Finite Group Databasebeta

← #29575584

Subgroups — #29575584

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839815C211yesmaximal, characteristic, complemented
2C2×#16839496C212yesmaximal
3#21444046C211yesmaximal, characteristic, complemented
4#21443697C212yesmaximal, complemented
5C61×#2854C211yesmaximal, characteristic
6#16839815—24no—
7C2×C4⋊#92418—21no—
8C2×C22⋊#92418C2212yes—
9C2×C4×#92418—21no—
10C2×#14519684—21no—
11C2×#14519684—21no—
12C2×#14519684C2212yes—
13#16839496—24no—
14C2×#123×C61—21no—
15C2×#121×C61C2211yescharacteristic
16C22×C42×C61C2211yescharacteristic
17C61×#390C411yescharacteristic, complemented
18C61×#390C411yescharacteristic, complemented
19C61×#389C411yescharacteristic, complemented
20C61×#389C411yescharacteristic, complemented
21C61×#388—21no—
22C61×#388—21no—
23C61×#386—21no—
24C61×#380C2211yescharacteristic
25C23×Dic61—22no—
26C22×#92418—22no—
27C4⋊#92418—24no—
28C22⋊#92418—22no—
29C22⋊#92418D414yes—
30C4×#92418—24no—
31#14519684—24no—
32#14519684—22no—
33#14519684—22no—
34#14519684—42no—
35C22×D4×C61—21no—
36C22×D4×C61C2×C411yescharacteristic
37C23×C4×C61D411yescharacteristic
38C23×C4×C61D411yescharacteristic
39C23×C4×C61C2311yescharacteristic
40#123×C61—42no—
41#123×C61—42no—
42#121×C61—22no—
43#121×C61—22no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C42×C61—22no—
56C2×C42×C61—22no—
57C2×C42×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C2×C42×C61D411yescharacteristic
61#95×C61—21no—
62#95×C61—21no—
63#95×C61—21no—
64C24×C61—21no—
65C24×C61C2×D411yescharacteristic
66C2×D4×C61—22no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—42no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—42no—
73C22×C4×C61—22no—
74C22×C4×C61—22no—
75C22×C4×C61—22no—
76C22×C4×C61—22no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61D812yes—
88C22×C4×C61SD1612yes—
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D412yes—
92C22×C4×C61#4112yes—
93C22×Dic61—24no—
94C22×Dic61—42no—
95C22×Dic61—42no—
96C22×Dic61—42no—
97C22×Dic61—42no—
98C22×Dic61—42no—
99C22×Dic61—42no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—42no—
104C4⋊C4×C61—42no—
105C22⋊C4×C61—42no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—42no—
109C22⋊C4×C61—42no—
110C22⋊C4×C61—42no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C42×C61—22no—
114C42×C61—22no—
115C42×C61—21no—
116C42×C61—21no—
117C42×C61—21no—
118C42×C61—21no—
119C2×#92418—24no—
120C2×#92418—42no—
121C2×#92418—42no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61C2×C22⋊C411yescharacteristic
134C23×C61#12112yes—
135C23×C61C2×D811yescharacteristic
136C23×C61C2×SD1611yescharacteristic
137C23×C61#13512yes—
138D4×C61—82no—
139D4×C61—82no—
140D4×C61—82no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—24no—
152C2×C4×C61—24no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61—44no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61#10212yes—
169C2×C4×C61#10212yes—
170C2×C4×C61#10412yes—
171C2×C4×C61C4×D412yes—
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12311yescharacteristic
174C2×Dic61—44no—
175C2×Dic61—44no—
176C2×Dic61—44no—
177C2×Dic61—82no—
178C2×Dic61—82no—
179C2×Dic61—82no—
180C2×Dic61—82no—
181#92418—44no—
182#9114—611nomaximal, Sylow
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—22no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61#38611yescharacteristic
199C22×C61#41011yescharacteristic
200C22×C61#41011yescharacteristic
201C22×C61C2×#10211yescharacteristic
202C22×C61#41611yescharacteristic
203C22×C61C2×#10411yescharacteristic
204C22×C61#42111yescharacteristic
205C22×C61#46512yes—
206C22×C61#46612yes—
207C4×C61—22no—
208C4×C61—22no—
209C4×C61—22no—
210C4×C61—21no—
211C4×C61—22no—
212C4×C61—21no—
213C4×C61—41no—
214C4×C61—81no—
215C4×C61—81no—
216C4×C61—81no—
217Dic61—84no—
218C2×#431—611no—
219#2854D6111yescharacteristic
220C2×#327—612no—
221#1434—611no—
222#1294—612no—
223C2×C61—22no—
224C2×C61—22no—
225C2×C61—161no—
226C2×C61#150011yescharacteristic
227C2×C61#150211yescharacteristic
228C2×C61#151711yescharacteristic
229C2×C61#152111yescharacteristic
230C2×C61#187111yescharacteristic
