Finite Group Databasebeta

← #29583437

Subgroups — #29583437

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#21450814C211yesmaximal, characteristic
2#21446780C211yesmaximal, characteristic, complemented
3#21446582C211yesmaximal, characteristic, complemented
4#21445820C211yesmaximal, characteristic
5C2×#16839509C211yesmaximal, characteristic, complemented
6C2×#16839491C211yesmaximal, characteristic
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519765—21no—
10C2×C4×D244C2211yescharacteristic
11C2×#14519708—21no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519699—21no—
14#16839689—22no—
15#16839668—21no—
16#16839632C2211yescharacteristic
17#16839619—21no—
18#16839619—21no—
19#16839525—22no—
20#16839525—21no—
21#16839524—21no—
22#16839509—22no—
23#16839491—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C4×C4⋊C4×C61C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35#14519765—42no—
36#14519765—42no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61D412yes—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758198—22no—
48C2×#11758198—22no—
49C2×#11758198—21no—
50#14519708—42no—
51C4⋊#92418—21no—
52C4⋊#92418D412yes—
53#14519699—42no—
54#14519684—22no—
55#14519684—22no—
56C22×C8×C61—21no—
57C22×C8×C61—21no—
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C42×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4×C8×C61—21no—
65C4×C8×C61—21no—
66#95×C61—21no—
67C23×D61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—22no—
75C22×Dic61—41no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244SD1612yes—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×Dic122—41no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C42×C61—41no—
105C42×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—22no—
116C4⋊Dic61—21no—
117C4⋊Dic61—22no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61—42no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125C2×#92418—22no—
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—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61#12111yescharacteristic
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×C61#13511yescharacteristic
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—42no—
159C2×Dic61—41no—
160C2×Dic61—42no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—41no—
164C2×Dic61—81no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167D244—22no—
168D244—22no—
169D244—41no—
170D244—41no—
171C4×D61—81no—
172C4×D61—81no—
173C4×D61—81no—
174C4×D61—81no—
175Dic122—81no—
176Dic122—81no—
177Dic122—81no—
178Dic122—81no—
179C8×C61—42no—
180C8×C61—81no—
181#92418—42no—
182#10417—611nomaximal, Sylow
183C22×C61#39411yescharacteristic
184C22×C61#44911yescharacteristic
185C22×C61#44911yescharacteristic
186C22×C61#45011yescharacteristic
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—81no—
200C4×C61—81no—
201C4×C61#46311yescharacteristic
202C4×C61#46411yescharacteristic
203C4×C61#46511yescharacteristic
204C4×C61#46911yescharacteristic
205C4×C61#48111yescharacteristic
206C4×C61#48211yescharacteristic
207C4×C61#48811yescharacteristic
208C4×C61#48911yescharacteristic
209Dic61—82no—
210Dic61—81no—
211Dic61—161no—
212#2547—611no—
213#1990—611no—
214#1948—611no—
215#1802—611no—
216C2×#332—611no—
217C2×D4⋊C8—611no—
218#1279D6111yescharacteristic, complemented
219C2×C61#162811yescharacteristic
220C2×C61#163511yescharacteristic
221C2×C61#165011yescharacteristic
222C2×C61#165411yescharacteristic
223C2×C61#203411yescharacteristic
224C2×C61#203811yescharacteristic
225C2×C61#204211yescharacteristic
226D61—82no—
227C2×C4⋊Q8—611no—
228C2×#124—1221no—
229C2×C4×D4—611no—
230C2×#106—1221no—
231C2×C4⋊C8—611no—
232C2×C4⋊C8C2×D6111yescharacteristic
233C2×#102—1221no—
234C2×C4×C8C2×D6111yescharacteristic
235#397—1222no—
236#391—1221no—
237#384—611no—
238#380—1221no—
239#380—1221no—
240C4×C4⋊C4C2×D6111yescharacteristic
241#340—1221no—
242#340—1222no—
243#340—1221no—
244#332—1222no—
245D4⋊C8—1222no—
246C61#1041711yescharacteristic, complemented, Sylow
247C22×Q8—1221no—
248C22×D4—611no—
249C23×C4—1221no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—1221no—
