Finite Group Databasebeta

← #15763684

Subgroups — #15763684

Order 3328.

568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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
1#13124844C211yesmaximal, characteristic
2#13124641C211yesmaximal, characteristic, complemented
3#13113399C211yesmaximal, characteristic, complemented
4#13113261C211yesmaximal, characteristic
5#13113231C211yesmaximal, characteristic, complemented
6#13112694C211yesmaximal, characteristic, complemented
7C13×#2536C211yesmaximal, characteristic
8C2×C13×C22⋊Q8—21no—
9C2×C4×Q8×C13C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11#11719175C2211yescharacteristic
12C13×#398—21no—
13C13×#394—21no—
14C13×#388—22no—
15C13×#382C2211yescharacteristic
16C13×#380—21no—
17#11718886—21no—
18#11718879—21no—
19#11718683—22no—
20#11718682—21no—
21#11718681—21no—
22#11718680—21no—
23C4×#6105—22no—
24#11718669—21no—
25#11718632—21no—
26#11718625—21no—
27#11718586C2211yescharacteristic
28#11718586C2211yescharacteristic
29#11718585C2211yescharacteristic
30Q8⋊#1055—22no—
31D4⋊#1055—22no—
32#11718044—22no—
33C22×Q8×C13D411yescharacteristic
34C22×D4×C13D411yescharacteristic
35C23×C4×C13—21no—
36C13×C22⋊Q8—42no—
37C13×C22⋊Q8—42no—
38C4×Q8×C13—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×D4×C13—21no—
43C4×D4×C13—21no—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C2×C13×C4⋊C4—22no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C22⋊C4—22no—
52C2×C13×C22⋊C4—22no—
53C2×C13×C22⋊C4—21no—
54C2×C42×C13—21no—
55C2×C42×C13C2311yescharacteristic
56C2×#6105—22no—
57#88180—21no—
58#88178—21no—
59#88178—21no—
60C2×#6099—21no—
61#88124—21no—
62#88123D411yescharacteristic
63#88123D411yescharacteristic
64C4×Dic26—21no—
65C4×Dic26—21no—
66C13×#95—22no—
67C13×#95—21no—
68C13×#95D412yes—
69#88075—22no—
70#88075—22no—
71#88072—22no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74#88050—22no—
75#88048—22no—
76#88048—22no—
77#88047—22no—
78C4⋊#1055—21no—
79C4⋊#1055—21no—
80C4⋊#1055—21no—
81C4⋊#1055D412yes—
82C4×#1055—21no—
83C4×#1055D412yes—
84#10001—131nomaximal, Sylow
85C24×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13SD1612yescomplemented
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—42no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C2×Dic26—21no—
109C2×Dic26—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—44no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C22⋊C4—44no—
120C13×C22⋊C4—44no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C42×C13—41no—
124C42×C13—41no—
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13C2×D411yescharacteristic
128C42×C13#4111yescharacteristic
129C22⋊Dic13—41no—
130#6105—44no—
131C4⋊Dic13—21no—
132C4⋊Dic13—21no—
133C4⋊Dic13—21no—
134C4⋊Dic13—21no—
135#6101—41no—
136#6101—41no—
137C4×Dic13—41no—
138#6099—41no—
139#6099—41no—
140C2×#1055—22no—
141C2×#1055—22no—
142C2×#1055—41no—
143#3101—131no—
144#3078—131no—
145#2536D1311yescharacteristic
146#1518—131no—
147#1486—131no—
148#1479—131no—
149#1286—131no—
150C23×C13—22no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13#12011yescharacteristic
158Q8×C13—22no—
159Q8×C13—22no—
160Q8×C13—41no—
161Q8×C13—41no—
162D4×C13—22no—
163D4×C13—22no—
164D4×C13—41no—
165D4×C13—41no—
166C2×C4×C13—22no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—42no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
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×SD1611yescharacteristic
190C2×C4×C13#13511yescharacteristic
191C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C13#13711yescharacteristic
193C2×Dic13—41no—
194C2×Dic13—41no—
195Dic26—42no—
196Dic26—81no—
197#1055—42no—
198#1055—42no—
199#1055—81no—
200#533—131no—
201C2×C22⋊Q8—21no—
202C2×C4×Q8C2×D1311yescharacteristic
203C2×C4×D4C2×D1311yescharacteristic
204#483—261no—
205#479—262no—
206#477—261no—
207#476—261no—
208#475—261no—
209#461—261no—
210#450—261no—
211C4×SD16—262no—
212#431—131no—
213#431—131no—
214#428—261no—
215#423—131no—
216#419—261no—
217#398—21no—
218#394—21no—
219#388—22no—
220#382C2×D1311yescharacteristic
221#380—21no—
222#328—262no—
223Q8⋊C8—262no—
224D4⋊C8—262no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—42no—
