Finite Group Databasebeta

← #29577058

Subgroups — #29577058

Order 15616.

520 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 89 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#21456625C211yesmaximal, characteristic
2#21448982C211yesmaximal, characteristic, complemented
3#21444348C211yesmaximal, characteristic
4#21444338C211yesmaximal, characteristic, complemented
5#21443725C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1964C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16840097C412yescomplemented
10#16840073—21no—
11#16840006—22no—
12#16839913C412yescomplemented
13#16839900—21no—
14#16839726C2211yescharacteristic
15#16839726C2211yescharacteristic
16#16839666—21no—
17#16839657—21no—
18#16839656—21no—
19#16839650—21no—
20#16839645—21no—
21#16839643—21no—
22#16839625C2211yescharacteristic
23#16839498—22no—
24#16839496—21no—
25#16839496—21no—
26C2×#121×C61C2211yescharacteristic
27C2×#99×C61—21no—
28C2×#99×C61—21no—
29C61×#380C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C2×#11758200—22no—
33C2×#11758194—21no—
34C2×#11758194—21no—
35#14519756—21no—
36#14519756—21no—
37#14519756C2×C412yes—
38#14519756D412yes—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—21no—
47#14519710—22no—
48#14519700—22no—
49#14519698—22no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418C2×C412yes—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684D411yescharacteristic
60#14519684D411yescharacteristic
61C22×D4×C61—21no—
62C22×D4×C61C2×C411yescharacteristic
63C23×C4×C61C2311yescharacteristic
64#121×C61—21no—
65#121×C61—21no—
66#121×C61—21no—
67#121×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61C2×C411yescharacteristic
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61D411yescharacteristic
73C2×C22⋊C4×C61D411yescharacteristic
74C2×C42×C61—21no—
75#99×C61—42no—
76#99×C61—42no—
77#95×C61—21no—
78#95×C61—21no—
79C24×C61—21no—
80C24×C61C2×D411yescharacteristic
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—81no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—41no—
94C22×C4×C61—81no—
95C22×C4×C61C22×C411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61#4111yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C2×Dic122—21no—
106C2×Dic122—81no—
107C2×Dic122C22⋊C412yes—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—81no—
111C22⋊C4×C61—22no—
112C22⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C42×C61—81no—
118C22⋊Dic61—22no—
119C22⋊Dic61—22no—
120C22⋊Dic61—81no—
121#11758200—82no—
122C4⋊Dic61—21no—
123C4⋊Dic61C22⋊C412yes—
124#11758196—22no—
125#11758196—22no—
126#11758196—81no—
127#11758196—81no—
128C4×Dic61—81no—
129C4×Dic61—81no—
130#11758194—81no—
131#11758194—81no—
132C2×#92418—22no—
133C2×#92418—41no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—81no—
142C23×C61—81no—
143C23×C61C4×D411yescharacteristic
144C23×C61#12011yescharacteristic
145C23×C61#12111yescharacteristic
146D4×C61—42no—
147D4×C61—81no—
148D4×C61—81no—
149D4×C61—81no—
150D4×C61—81no—
151D4×C61—81no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—81no—
169C2×C4×C61—81no—
170C2×C4×C61C2×C22⋊C411yescharacteristic
171C2×C4×C61C4×D411yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12311yescharacteristic
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186Dic122—42no—
187Dic122—81no—
188#92418—42no—
189#92418—81no—
190#9344—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—81no—
202C22×C61—81no—
203C22×C61—81no—
204C22×C61—161no—
205C22×C61—161no—
206C22×C61#38611yescharacteristic
207C22×C61#45311yescharacteristic
208C22×C61#45411yescharacteristic
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61—82no—
216C4×C61—81no—
217Dic61—42no—
218Dic61—42no—
219Dic61—81no—
220Dic61—81no—
221#3193—611no—
222#2378—611no—
223#1964D6111yescharacteristic
