Finite Group Databasebeta

← #29575757

Subgroups — #29575757

Order 15616.

756 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
1#21454151C211yesmaximal, characteristic
2C2×#16839607C211yesmaximal, characteristic, complemented
3#21445885C211yesmaximal, characteristic, complemented
4C2×#16839497C211yesmaximal, characteristic
5C2×#16839495C211yesmaximal, characteristic
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C2×#14519761—21no—
9C2×#14519751C2211yescharacteristic
10C22×C4×Dic61—21no—
11C22×C4×Dic61C2211yescharacteristic
12C2×C22⋊#92418C2211yescharacteristic
13#16839663C412yescomplemented
14#16839661C412yescomplemented
15#16839654—22no—
16#16839639—21no—
17#16839607—22no—
18#16839607—22no—
19C2×#14519684—21no—
20C2×#14519684C2211yescharacteristic
21#16839516—22no—
22#16839497—22no—
23#16839495—22no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61—21no—
30C23×Dic61D411yescharacteristic
31C23×Dic61D411yescharacteristic
32C22×#92418—21no—
33#14519761—42no—
34#14519761—42no—
35#14519751—21no—
36#14519751—21no—
37#14519751—21no—
38#14519751—21no—
39C2×C4⋊Dic61—22no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—22no—
43C2×#11758198—22no—
44C2×C4×Dic61—28no—
45C2×C4×Dic61—24no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61C2×C412yes—
51C2×C4×Dic61D412yes—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519684—24no—
55#14519684—21no—
56#14519684—22no—
57#14519684D412yes—
58C23×C4×C61—21no—
59C23×C4×C61C2311yescharacteristic
60C22×C8×C61—21no—
61C2×C4⋊C4×C61C2×C412yes—
62C2×C22⋊C4×C61—21no—
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65#95×C61—21no—
66#95×C61—21no—
67#95×C61D412yes—
68C24×C61C2×D411yescharacteristic
69C23×D61—21no—
70C22×C4×C61—24no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—42no—
74C22×C4×C61—42no—
75C22×C4×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—24no—
92C22×Dic61—24no—
93C22×Dic61—22no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61—42no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61C22⋊C412yes—
105C22×Dic61C22⋊C412yes—
106C2×D244—21no—
107C2×D244—21no—
108C2×D244—42no—
109C2×C8×C61—42no—
110C2×C8×C61—41no—
111C4⋊C4×C61—42no—
112C22⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114#11758198—44no—
115#11758198—41no—
116#11758198—41no—
117#11758198—44no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—44no—
121C4×Dic61—216no—
122C4×Dic61—22no—
123C4×Dic61—22no—
124C4×Dic61—22no—
125C4×Dic61—22no—
126C2×#92418—42no—
127C2×#92418—41no—
128C23×C61—22no—
129C23×C61—22no—
130C23×C61C2×C22⋊C411yescharacteristic
131C23×C61#12011yescharacteristic
132C23×C61#12311yescharacteristic
133C23×C61#13511yescharacteristic
134C23×C61#13511yescharacteristic
135C23×C61AGL(1,ℤ/8)11yescharacteristic
136C23×C61AGL(1,ℤ/8)11yescharacteristic
137C22×D61—41no—
138C22×D61—42no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—42no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61—24no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—44no—
151C2×C4×C61—44no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C22⋊D61—81no—
161C22⋊D61—81no—
162C22⋊D61—81no—
163C22⋊D61—81no—
164C2×Dic61—24no—
165C2×Dic61—24no—
166C2×Dic61—22no—
167C2×Dic61—22no—
168C2×Dic61—24no—
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—22no—
172C2×Dic61—42no—
173C2×Dic61—44no—
174C2×Dic61—44no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—42no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61#10414yes—
184D244—81no—
185D244—81no—
186C8×C61—81no—
187#92418—81no—
188#9149—611nomaximal, Sylow
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—22no—
194C22×C61—22no—
195C22×C61—22no—
196C22×C61—22no—
197C22×C61#38611yescharacteristic
198C22×C61#41012yes—
199C22×C61#41611yescharacteristic
200C22×C61#41811yescharacteristic
201C22×C61C2×#10412yes—
202C22×C61#44911yescharacteristic
203C22×C61#44911yescharacteristic
204C22×C61#48211yescharacteristic
205C22×C61#48211yescharacteristic
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—82no—
210C2×D61—82no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—44no—
216C4×C61—82no—
217Dic61—24no—
218Dic61—44no—
219Dic61—42no—
220Dic61—81no—
221#2854—611no—
222C2×#376—611no—
223#1817—611no—
224C2×#327—611no—
225C2×#327—611no—
226#1294—611no—
227#1294D6111yescharacteristic, complemented
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61#150012yes—
233C2×C61#150512yes—
234C2×C61#187511yescharacteristic
235C2×C61#189611yescharacteristic
