Finite Group Databasebeta

← #15754737

Subgroups — #15754737

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115144C212yesmaximal
2C2×#11718130C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic
4#13113089C211yesmaximal, characteristic
5C2×C13×#544C211yesmaximal, characteristic
6C13×#544—24no—
7C13×#544—22no—
8C13×#544C414yescomplemented
9C2×C13×C4⋊Q8—22no—
10C2×C13×#125—22no—
11C2×C13×C22⋊Q8—21no—
12C2×C13×C22⋊Q8C2212yes—
13C2×C13×#117—21no—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C2×#88075—22no—
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88071C2211yescharacteristic
20C2×C22⋊#1055C2212yes—
21#11718130—24no—
22#11718121—22no—
23#11718120—22no—
24C22×Q8×C13—21no—
25C22×Q8×C13D412yes—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C23×Dic13—21no—
30C23×Dic13—21no—
31C13×C4⋊Q8—28no—
32C13×C4⋊Q8—28no—
33C13×#125—28no—
34C13×#125—28no—
35C13×C22⋊Q8—24no—
36C13×C22⋊Q8—24no—
37C13×C22⋊Q8—22no—
38C13×C22⋊Q8—22no—
39C13×C22⋊Q8C2×C414yes—
40C13×C22⋊Q8D414yes—
41C13×#117—24no—
42C13×#117—24no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—22no—
47C2×C13×C4⋊C4—22no—
48C2×C13×C4⋊C4—22no—
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4C2×C412yes—
51C2×C13×C4⋊C4D412yes—
52C2×C13×C4⋊C4D412yes—
53C2×C13×C22⋊C4—22no—
54C2×C42×C13—22no—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13—42no—
57C22×#1055—22no—
58#88075—44no—
59#88071—22no—
60#88071—42no—
61#88071—42no—
62C22⋊#1055—22no—
63C22⋊#1055—22no—
64#8406—131nomaximal, Sylow
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—24no—
67C2×Q8×C13—22no—
68C2×Q8×C13—42no—
69C2×Q8×C13—42no—
70C2×Q8×C13—81no—
71C2×Q8×C13—81no—
72C2×Q8×C13C22⋊C414yes—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13C22⋊C412yes—
86C22×C4×C13C22⋊C412yes—
87C22×C4×C13SD1612yes—
88C22×C4×C13Q1612yes—
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2×D412yes—
92C22×C4×C13C2×D411yescharacteristic
93C22×Dic13—22no—
94C22×Dic13—22no—
95C22×Dic13—41no—
96C22×Dic13—41no—
97C22×Dic13—41no—
98C22×Dic13—41no—
99C22×Dic13—41no—
100C22×Dic13—41no—
101C22×Dic13—41no—
102C22×Dic13—41no—
103C22×Dic13—41no—
104C22×Dic13—41no—
105C22×Dic13—41no—
106C22×Dic13—41no—
107C13×C4⋊C4—24no—
108C13×C4⋊C4—24no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—28no—
111C13×C4⋊C4—24no—
112C13×C4⋊C4—24no—
113C13×C4⋊C4—24no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4C22⋊C414yes—
117C13×C22⋊C4—24no—
118C13×C22⋊C4—24no—
119C42×C13—28no—
120C4⋊Dic13—24no—
121C4⋊Dic13—42no—
122C2×#1055—42no—
123C2×#1055—42no—
124C2×#1055—42no—
125C2×#544D1311yescharacteristic
126#1872—132no—
127C2×#328—132no—
128C2×#324—131no—
129#1441—131no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13C2×C22⋊C411yescharacteristic
135C23×C13#12011yescharacteristic
136C23×C13#12011yescharacteristic
137C23×C13C2×SD1611yescharacteristic
138C23×C13C2×Q1611yescharacteristic
139C23×C13#13711yescharacteristic
140C23×C13#13711yescharacteristic
141Q8×C13—44no—
142Q8×C13—82no—
143Q8×C13—84no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—24no—
153C2×C4×C13—24no—
154C2×C4×C13—22no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—41no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—81no—
166C2×C4×C13#10314yescomplemented
167C2×C4×C13C2×C22⋊C412yes—
168C2×C4×C13#12012yes—
169C2×Dic13—42no—
170C2×Dic13—42no—
171C2×Dic13—42no—
172C2×Dic13—42no—
173C2×Dic13—42no—
174C2×Dic13—42no—
175C2×Dic13—81no—
176C2×Dic13—81no—
177C2×Dic13—81no—
178C2×Dic13—81no—
179C2×Dic13—81no—
180C2×Dic13—81no—
181C2×Dic13—81no—
182C2×Dic13—81no—
183#1055—82no—
184#544—24no—
185#544—22no—
186#544Dic1314yescomplemented
187C2×C4⋊Q8—22no—
188C2×#125—22no—
189C2×C22⋊Q8—21no—
190C2×C22⋊Q8C2×D1312yes—
191C2×#117—21no—
192C22×C4⋊C4—131no—
193C22×C4⋊C4C2×D1311yescharacteristic
194C2×#103—262no—
195C2×C22⋊C8—132no—
196C2×#95—131no—
197C2×#95—261no—
198C2×#95—261no—
199#340—262no—
200#328—264no—
201#324—262no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13#37911yescharacteristic
215C22×C13C2×#10311yescharacteristic
216C22×C13#41911yescharacteristic
217C22×C13#44811yescharacteristic
218C22×C13#44811yescharacteristic
219C22×C13#45111yescharacteristic
220C22×C13#45111yescharacteristic
221C22×C13#45411yescharacteristic
