Finite Group Databasebeta

← #15765245

Subgroups — #15765245

Order 3328.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic
2#13119754C211yesmaximal, characteristic
3#13115798C211yesmaximal, characteristic, complemented
4C2×Q8⋊#1055C211yesmaximal, characteristic, complemented
5C2×#11718075C211yesmaximal, characteristic
6#13112720C211yesmaximal, characteristic, complemented
7C2×C13×#462C211yesmaximal, characteristic, complemented
8C22×C13×Q16—21no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C13C2211yescharacteristic
11C2×#88200—21no—
12C2×C4×D52C2211yescharacteristic
13C13×#462—22no—
14C13×#462—22no—
15C2×C13×C4⋊C8C2211yescharacteristic
16C2×C13×#103—21no—
17#11718748—22no—
18#11718748—22no—
19#11718655—22no—
20#11718648—21no—
21C2×#88049—21no—
22C2×#88047—21no—
23#11718600—21no—
24#11718596C2211yescharacteristic
25#11718589—21no—
26C2×C4⋊#1055C2211yescharacteristic
27C2×C4×#1055C2211yescharacteristic
28Q8⋊#1055—22no—
29#11718121—22no—
30#11718075—22no—
31C22×Q8×C13—21no—
32C22×Q8×C13D411yescharacteristic
33C22×D52D411yescharacteristic
34C22×C4×D13—21no—
35C2×C13×Q16—24no—
36C2×C13×Q16—42no—
37C2×C13×Q16—42no—
38C22×C8×C13—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8D412yes—
43C4×Q8×C13—21no—
44C4×Q8×C13—21no—
45C4×Q8×C13—21no—
46C4×Q8×C13—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C42×C13—21no—
52C2×C42×C13C2311yescharacteristic
53#88200—42no—
54#88200—42no—
55C2×#6103—22no—
56C2×#6103—21no—
57C2×#6103—22no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13D411yescharacteristic
61C2×C4⋊Dic13D412yes—
62C2×#6101—22no—
63C22×#1055—21no—
64C22×#1055—21no—
65C4×D52—21no—
66C4×D52—21no—
67C4×D52—21no—
68C4×D52—21no—
69C13×C4⋊C8—21no—
70C13×C4⋊C8D412yes—
71C13×#103—24no—
72#88071—22no—
73#88049—24no—
74#88047—24no—
75C4⋊#1055—21no—
76C4⋊#1055D412yes—
77C4×#1055—21no—
78C4×#1055—21no—
79#10233—131nomaximal, Sylow
80C23×D13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—22no—
84C2×Q8×C13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—41no—
88C2×Q8×C13—41no—
89C2×Q8×C13—41no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×Q8×C13D812yes—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—41no—
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×Dic13—21no—
100C22×Dic13—22no—
101C2×D52—21no—
102C2×D52—21no—
103C2×D52—21no—
104C2×D52—21no—
105C2×D52—21no—
106C2×D52Q1612yescomplemented
107C2×C4×D13—41no—
108C2×C4×D13—41no—
109C2×C4×D13—41no—
110C2×C4×D13—41no—
111C2×C4×D13—41no—
112C2×C4×D13—41no—
113C13×Q16—48no—
114C2×C8×C13—22no—
115C2×C8×C13—41no—
116C2×C8×C13—41no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—41no—
125C42×C13—41no—
126C42×C13—41no—
127C42×C13C2×D411yescharacteristic
128C42×C13C2×D411yescharacteristic
129C42×C13C2×D411yescharacteristic
130C42×C13#4111yescharacteristic
131#6103—44no—
132#6103—41no—
133#6103—41no—
134#6103—82no—
135C4⋊Dic13—21no—
136C4⋊Dic13—21no—
137C4⋊Dic13—41no—
138C4⋊Dic13—41no—
139C4⋊Dic13—41no—
140C4⋊Dic13—41no—
141C4⋊Dic13—42no—
142#6101—44no—
143C2×#1055—22no—
144C2×#1055—22no—
145C2×#1055—41no—
146C2×#1055—41no—
147C2×#1055—41no—
148C2×#1055—41no—
149C2×#474—131no—
150C2×#462D1311yescharacteristic, complemented
151#2538—131no—
152#1990—131no—
153C2×Q8⋊C8—131no—
154C2×D4⋊C8—131no—
155#1296—131no—
156C23×C13#12011yescharacteristic
157C22×D13—22no—
158C22×D13—41no—
159C22×D13—41no—
160C22×D13—41no—
161C22×D13—41no—
162C22×D13—41no—
163C22×D13—41no—
164Q8×C13—22no—
165Q8×C13—22no—
166Q8×C13—41no—
