Finite Group Databasebeta

← #29573431

Subgroups — #29573431

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#384×D61C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4#21443703C211yesmaximal, characteristic, complemented
5#21443703C211yesmaximal, characteristic, complemented
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D61—21no—
9C2×C4⋊C4×D61—21no—
10C2×C4⋊C4×D61C412yes—
11C2×C42×D61C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519689—21no—
15C2×#14519689—21no—
16#16839632C2211yescharacteristic
17#16839631—21no—
18#16839631—21no—
19#16839631C412yes—
20#16839516—21no—
21#16839516—21no—
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C61×#384C2211yescharacteristic
25C22×C4×D61—22no—
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×#92418—21no—
30C22×#92418—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C412yes—
34C2×#11758196—22no—
35C2×#11758196—22no—
36C2×#11758196—22no—
37C4⋊C4×D61—42no—
38C4⋊C4×D61—42no—
39C4⋊C4×D61—42no—
40C4⋊C4×D61—42no—
41C4⋊C4×D61—44no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C42×D61—21no—
46C42×D61—21no—
47C42×D61—21no—
48C42×D61—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53#14519689—42no—
54#14519689—42no—
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C412yes—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—22no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—22no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C2×C4×D61—22no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—22no—
86C2×C4×D61—44no—
87C2×C4×D61—44no—
88C2×C4×D61—44no—
89C2×C4×D61D812yes—
90C2×C4×D61SD1612yes—
91C2×C4×D61SD1612yes—
92C2×C4×D61Q1612yes—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C4⋊C4×C61—42no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C42×C61#4111yescharacteristic
105C42×C61#4111yescharacteristic
106C42×C61#4111yescharacteristic
107C42×C61#4111yescharacteristic
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61—42no—
113#11758196—44no—
114#11758196—44no—
115#11758196—44no—
116C4×Dic61—21no—
117C4×Dic61—21no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C23×C61C2×C22⋊C411yescharacteristic
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61#10112yes—
134C22×D61#10212yes—
135C22×D61#10312yes—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61#11711yescharacteristic
142C2×C4×C61#11711yescharacteristic
143C2×C4×C61#12311yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61#12311yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61C2×SD1611yescharacteristic
149C2×C4×C61C2×SD1611yescharacteristic
150C2×C4×C61C2×Q1611yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C2×C4×C61#13711yescharacteristic
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—42no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61#10012yes—
165C2×Dic61#10212yes—
166C2×Dic61#10312yes—
167C4×D61—24no—
168C4×D61—24no—
169C4×D61—22no—
170C4×D61—22no—
171C4×D61—22no—
172C4×D61—22no—
173C4×D61—22no—
174C4×D61—22no—
175C4×D61—22no—
176C4×D61—22no—
177C4×D61—88no—
178C8×C61—81no—
179C8×C61—81no—
180#92418—81no—
181#92418—81no—
182#8724—611nomaximal, Sylow
183C22×C61#38111yescharacteristic
184C22×C61C2×#10011yescharacteristic
185C22×C61C2×#10111yescharacteristic
186C22×C61C2×#10211yescharacteristic
187C22×C61C2×#10311yescharacteristic
188C22×C61#41811yescharacteristic
189C22×C61#41911yescharacteristic
190C2×D61—22no—
191C2×D61—22no—
192C2×D61—22no—
193C2×D61—22no—
194C2×D61—22no—
195C2×D61—22no—
196C2×D61#33214yes—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—82no—
200C4×C61#48011yescharacteristic
201C4×C61#48011yescharacteristic
202C4×C61#48111yescharacteristic
203C4×C61#48111yescharacteristic
204C4×C61#48311yescharacteristic
205C4×C61#48311yescharacteristic
206C4×C61#48411yescharacteristic
207C4×C61#48411yescharacteristic
208Dic61—22no—
209Dic61—22no—
210Dic61—22no—
211Dic61—82no—
212C2×#384—611no—
213#1797—611no—
214#1797—611no—
215#1296—611no—
216#1296—611no—
217#1296—611no—
218#1296D6111yescharacteristic, complemented
219C2×C61C2×#33211yescharacteristic
220C2×C61#154511yescharacteristic
221C2×C61#154811yescharacteristic
222C2×C61#155611yescharacteristic
223C2×C61#182111yescharacteristic
224C2×C61#182311yescharacteristic
225C2×C61#182411yescharacteristic
226D61—24no—
