Finite Group Databasebeta

← #30603441

Subgroups — #30603441

Order 15616.

762 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462299C211yesmaximal, characteristic
2#21461522C211yesmaximal, characteristic
3#21461506C212yesmaximal
4C2×#16840633C212yesmaximal
5#382×D61C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×#14519856C2212yes—
8#16840713—24no—
9#16840704—22no—
10#16840642—22no—
11#16840635—24no—
12#16840633—24no—
13C2×C4⋊C4×D61C2211yescharacteristic
14C2×C4⋊C4×D61C2211yescharacteristic
15C2×C42×D61C2211yescharacteristic
16#16839628C411yescharacteristic, complemented
17#16839627C411yescharacteristic, complemented
18#16839627C411yescharacteristic, complemented
19#16839626—22no—
20#95×D61—22no—
21C61×#382C411yescharacteristic, complemented
22C2×#11758213—22no—
23D61⋊M16—22no—
24D61⋊M16—22no—
25D61⋊M16—22no—
26D61⋊M16Q814yes—
27C2×#11758217—22no—
28C2×D61⋊C8—22no—
29#14519856—22no—
30#14519856—22no—
31#14519856—22no—
32#14519856—22no—
33C2×C4⋊#6923—24no—
34C2×C4⋊#6923D414yes—
35C2×C22⋊#6923—22no—
36C2×C4×#6923—22no—
37(C2×#6923)⋊C4—24no—
38C22×C4×D61—21no—
39C22×C4×D61—21no—
40C22×C4×D61D412yes—
41C22×C4×D61C2311yescharacteristic
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196D412yes—
46C4⋊C4×D61—22no—
47C4⋊C4×D61—22no—
48C4⋊C4×D61—22no—
49C4⋊C4×D61—22no—
50C2×C4×Dic61—21no—
51C2×C4×Dic61C2×C411yescharacteristic
52C42×D61—21no—
53C42×D61—21no—
54C42×D61D412yes—
55C42×D61Q812yes—
56#14519684—22no—
57#14519684—22no—
58#14519684—22no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2×C411yescharacteristic
62#95×C61—22no—
63C23×D61C2×D411yescharacteristic
64C22×#6923—24no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C412yes—
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C412yes—
72C22×Dic61C2×D411yescharacteristic
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—44no—
80C2×C4×D61—44no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61C2×D411yescharacteristic
84C2×C4×D61C2×D412yes—
85C2×C4×D61C2×Q812yes—
86C2×C4×D61C2×Q811yescharacteristic
87C2×C4×D61#4112yes—
88C2×C4×D61#4111yescharacteristic
89C2×C4×D61#4112yes—
90C2×C4×D61#4111yescharacteristic
91C22⋊#6923—42no—
92C22⋊#6923—42no—
93#11758217—24no—
94#11758217—42no—
95C2×#92420—42no—
96C4⋊#6923—24no—
97C4⋊#6923—24no—
98C4⋊#6923—84no—
99C4×#6923—42no—
100C4×#6923—42no—
101#11758213—24no—
102#11758213—42no—
103D61⋊C8—24no—
104D61⋊C8—42no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—22no—
107C42×C61—21no—
108C42×C61C4⋊C412yescomplemented
109C4⋊Dic61—22no—
110C4⋊Dic61—22no—
111#11758196—24no—
112#11758196—42no—
113C4×Dic61—21no—
114C4×Dic61—22no—
115C4×Dic61—22no—
116C4×Dic61C4⋊C412yescomplemented
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—22no—
119C22×D61—22no—
120C22×D61#12011yescharacteristic
121C22×D61#12111yescharacteristic
122C22×D61C22⋊Q811yescharacteristic
123C22×D61#12311yescharacteristic
124C22×D61#12411yescharacteristic
125C22×D61C4⋊Q811yescharacteristic
126C2×#6923—44no—
127C2×#6923—44no—
128C2×#6923—44no—
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61C2×C4⋊C411yescharacteristic
137C2×C4×C61#11711yescharacteristic
138C2×C4×C61C4×D412yes—
139C2×C4×C61C4×Q812yes—
140C2×Dic61—22no—
141C2×Dic61—22no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61#12111yescharacteristic
148C2×Dic61#12112yes—
149C2×Dic61C22⋊Q812yes—
150C2×Dic61C22⋊Q811yescharacteristic
151C4×D61—44no—
152C4×D61—44no—
153C4×D61—44no—
154C4×D61—82no—
155C4×D61—82no—
156C4×D61—82no—
157C4×D61#12112yes—
158C4×D61C22⋊Q812yes—
159C4×D61C22⋊Q812yes—
160C4×D61#12312yes—
161C4×D61#12512yes—
162C4×D61#12512yes—
163C4×D61#12612yes—
164C4×D61C4⋊Q812yes—
165#92420—44no—
166#11211—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#38011yescharacteristic
170C22×C61#38611yescharacteristic
171C22×C61#39111yescharacteristic
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—22no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—22no—
178C2×D61#39411yescharacteristic
179C2×D61#39511yescharacteristic
180C2×D61#39811yescharacteristic
181C2×D61#40011yescharacteristic
182C2×D61#45412yes—
183C2×D61#45512yes—
184#6923—84no—
185C4×C61—42no—
186C4×C61—42no—
187C4×C61—81no—
188C4×C61#38712yes—
189C4×C61#38912yes—
190Dic61—42no—
191Dic61—42no—
192Dic61—81no—
