Finite Group Databasebeta

← #29569000

Subgroups — #29569000

Order 15616.

536 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 81 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#21452844C211yesmaximal, characteristic
2#21446957C211yesmaximal, characteristic, complemented
3#21446902C211yesmaximal, characteristic, complemented
4#21443644C211yesmaximal, characteristic, complemented
5#21443640C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#2023C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C2×#14519763—21no—
10C2×#14519701—21no—
11C2×#14519700—21no—
12#16839678—21no—
13#16839671—21no—
14#16839670—21no—
15#16839668C2211yescharacteristic
16#16839664C2211yescharacteristic
17#16839655—21no—
18#16839652—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×#102×C61—21no—
24C61×#390C2211yescharacteristic
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C22×C22⋊D61—21no—
30C22×C22⋊D61—21no—
31C2×#11758201—42no—
32C2×#11758201—42no—
33C2×#11758201—42no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519763—42no—
37#14519763—42no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61—21no—
47#14519701—42no—
48#14519700—42no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×Q8×C61—21no—
53C22×D4×C61D411yescharacteristic
54C22×C8×C61—21no—
55C4⋊Q8×C61—42no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2311yescharacteristic
62#102×C61—42no—
63C24×C61—21no—
64C23×D61—21no—
65C2×Q8×C61—22no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C2×C22⋊D61—42no—
81C2×C22⋊D61—81no—
82C2×C22⋊D61—81no—
83C2×C22⋊D61—81no—
84C2×C22⋊D61—81no—
85C2×C22⋊D61—81no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—41no—
92C2×D244—41no—
93C2×Dic122—21no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×Dic122SD1612yescomplemented
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C42×C61—41no—
110C22⋊Dic61—42no—
111C22⋊Dic61—81no—
112#11758201—48no—
113#11758198—42no—
114#11758198—41no—
115#11758198—41no—
116#11758198—41no—
117#11758198—41no—
118#11758198—81no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4×Dic61—42no—
122C2×#92418—22no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61#12011yescharacteristic
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143Q8×C61—42no—
144Q8×C61—42no—
145Q8×C61—81no—
146Q8×C61—81no—
147D4×C61—42no—
148D4×C61—81no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61C2×SD1611yescharacteristic
162C2×C4×C61#13511yescharacteristic
163C2×C4×C61#13511yescharacteristic
164C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C61#13711yescharacteristic
167C22⋊D61—84no—
168C22⋊D61—84no—
169C2×Dic61—22no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178D244—42no—
179D244—81no—
180Dic122—42no—
181Dic122—81no—
182C8×C61—81no—
183#92418—42no—
184#92418—81no—
185#7781—611nomaximal, Sylow
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61#44911yescharacteristic
194C22×C61#45011yescharacteristic
195C22×C61#45211yescharacteristic
196C22×C61#45311yescharacteristic
197C22×C61#45511yescharacteristic
198C22×C61#45511yescharacteristic
199C22×C61B(4,𝔽2)11yescharacteristic
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—82no—
214C4×C61—81no—
215Dic61—42no—
216Dic61—81no—
217Dic61—81no—
218#2733—611no—
219#2024—611no—
220#2023D6111yescharacteristic, complemented
221#2013—611no—
222#1272—611no—
223#1270—611no—
224#1270—611no—
225C2×C61—161no—
226C2×C61#160011yescharacteristic
227C2×C61#160111yescharacteristic
228C2×C61#160611yescharacteristic
229C2×C61#163111yescharacteristic
230C2×C61#164211yescharacteristic
231C2×C61#164611yescharacteristic
232C2×C61#165911yescharacteristic
233D61—161no—
234C22×SD16—1221no—
235C2×C4⋊Q8C2×D6111yescharacteristic
236C2×#124—1221no—
237C2×#103—1221no—
238C2×#103—1221no—
239C2×#102—21no—
240#394—1221no—