227C22×C4⋊C4—612no—
228C22×C4⋊C4—1221no—
229C22×C4⋊C4—1221no—
230C22×C42—611no—
231C2×C4⋊C8—611no—
232C2×C4⋊C8—611no—
233C2×C4⋊C8C2×D6111yescharacteristic
234C2×C4⋊C8C2×D6111yescharacteristic
235C2×C22⋊C8—1221no—
236C2×C22⋊C8—1221no—
237#384—612no—
238#384—611no—
239#384—1221no—
240#384—1221no—
241#384C2×D6111yescharacteristic
242#336—1221no—
243#336—1221no—
244C61#872411yescharacteristic, complemented, Sylow
245C23×C4—611no—
246C23×C4—611no—
247C23×C4—611no—
248C23×C4—1222no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—1221no—
252C22×C8—1221no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—612no—
256C2×C4⋊C4—1222no—
257C2×C4⋊C4—1222no—
258C2×C4⋊C4—1222no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—2442no—
262C2×C4⋊C4—2442no—
263C2×C4⋊C4—2442no—
264C2×C4⋊C4—2442no—
265C2×C4⋊C4—2444no—
266C2×C4⋊C4C4×D6112yes—
267C2×C42—611no—
268C2×C42—611no—
269C2×C42—611no—
270C2×C42—1221no—
271C2×C42—1221no—
272C2×C42—1221no—
273C2×C42—1221no—
274C2×C42C22×D6111yescharacteristic
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281C4⋊C8—1221no—
282C4⋊C8—1221no—
283C22⋊C8—2442no—
284C22⋊C8—2442no—
285C24—611no—
286C22×C4—22no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—612no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1222no—
307C22×C4—2444no—
308C22×C4—2444no—
309C22×C4—2444no—
310C22×C4C2×C4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4D4×D6111yescharacteristic
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C4⋊C4—42no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—2442no—
331C4⋊C4—2444no—
332C4⋊C4—2444no—
333C4⋊C4—2444no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C4⋊C4—2441no—
338C42—1221no—
339C42—1221no—
340C42—1221no—
341C42—1221no—
342C42—1221no—
343C42—1221no—
344C42#1175822211yescharacteristic
345C42#1175822211yescharacteristic
346C42#1175822411yescharacteristic
347C42#1175822611yescharacteristic
348C23—612no—
349C23—612no—
350C23—612no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23C22⋊C4×D6111yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—612no—
362C2×C4—612no—
363C2×C4—612no—
364C2×C4—1224no—
365C2×C4—1224no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4—1222no—
375C2×C4—1222no—
376C2×C4—1222no—
377C2×C4—1222no—
378C2×C4—1222no—
379C2×C4—1222no—
380C2×C4—4888no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4#1451973411yescharacteristic
385C2×C4#1451973511yescharacteristic
386C2×C4#1451975911yescharacteristic
387C2×C4#1451975911yescharacteristic
388C2×C4#1451976211yescharacteristic
389C2×C4#1451976211yescharacteristic
390C2×C4D8×D6111yescharacteristic
391C2×C4SD16×D6111yescharacteristic
392C2×C4SD16×D6111yescharacteristic
393C2×C4Q16×D6111yescharacteristic
394C2×C4#1451980111yescharacteristic
395C2×C4#1451980411yescharacteristic
396C2×C4#1451980611yescharacteristic
397C2×C4#1451980911yescharacteristic
398C8—81no—
399C8—81no—
400C8—4881no—
401C8—4881no—
402C22—614no—
403C22—1222no—
404C22—1222no—
405C22—1222no—
406C22—1222no—
407C22—1222no—
408C22—1222no—
409C22#1683962411yescharacteristic
410C22#100×D6111yescharacteristic
411C22#101×D6111yescharacteristic
412C22#102×D6111yescharacteristic
413C22#103×D6111yescharacteristic
414C22#1683976511yescharacteristic
415C22#1683976911yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—1222no—
420C4—1222no—
421C4—1222no—
422C4—4882no—
423C4#1684007411yescharacteristic
424C4#1684007711yescharacteristic
425C4#1684007911yescharacteristic
426C4#1684008211yescharacteristic
427C4#1684009111yescharacteristic
428C4#1684009411yescharacteristic
429C4#1684009611yescharacteristic
430C4#1684009911yescharacteristic
431C2—1224no—
432C2#332×D6111yescharacteristic
433C2#2144448511yescharacteristic
434C2#2144449811yescharacteristic
435C2#2144453411yescharacteristic
436C2#2144589811yescharacteristic
437C2#2144590411yescharacteristic
438C2#2144590811yescharacteristic
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#8724
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. #21443703C2semidirect
5. #21443703C2semidirect
6. #21443702C2semidirect
7. C61×#1296C2semidirect
218. #1296D61semidirect
244. C61#8724semidirect

Maximal subgroups

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

subgroupindex
#384×D612
#214457962
#214437032
#214437022
C61×#12962
#872461