Finite Group Databasebeta

← #29583837

Subgroups — #29583837

Order 15616.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839964C211yesmaximal, characteristic
2#21446613C211yesmaximal, characteristic
3#21445816C211yesmaximal, characteristic
4C2×#16839513C211yesmaximal, characteristic, complemented
5C2×#16839508C211yesmaximal, characteristic, complemented
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1990C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C2×C4×D244C2211yescharacteristic
10#16839964—22no—
11#16839964—22no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519701—21no—
16C2×#14519697—21no—
17C2×#14519689—21no—
18C2×#14519689—21no—
19#16839524—21no—
20#16839513—22no—
21#16839508—22no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×C4×C8×C61C2211yescharacteristic
24C61×#384C2211yescharacteristic
25C61×#340—21no—
26C61×#340—21no—
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C2×#11758201—24no—
30C2×#11758201—42no—
31C2×#11758201—42no—
32C22×#92418—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35C4×D244—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758198—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418D412yes—
47#14519701—24no—
48#14519697—42no—
49#14519689—42no—
50#14519689—42no—
51C22×Q8×C61—21no—
52C22×C8×C61D411yescharacteristic
53C22×C8×C61D411yescharacteristic
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61D412yes—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C42×C61C2311yescharacteristic
64C4×C8×C61—21no—
65C4×C8×C61—21no—
66C23×D61—21no—
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×Dic61—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244SD1612yes—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61SD1612yescomplemented
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—81no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110#11758201—48no—
111#11758198—41no—
112#11758198—41no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C2×#92418—22no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C23×C61#12111yescharacteristic
125C22×D61—22no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132Q8×C61—42no—
133Q8×C61—42no—
134Q8×C61—81no—
135Q8×C61—81no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—42no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61—81no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12311yescharacteristic
148C2×C4×C61#12311yescharacteristic
149C2×C4×C61#12411yescharacteristic
150C2×C4×C61C2×SD1611yescharacteristic
151C2×C4×C61C2×SD1611yescharacteristic
152C2×C4×C61#13511yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61#13711yescharacteristic
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161D244—22no—
162D244—22no—
163D244—41no—
164D244—41no—
165C4×D61—81no—
166C4×D61—81no—
167C4×D61—81no—
168C4×D61—81no—
169C8×C61—22no—
170C8×C61—41no—
171#92418—42no—
172#92418—81no—
173#92418—81no—
174#10477—611nomaximal, Sylow
175C22×C61#39411yescharacteristic
176C22×C61#46111yescharacteristic
177C22×C61#46311yescharacteristic
178C22×C61#46511yescharacteristic
179C22×C61#46911yescharacteristic
180C22×C61#47111yescharacteristic
181C22×C61#47311yescharacteristic
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—82no—
192C4×C61—161no—
193C4×C61#44911yescharacteristic
194C4×C61#45011yescharacteristic
195C4×C61#46011yescharacteristic
196C4×C61#46411yescharacteristic
197C4×C61#46511yescharacteristic
198C4×C61#46811yescharacteristic
199C4×C61#48111yescharacteristic
200C4×C61#48211yescharacteristic
201Dic61—81no—
202C2×#461—611no—
203#1990D6111yescharacteristic, complemented
204#1954—611no—
205#1802—611no—
206C2×#334—611no—
207C2×#332—611no—
208#1296—611no—
209C2×C61#167111yescharacteristic
210C2×C61#167911yescharacteristic
211C2×C61#169311yescharacteristic
212C2×C61#170111yescharacteristic
213C2×C61#203411yescharacteristic
214C2×C61#205211yescharacteristic
215C2×C61#205511yescharacteristic
216D61—82no—
217C22×SD16—1221no—
218C2×C4⋊Q8C2×D6111yescharacteristic
219C2×C4×D4—611no—
220#461—1222no—
221#461—1222no—
222C2×C4⋊C8—611no—
223C2×C4⋊C8—611no—
224C2×C4⋊C8—611no—
225C2×#103—1221no—
226C2×#102—1221no—
227C2×C22⋊C8—1221no—
