Finite Group Databasebeta

← #29574617

Subgroups — #29574617

Order 15616.

636 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D488C211yesmaximal, characteristic
2C2×#16839839C211yesmaximal, characteristic, complemented
3#21446612C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic, complemented
6#21443646C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C22×D488C411yescharacteristic
9C22×#11758189—21no—
10C2×C4×D244C2211yescharacteristic
11C2×C4×D244C2211yescharacteristic
12C4×D488—22no—
13C4×D488—22no—
14#16839839—22no—
15#16839839—22no—
16C2×#14519711C411yescharacteristic
17C2×#14519699C411yescharacteristic
18C2×#14519699C411yescharacteristic
19C2×#14519689—21no—
20C2×#14519689—21no—
21C2×#14519689—21no—
22C2×C4×#92418C2211yescharacteristic
23C2×C4×#92418C2211yescharacteristic
24#16839489—22no—
25#16839489—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×C4×C8×C61C2211yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×D244C2×C411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C2×D488—22no—
34C2×D488—22no—
35C2×D488—22no—
36C2×#11758189—24no—
37C2×#11758189—42no—
38C2×#11758189—42no—
39C22×#92418—21no—
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244—21no—
46C4×D244—21no—
47C4×D244—21no—
48C4×D244D412yes—
49C4×D244D412yes—
50C2×C4⋊Dic61C2×C411yescharacteristic
51C2×C4⋊Dic61C2×C411yescharacteristic
52C2×#11758198—21no—
53C2×#11758198—21no—
54#14519711—22no—
55#14519699—22no—
56#14519699—22no—
57#14519689—24no—
58#14519689—42no—
59#14519689—42no—
60C4×#92418—21no—
61C4×#92418—21no—
62C4×#92418—21no—
63C4×#92418—21no—
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66C22×C8×C61C2×C411yescharacteristic
67C22×C8×C61C2×C411yescharacteristic
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61D412yes—
73C4×C8×C61—21no—
74C4×C8×C61—21no—
75C23×D61—21no—
76C23×D61—21no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244C22⋊C412yes—
93C2×D244M1612yescomplemented
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C8×C61—21no—
107C2×C8×C61—21no—
108C2×C8×C61—21no—
109C2×C8×C61—22no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61M1612yescomplemented
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122#11758198—22no—
123#11758198—22no—
124#11758198—41no—
125#11758198—41no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61C22⋊C412yes—
130C2×#92418—21no—
131C2×#92418—21no—
132C2×#92418—22no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418—21no—
136C2×#92418—41no—
137C2×#92418—41no—
138C2×#92418D812yescomplemented
139D488—28no—
140#11758189—48no—
141C23×C61C4×D411yescharacteristic
142C22×D61—22no—
143C22×D61—22no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61C2×C22⋊C411yescharacteristic
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61#12011yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12311yescharacteristic
164C2×C4×C61C2×M1611yescharacteristic
165C2×C4×C61C2×M1611yescharacteristic
166C2×C4×C61#13111yescharacteristic
167C2×C4×C61#13111yescharacteristic
168C2×C4×C61C2×D811yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×Dic61—22no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178D244—22no—
179D244—22no—
180D244—22no—
181D244—22no—
182D244—41no—
183D244—41no—
184D244—41no—
185D244—41no—
186C4×D61—42no—
187C4×D61—42no—
