Finite Group Databasebeta

← #29575687

Subgroups — #29575687

Order 15616.

612 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839784C211yesmaximal, characteristic
2#21454172C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C2×#16839510C211yesmaximal, characteristic, complemented
5C2×#16839510C211yesmaximal, characteristic, complemented
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519757C412yes—
11C2×C42×D61C2211yescharacteristic
12#16839784—22no—
13#16839784—22no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×C4⋊#92418C2211yescharacteristic
16C2×#14519706—21no—
17C2×#14519689—21no—
18#16839667C412yes—
19#16839661—21no—
20#16839661—21no—
21#16839619—21no—
22#16839619—21no—
23#16839516—21no—
24#16839510—22no—
25#16839510—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#384C2211yescharacteristic
29C22×Dic122C2×C412yes—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758189—24no—
34C2×#11758189—42no—
35C2×#11758189—42no—
36C22×#92418—21no—
37C22×#92418—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777—21no—
42#14519757—44no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—22no—
46C2×#11758198—22no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C42×D61—21no—
51C42×D61—21no—
52C42×D61—21no—
53C42×D61—21no—
54C4⋊#92418—21no—
55C4⋊#92418—21no—
56C4⋊#92418—21no—
57C4⋊#92418D412yes—
58#14519706—24no—
59#14519689—42no—
60#14519684—22no—
61#14519684—22no—
62C22×C8×C61—21no—
63C22×C8×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61C2×C412yes—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61D412yes—
72C23×D61C22⋊C411yescharacteristic
73C22×C4×C61—22no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—22no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—22no—
94C2×C4×D61—41no—
95C2×C4×D61SD1612yes—
96C2×C4×D61Q1612yes—
97C2×Dic122—22no—
98C2×Dic122—22no—
99C2×Dic122—42no—
100C2×Dic122—42no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C4⋊C4×C61—42no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61#4111yescharacteristic
115C42×C61#4111yescharacteristic
116#11758198—44no—
117C4⋊Dic61—41no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—44no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C2×#92418—22no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134#11758189—48no—
135C23×C61C2×C22⋊C411yescharacteristic
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61#10312yes—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×C4×C61C2×SD1611yescharacteristic
155C2×C4×C61C2×Q1611yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61#13711yescharacteristic
159C2×C4×C61#13711yescharacteristic
160C2×C4×C61#13711yescharacteristic
161C2×C4×C61#13711yescharacteristic
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61#10012yes—
173C2×Dic61#10312yes—
174C4×D61—22no—
175C4×D61—22no—
176C4×D61—22no—
177C4×D61—22no—
178C4×D61—42no—
179C4×D61—42no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184Dic122—82no—
185Dic122—82no—
186C8×C61—42no—
187C8×C61—81no—
188#92418—42no—
189#92418—81no—
190#9135—611nomaximal, Sylow
191C22×C61#38611yescharacteristic
192C22×C61C2×#10011yescharacteristic
193C22×C61#41311yescharacteristic
194C22×C61C2×#10311yescharacteristic
195C22×C61#41711yescharacteristic
196C22×C61#41711yescharacteristic
197C22×C61#41911yescharacteristic
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—82no—
208C4×C61#45011yescharacteristic
209C4×C61#45111yescharacteristic
210C4×C61#46811yescharacteristic
211C4×C61#46811yescharacteristic
212C4×C61#47011yescharacteristic
213C4×C61#47011yescharacteristic
214C4×C61#48311yescharacteristic
215C4×C61#48411yescharacteristic
216Dic61—22no—
217Dic61—22no—
218Dic61—41no—
219Dic61—82no—
220C2×#423—611no—
221#2857—611no—
222#1797—611no—
223C2×#333—611no—
224C2×#333—611no—
225#1296—611no—
226#1296D6111yescharacteristic, complemented
227C2×C61#154811yescharacteristic
228C2×C61#155011yescharacteristic
229C2×C61#155911yescharacteristic
230C2×C61#156011yescharacteristic
231C2×C61#187211yescharacteristic
232C2×C61#189411yescharacteristic
233C2×C61#190011yescharacteristic
234D61—42no—
235C22×M16—1221no—
236C2×C4⋊Q8—611no—
237C2×C22⋊Q8—612no—
238C22×C42—611no—
239#423—1222no—
240#423—1222no—
241C2×C4⋊C8—611no—
242C2×C4⋊C8—611no—
243C2×C4⋊C8—1221no—
244C2×C4⋊C8C2×D6111yescharacteristic