241#392—1221no—
242#392—1221no—
243#391—611no—
244#390—611no—
245#390C2×D6111yescharacteristic
246#388—1221no—
247#388—1221no—
248#340—21no—
249#340—1221no—
250#336—611no—
251#336—611no—
252#336C2×D6111yescharacteristic
253C61#778111yescharacteristic, complemented, Sylow
254C22×Q8—21no—
255C22×Q8—611no—
256C22×D4—611no—
257C22×D4—1221no—
258C22×D4—1221no—
259C22×D4C22⋊D6111yescharacteristic
260C2×SD16—2442no—
261C2×SD16—2442no—
262C2×SD16—2442no—
263C22×C8—21no—
264C22×C8—1221no—
265C22×C8—1221no—
266C4⋊Q8—42no—
267#124—2442no—
268#124—2442no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4C22⋊D6111yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C42—1221no—
283C2×C42C22×D6111yescharacteristic
284#103—2442no—
285#103—2442no—
286#102—42no—
287#95—1221no—
288#95—1221no—
289#95—1221no—
290C24—21no—
291C24—1221no—
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—612no—
299C2×Q8—1221no—
300C2×Q8—2441no—
301C2×Q8—2441no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—4881no—
309C2×D4—4881no—
310C2×D4—4881no—
311C2×D4—4881no—
312C2×D4—4881no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4—2442no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4D4×D6111yescharacteristic
322C22×C4D4×D6111yescharacteristic
323C22×C4C2×C22⋊D6111yescharacteristic
324SD16—2448no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—1222no—
329C2×C8—2441no—
330C2×C8—2441no—
331C2×C8—2441no—
332C2×C8—2441no—
333C2×C8—2441no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—2441no—
340C4⋊C4—2441no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—4881no—
346C22⋊C4—4881no—
347C22⋊C4—2442no—
348C22⋊C4—2442no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C42—41no—
354C42—2442no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—2441no—
363C23—2441no—
364C23—2441no—
365C23—2441no—
366C23—2441no—
367C23—2441no—
368C23—2441no—
369C23#1451974511yescharacteristic
370Q8—42no—
371Q8—42no—
372Q8—81no—
373Q8—81no—
374Q8—4881no—
375Q8—2442no—
376D4—42no—
377D4—81no—
378D4—4881no—
379D4—4884no—
380D4—4884no—
381D4—2442no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—1222no—
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×C4SD16×D6111yescharacteristic
404C2×C4#1451979611yescharacteristic
405C2×C4#1451979711yescharacteristic
406C2×C4#1451980111yescharacteristic
407C2×C4#1451980411yescharacteristic
408C2×C4#1451980811yescharacteristic
409C8—81no—
410C8—4881no—
411C8—2442no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—4881no—
420C22—4881no—
421C22—4881no—
422C22—4881no—
423C22—4881no—
424C22—4881no—
425C22—4881no—
426C22#1683990411yescharacteristic
427C22#1683991111yescharacteristic
428C22#1683992211yescharacteristic
429C22#1683992811yescharacteristic
430C22#1683993811yescharacteristic
431C22#1683993911yescharacteristic
432C22#1683994811yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—81no—
440C4—82no—
441C4—4881no—
442C4—4881no—
443C4—2442no—
444C2—161no—
445C2—9761no—
446C2#2144476211yescharacteristic
447C2#2144476911yescharacteristic
448C2#2144479711yescharacteristic
449C2#2144494511yescharacteristic
450C2#2144501611yescharacteristic
451C2#2144504611yescharacteristic
452C2#2144512411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2023C2
socleC23×C61#120
prime radical#21452844C2
hypercenter#2023D61
hypocenterC61#7781
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
2. #21446957C2semidirect
3. #21446902C2semidirect
4. #21443644C2semidirect
5. #21443640C2semidirect
6. #21443639C2semidirect
7. C61×#2023C2semidirect
96. C2×Dic122SD16semidirect
220. #2023D61semidirect
253. C61#7781semidirect

Maximal subgroups

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

subgroupindex
#214528442
#214469572
#214469022
#214436442
#214436402
#214436392
C61×#20232
#778161