Finite Group Databasebeta

← #29578917

Subgroups — #29578917

Order 15616.

586 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758199C211yesmaximal, characteristic
2#21446614C211yesmaximal, characteristic, complemented
3#21446612C211yesmaximal, characteristic, complemented
4C2×#16839512C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic, complemented
6C2×#16839483C211yesmaximal, characteristic, complemented
7C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×#11758199C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10C4×#11758199—22no—
11C4×#11758199—22no—
12C2×#14519710C411yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519698C411yescharacteristic
15C2×#14519697C411yescharacteristic
16C2×C22⋊#92418—22no—
17C2×#14519689—22no—
18C2×C4×#92418C2211yescharacteristic
19C2×C4×#92418C2211yescharacteristic
20#16839512—22no—
21#16839491—22no—
22#16839483—22no—
23C2×C4×D4×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C61×D4⋊C8—22no—
27C22×D244C2×C411yescharacteristic
28C22×C4×D61—21no—
29C2×#11758199—22no—
30C2×#11758199—22no—
31C2×#11758199—22no—
32C22×#92418—21no—
33C22×#92418C2×C411yescharacteristic
34C22×#92418C2×C411yescharacteristic
35C22×#92418D412yes—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758198—21no—
42#14519710—22no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45#14519698—22no—
46#14519697—22no—
47C22⋊#92418—44no—
48#14519689—44no—
49C4×#92418—21no—
50C4×#92418—21no—
51C4×#92418D412yes—
52C4×#92418D412yes—
53C22×D4×C61C2×C411yescharacteristic
54C23×C4×C61—21no—
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C4×D4×C61—21no—
58C4×D4×C61—21no—
59C4×D4×C61—21no—
60C4×D4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61—21no—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61D412yes—
68C24×C61—21no—
69C23×D61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61M1612yes—
76C22×C4×C61—21no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—42no—
80C22×C4×C61—42no—
81C22×C4×C61C22×C411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C22×Dic61—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244M1612yes—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C8×C61—24no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C2×C8×C61—42no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107#11758199—28no—
108#11758198—41no—
109#11758198—41no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—22no—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418—41no—
120C2×#92418—42no—
121C2×#92418C22⋊C412yes—
122C2×#92418C22⋊C412yes—
123C23×C61—22no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61C4×D411yescharacteristic
129C22×D61—22no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—42no—
133C22×D61—42no—
134D4×C61—22no—
135D4×C61—22no—
136D4×C61—41no—
137D4×C61—41no—
138C2×C4×C61—22no—
139C2×C4×C61—41no—
140C2×C4×C61—42no—
141C2×C4×C61—82no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61C4×D411yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12411yescharacteristic
149C2×C4×C61#12711yescharacteristic
150C2×C4×C61C2×M1611yescharacteristic
151C2×C4×C61C2×M1611yescharacteristic
152C2×C4×C61#13111yescharacteristic
153C2×C4×C61#13111yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)12yes—
155C2×C4×C61AGL(1,ℤ/8)12yes—
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—24no—
166C8×C61—81no—
167#92418—22no—
168#92418—22no—
169#92418—42no—
170#92418—81no—
171#9665—611nomaximal, Sylow
172C22×C61—44no—
173C22×C61—42no—
174C22×C61—82no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61#39011yescharacteristic
178C22×C61#43511yescharacteristic
179C22×C61#43511yescharacteristic
180C22×C61#44212yes—
181C22×C61#44312yes—
182C2×D61—44no—
183C2×D61—42no—
184C2×D61—82no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—81no—
190C4×C61#40711yescharacteristic
191C4×C61#40811yescharacteristic
192C4×C61#43511yescharacteristic
193C4×C61#43511yescharacteristic
194C4×C61#46912yes—
195C4×C61#49611yescharacteristic
196C4×C61#49611yescharacteristic
197Dic61—81no—
198C2×C4×D8—611no—
199#1954—611no—
200#1954—611no—
201C2×#334—611no—
202C2×D4⋊C8—611no—
203C2×D4⋊C8D6111yescharacteristic, complemented
204C2×#322—611no—
205C2×C61—82no—
206C2×C61#158612yes—
207C2×C61#158612yes—
208C2×C61#195511yescharacteristic
209C2×C61#197211yescharacteristic
210C2×C61#197411yescharacteristic
