Finite Group Databasebeta

← #29568024

Subgroups — #29568024

Order 15616.

708 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448308C211yesmaximal, characteristic
2#21445886C211yesmaximal, characteristic, complemented
3#336×D61C211yesmaximal, characteristic, complemented
4#21443645C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#1272C211yesmaximal, characteristic, complemented
8C22×#11758226C411yescharacteristic
9C22×C8×D61—21no—
10C2×#14519735C411yescharacteristic
11C2×C42×D61C2211yescharacteristic
12C2×#14519689—21no—
13#16839669C411yescharacteristic
14#16839664C2211yescharacteristic
15#16839663C411yescharacteristic
16#16839640—21no—
17#16839640—21no—
18#16839609—21no—
19#16839609—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C2×#11758226—22no—
28C2×#11758226—42no—
29C2×#11758226—42no—
30C2×#11758226C814yescomplemented
31C22×D244—21no—
32C22×D244C2×C411yescharacteristic
33C22×C4×D61—21no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×#92418—21no—
38C22×#92418—21no—
39C2×C8×D61—24no—
40C2×C8×D61—42no—
41C2×C8×D61—42no—
42#14519735—42no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C42×D61—42no—
54#14519689—42no—
55#14519684—21no—
56#14519684—21no—
57C22×Q8×C61C2×C411yescharacteristic
58C22×C8×C61—21no—
59C22×C8×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#95×C61—21no—
63#95×C61—21no—
64C23×D61—21no—
65C23×D61C22⋊C411yescharacteristic
66C2×Q8×C61—21no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61C2×C812yescomplemented
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79#11758226—48no—
80#11758226—48no—
81C2×D244—24no—
82C2×D244—21no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—42no—
86C2×D244—42no—
87C2×D244C2×C812yescomplemented
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—24no—
98C2×C4×D61—41no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61C2×C812yes—
102C2×C4×D61M1612yes—
103C2×C8×C61—22no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C4⋊C4×C61—41no—
110C42×C61—41no—
111#11758198—42no—
112#11758198—42no—
113#11758198—41no—
114#11758198—41no—
115#11758198—41no—
116#11758198—41no—
117#11758198—42no—
118C4⋊Dic61—41no—
119C4×Dic61—41no—
120C4×Dic61—41no—
121C4×Dic61—41no—
122C4×Dic61—42no—
123C2×#92418—22no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C2×#92418—41no—
129C8×D61—48no—
130C23×C61C2×C22⋊C411yescharacteristic
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—22no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61C22⋊C812yes—
143C22×D61#9912yes—
144C22×D61#10012yes—
145Q8×C61—42no—
146Q8×C61—42no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—22no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61C22×C811yescharacteristic
160C2×C4×C61C2×M1611yescharacteristic
161C2×C4×C61#13511yescharacteristic
162C2×C4×C61#13511yescharacteristic
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C61#13711yescharacteristic
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61C22⋊C812yes—
176C2×Dic61#10412yes—
177D244—42no—
178D244—42no—
179D244—48no—
180C4×D61—24no—
181C4×D61—24no—
182C4×D61—24no—
183C4×D61—24no—
184C4×D61—48no—
185C4×D61—42no—
186C4×D61—42no—
187C8×C61—42no—
188C8×C61—81no—
189#92418—42no—
190#92418—81no—
191#7578—611nomaximal, Sylow
192C22×C61C2×C22⋊C811yescharacteristic
193C22×C61C2×#9911yescharacteristic
194C22×C61C2×#10011yescharacteristic
195C22×C61#41611yescharacteristic
196C22×C61#41711yescharacteristic
197C22×C61C2×#10411yescharacteristic
198C22×C61#42111yescharacteristic
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—42no—
206C2×D61—42no—
207C2×D61—42no—
208C2×D61—81no—
209C2×D61—81no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61#32314yes—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—42no—
220C4×C61—81no—
221Dic61—22no—
222Dic61—22no—
223Dic61—41no—
224Dic61—81no—
225#2297—611no—
226#1817—611no—
227C2×#336—611no—
228#1272—611no—
229#1272D6111yescharacteristic, complemented
230#1270—611no—
231#1270—611no—
232C2×C61C2×#32311yescharacteristic
233C2×C61#147611yescharacteristic
234C2×C61#147711yescharacteristic
235C2×C61#150411yescharacteristic
236C2×C61#151611yescharacteristic
237C2×C61#153011yescharacteristic
238C2×C61#155111yescharacteristic
239D61—24no—
240D61—82no—
241C22×#41—611no—
242C23×C8—1221no—
243C2×#117—611no—
