Finite Group Databasebeta

← #15755141

Subgroups — #15755141

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115826C211yesmaximal, characteristic, complemented
2#13115681C211yesmaximal, characteristic, complemented
3#13113571C211yesmaximal, characteristic, complemented
4#13113428C211yesmaximal, characteristic, complemented
5#13113275C211yesmaximal, characteristic, complemented
6#13113275C211yesmaximal, characteristic, complemented
7C13×#3511C211yesmaximal, characteristic
8C13×#556—21no—
9C13×#555—21no—
10C13×#554—21no—
11C13×#553—22no—
12C13×#548—22no—
13C13×#547—21no—
14C13×#542—22no—
15C13×#537C412yes—
16C13×#533—21no—
17C13×#532—21no—
18C13×#532C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic
20C13×#520C412yes—
21C4×C13×#41C2211yescharacteristic
22C2×#88076—22no—
23#11718585C2211yescharacteristic
24#11718585C2211yescharacteristic
25C4×#6099C2211yescharacteristic
26C4×#6099C2211yescharacteristic
27#11718138—21no—
28#11718136—21no—
29#11718132—22no—
30Q8⋊#1055—21no—
31Q8⋊#1055—21no—
32D4⋊#1055—21no—
33D4⋊#1055—21no—
34#11718122—22no—
35C2×C13×#41—22no—
36C2×C13×#41C2×C411yescharacteristic
37C2×C13×#41C2×C412yes—
38C22×Q8×C13D412yes—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8D411yescharacteristic
44C13×#127D411yescharacteristic
45C13×#126—24no—
46C13×#125—22no—
47C13×#124—22no—
48C13×#124—24no—
49C13×#124D412yes—
50C13×#123—24no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—24no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—22no—
55C13×#121—22no—
56C13×#121—22no—
57C13×#121—22no—
58C13×#121—24no—
59C13×#121—21no—
60C13×#121—21no—
61C4×Q8×C13—22no—
62C4×Q8×C13—22no—
63C4×Q8×C13D411yescharacteristic
64C4×Q8×C13D411yescharacteristic
65C4×D4×C13—22no—
66C4×D4×C13—22no—
67C4×D4×C13—24no—
68C4×D4×C13—21no—
69C4×D4×C13—21no—
70C4×D4×C13—21no—
71C4×D4×C13—21no—
72C4×D4×C13D411yescharacteristic
73C4×D4×C13D411yescharacteristic
74C13×#117—22no—
75C13×#117—22no—
76C13×#117—21no—
77C13×#117C2×C411yescharacteristic
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4C2×C412yes—
80C2×C13×C4⋊C4D412yes—
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×#6099—21no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099—21no—
87#88076—44no—
88C4⋊#1055—21no—
89C4⋊#1055—21no—
90C4⋊#1055—21no—
91C4⋊#1055—21no—
92#88043—21no—
93#88043—21no—
94C4×#1055—21no—
95C4×#1055—21no—
96#8470—131nomaximal, Sylow
97C13×#41—42no—
98C13×#41—44no—
99C13×#41—82no—
100C13×#41—82no—
101C2×Q8×C13—22no—
102C2×Q8×C13—22no—
103C2×Q8×C13—42no—
104C2×Q8×C13—42no—
105C2×Q8×C13C22⋊C411yescharacteristic
106C2×Q8×C13C22⋊C412yes—
107C2×D4×C13—22no—
108C2×D4×C13—21no—
109C2×D4×C13—24no—
110C2×D4×C13—21no—
111C2×D4×C13—21no—
112C2×D4×C13C22⋊C411yescharacteristic
113C2×D4×C13C22⋊C412yes—
114C22×C4×C13—24no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13C22⋊C414yes—
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C13×C4⋊C4—24no—
124C13×C4⋊C4—24no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—22no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4C22⋊C411yescharacteristic
134C13×C4⋊C4C22⋊C411yescharacteristic
135C13×C22⋊C4—24no—
136C13×C22⋊C4—24no—
137C13×C22⋊C4—24no—
138C13×C22⋊C4—21no—
139C13×C22⋊C4—21no—
140C13×C22⋊C4—21no—
