Finite Group Databasebeta

← #29590645

Subgroups — #29590645

Order 15616.

572 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 73 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#21449179C211yesmaximal, characteristic
2#21445610C211yesmaximal, characteristic
3#21444156C211yesmaximal, characteristic
4#21443850C211yesmaximal, characteristic, complemented
5#21443849C211yesmaximal, characteristic, complemented
6#21443848C211yesmaximal, characteristic, complemented
7C61×#1354C211yesmaximal, characteristic, complemented
8C22×Q8×D61C411yescharacteristic
9C2×#14519755—21no—
10C2×#14519739C2211yescharacteristic
11C2×#14519693—21no—
12#16839724—21no—
13M16×Dic61—21no—
14#16839682C2211yescharacteristic
15#16839675C411yescharacteristic
16#16839673C411yescharacteristic
17#16839666—21no—
18#16839640—21no—
19#16839633—21no—
20#16839621C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122C2×C411yescharacteristic
29C2×Q8×D61—44no—
30C2×Q8×D61—41no—
31C2×Q8×D61—41no—
32C22×D244D411yescharacteristic
33C22×C4×D61—21no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×#11758194—21no—
37C2×#11758189—41no—
38#14519755—44no—
39#14519739—41no—
40#14519739—41no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519693—24no—
50C22⋊#92418—21no—
51#14519689—41no—
52#14519687—41no—
53C8×Dic61—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C22×Q8×C61C2×C411yescharacteristic
59C2×M16×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63#95×C61—21no—
64#95×C61C2×C411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C23×D61C22⋊C411yescharacteristic
67C2×Q8×C61—42no—
68C2×Q8×C61—41no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78Q8×D61—44no—
79Q8×D61—44no—
80Q8×D61—44no—
81Q8×D61—44no—
82C2×D244—22no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—41no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×Dic122—24no—
96C2×Dic122—42no—
97C2×Dic122—41no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100C2×Dic122—42no—
101M16×C61—22no—
102M16×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—42no—
107#11758198—41no—
108#11758198—41no—
109#11758198—42no—
110#11758198—42no—
111#11758198—42no—
112#11758196—42no—
113#11758196—42no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116#11758194—22no—
117#11758194—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120#11758189—82no—
121C23×C61C2×C22⋊C411yescharacteristic
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61#10412yes—
132Q8×C61—42no—
133Q8×C61—42no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—22no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61#13711yescharacteristic
147C2×C4×C61#13711yescharacteristic
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#9911yescharacteristic
158C2×Dic61#9911yescharacteristic
159D244—42no—
160D244—42no—
161C4×D61—42no—
162C4×D61—48no—
163C4×D61—42no—
164C4×D61—42no—
165C4×D61—81no—
166Dic122—44no—
167Dic122—42no—
168Dic122—44no—
169Dic122—42no—
170C8×C61—42no—
171C8×C61—81no—
172#92418—42no—
173#92418—81no—
174#11791—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61C2×#9911yescharacteristic
178C22×C61#41911yescharacteristic
179C22×C61C2×#10411yescharacteristic
180C2×D61—22no—
181C2×D61—42no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—81no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—41no—
193C4×C61—42no—
194C4×C61—41no—
195C4×C61—81no—
196Dic61—21no—
197Dic61—42no—
198Dic61—41no—
199Dic61—81no—
200Dic61AΣL(1,𝔽16)12yes—
201#2409—611no—
202C4×#100—611no—
203#1465—611no—
204#1354—611no—
205#1354—611no—
206#1354—611no—
207#1354D6111yescharacteristic, complemented
208C2×C61—21no—
209C2×C61—21no—
210C2×C61#150811yescharacteristic
211C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
