Finite Group Databasebeta

← #29584379

Subgroups — #29584379

Order 15616.

464 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 79 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#21456621C211yesmaximal, characteristic
2#21446288C211yesmaximal, characteristic, complemented
3#21446255C211yesmaximal, characteristic
4#21446026C211yesmaximal, characteristic, complemented
5#21444178C211yesmaximal, characteristic
6#21443725C211yesmaximal, characteristic, complemented
7C61×#1520C211yesmaximal, characteristic, complemented
8C22×#11758194C2211yescharacteristic
9C2×#14519751C2211yescharacteristic
10#16840095—21no—
11#16840075—21no—
12#16840010—21no—
13#16840010—21no—
14#16839912—21no—
15#16839901—21no—
16C2×#14519713—21no—
17C2×#14519697—21no—
18C2×#14519696—21no—
19#16839726C2211yescharacteristic
20#16839726C2211yescharacteristic
21#16839531—21no—
22#16839527—21no—
23#16839524—21no—
24#16839485—22no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#328—22no—
29C22×D244D411yescharacteristic
30C22×C22⋊D61—21no—
31C2×#11758201—21no—
32C2×#11758201—21no—
33C2×#11758194—21no—
34C2×#11758194—21no—
35C2×#11758194—21no—
36C2×#11758194—42no—
37C2×#11758194D411yescharacteristic
38C2×#11758194D411yescharacteristic
39C22×#92418—21no—
40#14519751—21no—
41#14519751—21no—
42#14519751—21no—
43#14519751—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758198—21no—
46#14519713—42no—
47#14519710—21no—
48#14519710—21no—
49#14519701—21no—
50#14519701—21no—
51#14519697—21no—
52#14519697—21no—
53#14519697—42no—
54#14519696—42no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C22×Q8×C61D411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C22×C8×C61—21no—
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61D412yes—
73#95×C61—21no—
74C24×C61#4111yescharacteristic
75C23×D61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C2×Q8×C61—41no—
79C2×Q8×C61—41no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—82no—
94C22×Dic61—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244—41no—
98C2×D244—41no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—81no—
111#11758201—81no—
112#11758201—81no—
113#11758198—41no—
114#11758198—41no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117#11758194—22no—
118#11758194—22no—
119#11758194—41no—
120#11758194—41no—
121#11758194—41no—
122#11758194—41no—
123#11758194—41no—
124#11758194—41no—
125C2×#92418—22no—
126C2×#92418—21no—
127C2×#92418—21no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61#12111yescharacteristic
136C23×C61#12311yescharacteristic
137C23×C61#12411yescharacteristic
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—81no—
142C22×D61—81no—
143Q8×C61—41no—
144Q8×C61—41no—
145Q8×C61—81no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—42no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61#12011yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12311yescharacteristic
166C22⋊D61—82no—
167C22⋊D61—82no—
168C2×Dic61—41no—
169C2×Dic61—81no—
170D244—42no—
171D244—41no—
172D244—41no—
173C8×C61—42no—
174#92418—42no—
175#92418—41no—
176#92418—41no—
177#92418—81no—
178#10561—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61#39411yescharacteristic
190C22×C61#47111yescharacteristic
191C22×C61#47311yescharacteristic
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—161no—
196C2×D61—161no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—81no—
201C4×C61—81no—
202C4×C61—161no—
203C4×C61B(4,𝔽2)11yescharacteristic
204C4×C61#45811yescharacteristic
205Dic61—81no—
206#3193—611no—
207#1901—611no—
208#1895—611no—
209#1855—611no—
210#1520D6111yescharacteristic, complemented
211#1471—611no—
212#1305—611no—
213C2×C61—21no—
214C2×C61—21no—
215C2×C61—41no—
216C2×C61—41no—
217C2×C61#204411yescharacteristic
218C2×C61#204811yescharacteristic
219C2×C61#205211yescharacteristic
220D61—161no—
221C22×M16—611no—
