Finite Group Databasebeta

← #29578817

Subgroups — #29578817

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519766C211yesmaximal, characteristic
2#21445935C211yesmaximal, characteristic, complemented
3#21445564C211yesmaximal, 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×C4×#92418C2211yescharacteristic
12#16839669C411yescharacteristic
13#16839663C411yescharacteristic
14#16839652—22no—
15#16839627C411yescharacteristic
16C4×#11758198—22no—
17C42×Dic61C2211yescharacteristic
18#16839516—22no—
19#16839516—22no—
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—
47C4×#92418—21no—
48C4×#92418D412yes—
49#14519684—22no—
50#14519684—22no—
51C22×Q8×C61C2×C411yescharacteristic
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C4×Q8×C61—21no—
55C4×Q8×C61—21no—
56C4×Q8×C61—21no—
57C4×Q8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C42×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4×C8×C61—21no—
65C4×C8×C61D412yes—
66C23×D61—21no—
67C2×Q8×C61—21no—
68C2×Q8×C61—21no—
69C2×Q8×C61—21no—
70C2×Q8×C61—21no—
71C2×Q8×C61—21no—
72C2×Q8×C61M1612yes—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61C22⋊C412yes—
80C22×Dic61C22⋊C412yes—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244M1612yes—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—42no—
90C2×C4×D61—42no—
91C2×C8×C61—22no—
92C2×C8×C61—42no—
93C2×C8×C61—41no—
94C2×C8×C61—42no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C42×C61—41no—
100C42×C61—41no—
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61#4111yescharacteristic
104C42×C61#4111yescharacteristic
105#11758198—28no—
106#11758198—44no—
107#11758198—41no—
108#11758198—41no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—22no—
116C4×Dic61—22no—
117C4×Dic61—42no—
118C2×#92418—22no—
119C2×#92418—42no—
120C2×#92418—41no—
121C2×#92418—42no—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—22no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—42no—
127C22×D61—42no—
128Q8×C61—22no—
129Q8×C61—22no—
130Q8×C61—41no—
131Q8×C61—41no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12411yescharacteristic
143C2×C4×C61#12711yescharacteristic
144C2×C4×C61C2×M1611yescharacteristic
145C2×C4×C61C2×M1611yescharacteristic
146C2×C4×C61#13111yescharacteristic
147C2×C4×C61#13111yescharacteristic
148C2×C4×C61#13512yes—
149C2×C4×C61#13512yes—
150C2×Dic61—22no—
151C2×Dic61—22no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—22no—
156C2×Dic61—41no—
157C2×Dic61—42no—
158D244—22no—
159D244—22no—
160D244—41no—
161D244—41no—
162C4×D61—82no—
163C4×D61—81no—
164C4×D61—81no—
165C8×C61—42no—
166C8×C61—81no—
167#92418—42no—
168#92418—81no—
169#9645—611nomaximal, Sylow
170C22×C61#39011yescharacteristic
171C22×C61#40711yescharacteristic
172C22×C61#40811yescharacteristic
173C22×C61#41612yes—
174C22×C61#42112yes—
175C2×D61—42no—
176C2×D61—44no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—82no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—42no—
183C4×C61—81no—
184C4×C61#43511yescharacteristic
185C4×C61#43511yescharacteristic
186C4×C61#43511yescharacteristic
187C4×C61#43511yescharacteristic
188C4×C61#48812yes—
189C4×C61#49511yescharacteristic
190C4×C61#49511yescharacteristic
191Dic61—42no—
192Dic61—42no—
193Dic61—81no—
194C4×#124—611no—
195#1831—611no—
196#1744—611no—
197C2×Q8⋊C8—611no—
198C2×Q8⋊C8D6111yescharacteristic, complemented
199C2×D4⋊C8—611no—
200C2×D4⋊C8—611no—
201C2×C61#148212yes—
202C2×C61#148812yes—
203C2×C61#195511yescharacteristic
204C2×C61#195811yescharacteristic
205C2×C61#196311yescharacteristic
206D61—82no—
207C2×#124—611no—
208C2×C4×Q8C2×D6111yescharacteristic
209C2×C4×D4—611no—
210C2×C4⋊C8—611no—
211C2×C4⋊C8C2×D6111yescharacteristic
212C2×C4×C8—611no—
213C2×C4×C8C2×D6111yescharacteristic
214#391—611no—
215#390—611no—
216#388—1222no—
217#382—611no—
