Finite Group Databasebeta

← #15759377

Subgroups — #15759377

Order 3328.

566 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#11718695C211yesmaximal, characteristic
2#13117715C211yesmaximal, characteristic, complemented
3#13115673C211yesmaximal, characteristic
4#13114927C211yesmaximal, characteristic, complemented
5#13112703C211yesmaximal, characteristic, complemented
6#13112682C211yesmaximal, characteristic, complemented
7C13×#1519C211yesmaximal, characteristic
8C2×C13×#121C2211yescharacteristic
9C22×C4⋊Dic13C2211yescharacteristic
10C2×C13×C22⋊C8C2211yescharacteristic
11C13×#380C2211yescharacteristic
12C2×#88074—21no—
13C2×#88074—21no—
14C2×#88072C412yescomplemented
15#11718873C2211yescharacteristic
16C4×C22⋊Dic13C2211yescharacteristic
17C2×C22⋊#1055C2211yescharacteristic
18#11718695—21no—
19#11718695—21no—
20#11718695—22no—
21C4⋊C4×Dic13—21no—
22#11718634—21no—
23C2×#88048C412yescomplemented
24#11718603—21no—
25C22⋊C4×Dic13—21no—
26#11718314—22no—
27C13×#327—22no—
28#11718143—22no—
29C22×D4×C13—21no—
30C22×D4×C13C2×C411yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C23×Dic13—21no—
33C22×C8×C13—21no—
34C13×#121—21no—
35C13×#121—21no—
36C13×#121—21no—
37C13×#121—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C22⋊Dic13—21no—
43C2×C22⋊Dic13D411yescharacteristic
44C2×C22⋊Dic13D411yescharacteristic
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13C2×C412yes—
50C2×C4⋊Dic13D411yescharacteristic
51C2×C4⋊Dic13D411yescharacteristic
52C2×C4⋊Dic13D412yes—
53C2×#6101—22no—
54C2×C4×Dic13—21no—
55C2×C4×Dic13—22no—
56C22×#1055C2×C412yes—
57C13×C22⋊C8—21no—
58C13×C22⋊C8—21no—
59C13×#95D412yes—
60#88074—42no—
61#88074—42no—
62#88072—22no—
63#88072—22no—
64#88071—22no—
65#88071—22no—
66#88071—21no—
67#88071—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70#88048—22no—
71#88048—22no—
72#9261—131nomaximal, Sylow
73C24×C13—21no—
74C24×C13C2×D411yescharacteristic
75C2×D4×C13—21no—
76C2×D4×C13—21no—
77C2×D4×C13—42no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C22×C4×C13—21no—
85C22×C4×C13—22no—
86C22×C4×C13—42no—
87C22×C4×C13C22×C411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13#4111yescharacteristic
92C22×C4×C13#4111yescharacteristic
93C22×Dic13—21no—
94C22×Dic13—21no—
95C22×Dic13—21no—
96C22×Dic13—22no—
97C22×Dic13—22no—
98C22×Dic13—21no—
99C22×Dic13—41no—
100C22×Dic13—82no—
101C2×C8×C13—42no—
102C2×C8×C13—41no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—42no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C22⋊Dic13—21no—
111C22⋊Dic13—21no—
112C22⋊Dic13—21no—
113C22⋊Dic13—41no—
114C22⋊Dic13—41no—
115C22⋊Dic13SD1612yes—
116C4⋊Dic13—22no—
117C4⋊Dic13—22no—
118C4⋊Dic13—21no—
119C4⋊Dic13—21no—
120C4⋊Dic13—42no—
121C4⋊Dic13C22⋊C412yes—
122C4⋊Dic13C22⋊C412yes—
123#6101—82no—
124C4×Dic13—42no—
125C4×Dic13—82no—
126C2×#1055—22no—
127C2×#1055—42no—
128C2×#481—131no—
129#2345—131no—
130#1964—131no—
131#1824—131no—
132#1519D1311yescharacteristic
133#1289—131no—
134#1282—131no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—81no—
141C23×C13—81no—
142C23×C13C4×D411yescharacteristic
143C23×C13#12011yescharacteristic
144C23×C13#12111yescharacteristic
145C23×C13C2×SD1611yescharacteristic
146C23×C13#13511yescharacteristic
147C23×C13AGL(1,ℤ/8)11yescharacteristic
148C23×C13#13711yescharacteristic
149D4×C13—42no—
150D4×C13—81no—
151D4×C13—81no—
152D4×C13—81no—
153D4×C13—81no—
154D4×C13—81no—
155C2×C4×C13—22no—
156C2×C4×C13—22no—
157C2×C4×C13—22no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—42no—
167C2×C4×C13C2×C22⋊C411yescharacteristic
168C2×C4×C13C4×D411yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12311yescharacteristic
171C2×Dic13—22no—
172C2×Dic13—22no—
173C2×Dic13—22no—
174C2×Dic13—41no—
175C2×Dic13—41no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—82no—
182C2×Dic13—82no—
183C2×Dic13—81no—
184C2×Dic13—81no—
185C2×Dic13—81no—
186C8×C13—81no—
187#1055—42no—
188C2×#121C2×D1311yescharacteristic
189C22×C4⋊C4—131no—
190#481—262no—
191#481—261no—
192#481—261no—
193C2×#106—132no—
194C2×#102—132no—
195C2×#99—261no—
196C2×#99—261no—
197C2×C22⋊C8—131no—
198C2×C22⋊C8C2×D1311yescharacteristic
199#389—261no—
200#387—262no—
201#380—131no—
202#380—261no—
203#380C2×D1311yescharacteristic
204C4×C4⋊C4—261no—
205C4×C22⋊C4—131no—
206C4×C22⋊C4—261no—
207#340—262no—
208#327—22no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—161no—
223C22×C13—161no—
