Finite Group Databasebeta

← #29568978

Subgroups — #29568978

Order 15616.

574 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 83 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#21452182C211yesmaximal, characteristic
2#21447149C211yesmaximal, characteristic, complemented
3#21446952C211yesmaximal, characteristic, complemented
4#21443641C211yesmaximal, characteristic, complemented
5#21443640C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#2013C211yesmaximal, characteristic, complemented
8C2×#14519759—21no—
9C2×#14519750—21no—
10C2×#14519708—21no—
11C2×#14519697—21no—
12#16839685—21no—
13#16839678—21no—
14#16839670—21no—
15#16839664C2211yescharacteristic
16#16839660C2211yescharacteristic
17#16839633—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C22×SD16×C61—21no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×#103×C61—21no—
25C61×#390C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30C22×C4×D61—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33#14519759—42no—
34#14519759—42no—
35#14519750—42no—
36#14519750—42no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47#14519708—42no—
48#14519697—42no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61—21no—
52C22×D4×C61D411yescharacteristic
53C2×SD16×C61—42no—
54C2×SD16×C61—42no—
55C2×SD16×C61—42no—
56C22×C8×C61—21no—
57C4⋊Q8×C61—42no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C42×C61C2311yescharacteristic
64#103×C61—42no—
65C24×C61—21no—
66C23×D61—21no—
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C22×C4×C61—21no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C2×C22⋊D61—42no—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—42no—
85C2×C22⋊D61—81no—
86C2×C22⋊D61—81no—
87C2×C22⋊D61—81no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C2×D244—21no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244SD1612yescomplemented
95C2×C4×D61—42no—
96C2×C4×D61—42no—
97C2×C4×D61—81no—
98SD16×C61—48no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C42×C61—41no—
112C22⋊Dic61—42no—
113C22⋊Dic61—81no—
114#11758198—42no—
115#11758198—41no—
116#11758198—41no—
117#11758198—41no—
118#11758198—41no—
119C4⋊Dic61—21no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61SD1612yescomplemented
123#11758196—42no—
124#11758196—41no—
125#11758196—41no—
126C2×#92418—22no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61#12011yescharacteristic
140C22×D61—22no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—41no—
147Q8×C61—42no—
148Q8×C61—42no—
149Q8×C61—81no—
150Q8×C61—81no—
151D4×C61—42no—
152D4×C61—81no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61C2×SD1611yescharacteristic
166C2×C4×C61C2×SD1611yescharacteristic
167C2×C4×C61#13511yescharacteristic
168C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C22⋊D61—84no—
172C22⋊D61—84no—
173C2×Dic61—22no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182D244—42no—
183D244—81no—
184C4×D61—84no—
185C8×C61—42no—
186#92418—42no—
187#92418—81no—
188#7778—611nomaximal, Sylow
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61#44911yescharacteristic
197C22×C61#45011yescharacteristic
198C22×C61#45011yescharacteristic
199C22×C61#45311yescharacteristic
200C22×C61#45511yescharacteristic
201C22×C61#45611yescharacteristic
202C22×C61B(4,𝔽2)11yescharacteristic
203C2×D61—42no—
204C2×D61—42no—
205C2×D61—42no—
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—81no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—82no—
217C4×C61—81no—
218Dic61—42no—
219Dic61—81no—
220Dic61—81no—
221#2682—611no—
222#2058—611no—
223#2023—611no—
224#2013D6111yescharacteristic, complemented
225#1271—611no—
226#1270—611no—
227#1270—611no—
228C2×C61—161no—
229C2×C61#160011yescharacteristic
230C2×C61#160111yescharacteristic
231C2×C61#160411yescharacteristic
232C2×C61#162911yescharacteristic
233C2×C61#164211yescharacteristic
234C2×C61#165411yescharacteristic
235C2×C61#166111yescharacteristic
236D61—82no—
237C22×SD16—21no—
238C2×C4⋊Q8C2×D6111yescharacteristic
