Finite Group Databasebeta

← #29574989

Subgroups — #29574989

Order 15616.

560 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454846C211yesmaximal, characteristic
2#21449076C211yesmaximal, characteristic
3#21445918C211yesmaximal, characteristic, complemented
4C4×#14519691C211yesmaximal, characteristic
5#21443705C211yesmaximal, characteristic, complemented
6#21443704C211yesmaximal, characteristic, complemented
7C61×#1826C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9#16839836—22no—
10#16839831—22no—
11#16839816—21no—
12C2×#14519691—21no—
13#16839726C2211yescharacteristic
14C22⋊C8×D61—21no—
15#16839700C411yescharacteristic, complemented
16#16839697C411yescharacteristic, complemented
17#16839693C411yescharacteristic, complemented
18#16839690—21no—
19#16839688C411yescharacteristic, complemented
20#16839677—21no—
21C4×#11758196—21no—
22C4×#11758198—21no—
23C4×C22⋊Dic61C2211yescharacteristic
24C4×C22⋊Dic61C2211yescharacteristic
25#16839528—21no—
26#16839521—22no—
27C2×#117×C61C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C4×C22⋊C4×C61C2211yescharacteristic
30C61×#339—22no—
31C22×C22⋊D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758194D412yes—
34C2×C8×D61—22no—
35C4×C22⋊D61—21no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196C2×C411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198C2×C411yescharacteristic
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61D411yescharacteristic
51#14519706—22no—
52#14519691—24no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55#14519689—22no—
56#14519687—22no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684C2×C411yescharacteristic
63#14519684C2×C411yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C2×M16×C61D412yes—
66#117×C61—21no—
67#117×C61—21no—
68#117×C61—21no—
69#117×C61—21no—
70C2×C4⋊C4×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C42×C61—21no—
75C2×C42×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78#95×C61—21no—
79C24×C61C2×D411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—42no—
84C22×C4×C61—41no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C2×C22⋊D61—21no—
92C2×C22⋊D61—21no—
93C2×C22⋊D61—22no—
94C2×C22⋊D61—41no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—41no—
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—42no—
104M16×C61—42no—
105C2×C8×C61—22no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C22⋊C4×C61—22no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C42×C61—42no—
115C42×C61—41no—
116C42×C61—41no—
117C22⋊Dic61—21no—
118C22⋊Dic61—21no—
119C22⋊Dic61—22no—
120C22⋊Dic61—42no—
121C22⋊Dic61—41no—
122#11758198—21no—
123#11758198—21no—
124#11758198—42no—
125#11758198—42no—
126#11758196—21no—
127#11758196—21no—
128#11758196—42no—
129#11758196—42no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C4×Dic61—42no—
133C4×Dic61—42no—
134#11758194—42no—
135C2×#92418—22no—
136C8×D61—82no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61C2×C22⋊C411yescharacteristic
142C23×C61#12111yescharacteristic
143C23×C61#12111yescharacteristic
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61#10412yes—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—42no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12311yescharacteristic
168C22⋊D61—42no—
169C22⋊D61—42no—
170C2×Dic61—22no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—42no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—81no—
185C2×Dic61—81no—
186C4×D61—42no—
187C4×D61—81no—
188C8×C61—42no—
189#92418—42no—
190#9011—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61#38611yescharacteristic
202C22×C61C2×#10411yescharacteristic
203C22×C61#42111yescharacteristic
204C2×D61—22no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—42no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—82no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61#45812yes—
216Dic61—42no—
217Dic61—41no—
218Dic61—41no—
219Dic61—41no—
220Dic61—81no—
221Dic61—82no—
222#2973—611no—
223#2395—611no—
224#1826—611no—
225#1826D6111yescharacteristic, complemented
226C4×#99—611no—
227#1297—611no—
228#1297—611no—
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—41no—
