Finite Group Databasebeta

← #29596877

Subgroups — #29596877

Order 15616.

494 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D61C211yesmaximal, characteristic, complemented
2#21454515C211yesmaximal, characteristic
3C2×#16839547C211yesmaximal, characteristic, complemented
4C2×#16839545C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic, complemented
6#21443908C211yesmaximal, characteristic, complemented
7C61×#1379C211yesmaximal, characteristic, complemented
8C2×#14519783C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10#16840274C411yescharacteristic
11C2×#14519717C2211yescharacteristic
12C2×#14519716—21no—
13M32×D61—22no—
14M32×D61—22no—
15C22×#11758185C2211yescharacteristic
16C2×C16×D61—21no—
17#16839835—21no—
18#16839835—21no—
19C8×D244—21no—
20C8×D244—21no—
21#16839789C411yescharacteristic
22#16839730C411yescharacteristic
23#16839725C411yescharacteristic
24#16839547—22no—
25#16839545—22no—
26#16839541—21no—
27#16839541—21no—
28C2×M32×C61C2211yescharacteristic
29C22×C16×C61C2211yescharacteristic
30C61×#405C2211yescharacteristic
31C2×#11758222C2×C411yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33#14519783—21no—
34#14519783—21no—
35#14519783—21no—
36#14519783—21no—
37C2×#11758194C2×C411yescharacteristic
38C2×#11758189—21no—
39C22×#92418C2×C411yescharacteristic
40C2×C8×D61—21no—
41C2×C8×D61—21no—
42C2×C8×D61—21no—
43C2×C8×D61—21no—
44C2×C8×D61—21no—
45C2×C8×D61D411yescharacteristic
46C2×C8×D61D411yescharacteristic
47C2×C8×D61D411yescharacteristic
48C2×C8×D61D411yescharacteristic
49#14519761—21no—
50#14519757C811yescharacteristic
51#14519757C811yescharacteristic
52#14519752C811yescharacteristic
53#14519752C811yescharacteristic
54#14519747—21no—
55C4×D244—21no—
56C4×D244—21no—
57#14519717—21no—
58#14519717D412yescomplemented
59#14519716—24no—
60C2×#11758185—21no—
61C2×#11758185—21no—
62C2×#11758185—21no—
63C2×#11758185—21no—
64C16×D61—24no—
65C4⋊#92418—21no—
66C4⋊#92418—21no—
67#14519689—21no—
68#14519689—21no—
69#14519689—21no—
70#14519689—21no—
71C2×M16×C61C2×C411yescharacteristic
72C22×C8×C61C2311yescharacteristic
73#117×C61C2×C411yescharacteristic
74M32×C61—21no—
75M32×C61D412yescomplemented
76C2×C16×C61—21no—
77C2×C16×C61—21no—
78C2×C16×C61—21no—
79C2×C16×C61—21no—
80#97×C61—21no—
81C4×C8×C61—21no—
82C23×D61M1611yescharacteristic
83C22×C4×C61C22×C411yescharacteristic
84C2×C22⋊D61—21no—
85C22×Dic61M1611yescharacteristic
86#11758222—21no—
87#11758222—21no—
88#11758222—21no—
89#11758222—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244C2×C811yescharacteristic
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61C22⋊C411yescharacteristic
99C2×C4×D61C22⋊C411yescharacteristic
100C2×C4×D61C2×C811yescharacteristic
101C2×C4×D61C2×C811yescharacteristic
102C2×Dic122C2×C811yescharacteristic
103M16×C61—21no—
104M16×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61#4111yescharacteristic
111C2×C8×C61#4111yescharacteristic
112C4⋊C4×C61C2×C811yescharacteristic
113C4⋊C4×C61C2×C811yescharacteristic
114C22⋊C4×C61—21no—
115C42×C61—21no—
116#11758198—21no—
117#11758198—21no—
118#11758198—21no—
119#11758198—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122#11758194—21no—
123#11758194—21no—
124C2×#92418—21no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418C22⋊C411yescharacteristic
128C2×#92418C22⋊C411yescharacteristic
129#11758189—41no—
130#11758189—41no—
131C8×D61—21no—
