Finite Group Databasebeta

← #28307512

Subgroups — #28307512

Order 13568.

778 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811626C211yesmaximal, characteristic
2C2×#16811503C212yesmaximal
3C2×#16811503C212yesmaximal
4#20290378C211yesmaximal, characteristic
5C2×#16810520C211yesmaximal, characteristic
6C22×#11719940C2212yes—
7C22×#11719940C2212yes—
8#16811626—24no—
9C2×#13133284—21no—
10C2×C4⋊#88324—21no—
11#16811503—24no—
12#16811503—24no—
13#16811489—21no—
14#16811489—21no—
15C22×C4⋊Dic53C411yescharacteristic
16C22×#11719919C411yescharacteristic
17C22×#11719919C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×C4×Dic53C2211yescharacteristic
20#16810520—21no—
21#16810520—21no—
22#16810520—21no—
23#16810520—21no—
24C2×#13133124C411yescharacteristic
25C2×#95×C53C411yescharacteristic
26C2×#11719940—22no—
27C2×#11719940—22no—
28C2×#11719940—22no—
29C2×#11719940—22no—
30C2×#11719940—22no—
31C2×#11719940—22no—
32C2×#11719940—22no—
33C2×#11719940—22no—
34C2×#11719940—22no—
35C2×#11719940—22no—
36C2×#11719940D414yes—
37C2×#11719940Q814yes—
38C22×#88324—22no—
39C22×#88324—22no—
40#13133284—24no—
41C4⋊#88324—24no—
42C23×Dic53C2×C411yescharacteristic
43C23×Dic53C2×C411yescharacteristic
44C23×Dic53C2×C411yescharacteristic
45C23×Dic53C2311yescharacteristic
46C2×C4⋊Dic53—21no—
47C2×C4⋊Dic53—21no—
48C2×C4⋊Dic53—42no—
49C2×#11719919—21no—
50C2×#11719919—21no—
51C2×#11719919—21no—
52C2×#11719919—21no—
53C2×#11719919—21no—
54C2×#11719919—21no—
55C2×#11719919—22no—
56C2×#11719919—21no—
57C2×#11719919—21no—
58C2×#11719919—22no—
59C2×#11719919—42no—
60C2×#11719919D412yes—
61C2×#11719919Q812yes—
62C2×C4×Dic53—22no—
63C2×C4×Dic53—22no—
64C2×C4×Dic53D411yescharacteristic
65C2×C4×Dic53D411yescharacteristic
66C2×C4×Dic53D411yescharacteristic
67C2×C4×Dic53D411yescharacteristic
68#13133124—21no—
69#13133124—21no—
70C23×C4×C53C2×C411yescharacteristic
71C23×C4×C53C2×C411yescharacteristic
72C23×C4×C53C2×C411yescharacteristic
73#95×C53—21no—
74#95×C53—21no—
75C24×C53C22×C411yescharacteristic
76C22×C4×C53—21no—
77C22×C4×C53—21no—
78C22×C4×C53—22no—
79C22×C4×C53—22no—
80C22×C4×C53—21no—
81C22×C4×C53—22no—
82C22×C4×C53—41no—
83C22×C4×C53—41no—
84C22×C4×C53—41no—
85C22×C4×C53—41no—
86C22×C4×C53—41no—
87C22×C4×C53C22⋊C411yescharacteristic
88C22×C4×C53C22⋊C411yescharacteristic
89C22×C4×C53C4⋊C412yes—
90C22×Dic53—21no—
91C22×Dic53—21no—
92C22×Dic53—22no—
93C22×Dic53—22no—
94C22×Dic53—21no—
95C22×Dic53—22no—
96C22×Dic53—41no—
97C22×Dic53—41no—
98C22×Dic53—41no—
99C22×Dic53—41no—
100C22×Dic53—41no—
101C22×Dic53C22⋊C411yescharacteristic
102C22×Dic53C22⋊C411yescharacteristic
103C22×Dic53C4⋊C412yes—
