Finite Group Databasebeta

← #16785737

Subgroups — #16785737

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊#108C211yesmaximal, characteristic
2C2×#11719089C211yesmaximal, characteristic
3#13130539C212yesmaximal
4#13130523C212yesmaximal
5C2×D13×#107C211yesmaximal, characteristic
6C2×#88237C2211yescharacteristic
7C2×D13⋊M16C2212yes—
8C2×D13⋊M16C2211yescharacteristic
9C22×C8×D13C2211yescharacteristic
10C2×C4⋊C4×D13C2212yes—
11D13⋊#108—22no—
12D13⋊#108C414yescomplemented
13C2×#88104—21no—
14C2×#88103—21no—
15#11719089—22no—
16#11719089C414yescomplemented
17C2×#88100—21no—
18C2×C8×#261—21no—
19C2×C13×#107C411yescharacteristic, complemented
20C2×#88058C411yescharacteristic, complemented
21C2×#88047C412yescomplemented
22D13×#107—21no—
23D13×#107—21no—
24D13×#107—21no—
25D13×#107—21no—
26#11718291—24no—
27#11718246—24no—
28C22×C4×D13—22no—
29C22×C4×D13C2311yescharacteristic
30C2×C22⋊#261—21no—
31C2×#6122—22no—
32C2×#6122D412yes—
33#88237—21no—
34#88237—21no—
35#88237C2×C412yes—
36#88237Q812yes—
37C2×C4⋊#261D412yes—
38C2×C4×#261—21no—
39D13⋊M16—21no—
40D13⋊M16—21no—
41D13⋊M16—22no—
42D13⋊M16—22no—
43D13⋊M16—22no—
44D13⋊M16C2×C414yes—
45D13⋊M16C2×C412yes—
46D13⋊M16Q812yes—
47C2×#6118—21no—
48C2×#6118—22no—
49C2×D13⋊C8—21no—
50C2×D13⋊C8—22no—
51C22×C8×C13C2×C411yescharacteristic
52C2×C13×C4⋊C4C2×C412yes—
53C2×C4⋊Dic13C2×C412yes—
54C2×#6101—22no—
55C22×#1055C2×C411yescharacteristic
56C2×C8×D13C2×C412yes—
57C2×C8×D13C2×C412yes—
58C2×C8×D13D412yes—
59C2×C8×D13D411yescharacteristic
60C2×C8×D13D411yescharacteristic
61C2×C8×D13D411yescharacteristic
62C2×C8×D13D411yescharacteristic
63C2×C8×D13Q812yes—
64C4⋊C4×D13—22no—
65C4⋊C4×D13—22no—
66C4⋊C4×D13—22no—
67C4⋊C4×D13—22no—
68#88104—24no—
69#88103—24no—
70#88100—24no—
71C8×#261—24no—
72C13×#107—21no—
73C13×#107—21no—
74#88058—21no—
75#88058—21no—
76#88047—22no—
77#88047—22no—
78#10870—131nomaximal, Sylow
79C23×D13#4111yescharacteristic
80C22×#261—22no—
81C22×C4×C13—22no—
82C22×C4×C13C22×C411yescharacteristic
83C22×Dic13—22no—
84C22×Dic13C2×D411yescharacteristic
85C2×C4×D13—42no—
86C2×C4×D13—42no—
87C2×C4×D13—84no—
88C2×C4×D13C22×C411yescharacteristic
89C2×C4×D13C22×C411yescharacteristic
90C2×C4×D13C2×D411yescharacteristic
91C2×C4×D13C2×D411yescharacteristic
92C2×C4×D13C2×D411yescharacteristic
93C2×C4×D13C2×D411yescharacteristic
94C2×C4×D13C2×Q811yescharacteristic
95C2×C4×D13C2×Q811yescharacteristic
96C2×C4×D13C2×Q811yescharacteristic
97C2×C4×D13#4111yescharacteristic
98C2×C4×D13#4111yescharacteristic
99C2×C4×D13#4111yescharacteristic
100C22⋊#261—22no—
101C22⋊#261—22no—
102#6122—22no—
103#6122—24no—
104#6122—42no—
105#6122C4⋊C414yes—
106C2×#1057—22no—
107C2×#1057—42no—
