Finite Group Databasebeta

← #29575373

Subgroups — #29575373

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758189C211yesmaximal, characteristic
2C4×#14519757C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C2×#16839494C211yesmaximal, characteristic, complemented
5C2×#16839492C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×#14519757C411yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11C2×C42×D61C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519689—21no—
14C4×#11758189—22no—
15C4×#11758189—22no—
16C2×#14519687—21no—
17C2×C4×#92418C2211yescharacteristic
18#16839667C411yescharacteristic
19#16839661C411yescharacteristic
20#16839647—21no—
21#16839636—21no—
22#16839619C411yescharacteristic
23C4×C4⋊Dic61—21no—
24C4×#11758198—21no—
25#16839516—21no—
26#16839494—22no—
27#16839492—22no—
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C4×C4⋊C4×C61C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C2×#11758189—24no—
36C2×#11758189—24no—
37C2×#11758189—24no—
38C22×#92418—21no—
39C22×#92418—21no—
40#14519757—22no—
41#14519757—22no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758196—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×C4×Dic61—21no—
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C42×D61—21no—
57C42×D61—21no—
58C42×D61—21no—
59C42×D61—21no—
60C4⋊#92418—21no—
61C4⋊#92418—21no—
62#14519689—42no—
63#14519687—24no—
64C4×#92418—21no—
65C4×#92418D412yes—
66#14519684—21no—
67#14519684—21no—
68#14519684—21no—
69#14519684—21no—
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C42×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61—21no—
77C4⋊C8×C61—21no—
78C4×C8×C61—21no—
79C4×C8×C61D412yes—
80#95×C61—21no—
81C23×D61C22⋊C411yescharacteristic
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C2×C4×D61—22no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—22no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×Dic122—21no—
109C2×Dic122—21no—
110C2×Dic122—21no—
111C2×Dic122—21no—
112C2×Dic122—21no—
113C2×Dic122M1612yescomplemented
114C2×C8×C61—22no—
115C2×C8×C61—22no—
116C2×C8×C61—22no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C2×C8×C61—41no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61M1612yescomplemented
124C42×C61—41no—
125C42×C61—41no—
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128C42×C61#4111yescharacteristic
129C42×C61#4111yescharacteristic
130#11758198—24no—
131#11758198—42no—
132C4⋊Dic61—24no—
133C4⋊Dic61—21no—
134C4⋊Dic61—21no—
135C4⋊Dic61—42no—
136#11758196—41no—
137#11758196—41no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—21no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144C4×Dic61—41no—
145C4×Dic61—41no—
146C2×#92418—22no—
147C2×#92418—22no—
148C2×#92418—22no—
149C2×#92418—41no—
150C2×#92418—41no—
151C2×#92418—41no—
152#11758189—216no—
153C23×C61C2×C22⋊C411yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61#10412yes—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—22no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61C4×D411yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12311yescharacteristic
175C2×C4×C61C2×M1611yescharacteristic
176C2×C4×C61C2×M1611yescharacteristic
177C2×C4×C61#13111yescharacteristic
178C2×C4×C61#13111yescharacteristic
179C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C61#13711yescharacteristic
181C2×C4×C61#13711yescharacteristic
182C2×C4×C61#13711yescharacteristic
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—22no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61#10412yes—
198C4×D61—24no—
199C4×D61—24no—
200C4×D61—41no—
201C4×D61—41no—
202C4×D61—41no—
203C4×D61—41no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—41no—
208Dic122—22no—
209Dic122—22no—
210Dic122—41no—
211Dic122—41no—
212C8×C61—24no—
213C8×C61—81no—
214#92418—24no—
215#92418—81no—
216#9077—611nomaximal, Sylow
217C22×C61#38611yescharacteristic
218C22×C61#40711yescharacteristic
219C22×C61#40811yescharacteristic
220C22×C61#41711yescharacteristic
221C22×C61#41911yescharacteristic
222C22×C61C2×#10411yescharacteristic
223C22×C61C2×#10411yescharacteristic
224C2×D61—22no—
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—41no—
228C2×D61—41no—
229C2×D61—41no—
230C2×D61—41no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—42no—
234C4×C61—81no—
235C4×C61#43511yescharacteristic
236C4×C61#43511yescharacteristic
237C4×C61#43611yescharacteristic
238C4×C61#43611yescharacteristic
239C4×C61#46811yescharacteristic
240C4×C61#46811yescharacteristic
241C4×C61#47011yescharacteristic
242C4×C61#47011yescharacteristic
243Dic61—22no—
244Dic61—42no—
245Dic61—41no—
246Dic61—41no—
247Dic61—81no—
248C2×C4×M16—611no—
249C4×C22⋊Q8—611no—
250#1797—611no—
251C2×Q8⋊C8—611no—
252C2×Q8⋊C8—611no—
253#1279—611no—
254#1279D6111yescharacteristic, complemented
255C2×C61#148311yescharacteristic
256C2×C61#148511yescharacteristic
257C2×C61#148911yescharacteristic
258C2×C61#149111yescharacteristic
259C2×C61#187011yescharacteristic