224C22×C13#38611yescharacteristic
225C22×C13C4×SD1611yescharacteristic
226C22×C13#44011yescharacteristic
227C22×C13#44811yescharacteristic
228C22×C13#44911yescharacteristic
229C22×C13#46011yescharacteristic
230C22×C13#46411yescharacteristic
231C4×C13—21no—
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—82no—
235C4×C13—81no—
236C4×C13#41012yes—
237Dic13—42no—
238Dic13—42no—
239Dic13—42no—
240Dic13—81no—
241Dic13—161no—
242C22×D4—21no—
243C22×D4C4×D1311yescharacteristic
244C23×C4—261no—
245C23×C4C22×D1311yescharacteristic
246C22×C8—21no—
247C22×C8—132no—
248#121—21no—
249#121—21no—
250#121—21no—
251#121—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—132no—
254C2×C4⋊C4—132no—
255C2×C4⋊C4—131no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—261no—
258C2×C4⋊C4—261no—
259C2×C4⋊C4—261no—
260C2×C4⋊C4—261no—
261C2×C4⋊C4—262no—
262C2×C4⋊C4C4×D1311yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—131no—
266C2×C22⋊C4—131no—
267C2×C22⋊C4—261no—
268C2×C42—261no—
269C2×C42—262no—
270#106—262no—
271#106—262no—
272#102—262no—
273#102—262no—
274#99—522no—
275#99—522no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—261no—
279C22⋊C8—261no—
280#95—262no—
281#95—262no—
282#95—261no—
283#95—261no—
284#95C22⋊D1312yes—
285C2×C13—21no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13—21no—
289C2×C13—21no—
290C2×C13—21no—
291C2×C13—161no—
292C2×C13#188011yescharacteristic
293C2×C13#189911yescharacteristic
294C2×C13#190411yescharacteristic
295C24—21no—
296C24D4×D1311yescharacteristic
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—42no—
309C22×C4—261no—
310C22×C4—261no—
311C22×C4—261no—
312C22×C4—262no—
313C22×C4—262no—
314C22×C4—261no—
315C22×C4—521no—
316C22×C4—1042no—
317C22×C4C2×C4×D1311yescharacteristic
318C22×C4#612711yescharacteristic
319C22×C4D4×D1311yescharacteristic
320C22×C4D4×D1311yescharacteristic
321C22×C4#612911yescharacteristic
322C22×C4C2×C22⋊D1311yescharacteristic
323C2×C8—42no—
324C2×C8—41no—
325C2×C8—262no—
326C2×C8—522no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—42no—
330C4⋊C4—132no—
331C4⋊C4—132no—
332C4⋊C4—261no—
333C4⋊C4—261no—
334C4⋊C4—262no—
335C4⋊C4—262no—
336C4⋊C4—522no—
337C4⋊C4—1042no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—132no—
343C22⋊C4—261no—
344C22⋊C4—261no—
345C22⋊C4—261no—
346C22⋊C4—521no—
347C22⋊C4—521no—
348C42—522no—
349C42—1042no—
350C13#926111yescharacteristic, complemented, Sylow
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—81no—
357C23—81no—
358C23#8813511yescharacteristic
359C23#8813811yescharacteristic
360C23#8816511yescharacteristic
361C23#8816611yescharacteristic
362C23SD16×D1311yescharacteristic
363C23#8816911yescharacteristic
364C23#8819111yescharacteristic
365D4—42no—
366D4—81no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—81no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—262no—
384C2×C4—262no—
385C2×C4—262no—
386C2×C4—521no—
387C2×C4—521no—
388C2×C4—522no—
389C2×C4—522no—
390C2×C4—521no—
391C2×C4—521no—
392C2×C4—521no—
393C2×C4—1042no—
394C2×C4—1042no—
395C2×C4—1041no—
396C2×C4—1041no—
397C2×C4—1041no—
398C2×C4C22⋊C4×D1311yescharacteristic
399C2×C4#8813711yescharacteristic
400C2×C4C4×C22⋊D1311yescharacteristic
401C2×C4#8819211yescharacteristic
402C8—81no—
403C8—522no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—161no—
418C22—161no—
419C22#1171841811yescharacteristic
420C22#1171841911yescharacteristic
421C22#1171842311yescharacteristic
422C22#1171842811yescharacteristic
423C22#1171861711yescharacteristic
424C22#1171881911yescharacteristic
425C22#1171883111yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—81no—
431C4—522no—
432C4—522no—
433C4—522no—
434C4—1041no—
435C4—2081no—
436C4#1171840112yes—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—161no—
444C2#1311518811yescharacteristic
445C2#1311529111yescharacteristic
446C2#1311532011yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1519C2
socleC22×C13#386
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#1519D13
hypocenterC13#9261
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #13117715C2semidirect
4. #13114927C2semidirect
5. #13112703C2semidirect
6. #13112682C2semidirect
14. C2×#88072C4semidirect
23. C2×#88048C4semidirect
350. C13#9261semidirect

Maximal subgroups

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

subgroupindex
C2×#117186952
#131177152
#131156732
#131149272
#131127032
#131126822
C13×#15192
#926113