Finite Group Databasebeta

← #29597021

Subgroups — #29597021

Order 15616.

560 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839999C211yesmaximal, characteristic
2C2×#108×D61C211yesmaximal, characteristic, complemented
3C2×#16839576C211yesmaximal, characteristic, complemented
4C2×#16839574C211yesmaximal, characteristic, complemented
5#21447429C211yesmaximal, characteristic, complemented
6#21443927C211yesmaximal, characteristic, complemented
7C61×#1387C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C2×M16×D61—21no—
10C22×C8×D61C2211yescharacteristic
11C2×#14519752—21no—
12C2×#14519717C2211yescharacteristic
13#16839999—21no—
14#16839999—21no—
15#16839999C412yes—
16#16839999C412yes—
17C2×#14519713C2211yescharacteristic
18C2×#14519712—21no—
19#108×D61—22no—
20#108×D61—22no—
21C2×#14519697—21no—
22#16839576—22no—
23#16839574—22no—
24#16839541—21no—
25#16839541—21no—
26C2×M32×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C22×D244—21no—
30C22×D244—41no—
31C22×C4×D61D411yescharacteristic
32C2×D488—21no—
33C2×D488—21no—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488—21no—
37C2×D488C2×C412yes—
38C2×#11758194—21no—
39C2×#11758189—41no—
40M16×D61—24no—
41M16×D61—42no—
42C22×#92418D411yescharacteristic
43C2×C8×D61—21no—
44C2×C8×D61—21no—
45C2×C8×D61—21no—
46C2×C8×D61—21no—
47C2×C8×D61—41no—
48C2×C8×D61C2×C411yescharacteristic
49C2×C8×D61C2×C411yescharacteristic
50C2×C8×D61D411yescharacteristic
51C2×C8×D61D411yescharacteristic
52#14519752—22no—
53#14519752—22no—
54#14519752—41no—
55#14519752—41no—
56C2×#11758198—41no—
57#14519717—21no—
58#14519717—21no—
59C2×#11758185—21no—
60#14519713—21no—
61#14519713D412yescomplemented
62#14519712—24no—
63#14519697—22no—
64#14519697—22no—
65C2×M16×C61—21no—
66C22×C8×C61C2311yescharacteristic
67C2×C4⋊C4×C61—21no—
68M32×C61—21no—
69M32×C61—21no—
70C2×C16×C61—21no—
71#108×C61—21no—
72#108×C61D412yescomplemented
73#107×C61—21no—
74#107×C61C2×C412yes—
75C23×D61—41no—
76C23×D61SD1611yescharacteristic
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61SD1611yescharacteristic
80C2×D244—22no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—42no—
86C2×D244—42no—
87C2×D244—41no—
88C2×D244—84no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61C22⋊C411yescharacteristic
94C2×C4×D61C22⋊C411yescharacteristic
95C2×C4×D61D811yescharacteristic
96C2×C4×D61D811yescharacteristic
97M16×C61—22no—
98M16×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61C22×C411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C2×C8×C61#4111yescharacteristic
106C4⋊C4×C61—22no—
107C4⋊C4×C61—41no—
108#11758198—42no—
109#11758198—42no—
110#11758194—22no—
111#11758194—41no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—41no—
115C2×#92418C22⋊C411yescharacteristic
116C2×#92418C22⋊C411yescharacteristic
117D488—22no—
118D488—22no—
119D488—41no—
120D488—41no—
121#11758189—44no—
122C8×D61—21no—
123C8×D61—21no—
124C8×D61—21no—
125C8×D61—21no—
126C8×D61—21no—
127C8×D61—21no—
128C8×D61—21no—
129C8×D61—21no—
130C8×D61—44no—
131C16×C61—41no—