108C4⋊#261—22no—
109C4⋊#261C4⋊C414yes—
110C4×#261—22no—
111C4×#261—22no—
112#6118—22no—
113#6118—22no—
114#6118—24no—
115#6118—42no—
116D13⋊C8—22no—
117D13⋊C8—22no—
118D13⋊C8—24no—
119D13⋊C8—42no—
120C2×C8×C13C4212yes—
121C2×C8×C13C22⋊C411yescharacteristic
122C2×C8×C13C22⋊C411yescharacteristic
123C2×C8×C13C4⋊C412yes—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—22no—
126C4⋊Dic13—22no—
127C4⋊Dic13—22no—
128#6101—42no—
129#6101—42no—
130C2×#1055C4212yes—
131C2×#1055C22⋊C411yescharacteristic
132C2×#1055C22⋊C411yescharacteristic
133C2×#1055C4⋊C412yes—
134C8×D13C22⋊C412yes—
135C8×D13C22⋊C412yes—
136C8×D13C22⋊C412yes—
137C8×D13C22⋊C412yes—
138C8×D13C4⋊C412yes—
139C8×D13C4⋊C412yes—
140C8×D13C4⋊C412yes—
141C8×D13C4⋊C412yes—
142C22×#108—131no—
143C22×#107—131no—
144C2×#405—131no—
145C2×#343—132no—
146#1736—132no—
147C23×C13C4×D411yescharacteristic
148C22×D13—22no—
149C22×D13—22no—
150C22×D13#11711yescharacteristic
151C22×D13C4×Q811yescharacteristic
152C22×D13#12111yescharacteristic
153C22×D13C22⋊Q811yescharacteristic
154C22×D13#12411yescharacteristic
155C22×D13#12511yescharacteristic
156C2×#261—24no—
157C2×#261—42no—
158C2×#261—42no—
159C2×C4×C13—42no—
160C2×C4×C13—82no—
161C2×C4×C13C2×C4211yescharacteristic
162C2×C4×C13C2×C22⋊C411yescharacteristic
163C2×C4×C13C2×C4⋊C411yescharacteristic
164C2×C4×C13C4×D411yescharacteristic
165C2×C4×C13C4×Q811yescharacteristic
166C2×C4×C13C4×Q811yescharacteristic
167C2×Dic13—42no—
168C2×Dic13—82no—
169C2×Dic13C2×C4⋊C411yescharacteristic
170C2×Dic13C4×D411yescharacteristic
171C2×Dic13#12111yescharacteristic
172C2×Dic13#12111yescharacteristic
173C2×Dic13#12711yescharacteristic
174C2×Dic13C4⋊Q811yescharacteristic
175C4×D13—84no—
176C4×D13—84no—
177C4×D13C2×C22⋊C411yescharacteristic
178C4×D13C2×C22⋊C411yescharacteristic
179C4×D13C2×C4⋊C411yescharacteristic
180C4×D13C2×C4⋊C411yescharacteristic
181C4×D13C2×C4⋊C411yescharacteristic
182C4×D13#11711yescharacteristic
183C4×D13C4×D411yescharacteristic
184C4×D13C4×Q811yescharacteristic
185C4×D13#12111yescharacteristic
186C4×D13C22⋊Q811yescharacteristic
187C4×D13C22⋊Q811yescharacteristic
188C4×D13C22⋊Q811yescharacteristic
189C4×D13#12411yescharacteristic
190C4×D13#12511yescharacteristic
191C4×D13C4⋊Q811yescharacteristic
192C4×D13C4⋊Q811yescharacteristic
193#1057—24no—
194#1057—44no—
195C8×C13#9512yes—
196C8×C13#9512yes—
197#1055#9512yes—
198#1055#9512yes—
199C22×M16—131no—
200C22×M16—132no—
201C23×C8—131no—
202C2×#117—131no—
203C22×C4⋊C4—132no—
204C2×#108—134no—
205C2×#108—261no—
206C2×#108—261no—
207C2×#108—262no—
208C2×#107—131no—
209C2×#107—132no—
210C2×#107—261no—
211C2×#107—261no—
212C2×#107—261no—
213C2×#107—261no—
214C2×#107#26111yescharacteristic, complemented