236C2×C61#189911yescharacteristic
237D61—161no—
238C2×#123—1221no—
239C2×#121—611no—
240C22×C42—611no—
241C22×C42—1221no—
242C2×C22⋊C8—611no—
243C2×C22⋊C8C2×D6111yescharacteristic
244#390—612no—
245#389—612no—
246#388—1222no—
247#386—1221no—
248#380C2×D6111yescharacteristic
249#376—1222no—
250#376—1222no—
251C2×#95—611no—
252C2×#95—1221no—
253C2×#95C2×D6111yescharacteristic
254#336—1222no—
255#327—1222no—
256#327—1222no—
257C61#914911yescharacteristic, complemented, Sylow
258C22×D4—611no—
259C22×D4—1221no—
260C23×C4—21no—
261C23×C4—611no—
262C23×C4—611no—
263C23×C4—1221no—
264C23×C4C22×D6111yescharacteristic
265C22×C8—21no—
266C22×C8—1221no—
267#123—2442no—
268#123—2442no—
269#121—1221no—
270#121—1221no—
271#121—1221no—
272#121—1221no—
273C2×C4⋊C4—611no—
274C2×C4⋊C4—1222no—
275C2×C4⋊C4C4×D6112yes—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—1222no—
278C2×C22⋊C4—1222no—
279C2×C22⋊C4—1221no—
280C2×C42—612no—
281C2×C42—612no—
282C2×C42—1224no—
283C2×C42—1228no—
284C2×C42—1221no—
285C2×C42—1221no—
286C2×C42—1221no—
287C2×C42—1221no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—1221no—
291C22⋊C8—1221no—
292#95—21no—
293#95—21no—
294#95—612no—
295#95—1222no—
296#95—1224no—
297#95—1221no—
298#95D24412yes—
299C24—1221no—
300C24D4×D6111yescharacteristic
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—2442no—
304C2×D4—2441no—
305C2×D4—2441no—
306C2×D4—2441no—
307C2×D4—2441no—
308C2×D4—2441no—
309C2×D4—2441no—
310C22×C4—24no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—612no—
318C22×C4—612no—
319C22×C4—1224no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1224no—
323C22×C4—1222no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—2442no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4C2×C4×D6111yescharacteristic
335C22×C4C2×D24411yescharacteristic
336C22×C4#1175822211yescharacteristic
337C22×C4D4×D6111yescharacteristic
338C22×C4D4×D6111yescharacteristic
339C22×C4#1175822611yescharacteristic
340C2×C8—42no—
341C2×C8—41no—
342C2×C8—2442no—
343C2×C8—2441no—
344C4⋊C4—42no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—2444no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—2444no—
351C22⋊C4—2444no—
352C22⋊C4—2441no—
353C22⋊C4—2441no—
354C42—12216no—
355C42—1222no—
356C42—1222no—
357C42—1222no—
358C42—1222no—
359C23—22no—
360C23—22no—
361C23—2442no—
362C23—2441no—
363C23—2441no—
364C23—2442no—
365C23—2441no—
366C23C22⋊C4×D6111yescharacteristic
367C23#1451974711yescharacteristic
368C23#1451976211yescharacteristic
369C23#1451979811yescharacteristic
370C23#1451980011yescharacteristic
371C23#1451980111yescharacteristic
372C23#1451980411yescharacteristic
373D4—4881no—
374D4—4881no—
375D4—4881no—
376D4—4881no—
377D4—4881no—
378D4—4881no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—614no—
394C2×C4—1224no—
395C2×C4—1224no—
396C2×C4—1222no—
397C2×C4—1222no—
398C2×C4—1224no—
399C2×C4—1222no—
400C2×C4—1222no—
401C2×C4—1222no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2442no—
406C2×C4—2444no—
407C2×C4—2444no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2442no—
413C2×C4#1451973911yescharacteristic
414C2×C4C4×D24411yescharacteristic
415C2×C4#1451975011yescharacteristic
416C2×C4#1451975211yescharacteristic
417C8—81no—
418C8—4881no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—4881no—
428C22—4881no—
429C22—4882no—
430C22—4882no—
431C22—4881no—
432C22#1683964011yescharacteristic
433C22#1683973412yes—
434C22#1683975711yescharacteristic
435C22#1683976511yescharacteristic
436C22#104×D6112yes—
437C22#1683990811yescharacteristic
438C22#1683991011yescharacteristic
439C22#1684008811yescharacteristic
440C22#1684008911yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—44no—
446C4—82no—
447C4—1224no—
448C4—4881no—
449C4—2444no—
450C4—2442no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—9761no—
456C2#2144430412yes—
457C2#2144432512yes—
458C2#2144614011yescharacteristic
459C2#2144626111yescharacteristic
460C2#2144627611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9149
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. C2×#16839607C2semidirect
3. #21445885C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
13. #16839663C4semidirect
14. #16839661C4semidirect
227. #1294D61semidirect
257. C61#9149semidirect

Maximal subgroups

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

subgroupindex
#214541512
C2×#168396072
#214458852
C2×#168394972
C2×#168394952
#214436972
C61×#12942
#914961