Finite Group Databasebeta

← #15755814

Subgroups — #15755814

Order 3328.

550 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C22⋊D13C211yesmaximal, characteristic
2#13114865C211yesmaximal, characteristic, complemented
3#13114821C212yesmaximal
4#13112703C212yesmaximal, complemented
5C13×#1808C211yesmaximal, characteristic, complemented
6C23×C8×C13C2211yescharacteristic
7C2×C4×C22⋊D13C2211yescharacteristic
8C22×C8×D13C411yescharacteristic, complemented
9C2×C13×#107—21no—
10C13×#380C2212yes—
11#11718873C2212yes—
12C2×C22⋊#1055C2211yescharacteristic
13C8×C22⋊D13—21no—
14C8×C22⋊D13—21no—
15C8×C22⋊D13—21no—
16C8×C22⋊D13—21no—
17C2×#88060C411yescharacteristic, complemented
18C2×#88058—21no—
19C2×#88054C411yescharacteristic, complemented
20C2×C8×Dic13C411yescharacteristic, complemented
21C2×#88046—22no—
22C13×#340—21no—
23#11718143—21no—
24#11718119—22no—
25C23×C4×C13C2311yescharacteristic
26C22×C22⋊D13D411yescharacteristic
27C22×C4×D13C2×C411yescharacteristic
28C22×C8×C13—42no—
29C22×C8×C13C2×C411yescharacteristic
30C22×C8×C13C2×C411yescharacteristic
31C22×C8×C13D411yescharacteristic
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C22×C8×C13D411yescharacteristic
35C2×C13×C4⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C22⋊Dic13—22no—
38C2×C22⋊Dic13D411yescharacteristic
39C4×C22⋊D13—21no—
40C4×C22⋊D13—21no—
41C4×C22⋊D13—21no—
42C4×C22⋊D13—21no—
43C2×#6103Q811yescharacteristic
44C2×C4⋊Dic13—22no—
45C2×#6101Q811yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C22×#1055C2×C411yescharacteristic
48C22×#1055C2×C411yescharacteristic
49C2×C8×D13—21no—
50C2×C8×D13—21no—
51C2×C8×D13—42no—
52C13×#107—42no—
53C13×#95—22no—
54#88071—22no—
55C22⋊#1055—21no—
56C22⋊#1055—21no—
57#88060—21no—
58#88060—21no—
59#88058—42no—
60#88054—21no—
61#88054—21no—
62C8×Dic13—21no—
63C8×Dic13—21no—
64#88046—44no—
65#8609—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C23×D13C4⋊C411yescharacteristic
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—42no—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×Q811yescharacteristic
75C22×C4×C13#4111yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C2×C22⋊D13—21no—
78C2×C22⋊D13—21no—
79C2×C22⋊D13—21no—
80C2×C22⋊D13—21no—
81C2×C22⋊D13D812yes—
82C2×C22⋊D13Q1612yes—
83C22×Dic13—42no—
84C22×Dic13C4⋊C411yescharacteristic
85C22×Dic13C4⋊C411yescharacteristic
86C22×Dic13C4⋊C411yescharacteristic
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×C4×D13—41no—
90C2×C4×D13—41no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13—22no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13C22⋊C411yescharacteristic
98C2×C8×C13C22⋊C411yescharacteristic
99C2×C8×C13C22⋊C411yescharacteristic
100C2×C8×C13C22⋊C411yescharacteristic
101C13×C4⋊C4—42no—
102C13×C4⋊C4—42no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—42no—
105C22⋊Dic13—21no—
106C22⋊Dic13—21no—
107C22⋊Dic13—42no—
108C22⋊Dic13—42no—
109#6103—21no—
110#6103—21no—
111C4⋊Dic13—42no—
112C4⋊Dic13—42no—
113#6101—21no—
114#6101—21no—
115C4×Dic13—21no—
116C4×Dic13—21no—
117C2×#1055—21no—
118C2×#1055—21no—
119C2×#1055—41no—
120C2×#1055—41no—
121C8×D13—42no—
122C8×D13—42no—
123C2×C8×D4—131no—
124#1808—131no—
125#1808D1311yescharacteristic, complemented