244C22×C42—611no—
245C2×C22⋊C8—1221no—
246#391—611no—
247#391C2×D6111yescharacteristic
248#390—611no—
249#390—611no—
250#386—1221no—
251#386—1221no—
252C4×C22⋊C4—1221no—
253C4×C22⋊C4—1221no—
254#336—611no—
255#336—611no—
256#336—1221no—
257#336—1221no—
258#336C2×D6111yescharacteristic
259#336C2×D6111yescharacteristic
260C61#757811yescharacteristic, complemented, Sylow
261C2×#41—614no—
262C2×#41—1222no—
263C2×#41—2442no—
264C2×#41—2442no—
265C22×Q8C4×D6111yescharacteristic
266C22×D4—611no—
267C22×D4—1221no—
268C23×C4—611no—
269C23×C4—611no—
270C23×C4—611no—
271C23×C4—1221no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—1224no—
275C22×C8—1221no—
276C22×C8—1221no—
277C22×C8—2442no—
278C22×C8—2442no—
279#117—2442no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4C4×D6111yescharacteristic
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C42—611no—
288C2×C42—611no—
289C2×C42—611no—
290C2×C42—1221no—
291C2×C42—2442no—
292C2×C42C22×D6111yescharacteristic
293C22⋊C8—2442no—
294#95—21no—
295#95—21no—
296#95—1221no—
297#95—1221no—
298C24—611no—
299C24—1221no—
300#41—2448no—
301#41—2448no—
302C2×Q8—21no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8C8×D6112yescomplemented
306C2×D4—612no—
307C2×D4—1224no—
308C2×D4—1221no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2442no—
312C2×D4—2442no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—612no—
318C22×C4—612no—
319C22×C4—611no—
320C22×C4—1222no—
321C22×C4—1224no—
322C22×C4—1222no—
323C22×C4—1222no—
324C22×C4—1222no—
325C22×C4—1222no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—2441no—
332C22×C4—2442no—
333C22×C4—2442no—
334C22×C4C2×C4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—1222no—
344C2×C8—2448no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C2×C8—2441no—
350C4⋊C4—41no—
351C4⋊C4—2441no—
352C22⋊C4—2442no—
353C22⋊C4—2442no—
354C22⋊C4—2442no—
355C22⋊C4—2441no—
356C22⋊C4—2441no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C42—41no—
360C42—2441no—
361C42—2441no—
362C42—2441no—
363C42—2442no—
364C23—612no—
365C23—612no—
366C23—612no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23—1222no—
372C23—2441no—
373C23—2441no—
374C23—2441no—
375C23—2441no—
376C23—2441no—
377C23—2441no—
378C23C22⋊C4×D6111yescharacteristic
379Q8—42no—
380Q8—42no—
381D4—2442no—
382D4—2442no—
383D4—2448no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—612no—
397C2×C4—612no—
398C2×C4—1224no—
399C2×C4—1224no—
400C2×C4—1224no—
401C2×C4—1224no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—2442no—
410C2×C4—2442no—
411C2×C4—2448no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4C2×C8×D6111yescharacteristic
416C2×C4M16×D6111yescharacteristic
417C2×C4#1451979811yescharacteristic
418C2×C4#1451980011yescharacteristic
419C2×C4#1451980411yescharacteristic
420C2×C4#1451980911yescharacteristic
421C8—42no—
422C8—81no—
423C8—4881no—
424C8—2442no—
425C22—614no—
426C22—1222no—
427C22—1222no—
428C22—1222no—
429C22—1222no—
430C22—1222no—
431C22—1222no—
432C22—4881no—
433C22—4881no—
434C22—4881no—
435C22—4881no—
436C22—2442no—
437C22—2442no—
438C22—2442no—
439C22C22⋊C8×D6111yescharacteristic
440C22#99×D6111yescharacteristic
441C22#100×D6111yescharacteristic
442C22#1683975711yescharacteristic
443C22#1683976211yescharacteristic
444C22#104×D6111yescharacteristic
445C22#1683977711yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—81no—
454C4—1222no—
455C4—1222no—
456C4—4881no—
457C4—2441no—
458C2—1224no—
459C2—4882no—
460C2#323×D6111yescharacteristic
461C2#2144420011yescharacteristic
462C2#2144420511yescharacteristic
463C2#2144432211yescharacteristic
464C2#2144437411yescharacteristic
465C2#2144442811yescharacteristic
466C2#2144451311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758226C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7578
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #21445886C2semidirect
3. #336×D61C2semidirect
4. #21443645C2semidirect
5. #21443639C2semidirect
6. #21443639C2semidirect
7. C61×#1272C2semidirect
30. C2×#11758226C8semidirect
69. C2×Q8×C61C2×C8semidirect
87. C2×D244C2×C8semidirect
229. #1272D61semidirect
260. C61#7578semidirect
305. C2×Q8C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214483082
#214458862
#336×D612
#214436452
#214436392
C61×#12722
#757861