Finite Group Databasebeta

← #29578948

Subgroups — #29578948

Order 15616.

498 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758199C211yesmaximal, characteristic
2#21444565C211yesmaximal, characteristic, complemented
3#21444209C211yesmaximal, characteristic, complemented
4#21444140C211yesmaximal, characteristic, complemented
5#21444139C211yesmaximal, characteristic, complemented
6#21444112C211yesmaximal, characteristic, complemented
7C61×#1478C211yesmaximal, characteristic, complemented
8C22×#11758199C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10C4×#11758199—21no—
11C4×#11758199—21no—
12C4×#11758199—21no—
13C4×#11758199—21no—
14#16839815C2211yescharacteristic
15#16839815C2211yescharacteristic
16C2×#14519710C411yescharacteristic
17C2×#14519698C411yescharacteristic
18C2×#14519697C411yescharacteristic
19C2×C4×#92418C2211yescharacteristic
20#16839514—21no—
21#16839512—21no—
22#16839489—22no—
23#16839486—22no—
24#16839485—22no—
25#16839484—21no—
26#16839483—21no—
27C2×C4×D4×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#431C2211yescharacteristic
30C61×D4⋊C8—22no—
31C22×D244C2×C411yescharacteristic
32C22×C4×D61—21no—
33C2×#11758199—22no—
34C2×#11758199—22no—
35C2×#11758199—21no—
36C2×#11758199—21no—
37C22×#92418C2×C411yescharacteristic
38C22×#92418C2×C411yescharacteristic
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758198—21no—
45#14519710—21no—
46#14519710—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49#14519698—21no—
50#14519698—21no—
51#14519697—21no—
52#14519697—21no—
53C22⋊#92418—21no—
54C22⋊#92418D412yes—
55C4×#92418—21no—
56C4×#92418—21no—
57C4×#92418D411yescharacteristic
58C4×#92418D411yescharacteristic
59C4×#92418D411yescharacteristic
60C4×#92418D411yescharacteristic
61C22×D4×C61C2×C411yescharacteristic
62C23×C4×C61—21no—
63C4×D4×C61—21no—
64C4×D4×C61—21no—
65C4×D4×C61—21no—
66C4×D4×C61—21no—
67C2×C4⋊C4×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61D412yes—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75C4×C8×C61—21no—
76C24×C61—21no—
77C23×D61—21no—
78C2×D4×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61M1612yes—
84C22×C4×C61—21no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—82no—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C22×Dic61—21no—
92C2×D244—21no—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244M1612yes—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—82no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111#11758199—24no—
112#11758199—24no—
113#11758198—41no—
114#11758198—41no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—22no—
122C2×#92418—41no—
123C2×#92418C22⋊C411yescharacteristic
124C2×#92418C22⋊C411yescharacteristic
125C2×#92418C22⋊C411yescharacteristic
126C2×#92418C22⋊C411yescharacteristic
127C23×C61—22no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—81no—
131C23×C61—81no—
132C23×C61C4×D411yescharacteristic
133C22×D61—22no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—81no—
137C22×D61—81no—
138D4×C61—22no—
139D4×C61—22no—
140D4×C61—41no—
141D4×C61—41no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—82no—
146C2×C4×C61—82no—
147C2×C4×C61—81no—
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12411yescharacteristic
153C2×C4×C61#12711yescharacteristic
154C2×C4×C61C2×M1611yescharacteristic
155C2×C4×C61C2×M1611yescharacteristic
156C2×C4×C61#13111yescharacteristic
157C2×C4×C61#13111yescharacteristic
158C2×Dic61—41no—
159C2×Dic61—81no—
160D244—22no—
161D244—22no—
162D244—41no—
163D244—41no—
164C4×D61—82no—
165C4×D61—82no—
166C8×C61—42no—
167C8×C61—81no—
168#92418—21no—
169#92418—21no—
170#92418—21no—
171#92418—21no—
172#92418—42no—
173#92418—81no—
174#9670—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—42no—
178C22×C61—82no—
179C22×C61—82no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61#39011yescharacteristic
183C22×C61#43511yescharacteristic
184C22×C61#43511yescharacteristic
185C2×D61—42no—
186C2×D61—82no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—82no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—81no—
194C4×C61#40711yescharacteristic
195C4×C61#40811yescharacteristic
196C4×C61#43511yescharacteristic
197C4×C61#43511yescharacteristic
198C4×C61#47212yes—
199Dic61—81no—
200C2×C4×D8—611no—
201#1564—611no—
202#1478—611no—
203#1478D6111yescharacteristic, complemented
204#1460—611no—
205#1460—611no—