141C13×C22⋊C4—22no—
142C13×C22⋊C4—22no—
143C42×C13—24no—
144C42×C13—21no—
145C42×C13—21no—
146C42×C13—21no—
147C42×C13C2×D411yescharacteristic
148C42×C13C2×D411yescharacteristic
149C42×C13C2×D411yescharacteristic
150C42×C13C2×D411yescharacteristic
151#6099—22no—
152#6099—22no—
153#6099—41no—
154#6099—41no—
155#6099—42no—
156#6099—42no—
157C2×#1055—41no—
158C2×#1055—41no—
159C2×#1055—41no—
160C2×#1055—41no—
161#3511D1311yescharacteristic
162#1997—131no—
163#1966—131no—
164#1560—131no—
165#1525—131no—
166#1489—131no—
167#1489—131no—
168C23×C13—21no—
169C23×C13—22no—
170C23×C13C2×C22⋊C411yescharacteristic
171Q8×C13—22no—
172Q8×C13—42no—
173Q8×C13—42no—
174Q8×C13—42no—
175Q8×C13—82no—
176D4×C13—22no—
177D4×C13—42no—
178D4×C13—42no—
179D4×C13—44no—
180D4×C13—41no—
181D4×C13—41no—
182D4×C13—41no—
183D4×C13—41no—
184D4×C13—84no—
185C2×C4×C13—22no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—22no—
193C2×C4×C13—21no—
194C2×C4×C13—24no—
195C2×C4×C13—42no—
196C2×C4×C13—44no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—44no—
202C2×C4×C13—84no—
203C2×C4×C13C2×C22⋊C411yescharacteristic
204C2×C4×C13C2×C22⋊C411yescharacteristic
205C2×C4×C13#12011yescharacteristic
206C2×C4×C13#12011yescharacteristic
207C2×C4×C13#12011yescharacteristic
208C2×C4×C13#12011yescharacteristic
209#1055—42no—
210#1055—42no—
211#1055—81no—
212#1055—81no—
213#556—21no—
214#555—21no—
215#554—21no—
216#553—22no—
217#548—22no—
218#547—21no—
219#542—22no—
220#537Dic1312yes—
221#533—21no—
222#532—21no—
223#532C2×D1311yescharacteristic
224C2×C4⋊Q8C2×D1311yescharacteristic
225#520Dic1312yes—
226C4×#41C2×D1311yescharacteristic
227#423—131no—
228#423—131no—
229C2×#101—262no—
230C4×M16—131no—
231C4×M16—131no—
232#343—262no—
233#333—261no—
234#331—261no—
235#329—262no—
236Q8⋊C8—261no—
237Q8⋊C8—261no—
238D4⋊C8—261no—
239D4⋊C8—261no—
240C22×C13—21no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—41no—
244C22×C13—42no—
245C22×C13—41no—
246C22×C13—42no—
247C22×C13—41no—
248C22×C13—42no—
249C22×C13#37911yescharacteristic
250C4×C13—21no—
251C4×C13—21no—
252C4×C13—21no—
253C4×C13—41no—
254C4×C13—44no—
255C4×C13—41no—
256C4×C13—41no—
257C4×C13—42no—
258C4×C13#41312yes—
259C4×C13#45311yescharacteristic
260C4×C13#45411yescharacteristic
261C4×C13#45511yescharacteristic
262C4×C13#45611yescharacteristic
263C2×#41—22no—
264C2×#41C2×Dic1311yescharacteristic
265C2×#41C2×Dic1312yes—
266C22×Q8C22⋊D1312yes—
267C2×M16—261no—
268C2×M16—261no—
269C2×M16—261no—
270C2×M16—261no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8C22⋊D1311yescharacteristic
276#127C22⋊D1311yescharacteristic
277#126—24no—
278#125—22no—
279#124—22no—
280#124—24no—
281#124C22⋊D1312yes—
282#123—24no—
283C22⋊Q8—22no—
284C22⋊Q8—24no—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287#121—22no—
288#121—22no—
289#121—22no—
290#121—24no—
291#121—21no—
292#121—21no—
293C4×Q8—22no—
294C4×Q8—22no—
295C4×Q8C22⋊D1311yescharacteristic
296C4×Q8C22⋊D1311yescharacteristic
297C4×D4—22no—
298C4×D4—22no—
299C4×D4—24no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4C22⋊D1311yescharacteristic
305C4×D4C22⋊D1311yescharacteristic
306#117—22no—
307#117—22no—
308#117—21no—
309#117C2×Dic1311yescharacteristic
