Finite Group Databasebeta

← #15754738

Subgroups — #15754738

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
1C2×#11719205C211yesmaximal, characteristic
2#13115143C212yesmaximal
3C2×#11718044C212yesmaximal
4C2×#11718120C211yesmaximal, characteristic
5C13×#1441C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88180—21no—
9C2×#88178—21no—
10C2×#88178C2212yes—
11#11719205—22no—
12#11719205—24no—
13#11719205C414yescomplemented
14C2×#88144—22no—
15C2×#88142—22no—
16C2×C13×#95—21no—
17C2×C13×#95—21no—
18C2×C13×#95C2211yescharacteristic
19C2×C22⋊#1055C2212yes—
20C2×#88050—22no—
21#11718121—22no—
22#11718120—22no—
23#11718044—24no—
24C23×C4×C13—21no—
25C23×C4×C13—21no—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C22×Dic26—21no—
30C22×Dic26D412yes—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—42no—
35C2×C13×C4⋊C4C2×C412yes—
36C2×C13×C4⋊C4D412yes—
37C2×C22⋊Dic13—22no—
38#88180—24no—
39#88180—24no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13D412yes—
44#88178—24no—
45#88178—24no—
46#88178—22no—
47#88178—22no—
48#88178C2×C414yes—
49#88178D414yes—
50C2×#6101—22no—
51C2×#6101—22no—
52C2×C4×Dic13—22no—
53C22×#1055—22no—
54#88144—28no—
55#88144—28no—
56#88142—28no—
57#88142—28no—
58C13×#95—22no—
59C13×#95—42no—
60C13×#95—42no—
61C22⋊#1055—22no—
62C22⋊#1055—22no—
63#88050—44no—
64#8406—131nomaximal, Sylow
65C24×C13C2×D411yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13C22⋊C412yes—
91C22×C4×C13C22⋊C412yes—
92C22×C4×C13SD1612yes—
93C22×C4×C13Q1612yes—
94C22×C4×C13C22×C411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D412yes—
97C22×C4×C13C2×D412yes—
98C22×Dic13—22no—
99C22×Dic13—22no—
100C2×Dic26—24no—
101C2×Dic26—22no—
102C2×Dic26—42no—
103C2×Dic26—42no—
104C2×Dic26—81no—
105C2×Dic26—81no—
106C2×Dic26C22⋊C414yes—
107C13×C4⋊C4—24no—
108C13×C4⋊C4—24no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—42no—
111C22⋊Dic13—24no—
112C22⋊Dic13—24no—
113C4⋊Dic13—24no—
114C4⋊Dic13—24no—
115C4⋊Dic13—24no—
116C4⋊Dic13—22no—
117C4⋊Dic13C22⋊C414yes—
118#6101—28no—
119#6101—24no—
120#6101—24no—
121C4×Dic13—28no—
122C2×#1055—42no—
123C2×#1055—42no—
124C2×#1055—42no—
125C2×#544—131no—
126#1872—132no—
127C2×#328—132no—
128C2×#324—131no—
129#1441D1311yescharacteristic
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
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
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—41no—
151C2×C4×C13—41no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—81no—
163C2×C4×C13—81no—
164C2×C4×C13—81no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13#10314yescomplemented
172C2×C4×C13C2×C22⋊C412yes—
173C2×C4×C13#12012yes—
174C2×Dic13—24no—
175C2×Dic13—24no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178C2×Dic13—42no—
179C2×Dic13—42no—
180Dic26—44no—
181Dic26—82no—
182Dic26—84no—
183#1055—82no—
184#544—134no—
185#544—264no—
186#544—262no—
187C2×C4⋊Q8—262no—
188C2×#125—262no—
189C2×C22⋊Q8—132no—
190C2×C22⋊Q8—261no—
191C2×#117—261no—
192C22×C4⋊C4C2×D1311yescharacteristic
193C22×C4⋊C4C2×D1311yescharacteristic
194C2×#103—262no—
195C2×C22⋊C8—132no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95C2×D1311yescharacteristic
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—42no—
229C4×C13—82no—
230C4×C13—82no—
231Dic13—44no—
232Dic13—44no—
233C22×Q8—132no—
234C22×Q8—261no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4C22⋊D1311yescharacteristic
