Finite Group Databasebeta

← #29574805

Subgroups — #29574805

Order 15616.

664 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840039C211yesmaximal, characteristic
2C4⋊C4×D244C211yesmaximal, characteristic
3#21446781C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic
5#21443703C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1981C211yesmaximal, characteristic, complemented
8C2×C4×D244—21no—
9C2×C4×D244C2211yescharacteristic
10C2×C4⋊C4×D61—21no—
11#16840039—22no—
12#16840039C414yescomplemented
13C2×#14519710—21no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519697—21no—
16C2×C4×#92418C2211yescharacteristic
17#16839660—21no—
18#16839636—22no—
19#16839632C2211yescharacteristic
20#16839619—21no—
21#16839524—22no—
22#16839489—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×#103×C61—21no—
26C2×#103×C61—21no—
27C4×C4⋊C4×C61C2211yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61—22no—
31C22×#92418—21no—
32C22×#92418—21no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—42no—
36C4×D244—42no—
37C4×D244C2×C412yes—
38C4×D244D412yes—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D412yes—
43C2×#11758196—22no—
44C4⋊C4×D61—42no—
45C4⋊C4×D61—42no—
46C2×#11758198—21no—
47C2×#11758198—22no—
48#14519710—24no—
49C4⋊#92418—21no—
50C4⋊#92418C2×C412yescomplemented
51#14519697—24no—
52C4×#92418—21no—
53C4×#92418—21no—
54#14519684—22no—
55C22×Q8×C61—21no—
56C22×C8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61C2×C412yescomplemented
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C42×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69#103×C61—42no—
70#103×C61—42no—
71#95×C61—21no—
72C23×D61—21no—
73C2×Q8×C61—22no—
74C2×Q8×C61—41no—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—41no—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—22no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244C22⋊C412yes—
91C2×D244SD1612yes—
92C2×D244Q1612yes—
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—44no—
100C2×C4×D61—44no—
101C2×C4×D61—82no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61D812yes—
113C42×C61—41no—
114C42×C61—41no—
115C42×C61C22×C411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118C42×C61#4111yescharacteristic
119#11758198—22no—
120#11758198—22no—
121#11758198—44no—
122C4⋊Dic61—21no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61—41no—
126C4⋊Dic61—41no—
127C4⋊Dic61—42no—
128C4⋊Dic61C22⋊C412yes—
129#11758196—44no—
130C2×#92418—22no—
131C2×#92418—22no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418—41no—
136C23×C61#12011yescharacteristic
137C22×D61—22no—
138C22×D61—22no—
139C22×D61—22no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144Q8×C61—42no—
145Q8×C61—42no—
146Q8×C61—81no—
147Q8×C61—81no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—22no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—81no—
158C2×C4×C61—81no—
159C2×C4×C61C2×C22⋊C411yescharacteristic
160C2×C4×C61C4×D411yescharacteristic
161C2×C4×C61C4×D411yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12311yescharacteristic
165C2×C4×C61C2×D811yescharacteristic
166C2×C4×C61C2×SD1611yescharacteristic
167C2×C4×C61C2×Q1611yescharacteristic
168C2×C4×C61#13511yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61#13711yescharacteristic
173C2×Dic61—22no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179D244—22no—
180D244—22no—
181D244—22no—
182D244#10314yescomplemented
183C4×D61—42no—
184C4×D61—42no—
185C4×D61—42no—
186C4×D61—42no—
187C4×D61—88no—
188C8×C61—81no—
189#92418—42no—
190#92418—42no—
191#8981—611nomaximal, Sylow
192C22×C61#38611yescharacteristic
193C22×C61#44711yescharacteristic
194C22×C61#44911yescharacteristic
195C22×C61#45011yescharacteristic
196C22×C61#45111yescharacteristic
197C22×C61#45511yescharacteristic
198C22×C61#45611yescharacteristic
199C2×D61—24no—
200C2×D61—42no—
201C2×D61—42no—
202C2×D61—42no—
203C2×D61—42no—
204C2×D61—42no—
205C2×D61—42no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—42no—
209C4×C61—82no—
210C4×C61—81no—
211C4×C61C2×#10311yescharacteristic
212C4×C61#41711yescharacteristic
213C4×C61C4×D811yescharacteristic
214C4×C61#44211yescharacteristic
215C4×C61#45911yescharacteristic
216C4×C61#46311yescharacteristic
217C4×C61#48311yescharacteristic
218C4×C61#48411yescharacteristic
219Dic61—42no—
220Dic61—82no—
221C2×#474—611no—
222D4×C4⋊C4—611no—
223#1990—611no—
224#1981D6111yescharacteristic, complemented
225C2×D4⋊C8—611no—
226#1296—611no—
227#1279—611no—
228C2×C61#163911yescharacteristic
229C2×C61#164411yescharacteristic
230C2×C61#164911yescharacteristic
231C2×C61#165411yescharacteristic
232C2×C61#187211yescharacteristic
233C2×C61#187911yescharacteristic
234C2×C61#188211yescharacteristic
235D61—44no—
236C2×C4⋊Q8C2×D6111yescharacteristic
237C2×C4×D4—611no—
238C2×C4×D4—1221no—
239C22×C4⋊C4—1221no—
240#474—614no—
241#474—1222no—