132#11758185—41no—
133C23×C61C2×SD1611yescharacteristic
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—22no—
137C22×D61—41no—
138C22×D61—42no—
139C22×D61—82no—
140C22×D61—82no—
141C22×D61—81no—
142C22×D61—81no—
143C22×D61#10211yescharacteristic
144C22×D61#10211yescharacteristic
145C2×C4×C61—42no—
146C2×C4×C61—82no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61#12011yescharacteristic
149C2×C4×C61#12311yescharacteristic
150C2×C4×C61C2×D811yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61#10211yescharacteristic
156C2×Dic61#10211yescharacteristic
157D244—42no—
158D244—42no—
159D244—84no—
160D244—84no—
161D244—81no—
162D244—81no—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—21no—
168C4×D61—21no—
169C4×D61—21no—
170C4×D61—21no—
171C8×C61—42no—
172C8×C61C4×D411yescharacteristic
173C8×C61C4×D411yescharacteristic
174C8×C61#12111yescharacteristic
175C8×C61#12111yescharacteristic
176#92418—21no—
177#92418—21no—
178#92418—42no—
179#13004—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61C2×#10211yescharacteristic
183C22×C61#44811yescharacteristic
184C22×C61#48111yescharacteristic
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—82no—
193C2×D61—82no—
194C2×D61—82no—
195C2×D61—162no—
196C2×D61—162no—
197C2×D61#36112yescomplemented
198C4×C61—82no—
199C4×C61#38611yescharacteristic
200C4×C61#41711yescharacteristic
201C4×C61#44711yescharacteristic
202C4×C61#48011yescharacteristic
203Dic61—21no—
204Dic61—21no—
205C2×#466—611no—
206C22×#108—611no—
207C2×#361—611no—
208C2×#361—611no—
209#2112—611no—
210#1387—611no—
211#1387D6111yescharacteristic, complemented
212C2×C61—21no—
213C2×C61—21no—
214C2×C61#187411yescharacteristic
215C2×C61C2×#36111yescharacteristic
216C2×C61#214811yescharacteristic
217D61—22no—
218D61—41no—
219D61—162no—
220C22×D8—611no—
221C22×M16—1221no—
222C23×C8—611no—
223C2×#121—1221no—
224C2×M32—611no—
225C2×M32C2×D6111yescharacteristic
226#466—612no—
227#466—612no—
228#466—1221no—
229#466—1221no—
230C2×#108—611no—
231C2×#108—1222no—
232C2×#108—1221no—
233C2×#108—1222no—
234C2×#108C2×D6111yescharacteristic
235C2×#107C2×D6111yescharacteristic
236C2×#102—1221no—
237#361—1222no—
238#361—1222no—
239C22⋊C16—1221no—
240C22⋊C16—1221no—
241C61#1300411yescharacteristic, complemented, Sylow
242C22×D4—1221no—
243C22×D4—2441no—
244C23×C4—611no—
245C2×D8—612no—
246C2×D8—1221no—
247C2×D8—1221no—
248C2×D8—1221no—
249C2×D8—1221no—
250C2×D8—1221no—
251C2×M16—21no—
252C2×M16—1224no—
253C2×M16—1221no—
254C2×M16—2441no—
255C2×M16—2442no—
256C22×C8—611no—
257C22×C8—611no—
258C22×C8—611no—
259C22×C8—611no—
260C22×C8—611no—
261C22×C8—1221no—
262C22×C8—1221no—
263C22×C8—1221no—
264C22×C8—1221no—
265C22×C8—2441no—
266C22×C8C22×D6111yescharacteristic
267#121—1222no—
268#121—1222no—
269#121—2441no—
270#121—2441no—
271C2×C4⋊C4—21no—
272C2×C22⋊C4—2441no—
273M32—21no—
274M32—21no—
275M32—1221no—
276M32—1221no—
277C2×C16—21no—
278C2×C16—1221no—
279#108—21no—
280#108—612no—
281#108—1224no—
282#108—1221no—
283#108D24412yescomplemented
284#107—21no—
285#107C4×D6112yes—
