Finite Group Databasebeta

← #15759396

Subgroups — #15759396

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123892C211yesmaximal, characteristic
2#13113340C211yesmaximal, characteristic
3C2×#11718130C211yesmaximal, characteristic, complemented
4#13113200C211yesmaximal, characteristic, complemented
5#13112724C211yesmaximal, characteristic, complemented
6#13112678C211yesmaximal, characteristic, complemented
7C13×#3190C211yesmaximal, characteristic
8C13×#525C2211yescharacteristic
9C2×C13×C22⋊Q8C2211yescharacteristic
10C13×#485—21no—
11C13×#483C411yescharacteristic, complemented
12C13×#480C411yescharacteristic, complemented
13C13×#467—21no—
14C13×#465—21no—
15C13×#452—21no—
16C13×#451C411yescharacteristic, complemented
17C13×#448C411yescharacteristic, complemented
18C2×C13×C22⋊C8C2211yescharacteristic
19#11718895—21no—
20C2×#88071C2211yescharacteristic
21#11718868C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23C2×C22⋊#1055C2211yescharacteristic
24#11718672—21no—
25#11718672—21no—
26D4×#1055—21no—
27D4×#1055—21no—
28#11718661—21no—
29#11718130—21no—
30#11718130—21no—
31#11718130—21no—
32#11718129—21no—
33#11718120—21no—
34#11718120—21no—
35C2×C13×#41D411yescharacteristic
36C22×Q8×C13C2×C411yescharacteristic
37C23×C4×C13C2311yescharacteristic
38C23×Dic13—21no—
39C2×C13×Q16—21no—
40C2×C13×SD16—21no—
41C22×C8×C13—21no—
42C13×#123—21no—
43C13×C22⋊Q8—21no—
44C13×C22⋊Q8—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8C2×C411yescharacteristic
48C13×C22⋊Q8D411yescharacteristic
49C13×#121C2×C411yescharacteristic
50C13×#121D411yescharacteristic
51C13×#120—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C13×#117D411yescharacteristic
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4C2×C411yescharacteristic
57C2×C13×C22⋊C4—21no—
58C2×#6099—21no—
59C2×#6099—21no—
60C22×#1055—21no—
61C22×#1055—21no—
62C22×#1055—21no—
63C13×#107—21no—
64C13×#106—21no—
65C13×#103—21no—
66C13×#103—21no—
67C13×#103—21no—
68C13×#102—21no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8C2×C411yescharacteristic
71C13×C22⋊C8C2×C411yescharacteristic
72#88071—21no—
73#88071—21no—
74C22⋊#1055—21no—
75C22⋊#1055—21no—
76C22⋊#1055—21no—
77C22⋊#1055—21no—
78C22⋊#1055—21no—
79C22⋊#1055—21no—
80C22⋊#1055D411yescharacteristic
81C22⋊#1055D411yescharacteristic
82C22⋊#1055D411yescharacteristic
83C22⋊#1055D411yescharacteristic
84C4⋊#1055—21no—
85C4⋊#1055—21no—
86#88043—21no—
87C4×#1055—21no—
88#9263—131nomaximal, Sylow
89C24×C13#4111yescharacteristic
90C13×#41—81no—
91C2×Q8×C13—21no—
92C2×Q8×C13—21no—
93C2×Q8×C13—81no—
94C2×Q8×C13C22⋊C411yescharacteristic
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—21no—
98C2×D4×C13C22⋊C411yescharacteristic
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—81no—
103C22×C4×C13C22×C411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C22×Dic13—22no—
110C22×Dic13—41no—
111C22×Dic13—41no—
112C22×Dic13—81no—
113C22×Dic13—81no—
114C13×Q16—81no—
115C13×SD16—81no—
116C2×C8×C13—21no—
117C2×C8×C13—21no—
118C2×C8×C13—81no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4C22⋊C411yescharacteristic
126C13×C4⋊C4C22⋊C411yescharacteristic
127C13×C22⋊C4—21no—
128C13×C22⋊C4—21no—
129C13×C22⋊C4—21no—
130C13×C22⋊C4—21no—