188C4×D61—42no—
189C4×D61—42no—
190C4×D61—81no—
191C4×D61—81no—
192C4×D61—81no—
193C4×D61—81no—
194C8×C61—22no—
195C8×C61—41no—
196C8×C61—42no—
197C8×C61—81no—
198#92418—22no—
199#92418—42no—
200#92418—41no—
201#8951—611nomaximal, Sylow
202C22×C61#38611yescharacteristic
203C22×C61#43511yescharacteristic
204C22×C61#43611yescharacteristic
205C22×C61C4×D811yescharacteristic
206C22×C61#44211yescharacteristic
207C22×C61#44311yescharacteristic
208C22×C61#44411yescharacteristic
209C2×D61—42no—
210C2×D61—42no—
211C2×D61—42no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C2×D61—81no—
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61#40711yescharacteristic
226C4×C61#40811yescharacteristic
227C4×C61#43511yescharacteristic
228C4×C61#43611yescharacteristic
229C4×C61#44711yescharacteristic
230C4×C61#44911yescharacteristic
231C4×C61#45911yescharacteristic
232C4×C61#46311yescharacteristic
233Dic61—42no—
234Dic61—81no—
235C2×C4×D8—611no—
236C2×#436—611no—
237#1954—611no—
238C2×D4⋊C8—611no—
239C2×D4⋊C8—611no—
240#1277D6111yescharacteristic, complemented
241#1273—611no—
242C2×C61#158111yescharacteristic
243C2×C61#158611yescharacteristic
244C2×C61#158911yescharacteristic
245C2×C61#159411yescharacteristic
246C2×C61#187011yescharacteristic
247C2×C61#187611yescharacteristic
248C2×C61#187911yescharacteristic
249D61—82no—
250D61—82no—
251C22×D8—611no—
252C22×M16—1221no—
253C2×C4×D4—611no—
254C2×C4×D4—611no—
255C4×D8—1222no—
256C4×D8—1222no—
257#436—1222no—
258#436—1222no—
259C2×#107—611no—
260C2×C4⋊C8C2×D6111yescharacteristic
261C2×C4⋊C8C2×D6111yescharacteristic
262C2×#102—611no—
263C2×#102—611no—
264C2×C22⋊C8—1221no—
265C2×C22⋊C8—1221no—
266C2×C22⋊C8—1221no—
267C2×C4×C8—611no—
268C2×C4×C8—611no—
269C2×C4×C8C2×D6111yescharacteristic
270D4⋊C8—1222no—
271D4⋊C8—1222no—
272C61#895111yescharacteristic, complemented, Sylow
273C22×D4—611no—
274C22×D4—611no—
275C23×C4—1221no—
276C23×C4—1221no—
277C2×D8—1222no—
278C2×D8—1222no—
279C2×D8—1222no—
280C2×M16—1224no—
281C2×M16—2442no—
282C2×M16—2442no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—611no—
286C22×C8—611no—
287C22×C8—1221no—
288C22×C8C4×D6111yescharacteristic
289C22×C8C4×D6111yescharacteristic
290C4×D4—612no—
291C4×D4—612no—
292C4×D4—1221no—
293C4×D4—1221no—
294C4×D4—1221no—
295C4×D4—1221no—
296C4×D4—1221no—
297C4×D4—1221no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—611no—
300C2×C22⋊C4—1221no—
301C2×C22⋊C4—1221no—
302C2×C42C22×D6111yescharacteristic
303#107—1222no—
304C4⋊C8—21no—
305C4⋊C8—21no—
306C4⋊C8—21no—
307C4⋊C8D24412yes—
308#102—1222no—
309#102—1222no—
310C22⋊C8—1224no—
311C22⋊C8—2442no—
312C22⋊C8—2442no—
313C4×C8—21no—
314C4×C8—21no—
315C4×C8—1221no—
316C4×C8—1221no—
317C4×C8—1221no—
318C4×C8—1221no—
319C24—1221no—
320C24—1221no—
321C2×D4—612no—
322C2×D4—612no—
323C2×D4—1221no—
324C2×D4—1221no—
325C2×D4—1221no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4—1221no—
331C2×D4—1221no—
332C2×D4—1221no—
333C22×C4—1221no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—1221no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4—2441no—
346C22×C4—2441no—
347C22×C4C2×C4×D6111yescharacteristic
348C22×C4D4×D6111yescharacteristic
349C22×C4#1175822611yescharacteristic
350D8—1228no—
351M16—2448no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—612no—
