Finite Group Databasebeta

← #29575750

Subgroups — #29575750

Order 15616.

800 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#21454145C211yesmaximal, characteristic
2C2×#16839613C211yesmaximal, characteristic, complemented
3#21445885C211yesmaximal, characteristic, complemented
4C2×#16839496C211yesmaximal, characteristic
5#21443699C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C2×C61×#327C211yesmaximal, characteristic
8C2×#14519758—21no—
9C22×#11758196—21no—
10C22×C4×Dic61—21no—
11C22×C4×Dic61C2211yescharacteristic
12C2×C22⋊#92418C2211yescharacteristic
13#16839665C412yescomplemented
14#16839658C412yescomplemented
15#16839650—22no—
16#16839642—21no—
17#16839622C2211yescharacteristic
18#16839613—22no—
19#16839613—22no—
20C2×#14519684C2211yescharacteristic
21#16839516—22no—
22#16839496—22no—
23C2×#121×C61C2211yescharacteristic
24C2×C22⋊C8×C61C2211yescharacteristic
25C2×#95×C61C2211yescharacteristic
26C61×#327—22no—
27C23×Dic61—21no—
28C23×Dic61D411yescharacteristic
29C23×Dic61D411yescharacteristic
30C22×#92418—21no—
31#14519758—42no—
32#14519758—42no—
33C2×C4⋊Dic61C2×C412yes—
34C2×#11758196—28no—
35C2×#11758196—24no—
36C2×#11758196—22no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—22no—
39C2×C22⋊Dic61—22no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—24no—
45C2×C4×Dic61—42no—
46C2×C4×Dic61—42no—
47C2×C4×Dic61C2×C412yes—
48C2×C4×Dic61D412yes—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—22no—
54#14519684D412yes—
55C22×D4×C61—21no—
56C22×D4×C61C2×C411yescharacteristic
57C23×C4×C61—21no—
58C23×C4×C61C2311yescharacteristic
59C22×C8×C61—21no—
60#121×C61—21no—
61#121×C61—21no—
62#121×C61—21no—
63#121×C61—21no—
64C2×C4⋊C4×C61C2×C411yescharacteristic
65C2×C22⋊C4×C61—21no—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68#95×C61—21no—
69#95×C61D412yes—
70C24×C61—21no—
71C24×C61C2×D411yescharacteristic
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—42no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C22×C4×C61—24no—
82C22×C4×C61—22no—
83C22×C4×C61—21no—
84C22×C4×C61—42no—
85C22×C4×C61—42no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—24no—
101C22×Dic61—24no—
102C22×Dic61—22no—
103C22×Dic61—22no—
104C22×Dic61—42no—
105C22×Dic61—41no—
106C22×Dic61—41no—
107C22×Dic61C22⋊C412yes—
108C22×Dic61C22⋊C412yes—
109C22×Dic61D812yes—
110C22×Dic61SD1612yes—
111C2×C8×C61—42no—
112C2×C8×C61—41no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊Dic61—41no—
118C22⋊Dic61—41no—
119C22⋊Dic61—44no—
120C22⋊Dic61—44no—
121C4⋊Dic61—42no—
122#11758196—216no—
123#11758196—44no—
124C4×Dic61—22no—
125C4×Dic61—22no—
126C4×Dic61—22no—
127C4×Dic61—22no—
128C4×Dic61—48no—
129C2×#92418—42no—
130C2×#92418—41no—
131C23×C61—22no—
132C23×C61—22no—
133C23×C61—41no—
134C23×C61—42no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—42no—
138C23×C61C2×C22⋊C411yescharacteristic
139C23×C61#12011yescharacteristic
140C23×C61#12311yescharacteristic
141C23×C61C2×D811yescharacteristic
142C23×C61C2×SD1611yescharacteristic
143C23×C61AGL(1,ℤ/8)11yescharacteristic
144C23×C61#13711yescharacteristic
145D4×C61—81no—
146D4×C61—81no—
147D4×C61—81no—
148D4×C61—81no—
149D4×C61—81no—
150D4×C61—81no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—24no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—44no—
160C2×C4×C61—44no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×Dic61—24no—
170C2×Dic61—24no—
171C2×Dic61—22no—
172C2×Dic61—22no—
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—22no—
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—24no—
180C2×Dic61—42no—
181C2×Dic61—44no—
182C2×Dic61—44no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—42no—
187C2×Dic61#10214yes—
188C2×Dic61#10414yes—
189C8×C61—81no—
190#92418—81no—
191#9148—611nomaximal, Sylow
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—22no—
199C22×C61—22no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61—82no—
204C22×C61—82no—
205C22×C61#38611yescharacteristic
206C22×C61#41012yes—
207C22×C61C2×#10211yescharacteristic
208C22×C61#41711yescharacteristic
209C22×C61C2×#10412yes—
210C22×C61#44711yescharacteristic
211C22×C61#44811yescharacteristic
212C22×C61#48011yescharacteristic
213C22×C61#48111yescharacteristic
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—44no—
219C4×C61—81no—
220Dic61—24no—
221Dic61—24no—
222Dic61—44no—
223Dic61—82no—
224#2854—611no—
225C2×C4×C4⋊C4—611no—
226#1817—611no—
227C2×#327—611no—
228C2×#327D6111yescharacteristic
229#1294—611no—
230#1294—611no—
231C2×C61—21no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61—161no—
