Finite Group Databasebeta

← #29576346

Subgroups — #29576346

Order 15616.

514 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839977C211yesmaximal, characteristic
2#21454854C211yesmaximal, characteristic, complemented
3#21444416C211yesmaximal, characteristic, complemented
4#21444172C211yesmaximal, characteristic, complemented
5#21443688C211yesmaximal, characteristic, complemented
6#21443670C211yesmaximal, characteristic, complemented
7C61×#1490C211yesmaximal, characteristic, complemented
8C22×#11758200C411yescharacteristic
9C22×#11758199C411yescharacteristic
10C2×#14519765C2211yescharacteristic
11#16839977—21no—
12#16839977—21no—
13#16839977—21no—
14#16839977—21no—
15#16839840—21no—
16#16839834—22no—
17D4×#92418—21no—
18#16839819C2211yescharacteristic
19#16839815C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519700C411yescharacteristic
22C2×#14519697C411yescharacteristic
23#16839726—21no—
24C2×C22⋊#92418—21no—
25#16839501—22no—
26#16839485—21no—
27#16839485—21no—
28C2×C4×D4×C61C2211yescharacteristic
29C61×#432C2211yescharacteristic
30C4×M16×C61C2211yescharacteristic
31C61×D4⋊C8—21no—
32C61×D4⋊C8—21no—
33C22×Dic122C2×C411yescharacteristic
34C22×D244C2×C411yescharacteristic
35C2×#11758200—21no—
36C2×#11758200—21no—
37C2×#11758200—42no—
38C2×#11758199—21no—
39C2×#11758199—21no—
40C2×#11758199—42no—
41C2×#11758194—22no—
42C22×#92418—22no—
43C22×#92418C2×C411yescharacteristic
44C22×#92418C2×C411yescharacteristic
45#14519765—21no—
46#14519765—21no—
47#14519765—21no—
48#14519765—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55#14519700—21no—
56#14519700—21no—
57#14519697—21no—
58#14519697—21no—
59C22⋊#92418—22no—
60C22⋊#92418—22no—
61C22⋊#92418—21no—
62C22⋊#92418D411yescharacteristic
63C22⋊#92418D411yescharacteristic
64#14519688D412yes—
65C4×#92418—21no—
66C22×D4×C61C2×C411yescharacteristic
67C23×C4×C61—21no—
68C2×M16×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61D411yescharacteristic
72C4×D4×C61D411yescharacteristic
73C4×D4×C61D411yescharacteristic
74C4×D4×C61D411yescharacteristic
75C2×C4⋊C4×C61C2×C411yescharacteristic
76C2×C22⋊C4×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80#97×C61—21no—
81#97×C61—21no—
82C4×C8×C61—21no—
83C24×C61—21no—
84C23×D61—21no—
85C2×D4×C61—22no—
86C2×D4×C61—21no—
87C2×D4×C61—41no—
88C2×D4×C61C22⋊C411yescharacteristic
89C2×D4×C61C22⋊C411yescharacteristic
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—82no—
96C22×C4×C61C22×C411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C22×Dic61—21no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—41no—
103C2×D244—41no—
104C2×Dic122—21no—
105C2×Dic122—21no—
106C2×Dic122—41no—
107C2×Dic122—41no—
108M16×C61—22no—
109M16×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61C22⋊C411yescharacteristic
114C4⋊C4×C61C22⋊C411yescharacteristic
115C22⋊C4×C61—21no—
116C22⋊C4×C61—21no—
117C22⋊C4×C61—21no—
118C22⋊C4×C61—21no—
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123#11758200—42no—
124#11758200—42no—
125#11758199—42no—
126#11758199—42no—
127#11758198—41no—
128#11758198—41no—
129#11758198—41no—
130#11758198—41no—
131#11758194—82no—
132C2×#92418—21no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418—21no—
136C2×#92418—22no—
137C2×#92418—41no—
138C2×#92418—41no—
139C2×#92418—82no—
140C23×C61—21no—
141C23×C61—21no—
142C23×C61—42no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—81no—
146C23×C61C4×D411yescharacteristic
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—81no—
151C22×D61—81no—
152D4×C61—21no—
153D4×C61—21no—
154D4×C61—21no—
155D4×C61—42no—
156D4×C61#10012yes—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61C2×C22⋊C411yescharacteristic
170C2×C4×C61C4×D411yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12311yescharacteristic
175C2×Dic61—41no—
176C2×Dic61—81no—
177D244—41no—
178D244—41no—
179D244—81no—
180Dic122—41no—
181Dic122—41no—
182Dic122—81no—
183C8×C61—42no—
184C8×C61—81no—
185#92418—41no—
186#92418—42no—
187#92418—41no—
188#92418—41no—
189#92418—41no—
190#9243—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—22no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—82no—
200C22×C61—82no—
201C22×C61#38611yescharacteristic
202C22×C61#44311yescharacteristic
203C22×C61#44411yescharacteristic
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—161no—
208C2×D61—161no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—41no—
215C4×C61—41no—
216C4×C61C2×#10011yescharacteristic
217C4×C61#41311yescharacteristic
218Dic61—81no—
219C2×#463—611no—
220#2974—611no—
221#1527—611no—
222#1490D6111yescharacteristic, complemented
