8—262no—
239C22×C13#39011yescharacteristic
240C22×C13#40711yescharacteristic
241C22×C13#40811yescharacteristic
242C22×C13#41611yescharacteristic
243C22×C13#41711yescharacteristic
244C22×C13C2×#10411yescharacteristic
245C22×C13#42111yescharacteristic
246C2×D13—42no—
247C2×D13—42no—
248C2×D13—42no—
249C2×D13—81no—
250C2×D13—81no—
251C2×D13—81no—
252C2×D13—81no—
253C4×C13—21no—
254C4×C13—21no—
255C4×C13—42no—
256C4×C13—81no—
257C4×C13#43511yescharacteristic
258C4×C13#43511yescharacteristic
259C4×C13#43511yescharacteristic
260C4×C13#43511yescharacteristic
261C4×C13#46311yescharacteristic
262C4×C13#46311yescharacteristic
263C4×C13#46411yescharacteristic
264C4×C13#46411yescharacteristic
265Dic13—22no—
266Dic13—41no—
267Dic13—41no—
268Dic13—41no—
269Dic13—81no—
270C22×Q8C4×D1311yescharacteristic
271C22×D4—131no—
272C23×C4—261no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—261no—
276C22×C8—261no—
277#124—262no—
278#124—262no—
279C4×Q8—21no—
280C4×Q8—21no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×D4—261no—
284C4×D4—261no—
285C4×D4—261no—
286C4×D4—261no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—131no—
289C2×C4⋊C4C4×D1311yescharacteristic
290C2×C22⋊C4—261no—
291C2×C22⋊C4—261no—
292C2×C22⋊C4—261no—
293C2×C22⋊C4—261no—
294C2×C22⋊C4—261no—
295C2×C42—21no—
296C2×C42—131no—
297C2×C42—131no—
298C2×C42—131no—
299C2×C42—131no—
300C2×C42—131no—
301C2×C42—131no—
302C2×C42C22×D1311yescharacteristic
303C4⋊C8—21no—
304C4⋊C8—132no—
305C4⋊C8—264no—
306C4⋊C8—261no—
307C4⋊C8C22⋊D1312yes—
308#97—522no—
309C4×C8—21no—
310C4×C8—21no—
311C4×C8—261no—
312C4×C8—261no—
313#95—261no—
314#95—261no—
315#95—261no—
316#95—261no—
317C2×C13#148811yescharacteristic
318C2×C13#148911yescharacteristic
319C2×C13#149411yescharacteristic
320C2×C13#149511yescharacteristic
321C2×C13#195511yescharacteristic
322C2×C13#198011yescharacteristic
323C2×C13#198311yescharacteristic
324D13—82no—
325C24—261no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8#609412yes—
332C2×D4—132no—
333C2×D4—261no—
334C2×D4—261no—
335C2×D4—261no—
336C2×D4—261no—
337C2×D4—261no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—131no—
341C22×C4—131no—
342C22×C4—131no—
343C22×C4—131no—
344C22×C4—261no—
345C22×C4—521no—
346C22×C4—521no—
347C22×C4—521no—
348C22×C4—521no—
349C22×C4—521no—
350C22×C4—521no—
351C22×C4C2×C4×D1311yescharacteristic
352C22×C4D4×D1311yescharacteristic
353C22×C4D4×D1311yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—262no—
361C2×C8—262no—
362C2×C8—521no—
363C2×C8—521no—
364C2×C8—521no—
365C2×C8—521no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—261no—
371C4⋊C4—261no—
372C22⋊C4—264no—
373C22⋊C4—264no—
374C22⋊C4—522no—
375C22⋊C4—522no—
376C22⋊C4—521no—
377C22⋊C4—521no—
378C42—41no—
379C42—41no—
380C42—262no—
381C42—261no—
382C42—261no—
383C42—261no—
384C42—261no—
385C42—261no—
386C42—261no—
387C42—261no—
388C42—261no—
389C42—521no—
390C42#612711yescharacteristic
391C42D4×D1311yescharacteristic
392C42#612911yescharacteristic
393C42C2×C22⋊D1311yescharacteristic
394C13#967611yescharacteristic, complemented, Sylow
395C23—262no—
396C23—521no—
397C23—521no—
398C23—521no—
399C23—521no—
400C23—521no—
401C23—521no—
402C23C22⋊C4×D1311yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407D4—262no—
408D4—262no—
409D4—521no—
410D4—521no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—132no—
420C2×C4—261no—
421C2×C4—261no—
422C2×C4—261no—
423C2×C4—261no—
424C2×C4—261no—
425C2×C4—261no—
426C2×C4—261no—
427C2×C4—261no—
428C2×C4—261no—
429C2×C4—261no—
430C2×C4—261no—
431C2×C4—521no—
432C2×C4—521no—
433C2×C4—521no—
434C2×C4—1041no—
435C2×C4—1041no—
436C2×C4—1041no—
437C2×C4—1041no—
438C2×C4#8813511yescharacteristic
439C2×C4#8813811yescharacteristic
440C2×C4#8813911yescharacteristic
441C2×C4C2×#609411yescharacteristic
442C2×C4#8815511yescharacteristic
443C2×C4M16×D1311yescharacteristic
444C2×C4#8816111yescharacteristic
445C2×C4#8816811yescharacteristic
446C2×C4#8817011yescharacteristic
447C2×C4#8817211yescharacteristic
448C2×C4#8817311yescharacteristic
449C2×C4C4×C22⋊D1311yescharacteristic
450C2×C4#8819311yescharacteristic
451C2×C4#8819411yescharacteristic
452C8—42no—
453C8—42no—
454C8—522no—
455C8—522no—
456C22—522no—
457C22—522no—
458C22—522no—
459C22—1041no—
460C22—1041no—
461C22—1041no—
462C22—1041no—
463C22#1171838711yescharacteristic
464C22#1171838811yescharacteristic
465C22#1171846411yescharacteristic
466C22#1171846511yescharacteristic
467C22D13×#10411yescharacteristic
468C22#1171848211yescharacteristic
469C22#1171861811yescharacteristic
470C4—21no—
471C4—21no—
472C4—42no—
473C4—81no—
474C4—262no—
475C4—521no—
476C4—521no—
477C4—521no—
478C4—1041no—
479C4#1171838911yescharacteristic
480C4#1171839111yescharacteristic
481C4#1171845911yescharacteristic
482C4#1171848011yescharacteristic
483C4#1171877211yescharacteristic
484C4#1171878811yescharacteristic
485C4#1171882611yescharacteristic
486C4#1171884611yescharacteristic
487C2—1042no—
488C2#1311326911yescharacteristic
489C2#1311327411yescharacteristic
490C2#1311329511yescharacteristic
491C2#1311330011yescharacteristic
492C2#1311563211yescharacteristic
493C2#1311575311yescharacteristic
494C2#1311576511yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×Q8⋊C8C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenterC2×Q8⋊C8D13
hypocenterC13#9676
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #13114691C2semidirect
3. C4×#88054C2semidirect
4. C2×Q8⋊#1055C2semidirect
7. C2×C13×Q8⋊C8C2semidirect
152. C2×Q8⋊C8D13semidirect
394. C13#9676semidirect

Maximal subgroups

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

subgroupindex
C4×#882012
#131146912
C4×#880542
C2×Q8⋊#10552
C2×#117180512
C2×#117180752
C2×C13×Q8⋊C82
#967613