126#1799—132no—
127#1289—132no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13C2×C4⋊C411yescharacteristic
131C23×C13#12111yescharacteristic
132C23×C13#12111yescharacteristic
133C23×C13C2×D811yescharacteristic
134C23×C13C2×Q1611yescharacteristic
135C23×C13#13511yescharacteristic
136C23×C13#13511yescharacteristic
137C22×D13—21no—
138C22×D13—21no—
139C22×D13—41no—
140C22×D13—41no—
141C22×D13#10712yescomplemented
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—82no—
152C2×C4×C13—82no—
153C2×C4×C13—82no—
154C2×C4×C13C2×C22⋊C411yescharacteristic
155C2×C4×C13#11711yescharacteristic
156C2×C4×C13C22⋊Q811yescharacteristic
157C2×C4×C13C22⋊Q811yescharacteristic
158C22⋊D13—22no—
159C22⋊D13—22no—
160C22⋊D13—22no—
161C22⋊D13—22no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—82no—
169C2×Dic13—82no—
170C2×Dic13—82no—
171C2×Dic13#10712yescomplemented
172C4×D13—42no—
173C4×D13—41no—
174C4×D13—41no—
175C8×C13—21no—
176C8×C13—21no—
177C8×C13—21no—
178C8×C13#9912yescomplemented
179#1055—41no—
180#1055—41no—
181C23×C8—131no—
182C23×C8C2×D1311yescharacteristic
183C2×C4×D4—131no—
184C8×D4—261no—
185C8×D4—261no—
186C8×D4—261no—
187C8×D4—261no—
188C2×#107—21no—
189C2×#107—261no—
190C2×C4⋊C8—131no—
191C2×#99—262no—
192C2×C22⋊C8—131no—
193C2×C22⋊C8—131no—
194C2×C4×C8—131no—
195#380—132no—
196#380C2×D1312yes—
197#342—262no—
198#340—21no—
199#340—261no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13#38011yescharacteristic
211C22×C13C2×#10711yescharacteristic
212C22×C13#42711yescharacteristic
213C22×C13#46611yescharacteristic
214C22×C13#46611yescharacteristic
215C22×C13#46711yescharacteristic
216C22×C13#46711yescharacteristic
217C2×D13—22no—
218C2×D13—42no—
219C2×D13—41no—
220C2×D13—41no—
221C2×D13—42no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—162no—
226C4×C13C2×#9911yescharacteristic
227C4×C13#41011yescharacteristic
228Dic13—22no—
229Dic13—41no—
230Dic13—41no—
231Dic13—162no—
232C22×D4—131no—
233C23×C4—131no—
234C23×C4C22×D1311yescharacteristic
235C22×C8—42no—
236C22×C8—131no—
237C22×C8—131no—
238C22×C8—261no—
239C22×C8—261no—
240C22×C8—522no—
241C22×C8C4×D1311yescharacteristic
242C22×C8C4×D1311yescharacteristic
243C22×C8D5211yescharacteristic
244C22×C8D5211yescharacteristic
245C22×C8C22⋊D1311yescharacteristic
246C22×C8C22⋊D1311yescharacteristic
247C4×D4—261no—
248C4×D4—261no—
249C4×D4—261no—
250C4×D4—261no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—131no—
253C2×C4⋊C4—262no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—131no—
256C2×C22⋊C4—131no—
257C2×C22⋊C4—262no—
258C2×C42—131no—
259#107—42no—
260#107—522no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263#99—524no—
264C22⋊C8—261no—
265C22⋊C8—261no—
266C22⋊C8—261no—
267C22⋊C8—261no—
268C4×C8—261no—
269C4×C8—261no—
270#95—22no—
271#95—262no—
272C2×C13—21no—
273C2×C13—21no—
274C2×C13—21no—
275C2×C13—21no—
276C2×C13—21no—
277C2×C13—21no—
278C2×C13#179911yescharacteristic
279C2×C13#180811yescharacteristic
280C2×C13#181211yescharacteristic
281D13—42no—
282C24—131no—
283C24D4×D1311yescharacteristic
284C2×D4—132no—
285C2×D4—132no—
286C2×D4—261no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—261no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—131no—