228C2×C22⋊C8—1221no—
229C2×C4×C8C2×D6111yescharacteristic
230#384C2×D6111yescharacteristic
231#340—21no—
232#340—21no—
233#340—1221no—
234#334—1222no—
235#332—1222no—
236C61#1047711yescharacteristic, complemented, Sylow
237C22×Q8—21no—
238C22×D4—611no—
239C23×C4—1221no—
240C2×SD16—1224no—
241C2×SD16—2442no—
242C2×SD16—2442no—
243C22×C8—1221no—
244C22×C8—1221no—
245C22×C8—1221no—
246C22×C8C22⋊D6111yescharacteristic
247C22×C8C22⋊D6111yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8D24412yes—
252C4×D4—1221no—
253C4×D4—1221no—
254C4×D4—1221no—
255C4×D4—1221no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—611no—
262C2×C22⋊C4—1221no—
263C2×C42C22×D6111yescharacteristic
264C4⋊C8—612no—
265C4⋊C8—1221no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270#103—1224no—
271#102—2442no—
272C22⋊C8—2442no—
273C22⋊C8—2442no—
274C4×C8—21no—
275C4×C8—21no—
276C24—1221no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—612no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—1221no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4D4×D6111yescharacteristic
299C22×C4#1175822411yescharacteristic
300C22×C4C2×C22⋊D6111yescharacteristic
301SD16—2448no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—1222no—
308C2×C8—2441no—
309C2×C8—2441no—
310C2×C8—2441no—
311C2×C8—2441no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2441no—
315C2×C8—2441no—
316C2×C8#1175820112yescomplemented
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—81no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C42C2×D24411yescharacteristic
331C42#1175822211yescharacteristic
332C42D4×D6111yescharacteristic
333C42#1175822411yescharacteristic
334C23—1222no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23#1451974811yescharacteristic
342Q8—42no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346D4—1222no—
347D4—1222no—
348D4—2441no—
349D4—2441no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4—4881no—
361C2×C4—4881no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4#1451974711yescharacteristic
366C2×C4#1451974911yescharacteristic
367C2×C4#1451975111yescharacteristic
368C2×C4#1451975911yescharacteristic
369C2×C4#1451976111yescharacteristic
370C2×C4#1451976311yescharacteristic
371C2×C4SD16×D6111yescharacteristic
372C2×C4C2×#1175820111yescharacteristic
373C2×C4#1451979711yescharacteristic
374C2×C4#1451979811yescharacteristic
375C2×C4#1451980111yescharacteristic
376C2×C4#1451980111yescharacteristic
377C2×C4#1451980211yescharacteristic
378C2×C4#1451980811yescharacteristic
379C8—22no—
380C8—41no—
381C8—4881no—
382C8—4881no—
383C8—2442no—
384C22—4881no—
385C22—4881no—
386C22—4881no—
387C22—4881no—
388C22—2442no—
389C22—2442no—
390C22—2442no—
391C22#1683967811yescharacteristic
392C22#1683996411yescharacteristic
393C22#1683997411yescharacteristic
394C22#1683998811yescharacteristic
395C22#1684001211yescharacteristic
396C22#1684002211yescharacteristic
397C22#1684003411yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—161no—
402C4—4881no—
403C4#1683990811yescharacteristic
404C4#1683991411yescharacteristic
405C4#1683996211yescharacteristic
406C4#1683998411yescharacteristic
407C4#1683999311yescharacteristic
408C4#1684001011yescharacteristic
409C4#1684007911yescharacteristic
410C4#1684008511yescharacteristic
411C2—4882no—
412C2#2144519111yescharacteristic
413C2#2144523911yescharacteristic
414C2#2144532911yescharacteristic
415C2#2144537711yescharacteristic
416C2#2144700711yescharacteristic
417C2#2144711911yescharacteristic
418C2#2144713411yescharacteristic
subgroupG/H
centerC23#14519748
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1990C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1990D61
hypocenterC61#10477
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. C2×#16839513C2semidirect
5. C2×#16839508C2semidirect
6. #21443702C2semidirect
7. C61×#1990C2semidirect
96. C2×C8×C61SD16semidirect
203. #1990D61semidirect
236. C61#10477semidirect
316. C2×C8#11758201semidirect

Maximal subgroups

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

subgroupindex
C2×#168399642
#214466132
#214458162
C2×#168395132
C2×#168395082
#214437022
C61×#19902
#1047761