131C13×C22⋊C4—21no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—41no—
134C42×C13—21no—
135#6099—81no—
136#6099—81no—
137C2×#1055—21no—
138C2×#1055—21no—
139C2×#1055—21no—
140C2×#1055—21no—
141C2×#1055—41no—
142C2×#1055—81no—
143C2×#1055—81no—
144C2×#1055—81no—
145#3190D1311yescharacteristic
146#2977—131no—
147#1504—131no—
148C2×#328—131no—
149#1472—131no—
150#1298—131no—
151#1280—131no—
152C23×C13—21no—
153C23×C13—21no—
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—21no—
157C23×C13—41no—
158C23×C13C4×D411yescharacteristic
159C23×C13#12111yescharacteristic
160C23×C13#12311yescharacteristic
161Q8×C13—41no—
162Q8×C13—41no—
163Q8×C13—41no—
164Q8×C13—81no—
165D4×C13—41no—
166D4×C13—41no—
167D4×C13—41no—
168D4×C13—41no—
169D4×C13—41no—
170D4×C13—81no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—81no—
187C2×C4×C13C2×C22⋊C411yescharacteristic
188C2×C4×C13C4×D411yescharacteristic
189C2×C4×C13#12011yescharacteristic
190C2×C4×C13#12111yescharacteristic
191C2×Dic13—42no—
192C2×Dic13—81no—
193C2×Dic13—82no—
194C2×Dic13—81no—
195C2×Dic13—82no—
196C8×C13—41no—
197C8×C13—41no—
198#1055—41no—
199#1055—41no—
200#1055—41no—
201#1055—41no—
202#1055—81no—
203#525C2×D1311yescharacteristic
204C2×C22⋊Q8C2×D1311yescharacteristic
205#485—21no—
206#483Dic1311yescharacteristic, complemented
207#480Dic1311yescharacteristic, complemented
208#467—21no—
209#465—21no—
210#452—21no—
211#451Dic1311yescharacteristic, complemented
212#448Dic1311yescharacteristic, complemented
213#435—261no—
214#435—261no—
215C8×D4—261no—
216C8×D4—261no—
217#433—261no—
218#408—261no—
219#407—131no—
220C2×C22⋊C8—131no—
221C2×C22⋊C8—131no—
222C2×C22⋊C8C2×D1311yescharacteristic
223C2×#95—131no—
224#328—261no—
225#328—261no—
226#328—261no—
227#327—261no—
228#324—261no—
229#324—261no—
230C22×C13—21no—
231C22×C13—21no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—21no—
236C22×C13—21no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13—41no—
242C22×C13—41no—
243C22×C13—41no—
244C22×C13#38611yescharacteristic
245C22×C13#44311yescharacteristic
246C22×C13#44411yescharacteristic
247C22×C13#47111yescharacteristic
248C22×C13#47311yescharacteristic
249C4×C13—21no—
250C4×C13—21no—
251C4×C13—21no—
252C4×C13—21no—
253C4×C13—41no—
254C4×C13—41no—
255C4×C13—41no—
256C4×C13—81no—
257C4×C13—81no—
258Dic13—82no—
259C2×#41C22⋊D1311yescharacteristic
260C22×Q8C2×Dic1311yescharacteristic
261C23×C4—261no—
262C23×C4C22×D1311yescharacteristic
263C2×Q16—21no—
264C2×SD16—21no—
265C2×M16—261no—
266C2×M16—261no—
267C22×C8—21no—
268C22×C8—261no—
269C22×C8—261no—
270C22×C8—261no—
271#123—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275C22⋊Q8—21no—
276C22⋊Q8C2×Dic1311yescharacteristic
277C22⋊Q8C22⋊D1311yescharacteristic
278#121C2×Dic1311yescharacteristic
279#121C22⋊D1311yescharacteristic
280#120—21no—
281C4×D4—21no—
282C4×D4—21no—
283#117C22⋊D1311yescharacteristic
284C2×C4⋊C4—21no—
285C2×C4⋊C4C2×Dic1311yescharacteristic
286C2×C22⋊C4—21no—
287#107—21no—
288#106—21no—
289C4⋊C8—261no—
290C4⋊C8—261no—
291#103—21no—
292#103—21no—
293#103—21no—
294#102—21no—
295C22⋊C8—21no—
296C22⋊C8—131no—
297C22⋊C8—131no—
298C22⋊C8—131no—
299C22⋊C8—131no—
300C22⋊C8—261no—
301C22⋊C8—261no—
302C22⋊C8—261no—
303C22⋊C8—261no—
304C22⋊C8—261no—
305C22⋊C8—261no—
306C22⋊C8C2×Dic1311yescharacteristic