193Dic61#39612yes—
194Dic61#39812yes—
195#2316—611no—
196C2×#382—611no—
197C2×#343—611no—
198#1736—612no—
199C2×#339—612no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#144111yescharacteristic
203C2×C61#188511yescharacteristic
204C2×C61#188811yescharacteristic
205D61—21no—
206D61—21no—
207D61#204012yes—
208D61#206112yes—
209C22×M16—612no—
210C2×#117—612no—
211C22×C4⋊C4—611no—
212C22×C4⋊C4—611no—
213C22×C42—611no—
214#389—1224no—
215#382—611no—
216#382—611no—
217#382—611no—
218#382—1222no—
219#382#692311yescharacteristic, complemented
220#380—1222no—
221C2×#95—1222no—
222#343—1222no—
223#340—1224no—
224#339—1224no—
225C61#1121111yescharacteristic, complemented, Sylow
226C23×C4—611no—
227C23×C4—612no—
228C23×C4—1221no—
229C23×C4—1221no—
230C2×M16—614no—
231C2×M16—1222no—
232C2×M16—1222no—
233C2×M16—1222no—
234C2×M16—1222no—
235C2×M16—1222no—
236C22×C8—1222no—
237#117—1222no—
238#117—1222no—
239#117—1222no—
240#117—1222no—
241C2×C4⋊C4—612no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—614no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1222no—
246C2×C4⋊C4—1222no—
247C2×C4⋊C4—1222no—
248C2×C4⋊C4—1222no—
249C2×C4⋊C4—1224no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4C2×#692311yescharacteristic
252C2×C4⋊C4C2×#692311yescharacteristic
253C2×C22⋊C4—1222no—
254C2×C42—611no—
255C2×C42—612no—
256C2×C42—612no—
257C2×C42—1221no—
258C2×C42—1221no—
259C2×C42—1221no—
260C2×C42—1222no—
261C2×C42C2×#692311yescharacteristic
262#95—22no—
263#95—1222no—
264#95—1222no—
265#95—1224no—
266#95—1222no—
267C24—611no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—612no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1221no—
285C22×C4—1224no—
286C22×C4—1221no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4—2444no—
290C22×C4—2444no—
291C22×C4—2442no—
292C22×C4—2442no—
293C22×C4C22⋊#692312yes—
294C22×C4C22×#692311yescharacteristic
295M16—1224no—
296M16—1224no—
297M16—2442no—
298M16—2442no—
299C2×C8—1224no—
300C2×C8—2442no—
301C2×C8—2442no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—1224no—
305C4⋊C4—1224no—
306C4⋊C4—1224no—
307C4⋊C4—1222no—
308C4⋊C4—1222no—
309C4⋊C4—4884no—
310C4⋊C4—2442no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C42—21no—
314C42—612no—
315C42—1222no—
316C42—1222no—
317C42—1221no—
318C42—2442no—
319C42—2442no—
320C42C4⋊#692312yescomplemented
321C23—611no—
322C23—611no—
323C23—611no—
324C23—611no—
325C23—611no—
326C23—611no—
327C23—1222no—
328C23—1222no—
329C23C2×C22⋊#692311yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—612no—
342C2×C4—612no—
343C2×C4—612no—
344C2×C4—612no—
345C2×C4—612no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—612no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—4882no—
352C2×C4—4882no—
353C2×C4—4882no—
354C2×C4—2444no—
355C2×C4—2444no—
356C2×C4—2444no—
357C2×C4—2442no—
358C2×C4—2444no—
359C2×C4—2444no—
360C2×C4—2444no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2442no—
365C2×C4C2×C4⋊#692311yescharacteristic
366C2×C4#1451985611yescharacteristic
367C2×C4D4×#692312yes—
368C2×C4Q8×#692312yes—
369C8—2444no—
370C22—21no—
371C22—21no—
372C22—611no—
373C22—611no—
374C22—612no—
375C22—612no—
376C22—611no—
377C22—611no—
378C22—1222no—
379C22—1222no—
380C22—1222no—
381C22—1222no—
382C22—1221no—
383C22—1221no—
384C22#1684070411yescharacteristic
385C22#1684071011yescharacteristic
386C22(C2×#6923)⋊Q811yescharacteristic
387C4—42no—
388C4—42no—
389C4—81no—
390C4—612no—
391C4—612no—
392C4—4884no—
393C4—4881no—
394C4—2442no—
395C4—2442no—
396C4#1684071112yes—
397C4#1684071312yes—
398C2—21no—
399C2—21no—
400C2—612no—
401C2—612no—
402C2—1221no—
403C2—1221no—
404C2#2146100411yescharacteristic
405C2#2146182411yescharacteristic
406C2#2146182711yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61#386
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#382#6923
hypocenterC61#11211
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
16. #16839628C4semidirect
17. #16839627C4semidirect
18. #16839627C4semidirect
21. C61×#382C4semidirect
108. C42×C61C4⋊C4semidirect
116. C4×Dic61C4⋊C4semidirect
219. #382#6923semidirect
225. C61#11211semidirect
320. C42C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
#214622992
#214615222
#214615062
C2×#168406332
#382×D612
#1121161