242C2×#107—1221no—
243C2×C4⋊C8—611no—
244C2×C4⋊C8C2×D6111yescharacteristic
245C2×#103—21no—
246C2×#103—21no—
247C2×#102—1221no—
248C2×C4×C8—611no—
249#389—1221no—
250#385—1222no—
251#384—611no—
252#380—1221no—
253C4×C4⋊C4C2×D6111yescharacteristic
254#340—1222no—
255D4⋊C8—1222no—
256C61#898111yescharacteristic, complemented, Sylow
257C22×Q8—21no—
258C22×D4—611no—
259C23×C4—1222no—
260C23×C4—1221no—
261C22×C8—21no—
262C22×C8—1221no—
263C22×C8—1221no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8C4×D6112yescomplemented
268C4×D4—612no—
269C4×D4—612no—
270C4×D4—1221no—
271C4×D4—1221no—
272C4×D4—2442no—
273C4×D4—2442no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—612no—
278C2×C4⋊C4—1222no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—2442no—
282C2×C4⋊C4—2442no—
283C2×C4⋊C4C22⋊D6111yescharacteristic
284C2×C4⋊C4C22⋊D6111yescharacteristic
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1222no—
287C2×C42—21no—
288C2×C42C22×D6111yescharacteristic
289#107—1224no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—612no—
293C4⋊C8—1221no—
294#103—42no—
295#103—42no—
296#102—1224no—
297C4×C8—1221no—
298C4×C8—1221no—
299#95—21no—
300#95—1222no—
301C24—1221no—
302C2×Q8—22no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—612no—
309C2×D4—612no—
310C2×D4—612no—
311C2×D4—1221no—
312C2×D4—1221no—
313C2×D4—1221no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—41no—
317C22×C4—1221no—
318C22×C4—1222no—
319C22×C4—1222no—
320C22×C4—1222no—
321C22×C4—4882no—
322C22×C4—2444no—
323C22×C4—2444no—
324C22×C4—2441no—
325C22×C4—2441no—
326C22×C4—2441no—
327C22×C4—2441no—
328C22×C4D4×D6111yescharacteristic
329C22×C4D4×D6111yescharacteristic
330C22×C4C2×C22⋊D6111yescharacteristic
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—1222no—
335C2×C8—1222no—
336C2×C8—2441no—
337C2×C8—2441no—
338C2×C8—2441no—
339C2×C8—2441no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—612no—
348C4⋊C4—1221no—
349C4⋊C4—2442no—
350C4⋊C4—2444no—
351C4⋊C4—2441no—
352C4⋊C4—2441no—
353C4⋊C4—2441no—
354C4⋊C4—2441no—
355C4⋊C4#1175819912yes—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C22⋊C4—2444no—
359C42—41no—
360C42—41no—
361C42C2×C4×D6111yescharacteristic
362C42#1175822211yescharacteristic
363C42D4×D6111yescharacteristic
364C42#1175822411yescharacteristic
365C23—1222no—
366C23—1222no—
367C23—1222no—
368C23—2441no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23#1451974511yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—81no—
376Q8—81no—
377D4—614no—
378D4—1222no—
379D4—1222no—
380D4—1222no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—1222no—
393C2×C4—4888no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4—2442no—
402C2×C4—2442no—
403C2×C4C22⋊C4×D6111yescharacteristic
404C2×C4#1451973711yescharacteristic
405C2×C4C4×C22⋊D6111yescharacteristic
406C2×C4#1451974811yescharacteristic
407C2×C4#1451975011yescharacteristic
408C2×C4#1451975911yescharacteristic
409C2×C4C2×#1175819911yescharacteristic
410C2×C4SD16×D6111yescharacteristic
411C2×C4Q16×D6111yescharacteristic
412C2×C4#1451979711yescharacteristic
413C2×C4#1451980211yescharacteristic
414C2×C4#1451980311yescharacteristic
415C2×C4#1451980411yescharacteristic
416C2×C4#1451980911yescharacteristic
417C8—81no—
418C8—2442no—
419C8—2442no—
420C22—1224no—
421C22—2442no—
422C22—2442no—
423C22—2442no—
424C22—2442no—
425C22—2442no—
426C22—2442no—
427C22#1683963811yescharacteristic
428C22#1683989511yescharacteristic
429C22#1683990511yescharacteristic
430C22#1683991111yescharacteristic
431C22#1683991611yescharacteristic
432C22#1683993811yescharacteristic
433C22#1683994311yescharacteristic
434C4—21no—
435C4—21no—
436C4—42no—
437C4—82no—
438C4—81no—
439C4—4882no—
440C4—2442no—
441C4#103×D6111yescharacteristic
442C4#1683976211yescharacteristic
443C4C4×#1175819911yescharacteristic
444C4#1683987211yescharacteristic
445C4#1683995411yescharacteristic
446C4#1683997411yescharacteristic
447C4#1684009111yescharacteristic
448C4#1684009611yescharacteristic
449C2—2444no—
450C2#2144499611yescharacteristic
451C2#2144503111yescharacteristic
452C2#2144506611yescharacteristic
453C2#2144510111yescharacteristic
454C2#2144612311yescharacteristic
455C2#2144617011yescharacteristic
456C2#2144618511yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1981C2
socleC23×C61#120
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1981D61
hypocenterC61#8981
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
3. #21446781C2semidirect
5. #21443703C2semidirect
6. #21443660C2semidirect
7. C61×#1981C2semidirect
12. #16840039C4semidirect
50. C4⋊#92418C2×C4semidirect
60. C4⋊Q8×C61C2×C4semidirect
182. D244#103semidirect
224. #1981D61semidirect
256. C61#8981semidirect
267. C4⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400392
C4⋊C4×D2442
#214467812
C2×#168394892
#214437032
#214436602
C61×#19812
#898161