238C23×C4C22⋊D1311yescharacteristic
239C23×C4C22×D1311yescharacteristic
240C22×C8—262no—
241C4⋊Q8—268no—
242C4⋊Q8—268no—
243#125—268no—
244#125—268no—
245C22⋊Q8—134no—
246C22⋊Q8—134no—
247C22⋊Q8—264no—
248C22⋊Q8—264no—
249C22⋊Q8—262no—
250C22⋊Q8—262no—
251#117—264no—
252#117—264no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—132no—
258C2×C4⋊C4—261no—
259C2×C4⋊C4—261no—
260C2×C4⋊C4—261no—
261C2×C4⋊C4—262no—
262C2×C4⋊C4—262no—
263C2×C4⋊C4C4×D1312yes—
264C2×C4⋊C4D5212yes—
265C2×C22⋊C4—262no—
266C2×C42—262no—
267#103—524no—
268C22⋊C8—262no—
269C22⋊C8—262no—
270#95—22no—
271#95—42no—
272#95—42no—
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—134no—
286C2×Q8—264no—
287C2×Q8—262no—
288C2×Q8—522no—
289C2×Q8—522no—
290C2×Q8—1041no—
291C2×Q8—1041no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—262no—
317C22×C4—262no—
318C22×C4#610312yes—
319C22×C4#610312yes—
320C22×C4#610512yes—
321C22×C4#610712yes—
322C22×C4C2×C4×D1311yescharacteristic
323C22×C4C2×D5211yescharacteristic
324C22×C4D4×D1312yes—
325C22×C4D4×D1312yes—
326C2×C8—522no—
327C2×C8—522no—
328C2×C8—522no—
329C4⋊C4—24no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—42no—
333C4⋊C4—134no—
334C4⋊C4—264no—
335C4⋊C4—264no—
336C4⋊C4—264no—
337C4⋊C4—268no—
338C4⋊C4—264no—
339C4⋊C4—262no—
340C4⋊C4—264no—
341C22⋊C4—264no—
342C22⋊C4—264no—
343C42—268no—
344C13#840611yescharacteristic, complemented, Sylow
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23C2×#610311yescharacteristic
350C23C2×#610511yescharacteristic
351C23#8819111yescharacteristic
352C23#8819111yescharacteristic
353C23C2×#610711yescharacteristic
354C23#8820511yescharacteristic
355C23#8820511yescharacteristic
356Q8—524no—
357Q8—1042no—
358Q8—1044no—
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—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—264no—
390C2×C4—264no—
391C2×C4—522no—
392C2×C4—522no—
393C2×C4—522no—
394C2×C4—522no—
395C2×C4#8805014yescomplemented
396C2×C4C22⋊C4×D1312yes—
397C2×C4#8813612yes—
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—
411C22#1171861611yescharacteristic
412C22C2×#8805011yescharacteristic
413C22#1171866511yescharacteristic
414C22#1171869311yescharacteristic
415C22#1171870111yescharacteristic
416C22#1171870111yescharacteristic
417C22#1171871111yescharacteristic
418C22#1171871111yescharacteristic
419C22#1171871411yescharacteristic
420C22#1171872311yescharacteristic
421C22#1171875611yescharacteristic
422C4—24no—
423C4—22no—
424C4—22no—
425C4—42no—
426C4—82no—
427C4—82no—
428C4—524no—
429C4—524no—
430C2—21no—
431C2—21no—
432C2—21no—
433C2—21no—
434C2#1311377511yescharacteristic
435C2#1311380911yescharacteristic
436C2#1311384311yescharacteristic
437C2#1311387711yescharacteristic
438C2#1311477011yescharacteristic
439C2#1311478311yescharacteristic
440C2#1311479411yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1441C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1441D13
hypocenterC13#8406
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1441

Complements

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

NH ≅ G/Ntype
13. #11719205C4semidirect
171. C2×C4×C13#103semidirect
344. C13#8406semidirect
395. C2×C4#88050semidirect

Maximal subgroups

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

subgroupindex
C2×#117192052
#131151432
C2×#117180442
C2×#117181202
C13×#14412
#840613