Finite Group Databasebeta

← #15765804

Subgroups — #15765804

Order 3328.

602 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 105 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#13125608C211yesmaximal, characteristic
2#13123175C211yesmaximal, characteristic
3#13114904C211yesmaximal, characteristic
4#13113408C211yesmaximal, characteristic
5#13113407C211yesmaximal, characteristic
6#13112703C211yesmaximal, characteristic
7C13×#2855C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C42×C13C2211yescharacteristic
10C2×#88178C2211yescharacteristic
11C13×#391—21no—
12C13×#389—21no—
13C13×#387—22no—
14C13×#385—21no—
15C13×#381—21no—
16C13×#380C2211yescharacteristic
17#11718889—21no—
18#11718873C2211yescharacteristic
19#11718872—21no—
20#11718871—21no—
21C2×C22⋊#1055C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23#11718712—22no—
24#11718711—21no—
25#11718705—21no—
26#11718631—21no—
27#11718594—22no—
28#11718590—21no—
29#11718589—21no—
30#11718130—22no—
31#11718116—22no—
32#11718044—22no—
33C22×Q8×C13D411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C22×Dic26D411yescharacteristic
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C2×C13×C4⋊C4—22no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C42×C13—21no—
49C2×C42×C13—21no—
50C2×C42×C13—21no—
51C2×C42×C13—21no—
52C2×C42×C13—21no—
53C2×C42×C13—21no—
54C2×C22⋊Dic13—21no—
55C2×C22⋊Dic13—21no—
56C2×#6107—22no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13D411yescharacteristic
59#88178—21no—
60#88178—21no—
61#88178—21no—
62#88178—21no—
63C2×#6101—22no—
64C2×#6101—21no—
65C22×#1055—21no—
66C22×#1055D412yes—
67C13×#95—22no—
68C13×#95—22no—
69C13×#95—22no—
70C13×#95D412yes—
71#88075—22no—
72#88071—22no—
73#88071—22no—
74#88071—22no—
75#88071D412yes—
76C22⋊#1055—21no—
77C22⋊#1055—21no—
78C22⋊#1055—21no—
79C22⋊#1055—21no—
80#88050—22no—
81#88047—22no—
82#10325—131nomaximal, Sylow
83C24×C13C2×D411yescharacteristic
84C2×Q8×C13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—42no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—42no—
100C22×C4×C13—42no—
101C22×C4×C13Q1612yescomplemented
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×Dic13—21no—
109C22×Dic13—22no—
110C22×Dic13—21no—
111C2×Dic26—21no—
112C2×Dic26—21no—
113C2×Dic26—42no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—42no—
117C13×C4⋊C4—44no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C42×C13—41no—
125C42×C13—41no—
126C42×C13—41no—
127C42×C13—41no—
128C22⋊Dic13—41no—
129C22⋊Dic13—41no—
130C22⋊Dic13—41no—
131C22⋊Dic13—41no—
132#6107—82no—
133C4⋊Dic13—21no—
134C4⋊Dic13—21no—
135C4⋊Dic13—42no—
136#6101—44no—
137#6101—41no—
138#6101—41no—
139C2×#1055—22no—
140C2×#1055—42no—
141C2×#1055—42no—
142C2×#1055—41no—
143#3189—131no—
144#2855—131no—
145#2855D1311yescharacteristic
146#1817—131no—
147#1520—131no—
148#1520—131no—
149#1289—131no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13#12011yescharacteristic
153C23×C13#12011yescharacteristic
154C23×C13#12111yescharacteristic
155C23×C13C2×Q1611yescharacteristic
156C23×C13#13511yescharacteristic
157C23×C13#13711yescharacteristic
158C23×C13#13711yescharacteristic
159Q8×C13—42no—
160Q8×C13—81no—
161C2×C4×C13—22no—
162C2×C4×C13—22no—
163C2×C4×C13—22no—
164C2×C4×C13—22no—
165C2×C4×C13—22no—
166C2×C4×C13—22no—
167C2×C4×C13—22no—
168C2×C4×C13—22no—
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×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—42no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—42no—
188C2×C4×C13#12011yescharacteristic
189C2×C4×C13#12111yescharacteristic
190C2×C4×C13#12111yescharacteristic
191C2×C4×C13#12711yescharacteristic
192C2×Dic13—42no—
193C2×Dic13—42no—
194C2×Dic13—42no—
195C2×Dic13—42no—
196C2×Dic13—41no—
197C2×Dic13—41no—
198C2×Dic13—42no—
199Dic26—42no—
200Dic26—81no—
201#1055—42no—
202#1055—81no—
203C2×C22⋊Q8—131no—
204C2×C22⋊Q8C2×D1311yescharacteristic
205C22×C42C2×D1311yescharacteristic
206#484—261no—
207#484—261no—
208#467—262no—
209#451—261no—
210#451—261no—
211C2×C22⋊C8—131no—
212C2×C22⋊C8—131no—
213#391—21no—
214#391—261no—
215#389—21no—
216#389—261no—
217#387—22no—
218#387—262no—
219#385—21no—
220#385—261no—
221#381—21no—
222#381—261no—
223#380—131no—
224#380C2×D1311yescharacteristic
225#336—262no—
226#328—262no—
227#328—262no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—21no—
