Finite Group Databasebeta

← #29575583

Subgroups — #29575583

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454150C211yesmaximal, characteristic
2C2×#16839497C212yesmaximal
3#21444046C211yesmaximal, characteristic, complemented
4#21443699C212yesmaximal, complemented
5C2×C61×#431C211yesmaximal, characteristic, complemented
6C2×#14519760—21no—
7C2×#14519751C2211yescharacteristic
8#16839664C411yescharacteristic, complemented
9#16839664C411yescharacteristic, complemented
10#16839660C411yescharacteristic, complemented
11#16839660C411yescharacteristic, complemented
12#16839653—21no—
13#16839653—21no—
14#16839641—21no—
15#16839622C2211yescharacteristic
16C2×#14519684—21no—
17C2×#14519684—21no—
18C2×#14519684C2212yes—
19#16839497—24no—
20C22×C42×C61C2211yescharacteristic
21C61×#431—24no—
22C2×C4⋊C8×C61—21no—
23C2×C22⋊C8×C61C2212yes—
24C2×C4×C8×C61—21no—
25C22×D244C2×C411yescharacteristic
26C22×C22⋊D61—21no—
27C23×Dic61—22no—
28#14519760—42no—
29#14519760—42no—
30#14519751—22no—
31#14519751—22no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43#14519684—24no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—22no—
48#14519684—22no—
49#14519684—42no—
50C23×C4×C61D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C22×C8×C61—22no—
54C2×C42×C61—22no—
55C2×C42×C61—22no—
56C2×C42×C61C2×C411yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C4⋊C8×C61—24no—
61C22⋊C8×C61—22no—
62C22⋊C8×C61D414yes—
63C4×C8×C61—24no—
64C24×C61C2×D411yescharacteristic
65C23×D61—21no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61D812yes—
78C22×C4×C61SD1612yes—
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D412yes—
82C22×C4×C61#4112yes—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—42no—
87C22×Dic61—24no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—42no—
92C22×Dic61—42no—
93C22×Dic61—42no—
94C22×Dic61—42no—
95C22×Dic61—42no—
96C22×Dic61—42no—
97C2×D244—22no—
98C2×D244—41no—
99C2×D244—41no—
100C2×C8×C61—24no—
101C2×C8×C61—42no—
102C2×C8×C61—42no—
103C42×C61—22no—
104C42×C61—22no—
105C42×C61—21no—
106C42×C61—21no—
107C42×C61—21no—
108C42×C61—21no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111#11758198—42no—
112#11758198—42no—
113#11758198—42no—
114#11758198—42no—
115#11758198—41no—
116#11758198—41no—
117C4⋊Dic61—22no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120#11758196—42no—
121#11758196—42no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61C2×C22⋊C411yescharacteristic
127C23×C61#12112yes—
128C23×C61C2×D811yescharacteristic
129C23×C61C2×SD1611yescharacteristic
130C23×C61#13512yes—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—24no—
149C2×C4×C61—24no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—44no—
156C2×C4×C61#10212yes—
157C2×C4×C61#10212yes—
158C2×C4×C61#10412yes—
159C2×C4×C61C4×D412yes—
160C2×C4×C61#12011yescharacteristic
161C2×C4×C61#12311yescharacteristic
162C22⋊D61—82no—
163C22⋊D61—82no—
164C2×Dic61—44no—
165C2×Dic61—44no—
166C2×Dic61—44no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—82no—
177C2×Dic61—82no—
178C2×Dic61—82no—
179C2×Dic61—82no—
180D244—82no—
181C8×C61—44no—
182#9114—611nomaximal, Sylow
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—22no—
191C22×C61#38611yescharacteristic
192C22×C61#41011yescharacteristic
193C22×C61#41011yescharacteristic
194C22×C61C2×#10211yescharacteristic
195C22×C61#41611yescharacteristic
196C22×C61C2×#10411yescharacteristic
197C22×C61#42111yescharacteristic
198C22×C61#46512yes—
199C22×C61#46612yes—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C4×C61—22no—
208C4×C61—22no—
209C4×C61—22no—
210C4×C61—21no—
211C4×C61—22no—
212C4×C61—21no—
213C4×C61—41no—
214Dic61—84no—
215Dic61—81no—
216Dic61—81no—
217Dic61—81no—
218C2×#431D6111yescharacteristic, complemented
219#2854—611no—
220C2×#327—612no—
221#1434—611no—
222#1294—612no—
223C2×C61—22no—
224C2×C61—22no—
225C2×C61#150011yescharacteristic
226C2×C61#150211yescharacteristic
227C2×C61#151711yescharacteristic
228C2×C61#152111yescharacteristic
229C2×C61#187111yescharacteristic
230C2×C61#189311yescharacteristic
231C2×C61#189911yescharacteristic
232D61—161no—
