Finite Group Databasebeta

← #29590915

Subgroups — #29590915

Order 15616.

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

normal subgroups only

This group has 572 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#21449155C211yesmaximal, characteristic
2#21445898C211yesmaximal, characteristic, complemented
3#324×D61C211yesmaximal, characteristic, complemented
4#21443849C211yesmaximal, characteristic, complemented
5#21443823C211yesmaximal, characteristic, complemented
6#21443821C211yesmaximal, characteristic, complemented
7C61×#1354C211yesmaximal, characteristic, complemented
8C22×#11758226C411yescharacteristic
9C2×#14519762—21no—
10C2×C4⋊C4×D61C2211yescharacteristic
11#16839725—21no—
12C22⋊C8×D61—21no—
13#16839681C411yescharacteristic
14#16839680C411yescharacteristic
15#16839679C2211yescharacteristic
16#16839640—21no—
17#16839636—21no—
18#16839633—21no—
19#16839624C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C2×#11758226—41no—
28C2×#11758226—41no—
29C2×#11758226—44no—
30C22×D244—21no—
31C22×D244C2×C411yescharacteristic
32C22×C4×D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×#11758194—21no—
37C2×C8×D61—41no—
38#14519762—44no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196C2×C411yescharacteristic
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—
50C22⋊#92418—21no—
51#14519689—41no—
52#14519689—41no—
53#14519689—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C22×Q8×C61C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61—21no—
65C23×D61C22⋊C411yescharacteristic
66C2×Q8×C61—42no—
67C2×Q8×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77#11758226—44no—
78#11758226—44no—
79#11758226—44no—
80#11758226—44no—
81C2×D244—24no—
82C2×D244—41no—
83C2×D244—42no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—42no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—41no—
96C2×C4×D61—42no—
97C2×C4×D61—42no—
98C2×C4×D61—42no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101M16×C61—41no—
102M16×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—42no—
107#11758198—42no—
108#11758198—42no—
109#11758198—42no—
110#11758198—42no—
111#11758198—41no—
112#11758198—41no—
113C4⋊Dic61—41no—
114#11758196—41no—
115#11758196—41no—
116#11758196—42no—
117#11758194—41no—
118#11758194—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C8×D61—82no—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—22no—
126C22×D61—22no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61#9911yescharacteristic
135C22×D61#9911yescharacteristic
136Q8×C61—42no—
137Q8×C61—42no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—22no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162D244—44no—
163D244—42no—
164D244—42no—
165D244—44no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61—41no—
169C4×D61—41no—
170C4×D61—42no—
171C4×D61—48no—
172C4×D61—42no—
173C4×D61—42no—
174C4×D61—81no—
175C8×C61—81no—
176C8×C61—81no—
177#92418—81no—
178#92418—81no—
179#11848—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61C2×#9911yescharacteristic
183C22×C61#41611yescharacteristic
184C22×C61#42111yescharacteristic
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—42no—
193C2×D61—42no—
194C2×D61—42no—
195C2×D61—81no—
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61AΣL(1,𝔽16)12yes—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—41no—
203C4×C61—42no—
204C4×C61—41no—
205C4×C61—81no—
206Dic61—41no—
207Dic61—41no—
208Dic61—41no—
209Dic61—81no—
210#2406—611no—
211#1821—611no—
212C2×#324—611no—
213#1354—611no—
214#1354D6111yescharacteristic, complemented
215#1345—611no—
216#1345—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61#151611yescharacteristic