260C2×C61#189411yescharacteristic
261C2×C61#189611yescharacteristic
262D61—42no—
263C22×M16—1221no—
264C2×C22⋊Q8—611no—
265C2×C4×Q8—611no—
266C22×C42—611no—
267C2×C4⋊C8—611no—
268C2×C4⋊C8C2×D6111yescharacteristic
269C2×C22⋊C8—1221no—
270C4×M16—1222no—
271C4×M16—1222no—
272C2×#97—1221no—
273C2×C4×C8—611no—
274C2×C4×C8C2×D6111yescharacteristic
275#391—611no—
276#389—611no—
277#387—1221no—
278#385—1221no—
279#380—611no—
280C4×C4⋊C4—1221no—
281C4×C4⋊C4C2×D6111yescharacteristic
282C4×C22⋊C4—1221no—
283#336—1221no—
284Q8⋊C8—1222no—
285Q8⋊C8—1222no—
286C61#907711yescharacteristic, complemented, Sylow
287C22×Q8—611no—
288C23×C4—611no—
289C23×C4—611no—
290C23×C4—611no—
291C2×M16—1224no—
292C2×M16—1224no—
293C2×M16—1224no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—1221no—
297C22×C8—1221no—
298C22⋊Q8—1222no—
299C22⋊Q8—1222no—
300C4×Q8—1221no—
301C4×Q8—1221no—
302C4×Q8—1221no—
303C4×Q8—1221no—
304C2×C4⋊C4—611no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4C4×D6111yescharacteristic
309C2×C4⋊C4C4×D6111yescharacteristic
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C42—21no—
313C2×C42—611no—
314C2×C42—611no—
315C2×C42—611no—
316C2×C42—1221no—
317C2×C42—1221no—
318C2×C42—1221no—
319C2×C42—1221no—
320C2×C42—1221no—
321C2×C42C22×D6111yescharacteristic
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8—1221no—
325C4⋊C8—1221no—
326C22⋊C8—2442no—
327#97—1224no—
328C4×C8—21no—
329C4×C8—612no—
330C4×C8—1221no—
331C4×C8D24412yes—
332#95—21no—
333#95—1221no—
334#95—1221no—
335#95—1221no—
336#95—1221no—
337C24—611no—
338C2×Q8—612no—
339C2×Q8—1221no—
340C2×Q8—1221no—
341C2×Q8—1221no—
342C2×Q8—1221no—
343C2×Q8—1221no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—1221no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4C2×C4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369C22×C4D4×D6111yescharacteristic
370M16—12216no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—1222no—
378C2×C8—1222no—
379C2×C8—1222no—
380C2×C8—2441no—
381C2×C8—2441no—
382C2×C8—2441no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—1224no—
387C4⋊C4—1221no—
388C4⋊C4—1221no—
389C4⋊C4—2442no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4#1175818912yescomplemented
393C22⋊C4—1224no—
394C22⋊C4—2442no—
395C42—41no—
396C42—41no—
397C42—1221no—
398C42—1221no—
399C42—1221no—
400C42—1221no—
401C42—1221no—
402C42—1221no—
403C42—2441no—
404C42—2441no—
405C42C2×D24411yescharacteristic
406C42#1175822211yescharacteristic
407C42D4×D6111yescharacteristic
408C42#1175822611yescharacteristic
409C23—612no—
410C23—1221no—
411C23—1221no—
412C23—1221no—
413C23—1221no—
414C23—1221no—
415C23—1221no—
416C23C22⋊C4×D6111yescharacteristic
417Q8—1222no—
418Q8—1222no—
419Q8—2441no—
420Q8—2441no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—612no—
430C2×C4—1224no—
431C2×C4—1224no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1222no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4#1451973911yescharacteristic
455C2×C4C4×D24411yescharacteristic
456C2×C4#1451974711yescharacteristic
457C2×C4#1451975011yescharacteristic
458C2×C4#1451975211yescharacteristic
459C2×C4#1451976211yescharacteristic
460C2×C4M16×D6111yescharacteristic
461C2×C4C2×#1175818911yescharacteristic
462C2×C4#1451978311yescharacteristic
463C2×C4#1451978511yescharacteristic
464C2×C4#1451980111yescharacteristic
465C2×C4#1451980611yescharacteristic
466C2×C4#1451980611yescharacteristic
467C2×C4#1451980911yescharacteristic
468C8—24no—
469C8—81no—
470C8—1224no—
471C8—4881no—
472C22—1222no—
473C22—1222no—
474C22—1222no—
475C22—2441no—
476C22—2441no—
477C22—2441no—
478C22—2441no—
479C22#1683964011yescharacteristic
480C22#1683972411yescharacteristic
481C22#1683972711yescharacteristic
482C22#1683976011yescharacteristic
483C22#1683976911yescharacteristic
484C22#104×D6111yescharacteristic
485C22#104×D6111yescharacteristic
486C4—21no—
487C4—21no—
488C4—42no—
489C4—81no—
490C4—1222no—
491C4—4881no—
492C4—2441no—
493C4—2441no—
494C4—2442no—
495C4#1683983211yescharacteristic
496C4#1683983511yescharacteristic
497C4#1683983911yescharacteristic
498C4#1683984111yescharacteristic
499C4#1684000711yescharacteristic
500C4#1684000911yescharacteristic
501C4#1684001911yescharacteristic
502C4#1684002111yescharacteristic
503C2—2442no—
504C2#2144422911yescharacteristic
505C2#2144423811yescharacteristic
506C2#2144425511yescharacteristic
507C2#2144426411yescharacteristic
508C2#2144611511yescharacteristic
509C2#2144625111yescharacteristic
510C2#2144626111yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#9077
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. C2×#16839494C2semidirect
5. C2×#16839492C2semidirect
6. #21443660C2semidirect
7. C61×#1279C2semidirect
113. C2×Dic122M16semidirect
123. C4⋊C4×C61M16semidirect
254. #1279D61semidirect
286. C61#9077semidirect
392. C4⋊C4#11758189semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581892
C4×#145197572
#214457962
C2×#168394942
C2×#168394922
#214436602
C61×#12792
#907761