211D61—82no—
212C22×D8—611no—
213C2×C4×D4—611no—
214C2×C4×D4C2×D6111yescharacteristic
215C4×D8—1222no—
216C4×D8—1222no—
217C2×#107—611no—
218C2×C4⋊C8—611no—
219C2×C4⋊C8C2×D6111yescharacteristic
220C2×#102—611no—
221C2×#102—611no—
222C2×C22⋊C8—1222no—
223C2×C22⋊C8—1222no—
224C2×C4×C8—611no—
225C2×C4×C8—611no—
226C2×C4×C8C2×D6111yescharacteristic
227#334—1222no—
228D4⋊C8—22no—
229D4⋊C8—1222no—
230#322—1222no—
231C61#966511yescharacteristic, complemented, Sylow
232C22×D4—611no—
233C22×D4C4×D6111yescharacteristic
234C23×C4—21no—
235C23×C4—1221no—
236C2×D8—1222no—
237C2×D8—1222no—
238C2×D8—1222no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—611no—
242C22×C8—611no—
243C22×C8—612no—
244C22×C8—1221no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—1221no—
250C4×D4—1221no—
251C4×D4—1221no—
252C4×D4—1221no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4C4×D6111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—1221no—
257C2×C42C22×D6111yescharacteristic
258#107—1222no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263#102—1222no—
264#102—1222no—
265C22⋊C8—2444no—
266C22⋊C8—2444no—
267C4×C8—21no—
268C4×C8—612no—
269C4×C8—612no—
270C4×C8—1221no—
271C4×C8—1221no—
272C4×C8C22⋊D6112yes—
273C24—21no—
274C24—1221no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—612no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4#1175818912yes—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—1221no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2442no—
296C22×C4—2442no—
297C22×C4C2×C4×D6111yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4#1175822411yescharacteristic
300D8—1228no—
301C2×C8—24no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—42no—
305C2×C8—612no—
306C2×C8—612no—
307C2×C8—1221no—
308C2×C8—1221no—
309C2×C8—1221no—
310C2×C8—1221no—
311C2×C8—1222no—
312C2×C8—1222no—
313C2×C8—1222no—
314C2×C8—2441no—
315C2×C8—2442no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C42#1175822211yescharacteristic
325C42D4×D6111yescharacteristic
326C42D4×D6111yescharacteristic
327C42C2×C22⋊D6111yescharacteristic
328C23—22no—
329C23—41no—
330C23—42no—
331C23—42no—
332C23—41no—
333C23—1222no—
334C23—2441no—
335C23—2442no—
336C23—2442no—
337C23—2441no—
338C23#1451973711yescharacteristic
339D4—22no—
340D4—22no—
341D4—41no—
342D4—41no—
343D4—1222no—
344D4—1222no—
345D4—2441no—
346D4—2441no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—82no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—4882no—
354C2×C4—4881no—
355C2×C4—4881no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4C22⋊C4×D6111yescharacteristic
359C2×C4C4×C22⋊D6111yescharacteristic
360C2×C4#1451974911yescharacteristic
361C2×C4#1451975011yescharacteristic
362C2×C4#1451976311yescharacteristic
363C2×C4#1451977311yescharacteristic
364C2×C4M16×D6111yescharacteristic
365C2×C4C2×#1175818911yescharacteristic
366C2×C4#1451978311yescharacteristic
367C2×C4#1451978511yescharacteristic
368C2×C4#1451980112yes—
369C2×C4#1451980412yes—
370C8—24no—
371C8—81no—
372C8—1222no—
373C8—1222no—
374C8—4881no—
375C8—2442no—
376C22—44no—
377C22—42no—
378C22—81no—
379C22—81no—
380C22—82no—
381C22—4881no—
382C22—4881no—
383C22—4882no—
384C22—2444no—
385C22—2442no—
386C22#1683966211yescharacteristic
387C22#1683983011yescharacteristic
388C22#1683983611yescharacteristic
389C22#1683987112yes—
390C22#1683987612yes—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—4881no—
395C4#1683972411yescharacteristic
396C4#1683972711yescharacteristic
397C4#1683983111yescharacteristic
398C4#1683983311yescharacteristic
399C4#1684001412yes—
400C4#1684014811yescharacteristic
401C4#1684015011yescharacteristic
402C2—82no—
403C2—4882no—
404C2#2144468012yes—
405C2#2144468612yes—
406C2#2144661511yescharacteristic
407C2#2144669211yescharacteristic
408C2#2144670411yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61C4×D4
prime radicalC22×#11758199C4
cosocleC2×C42×C61C23
hypercenterC2×D4⋊C8D61
hypocenterC61#9665
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21446614C2semidirect
3. #21446612C2semidirect
4. C2×#16839512C2semidirect
5. C2×#16839491C2semidirect
6. C2×#16839483C2semidirect
7. C2×C61×D4⋊C8C2semidirect
203. C2×D4⋊C8D61semidirect
231. C61#9665semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581992
#214466142
#214466122
C2×#168395122
C2×#168394912
C2×#168394832
C2×C61×D4⋊C82
#966561