215#405—134no—
216#405—262no—
217C2×#97—261no—
218C2×C4×C8—261no—
219#343—264no—
220#340—264no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13C4×C4⋊C411yescharacteristic
224C22×C13#38911yescharacteristic
225C22×C13#39011yescharacteristic
226C2×D13—21no—
227C2×D13—21no—
228C2×D13—22no—
229C2×D13—22no—
230C2×D13—22no—
231C2×D13—22no—
232C2×D13#38011yescharacteristic
233C2×D13#38211yescharacteristic
234C2×D13#38911yescharacteristic
235C2×D13#39111yescharacteristic
236C2×D13#47212yes—
237C2×D13#47312yes—
238#261—44no—
239C4×C13—82no—
240C4×C13C2×#9511yescharacteristic
241C4×C13C4×C4⋊C411yescharacteristic
242C4×C13#38911yescharacteristic
243C4×C13#39111yescharacteristic
244Dic13—82no—
245Dic13#38011yescharacteristic
246Dic13#38411yescharacteristic
247Dic13#38911yescharacteristic
248Dic13#39011yescharacteristic
249C23×C4—131no—
250C23×C4—262no—
251C2×M16—132no—
252C2×M16—132no—
253C2×M16—132no—
254C2×M16—134no—
255C2×M16—261no—
256C2×M16—261no—
257C2×M16—261no—
258C2×M16—262no—
259C2×M16—262no—
260C2×M16—262no—
261C2×M16—262no—
262C2×M16—262no—
263C22×C8—131no—
264C22×C8—132no—
265C22×C8—132no—
266C22×C8—132no—
267C22×C8—132no—
268C22×C8—131no—
269C22×C8—131no—
270C22×C8—131no—
271C22×C8—131no—
272C22×C8—261no—
273C22×C8—262no—
274C22×C8C2×#26111yescharacteristic
275#117—132no—
276#117—132no—
277#117—261no—
278#117—261no—
279C2×C4⋊C4—132no—
280C2×C4⋊C4—132no—
281C2×C4⋊C4—262no—
282C2×C4⋊C4—262no—
283C2×C4⋊C4—262no—
284C2×C4⋊C4—262no—
285C2×C4⋊C4—262no—
286C2×C4⋊C4C2×#26112yes—
287C2×C22⋊C4—261no—
288C2×C42—261no—
289#108—264no—
290#108—264no—
291#107—21no—
292#107—21no—
293#107—262no—
294#107—262no—
295#107—261no—
296#107—261no—
297#97—264no—
298C4×C8—264no—
299C2×C13—21no—
300C2×C13—21no—
301C2×C13C4⋊#9511yescharacteristic
302C2×C13#197811yescharacteristic
303C2×C13#197911yescharacteristic
304D13—21no—
305D13—21no—
306D13#181612yes—
307D13#195212yes—
308C24—131no—
309C22×C4—22no—
310C22×C4—131no—
311C22×C4—131no—
312C22×C4—131no—
313C22×C4—131no—
314C22×C4—131no—
315C22×C4—131no—
316C22×C4—131no—
317C22×C4—131no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—131no—
322C22×C4—131no—
323C22×C4—262no—
324C22×C4—262no—
325C22×C4—522no—
326C22×C4—522no—
327C22×C4—1044no—
328C22×C4C22×#26111yescharacteristic
329M16—134no—
330M16—262no—
331M16—262no—
332M16—262no—
333M16—264no—
334M16—264no—
335M16—522no—
336M16—522no—
337C2×C8—132no—
338C2×C8—132no—
339C2×C8—131no—
340C2×C8—131no—
341C2×C8—132no—
342C2×C8—132no—
343C2×C8—132no—
344C2×C8—132no—
345C2×C8—132no—
346C2×C8—132no—
347C2×C8—132no—
348C2×C8—132no—
349C2×C8—262no—
350C2×C8—262no—
351C2×C8—262no—
352C2×C8—264no—
353C2×C8—522no—
354C2×C8—522no—