231C2×C61#189311yescharacteristic
232C2×C61#189911yescharacteristic
233C2×#123—21no—
234C2×#121C2×D6111yescharacteristic
235C22×C42C2×D6111yescharacteristic
236#431—1224no—
237C2×C4⋊C8—1221no—
238C2×C22⋊C8—612no—
239C2×C4×C8—1221no—
240#390Dic6111yescharacteristic, complemented
241#390Dic6111yescharacteristic, complemented
242#389Dic6111yescharacteristic, complemented
243#389Dic6111yescharacteristic, complemented
244#388—21no—
245#388—21no—
246#386—21no—
247#380C2×D6111yescharacteristic
248C2×#95—612no—
249C2×#95—1221no—
250C2×#95—1221no—
251#327—1224no—
252C61#911411yescharacteristic, complemented, Sylow
253C22×D4—21no—
254C22×D4C2×Dic6111yescharacteristic
255C23×C4—1222no—
256C23×C4C22⋊D6111yescharacteristic
257C23×C4C22⋊D6111yescharacteristic
258C23×C4C22×D6111yescharacteristic
259C22×C8—1222no—
260#123—42no—
261#123—42no—
262#121—22no—
263#121—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×Dic6111yescharacteristic
267C2×C4⋊C4C2×Dic6111yescharacteristic
268C2×C4⋊C4C2×Dic6111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42C2×Dic6111yescharacteristic
278C2×C42C2×Dic6111yescharacteristic
279C2×C42C22⋊D6111yescharacteristic
280C2×C42C22⋊D6111yescharacteristic
281C4⋊C8—1224no—
282C22⋊C8—614no—
283C22⋊C8—1222no—
284C4×C8—1224no—
285#95—21no—
286#95—21no—
287#95—21no—
288#95—1224no—
289#95—1222no—
290#95—1222no—
291#95—2442no—
292C24—21no—
293C24C2×C22⋊D6111yescharacteristic
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—42no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—1224no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4—2442no—
315C22×C4—2442no—
316C22×C4—2442no—
317C22×C4—2442no—
318C22×C4#1175819912yes—
319C22×C4#1175820012yes—
320C22×C4C22⋊Dic6111yescharacteristic
321C22×C4C22⋊Dic6111yescharacteristic
322C22×C4C22⋊Dic6111yescharacteristic
323C22×C4C22⋊Dic6111yescharacteristic
324C22×C4D4×D6112yes—
325C22×C4#1175822412yes—
326C22×C4C22×Dic6111yescharacteristic
327C22×C4C2×C22⋊D6111yescharacteristic
328C2×C8—1224no—
329C2×C8—2442no—
330C2×C8—2442no—
331C4⋊C4—22no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C42—22no—
345C42—22no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23C2×C22⋊Dic6111yescharacteristic
362C23#1451974912yes—
363C23C2×#1175819911yescharacteristic
364C23C2×#1175820011yescharacteristic
365C23#1451979712yes—
366D4—82no—
367D4—82no—
368D4—82no—
369C2×C4—24no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—4882no—
397C2×C4—4882no—
398C2×C4—4882no—
399C2×C4—4882no—
400C2×C4—2444no—
401C2×C4—2444no—
402C2×C4—2444no—
403C2×C4#1451969812yes—
404C2×C4#1451969812yes—
405C2×C4#1451970412yes—
406C2×C4D4×Dic6112yes—
407C2×C4#1451974511yescharacteristic
408C2×C4#1451975811yescharacteristic
409C8—2444no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22#1683964211yescharacteristic
426C22#1683973611yescharacteristic
427C22#1683973611yescharacteristic
428C22C2×#1451969811yescharacteristic
429C22#1683975811yescharacteristic
430C22C2×#1451970411yescharacteristic
431C22#1683977911yescharacteristic
432C22#1683998912yes—
433C22#1683999612yes—
434C4—22no—
435C4—22no—
436C4—21no—
437C4—22no—
438C4—21no—
439C4—22no—
440C4—41no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—4884no—
445C2—22no—
446C2—22no—
447C2—161no—
448C2#2144430511yescharacteristic
449C2#2144431411yescharacteristic
450C2#2144437911yescharacteristic
451C2#2144439611yescharacteristic
452C2#2144612211yescharacteristic
453C2#2144624811yescharacteristic
454C2#2144627811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2854C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenter#2854D61
hypocenterC61#9114
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#16839815C2semidirect
3. #21444046C2semidirect
4. #21443697C2semidirect
17. C61×#390C4semidirect
18. C61×#390C4semidirect
19. C61×#389C4semidirect
20. C61×#389C4semidirect
240. #390Dic61semidirect
241. #390Dic61semidirect
242. #389Dic61semidirect
243. #389Dic61semidirect
252. C61#9114semidirect

Maximal subgroups

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

subgroupindex
C2×#168398152
C2×#168394962
#214440462
#214436972
C61×#28542
#911461