222C2×C22⋊Q8C2×D6111yescharacteristic
223C2×#121—611no—
224#484—1221no—
225#480—1221no—
226#468—1221no—
227#468—1221no—
228#450—1221no—
229#448—1221no—
230C2×#108—1221no—
231C2×#102—1221no—
232C2×#101—1221no—
233#407—611no—
234#407—611no—
235C2×C22⋊C8C2×D6111yescharacteristic
236#380C2×D6111yescharacteristic
237#343—1221no—
238#341—1221no—
239#340—1221no—
240#328—22no—
241#323—1222no—
242C61#1056111yescharacteristic, complemented, Sylow
243C22×Q8D24411yescharacteristic
244C22×D4—611no—
245C22×D4—1221no—
246C23×C4C22×D6111yescharacteristic
247C2×SD16—1221no—
248C2×SD16—1221no—
249C2×M16—611no—
250C2×M16—611no—
251C2×M16—1221no—
252C2×M16—1221no—
253C2×M16—1221no—
254C2×M16—2442no—
255C22×C8—21no—
256C22×C8—1221no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261#121—1221no—
262#121—1221no—
263#121—1221no—
264#121—1221no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4D24411yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—1221no—
272#108—2442no—
273#107—1221no—
274#107—1221no—
275#103—1221no—
276#103—1221no—
277#102—1221no—
278#102—1221no—
279#102—2442no—
280#101—2442no—
281C22⋊C8—21no—
282C22⋊C8—1221no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286C22⋊C8C22⋊D6112yes—
287#95—21no—
288C24—1221no—
289C24#1175822411yescharacteristic
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—4882no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—1221no—
307C22×C4C2×D24411yescharacteristic
308C22×C4#1175822211yescharacteristic
309C22×C4D4×D6111yescharacteristic
310C22×C4D4×D6111yescharacteristic
311C22×C4#1175822411yescharacteristic
312C22×C4C2×C22⋊D6111yescharacteristic
313SD16—4881no—
314SD16—4881no—
315M16—1222no—
316M16—1222no—
317M16—2441no—
318M16—2441no—
319M16—2441no—
320M16—2441no—
321M16—2441no—
322M16—2441no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—1222no—
327C2×C8—1221no—
328C2×C8—1221no—
329C2×C8—2441no—
330C2×C8—2441no—
331C2×C8—2441no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—1221no—
339C4⋊C4—1221no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—81no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C23—21no—
346C23—21no—
347C23—41no—
348C23—41no—
349C23—4881no—
350C23—4881no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23#1451974811yescharacteristic
355C23#1451976111yescharacteristic
356C23#1451976311yescharacteristic
357Q8—41no—
358Q8—41no—
359Q8—81no—
360D4—4882no—
361D4—4882no—
362D4—2442no—
363D4—2441no—
364D4—2441no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—4881no—
382C2×C4—2441no—
383C2×C4#1451974711yescharacteristic
384C2×C4#1451974911yescharacteristic
385C2×C4#1451975111yescharacteristic
386C2×C4#1451975911yescharacteristic
387C8—42no—
388C8—4881no—
389C8—2442no—
390C8—2441no—
391C8—2441no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—81no—
401C22—81no—
402C22—9761no—
403C22—9761no—
404C22—4881no—
405C22—4881no—
406C22—4881no—
407C22#1683967811yescharacteristic
408C22#1684002211yescharacteristic
409C22#1684003411yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—81no—
414C4—81no—
415C4—161no—
416C4—4881no—
417C4#1683995011yescharacteristic
418C4#1683995311yescharacteristic
419C2—21no—
420C2—21no—
421C2—41no—
422C2—41no—
423C2—9761no—
424C2#2144706911yescharacteristic
425C2#2144709311yescharacteristic
426C2#2144711911yescharacteristic
subgroupG/H
centerC22#16839678
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1520C2
socleC22×C61#394
prime radicalC2×#14519751C22
hypercenter#1520D61
hypocenterC61#10561
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
2. #21446288C2semidirect
4. #21446026C2semidirect
6. #21443725C2semidirect
7. C61×#1520C2semidirect
210. #1520D61semidirect
242. C61#10561semidirect

Maximal subgroups

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

subgroupindex
#214566212
#214462882
#214462552
#214460262
#214441782
#214437252
C61×#15202
#1056161