286#102—1222no—
287#102—1222no—
288C24—611no—
289C24—2441no—
290C2×D4—1222no—
291C2×D4—4884no—
292C2×D4—2442no—
293C2×D4—2442no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C22×C4—41no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4D4×D6111yescharacteristic
310D8—1222no—
311D8—1222no—
312D8—2441no—
313D8—2441no—
314M16—22no—
315M16—41no—
316M16—1222no—
317M16—2444no—
318M16—2441no—
319C2×C8—41no—
320C2×C8—611no—
321C2×C8—611no—
322C2×C8—1221no—
323C2×C8—1221no—
324C2×C8—1221no—
325C2×C8—1221no—
326C2×C8—1221no—
327C2×C8—1221no—
328C2×C8—1221no—
329C2×C8—1221no—
330C2×C8—1221no—
331C2×C8—1221no—
332C2×C8—2444no—
333C2×C8—2441no—
334C2×C8C2×C4×D6111yescharacteristic
335C2×C8C2×D24411yescharacteristic
336C2×C8#1175822211yescharacteristic
337C2×C8D4×D6111yescharacteristic
338C2×C8D4×D6111yescharacteristic
339C2×C8#1175822611yescharacteristic
340C4⋊C4—22no—
341C4⋊C4—41no—
342C22⋊C4—2442no—
343C22⋊C4—2442no—
344C16—41no—
345C16—2441no—
346C23—611no—
347C23—611no—
348C23—1222no—
349C23—1221no—
350C23—1221no—
351C23—4882no—
352C23—4882no—
353C23—4881no—
354C23—4881no—
355C23—2441no—
356C23—2442no—
357C23SD16×D6111yescharacteristic
358D4—4884no—
359D4—4884no—
360D4—4881no—
361D4—4881no—
362D4—2442no—
363D4—2442no—
364C2×C4—42no—
365C2×C4—82no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4C22⋊C4×D6111yescharacteristic
379C2×C4#1451974711yescharacteristic
380C2×C4#1451976211yescharacteristic
381C2×C4D8×D6111yescharacteristic
382C2×C4#1451980411yescharacteristic
383C2×C4#1451980911yescharacteristic
384C8—42no—
385C8—1221no—
386C8—1221no—
387C8—2442no—
388C8#1451973911yescharacteristic
389C8C4×D24411yescharacteristic
390C8#1451975011yescharacteristic
391C8#1451975211yescharacteristic
392C22—21no—
393C22—21no—
394C22—612no—
395C22—1221no—
396C22—1221no—
397C22—1221no—
398C22—1221no—
399C22—1221no—
400C22—9762no—
401C22—9762no—
402C22—4882no—
403C22—4882no—
404C22—4882no—
405C22—2442no—
406C22—2442no—
407C22#102×D6111yescharacteristic
408C22#1683990211yescharacteristic
409C22#1684008211yescharacteristic
410C4—82no—
411C4—1221no—
412C4—1221no—
413C4#1683964011yescharacteristic
414C4#1683976211yescharacteristic
415C4#1683989711yescharacteristic
416C4#1684007711yescharacteristic
417C2—21no—
418C2—21no—
419C2—1222no—
420C2—9762no—
421C2—2441no—
422C2#2144613511yescharacteristic
423C2#361×D6111yescharacteristic
424C2#2144756711yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1387C2
socleC22×C61C2×#102
prime radicalC2×#16839999C2
cosocleC22×C8×C61C23
hypercenter#1387D61
hypocenterC61#13004
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
2. C2×#108×D61C2semidirect
3. C2×#16839576C2semidirect
4. C2×#16839574C2semidirect
5. #21447429C2semidirect
6. #21443927C2semidirect
7. C61×#1387C2semidirect
61. #14519713D4semidirect
72. #108×C61D4semidirect
197. C2×D61#361semidirect
211. #1387D61semidirect
241. C61#13004semidirect
283. #108D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168399992
C2×#108×D612
C2×#168395762
C2×#168395742
#214474292
#214439272
C61×#13872
#1300461