233C2×#123—1221no—
234C2×#121—611no—
235C22×C42C2×D6111yescharacteristic
236#431—24no—
237C2×C4⋊C8—21no—
238C2×C22⋊C8C2×D6112yes—
239C2×C4×C8—21no—
240#390—611no—
241#390—611no—
242#389—611no—
243#389—611no—
244#388—1221no—
245#388—1221no—
246#386—1221no—
247#380—611no—
248C2×#95—612no—
249C2×#95—1221no—
250C2×#95—1221no—
251#327—1224no—
252C61#911411yescharacteristic, complemented, Sylow
253C22×D4—611no—
254C22×D4—1221no—
255C23×C4—1222no—
256C23×C4D24411yescharacteristic
257C23×C4D24411yescharacteristic
258C23×C4C22×D6111yescharacteristic
259C22×C8—22no—
260#123—2442no—
261#123—2442no—
262#121—1222no—
263#121—1222no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42C4×D6111yescharacteristic
278C2×C42C4×D6111yescharacteristic
279C2×C42C22⋊D6111yescharacteristic
280C2×C42C22⋊D6111yescharacteristic
281C4⋊C8—24no—
282C22⋊C8—22no—
283C22⋊C8C22⋊D6114yes—
284C4×C8—24no—
285#95—1224no—
286#95—1221no—
287#95—1221no—
288#95—1221no—
289#95—1222no—
290#95—1222no—
291#95—2442no—
292C24—1221no—
293C24C2×D24411yescharacteristic
294C2×D4—1222no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2442no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2442no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—1224no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4—2442no—
315C22×C4—2442no—
316C22×C4—2442no—
317C22×C4—2442no—
318C22×C4#1175819012yes—
319C22×C4D48812yes—
320C22×C4#1175819811yescharacteristic
321C22×C4#1175819811yescharacteristic
322C22×C4#1175819811yescharacteristic
323C22×C4#1175819811yescharacteristic
324C22×C4C2×C4×D6111yescharacteristic
325C22×C4#1175822212yes—
326C22×C4C2×C22⋊D6111yescharacteristic
327C22×C4C2×C22⋊D6112yes—
328C2×C8—24no—
329C2×C8—42no—
330C2×C8—42no—
331C4⋊C4—1222no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C4⋊C4—2442no—
335C4⋊C4—2442no—
336C22⋊C4—2442no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C22⋊C4—2442no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C42—22no—
345C42—22no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—2441no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23C2×#1175819811yescharacteristic
362C23#1451975112yes—
363C23C2×D48811yescharacteristic
364C23C2×#1175819011yescharacteristic
365C23#1451979912yes—
366D4—4882no—
367D4—4882no—
368D4—4882no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—4882no—
388C2×C4—4882no—
389C2×C4—4882no—
390C2×C4—4882no—
391C2×C4—2444no—
392C2×C4—2444no—
393C2×C4—2444no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4#1451969912yes—
404C2×C4#1451969912yes—
405C2×C4#1451970312yes—
406C2×C4C4×C22⋊D6112yes—
407C2×C4#1451974611yescharacteristic
408C2×C4#1451976011yescharacteristic
409C8—44no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—4881no—
419C22—4881no—
420C22—4881no—
421C22—4881no—
422C22—4881no—
423C22—4881no—
424C22—4881no—
425C22#1683964111yescharacteristic
426C22#1683973511yescharacteristic
427C22#1683973511yescharacteristic
428C22C2×#1451969911yescharacteristic
429C22#1683975911yescharacteristic
430C22C2×#1451970311yescharacteristic
431C22#1683977811yescharacteristic
432C22#1683999112yes—
433C22#1683999812yes—
434C4—22no—
435C4—22no—
436C4—21no—
437C4—22no—
438C4—21no—
439C4—22no—
440C4—41no—
441C4—4884no—
442C4—4881no—
443C4—4881no—
444C4—4881no—
445C2—22no—
446C2—22no—
447C2—9761no—
448C2#2144430611yescharacteristic
449C2#2144431511yescharacteristic
450C2#2144438011yescharacteristic
451C2#2144439711yescharacteristic
452C2#2144612111yescharacteristic
453C2#2144624711yescharacteristic
454C2#2144627711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#431C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenterC2×#431D61
hypocenterC61#9114
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. #21444046C2semidirect
4. #21443699C2semidirect
5. C2×C61×#431C2semidirect
8. #16839664C4semidirect
9. #16839664C4semidirect
10. #16839660C4semidirect
11. #16839660C4semidirect
218. C2×#431D61semidirect
252. C61#9114semidirect

Maximal subgroups

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

subgroupindex
#214541502
C2×#168394972
#214440462
#214436992
C2×C61×#4312
#911461