Finite Group Databasebeta

← #29583425

Subgroups — #29583425

Order 15616.

520 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#21450815C211yesmaximal, characteristic
2#21446575C211yesmaximal, characteristic, complemented
3#21445816C211yesmaximal, characteristic
4C2×#16839508C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1990C211yesmaximal, characteristic, complemented
8C2×#14519766—21no—
9C2×C4×D244C2211yescharacteristic
10C2×#14519710—21no—
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519697—21no—
14#16839688—22no—
15#16839669—21no—
16#16839619—21no—
17#16839619—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19#16839524—21no—
20#16839524—21no—
21#16839508—22no—
22#16839491—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4×C8×C61C2211yescharacteristic
25C61×#384C2211yescharacteristic
26C61×#340—22no—
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519766—42no—
32#14519766—42no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—21no—
36C4×D244—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758198—22no—
41C2×#11758198—22no—
42C2×#11758198—21no—
43C2×C4×Dic61—21no—
44#14519710—42no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418D412yes—
49#14519697—42no—
50#14519684—22no—
51#14519684—22no—
52#14519684—21no—
53C22×Q8×C61—21no—
54C22×C8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61D412yes—
64C2×C42×C61C2311yescharacteristic
65C4×C8×C61—21no—
66C4×C8×C61—21no—
67C23×D61—21no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C2×Q8×C61—41no—
74C22×C4×C61—22no—
75C22×C4×C61—41no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244D812yes—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—42no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61#4111yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110#11758198—44no—
111#11758198—44no—
112#11758198—41no—
113#11758198—41no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4×Dic61—41no—
121C4×Dic61—41no—
122C2×#92418—22no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C23×C61#12011yescharacteristic
129C22×D61—22no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136Q8×C61—81no—
137Q8×C61—81no—
138Q8×C61—81no—
139Q8×C61—81no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—81no—
146C2×C4×C61—81no—
147C2×C4×C61—81no—
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×C4×C61#12311yescharacteristic
153C2×C4×C61#12411yescharacteristic
154C2×C4×C61C2×D811yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61#13711yescharacteristic
161C2×C4×C61#13711yescharacteristic
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171D244—22no—
172D244—22no—
173D244—41no—
174D244—41no—
175C4×D61—81no—
176C4×D61—81no—
177C4×D61—81no—
178C4×D61—81no—
179C8×C61—42no—
180#92418—42no—
181#92418—81no—
182#10416—611nomaximal, Sylow
183C22×C61#39411yescharacteristic
184C22×C61#44711yescharacteristic
185C22×C61#44911yescharacteristic
186C22×C61#45211yescharacteristic
187C22×C61#45211yescharacteristic
188C22×C61#45411yescharacteristic
189C22×C61#45611yescharacteristic
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—42no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—82no—
200C4×C61—161no—
201C4×C61#46311yescharacteristic
202C4×C61#46411yescharacteristic
203C4×C61#46611yescharacteristic
204C4×C61#46811yescharacteristic
205C4×C61#48011yescharacteristic
206C4×C61#48211yescharacteristic
207C4×C61#48811yescharacteristic
208C4×C61#48911yescharacteristic
209Dic61—81no—
210Dic61—81no—
211Dic61—81no—
212#2547—611no—
213#1990D6111yescharacteristic, complemented
214#1947—611no—
215#1802—611no—
216C2×#332—611no—
217C2×D4⋊C8—611no—
218#1279—611no—
219C2×C61#162511yescharacteristic
220C2×C61#163811yescharacteristic
221C2×C61#164711yescharacteristic
222C2×C61#165211yescharacteristic
223C2×C61#203311yescharacteristic
224C2×C61#203811yescharacteristic
225C2×C61#204211yescharacteristic
226D61—82no—
227C2×C4⋊Q8C2×D6111yescharacteristic
228C2×#124—1221no—
229C2×C4×D4—611no—
230C2×#107—1221no—
231C2×C4⋊C8—611no—
232C2×C4⋊C8—611no—
233C2×#102—1221no—
234C2×C4×C8C2×D6111yescharacteristic