239C2×#123—1221no—
240C2×#121—1221no—
241C2×#106—1221no—
242C2×#103—21no—
243C2×#102—1221no—
244#396—1221no—
245#394—1221no—
246#392—1221no—
247#390—611no—
248#390C2×D6111yescharacteristic
249#389—611no—
250#385—1221no—
251#340—1221no—
252#340—1221no—
253#336—611no—
254#336—611no—
255#336C2×D6111yescharacteristic
256C61#777811yescharacteristic, complemented, Sylow
257C22×Q8—21no—
258C22×D4—611no—
259C22×D4—1221no—
260C22×D4—1221no—
261C22×D4C22⋊D6111yescharacteristic
262C23×C4—1221no—
263C2×SD16—42no—
264C2×SD16—42no—
265C2×SD16—42no—
266C22×C8—21no—
267C22×C8—1221no—
268C22×C8—1221no—
269C4⋊Q8—42no—
270#123—2442no—
271#123—2442no—
272#121—2442no—
273#121—2442no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4C22⋊D6111yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C42C22×D6111yescharacteristic
290#106—2442no—
291#103—42no—
292#102—2442no—
293#95—1221no—
294#95—1221no—
295C24—21no—
296C24—1221no—
297C2×Q8—22no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—612no—
308C2×D4—1221no—
309C2×D4—4881no—
310C2×D4—4881no—
311C2×D4—4881no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2442no—
315C2×D4—2442no—
316C2×D4—2442no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—4881no—
323C22×C4—2442no—
324C22×C4—2442no—
325C22×C4D4×D6111yescharacteristic
326C22×C4D4×D6111yescharacteristic
327C22×C4C2×C22⋊D6111yescharacteristic
328SD16—48no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—1222no—
333C2×C8—2441no—
334C2×C8—2441no—
335C2×C8—2441no—
336C2×C8—2441no—
337C2×C8—2441no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—612no—
344C4⋊C4—1221no—
345C4⋊C4—2441no—
346C4⋊C4—2441no—
347C4⋊C4—2442no—
348C4⋊C4—2441no—
349C4⋊C4—2441no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—4881no—
355C22⋊C4—2442no—
356C22⋊C4—2442no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C42—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—1222no—
370C23—2441no—
371C23—2441no—
372C23—2441no—
373C23—2441no—
374C23—2441no—
375C23—2441no—
376C23#1451974511yescharacteristic
377Q8—42no—
378Q8—42no—
379Q8—81no—
380Q8—81no—
381D4—42no—
382D4—81no—
383D4—4881no—
384D4—4884no—
385D4—4884no—
386D4—2442no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—1222no—
400C2×C4—4884no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4SD16×D6111yescharacteristic
410C2×C4SD16×D6111yescharacteristic
411C2×C4#1451979711yescharacteristic
412C2×C4#1451980311yescharacteristic
413C2×C4#1451980411yescharacteristic
414C2×C4#1451980411yescharacteristic
415C8—42no—
416C8—4881no—
417C8—2442no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—4881no—
426C22—4881no—
427C22—4881no—
428C22—4881no—
429C22—2442no—
430C22—2442no—
431C22—2442no—
432C22#1683990511yescharacteristic
433C22#1683991111yescharacteristic
434C22#1683991111yescharacteristic
435C22#1683992911yescharacteristic
436C22#1683993811yescharacteristic
437C22#1683994311yescharacteristic
438C22#1683994811yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—82no—
447C4—4881no—
448C4—4881no—
449C4—2442no—
450C2—161no—
451C2—4882no—
452C2#2144476311yescharacteristic
453C2#2144476911yescharacteristic
454C2#2144478611yescharacteristic
455C2#2144493311yescharacteristic
456C2#2144501711yescharacteristic
457C2#2144510111yescharacteristic
458C2#2144513311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2013C2
socleC23×C61#120
prime radical#21452182C2
hypercenter#2013D61
hypocenterC61#7778
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2013

Complements

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

NH ≅ G/Ntype
2. #21447149C2semidirect
3. #21446952C2semidirect
4. #21443641C2semidirect
5. #21443640C2semidirect
6. #21443639C2semidirect
7. C61×#2013C2semidirect
94. C2×D244SD16semidirect
122. C4⋊Dic61SD16semidirect
224. #2013D61semidirect
256. C61#7778semidirect

Maximal subgroups

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

subgroupindex
#214521822
#214471492
#214469522
#214436412
#214436402
#214436392
C61×#20132
#777861