253C4⋊Q8—1221no—
254C4⋊Q8—1221no—
255C4⋊Q8—1221no—
256C4⋊Q8—1221no—
257#124—2442no—
258#124—2442no—
259C4×D4—1221no—
260C4×D4—1221no—
261C4×D4—1221no—
262C4×D4—1221no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4—612no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4D24411yescharacteristic
270C2×C4⋊C4D24411yescharacteristic
271C2×C22⋊C4—1222no—
272C2×C22⋊C4—1222no—
273C2×C22⋊C4—1221no—
274C2×C42—21no—
275C2×C42C22×D6111yescharacteristic
276#106—2442no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—612no—
280C4⋊C8—1221no—
281#102—2442no—
282C4×C8—21no—
283C4×C8—21no—
284#95—21no—
285#95—1222no—
286#95—1222no—
287C24—1221no—
288C2×Q8—2441no—
289C2×Q8—2441no—
290C2×Q8—2441no—
291C2×Q8—2441no—
292C2×Q8—2441no—
293C2×Q8—2441no—
294C2×D4—612no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1221no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—1221no—
303C22×C4—1222no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2441no—
311C22×C4C2×D24411yescharacteristic
312C22×C4D4×D6111yescharacteristic
313C22×C4D4×D6111yescharacteristic
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—1222no—
321C2×C8—2441no—
322C2×C8—2441no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—1221no—
328C4⋊C4—1222no—
329C4⋊C4—1221no—
330C4⋊C4—1222no—
331C4⋊C4—2442no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C4⋊C4—2441no—
338C22⋊C4—2444no—
339C22⋊C4—2444no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C42—41no—
343C42—41no—
344C42#1175822211yescharacteristic
345C42#1175822211yescharacteristic
346C42D4×D6111yescharacteristic
347C42#1175822611yescharacteristic
348C23—1222no—
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23#1451974711yescharacteristic
356Q8—4881no—
357Q8—4881no—
358Q8—4881no—
359Q8—4881no—
360D4—1222no—
361D4—1222no—
362D4—2441no—
363D4—2441no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—4881no—
373C2×C4—4881no—
374C2×C4—4881no—
375C2×C4—4881no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—4881no—
379C2×C4—2441no—
380C2×C4—2442no—
381C2×C4—2441no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2441no—
385C2×C4#1451975011yescharacteristic
386C2×C4#1451975011yescharacteristic
387C2×C4#1451975211yescharacteristic
388C2×C4#1451976211yescharacteristic
389C2×C4#1451976211yescharacteristic
390C2×C4#1451976511yescharacteristic
391C2×C4SD16×D6111yescharacteristic
392C2×C4#1451979911yescharacteristic
393C2×C4#1451979911yescharacteristic
394C2×C4#1451980011yescharacteristic
395C2×C4#1451980111yescharacteristic
396C2×C4#1451980411yescharacteristic
397C2×C4#1451980511yescharacteristic
398C2×C4#1451981011yescharacteristic
399C8—42no—
400C8—81no—
401C8—2442no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22—4881no—
406C22—2442no—
407C22—2442no—
408C22—2442no—
409C22#1683968011yescharacteristic
410C22#1683990911yescharacteristic
411C22#1683991011yescharacteristic
412C22#1683991411yescharacteristic
413C22#1683992611yescharacteristic
414C22#1683993611yescharacteristic
415C22#1683994611yescharacteristic
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—9761no—
421C4—4882no—
422C4—4881no—
423C4#1683997811yescharacteristic
424C4#1683998511yescharacteristic
425C4#1683999411yescharacteristic
426C4#1684001411yescharacteristic
427C4#1684008211yescharacteristic
428C4#1684008911yescharacteristic
429C4#1684011711yescharacteristic
430C4#1684012211yescharacteristic
431C2—4882no—
432C2#2144493211yescharacteristic
433C2#2144497311yescharacteristic
434C2#2144507811yescharacteristic
435C2#2144510511yescharacteristic
436C2#2144701111yescharacteristic
437C2#2144703911yescharacteristic
438C2#2144706111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1279D61
hypocenterC61#10417
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #21446780C2semidirect
3. #21446582C2semidirect
5. C2×#16839509C2semidirect
7. C61×#1279C2semidirect
218. #1279D61semidirect
246. C61#10417semidirect

Maximal subgroups

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

subgroupindex
#214508142
#214467802
#214465822
#214458202
C2×#168395092
C2×#168394912
C61×#12792
#1041761