296C22×C4—261no—
297C22×C4—261no—
298C22×C4—521no—
299C22×C4—521no—
300C22×C4—522no—
301C22×C4C2×C4×D1311yescharacteristic
302C22×C4C2×D5211yescharacteristic
303C22×C4#612911yescharacteristic
304C22×C4Q8×D1311yescharacteristic
305C22×C4#613111yescharacteristic
306C22×C4C2×C22⋊D1311yescharacteristic
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—261no—
314C2×C8—261no—
315C2×C8—522no—
316C2×C8—522no—
317C2×C8—521no—
318C2×C8—521no—
319C2×C8#610311yescharacteristic
320C2×C8#610311yescharacteristic
321C2×C8#610311yescharacteristic
322C2×C8#610311yescharacteristic
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—261no—
326C4⋊C4—261no—
327C4⋊C4—522no—
328C4⋊C4—522no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C22⋊C4—261no—
334C22⋊C4—261no—
335C22⋊C4—522no—
336C22⋊C4—522no—
337C42—261no—
338C42—261no—
339C13#860911yescharacteristic, complemented, Sylow
340C23—41no—
341C23—41no—
342C23—132no—
343C23—261no—
344C23—261no—
345C23—521no—
346C23—521no—
347C23C4⋊C4×D1311yescharacteristic
348C23#8814911yescharacteristic
349C23D8×D1311yescharacteristic
350C23#8816611yescharacteristic
351C23Q16×D1311yescharacteristic
352C23#8817311yescharacteristic
353C23#8819211yescharacteristic
354D4—262no—
355D4—262no—
356D4—262no—
357D4—262no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—132no—
371C2×C4—261no—
372C2×C4—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—522no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4—521no—
379C2×C4—521no—
380C2×C4—1042no—
381C2×C4—1042no—
382C2×C4—1042no—
383C2×C4#8814611yescharacteristic
384C2×C4#8815111yescharacteristic
385C2×C4C2×#610311yescharacteristic
386C2×C4#8820011yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—521no—
391C8—521no—
392C8#8804612yescomplemented
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—262no—
404C22—522no—
405C22—522no—
406C22—521no—
407C22—521no—
408C22D13×#10711yescharacteristic
409C22#1171854111yescharacteristic
410C22#1171854411yescharacteristic
411C22#1171854811yescharacteristic
412C22#1171864811yescharacteristic
413C22#1171881811yescharacteristic
414C22#1171884911yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—162no—
419C4—262no—
420C4—521no—
421C4—521no—
422C4—2082no—
423C4C2×#8804611yescharacteristic
424C4#1171866711yescharacteristic
425C2—21no—
426C2—21no—
427C2—21no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—522no—
432C2#1311482111yescharacteristic
433C2#1311486211yescharacteristic
434C2#1311487911yescharacteristic
subgroupG/H
centerC22#11718648
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1808C2
socleC22×C13#380
prime radicalC22×C22⋊D13D4
cosocleC23×C4×C13C23
hypercenter#1808D13
hypocenterC13#8609
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. #13114865C2semidirect
4. #13112703C2semidirect
5. C13×#1808C2semidirect
8. C22×C8×D13C4semidirect
17. C2×#88060C4semidirect
19. C2×#88054C4semidirect
20. C2×C8×Dic13C4semidirect
125. #1808D13semidirect
141. C22×D13#107semidirect
171. C2×Dic13#107semidirect
178. C8×C13#99semidirect
339. C13#8609semidirect
392. C8#88046semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D132
#131148652
#131148212
#131127032
C13×#18082
#860913