231C22×C13—21no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—41no—
235C22×C13—41no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13#39211yescharacteristic
239C22×C13#45111yescharacteristic
240C22×C13#45111yescharacteristic
241C22×C13#45211yescharacteristic
242C22×C13#45211yescharacteristic
243C22×C13#46711yescharacteristic
244C22×C13#47011yescharacteristic
245C4×C13—21no—
246C4×C13—21no—
247C4×C13—21no—
248C4×C13—42no—
249C4×C13—42no—
250C4×C13—82no—
251C4×C13—81no—
252C4×C13—81no—
253C4×C13#45812yes—
254Dic13—82no—
255Dic13—81no—
256Dic13—81no—
257C22×Q8—131no—
258C22×Q8C22⋊D1311yescharacteristic
259C23×C4C22⋊D1311yescharacteristic
260C23×C4C22⋊D1311yescharacteristic
261C23×C4C22×D1311yescharacteristic
262C2×Q16—262no—
263C22×C8—132no—
264C22×C8—261no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—261no—
270C22⋊Q8—261no—
271C22⋊Q8—261no—
272C22⋊Q8—261no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—131no—
277C2×C4⋊C4—262no—
278C2×C4⋊C4—261no—
279C2×C4⋊C4—261no—
280C2×C4⋊C4C22⋊D1311yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—261no—
284C2×C22⋊C4—261no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291#107—262no—
292#103—262no—
293#103—262no—
294C22⋊C8—261no—
295C22⋊C8—261no—
296C22⋊C8—261no—
297C22⋊C8—261no—
298#95—22no—
299#95—22no—
300#95—22no—
301#95—132no—
302#95—262no—
303#95—262no—
304#95—262no—
305#95C22⋊D1312yes—
306C2×C13—21no—
307C2×C13—21no—
308C2×C13—21no—
309C2×C13—21no—
310C2×C13—21no—
311C2×C13—21no—
312C2×C13#200111yescharacteristic
313C2×C13#201011yescharacteristic
314C2×C13#202211yescharacteristic
315C24C2×C22⋊D1311yescharacteristic
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—42no—
319C2×Q8—261no—
320C2×Q8—261no—
321C2×Q8—522no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—262no—
337C22×C4—261no—
338C22×C4—261no—
339C22×C4#610712yescomplemented
340C22×C4D4×D1311yescharacteristic
341C22×C4D4×D1311yescharacteristic
342C22×C4D4×D1311yescharacteristic
343C22×C4#612911yescharacteristic
344C22×C4C2×C22⋊D1311yescharacteristic
345C22×C4C2×C22⋊D1311yescharacteristic
346Q16—1042no—
347C2×C8—262no—
348C2×C8—522no—
349C2×C8—522no—
350C2×C8—521no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—42no—
354C4⋊C4—44no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—261no—
358C4⋊C4—261no—
359C4⋊C4—524no—
360C4⋊C4—522no—
361C4⋊C4—521no—
362C4⋊C4—521no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—521no—
368C22⋊C4—521no—
369C22⋊C4—521no—
370C22⋊C4—521no—
371C42—41no—
372C42—41no—
373C42—41no—
374C42—41no—
375C13#1032511yescharacteristic, complemented, Sylow
376C23—41no—
377C23—41no—
378C23#8819111yescharacteristic
379C23#8819311yescharacteristic
380C23#8819611yescharacteristic
381C23C2×#610711yescharacteristic
382C23#8820411yescharacteristic
383C23#8820511yescharacteristic
384C23#8820711yescharacteristic
385Q8—42no—
386Q8—81no—
387Q8—522no—
388Q8—1041no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—522no—
417C2×C4—522no—
418C2×C4—522no—
419C2×C4—522no—
420C2×C4—522no—
421C2×C4—521no—
422C2×C4—521no—
423C2×C4#8819111yescharacteristic
424C2×C4#8819211yescharacteristic
425C2×C4#8819311yescharacteristic
426C2×C4#8819411yescharacteristic
427C8—522no—
428C8—1041no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22#1171870811yescharacteristic
440C22#1171871111yescharacteristic
441C22#1171871211yescharacteristic
442C22#1171871311yescharacteristic
443C22#1171888411yescharacteristic
444C22#1171888911yescharacteristic
445C22#1171890011yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—42no—
451C4—82no—
452C4—81no—
453C4—81no—
454C4—1042no—
455C4—1041no—
456C4—1041no—
457C4#1171871412yes—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—21no—
464C2#1311584411yescharacteristic
465C2#1311590111yescharacteristic
466C2#1311596411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2855C2
socleC22×C13#392
prime radicalC24×C13C2×D4
hypercenter#2855D13
hypocenterC13#10325
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2855

Complements

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

NH ≅ G/Ntype
101. C22×C4×C13Q16semidirect
339. C22×C4#6107semidirect
375. C13#10325semidirect

Maximal subgroups

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

subgroupindex
#131256082
#131231752
#131149042
#131134082
#131134072
#131127032
C13×#28552
#1032513