218C4×C22⋊C4—1222no—
219C43—611no—
220#336—1222no—
221#336—1222no—
222Q8⋊C8—22no—
223Q8⋊C8—1222no—
224D4⋊C8—1222no—
225D4⋊C8—1222no—
226C61#964511yescharacteristic, complemented, Sylow
227C22×Q8C4×D6111yescharacteristic
228C22×D4—611no—
229C23×C4—1221no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—1221no—
233C22×C8—1221no—
234#124—1222no—
235#124—1222no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—1221no—
241C4×D4—1221no—
242C4×D4—1221no—
243C4×D4—1221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4C4×D6111yescharacteristic
247C2×C22⋊C4—1222no—
248C2×C22⋊C4—1222no—
249C2×C22⋊C4—1221no—
250C2×C42—21no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—612no—
254C2×C42—612no—
255C2×C42C22×D6111yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4×C8—21no—
261C4×C8—612no—
262C4×C8—1221no—
263C4×C8C22⋊D6112yes—
264#95—1222no—
265#95—1222no—
266C24—1221no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8#1175818912yes—
273C2×D4—612no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—612no—
282C22×C4—612no—
283C22×C4—1221no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4C2×C4×D6111yescharacteristic
289C22×C4D4×D6111yescharacteristic
290C22×C4D4×D6111yescharacteristic
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—41no—
294C2×C8—42no—
295C2×C8—1222no—
296C2×C8—2441no—
297C2×C8—2442no—
298C2×C8—2442no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C22⋊C4—1228no—
306C22⋊C4—2444no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42—41no—
310C42—41no—
311C42—1221no—
312C42—1221no—
313C42—1221no—
314C42—1221no—
315C42—1222no—
316C42—1222no—
317C42—2442no—
318C42#1175822211yescharacteristic
319C42D4×D6111yescharacteristic
320C42#1175822411yescharacteristic
321C42C2×C22⋊D6111yescharacteristic
322C23—1222no—
323C23—2441no—
324C23—2442no—
325C23—2442no—
326C23—2441no—
327C23C22⋊C4×D6111yescharacteristic
328Q8—22no—
329Q8—22no—
330Q8—41no—
331Q8—41no—
332D4—1222no—
333D4—1222no—
334D4—2441no—
335D4—2441no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—1222no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—4882no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4#1451973711yescharacteristic
354C2×C4C4×C22⋊D6111yescharacteristic
355C2×C4#1451974911yescharacteristic
356C2×C4#1451975011yescharacteristic
357C2×C4#1451976311yescharacteristic
358C2×C4#1451977311yescharacteristic
359C2×C4M16×D6111yescharacteristic
360C2×C4C2×#1175818911yescharacteristic
361C2×C4#1451978311yescharacteristic
362C2×C4#1451978511yescharacteristic
363C2×C4#1451979812yes—
364C2×C4#1451980012yes—
365C8—42no—
366C8—81no—
367C8—4881no—
368C8—2442no—
369C22—4882no—
370C22—4881no—
371C22—4881no—
372C22—2444no—
373C22—2442no—
374C22#1683966211yescharacteristic
375C22#1683972411yescharacteristic
376C22#1683972711yescharacteristic
377C22#1683975712yes—
378C22#1683977712yes—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—81no—
383C4—4881no—
384C4—2442no—
385C4—2442no—
386C4#1683983011yescharacteristic
387C4#1683983111yescharacteristic
388C4#1683983311yescharacteristic
389C4#1683983611yescharacteristic
390C4#1684011812yes—
391C4#1684014311yescharacteristic
392C4#1684014711yescharacteristic
393C2—4882no—
394C2#2144422612yes—
395C2#2144425212yes—
396C2#2144661511yescharacteristic
397C2#2144662711yescharacteristic
398C2#2144664911yescharacteristic
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#9645
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. #21445935C2semidirect
3. #21445564C2semidirect
4. C2×Q8⋊#92418C2semidirect
7. C2×C61×Q8⋊C8C2semidirect
198. C2×Q8⋊C8D61semidirect
226. C61#9645semidirect

Maximal subgroups

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

subgroupindex
C4×#145197662
#214459352
#214455642
C2×Q8⋊#924182
C2×#168394912
C2×#168394892
C2×C61×Q8⋊C82
#964561