364C2×C8—1221no—
365C2×C8—1221no—
366C2×C8—1222no—
367C2×C8—1221no—
368C2×C8—1221no—
369C2×C8—1221no—
370C2×C8—2441no—
371C2×C8—2441no—
372C2×C8#1175818912yescomplemented
373C4⋊C4—612no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C22⋊C4—1222no—
378C22⋊C4—1222no—
379C22⋊C4—2441no—
380C22⋊C4—2441no—
381C42C2×D24411yescharacteristic
382C42#1175822211yescharacteristic
383C42D4×D6111yescharacteristic
384C42D4×D6111yescharacteristic
385C23—1222no—
386C23—1222no—
387C23—2441no—
388C23—2441no—
389C23—2441no—
390C23—2441no—
391C23—2441no—
392C23—2441no—
393C23—2441no—
394C23—2441no—
395C23—2441no—
396C23—2441no—
397C23—2441no—
398C23—2441no—
399C23#1451973911yescharacteristic
400D4—1222no—
401D4—1222no—
402D4—1222no—
403D4—1222no—
404D4—2441no—
405D4—2441no—
406D4—2441no—
407D4—2441no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—1222no—
411C2×C4—4881no—
412C2×C4—4881no—
413C2×C4—4881no—
414C2×C4—4881no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2442no—
424C2×C4C22⋊C4×D6111yescharacteristic
425C2×C4C4×D24411yescharacteristic
426C2×C4#1451974711yescharacteristic
427C2×C4#1451975011yescharacteristic
428C2×C4#1451975211yescharacteristic
429C2×C4#1451976211yescharacteristic
430C2×C4M16×D6111yescharacteristic
431C2×C4C2×#1175818911yescharacteristic
432C2×C4#1451978311yescharacteristic
433C2×C4#1451978511yescharacteristic
434C2×C4D8×D6111yescharacteristic
435C2×C4#1451980011yescharacteristic
436C2×C4#1451980411yescharacteristic
437C2×C4#1451980411yescharacteristic
438C8—22no—
439C8—41no—
440C8—42no—
441C8—81no—
442C8—1222no—
443C8—2442no—
444C8—2441no—
445C22—4881no—
446C22—4881no—
447C22—4881no—
448C22—4881no—
449C22—4881no—
450C22—4881no—
451C22—4881no—
452C22—4881no—
453C22—2442no—
454C22—2442no—
455C22—2442no—
456C22—2442no—
457C22—2442no—
458C22—2442no—
459C22#1683964011yescharacteristic
460C22#1683983211yescharacteristic
461C22#1683983911yescharacteristic
462C22#1683984411yescharacteristic
463C22#1683987311yescharacteristic
464C22#1683987811yescharacteristic
465C22#1683988311yescharacteristic
466C4—21no—
467C4—21no—
468C4—4881no—
469C4—2442no—
470C4#1683972411yescharacteristic
471C4#1683972711yescharacteristic
472C4#1683983511yescharacteristic
473C4#1683984111yescharacteristic
474C4#1683989711yescharacteristic
475C4#1683991011yescharacteristic
476C4#1683995611yescharacteristic
477C4#1683998011yescharacteristic
478C2—4882no—
479C2—4882no—
480C2#2144464711yescharacteristic
481C2#2144468211yescharacteristic
482C2#2144470311yescharacteristic
483C2#2144473211yescharacteristic
484C2#2144611511yescharacteristic
485C2#2144614711yescharacteristic
486C2#2144616811yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61C4×D4
prime radicalC22×D488C4
cosocleC2×C42×C61C23
hypercenter#1277D61
hypocenterC61#8951
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. C2×#16839839C2semidirect
3. #21446612C2semidirect
4. C2×#16839489C2semidirect
5. C2×#16839489C2semidirect
6. #21443646C2semidirect
7. C61×#1277C2semidirect
93. C2×D244M16semidirect
117. C2×C8×C61M16semidirect
138. C2×#92418D8semidirect
240. #1277D61semidirect
272. C61#8951semidirect
372. C2×C8#11758189semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4882
C2×#168398392
#214466122
C2×#168394892
#214436462
C61×#12772
#895161