132C8×D61—21no—
133C8×D61—21no—
134C8×D61—21no—
135C8×D61—21no—
136C8×D61—21no—
137C8×D61—21no—
138C8×D61—21no—
139C8×D61—41no—
140C8×D61—41no—
141C16×C61—22no—
142C16×C61—41no—
143#11758185—22no—
144#11758185—41no—
145C23×C61C2×M1611yescharacteristic
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—22no—
149C22×D61—21no—
150C22×D61—41no—
151C22×D61C22⋊C811yescharacteristic
152C22×D61C22⋊C811yescharacteristic
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61C22×C811yescharacteristic
159C2×C4×C61#13111yescharacteristic
160C2×C4×C61#13111yescharacteristic
161C22⋊D61—41no—
162C22⋊D61—41no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61C22⋊C811yescharacteristic
167C2×Dic61C22⋊C811yescharacteristic
168D244—21no—
169D244—21no—
170D244—42no—
171D244—42no—
172C4×D61—21no—
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—21no—
176C4×D61—21no—
177C4×D61—21no—
178C4×D61—21no—
179C4×D61—21no—
180C4×D61—41no—
181C4×D61—41no—
182Dic122—21no—
183Dic122—21no—
184C8×C61—41no—
185C8×C61#12011yescharacteristic
186C8×C61#12111yescharacteristic
187C8×C61#12111yescharacteristic
188C8×C61#12311yescharacteristic
189#92418—21no—
190#92418—21no—
191#92418—41no—
192#12978—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61C2×C22⋊C811yescharacteristic
196C22×C61#43511yescharacteristic
197C22×C61#43511yescharacteristic
198C2×D61—21no—
199C2×D61—21no—
200C2×D61—21no—
201C2×D61—21no—
202C2×D61—21no—
203C2×D61—42no—
204C2×D61—42no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61#35012yescomplemented
209C4×C61—41no—
210C4×C61—41no—
211C4×C61#38611yescharacteristic
212C4×C61#40811yescharacteristic
213C4×C61C8×D411yescharacteristic
214C4×C61C8×D411yescharacteristic
215Dic61—21no—
216Dic61—21no—
217Dic61—41no—
218C22×M32—611no—
219#2929—611no—
220C2×#350—611no—
221C2×#350—611no—
222C2×C22⋊C16—611no—
223#1379—611no—
224#1379D6111yescharacteristic, complemented
225C2×C61—21no—
226C2×C61—21no—
227C2×C61#186911yescharacteristic
228C2×C61C2×#35011yescharacteristic
229C2×C61#211711yescharacteristic
230D61—22no—
231D61—41no—
232D61—81no—
233C2×#131—611no—
234C23×C8—611no—
235#525—611no—
236C2×M32—611no—
237C2×M32—1221no—
238C2×M32—1222no—
239C2×M32—1222no—
240C2×M32C2×D6111yescharacteristic
241C22×C16—611no—
242C22×C16—1221no—
243C22×C16C2×D6111yescharacteristic
244#435—1221no—
245#435—1221no—
246C8×D4—1221no—
247C8×D4—1221no—
248#424—611no—
249#408—611no—
250#407—611no—
251#405C2×D6111yescharacteristic
252#350—1222no—
253#350—1222no—
254C22⋊C16—1221no—
255C22⋊C16—1221no—
256C61#1297811yescharacteristic, complemented, Sylow
257C2×#41—611no—
258C23×C4—611no—
259#131—1221no—
260#131—1221no—
261#131—1221no—
262#131—1221no—
263C2×M16—611no—
264C2×M16—1221no—
265C2×M16C4×D6111yescharacteristic
266C22×C8—611no—
267C22×C8—611no—
268C22×C8—611no—
269C22×C8—611no—
270C22×C8—611no—
271C22×C8—1221no—
272C22×C8—1221no—
273C22×C8—1221no—
274C22×C8—1221no—
275C22×C8—1221no—
276C22×C8C22×D6111yescharacteristic
277#123—1221no—
278C22⋊Q8—611no—
279C22⋊Q8—611no—
280#121—611no—
281#121—611no—
282#120—1221no—
283C4×D4—1221no—
284C4×D4—1221no—
285#117C4×D6111yescharacteristic
286M32—21no—
287M32—612no—
288M32—1224no—
289M32—1221no—
290M32D24412yescomplemented
291C2×C16—21no—
292C2×C16—21no—
293C2×C16—21no—
294C2×C16—21no—
295C2×C16—1224no—
296C2×C16—1221no—
297C2×C16—1221no—
298C2×C16—1221no—
299C2×C16—1221no—
300C4⋊C8—1221no—
301C4⋊C8—1221no—