223#1469—611no—
224#1290—611no—
225#1283—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—42no—
229C2×C61—81no—
230C2×C61#187611yescharacteristic
231C2×C61#190011yescharacteristic
232C2×C61#190411yescharacteristic
233D61—161no—
234C22×SD16—611no—
235C22×D8—611no—
236C2×#124—611no—
237C2×C4×D4C2×D6111yescharacteristic
238#463—1221no—
239#463—1221no—
240#463—1221no—
241#463—1221no—
242#436—1221no—
243#435—1222no—
244C8×D4—1221no—
245#432—611no—
246#432C2×D6111yescharacteristic
247#431—611no—
248C2×C4⋊C8—611no—
249C2×#103—611no—
250C2×#102—611no—
251#407—1221no—
252C2×C22⋊C8—1221no—
253C4×M16C2×D6111yescharacteristic
254#329—1222no—
255D4⋊C8—21no—
256D4⋊C8—21no—
257#323—1221no—
258#323—1221no—
259C61#924311yescharacteristic, complemented, Sylow
260C22×Q8—611no—
261C22×D4—611no—
262C22×D4C4×D6111yescharacteristic
263C23×C4—21no—
264C2×SD16—1221no—
265C2×SD16—1221no—
266C2×SD16—2442no—
267C2×D8—1221no—
268C2×D8—1221no—
269C2×D8—2442no—
270C2×M16—21no—
271C2×M16—1222no—
272C22×C8—611no—
273C22×C8—611no—
274C22×C8—1222no—
275#124—1221no—
276#124—1221no—
277#124—1221no—
278#124—1221no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4D24411yescharacteristic
282C4×D4D24411yescharacteristic
283C4×D4C22⋊D6111yescharacteristic
284C4×D4C22⋊D6111yescharacteristic
285C2×C4⋊C4C4×D6111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C42C22×D6111yescharacteristic
290C4⋊C8—21no—
291C4⋊C8—1221no—
292C4⋊C8—1221no—
293C4⋊C8—1221no—
294C4⋊C8—1221no—
295#103—1221no—
296#103—1221no—
297#102—1221no—
298#102—1221no—
299C22⋊C8—21no—
300C22⋊C8—611no—
301C22⋊C8—611no—
302C22⋊C8—1222no—
303C22⋊C8—1222no—
304C22⋊C8—1221no—
305#97—21no—
306#97—21no—
307#97—612no—
308C4×C8—21no—
309C4×C8—1221no—
310C24—21no—
311C24—1221no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×Q8—2441no—
315C2×Q8—2441no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4#1175819811yescharacteristic
324C2×D4#1175819811yescharacteristic
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—82no—
331C22×C4—1221no—
332C22×C4C2×C4×D6111yescharacteristic
333C22×C4D4×D6111yescharacteristic
334C22×C4#1175822411yescharacteristic
335SD16—2442no—
336SD16—2442no—
337D8—2442no—
338D8—2442no—
339M16—22no—
340M16—41no—
341M16—4882no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—1221no—
345C2×C8—1221no—
346C2×C8—1221no—
347C2×C8—1221no—
348C2×C8—1222no—
349C2×C8—4882no—
350C2×C8—2441no—
351C2×C8—2441no—
352C4⋊C4—21no—
353C4⋊C4#1175819811yescharacteristic
354C4⋊C4#1175819811yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C22⋊C4—2441no—
362C22⋊C4—2441no—
363C42C2×D24411yescharacteristic
364C42D4×D6111yescharacteristic
365C42#1175822411yescharacteristic
366C42C2×C22⋊D6111yescharacteristic
367C23—21no—
368C23—21no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—81no—
373C23—4881no—
374C23—4881no—
375C23—2441no—
376C23—2441no—
377C23—2441no—
378C23#1451973711yescharacteristic
379Q8—4881no—
380Q8—2441no—
381Q8—2441no—
382D4—21no—
383D4—21no—
384D4—21no—
385D4—42no—
386D4—4881no—
387D4—2441no—
388D4—2441no—
389D4#1451969312yes—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—4881no—
403C2×C4—2441no—
404C2×C4C2×#1175819811yescharacteristic
405C2×C4#1451973711yescharacteristic
406C2×C4#1451974711yescharacteristic
407C2×C4#1451974911yescharacteristic
408C2×C4#1451974911yescharacteristic
409C2×C4#1451976111yescharacteristic
410C8—42no—
411C8—81no—
412C8—2441no—
413C8—2442no—
414C8—2441no—
415C8—2441no—
416C8—2441no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—82no—
426C22—82no—
427C22—9761no—
428C22—9761no—
429C22—4881no—
430C22—4881no—
431C22—4881no—
432C22#1683963911yescharacteristic
433C22#1683987611yescharacteristic
434C22#1683988111yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—4881no—
443C4C2×#1451969311yescharacteristic
444C4#1683974411yescharacteristic
445C2—21no—
446C2—21no—
447C2—42no—
448C2—81no—
449C2—9761no—
450C2#2144614411yescharacteristic
451C2#2144628011yescharacteristic
452C2#2144630411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1490C2
socleC22×C61#386
prime radicalC22×#11758199C4
cosocleC2×C42×C61C23
hypercenter#1490D61
hypocenterC61#9243
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #21454854C2semidirect
3. #21444416C2semidirect
4. #21444172C2semidirect
5. #21443688C2semidirect
6. #21443670C2semidirect
7. C61×#1490C2semidirect
222. #1490D61semidirect
259. C61#9243semidirect

Maximal subgroups

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

subgroupindex
C2×#168399772
#214548542
#214444162
#214441722
#214436882
#214436702
C61×#14902
#924361