355C2×C8C4×#26112yes—
356C2×C8C4⋊#26112yes—
357C2×C8C22⋊#26111yescharacteristic
358C2×C8C22⋊#26111yescharacteristic
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—134no—
362C4⋊C4—262no—
363C4⋊C4—262no—
364C4⋊C4—262no—
365C4⋊C4—522no—
366C4⋊C4—522no—
367C22⋊C4—262no—
368C22⋊C4—262no—
369C42—262no—
370C42—262no—
371C13#1087011yescharacteristic, complemented, Sylow
372C23—131no—
373C23—131no—
374C23—131no—
375C23—131no—
376C23—131no—
377C23—131no—
378C23—262no—
379C23—262no—
380C23D4×#26111yescharacteristic
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—131no—
384C2×C4—131no—
385C2×C4—131no—
386C2×C4—131no—
387C2×C4—131no—
388C2×C4—131no—
389C2×C4—131no—
390C2×C4—131no—
391C2×C4—131no—
392C2×C4—131no—
393C2×C4—131no—
394C2×C4—131no—
395C2×C4—131no—
396C2×C4—131no—
397C2×C4—131no—
398C2×C4—131no—
399C2×C4—131no—
400C2×C4—131no—
401C2×C4—131no—
402C2×C4—131no—
403C2×C4—131no—
404C2×C4—131no—
405C2×C4—264no—
406C2×C4—522no—
407C2×C4—522no—
408C2×C4—522no—
409C2×C4—1044no—
410C2×C4—1044no—
411C2×C4—1042no—
412C2×C4C2×C4×#26111yescharacteristic
413C2×C4C2×C4⋊#26111yescharacteristic
414C2×C4D4×#26111yescharacteristic
415C2×C4Q8×#26111yescharacteristic
416C2×C4Q8×#26111yescharacteristic
417C2×C4C2×C22⋊#26111yescharacteristic
418C8—132no—
419C8—132no—
420C8—264no—
421C8—524no—
422C8(C2×#261)⋊C412yes—
423C8(C2×#261)⋊C412yes—
424C22—21no—
425C22—21no—
426C22—131no—
427C22—131no—
428C22—132no—
429C22—132no—
430C22—131no—
431C22—131no—
432C22—262no—
433C22—262no—
434C22—262no—
435C22—262no—
436C22—261no—
437C22—261no—
438C22C4⋊C4×#26111yescharacteristic
439C22#1171908311yescharacteristic
440C22#1171915111yescharacteristic
441C4—82no—
442C4—131no—
443C4—131no—
444C4—131no—
445C4—131no—
446C4—524no—
447C4—1042no—
448C4C4⋊C4×#26111yescharacteristic
449C4#1171908311yescharacteristic
450C4C2×(C2×#261)⋊C411yescharacteristic
451C4(C2×#261)⋊Q811yescharacteristic
452C2—21no—
453C2—21no—
454C2—132no—
455C2—132no—
456C2—261no—
457C2—261no—
458C2#1313001311yescharacteristic
459C2#1313099711yescharacteristic
460C2#1313099811yescharacteristic
subgroupG/H
centerC22#11719151
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C13×#107C4
socleC22×C13#390
prime radicalC23×D13#41
cosocleC22×C4×D13C23
hypercenterC2×#107#261
hypocenterC13#10870
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
12. D13⋊#108C4semidirect
16. #11719089C4semidirect
19. C2×C13×#107C4semidirect
20. C2×#88058C4semidirect
21. C2×#88047C4semidirect
214. C2×#107#261semidirect
371. C13#10870semidirect

Maximal subgroups

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

subgroupindex
C2×D13⋊#1082
C2×#117190892
#131305392
#131305232
C2×D13×#1072
#1087013