Finite Group Databasebeta

← #29578822

Subgroups — #29578822

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519766C211yesmaximal, characteristic
2#21445970C211yesmaximal, characteristic, complemented
3C4×#14519687C211yesmaximal, characteristic, complemented
4C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic
6C2×#16839489C211yesmaximal, characteristic
7C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#14519766C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519706—22no—
12C2×#14519687—22no—
13C2×C4×#92418C2211yescharacteristic
14#16839669C411yescharacteristic
15#16839663C411yescharacteristic
16#16839652—22no—
17#16839627C411yescharacteristic
18C4×#11758198—22no—
19C42×Dic61C2211yescharacteristic
20Q8⋊#92418—22no—
21#16839491—22no—
22#16839489—22no—
23C2×C4×Q8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C61×Q8⋊C8—22no—
27C22×D244C2×C411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519766—22no—
32#14519766—22no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—21no—
36C4×D244—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758198—22no—
39C2×#11758198—21no—
40C2×#11758198—22no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D412yes—
44C2×C4×Dic61D412yes—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47#14519706—44no—
48#14519687—28no—
49C4×#92418—21no—
50C4×#92418D412yes—
51#14519684—22no—
52#14519684—22no—
53C22×Q8×C61C2×C411yescharacteristic
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C4×Q8×C61—21no—
57C4×Q8×C61—21no—
58C4×Q8×C61—21no—
59C4×Q8×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C42×C61—21no—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61D412yes—
68C23×D61—21no—
69C2×Q8×C61—21no—
70C2×Q8×C61—21no—
71C2×Q8×C61—21no—
72C2×Q8×C61—21no—
73C2×Q8×C61—21no—
74C2×Q8×C61M1612yes—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61C22⋊C412yes—
82C22×Dic61C22⋊C412yes—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244M1612yes—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C8×C61—24no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C2×C8×C61—42no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61—41no—
102C42×C61—41no—
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106C42×C61#4111yescharacteristic
107#11758198—28no—
108#11758198—41no—
109#11758198—41no—
110#11758198—44no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C4×Dic61—22no—
118C4×Dic61—22no—
119C4×Dic61—24no—
120C2×#92418—24no—
121C2×#92418—22no—
122C2×#92418—41no—
123C2×#92418—42no—
124C23×C61C2×C22⋊C411yescharacteristic
125C22×D61—22no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—42no—
129C22×D61—42no—
130Q8×C61—22no—
131Q8×C61—22no—
132Q8×C61—41no—
133Q8×C61—41no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12411yescharacteristic
145C2×C4×C61#12711yescharacteristic
146C2×C4×C61C2×M1611yescharacteristic
147C2×C4×C61C2×M1611yescharacteristic
148C2×C4×C61#13111yescharacteristic
149C2×C4×C61#13111yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)12yes—
151C2×C4×C61#13712yes—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—22no—
156C2×Dic61—22no—
157C2×Dic61—41no—
158C2×Dic61—42no—
159C2×Dic61#10414yes—
160D244—22no—
161D244—22no—
162D244—41no—
163D244—41no—
164C4×D61—82no—
165C4×D61—81no—
166C4×D61—81no—
167C8×C61—24no—
168C8×C61—81no—
169#92418—24no—
170#92418—81no—
171#9646—611nomaximal, Sylow
172C22×C61#39011yescharacteristic
173C22×C61#40711yescharacteristic
174C22×C61#40811yescharacteristic
175C22×C61#41712yes—
176C22×C61C2×#10412yes—
177C2×D61—42no—
178C2×D61—44no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—82no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—42no—
185C4×C61—81no—
186C4×C61#43511yescharacteristic
187C4×C61#43511yescharacteristic
188C4×C61#43511yescharacteristic
189C4×C61#43511yescharacteristic
190C4×C61#48912yes—
191C4×C61#49611yescharacteristic
192C4×C61#49711yescharacteristic
193Dic61—24no—
194Dic61—42no—
195Dic61—81no—
196C4×#124—611no—
197#1842—611no—
198C4×#97—611no—
199C2×Q8⋊C8—611no—
200C2×Q8⋊C8D6111yescharacteristic, complemented
201C2×D4⋊C8—611no—
202C2×D4⋊C8—611no—
203C2×C61#148312yes—
204C2×C61#148912yes—
205C2×C61#195511yescharacteristic