206#1452—611no—
207C2×C61—21no—
208C2×C61—21no—
209C2×C61—82no—
210C2×C61#195511yescharacteristic
211C2×C61#197611yescharacteristic
212C2×C61#197811yescharacteristic
213D61—82no—
214C22×D8—611no—
215C2×C4×D4—611no—
216C2×C4×D4C2×D6111yescharacteristic
217C4×D8—1221no—
218C4×D8—1221no—
219C4×D8—1221no—
220C4×D8—1221no—
221#431—611no—
222#431—611no—
223#431C2×D6111yescharacteristic
224#431C2×D6111yescharacteristic
225C2×#107—611no—
226C2×#102—611no—
227C2×#102—611no—
228C2×C4×C8—611no—
229#335—1221no—
230#334—1221no—
231D4⋊C8—22no—
232D4⋊C8—1222no—
233#323—1222no—
234#323—1222no—
235#322—1221no—
236#322—1221no—
237C61#967011yescharacteristic, complemented, Sylow
238C22×D4—611no—
239C22×D4C4×D6111yescharacteristic
240C23×C4—21no—
241C23×C4—1221no—
242C2×D8—1221no—
243C2×D8—1221no—
244C2×D8—1222no—
245C2×D8—1222no—
246C22×C8—611no—
247C22×C8—611no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—1221no—
253C4×D4—1221no—
254C4×D4—1221no—
255C4×D4—1221no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4C4×D6111yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—1221no—
260C2×C42C22×D6111yescharacteristic
261#107—1221no—
262#107—1221no—
263C4⋊C8—21no—
264C4⋊C8—1221no—
265C4⋊C8—1221no—
266C4⋊C8C22⋊D6112yes—
267#102—1221no—
268#102—1221no—
269#102—1221no—
270#102—1221no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—612no—
274C22⋊C8—1221no—
275C4×C8—21no—
276C4×C8—21no—
277C4×C8—611no—
278C4×C8—611no—
279C4×C8—611no—
280C4×C8—611no—
281C4×C8—1221no—
282C4×C8—1221no—
283C24—21no—
284C24—1221no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—612no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4#1175818912yes—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—82no—
301C22×C4—1221no—
302C22×C4—4882no—
303C22×C4—2441no—
304C22×C4—2441no—
305C22×C4C2×C4×D6111yescharacteristic
306C22×C4D4×D6111yescharacteristic
307C22×C4#1175822411yescharacteristic
308D8—1224no—
309D8—1224no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—611no—
313C2×C8—611no—
314C2×C8—611no—
315C2×C8—611no—
316C2×C8—1221no—
317C2×C8—1221no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—1222no—
321C2×C8—2441no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C42#1175822211yescharacteristic
331C42D4×D6111yescharacteristic
332C42D4×D6111yescharacteristic
333C42C2×C22⋊D6111yescharacteristic
334C23—22no—
335C23—41no—
336C23—41no—
337C23—81no—
338C23—81no—
339C23—1222no—
340C23—4881no—
341C23—4881no—
342C23—2441no—
343C23—2441no—
344C23#1451973711yescharacteristic
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—1222no—
350D4—1222no—
351D4—2441no—
352D4—2441no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—4882no—
360C2×C4—4882no—
361C2×C4—4881no—
362C2×C4—2441no—
363C2×C4C22⋊C4×D6111yescharacteristic
364C2×C4C4×C22⋊D6111yescharacteristic
365C2×C4#1451974911yescharacteristic
366C2×C4#1451975011yescharacteristic
367C2×C4#1451976311yescharacteristic
368C2×C4#1451977311yescharacteristic
369C2×C4M16×D6111yescharacteristic
370C2×C4C2×#1175818911yescharacteristic
371C2×C4#1451978311yescharacteristic
372C2×C4#1451978511yescharacteristic
373C8—42no—
374C8—81no—
375C8—1221no—
376C8—1221no—
377C8—1221no—
378C8—1221no—
379C8—4881no—
380C8—2442no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—82no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22—4882no—
389C22—4882no—
390C22—4881no—
391C22—4881no—
392C22—2442no—
393C22#1683966211yescharacteristic
394C22#1683983011yescharacteristic
395C22#1683983611yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—4881no—
401C4#1683972411yescharacteristic
402C4#1683972711yescharacteristic
403C4#1683983111yescharacteristic
404C4#1683983311yescharacteristic
405C4#1684003012yes—
406C2—21no—
407C2—21no—
408C2—82no—
409C2—4882no—
410C2#2144661511yescharacteristic
411C2#2144671611yescharacteristic
412C2#2144672811yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1478C2
socleC22×C61#390
prime radicalC22×#11758199C4
cosocleC2×C42×C61C23
hypercenter#1478D61
hypocenterC61#9670
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #21444565C2semidirect
3. #21444209C2semidirect
4. #21444140C2semidirect
5. #21444139C2semidirect
6. #21444112C2semidirect
7. C61×#1478C2semidirect
203. #1478D61semidirect
237. C61#9670semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581992
#214445652
#214442092
#214441402
#214441392
#214441122
C61×#14782
#967061