Finite Group Databasebeta

← #29580471

Subgroups — #29580471

Order 15616.

610 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 109 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#21456577C211yesmaximal, characteristic
2C2×#16840081C211yesmaximal, characteristic
3#21450297C211yesmaximal, characteristic, complemented
4#21446655C211yesmaximal, characteristic
5#21445910C211yesmaximal, characteristic, complemented
6#21444392C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8C2×#14519756C2211yescharacteristic
9C2×#14519751C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11#16840093—21no—
12#16840081—22no—
13#16840081—21no—
14#16840081—22no—
15#16839991—22no—
16#16839915—21no—
17#16839903—21no—
18C2×#14519709—21no—
19C2×#14519699—21no—
20C2×#14519691—22no—
21#16839694—22no—
22#16839668—21no—
23#16839637—22no—
24#16839632—21no—
25#16839622C2211yescharacteristic
26#16839525—22no—
27#16839500—22no—
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C22×D244D411yescharacteristic
33C22×C22⋊D61—21no—
34C23×Dic61—21no—
35C2×#11758190—22no—
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40#14519751—21no—
41#14519751—21no—
42#14519751—21no—
43#14519751—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—24no—
51C2×C4⋊Dic61D412yes—
52C2×C4⋊Dic61D411yescharacteristic
53C2×C4⋊Dic61D411yescharacteristic
54C2×#11758196—21no—
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×#11758198—21no—
58#14519709—22no—
59#14519709—24no—
60#14519702—22no—
61#14519699—22no—
62#14519699—24no—
63#14519691—44no—
64#14519684—24no—
65#14519684—21no—
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68C22×C8×C61D412yes—
69C2×C22⋊C4×C61D412yes—
70C2×C42×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D412yes—
75#95×C61—21no—
76C24×C61C2×D411yescharacteristic
77C23×D61—21no—
78C22×C4×C61—22no—
79C22×C4×C61—42no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—42no—
89C2×C22⋊D61—42no—
90C22×Dic61—22no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—41no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61—82no—
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—42no—
101C2×Dic122—21no—
102C2×Dic122—21no—
103C2×Dic122—42no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61—42no—
107C2×C8×C61—42no—
108C22⋊C4×C61—22no—
109C22⋊C4×C61SD1614yescomplemented
110C42×C61—42no—
111C22⋊Dic61—41no—
112C22⋊Dic61—41no—
113C22⋊Dic61—42no—
114#11758198—41no—
115#11758198—41no—
116C4⋊Dic61—22no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—22no—
121C4⋊Dic61—21no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61—42no—
125C4⋊Dic61—84no—
126#11758196—41no—
127#11758196—41no—
128#11758190—82no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61#12011yescharacteristic
132C23×C61#12111yescharacteristic
133C23×C61#12711yescharacteristic
134C23×C61C2×SD1612yes—
135C23×C61#13712yes—
136C22×D61—41no—
137C22×D61—42no—
138C22×D61—81no—
139C22×D61—81no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—24no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—42no—
148C2×C4×C61—42no—
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C22⋊D61—82no—
154C22⋊D61—81no—
155C22⋊D61—81no—
156C2×Dic61—42no—
157C2×Dic61—44no—
158C2×Dic61—42no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—42no—
162C2×Dic61—41no—
163C2×Dic61—42no—
164C2×Dic61—82no—
165C2×Dic61—82no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61—81no—
169D244—42no—
170D244—42no—
171Dic122—42no—
172Dic122—81no—
173C8×C61—42no—
174C8×C61—42no—
175#9951—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—42no—
183C22×C61—42no—
184C22×C61#39211yescharacteristic
185C22×C61#44812yes—
186C22×C61#46112yes—
187C22×C61#49211yescharacteristic
188C22×C61#49711yescharacteristic
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—162no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—44no—
197C4×C61#45812yes—
198Dic61—81no—
199Dic61—82no—
200Dic61—81no—
201Dic61—81no—
202Dic61—161no—
203#3187—611no—
204C2×#481—611no—
205#2502—611no—
206#1964—611no—
207#1824—611no—
208#1520—611no—
209#1282D6111yescharacteristic, complemented
210C2×C61—21no—
211C2×C61—22no—
212C2×C61—22no—
213C2×C61—21no—
214C2×C61#200811yescharacteristic
215C2×C61#201311yescharacteristic