232C2×C61—41no—
233C2×C61#187111yescharacteristic
234C2×C61#188411yescharacteristic
235C2×C61#189011yescharacteristic
236D61—42no—
237C2×C4×D4—611no—
238C2×#117C2×D6111yescharacteristic
239#435—1222no—
240#435—1222no—
241#432—1221no—
242C2×#99—1221no—
243#407—611no—
244#407C2×D6111yescharacteristic
245C2×C22⋊C8—1221no—
246#400—611no—
247#399—611no—
248#398—611no—
249#397—611no—
250#397—1221no—
251#394—1221no—
252C4×C4⋊C4—1221no—
253C4×C22⋊C4—611no—
254C4×C22⋊C4—611no—
255C4×C22⋊C4—1221no—
256C4×C22⋊C4C2×D6111yescharacteristic
257#342—1221no—
258#339—22no—
259#339—1222no—
260C61#901111yescharacteristic, complemented, Sylow
261C22×D4—611no—
262C23×C4—611no—
263C23×C4C22×D6111yescharacteristic
264C2×M16—612no—
265C2×M16C22⋊D6112yes—
266C22×C8—1222no—
267C4×D4—1221no—
268C4×D4—1221no—
269C4×D4—1221no—
270C4×D4—1221no—
271#117—21no—
272#117—21no—
273#117—21no—
274#117—21no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4C4×D6111yescharacteristic
279C2×C4⋊C4C4×D6111yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—611no—
291C2×C42—1221no—
292C2×C42—1221no—
293C4⋊C8—1222no—
294#99—1224no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—1222no—
298C22⋊C8—1221no—
299C22⋊C8—1221no—
300#97—1222no—
301#95—21no—
302#95—611no—
303#95—611no—
304#95—1221no—
305#95—1221no—
306#95—1221no—
307#95—1221no—
308#95—1221no—
309C24—611no—
310C24D4×D6111yescharacteristic
311C2×D4—1222no—
312C2×D4—1221no—
313C2×D4—1221no—
314C2×D4—2441no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—2442no—
327C22×C4—2441no—
328C22×C4C2×C4×D6111yescharacteristic
329C22×C4#1175822211yescharacteristic
330C22×C4D4×D6111yescharacteristic
331C22×C4D4×D6111yescharacteristic
332C22×C4#1175822411yescharacteristic
333C22×C4C2×C22⋊D6111yescharacteristic
334M16—42no—
335M16—2442no—
336C2×C8—22no—
337C2×C8—1222no—
338C2×C8—4882no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—1221no—
344C4⋊C4—1221no—
345C4⋊C4—2442no—
346C4⋊C4—2442no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—1221no—
352C22⋊C4—1221no—
353C22⋊C4—1221no—
354C22⋊C4—1221no—
355C22⋊C4—1222no—
356C22⋊C4—2442no—
357C22⋊C4—2442no—
358C22⋊C4—2442no—
359C22⋊C4—2441no—
360C42—42no—
361C42—41no—
362C42—41no—
363C42—1221no—
364C42—1221no—
365C42—2442no—
366C42—2442no—
367C23—21no—
368C23—21no—
369C23—41no—
370C23—41no—
371C23—612no—
372C23—1221no—
373C23—1221no—
374C23—2441no—
375C23—2441no—
376C23C22⋊C4×D6111yescharacteristic
377C23#1451974811yescharacteristic
378C23#1451975011yescharacteristic
379D4—2442no—
380D4—2442no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—1222no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—2441no—
406C2×C4—2442no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2442no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4#1451973711yescharacteristic
415C2×C4C4×C22⋊D6111yescharacteristic
416C2×C4#1451974511yescharacteristic
417C2×C4#1451975911yescharacteristic
418C8—42no—
419C8—2442no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—81no—
429C22—81no—
430C22—1222no—
431C22—4881no—
432C22—2442no—
433C22—2441no—
434C22—2441no—
435C22#1683963811yescharacteristic
436C22#104×D6111yescharacteristic
437C22#1683977711yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4—4881no—
445C4—4882no—
446C4—2442no—
447C4—2441no—
448C4—2441no—
449C4—2441no—
450C4#1683995112yes—
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—2442no—
456C2#2144611811yescharacteristic
457C2#2144619911yescharacteristic
458C2#2144622911yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1826C2
socleC22×C61#386
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1826D61
hypocenterC61#9011
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #21445918C2semidirect
5. #21443705C2semidirect
6. #21443704C2semidirect
7. C61×#1826C2semidirect
15. #16839700C4semidirect
16. #16839697C4semidirect
17. #16839693C4semidirect
19. #16839688C4semidirect
225. #1826D61semidirect
260. C61#9011semidirect

Maximal subgroups

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

subgroupindex
#214548462
#214490762
#214459182
C4×#145196912
#214437052
#214437042
C61×#18262
#901161