Finite Group Databasebeta

← #29573567

Subgroups — #29573567

Order 15616.

472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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#21448761C211yesmaximal, characteristic
2#21445804C211yesmaximal, characteristic
3#21444135C211yesmaximal, characteristic
4#21443699C211yesmaximal, characteristic, complemented
5#21443697C211yesmaximal, characteristic, complemented
6#21443686C211yesmaximal, characteristic, complemented
7C61×#1289C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9C2×#14519691—21no—
10C2×C22⋊#92418C2211yescharacteristic
11#16839652—21no—
12#16839643—21no—
13#16839639—21no—
14#16839629C411yescharacteristic, complemented
15#16839624C411yescharacteristic, complemented
16#16839622C2211yescharacteristic
17C22⋊C4×Dic61—21no—
18#16839609C411yescharacteristic, complemented
19#16839607C411yescharacteristic, complemented
20C2×#14519684C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839485—21no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C61×#380C2211yescharacteristic
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×#92418—21no—
31C4×C22⋊D61—21no—
32C4×C22⋊D61—21no—
33C4×C22⋊D61—21no—
34C4×C22⋊D61—21no—
35C2×C4⋊Dic61—21no—
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61D411yescharacteristic
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198D411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45#14519691—42no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55#14519684C2×C411yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C22×C8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66#95×C61C2×C411yescharacteristic
67C24×C61C2×D411yescharacteristic
68C23×D61C22⋊C411yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—81no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81C2×C22⋊D61—21no—
82C2×C22⋊D61—21no—
83C2×C22⋊D61—21no—
84C2×C22⋊D61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—42no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—81no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C22⋊C411yescharacteristic
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—81no—
98C2×C8×C61—41no—
99C2×C8×C61—81no—
100C4⋊C4×C61—81no—
101C4⋊C4×C61—81no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊Dic61—21no—
107C22⋊Dic61—21no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110#11758198—21no—
111#11758198—21no—
112#11758198—42no—
113#11758198—81no—
114C4⋊Dic61—81no—
115#11758196—21no—
116#11758196—21no—
117C4×Dic61—21no—
118C4×Dic61—21no—
119C4×Dic61—42no—
120C4×Dic61—81no—
121C2×#92418—41no—
122C2×#92418—81no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61C2×C22⋊C411yescharacteristic
126C23×C61#12311yescharacteristic
127C23×C61#12311yescharacteristic
128C23×C61#13511yescharacteristic
129C23×C61#13511yescharacteristic
130C23×C61AGL(1,ℤ/8)11yescharacteristic
131C23×C61#13711yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—41no—
136C22×D61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—81no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61#11711yescharacteristic
153C2×C4×C61#11711yescharacteristic
154C2×C4×C61#12311yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C22⋊D61—41no—
157C22⋊D61—41no—
158C22⋊D61—41no—
159C22⋊D61—41no—
160C2×Dic61—22no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—82no—
174C2×Dic61—82no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178C4×D61—81no—
179C4×D61—81no—
180C8×C61—81no—
181#92418—81no—
182#8762—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61#38111yescharacteristic
194C22×C61#41611yescharacteristic
195C22×C61#41711yescharacteristic
196C22×C61#48211yescharacteristic
197C22×C61#48211yescharacteristic
198C22×C61#48511yescharacteristic
199C22×C61#48511yescharacteristic
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—81no—
204C2×D61—81no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—81no—
210C4×C61—81no—
211C4×C61—161no—
212Dic61—42no—
213Dic61—41no—
214Dic61—41no—
215Dic61—41no—
216Dic61—81no—
217Dic61—161no—
218#2353—611no—
219#1799—611no—
220#1459—611no—
221#1294—611no—
222#1294—611no—
223#1289—611no—
224#1289D6111yescharacteristic, complemented
225C2×C61—21no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—21no—