228C22×C13—42no—
229C22×C13—42no—
230C22×C13—81no—
231C22×C13—81no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13#39211yescharacteristic
235C22×C13#45011yescharacteristic
236C22×C13#45211yescharacteristic
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—21no—
241C4×C13—42no—
242C4×C13—82no—
243C4×C13—81no—
244C4×C13—81no—
245C4×C13#44811yescharacteristic
246C4×C13#44911yescharacteristic
247C4×C13#46511yescharacteristic
248C4×C13#46811yescharacteristic
249Dic13—81no—
250Dic13—81no—
251C22×Q8C22⋊D1311yescharacteristic
252C22×D4C22⋊D1311yescharacteristic
253C23×C4—21no—
254C2×SD16—262no—
255C2×M16—261no—
256C4⋊Q8—131no—
257C4⋊Q8—131no—
258#125—261no—
259C22⋊Q8—42no—
260C22⋊Q8—42no—
261C22⋊Q8—261no—
262C22⋊Q8—261no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—261no—
268C4×Q8—261no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273#117—261no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4C22⋊D1311yescharacteristic
278C2×C4⋊C4C22⋊D1311yescharacteristic
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C42—21no—
283C2×C42C22×D1311yescharacteristic
284#107—262no—
285#106—262no—
286#106—262no—
287C4⋊C8—132no—
288C4⋊C8—261no—
289C4⋊C8—261no—
290C4⋊C8—261no—
291#103—262no—
292#103—262no—
293#103—262no—
294#102—262no—
295C22⋊C8—261no—
296C22⋊C8—261no—
297C4×C8—132no—
298C4×C8—261no—
299#95—22no—
300#95—21no—
301#95C22⋊D1312yes—
302C2×C13—21no—
303C2×C13—21no—
304C2×C13—82no—
305C2×C13#200011yescharacteristic
306C2×C13#200911yescharacteristic
307C2×C13#201011yescharacteristic
308C24—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—261no—
315C2×Q8—261no—
316C2×Q8#610512yescomplemented
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—42no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4C2×C22⋊D1311yescharacteristic
331C22×C4C2×C22⋊D1311yescharacteristic
332C22×C4C2×C22⋊D1311yescharacteristic
333SD16—524no—
334M16—521no—
335M16—521no—
336C2×C8—262no—
337C2×C8—262no—
338C2×C8—521no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—44no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—261no—
349C4⋊C4—261no—
350C4⋊C4—261no—
351C4⋊C4—261no—
352C4⋊C4—521no—
353C4⋊C4—521no—
354C22⋊C4—44no—
355C22⋊C4—44no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—521no—
359C42—41no—
360C42—41no—
361C42—521no—
362C42D4×D1311yescharacteristic
363C42D4×D1311yescharacteristic
364C42D4×D1311yescharacteristic
365C42#612911yescharacteristic
366C13#1000111yescharacteristic, complemented, Sylow
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#8820711yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—522no—
380Q8—1041no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—521no—
403C2×C4—521no—
404C2×C4#8818611yescharacteristic
405C2×C4C2×#610511yescharacteristic
406C2×C4#8819111yescharacteristic
407C2×C4#8819111yescharacteristic
408C2×C4#8819211yescharacteristic
409C2×C4#8819311yescharacteristic
410C2×C4#8819311yescharacteristic
411C2×C4#8819411yescharacteristic
412C2×C4#8820411yescharacteristic
413C2×C4#8820511yescharacteristic
414C8—522no—
415C8—522no—
416C8—1041no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1171887911yescharacteristic
427C22#1171888411yescharacteristic
428C22#1171890011yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—82no—
435C4—81no—
436C4—81no—
437C4—1041no—
438C4—1041no—
439C4#1171869811yescharacteristic
440C4#1171870111yescharacteristic
441C4#1171870211yescharacteristic
442C4#1171870311yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2#1311583911yescharacteristic
447C2#1311589611yescharacteristic
448C2#1311590111yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2536C2
socleC22×C13#392
prime radicalC22×D4×C13D4
hypercenter#2536D13
hypocenterC13#10001
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. #13124641C2semidirect
3. #13113399C2semidirect
5. #13113231C2semidirect
6. #13112694C2semidirect
91. C2×Q8×C13SD16semidirect
316. C2×Q8#6105semidirect
366. C13#10001semidirect

Maximal subgroups

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

subgroupindex
#131248442
#131246412
#131133992
#131132612
#131132312
#131126942
C13×#25362
#1000113