310C2×C4⋊C4—22no—
311C2×C4⋊C4C2×Dic1312yes—
312C2×C4⋊C4C22⋊D1312yes—
313C2×C42—21no—
314C2×C42C22×D1311yescharacteristic
315C4⋊C8—261no—
316C4⋊C8—261no—
317C4⋊C8—261no—
318C4⋊C8—261no—
319#101—524no—
320#97—261no—
321#97—261no—
322C4×C8—261no—
323C4×C8—261no—
324C2×C13—41no—
325C2×C13—81no—
326C2×C13—82no—
327C2×C13#178511yescharacteristic
328C2×C13#179211yescharacteristic
329C2×C13#179311yescharacteristic
330#41—42no—
331#41—44no—
332#41—82no—
333#41—82no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—42no—
337C2×Q8—42no—
338C2×Q8C22⋊Dic1311yescharacteristic
339C2×Q8C22⋊Dic1312yes—
340C2×D4—22no—
341C2×D4—21no—
342C2×D4—24no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4C22⋊Dic1311yescharacteristic
346C2×D4C22⋊Dic1312yes—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4C22⋊Dic1314yes—
353C22×C4C22×Dic1311yescharacteristic
354C22×C4C2×C22⋊D1311yescharacteristic
355C22×C4C2×C22⋊D1311yescharacteristic
356M16—262no—
357M16—262no—
358M16—521no—
359M16—521no—
360M16—522no—
361M16—522no—
362C2×C8—521no—
363C2×C8—521no—
364C2×C8—521no—
365C2×C8—521no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4C22⋊Dic1311yescharacteristic
377C4⋊C4C22⋊Dic1311yescharacteristic
378C22⋊C4—24no—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—21no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C42—24no—
387C42—21no—
388C42—21no—
389C42—21no—
390C42C2×C22⋊D1311yescharacteristic
391C42C2×C22⋊D1311yescharacteristic
392C42C2×C22⋊D1311yescharacteristic
393C42C2×C22⋊D1311yescharacteristic
394C13#847011yescharacteristic, complemented, Sylow
395C23—21no—
396C23—22no—
397C23C2×C22⋊Dic1311yescharacteristic
398Q8—22no—
399Q8—42no—
400Q8—42no—
401Q8—42no—
402Q8—82no—
403D4—22no—
404D4—42no—
405D4—42no—
406D4—44no—
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—84no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—44no—
429C2×C4—84no—
430C2×C4C2×C22⋊Dic1311yescharacteristic
431C2×C4C2×C22⋊Dic1311yescharacteristic
432C2×C4#8820711yescharacteristic
433C2×C4#8820711yescharacteristic
434C2×C4#8820711yescharacteristic
435C2×C4#8820711yescharacteristic
436C8—522no—
437C8—522no—
438C8—1041no—
439C8—1041no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—41no—
444C22—42no—
445C22—41no—
446C22—42no—
447C22—41no—
448C22—42no—
449C22#1171890811yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—41no—
454C4—42no—
455C4—41no—
456C4—44no—
457C4—41no—
458C4#1171889812yes—
459C4#1171890211yescharacteristic
460C4#1171890311yescharacteristic
461C4#1171890611yescharacteristic
462C4#1171890711yescharacteristic
463C2—41no—
464C2—81no—
465C2—82no—
466C2#1311476411yescharacteristic
467C2#1311479011yescharacteristic
468C2#1311479511yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3511C2
socleC22×C13#379
cosocleC2×C42×C13C23
hypercenter#3511D13
hypocenterC13#8470
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13115826C2semidirect
2. #13115681C2semidirect
3. #13113571C2semidirect
4. #13113428C2semidirect
5. #13113275C2semidirect
6. #13113275C2semidirect
394. C13#8470semidirect

Maximal subgroups

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

subgroupindex
#131158262
#131156812
#131135712
#131134282
#131132752
C13×#35112
#847013