104C22×Dic53C2×D412yes—
105C22×Dic53C2×D411yescharacteristic
106C22×Dic53C2×D411yescharacteristic
107C22×Dic53C2×D411yescharacteristic
108C22×Dic53C2×Q812yes—
109C22×Dic53C2×Q811yescharacteristic
110C22×Dic53#4111yescharacteristic
111C22×Dic53#4111yescharacteristic
112C22×Dic53#4112yes—
113C22×Dic53#4112yes—
114#11719940—24no—
115#11719940—24no—
116#11719940—24no—
117#11719940—24no—
118#11719940—42no—
119#11719940—42no—
120#11719940—42no—
121#11719940—42no—
122C2×#88324—24no—
123C2×#88324—24no—
124C2×#88324—42no—
125C2×#88324—42no—
126C2×#88324—42no—
127C2×#88324—42no—
128C4⋊Dic53—42no—
129C4⋊Dic53—42no—
130#11719919—22no—
131#11719919—22no—
132#11719919—22no—
133#11719919—22no—
134#11719919—42no—
135#11719919—42no—
136#11719919—41no—
137#11719919—42no—
138#11719919—41no—
139C4×Dic53—21no—
140C4×Dic53—21no—
141C4×Dic53—22no—
142C4×Dic53—22no—
143C4×Dic53—21no—
144C4×Dic53—21no—
145C23×C53—21no—
146C23×C53—21no—
147C23×C53—21no—
148C23×C53—21no—
149C23×C53C2×C22⋊C411yescharacteristic
150C23×C53C2×C4⋊C411yescharacteristic
151C23×C53#11711yescharacteristic
152C23×C53C4×D412yes—
153C23×C53C4×Q812yes—
154C2×C4×C53—21no—
155C2×C4×C53—21no—
156C2×C4×C53—22no—
157C2×C4×C53—21no—
158C2×C4×C53—21no—
159C2×C4×C53—21no—
160C2×C4×C53—44no—
161C2×C4×C53—42no—
162C2×C4×C53—41no—
163C2×C4×C53—41no—
164C2×C4×C53—42no—
165C2×C4×C53—41no—
166C2×C4×C53—41no—
167C2×C4×C53—41no—
168C2×C4×C53—82no—
169C2×C4×C53#10112yes—
170C2×Dic53—21no—
171C2×Dic53—21no—
172C2×Dic53—22no—
173C2×Dic53—21no—
174C2×Dic53—21no—
175C2×Dic53—21no—
176C2×Dic53—44no—
177C2×Dic53—42no—
178C2×Dic53—41no—
179C2×Dic53—41no—
180C2×Dic53—42no—
181C2×Dic53—41no—
182C2×Dic53—41no—
183C2×Dic53—41no—
184C2×Dic53—82no—
185C2×Dic53#10012yes—
186C2×Dic53#12011yescharacteristic
187C2×Dic53#12112yes—
188C2×Dic53#12111yescharacteristic
189C2×Dic53#12111yescharacteristic
190C2×Dic53#12112yes—
191C2×Dic53C22⋊Q812yes—
192C2×Dic53C22⋊Q811yescharacteristic
193C2×Dic53C22⋊Q812yes—
194C2×Dic53C22⋊Q812yes—
195C2×Dic53C22⋊Q811yescharacteristic
196C2×Dic53#12312yes—
197C2×Dic53#12311yescharacteristic
198C2×Dic53#12411yescharacteristic
199C2×Dic53#12512yes—
200C2×Dic53#12512yes—
201C2×Dic53#12612yes—
202C2×Dic53C4⋊Q812yes—
203C2×Dic53C4⋊Q811yescharacteristic
204#88324—44no—
205#88324—44no—
206#11204—531nomaximal, Sylow
207C22×C53—21no—
208C22×C53—21no—
209C22×C53—21no—
210C22×C53—21no—
211C22×C53—22no—
212C22×C53—22no—
213C22×C53—22no—
214C22×C53—22no—
215C22×C53#38011yescharacteristic
216C22×C53#38611yescharacteristic
217C22×C53#38712yes—
218C22×C53#38912yes—
219C22×C53#39111yescharacteristic
220C22×C53C2×#10011yescharacteristic
221C22×C53C2×#10111yescharacteristic