235#397—1222no—
236#391—1221no—
237#384C2×D6111yescharacteristic
238#380—1221no—
239#380—1221no—
240C4×C4⋊C4—611no—
241#340—22no—
242#340—1221no—
243#340—1221no—
244#332—1222no—
245D4⋊C8—1222no—
246C61#1041611yescharacteristic, complemented, Sylow
247C22×Q8—21no—
248C22×D4—611no—
249C23×C4—1221no—
250C22×C8—21no—
251C22×C8—1221no—
252C22×C8—1221no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257#124—2442no—
258#124—2442no—
259C4×D4—1221no—
260C4×D4—1221no—
261C4×D4—1221no—
262C4×D4—1221no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4C22⋊D6112yes—
271C2×C22⋊C4—1222no—
272C2×C22⋊C4—1222no—
273C2×C22⋊C4—1221no—
274C2×C42—1221no—
275C2×C42C22×D6111yescharacteristic
276#107—2442no—
277C4⋊C8—612no—
278C4⋊C8—1221no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281#102—2442no—
282C4×C8—21no—
283C4×C8—21no—
284#95—1222no—
285#95—1222no—
286#95—1221no—
287C24—1221no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—612no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1221no—
300C22×C4—22no—
301C22×C4—41no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2441no—
311C22×C4D4×D6111yescharacteristic
312C22×C4D4×D6111yescharacteristic
313C22×C4C2×C22⋊D6111yescharacteristic
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—1222no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—42no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—1221no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C22⋊C4—2444no—
339C22⋊C4—2444no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C42—2441no—
343C42—2441no—
344C42#1175822211yescharacteristic
345C42#1175822211yescharacteristic
346C42D4×D6111yescharacteristic
347C42#1175822411yescharacteristic
348C23—1222no—
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23#1451974511yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—1222no—
361D4—1222no—
362D4—2441no—
363D4—2441no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—4881no—
373C2×C4—4881no—
374C2×C4—4881no—
375C2×C4—4881no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4#1451974911yescharacteristic
386C2×C4#1451975011yescharacteristic
387C2×C4#1451975011yescharacteristic
388C2×C4#1451975911yescharacteristic
389C2×C4#1451976011yescharacteristic
390C2×C4#1451976311yescharacteristic
391C2×C4D8×D6111yescharacteristic
392C2×C4#1451979811yescharacteristic
393C2×C4#1451979811yescharacteristic
394C2×C4#1451980011yescharacteristic
395C2×C4#1451980111yescharacteristic
396C2×C4#1451980411yescharacteristic
397C2×C4#1451980611yescharacteristic
398C2×C4#1451980911yescharacteristic
399C8—42no—
400C8—4881no—
401C8—2442no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22—4881no—
406C22—2442no—
407C22—2442no—
408C22—2442no—
409C22#1683967711yescharacteristic
410C22#1683989411yescharacteristic
411C22#1683990611yescharacteristic
412C22#1683992111yescharacteristic
413C22#1683992311yescharacteristic
414C22#1683993411yescharacteristic
415C22#1683994411yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—161no—
420C4—4881no—
421C4—4881no—
422C4—4881no—
423C4#1683998011yescharacteristic
424C4#1683998711yescharacteristic
425C4#1683999711yescharacteristic
426C4#1684000711yescharacteristic
427C4#1684007411yescharacteristic
428C4#1684008511yescharacteristic
429C4#1684011811yescharacteristic
430C4#1684012311yescharacteristic
431C2—4882no—
432C2#2144490511yescharacteristic
433C2#2144498811yescharacteristic
434C2#2144505111yescharacteristic
435C2#2144508611yescharacteristic
436C2#2144699911yescharacteristic
437C2#2144703611yescharacteristic
438C2#2144705611yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1990C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1990D61
hypocenterC61#10416
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
2. #21446575C2semidirect
4. C2×#16839508C2semidirect
6. #21443659C2semidirect
7. C61×#1990C2semidirect
213. #1990D61semidirect
246. C61#10416semidirect

Maximal subgroups

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

subgroupindex
#214508152
#214465752
#214458162
C2×#168395082
C2×#168394912
#214436592
C61×#19902
#1041661