224#1510—611no—
225#1508—611no—
226#1305—611no—
227#1284—611no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—41no—
231C2×C61—41no—
232C2×C61—161no—
233C2×C61#188311yescharacteristic
234C2×C61#190511yescharacteristic
235C2×C61#191311yescharacteristic
236C2×C22⋊Q8—611no—
237C2×#121C2×D6111yescharacteristic
238#484—612no—
239#480—1221no—
240#468—1222no—
241#450—612no—
242#448—1221no—
243C2×#99—21no—
244C2×#99—21no—
245#407—611no—
246#407—611no—
247#391—1221no—
248#389—1221no—
249#388—1221no—
250#388—1221no—
251#387—1221no—
252#387—1221no—
253#381—611no—
254#380C2×D6111yescharacteristic
255C4×C22⋊C4C2×D6111yescharacteristic
256#328—1222no—
257#327—1221no—
258#327—1221no—
259C61#934411yescharacteristic, complemented, Sylow
260C22×Q8—611no—
261C22×D4—21no—
262C22×D4C4×D6111yescharacteristic
263C23×C4C22×D6111yescharacteristic
264C2×SD16—1222no—
265C2×M16—1221no—
266C2×M16—1221no—
267C22⋊Q8—612no—
268C22⋊Q8—612no—
269C22⋊Q8—1221no—
270C22⋊Q8—1221no—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4C4×D6111yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4C22⋊D6111yescharacteristic
286C2×C22⋊C4C22⋊D6111yescharacteristic
287C2×C42—21no—
288C2×C42—1221no—
289C2×C42—1221no—
290#107—1222no—
291#103—1222no—
292#102—1222no—
293#99—42no—
294#99—42no—
295C22⋊C8—612no—
296C22⋊C8—1221no—
297C22⋊C8—1221no—
298C22⋊C8—1221no—
299#95—21no—
300#95—21no—
301#95—611no—
302#95—611no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306#95—1221no—
307#95—1221no—
308C24—21no—
309C24C2×C22⋊D6111yescharacteristic
310C2×Q8—612no—
311C2×Q8—1221no—
312C2×Q8—4881no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—81no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—81no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4C2×C4×D6111yescharacteristic
332C22×C4#1175822211yescharacteristic
333C22×C4D4×D6111yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4#1175822411yescharacteristic
337SD16—4882no—
338M16—4881no—
339M16—4881no—
340C2×C8—1222no—
341C2×C8—2441no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—81no—
345C4⋊C4—612no—
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—1221no—
349C4⋊C4—4881no—
350C4⋊C4—4881no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—1222no—
358C22⋊C4—1222no—
359C22⋊C4—4881no—
360C42—81no—
361C42—4881no—
362C42—4881no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23C4×C22⋊D6111yescharacteristic
373C23#1451974511yescharacteristic
374C23#1451974811yescharacteristic
375Q8—4881no—
376Q8—2442no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—1222no—
402C2×C4—1222no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4C22⋊C4×D6111yescharacteristic
414C2×C4#1451973711yescharacteristic
415C2×C4#1451975011yescharacteristic
416C2×C4#1451975911yescharacteristic
417C8—4881no—
418C8—2442no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—161no—
433C22—161no—
434C22#1683963811yescharacteristic
435C22#1683992911yescharacteristic
436C22#1683993411yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—82no—
444C4—81no—
445C4—4881no—
446C4—4881no—
447C4—2442no—
448C4—2442no—
449C2—21no—
450C2—21no—
451C2—41no—
452C2—41no—
453C2—161no—
454C2#2144619811yescharacteristic
455C2#2144631611yescharacteristic
456C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1964C2
socleC22×C61#386
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenter#1964D61
hypocenterC61#9344
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #21448982C2semidirect
4. #21444338C2semidirect
5. #21443725C2semidirect
6. #21443672C2semidirect
9. #16840097C4semidirect
12. #16839913C4semidirect
259. C61#9344semidirect

Maximal subgroups

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

subgroupindex
#214566252
#214489822
#214443482
#214443382
#214437252
#214436722
C61×#19642
#934461