212C2×C61#213511yescharacteristic
213D61—42no—
214D61—81no—
215C23×Q8—611no—
216C2×C22⋊Q8—1221no—
217C2×C4×D4—611no—
218C2×#100—1221no—
219#407—1221no—
220C4×M16—1221no—
221#395—611no—
222#395C2×D6111yescharacteristic
223#393—611no—
224#393—611no—
225#391—1221no—
226#386—1221no—
227#385—1221no—
228#380—611no—
229#343—611no—
230#343C2×D6111yescharacteristic
231#324—611no—
232#324C2×D6111yescharacteristic
233#323—1221no—
234C61#1179111yescharacteristic, complemented, Sylow
235C22×Q8—611no—
236C22×Q8—1221no—
237C22×Q8—2441no—
238C22×Q8—2441no—
239C22×Q8—2444no—
240C22×Q8C4×D6111yescharacteristic
241C22×D4—611no—
242C23×C4—611no—
243C23×C4—611no—
244C23×C4—1221no—
245C2×M16—21no—
246C2×M16—1221no—
247C2×M16—2441no—
248C22⋊Q8—2444no—
249C4×D4—2441no—
250C4×D4—2441no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4C22×D6111yescharacteristic
255C2×C22⋊C4—611no—
256C2×C22⋊C4—611no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C42—611no—
261#100—1224no—
262C22⋊C8—21no—
263C22⋊C8—1221no—
264C22⋊C8—2441no—
265#97—2441no—
266C4×C8—2441no—
267#95—21no—
268#95—611no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272#95C4×D6111yescharacteristic
273C24—611no—
274C24—611no—
275C2×Q8—42no—
276C2×Q8—41no—
277C2×Q8—1224no—
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×Q8—2442no—
282C2×Q8—2442no—
283C2×Q8—2444no—
284C2×Q8—2444no—
285C2×Q8—2444no—
286C2×Q8—2444no—
287C2×D4—1222no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—2441no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—2442no—
302C22×C4—2442no—
303C22×C4—2442no—
304C22×C4—2442no—
305C22×C4—2442no—
306C22×C4C2×C4×D6111yescharacteristic
307C22×C4D4×D6111yescharacteristic
308C22×C4D4×D6111yescharacteristic
309M16—22no—
310M16—41no—
311M16—1222no—
312M16—4882no—
313M16—2441no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—2441no—
317C2×C8—2441no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—2442no—
321C4⋊C4—2442no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C22⋊C4—2442no—
325C22⋊C4—2442no—
326C22⋊C4—2442no—
327C42—1221no—
328C42—1221no—
329C23—612no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23—1221no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23C22⋊C4×D6111yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—2444no—
343Q8—2444no—
344Q8—2442no—
345Q8—2442no—
346D4—2442no—
347D4—2442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4—1221no—
365C2×C4—4881no—
366C2×C4—2442no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2448no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4#1451980611yescharacteristic
377C2×C4#1451980911yescharacteristic
378C8—42no—
379C8—81no—
380C8—4881no—
381C8—2442no—
382C22—21no—
383C22—21no—
384C22—1222no—
385C22—4881no—
386C22—2442no—
387C22—2442no—
388C22—2442no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22#99×D6111yescharacteristic
395C22#1683976911yescharacteristic
396C22#104×D6111yescharacteristic
397C4—21no—
398C4—21no—
399C4—41no—
400C4—42no—
401C4—41no—
402C4—81no—
403C4—612no—
404C4—1221no—
405C4—4881no—
406C4—2442no—
407C4—2441no—
408C2—21no—
409C2—21no—
410C2—4881no—
411C2—2442no—
412C2#2144433711yescharacteristic
413C2AΣL(1,𝔽16)×D6111yescharacteristic
414C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC22×D244D4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11791
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #21443850C2semidirect
5. #21443849C2semidirect
6. #21443848C2semidirect
7. C61×#1354C2semidirect
207. #1354D61semidirect
234. C61#11791semidirect

Maximal subgroups

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

subgroupindex
#214491792
#214456102
#214441562
#214438502
#214438492
#214438482
C61×#13542
#1179161