302C22⋊C8—1221no—
303C22⋊C8—1221no—
304C22⋊C8—1221no—
305C22⋊C8—1221no—
306#97—21no—
307C4×C8—21no—
308C24—611no—
309#41—1221no—
310#41—1221no—
311#41—1221no—
312#41—1221no—
313C2×Q8—611no—
314C2×D4—611no—
315C2×D4—1221no—
316C2×D4—1221no—
317C2×D4—1221no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4C2×C4×D6111yescharacteristic
329M16—21no—
330M16—21no—
331M16—1221no—
332M16—1221no—
333M16—2441no—
334M16—2441no—
335C2×C8—21no—
336C2×C8—611no—
337C2×C8—611no—
338C2×C8—1221no—
339C2×C8—1221no—
340C2×C8—1221no—
341C2×C8—1221no—
342C2×C8—1221no—
343C2×C8—1221no—
344C2×C8—1221no—
345C2×C8—1221no—
346C2×C8—1221no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—2441no—
350C2×C8—2441no—
351C2×C8C2×D24411yescharacteristic
352C2×C8#1175822211yescharacteristic
353C2×C8D4×D6111yescharacteristic
354C2×C8D4×D6111yescharacteristic
355C2×C8D4×D6111yescharacteristic
356C2×C8#1175822611yescharacteristic
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C4⋊C4C8×D6111yescharacteristic
360C4⋊C4C8×D6111yescharacteristic
361C22⋊C4—21no—
362C22⋊C4—1221no—
363C22⋊C4—1221no—
364C22⋊C4—1221no—
365C22⋊C4—1221no—
366C42—21no—
367C16—22no—
368C16—41no—
369C16—1222no—
370C16—2441no—
371C23—611no—
372C23—611no—
373C23—1222no—
374C23—1221no—
375C23—1221no—
376C23—1221no—
377C23—2441no—
378C23M16×D6111yescharacteristic
379Q8—1221no—
380Q8—1221no—
381D4—1221no—
382D4—1221no—
383D4—2442no—
384D4—2442no—
385D4—2441no—
386D4—2441no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—611no—
390C2×C4—611no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4C22⋊C4×D6111yescharacteristic
405C2×C4#1451973911yescharacteristic
406C2×C4C4×D24411yescharacteristic
407C2×C4C2×C8×D6111yescharacteristic
408C2×C4#1451978311yescharacteristic
409C2×C4#1451978511yescharacteristic
410C8—41no—
411C8—1221no—
412C8—1221no—
413C8—2441no—
414C8#1451974711yescharacteristic
415C8#1451975011yescharacteristic
416C8#1451975211yescharacteristic
417C8#1451976211yescharacteristic
418C22—21no—
419C22—21no—
420C22—612no—
421C22—1221no—
422C22—1221no—
423C22—1221no—
424C22—1221no—
425C22—1221no—
426C22—2442no—
427C22—2442no—
428C22—2441no—
429C22—2441no—
430C22—2441no—
431C22C22⋊C8×D6111yescharacteristic
432C22#1683983211yescharacteristic
433C22#1683983511yescharacteristic
434C4—41no—
435C4—41no—
436C4—1221no—
437C4—1221no—
438C4—2441no—
439C4#1683964011yescharacteristic
440C4#1683972711yescharacteristic
441C4#1683982711yescharacteristic
442C4C8×D24411yescharacteristic
443C2—21no—
444C2—21no—
445C2—1222no—
446C2—4881no—
447C2—2441no—
448C2#2144611011yescharacteristic
449C2#350×D6111yescharacteristic
450C2#2144744511yescharacteristic
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1379C2
socleC22×C61C2×C22⋊C8
prime radical#16840274C4
cosocleC22×C8×C61C23
hypercenter#1379D61
hypocenterC61#12978
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1379

Complements

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

NH ≅ G/Ntype
1. C2×M32×D61C2semidirect
3. C2×#16839547C2semidirect
4. C2×#16839545C2semidirect
5. C2×#16839541C2semidirect
6. #21443908C2semidirect
7. C61×#1379C2semidirect
58. #14519717D4semidirect
75. M32×C61D4semidirect
208. C2×D61#350semidirect
224. #1379D61semidirect
256. C61#12978semidirect
290. M32D244semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D612
#214545152
C2×#168395472
C2×#168395452
C2×#168395412
#214439082
C61×#13792
#1297861