222C22×C53#41311yescharacteristic
223C22×C53#41311yescharacteristic
224C4×C53—22no—
225C4×C53—42no—
226C4×C53—41no—
227C4×C53—81no—
228Dic53—22no—
229Dic53—42no—
230Dic53—41no—
231Dic53—81no—
232Dic53#39411yescharacteristic
233Dic53#39511yescharacteristic
234Dic53#39612yes—
235Dic53#39811yescharacteristic
236Dic53#39812yes—
237Dic53#40011yescharacteristic
238C2×#423—531no—
239C2×#389—531no—
240C2×#343—532no—
241C2×#343—532no—
242#1728—531no—
243C2×C53—22no—
244C2×C53—22no—
245C2×C53#144111yescharacteristic
246C2×C53#180011yescharacteristic
247C2×C53#180111yescharacteristic
248C2×C53#190011yescharacteristic
249C2×C53#190111yescharacteristic
250C2×C53#199711yescharacteristic
251C2×C53#199811yescharacteristic
252C22×M16—532no—
253C22×M16—532no—
254C22×C4⋊C4—531no—
255C22×C4⋊C4—531no—
256C22×C4⋊C4—531no—
257C22×C4⋊C4—531no—
258C22×C42—531no—
259#423—1064no—
260C2×C4⋊C8—1061no—
261C2×C4⋊C8—1061no—
262#389—1061no—
263#389—1061no—
264#389—1061no—
265#389—1061no—
266C2×#95—531no—
267C2×#95#615711yescharacteristic
268#343—1064no—
269#343—1064no—
270#336—1061no—
271#336—1061no—
272C53#1120411yescharacteristic, complemented, Sylow
273C23×C4—531no—
274C23×C4—531no—
275C23×C4—531no—
276C23×C4—531no—
277C23×C4C2×#615711yescharacteristic
278C23×C4C2×#615711yescharacteristic
279C23×C4C2×#615711yescharacteristic
280C2×M16—534no—
281C2×M16—534no—
282C2×M16—1062no—
283C2×M16—1062no—
284C2×M16—1062no—
285C2×M16—1062no—
286C2×M16—1062no—
287C2×M16—1062no—
288C2×M16—1062no—
289C2×M16—1062no—
290C2×M16—1062no—
291C2×M16—1062no—
292C22×C8—1062no—
293C22×C8—1062no—
294C2×C4⋊C4—532no—
295C2×C4⋊C4—532no—
296C2×C4⋊C4—1061no—
297C2×C4⋊C4—1061no—
298C2×C4⋊C4—1061no—
299C2×C4⋊C4—1061no—
300C2×C4⋊C4—1062no—
301C2×C4⋊C4—1062no—
302C2×C4⋊C4—1061no—
303C2×C4⋊C4—1061no—
304C2×C4⋊C4—1061no—
305C2×C4⋊C4—1061no—
306C2×C4⋊C4—1061no—
307C2×C4⋊C4—1061no—
308C2×C4⋊C4—2122no—
309C2×C4⋊C4—2122no—
310C2×C42—531no—
311C2×C42—531no—
312C2×C42—531no—
313C2×C42—531no—
314C2×C42—1062no—
315C2×C42—1062no—
316C4⋊C8—1064no—
317C4⋊C8—1064no—
318#95—21no—
319#95—21no—
320#95—1061no—
321#95—1061no—
322C24C22×#615711yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—531no—
335C22×C4—531no—
336C22×C4—531no—
337C22×C4—531no—
338C22×C4—531no—
339C22×C4—531no—
340C22×C4—532no—
341C22×C4—532no—
342C22×C4—532no—
343C22×C4—532no—
344C22×C4—531no—
345C22×C4—531no—
346C22×C4—532no—
347C22×C4—1062no—
348C22×C4—1061no—
349C22×C4—1061no—
350C22×C4—1062no—
351C22×C4—1062no—
352C22×C4—1061no—
353C22×C4—2121no—
354C22×C4—2121no—
355C22×C4—2121no—
356C22×C4—2121no—
357C22×C4—2121no—
358C22×C4C4⋊#615712yes—
359C22×C4C22⋊#615711yescharacteristic