236C2×C61#150212yes—
237C2×C61#150912yes—
238C2×C61#187411yescharacteristic
239C2×C61#189611yescharacteristic
240C2×C61#189911yescharacteristic
241C2×#123—1221no—
242C2×#121C2×D6111yescharacteristic
243C22×C4⋊C4—1221no—
244C22×C42—611no—
245C22×C42—1221no—
246C2×C22⋊C8—611no—
247C2×C22⋊C8C2×D6111yescharacteristic
248#390—612no—
249#389—612no—
250#388—1222no—
251#386—1221no—
252#380—611no—
253C4×C4⋊C4—1222no—
254C4×C4⋊C4—1222no—
255C2×#95—611no—
256C2×#95C2×D6111yescharacteristic
257#336—1222no—
258#327—22no—
259#327—1222no—
260C61#914811yescharacteristic, complemented, Sylow
261C22×D4—21no—
262C22×D4C4×D6111yescharacteristic
263C23×C4—21no—
264C23×C4—611no—
265C23×C4—611no—
266C23×C4—1221no—
267C23×C4C22×D6111yescharacteristic
268C22×C8—21no—
269C22×C8—1221no—
270#123—2442no—
271#123—2442no—
272#121—21no—
273#121—21no—
274#121—21no—
275#121—21no—
276C2×C4⋊C4—612no—
277C2×C4⋊C4—1224no—
278C2×C4⋊C4—1228no—
279C2×C4⋊C4—1222no—
280C2×C4⋊C4C4×D6111yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—1222no—
283C2×C22⋊C4—1222no—
284C2×C22⋊C4—1221no—
285C2×C42—612no—
286C2×C42—612no—
287C2×C42—1221no—
288C2×C42—1221no—
289C2×C42—1221no—
290C2×C42—1221no—
291C2×C42—1224no—
292C2×C42—2442no—
293C2×C42—2442no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—1221no—
297C22⋊C8—1221no—
298#95—21no—
299#95—612no—
300#95—1222no—
301#95—1221no—
302#95—1221no—
303#95C22⋊D6112yes—
304C24—21no—
305C24D4×D6111yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—42no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—612no—
323C22×C4—612no—
324C22×C4—612no—
325C22×C4—612no—
326C22×C4—1224no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—1224no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—2442no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4C2×C4×D6111yescharacteristic
340C22×C4#1175822211yescharacteristic
341C22×C4D4×D6111yescharacteristic
342C22×C4D4×D6111yescharacteristic
343C22×C4#1175822411yescharacteristic
344C22×C4C2×C22⋊D6111yescharacteristic
345C2×C8—42no—
346C2×C8—41no—
347C2×C8—2442no—
348C2×C8—2441no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—12216no—
352C4⋊C4—2442no—
353C4⋊C4—2444no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—2444no—
357C22⋊C4—2444no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—1222no—
361C42—1222no—
362C42—1222no—
363C42—1222no—
364C42—2448no—
365C23—22no—
366C23—22no—
367C23—42no—
368C23—41no—
369C23—41no—
370C23—42no—
371C23—41no—
372C23C22⋊C4×D6111yescharacteristic
373C23#1451974511yescharacteristic
374C23#1451975911yescharacteristic
375C23D8×D6111yescharacteristic
376C23SD16×D6111yescharacteristic
377C23#1451980111yescharacteristic
378C23#1451980611yescharacteristic
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—614no—
400C2×C4—614no—
401C2×C4—1224no—
402C2×C4—1224no—
403C2×C4—1222no—
404C2×C4—1222no—
405C2×C4—1222no—
406C2×C4—1222no—
407C2×C4—1222no—
408C2×C4—1222no—
409C2×C4—1222no—
410C2×C4—1222no—
411C2×C4—1224no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4—2444no—
417C2×C4—2444no—
418C2×C4—2442no—
419C2×C4#1451973711yescharacteristic
420C2×C4C4×C22⋊D6111yescharacteristic
421C2×C4#1451974811yescharacteristic
422C2×C4#1451975011yescharacteristic
423C8—81no—
424C8—4881no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—81no—
434C22—81no—
435C22—82no—
436C22—82no—
437C22—81no—
438C22#1683963811yescharacteristic
439C22#1683973412yes—
440C22#102×D6111yescharacteristic
441C22#1683976011yescharacteristic
442C22#104×D6112yes—
443C22#1683989411yescharacteristic
444C22#1683989911yescharacteristic
445C22#1684007411yescharacteristic
446C22#1684007911yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—44no—
452C4—81no—
453C4—1224no—
454C4—1224no—
455C4—4882no—
456C4—2444no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—161no—
462C2#2144431212yes—
463C2#2144434112yes—
464C2#2144613311yescharacteristic
465C2#2144625911yescharacteristic
466C2#2144627411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#327C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenterC2×#327D61
hypocenterC61#9148
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#16839613C2semidirect
3. #21445885C2semidirect
5. #21443699C2semidirect
6. #21443698C2semidirect
13. #16839665C4semidirect
14. #16839658C4semidirect
260. C61#9148semidirect

Maximal subgroups

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

subgroupindex
#214541452
C2×#168396132
#214458852
C2×#168394962
#214436992
#214436982
C2×C61×#3272
#914861