Finite Group Databasebeta

← #29574826

Subgroups — #29574826

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840039C211yesmaximal, characteristic
2#21448766C211yesmaximal, characteristic
3#21446781C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic
5#21443703C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1981C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×#14519735—21no—
10#16840039—22no—
11#16840039C414yescomplemented
12C2×#14519710—21no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519697—21no—
15C2×C4×#92418C2211yescharacteristic
16#16839664—21no—
17#16839654—22no—
18#16839632C2211yescharacteristic
19#16839619—21no—
20C4×C4⋊Dic61—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×#92418—21no—
31C22×#92418—21no—
32C4×D244—21no—
33C4×D244—21no—
34C4×D244C2×C412yes—
35C4×D244D412yes—
36#14519735—42no—
37#14519735—42no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D412yes—
42C2×#11758198—21no—
43C2×#11758198—22no—
44C2×#11758198—22no—
45C2×C4×Dic61—22no—
46#14519710—24no—
47C4⋊#92418—21no—
48C4⋊#92418C2×C412yes—
49#14519697—24no—
50C4×#92418—21no—
51C4×#92418—21no—
52#14519684—22no—
53C22×Q8×C61—21no—
54C22×C8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61C2×C412yes—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61D411yescharacteristic
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C42×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67#103×C61—42no—
68#103×C61—42no—
69#95×C61—21no—
70C23×D61—21no—
71C2×Q8×C61—22no—
72C2×Q8×C61—41no—
73C2×Q8×C61—41no—
74C2×Q8×C61—41no—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—41no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—21no—
84C22×Dic61—22no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244C22⋊C412yes—
91C2×C4×D61—22no—
92C2×C4×D61—22no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61D812yes—
108C42×C61—41no—
109C42×C61—41no—
110C42×C61C22×C411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113C42×C61#4111yescharacteristic
114#11758198—22no—
115#11758198—22no—
116#11758198—44no—
117#11758198—82no—
118C4⋊Dic61—21no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—42no—
124C4⋊Dic61C22⋊C412yes—
125C4×Dic61—44no—
126C2×#92418—22no—
127C2×#92418—22no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C23×C61#12011yescharacteristic
133C22×D61—22no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140Q8×C61—42no—
141Q8×C61—42no—
142Q8×C61—81no—
143Q8×C61—81no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—81no—
154C2×C4×C61—81no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×C4×C61C2×D811yescharacteristic
162C2×C4×C61#13511yescharacteristic
163C2×C4×C61#13511yescharacteristic
164C2×C4×C61#13511yescharacteristic
165C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C61#13711yescharacteristic
168C2×C4×C61#13711yescharacteristic
169C2×Dic61—22no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175D244—22no—
176D244—22no—
177D244—41no—
178D244—41no—
179C4×D61—42no—
180C4×D61—42no—
181C4×D61—42no—
182C4×D61—42no—
183C8×C61—81no—
184#92418—42no—
185#92418—42no—
186#8984—611nomaximal, Sylow
187C22×C61#38611yescharacteristic
188C22×C61#44711yescharacteristic
189C22×C61#44911yescharacteristic
190C22×C61#45211yescharacteristic
191C22×C61#45211yescharacteristic
192C22×C61#45511yescharacteristic
193C22×C61#45611yescharacteristic
194C2×D61—42no—
195C2×D61—42no—
196C2×D61—42no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—42no—
204C4×C61—82no—
205C4×C61—81no—
206C4×C61#41611yescharacteristic
207C4×C61#41911yescharacteristic
208C4×C61C4×D811yescharacteristic
209C4×C61#44211yescharacteristic
210C4×C61#45911yescharacteristic
211C4×C61#46311yescharacteristic
212C4×C61#48511yescharacteristic
213C4×C61#48511yescharacteristic
214Dic61—42no—
215Dic61—82no—
216C2×#474—611no—
217#2354—611no—
218#1990—611no—
219#1981D6111yescharacteristic, complemented
220C2×D4⋊C8—611no—
221#1296—611no—
222#1279—611no—
223C2×C61#164111yescharacteristic
224C2×C61#164611yescharacteristic
225C2×C61#164711yescharacteristic
226C2×C61#165211yescharacteristic
227C2×C61#187311yescharacteristic
228C2×C61#187911yescharacteristic
229C2×C61#188211yescharacteristic
230D61—82no—
231C2×C4⋊Q8C2×D6111yescharacteristic
232C2×C4×D4—611no—
233C2×#117—1221no—
234#474—614no—
235#474—1222no—
236C2×#107—1221no—
237C2×C4⋊C8—611no—
