Finite Group Databasebeta

← #29589568

Subgroups — #29589568

Order 15616.

496 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450287C211yesmaximal, characteristic
2#21444147C211yesmaximal, characteristic, complemented
3#324×D61C211yesmaximal, characteristic, complemented
4#21443765C211yesmaximal, characteristic, complemented
5#21443750C211yesmaximal, characteristic, complemented
6#21443750C211yesmaximal, characteristic, complemented
7C61×#1325C211yesmaximal, characteristic, complemented
8C2×#14519762—21no—
9C2×#14519762—21no—
10C2×#14519752C411yescharacteristic
11C2×C4⋊C4×D61C2211yescharacteristic
12#16839724—21no—
13C22⋊C8×D61—21no—
14#16839697—21no—
15#16839697—21no—
16#16839664C411yescharacteristic
17#16839663C2211yescharacteristic
18#16839631C411yescharacteristic
19C4×#11758198C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839487—21no—
23#16839487—21no—
24C61×#384C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758189—41no—
33C2×C8×D61—41no—
34#14519762—44no—
35#14519762—44no—
36#14519752—41no—
37#14519752—41no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×#11758196D411yescharacteristic
43C4⋊C4×D61—41no—
44C4⋊C4×D61—41no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×C4×Dic61C2×C411yescharacteristic
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519689—41no—
55#14519689—41no—
56#14519684—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2311yescharacteristic
61C2×C42×C61C2×C411yescharacteristic
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C23×D61—21no—
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—42no—
80C2×D244—42no—
81C2×D244—41no—
82C2×D244—41no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—41no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—42no—
98C4⋊C4×C61—42no—
99C4⋊C4×C61—41no—
100C42×C61—21no—
101C42×C61—21no—
102#11758198—24no—
103#11758198—42no—
104#11758198—42no—
105#11758198—42no—
106#11758198—42no—
107#11758198—42no—
108C4⋊Dic61—41no—
109#11758196—41no—
110#11758196—41no—
111#11758196—42no—
112#11758196—42no—
113C4×Dic61—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116#11758189—82no—
117C8×D61—82no—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—22no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61#9911yescharacteristic
131C22×D61#9911yescharacteristic
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—22no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61#13111yescharacteristic
145C2×C4×C61#13111yescharacteristic
146C2×Dic61—22no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156D244—81no—
157D244—81no—
158D244—82no—
159D244—82no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—42no—
165C4×D61—42no—
166C4×D61—81no—
167C4×D61—81no—
168C8×C61—81no—
169C8×C61—81no—
170#92418—81no—
171#92418—81no—
172#11549—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61#40811yescharacteristic
176C22×C61C2×#9911yescharacteristic
177C22×C61#41311yescharacteristic
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61#35312yes—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—42no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—81no—
199Dic61—42no—
200Dic61—41no—
201Dic61—41no—
202Dic61—41no—
203#2501—611no—
204#1463—611no—
205C2×#324—611no—
206#1325—611no—
207#1325D6111yescharacteristic, complemented
208#1318—611no—
209#1318—611no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61#146811yescharacteristic
213C2×C61C2×#35311yescharacteristic
214C2×C61#213311yescharacteristic
215D61—22no—
216D61—41no—
217D61—161no—
218C2×#123—1221no—
219C2×#123—1221no—
220C2×#121—611no—
221C22×C4⋊C4—611no—
222#407—1221no—
223C2×C22⋊C8—1221no—
224#399—1221no—
225#399—1221no—
226#390—611no—
227#390—611no—
228#384—611no—
229#384C2×D6111yescharacteristic
230C4×C22⋊C4—611no—
231#324—611no—
232#324—611no—
233#324—1221no—
234#324—1221no—
235#324C2×D6111yescharacteristic
236#324C2×D6111yescharacteristic
237C61#1154911yescharacteristic, complemented, Sylow
238C22×D4—611no—
239C22×D4—1221no—
240C23×C4—611no—
241C23×C4—611no—
242C23×C4—611no—
243C2×M16—2441no—
244C22×C8—2441no—
245#123—2444no—
246#123—2444no—
247#121—2441no—
248#121—2441no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—2441no—
257C2×C4⋊C4—2441no—
258C2×C4⋊C4C4×D6111yescharacteristic
259C2×C4⋊C4C22×D6111yescharacteristic
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C42—611no—
267C2×C42C4×D6111yescharacteristic
268C22⋊C8—21no—
269C22⋊C8—21no—
270C22⋊C8—1221no—
271C22⋊C8—1221no—
272C22⋊C8—2441no—
273C22⋊C8—2441no—
274#95—1221no—
275C24—611no—
276C24—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2442no—
284C2×D4—2442no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—2441no—
300C22×C4—2442no—
301C22×C4—2442no—
302C22×C4C2×C4×D6111yescharacteristic
303C22×C4D4×D6111yescharacteristic
304C22×C4D4×D6111yescharacteristic
305M16—4882no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—4882no—
309C2×C8—2441no—
310C2×C8—2441no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C4⋊C4—2442no—
319C4⋊C4—2442no—
320C22⋊C4—1224no—
321C22⋊C4—2442no—
322C22⋊C4—2442no—
323C22⋊C4—2442no—
324C22⋊C4—2442no—
325C22⋊C4—2442no—
326C42—21no—
327C42—21no—
328C42—2441no—
329C23—611no—
330C23—611no—
331C23—1222no—
332C23—1221no—
333C23—1221no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23C22⋊C4×D6111yescharacteristic
343D4—4881no—
344D4—4881no—
345D4—4882no—
346D4—4882no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—1222no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—4881no—
366C2×C4—4881no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4#1451978311yescharacteristic
378C2×C4#1451978511yescharacteristic
379C8—81no—
380C8—81no—
381C8—4881no—
382C8—4881no—
383C22—21no—
384C22—21no—
385C22—612no—
386C22—1221no—
387C22—1221no—
388C22—1221no—
389C22—1221no—
390C22—1221no—
391C22—4881no—
392C22—4881no—
393C22—4881no—
394C22—4881no—
395C22—4881no—
396C22—4881no—
397C22—4881no—
398C22—2442no—
399C22—2442no—
400C22#1683972711yescharacteristic
401C22#99×D6111yescharacteristic
402C22#1683974511yescharacteristic
403C4—21no—
404C4—21no—
405C4—42no—
406C4—41no—
407C4—41no—
408C4—81no—
409C4—2442no—
410C4—2441no—
411C4—2441no—
412C4—2441no—
413C2—21no—
414C2—21no—
415C2—1222no—
416C2—9761no—
417C2—2441no—
418C2#2144416611yescharacteristic
419C2#353×D6111yescharacteristic
420C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1325C2
socleC22×C61C2×#99
prime radicalC2×#14519752C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1325D61
hypocenterC61#11549
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #21444147C2semidirect
3. #324×D61C2semidirect
4. #21443765C2semidirect
5. #21443750C2semidirect
6. #21443750C2semidirect
7. C61×#1325C2semidirect
207. #1325D61semidirect
237. C61#11549semidirect

Maximal subgroups

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

subgroupindex
#214502872
#214441472
#324×D612
#214437652
#214437502
C61×#13252
#1154961