220C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
221C2×C61#213311yescharacteristic
222D61—22no—
223D61—41no—
224D61—82no—
225C22×#41—611no—
226C2×#123—1221no—
227C22×C4⋊C4—611no—
228#407—1221no—
229C2×C22⋊C8—1221no—
230#395—611no—
231#395C2×D6111yescharacteristic
232#394—611no—
233#394—611no—
234#386—1221no—
235#385—1221no—
236#385—1221no—
237#381—611no—
238#343—611no—
239#343—1221no—
240#343C2×D6111yescharacteristic
241#324—611no—
242#324—1221no—
243#324C2×D6111yescharacteristic
244C61#1184811yescharacteristic, complemented, Sylow
245C2×#41—2441no—
246C2×#41—2441no—
247C2×#41—2444no—
248C22×Q8C4×D6111yescharacteristic
249C22×D4—611no—
250C22×D4—1221no—
251C23×C4—611no—
252C23×C4—611no—
253C23×C4—611no—
254C23×C4—1221no—
255C2×M16—21no—
256C2×M16—1221no—
257C22×C8—2441no—
258#123—2444no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—2441no—
265C2×C4⋊C4—2441no—
266C2×C4⋊C4C22×D6111yescharacteristic
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C22⋊C8—21no—
273C22⋊C8—1221no—
274C22⋊C8—2441no—
275C22⋊C8—2441no—
276C22⋊C8—2441no—
277#95—21no—
278#95—611no—
279#95—1221no—
280#95—1221no—
281#95C4×D6111yescharacteristic
282C24—611no—
283C24—1221no—
284#41—2444no—
285#41—2444no—
286#41—2444no—
287#41—2444no—
288C2×Q8—42no—
289C2×Q8—41no—
290C2×D4—1224no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2442no—
295C2×D4—2442no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—2441no—
311C22×C4—2442no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4—2442no—
315C22×C4—2442no—
316C22×C4C2×C4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318C22×C4D4×D6111yescharacteristic
319M16—41no—
320M16—41no—
321M16—2441no—
322M16—2441no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—4882no—
326C2×C8—2441no—
327C2×C8—2441no—
328C4⋊C4—41no—
329C4⋊C4—42no—
330C4⋊C4—2441no—
331C4⋊C4—2441no—
332C4⋊C4—2441no—
333C4⋊C4—2442no—
334C22⋊C4—2442no—
335C22⋊C4—2442no—
336C22⋊C4—2442no—
337C22⋊C4—2442no—
338C22⋊C4—2441no—
339C22⋊C4—2441no—
340C23—611no—
341C23—611no—
342C23—1222no—
343C23—1222no—
344C23—1221no—
345C23—1221no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23C22⋊C4×D6111yescharacteristic
354Q8—42no—
355Q8—42no—
356D4—2444no—
357D4—2444no—
358D4—2442no—
359D4—2442no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—4881no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2448no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4#1451979811yescharacteristic
392C2×C4#1451980011yescharacteristic
393C8—81no—
394C8—81no—
395C8—4881no—
396C8—4881no—
397C22—21no—
398C22—21no—
399C22—612no—
400C22—1221no—
401C22—1221no—
402C22—1221no—
403C22—1221no—
404C22—1221no—
405C22—4881no—
406C22—4881no—
407C22—4881no—
408C22—4881no—
409C22—2442no—
410C22—2442no—
411C22—2442no—
412C22—2442no—
413C22—2442no—
414C22#99×D6111yescharacteristic
415C22#1683975711yescharacteristic
416C22#1683977711yescharacteristic
417C4—21no—
418C4—21no—
419C4—41no—
420C4—42no—
421C4—41no—
422C4—81no—
423C4—4881no—
424C4—2441no—
425C4—2441no—
426C4—2441no—
427C2—21no—
428C2—21no—
429C2—1222no—
430C2—4882no—
431C2—2441no—
432C2#2144437411yescharacteristic
433C2AΣL(1,𝔽16)×D6111yescharacteristic
434C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC22×#11758226C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11848
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
2. #21445898C2semidirect
3. #324×D61C2semidirect
4. #21443849C2semidirect
5. #21443823C2semidirect
6. #21443821C2semidirect
7. C61×#1354C2semidirect
214. #1354D61semidirect
244. C61#11848semidirect

Maximal subgroups

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

subgroupindex
#214491552
#214458982
#324×D612
#214438492
#214438232
#214438212
C61×#13542
#1184861