238C2×C4⋊C8C2×D6111yescharacteristic
239C2×#103—21no—
240C2×#103—21no—
241C2×#102—1221no—
242C2×C4×C8—611no—
243#390—1221no—
244#388—1222no—
245#384—611no—
246#380—1221no—
247C4×C4⋊C4—1221no—
248C4×C4⋊C4C2×D6111yescharacteristic
249#340—1222no—
250D4⋊C8—1222no—
251C61#898411yescharacteristic, complemented, Sylow
252C22×Q8—21no—
253C22×D4—611no—
254C23×C4—1221no—
255C22×C8—21no—
256C22×C8—1221no—
257C22×C8—1221no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8C4×D6112yes—
262C4×D4—612no—
263C4×D4—612no—
264C4×D4—1221no—
265C4×D4—1221no—
266#117—2442no—
267#117—2442no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—611no—
271C2×C4⋊C4—612no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4C22⋊D6111yescharacteristic
275C2×C4⋊C4C22⋊D6111yescharacteristic
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1222no—
278C2×C22⋊C4—1222no—
279C2×C42—21no—
280C2×C42—1222no—
281C2×C42C22×D6111yescharacteristic
282#107—1224no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—612no—
286C4⋊C8—1221no—
287#103—42no—
288#103—42no—
289#102—1224no—
290C4×C8—1221no—
291C4×C8—1221no—
292#95—21no—
293#95—1222no—
294C24—1221no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×D4—612no—
302C2×D4—1221no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—1221no—
311C22×C4—1222no—
312C22×C4—1222no—
313C22×C4—1222no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4D4×D6111yescharacteristic
319C22×C4D4×D6111yescharacteristic
320C22×C4C2×C22⋊D6111yescharacteristic
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—1222no—
325C2×C8—1222no—
326C2×C8—2441no—
327C2×C8—2441no—
328C2×C8—2441no—
329C2×C8—2441no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—612no—
338C4⋊C4—1221no—
339C4⋊C4—2442no—
340C4⋊C4—2441no—
341C4⋊C4—2441no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C4⋊C4#1175819912yes—
345C22⋊C4—1222no—
346C22⋊C4—1222no—
347C22⋊C4—4882no—
348C22⋊C4—2444no—
349C42—41no—
350C42—41no—
351C42—2444no—
352C42C2×C4×D6111yescharacteristic
353C42#1175822211yescharacteristic
354C42D4×D6111yescharacteristic
355C42#1175822411yescharacteristic
356C23—1222no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23#1451974511yescharacteristic
364Q8—42no—
365Q8—42no—
366Q8—81no—
367Q8—81no—
368D4—1222no—
369D4—1222no—
370D4—2441no—
371D4—2441no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—1222no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2442no—
390C2×C4—2442no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4C22⋊C4×D6111yescharacteristic
394C2×C4#1451973711yescharacteristic
395C2×C4C4×C22⋊D6111yescharacteristic
396C2×C4#1451974811yescharacteristic
397C2×C4#1451975011yescharacteristic
398C2×C4#1451975911yescharacteristic
399C2×C4C2×#1175819911yescharacteristic
400C2×C4#1451979711yescharacteristic
401C2×C4#1451979811yescharacteristic
402C2×C4#1451980011yescharacteristic
403C2×C4#1451980211yescharacteristic
404C2×C4#1451980311yescharacteristic
405C2×C4#1451980611yescharacteristic
406C2×C4#1451980911yescharacteristic
407C8—81no—
408C8—2442no—
409C8—2442no—
410C22—4881no—
411C22—4881no—
412C22—4881no—
413C22—4881no—
414C22—2442no—
415C22—2442no—
416C22—2442no—
417C22#1683963811yescharacteristic
418C22#1683989511yescharacteristic
419C22#1683990511yescharacteristic
420C22#1683992111yescharacteristic
421C22#1683992311yescharacteristic
422C22#1683993811yescharacteristic
423C22#1683994311yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—82no—
428C4—81no—
429C4—4882no—
430C4—2442no—
431C4#1683975711yescharacteristic
432C4#1683976911yescharacteristic
433C4C4×#1175819911yescharacteristic
434C4#1683987211yescharacteristic
435C4#1683995411yescharacteristic
436C4#1683997411yescharacteristic
437C4#1684010111yescharacteristic
438C4#1684010211yescharacteristic
439C2—4882no—
440C2#2144501011yescharacteristic
441C2#2144504511yescharacteristic
442C2#2144505211yescharacteristic
443C2#2144508711yescharacteristic
444C2#2144612811yescharacteristic
445C2#2144617011yescharacteristic
446C2#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#8984
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
11. #16840039C4semidirect
219. #1981D61semidirect
251. C61#8984semidirect

Maximal subgroups

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

subgroupindex
C2×#168400392
#214487662
#214467812
C2×#168394892
#214437032
#214436602
C61×#19812
#898461