216C2×C61#202211yescharacteristic
217D61—161no—
218C2×C22⋊Q8—611no—
219C2×#121—611no—
220C22×C4⋊C4—611no—
221#483—1221no—
222#481—1222no—
223#481—1221no—
224#481—1222no—
225#465—1222no—
226#450—1221no—
227#448—1221no—
228C2×#106—1221no—
229C2×#102—1221no—
230C2×#99—1222no—
231C2×C22⋊C8C2×D6111yescharacteristic
232C2×C22⋊C8C2×D6111yescharacteristic
233#398—1222no—
234#391—1221no—
235#385—1222no—
236#384—1221no—
237#380—611no—
238C4×C22⋊C4C2×D6111yescharacteristic
239#340—1222no—
240#328—1222no—
241C61#995111yescharacteristic, complemented, Sylow
242C22×Q8—611no—
243C22×D4—611no—
244C22×D4—1221no—
245C23×C4—1221no—
246C23×C4C22×D6111yescharacteristic
247C2×SD16—1222no—
248C22×C8—21no—
249C22×C8D24412yes—
250C22⋊Q8—1221no—
251C22⋊Q8—1221no—
252C22⋊Q8—1221no—
253C22⋊Q8—1221no—
254#121—1221no—
255#121—1221no—
256#121—1221no—
257#121—1221no—
258C2×C4⋊C4—612no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1224no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4D24412yes—
273C2×C42—21no—
274#106—1224no—
275#106—1222no—
276#103—1222no—
277#102—1224no—
278#102—1222no—
279#99—2444no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8D24412yes—
284#95—21no—
285#95—1224no—
286#95—1221no—
287C24—1221no—
288C24C2×D24411yescharacteristic
289C2×Q8—1221no—
290C2×Q8—1221no—
291C2×Q8—2442no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—2442no—
295C2×D4—2442no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2442no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—1221no—
302C22×C4—1222no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—4882no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4C2×D24411yescharacteristic
310C22×C4C2×D24411yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4D4×D6111yescharacteristic
313C22×C4D4×D6111yescharacteristic
314C22×C4#1175822611yescharacteristic
315SD16—4882no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—42no—
319C2×C8—42no—
320C4⋊C4—1222no—
321C4⋊C4—1221no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—1222no—
325C4⋊C4—1221no—
326C4⋊C4—4884no—
327C4⋊C4—2442no—
328C4⋊C4—2441no—
329C4⋊C4—2441no—
330C4⋊C4—2441no—
331C4⋊C4—2441no—
332C22⋊C4—22no—
333C22⋊C4—2442no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4#1175819014yescomplemented
339C42—42no—
340C23—41no—
341C23—41no—
342C23—4881no—
343C23—4881no—
344C23—2442no—
345C23—2441no—
346C23#1451974711yescharacteristic
347C23#1451975211yescharacteristic
348C23#1451977411yescharacteristic
349C23C2×#1175819012yes—
350C23#1451981012yes—
351Q8—4881no—
352Q8—2442no—
353D4—4881no—
354D4—4881no—
355D4—4882no—
356D4—2442no—
357D4—2442no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—4881no—
368C2×C4—4881no—
369C2×C4—4881no—
370C2×C4—4882no—
371C2×C4—4882no—
372C2×C4—2442no—
373C2×C4—2444no—
374C2×C4—2442no—
375C2×C4—2442no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2442no—
380C2×C4#1451974711yescharacteristic
381C2×C4#1451974711yescharacteristic
382C2×C4#1451975211yescharacteristic
383C2×C4#1451975211yescharacteristic
384C8—42no—
385C8—42no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22—9762no—
395C22—4881no—
396C22—4881no—
397C22—4881no—
398C22#1683967211yescharacteristic
399C22#1683990312yes—
400C22#1683996812yes—
401C22#1684013511yescharacteristic
402C22#1684015611yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—44no—
407C4—9761no—
408C4—4881no—
409C4—4882no—
410C4—4881no—
411C4—4881no—
412C4#1683995312yes—
413C2—22no—
414C2—21no—
415C2—22no—
416C2—21no—
417C2—9761no—
418C2#2144687511yescharacteristic
419C2#2144690411yescharacteristic
420C2#2144695111yescharacteristic
subgroupG/H
centerC22#16839672
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1282C2
socleC22×C61#392
prime radicalC2×#14519751C22
hypercenter#1282D61
hypocenterC61#9951
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
3. #21450297C2semidirect
5. #21445910C2semidirect
6. #21444392C2semidirect
7. C61×#1282C2semidirect
109. C22⋊C4×C61SD16semidirect
209. #1282D61semidirect
241. C61#9951semidirect
338. C22⋊C4#11758190semidirect

Maximal subgroups

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

subgroupindex
#214565772
C2×#168400812
#214502972
#214466552
#214459102
#214443922
C61×#12822
#995161