222C22×C13#45611yescharacteristic
223C22×C13B(4,𝔽2)11yescharacteristic
224C22×C13#45811yescharacteristic
225C4×C13—24no—
226C4×C13—22no—
227C4×C13—22no—
228C4×C13—44no—
229C4×C13—42no—
230C4×C13—44no—
231Dic13—82no—
232Dic13—82no—
233C22×Q8—21no—
234C22×Q8C22⋊D1312yes—
235C23×C4—261no—
236C23×C4—261no—
237C23×C4C22⋊D1311yescharacteristic
238C23×C4C22⋊D1311yescharacteristic
239C23×C4C22×D1311yescharacteristic
240C22×C8—262no—
241C4⋊Q8—28no—
242C4⋊Q8—28no—
243#125—28no—
244#125—28no—
245C22⋊Q8—24no—
246C22⋊Q8—24no—
247C22⋊Q8—22no—
248C22⋊Q8—22no—
249C22⋊Q8C2×Dic1314yes—
250C22⋊Q8C22⋊D1314yes—
251#117—24no—
252#117—24no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—262no—
261C2×C4⋊C4—522no—
262C2×C4⋊C4C2×Dic1312yes—
263C2×C4⋊C4C22⋊D1312yes—
264C2×C4⋊C4C22⋊D1312yes—
265C2×C22⋊C4—22no—
266C2×C42—22no—
267#103—524no—
268C22⋊C8—262no—
269C22⋊C8—262no—
270#95—262no—
271#95—522no—
272#95—522no—
273C2×C13—21no—
274C2×C13—21no—
275C2×C13—21no—
276C2×C13—21no—
277C2×C13#159911yescharacteristic
278C2×C13#160511yescharacteristic
279C2×C13#161111yescharacteristic
280C2×C13#161711yescharacteristic
281C2×C13#178711yescharacteristic
282C2×C13#179011yescharacteristic
283C2×C13#179311yescharacteristic
284C24C2×C22⋊D1311yescharacteristic
285C2×Q8—24no—
286C2×Q8—22no—
287C2×Q8—42no—
288C2×Q8—42no—
289C2×Q8—81no—
290C2×Q8—81no—
291C2×Q8C22⋊Dic1314yes—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—262no—
305C22×C4—262no—
306C22×C4—521no—
307C22×C4—521no—
308C22×C4—521no—
309C22×C4—521no—
310C22×C4—521no—
311C22×C4—521no—
312C22×C4—521no—
313C22×C4—521no—
314C22×C4—521no—
315C22×C4—521no—
316C22×C4—521no—
317C22×C4—521no—
318C22×C4#610612yes—
319C22×C4#610712yes—
320C22×C4C22⋊Dic1312yes—
321C22×C4C22⋊Dic1312yes—
322C22×C4C22×Dic1311yescharacteristic
323C22×C4C2×C22⋊D1312yes—
324C22×C4C2×C22⋊D1312yes—
325C22×C4C2×C22⋊D1311yescharacteristic
326C2×C8—522no—
327C2×C8—522no—
328C2×C8—522no—
329C4⋊C4—24no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—28no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—22no—
338C4⋊C4—264no—
339C4⋊C4—522no—
340C4⋊C4C22⋊Dic1314yes—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C42—28no—
344C13#840611yescharacteristic, complemented, Sylow
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23C2×#610611yescharacteristic
350C23#8819611yescharacteristic
351C23#8819611yescharacteristic
352C23C2×#610711yescharacteristic
353C23C2×C22⋊Dic1311yescharacteristic
354C23#8820711yescharacteristic
355C23#8820711yescharacteristic
356Q8—44no—
357Q8—82no—
358Q8—84no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—522no—
382C2×C4—522no—
383C2×C4—522no—
384C2×C4—522no—
385C2×C4—522no—
386C2×C4—522no—
387C2×C4—1041no—
388C2×C4—1041no—
389C2×C4—1041no—
390C2×C4—1041no—
391C2×C4—1041no—
392C2×C4—1041no—
393C2×C4—1041no—
394C2×C4—1041no—
395C2×C4#8807514yescomplemented
396C2×C4C2×C22⋊Dic1312yes—
397C2×C4#8820712yes—
398C8—1042no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22C2×#8807511yescharacteristic
412C22#1171888611yescharacteristic
413C22#1171888811yescharacteristic
414C22#1171888811yescharacteristic
415C22#1171888911yescharacteristic
416C22#1171888911yescharacteristic
417C22#1171890411yescharacteristic
418C22#1171890511yescharacteristic
419C22#1171890611yescharacteristic
420C22#1171890711yescharacteristic
421C22#1171890811yescharacteristic
422C4—24no—
423C4—22no—
424C4—22no—
425C4—42no—
426C4—44no—
427C4—44no—
428C4—1042no—
429C4—1042no—
430C2—21no—
431C2—21no—
432C2—21no—
433C2—21no—
434C2#1311377611yescharacteristic
435C2#1311381011yescharacteristic
436C2#1311384411yescharacteristic
437C2#1311387811yescharacteristic
438C2#1311477111yescharacteristic
439C2#1311478411yescharacteristic
440C2#1311479511yescharacteristic
subgroupG/H
centerC23#88207
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#544C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#544D13
hypocenterC13#8406
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
8. C13×#544C4semidirect
166. C2×C4×C13#103semidirect
186. #544Dic13semidirect
344. C13#8406semidirect
395. C2×C4#88075semidirect

Maximal subgroups

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

subgroupindex
#131151442
C2×#117181302
C2×#117181202
#131130892
C2×C13×#5442
#840613