167Q8×C13—41no—
168Q8×C13—42no—
169Q8×C13—42no—
170Q8×C13—81no—
171Q8×C13—81no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—22no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—42no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—81no—
182C2×C4×C13—81no—
183C2×C4×C13#12011yescharacteristic
184C2×C4×C13#12011yescharacteristic
185C2×C4×C13#12111yescharacteristic
186C2×C4×C13#12111yescharacteristic
187C2×C4×C13#12111yescharacteristic
188C2×C4×C13#12711yescharacteristic
189C2×C4×C13C2×D811yescharacteristic
190C2×C4×C13C2×Q1611yescharacteristic
191C2×C4×C13#13511yescharacteristic
192C2×C4×C13#13511yescharacteristic
193C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C13#13711yescharacteristic
196C2×C4×C13#13711yescharacteristic
197C2×Dic13—41no—
198C2×Dic13—41no—
199C2×Dic13—42no—
200C2×Dic13—41no—
201C2×Dic13—42no—
202C2×Dic13—42no—
203D52—22no—
204D52—22no—
205D52—41no—
206D52—41no—
207C4×D13—81no—
208C4×D13—81no—
209C4×D13—81no—
210C4×D13—81no—
211C8×C13—42no—
212#1055—42no—
213#1055—42no—
214C22×Q16—21no—
215C2×C4⋊Q8C2×D1311yescharacteristic
216C2×C22⋊Q8—261no—
217C2×C4×Q8C2×D1311yescharacteristic
218C2×C4×D4—131no—
219#474—262no—
220#474—262no—
221#462—22no—
222#462—22no—
223C2×#107—261no—
224C2×C4⋊C8—131no—
225C2×C4⋊C8C2×D1311yescharacteristic
226C2×#103—21no—
227C2×#102—261no—
228C2×C4×C8—131no—
229#396—262no—
230#390—261no—
231#389—261no—
232#384—131no—
233#380—261no—
234#340—262no—
235Q8⋊C8—262no—
236D4⋊C8—262no—
237C22×C13#39211yescharacteristic
238C22×C13#44711yescharacteristic
239C22×C13#44911yescharacteristic
240C22×C13#45111yescharacteristic
241C22×C13#45211yescharacteristic
242C22×C13#45511yescharacteristic
243C22×C13#45611yescharacteristic
244C2×D13—42no—
245C2×D13—42no—
246C2×D13—42no—
247C2×D13—81no—
248C2×D13—81no—
249C2×D13—81no—
250C2×D13—81no—
251C4×C13—21no—
252C4×C13—21no—
253C4×C13—42no—
254C4×C13—82no—
255C4×C13—81no—
256C4×C13#44711yescharacteristic
257C4×C13#44911yescharacteristic
258C4×C13#45111yescharacteristic
259C4×C13#45211yescharacteristic
260C4×C13#46611yescharacteristic
261C4×C13#46711yescharacteristic
262C4×C13#46911yescharacteristic
263C4×C13#47011yescharacteristic
264Dic13—82no—
265Dic13—81no—
266C22×Q8—21no—
267C22×Q8C22⋊D1311yescharacteristic
268C22×D4—131no—
269C23×C4—261no—
270C2×Q16—24no—
271C2×Q16—42no—
272C2×Q16—42no—
273C22×C8—21no—
274C22×C8—261no—
275C22×C8—261no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8C22⋊D1312yes—
280C22⋊Q8—522no—
281C22⋊Q8—522no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—261no—
287C4×D4—261no—
288C4×D4—261no—
289C4×D4—261no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—131no—
294C2×C4⋊C4—132no—
295C2×C4⋊C4—262no—
296C2×C4⋊C4—261no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4C22⋊D1311yescharacteristic
299C2×C22⋊C4—262no—
300C2×C22⋊C4—261no—
301C2×C22⋊C4—262no—
302C2×C42—21no—
303C2×C42C22×D1311yescharacteristic
304#107—264no—
305C4⋊C8—21no—
306C4⋊C8—132no—
307C4⋊C8—261no—
308C4⋊C8C22⋊D1312yes—
309#103—24no—
310#102—264no—
311C4×C8—261no—
312C4×C8—261no—
313#95—262no—
314C2×C13#164111yescharacteristic
315C2×C13#164411yescharacteristic
316C2×C13#164911yescharacteristic
317C2×C13#165211yescharacteristic
318C2×C13#199911yescharacteristic
319C2×C13#200111yescharacteristic
320C2×C13#200711yescharacteristic
321D13—82no—
322C24—261no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—41no—
330C2×Q8—41no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8#610412yes—