360C22×C4C22⋊#615711yescharacteristic
361M16—1064no—
362M16—1064no—
363M16—1064no—
364M16—1064no—
365M16—2122no—
366M16—2122no—
367M16—2122no—
368M16—2122no—
369C2×C8—1064no—
370C2×C8—1064no—
371C2×C8—2122no—
372C2×C8—2122no—
373C2×C8—2122no—
374C2×C8—2122no—
375C4⋊C4—1062no—
376C4⋊C4—1062no—
377C4⋊C4—1062no—
378C4⋊C4—1062no—
379C4⋊C4—2121no—
380C4⋊C4—2122no—
381C4⋊C4—2121no—
382C4⋊C4—2122no—
383C4⋊C4—2122no—
384C4⋊C4—2122no—
385C4⋊C4—2122no—
386C42—1061no—
387C42—1061no—
388C42—1062no—
389C42—1061no—
390C42—1062no—
391C42—1061no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23C2×C22⋊#615711yescharacteristic
397C23C2×C4⋊#615711yescharacteristic
398C23#1313329611yescharacteristic
399C23D4×#615712yes—
400C23Q8×#615712yes—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4—531no—
417C2×C4—531no—
418C2×C4—531no—
419C2×C4—531no—
420C2×C4—531no—
421C2×C4—532no—
422C2×C4—531no—
423C2×C4—532no—
424C2×C4—532no—
425C2×C4—532no—
426C2×C4—532no—
427C2×C4—532no—
428C2×C4—532no—
429C2×C4—532no—
430C2×C4—532no—
431C2×C4—532no—
432C2×C4—531no—
433C2×C4—531no—
434C2×C4—532no—
435C2×C4—1061no—
436C2×C4—1061no—
437C2×C4—1062no—
438C2×C4—1061no—
439C2×C4—1061no—
440C2×C4—1061no—
441C2×C4—4242no—
442C2×C4—2124no—
443C2×C4—2121no—
444C2×C4—2121no—
445C2×C4—2121no—
446C2×C4—2122no—
447C2×C4—2121no—
448C2×C4—2121no—
449C2×C4—2122no—
450C2×C4#1313327812yes—
451C8—2124no—
452C8—2124no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22#1681156511yescharacteristic
462C22#1681157111yescharacteristic
463C22#1681157212yes—
464C22#1681157412yes—
465C22(C2×#6157)⋊Q811yescharacteristic
466C22D53⋊#10011yescharacteristic
467C22C2×#1313327811yescharacteristic
468C22#1681160911yescharacteristic
469C22#1681161011yescharacteristic
470C4—22no—
471C4—42no—
472C4—41no—
473C4—81no—
474C4—531no—
475C4—532no—
476C4—531no—
477C4—531no—
478C4—532no—
479C4—531no—
480C4—1062no—
481C4—4241no—
482C4—2122no—
483C4—2121no—
484C2—22no—
485C2—22no—
486C2#2028990011yescharacteristic
487C2#2029058011yescharacteristic
488C2#2029058111yescharacteristic
489C2#2029074111yescharacteristic
490C2#2029074211yescharacteristic
491C2#2029090811yescharacteristic
492C2#2029090911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutator, prime radicalC24×C53C22×C4
FrattiniC24C22×#6157
FittingC2×#95×C53C4
socleC23×C53C2×C22⋊C4
cosocleC23×Dic53C23
hypercenterC2×#95#6157
hypocenterC53#11204
LCSG ▷ C24×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
272. C53#11204semidirect

Maximal subgroups

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

subgroupindex
C2×#168116262
C2×#168115032
#202903782
C2×#168105202
#1120453