231C2×C61#182511yescharacteristic
232C2×C61#182711yescharacteristic
233C2×C61#182811yescharacteristic
234D61—81no—
235C2×C4×D4—611no—
236C2×#99—1221no—
237C2×C22⋊C8—611no—
238C2×C22⋊C8C2×D6111yescharacteristic
239#388—1221no—
240#387—1221no—
241#386—1221no—
242#383—611no—
243#381—611no—
244#380—611no—
245#380C2×D6111yescharacteristic
246#380C2×D6111yescharacteristic
247C4×C22⋊C4—611no—
248C4×C22⋊C4—1221no—
249#376—611no—
250C2×#95—611no—
251#342—1221no—
252#324—1221no—
253#323—1221no—
254C61#876211yescharacteristic, complemented, Sylow
255C22×D4—611no—
256C23×C4—611no—
257C23×C4—1221no—
258C23×C4C22×D6111yescharacteristic
259C22×C8—21no—
260C22×C8—1221no—
261C4×D4—1221no—
262C4×D4—1221no—
263C4×D4—1221no—
264C4×D4—1221no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—1221no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C42—611no—
277C2×C42—1221no—
278C2×C42—1221no—
279#99—2442no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—1221no—
283C22⋊C8—1221no—
284#95—21no—
285#95—611no—
286#95—611no—
287#95—1221no—
288#95—1221no—
289#95—1221no—
290#95—1221no—
291#95—1221no—
292#95—1221no—
293#95C4×D6111yescharacteristic
294#95C4×D6111yescharacteristic
295C24—611no—
296C24D4×D6111yescharacteristic
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—1221no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—81no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—4881no—
315C22×C4—4881no—
316C22×C4—2442no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4C2×C4×D6111yescharacteristic
321C22×C4#1175822211yescharacteristic
322C22×C4#1175822211yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C22×C4#1175822411yescharacteristic
325C22×C4#1175822611yescharacteristic
326C2×C8—41no—
327C2×C8—81no—
328C2×C8—4881no—
329C2×C8—2441no—
330C4⋊C4—81no—
331C4⋊C4—81no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—4881no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—4881no—
344C22⋊C4—2442no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C42—1221no—
348C42—1221no—
349C42—4881no—
350C42—2442no—
351C23—41no—
352C23—41no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—2441no—
357C23—2441no—
358C23C22⋊C4×D6111yescharacteristic
359C23#1451975911yescharacteristic
360C23#1451976211yescharacteristic
361C23#1451979611yescharacteristic
362C23#1451979811yescharacteristic
363C23#1451980411yescharacteristic
364C23#1451980911yescharacteristic
365D4—2441no—
366D4—2441no—
367D4—2441no—
368D4—2441no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—1222no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—4881no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—4881no—
394C2×C4—4881no—
395C2×C4—4882no—
396C2×C4—4882no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4#1451973411yescharacteristic
405C2×C4#1451973511yescharacteristic
406C2×C4#1451975911yescharacteristic
407C2×C4#1451976211yescharacteristic
408C8—81no—
409C8—4881no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—4881no—
421C22—4881no—
422C22—2441no—
423C22—2441no—
424C22—2441no—
425C22#1683962411yescharacteristic
426C22#1683975511yescharacteristic
427C22#1683976211yescharacteristic
428C22#1684008411yescharacteristic
429C22#1684008811yescharacteristic
430C22#1684010111yescharacteristic
431C22#1684010511yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—161no—
439C4—9761no—
440C4—4881no—
441C4—2442no—
442C4—2441no—
443C4—2441no—
444C4—2441no—
445C2—21no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—4881no—
452C2#2144591211yescharacteristic
453C2#2144592111yescharacteristic
454C2#2144592611yescharacteristic
subgroupG/H
centerC22#16839624
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1289C2
socleC22×C61#381
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1289D61
hypocenterC61#8762
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
4. #21443699C2semidirect
5. #21443697C2semidirect
6. #21443686C2semidirect
7. C61×#1289C2semidirect
14. #16839629C4semidirect
15. #16839624C4semidirect
18. #16839609C4semidirect
19. #16839607C4semidirect
224. #1289D61semidirect
254. C61#8762semidirect

Maximal subgroups

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

subgroupindex
#214487612
#214458042
#214441352
#214436992
#214436972
#214436862
C61×#12892
#876261