Finite Group Databasebeta

← #30600560

Subgroups — #30600560

Order 15616.

622 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 94 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#21462299C211yesmaximal, characteristic, complemented
2#21461255C212yesmaximal
3D61⋊#324C211yesmaximal, characteristic, complemented
4#21460681C212yesmaximal, complemented
5#21451560C211yesmaximal, characteristic
6C2×#14519856—21no—
7D61⋊(C22⋊C8)C2212yes—
8#16840713—24no—
9#16840704—21no—
10#16840704C2212yes—
11#16840613—24no—
12#16840608—21no—
13#16840607—21no—
14C2×#14519759—21no—
15C2×#14519748C2211yescharacteristic
16C2×C4⋊C4×D61C2211yescharacteristic
17#16839694C411yescharacteristic, complemented
18#16839692C411yescharacteristic, complemented
19#16839685—21no—
20#16839685—21no—
21#16839676C411yescharacteristic, complemented
22#16839638—21no—
23#16839621C2211yescharacteristic
24C61×#394C411yescharacteristic, complemented
25C2×D61⋊C8—22no—
26#14519856—42no—
27#14519856—42no—
28C2×C4⋊#6923—22no—
29C2×C4⋊#6923—22no—
30C2×C4⋊#6923—22no—
31C2×C22⋊#6923—22no—
32C2×C4×#6923—22no—
33#14519834—22no—
34C22⋊#92420—22no—
35(C2×#6923)⋊C4—22no—
36(C2×#6923)⋊C4D414yes—
37C22×C22⋊D61—21no—
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C22×C4×D61C2311yescharacteristic
41#14519759—42no—
42#14519759—42no—
43#14519748—22no—
44#14519748—22no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×C4⋊Dic61D411yescharacteristic
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×#11758196C2×C411yescharacteristic
51C2×#11758196D411yescharacteristic
52C4⋊C4×D61—22no—
53C4⋊C4×D61—22no—
54C2×C22⋊Dic61—21no—
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×#11758198—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684C2×C411yescharacteristic
61C22×D4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—21no—
65#95×C61C2×C411yescharacteristic
66C24×C61—21no—
67C23×D61C2×D411yescharacteristic
68C22×#6923—24no—
69C2×D4×C61—22no—
70C2×D4×C61—81no—
71C22×C4×C61—21no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C2×D411yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—81no—
93C2×C4×D61—81no—
94C2×C4×D61D812yes—
95C2×C4×D61SD1612yes—
96C2×C4×D61C2×D412yes—
97C2×C4×D61#4112yes—
98C22⋊#6923—42no—
99C22⋊#6923—42no—
100C2×#92420—42no—
101C4⋊#6923—44no—
102C4⋊#6923—82no—
103C4⋊#6923—82no—
104C4×#6923—44no—
105D61⋊C8—82no—
106C4⋊C4×C61—22no—
107C22⋊C4×C61—42no—
108C22⋊C4×C61—81no—
109C22⋊Dic61—42no—
110C22⋊Dic61—42no—
111C22⋊Dic61—81no—
112#11758198—41no—
113#11758198—41no—
114C4⋊Dic61—22no—
115C4⋊Dic61—22no—
116C4⋊Dic61—42no—
117#11758196—22no—
118#11758196—22no—
119#11758196—42no—
120#11758196—81no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61C2×C22⋊C411yescharacteristic
129C22×D61—41no—
130C22×D61—41no—
131C22×D61#12011yescharacteristic
132C22×D61#12311yescharacteristic
133C22×D61C2×D811yescharacteristic
134C22×D61C2×SD1611yescharacteristic
135C22×D61AGL(1,ℤ/8)11yescharacteristic
136C22×D61#13711yescharacteristic
137C2×#6923—44no—
138C2×#6923—44no—
139C2×#6923—44no—
140D4×C61—82no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61#10212yes—
150C2×C4×C61C4×D412yes—
151C22⋊D61—81no—
152C22⋊D61—81no—
153C22⋊D61—81no—
154C22⋊D61—81no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61#10212yes—
167C2×Dic61#12112yes—
168C4×D61—22no—
169C4×D61—22no—
170C4×D61—22no—
171C4×D61—22no—
172C4×D61—42no—
173C4×D61—42no—
174C4×D61—42no—
175C4×D61—81no—
176#92420—82no—
177#9204—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61#38611yescharacteristic
188C22×C61C2×#10211yescharacteristic
189C22×C61#41711yescharacteristic
190C2×D61—21no—
191C2×D61—21no—
192C2×D61—21no—
193C2×D61—21no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61#44711yescharacteristic
199C2×D61#44811yescharacteristic
200C2×D61#48011yescharacteristic
201C2×D61#48111yescharacteristic
202#6923—84no—
203C4×C61—22no—
204C4×C61—22no—
205C4×C61—41no—
206C4×C61—81no—
207Dic61—22no—
208Dic61—22no—
209Dic61—41no—
210Dic61—81no—
211Dic61—81no—
212#2618—611no—
213#2316—611no—
214#1519—612no—
215C2×#324—611no—
216#1289—612no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—161no—