335C2×D4—132no—
336C2×D4—261no—
337C2×D4—261no—
338C2×D4—261no—
339C2×D4—261no—
340C2×D4—261no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—41no—
344C22×C4—261no—
345C22×C4—262no—
346C22×C4—521no—
347C22×C4—521no—
348C22×C4—521no—
349C22×C4—521no—
350C22×C4—521no—
351C22×C4—521no—
352C22×C4D4×D1311yescharacteristic
353C22×C4D4×D1311yescharacteristic
354C22×C4C2×C22⋊D1311yescharacteristic
355Q16—48no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—262no—
360C2×C8—262no—
361C2×C8—521no—
362C2×C8—521no—
363C2×C8—521no—
364C2×C8—521no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—261no—
374C4⋊C4—261no—
375C4⋊C4—522no—
376C4⋊C4—524no—
377C4⋊C4—521no—
378C4⋊C4—521no—
379C4⋊C4—521no—
380C4⋊C4—521no—
381C22⋊C4—524no—
382C22⋊C4—521no—
383C22⋊C4—521no—
384C22⋊C4—1042no—
385C42—41no—
386C42—41no—
387C42D4×D1311yescharacteristic
388C42#612911yescharacteristic
389C42C2×C22⋊D1311yescharacteristic
390C42C2×C22⋊D1311yescharacteristic
391C13#1023311yescharacteristic, complemented, Sylow
392C23—262no—
393C23—521no—
394C23—521no—
395C23—521no—
396C23—521no—
397C23—521no—
398C23—521no—
399C23#8819111yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—41no—
403Q8—41no—
404Q8—42no—
405Q8—42no—
406Q8—81no—
407Q8—81no—
408D4—262no—
409D4—262no—
410D4—521no—
411D4—521no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—522no—
424C2×C4—521no—
425C2×C4—521no—
426C2×C4—522no—
427C2×C4—522no—
428C2×C4—521no—
429C2×C4—1041no—
430C2×C4—1041no—
431C2×C4—1041no—
432C2×C4—1041no—
433C2×C4Q16×D1311yescharacteristic
434C2×C4#8817211yescharacteristic
435C2×C4#8817211yescharacteristic
436C2×C4#8817311yescharacteristic
437C2×C4C2×#610411yescharacteristic
438C2×C4#8818611yescharacteristic
439C2×C4#8819111yescharacteristic
440C2×C4#8819211yescharacteristic
441C2×C4#8819311yescharacteristic
442C2×C4#8819311yescharacteristic
443C2×C4#8819411yescharacteristic
444C2×C4#8820311yescharacteristic
445C2×C4#8820411yescharacteristic
446C2×C4#8820711yescharacteristic
447C8—42no—
448C8—522no—
449C8—522no—
450C22—522no—
451C22—522no—
452C22—522no—
453C22—1041no—
454C22—1041no—
455C22—1041no—
456C22—1041no—
457C22#1171869711yescharacteristic
458C22#1171869811yescharacteristic
459C22#1171884711yescharacteristic
460C22#1171884811yescharacteristic
461C22#1171886311yescharacteristic
462C22#1171886611yescharacteristic
463C22#1171888411yescharacteristic
464C4—21no—
465C4—21no—
466C4—42no—
467C4—82no—
468C4—81no—
469C4—1042no—
470C4—1041no—
471C4#1171869911yescharacteristic
472C4#1171870011yescharacteristic
473C4#1171884711yescharacteristic
474C4#1171884811yescharacteristic
475C4#1171884911yescharacteristic
476C4#1171885011yescharacteristic
477C4#1171887811yescharacteristic
478C4#1171889911yescharacteristic
479C2—1042no—
480C2#1311402711yescharacteristic
481C2#1311404811yescharacteristic
482C2#1311408311yescharacteristic
483C2#1311410411yescharacteristic
484C2#1311583211yescharacteristic
485C2#1311584311yescharacteristic
486C2#1311588111yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#462C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#462D13
hypocenterC13#10233
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13115798C2semidirect
4. C2×Q8⋊#1055C2semidirect
6. #13112720C2semidirect
7. C2×C13×#462C2semidirect
106. C2×D52Q16semidirect
150. C2×#462D13semidirect
391. C13#10233semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
#131197542
#131157982
C2×Q8⋊#10552
C2×#117180752
#131127202
C2×C13×#4622
#1023313