Finite Group Databasebeta

← #29575610

Subgroups — #29575610

Order 15616.

684 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839714C211yesmaximal, characteristic, complemented
2#21454115C211yesmaximal, characteristic
3#21445582C211yesmaximal, characteristic, complemented
4C2×#16839502C211yesmaximal, characteristic, complemented
5#21443701C211yesmaximal, characteristic, complemented
6#21443701C211yesmaximal, characteristic, complemented
7C2×C61×#329C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×#14519753C411yescharacteristic
10C2×#14519748C411yescharacteristic
11C2×C42×D61C2211yescharacteristic
12C2×#14519689—21no—
13#16839714—22no—
14#16839714—22no—
15C2×#14519688C2211yescharacteristic
16C2×#14519688C2211yescharacteristic
17C2×C8×Dic61—21no—
18#16839669C411yescharacteristic
19#16839665C411yescharacteristic
20#16839650—21no—
21#16839650—21no—
22#16839638—21no—
23#16839638—21no—
24#16839628C2211yescharacteristic
25#16839516—21no—
26#16839502—22no—
27C2×#124×C61C2211yescharacteristic
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#329—22no—
31C22×C22⋊D61—21no—
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#14519753—42no—
41#14519748—42no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C42×D61—21no—
53C42×D61—21no—
54C42×D61—21no—
55C42×D61—21no—
56#14519689—24no—
57#14519688—21no—
58#14519688—21no—
59#14519688—21no—
60#14519688D412yescomplemented
61C8×Dic61—24no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66C22×Q8×C61C2×C411yescharacteristic
67C22×D4×C61C2×C411yescharacteristic
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70#124×C61—21no—
71#124×C61—21no—
72#124×C61—21no—
73#124×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C2×C42×C61C2311yescharacteristic
77#97×C61—21no—
78#97×C61—21no—
79#97×C61—21no—
80#97×C61D412yescomplemented
81C24×C61—21no—
82C23×D61C22⋊C411yescharacteristic
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—41no—
86C2×Q8×C61—41no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C22×C4×C61—21no—
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C2×C22⋊D61—42no—
96C2×C22⋊D61—42no—
97C2×C22⋊D61—42no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C2×C4×D61—22no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—22no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—22no—
112C2×C4×D61—22no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C8×C61—22no—
116C2×C8×C61—22no—
117C2×C8×C61—22no—
118C2×C8×C61—22no—
119C2×C8×C61—41no—
120C2×C8×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C42×C61C2×D411yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61#4111yescharacteristic
128C42×C61#4111yescharacteristic
129C22⋊Dic61—42no—
130C22⋊Dic61—42no—
131C22⋊Dic61—42no—
132#11758198—42no—
133C4⋊Dic61—41no—
134C4⋊Dic61—41no—
135#11758196—42no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—21no—
142C2×#92418—22no—
143C2×#92418—22no—
144C2×#92418—22no—
145C2×#92418—22no—
146C2×#92418—41no—
147C2×#92418—41no—
148#11758189—216no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61C2×C22⋊C411yescharacteristic
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61#10412yes—
164Q8×C61—81no—
165Q8×C61—81no—
166D4×C61—81no—
167D4×C61—81no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61C4×D411yescharacteristic
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12311yescharacteristic
183C22⋊D61—84no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61#10012yes—
197C2×Dic61#10412yes—
198C2×Dic61#10412yes—
199C4×D61—24no—
200C4×D61—24no—
201C4×D61—42no—
202C4×D61—42no—
203C4×D61—42no—
204C4×D61—42no—
205C8×C61—24no—
206C8×C61—42no—
207#92418—24no—
208#92418—42no—
209#9120—611nomaximal, Sylow
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61#38611yescharacteristic
218C22×C61C2×#10011yescharacteristic
219C22×C61#41311yescharacteristic
220C22×C61C2×#10411yescharacteristic
221C22×C61C2×#10411yescharacteristic
222C22×C61C2×#10411yescharacteristic
223C22×C61#42111yescharacteristic
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—21no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—81no—
238Dic61—22no—
239Dic61—22no—
240Dic61—22no—
241Dic61—81no—
242Dic61—81no—
243C2×C4×M16—611no—
244#2850—611no—
245#1749—611no—
246C2×#329—611no—
247C2×#329D6111yescharacteristic, complemented
248#1295—611no—
249#1295—611no—
250C2×C61—161no—
251C2×C61#152411yescharacteristic
252C2×C61#152511yescharacteristic
253C2×C61#152711yescharacteristic
254C2×C61#152911yescharacteristic