220C2×C61#187411yescharacteristic
221C2×C61#191211yescharacteristic
222C2×C61#191311yescharacteristic
223D61—21no—
224D61—21no—
225D61—21no—
226D61—21no—
227C2×#123—1221no—
228C2×#121—611no—
229C2×#117—1221no—
230C22×C4⋊C4—611no—
231C2×C22⋊C8—612no—
232#398—611no—
233#398—611no—
234#396—1221no—
235#396—1221no—
236#394—611no—
237#394#692311yescharacteristic, complemented
238#389—1224no—
239#386—1221no—
240#380—612no—
241#380—611no—
242#380—1221no—
243#327—1224no—
244#324—1221no—
245#324—1221no—
246C61#920411yescharacteristic, complemented, Sylow
247C22×D4—1221no—
248C22×D4C2×#692311yescharacteristic
249C23×C4—611no—
250C23×C4—611no—
251C23×C4—611no—
252C22×C8—1222no—
253#123—2442no—
254#123—2442no—
255#121—1222no—
256#121—1222no—
257#117—2442no—
258#117—2442no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4—1222no—
264C2×C4⋊C4—1222no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1222no—
267C2×C4⋊C4—1222no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1222no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4C2×#692311yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1222no—
279C2×C42—1222no—
280C22⋊C8—1222no—
281C22⋊C8—1222no—
282#95—614no—
283#95—611no—
284#95—1221no—
285#95—1222no—
286#95—1221no—
287#95C2×#692311yescharacteristic
288C24—21no—
289C24—611no—
290C2×D4—22no—
291C2×D4—81no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C22×C4—21no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—612no—
302C22×C4—612no—
303C22×C4—612no—
304C22×C4—612no—
305C22×C4—611no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1224no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—4881no—
316C22×C4—4881no—
317C22×C4C22⋊#692311yescharacteristic
318C22×C4C22⋊#692311yescharacteristic
319C22×C4C22×#692311yescharacteristic
320C2×C8—4882no—
321C2×C8—2442no—
322C4⋊C4—22no—
323C4⋊C4—1222no—
324C4⋊C4—1222no—
325C4⋊C4—1222no—
326C4⋊C4—1222no—
327C4⋊C4—4881no—
328C4⋊C4—4882no—
329C4⋊C4—4882no—
330C4⋊C4—2442no—
331C4⋊C4—2444no—
332C4⋊C4—2442no—
333C22⋊C4—42no—
334C22⋊C4—81no—
335C22⋊C4—4881no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4—2442no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C22⋊C4—2442no—
342C42—2444no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—611no—
351C23—611no—
352C23—611no—
353C23—611no—
354C23—611no—
355C23—611no—
356C23—2441no—
357C23—2441no—
358C23C2×C22⋊#692311yescharacteristic
359D4—82no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—4881no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—612no—
373C2×C4—612no—
374C2×C4—1222no—
375C2×C4—1222no—
376C2×C4—1222no—
377C2×C4—1222no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—4881no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2444no—
389C2×C4—2444no—
390C2×C4—2444no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4#1451983912yes—
397C2×C4D4×#692312yes—
398C8—4882no—
399C22—21no—
400C22—21no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—611no—
409C22—611no—
410C22—611no—
411C22—611no—
412C22—1221no—
413C22—1221no—
414C22—1221no—
415C22—1221no—
416C22—2441no—
417C22—2441no—
418C22—2441no—
419C22—2441no—
420C22#1684071011yescharacteristic
421C22C2×#1451983911yescharacteristic
422C22#1684075311yescharacteristic
423C4—22no—
424C4—22no—
425C4—41no—
426C4—81no—
427C4—1222no—
428C4—1222no—
429C4—4881no—
430C4—4884no—
431C4—4881no—
432C4—2441no—
433C2—21no—
434C2—21no—
435C2—161no—
436C2—1221no—
437C2—1221no—
438C2—1221no—
439C2—1221no—
440C2#2146180611yescharacteristic
441C2#2146186711yescharacteristic
442C2#2146186811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#394C4
socleC22×C61#386
prime radicalC2×#14519748C22
cosocleC22×C4×D61C23
hypercenter#394#6923
hypocenterC61#9204
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #21462299C2semidirect
3. D61⋊#324C2semidirect
4. #21460681C2semidirect
17. #16839694C4semidirect
18. #16839692C4semidirect
21. #16839676C4semidirect
24. C61×#394C4semidirect
237. #394#6923semidirect
246. C61#9204semidirect

Maximal subgroups

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

subgroupindex
#214622992
#214612552
D61⋊#3242
#214606812
#214515602
#920461