307C22⋊C8C2×Dic1311yescharacteristic
308#97—261no—
309C4×C8—261no—
310#95—261no—
311#95—261no—
312C2×C13—21no—
313C2×C13—21no—
314C2×C13—21no—
315C2×C13—21no—
316C2×C13—41no—
317C2×C13—81no—
318C2×C13#187611yescharacteristic
319C2×C13#190811yescharacteristic
320C2×C13#191311yescharacteristic
321C24#612911yescharacteristic
322#41—81no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—81no—
326C2×Q8C22⋊Dic1311yescharacteristic
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4C22⋊Dic1311yescharacteristic
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—81no—
335C22×C4—262no—
336C22×C4—521no—
337C22×C4—521no—
338C22×C4—1041no—
339C22×C4—1041no—
340C22×C4D4×D1311yescharacteristic
341C22×C4D4×D1311yescharacteristic
342C22×C4#612911yescharacteristic
343C22×C4C22×Dic1311yescharacteristic
344C22×C4C2×C22⋊D1311yescharacteristic
345C22×C4C2×C22⋊D1311yescharacteristic
346Q16—81no—
347SD16—81no—
348M16—1041no—
349M16—1041no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—81no—
353C2×C8—261no—
354C2×C8—261no—
355C2×C8—261no—
356C2×C8—261no—
357C2×C8—521no—
358C2×C8—1041no—
359C2×C8—1041no—
360C2×C8—1041no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4C22⋊Dic1311yescharacteristic
368C4⋊C4C22⋊Dic1311yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C42—21no—
377C13#926311yescharacteristic, complemented, Sylow
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23D4×Dic1311yescharacteristic
385C23#8818911yescharacteristic
386C23#8819311yescharacteristic
387Q8—41no—
388Q8—41no—
389Q8—41no—
390Q8—81no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—81no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—81no—
413C2×C4—522no—
414C2×C4—1041no—
415C2×C4—1042no—
416C2×C4—1041no—
417C2×C4—1042no—
418C2×C4D4×Dic1311yescharacteristic
419C2×C4#8819111yescharacteristic
420C2×C4#8819311yescharacteristic
421C2×C4C2×C22⋊Dic1311yescharacteristic
422C8—41no—
423C8—41no—
424C8—521no—
425C8—521no—
426C8—521no—
427C8—521no—
428C8—1041no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22#1171885711yescharacteristic
444C22#1171885811yescharacteristic
445C22#1171886411yescharacteristic
446C22#1171886511yescharacteristic
447C22#1171888111yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—81no—
456C4—81no—
457C4—1042no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—41no—
463C2—81no—
464C2#1311516511yescharacteristic
465C2#1311535311yescharacteristic
466C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#3190C2
socleC22×C13#386
prime radicalC13×#525C22
cosocleC23×C4×C13C23
hypercenter#3190D13
hypocenterC13#9263
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3190

Complements

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

NH ≅ G/Ntype
3. C2×#11718130C2semidirect
4. #13113200C2semidirect
5. #13112724C2semidirect
6. #13112678C2semidirect
11. C13×#483C4semidirect
12. C13×#480C4semidirect
16. C13×#451C4semidirect
17. C13×#448C4semidirect
206. #483Dic13semidirect
207. #480Dic13semidirect
211. #451Dic13semidirect
212. #448Dic13semidirect
377. C13#9263semidirect

Maximal subgroups

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

subgroupindex
#131238922
#131133402
C2×#117181302
#131132002
#131127242
#131126782
C13×#31902
#926313