255C2×C61#187111yescharacteristic
256C2×C61#189611yescharacteristic
257C2×C61#190011yescharacteristic
258D61—42no—
259C22×M16—1221no—
260C2×#124C2×D6111yescharacteristic
261C2×C22⋊Q8—611no—
262C2×#121—611no—
263C22×C42—611no—
264C2×C22⋊C8—1221no—
265C4×M16—1222no—
266C4×M16—1222no—
267C2×#97—611no—
268C2×#97—611no—
269C2×#97C2×D6111yescharacteristic
270C2×#97C2×D6111yescharacteristic
271C2×C4×C8—1221no—
272#391—611no—
273#390—611no—
274#388—1221no—
275#388—1221no—
276#386—1221no—
277#386—1221no—
278#382—611no—
279#336—1221no—
280#329—22no—
281#329—1222no—
282C61#912011yescharacteristic, complemented, Sylow
283C22×Q8C4×D6111yescharacteristic
284C22×D4—1221no—
285C22×D4C4×D6111yescharacteristic
286C23×C4—611no—
287C23×C4—611no—
288C23×C4—611no—
289C2×M16—1224no—
290C2×M16—1224no—
291C2×M16—1224no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—1221no—
295C22×C8—1221no—
296#124—21no—
297#124—21no—
298#124—21no—
299#124—21no—
300C22⋊Q8—2442no—
301#121—2442no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—1221no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C42—611no—
312C2×C42—611no—
313C2×C42—611no—
314C2×C42—1221no—
315C2×C42—1221no—
316C2×C42—1221no—
317C2×C42—1221no—
318C2×C42C22×D6111yescharacteristic
319C22⋊C8—1224no—
320#97—21no—
321#97—21no—
322#97—21no—
323#97—612no—
324#97—1221no—
325#97—1221no—
326#97—1221no—
327#97C22⋊D6112yescomplemented
328C4×C8—1224no—
329#95—1221no—
330#95—1221no—
331#95—1221no—
332#95—1221no—
333C24—21no—
334C24—611no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—2442no—
344C2×D4—2442no—
345C2×D4—2442no—
346C22×C4—21no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
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—2441no—
363C22×C4—2441no—
364C22×C4C2×C4×D6111yescharacteristic
365C22×C4D4×D6111yescharacteristic
366C22×C4D4×D6111yescharacteristic
367M16—12216no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—1222no—
375C2×C8—1222no—
376C2×C8—1222no—
377C2×C8—1222no—
378C2×C8—2441no—
379C2×C8—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2442no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—2442no—
388C22⋊C4—2442no—
389C22⋊C4—2442no—
390C22⋊C4—2442no—
391C42—1221no—
392C42—1221no—
393C42—1221no—
394C42—1221no—
395C42—1221no—
396C42—1221no—
397C42#1175822211yescharacteristic
398C42D4×D6111yescharacteristic
399C42#1175822411yescharacteristic
400C42C2×C22⋊D6111yescharacteristic
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—612no—
409C23—1221no—
410C23—1221no—
411C23—1221no—
412C23—1221no—
413C23—1221no—
414C23—1221no—
415C23C22⋊C4×D6111yescharacteristic
416Q8—81no—
417Q8—81no—
418D4—81no—
419D4—81no—
420D4—4884no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—612no—
431C2×C4—612no—
432C2×C4—612no—
433C2×C4—1224no—
434C2×C4—1224no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4#1451973711yescharacteristic
452C2×C4C4×C22⋊D6111yescharacteristic
453C2×C4#1451974511yescharacteristic
454C2×C4#1451974811yescharacteristic
455C2×C4#1451975011yescharacteristic
456C2×C4#1451975911yescharacteristic
457C8—24no—
458C8—42no—
459C8—1224no—
460C8—2442no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—1222no—
469C22—1222no—
470C22—1222no—
471C22—2441no—
472C22—2441no—
473C22—2441no—
474C22—2441no—
475C22#1683963811yescharacteristic
476C22#100×D6111yescharacteristic
477C22#1683974311yescharacteristic
478C22#104×D6111yescharacteristic
479C22#104×D6111yescharacteristic
480C22#104×D6111yescharacteristic
481C22#1683977711yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—81no—
489C4—1222no—
490C4—1222no—
491C4—1222no—
492C4—4881no—
493C4—4881no—
494C2—161no—
495C2—2442no—
496C2#2144440411yescharacteristic
497C2#2144440911yescharacteristic
498C2#2144441511yescharacteristic
499C2#2144442311yescharacteristic
500C2#2144611811yescharacteristic
501C2#2144625911yescharacteristic
502C2#2144627911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#329C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C42×C61C23
hypercenterC2×#329D61
hypocenterC61#9120
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
1. C2×#16839714C2semidirect
3. #21445582C2semidirect
4. C2×#16839502C2semidirect
5. #21443701C2semidirect
6. #21443701C2semidirect
7. C2×C61×#329C2semidirect
60. #14519688D4semidirect
80. #97×C61D4semidirect
247. C2×#329D61semidirect
282. C61#9120semidirect
327. #97C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397142
#214541152
#214455822
C2×#168395022
#214437012
C2×C61×#3292
#912061