206C2×C61#195911yescharacteristic
207C2×C61#196211yescharacteristic
208D61—82no—
209C2×#124—611no—
210C2×C4×Q8C2×D6111yescharacteristic
211C2×C4×D4—611no—
212C2×C4⋊C8—611no—
213C2×C4⋊C8—1222no—
214C2×C4⋊C8C2×D6111yescharacteristic
215C2×#97—1222no—
216C2×C4×C8—611no—
217C2×C4×C8C2×D6111yescharacteristic
218#391—611no—
219#390—611no—
220#388—1222no—
221#382—611no—
222C4×C22⋊C4—1222no—
223C43—611no—
224Q8⋊C8—22no—
225Q8⋊C8—1222no—
226D4⋊C8—1222no—
227D4⋊C8—1222no—
228C61#964611yescharacteristic, complemented, Sylow
229C22×Q8C4×D6111yescharacteristic
230C22×D4—611no—
231C23×C4—1221no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—1221no—
235C22×C8—1221no—
236#124—1222no—
237#124—1222no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×D4—1221no—
243C4×D4—1221no—
244C4×D4—1221no—
245C4×D4—1221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4C4×D6111yescharacteristic
249C2×C22⋊C4—1222no—
250C2×C22⋊C4—1222no—
251C2×C22⋊C4—1221no—
252C2×C42—21no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—612no—
256C2×C42—612no—
257C2×C42C22×D6111yescharacteristic
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C4⋊C8—2444no—
263#97—1228no—
264C4×C8—21no—
265C4×C8—612no—
266C4×C8—1221no—
267C4×C8C22⋊D6112yes—
268#95—1222no—
269#95—1222no—
270C24—1221no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8#1175818912yes—
277C2×D4—612no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—612no—
286C22×C4—612no—
287C22×C4—1221no—
288C22×C4—2442no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4—2442no—
292C22×C4C2×C4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C2×C8—24no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—42no—
299C2×C8—1224no—
300C2×C8—1222no—
301C2×C8—2441no—
302C2×C8—2442no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C22⋊C4—1228no—
310C22⋊C4—2444no—
311C22⋊C4—2441no—
312C22⋊C4—2441no—
313C42—41no—
314C42—41no—
315C42—1224no—
316C42—1222no—
317C42—1221no—
318C42—1221no—
319C42—1221no—
320C42—1221no—
321C42—1222no—
322C42#1175822211yescharacteristic
323C42D4×D6111yescharacteristic
324C42#1175822411yescharacteristic
325C42C2×C22⋊D6111yescharacteristic
326C23—1222no—
327C23—2441no—
328C23—2442no—
329C23—2442no—
330C23—2441no—
331C23C22⋊C4×D6111yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336D4—1222no—
337D4—1222no—
338D4—2441no—
339D4—2441no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—614no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—4882no—
353C2×C4—4881no—
354C2×C4—4881no—
355C2×C4—2442no—
356C2×C4—2441no—
357C2×C4#1451973711yescharacteristic
358C2×C4C4×C22⋊D6111yescharacteristic
359C2×C4#1451974911yescharacteristic
360C2×C4#1451975011yescharacteristic
361C2×C4#1451976311yescharacteristic
362C2×C4#1451977311yescharacteristic
363C2×C4M16×D6111yescharacteristic
364C2×C4C2×#1175818911yescharacteristic
365C2×C4#1451978311yescharacteristic
366C2×C4#1451978511yescharacteristic
367C2×C4#1451980412yes—
368C2×C4#1451980912yes—
369C8—24no—
370C8—81no—
371C8—1224no—
372C8—4881no—
373C22—4882no—
374C22—4881no—
375C22—4881no—
376C22—2444no—
377C22—2442no—
378C22#1683966211yescharacteristic
379C22#1683972411yescharacteristic
380C22#1683972711yescharacteristic
381C22#1683976212yes—
382C22#104×D6112yes—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—81no—
387C4—1224no—
388C4—4881no—
389C4—2442no—
390C4#1683983011yescharacteristic
391C4#1683983111yescharacteristic
392C4#1683983311yescharacteristic
393C4#1683983611yescharacteristic
394C4#1684012312yes—
395C4#1684014811yescharacteristic
396C4#1684015511yescharacteristic
397C2—4882no—
398C2#2144423112yes—
399C2#2144425712yes—
400C2#2144661511yescharacteristic
401C2#2144663211yescharacteristic
402C2#2144664511yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenterC2×Q8⋊C8D61
hypocenterC61#9646
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #21445970C2semidirect
3. C4×#14519687C2semidirect
4. C2×Q8⋊#92418C2semidirect
7. C2×C61×Q8⋊C8C2semidirect
200. C2×Q8⋊C8D61semidirect
228. C61#9646semidirect

Maximal subgroups

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

subgroupindex
C4×#145197662
#214459702
C4×#145196872
C2×Q8⋊#924182
C2×#168394912
C2×#168394892
C2×C61×Q8⋊C82
#964661