245C2×C4⋊C8C2×D6111yescharacteristic
246C2×C22⋊C8—1221no—
247#391—612no—
248#389—1221no—
249#389—1221no—
250#384C2×D6111yescharacteristic
251#380—1221no—
252#380—1221no—
253#336—1221no—
254#333—1222no—
255#333—1222no—
256C61#913511yescharacteristic, complemented, Sylow
257C22×Q8—612no—
258C23×C4—611no—
259C23×C4—611no—
260C23×C4—611no—
261C2×M16—1224no—
262C2×M16—2442no—
263C2×M16—2442no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—1221no—
267C22×C8—1221no—
268C4⋊Q8—1221no—
269C4⋊Q8—1221no—
270C4⋊Q8—1221no—
271C4⋊Q8—1221no—
272C22⋊Q8—2444no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—1222no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4C4×D6112yes—
279C2×C22⋊C4—1222no—
280C2×C42—611no—
281C2×C42—611no—
282C2×C42—611no—
283C2×C42—1221no—
284C2×C42—1221no—
285C2×C42—1221no—
286C2×C42—1221no—
287C2×C42C22×D6111yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—612no—
292C4⋊C8—1224no—
293C4⋊C8—1221no—
294C4⋊C8—1221no—
295C4⋊C8—1221no—
296C4⋊C8D24412yes—
297C22⋊C8—2442no—
298#95—1222no—
299#95—1222no—
300C24—611no—
301C2×Q8—1222no—
302C2×Q8—1222no—
303C2×Q8—2442no—
304C2×Q8—2442no—
305C22×C4—22no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—612no—
309C22×C4—612no—
310C22×C4—611no—
311C22×C4—1222no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1222no—
325C22×C4—2441no—
326C22×C4C2×C4×D6111yescharacteristic
327C22×C4D4×D6111yescharacteristic
328C22×C4D4×D6111yescharacteristic
329M16—2448no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—1222no—
337C2×C8—2441no—
338C2×C8—2441no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8—2441no—
342C4⋊C4—42no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—2444no—
348C4⋊C4—2441no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C4⋊C4—2441no—
352C22⋊C4—2444no—
353C42—1221no—
354C42—1221no—
355C42—1221no—
356C42—1221no—
357C42—1221no—
358C42—1221no—
359C42C2×D24411yescharacteristic
360C42#1175822211yescharacteristic
361C42D4×D6111yescharacteristic
362C42#1175822611yescharacteristic
363C23—612no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23C22⋊C4×D6111yescharacteristic
371Q8—4882no—
372Q8—4882no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—612no—
379C2×C4—612no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1222no—
385C2×C4—1222no—
386C2×C4—1222no—
387C2×C4—1222no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4#1451973911yescharacteristic
401C2×C4C4×D24411yescharacteristic
402C2×C4#1451974711yescharacteristic
403C2×C4#1451975011yescharacteristic
404C2×C4#1451975211yescharacteristic
405C2×C4#1451976211yescharacteristic
406C2×C4SD16×D6111yescharacteristic
407C2×C4Q16×D6111yescharacteristic
408C2×C4#1451980111yescharacteristic
409C2×C4#1451980111yescharacteristic
410C2×C4#1451980611yescharacteristic
411C2×C4#1451980611yescharacteristic
412C2×C4#1451980611yescharacteristic
413C2×C4#1451980911yescharacteristic
414C8—42no—
415C8—81no—
416C8—4881no—
417C8—2442no—
418C22—1222no—
419C22—1222no—
420C22—1222no—
421C22—2441no—
422C22—2441no—
423C22—2441no—
424C22—2441no—
425C22#1683964011yescharacteristic
426C22#100×D6111yescharacteristic
427C22#1683974511yescharacteristic
428C22#103×D6111yescharacteristic
429C22#1683976011yescharacteristic
430C22#1683976011yescharacteristic
431C22#1683976911yescharacteristic
432C4—21no—
433C4—21no—
434C4—82no—
435C4—1222no—
436C4—1222no—
437C4—4882no—
438C4—2441no—
439C4#1683991411yescharacteristic
440C4#1683991911yescharacteristic
441C4#1684000711yescharacteristic
442C4#1684000911yescharacteristic
443C4#1684001911yescharacteristic
444C4#1684002111yescharacteristic
445C4#1684009411yescharacteristic
446C4#1684009911yescharacteristic
447C2—2442no—
448C2#2144449811yescharacteristic
449C2#2144450811yescharacteristic
450C2#2144454811yescharacteristic
451C2#2144455111yescharacteristic
452C2#2144612511yescharacteristic
453C2#2144625111yescharacteristic
454C2#2144628111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#9135
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. C2×#16839510C2semidirect
5. C2×#16839510C2semidirect
6. #21443702C2semidirect
7. C61×#1296C2semidirect
226. #1296D61semidirect
256. C61#9135semidirect

Maximal subgroups

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

subgroupindex
C2×#168397842
#214541722
#214457962
C2×#168395102
#214437022
C61×#12962
#913561