Finite Group Databasebeta

← #29590913

Subgroups — #29590913

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#21449149C211yesmaximal, characteristic
2#21445898C211yesmaximal, characteristic, complemented
3#324×D61C211yesmaximal, characteristic, complemented
4#21443850C211yesmaximal, characteristic, complemented
5#21443848C211yesmaximal, characteristic, complemented
6#21443822C211yesmaximal, characteristic, complemented
7C61×#1345C211yesmaximal, characteristic, complemented
8C22×#11758224C411yescharacteristic
9C2×#14519759—21no—
10C2×C4⋊C4×D61C2211yescharacteristic
11#16839725—21no—
12C22⋊C8×D61—21no—
13#16839683C411yescharacteristic
14#16839682C2211yescharacteristic
15#16839676C411yescharacteristic
16#16839638—21no—
17#16839637—21no—
18#16839634—21no—
19#16839624C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C2×#11758224—41no—
28C2×#11758224—41no—
29C2×#11758224—44no—
30C22×Dic122C2×C411yescharacteristic
31C22×C22⋊D61—21no—
32C23×Dic61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×#11758194—21no—
37C2×C8×D61—41no—
38#14519759—44no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C4⋊C4×D61—41no—
45C4⋊C4×D61—41no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49C22⋊#92418—21no—
50#14519689—41no—
51#14519689—41no—
52#14519689—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C22×D4×C61C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61C2311yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C22⋊C8×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61—21no—
65C23×D61C22⋊C411yescharacteristic
66C2×D4×C61—41no—
67C2×D4×C61—42no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—24no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—42no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84#11758224—44no—
85#11758224—44no—
86#11758224—44no—
87#11758224—44no—
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—21no—
96C2×C4×D61—41no—
97C2×C4×D61—42no—
98C2×C4×D61—42no—
99C2×Dic122—41no—
100C2×Dic122—42no—
101M16×C61—41no—
102M16×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C4⋊C4×C61—41no—
106C22⋊C4×C61—42no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊Dic61—42no—
110C22⋊Dic61—42no—
111#11758198—42no—
112C4⋊Dic61—41no—
113C4⋊Dic61—42no—
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×C61—22no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61C2×C22⋊C411yescharacteristic
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—22no—
133C22×D61—41no—
134C22×D61#9911yescharacteristic
135C22×D61#9911yescharacteristic
136D4×C61—42no—
137D4×C61—42no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C22⋊D61—44no—
150C22⋊D61—44no—
151C2×Dic61—22no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—48no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C4×D61—41no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61—41no—
169C4×D61—42no—
170C4×D61—42no—
171C4×D61—42no—
172C4×D61—81no—
173Dic122—42no—
174Dic122—42no—
175C8×C61—81no—
176C8×C61—81no—
177#92418—81no—
178#92418—81no—
179#11848—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—42no—
183C22×C61—42no—
184C22×C61—42no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61C2×#9911yescharacteristic
190C22×C61#41611yescharacteristic
191C22×C61#42111yescharacteristic
192C2×D61—21no—
193C2×D61—21no—
194C2×D61—21no—
195C2×D61—21no—
196C2×D61—21no—
197C2×D61—42no—
198C2×D61—42no—
199C2×D61AΣL(1,𝔽16)12yes—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—41no—
203C4×C61—41no—
204C4×C61—81no—
205Dic61—42no—
206Dic61—41no—
207Dic61—41no—
208Dic61—41no—
209Dic61—81no—
210#2406—611no—
211#1821—611no—
212C2×#324—611no—
213#1354—611no—
214#1354—611no—
215#1345—611no—
216#1345D6111yescharacteristic, complemented
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—82no—
220C2×C61#151611yescharacteristic
221C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
222C2×C61#213311yescharacteristic
223D61—22no—
224D61—41no—
225C22×#41—611no—
226C2×#123—1221no—
227C22×C4⋊C4—611no—
228#407—1221no—
229C2×C22⋊C8—1221no—
230#395—611no—
231#395—611no—
232#394—611no—
233#394C2×D6111yescharacteristic
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×Q8—611no—
249C22×D4—1221no—
250C22×D4C4×D6111yescharacteristic
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—611no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—2441no—
265C2×C4⋊C4—2441no—
266C2×C4⋊C4C22×D6111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
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—611no—
278#95—1221no—
279#95—1221no—
280#95—1221no—
281#95C4×D6111yescharacteristic
282C24—21no—
283C24—611no—
284#41—2444no—
285#41—2444no—
286#41—2444no—
287#41—2444no—
288C2×Q8—2441no—
289C2×Q8—2442no—
290C2×D4—41no—
291C2×D4—42no—
292C2×D4—1224no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2442no—
296C22×C4—21no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—1221no—
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—2441no—
330C4⋊C4—2441no—
331C4⋊C4—2441no—
332C4⋊C4—2442no—
333C4⋊C4—2442no—
334C22⋊C4—42no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—2442no—
338C22⋊C4—2442no—
339C22⋊C4—2442no—
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—611no—
348C23—611no—
349C23—1222no—
350C23—1221no—
351C23—1221no—
352C23—2441no—
353C23C22⋊C4×D6111yescharacteristic
354Q8—2442no—
355Q8—2442no—
356D4—42no—
357D4—42no—
358D4—2444no—
359D4—2444no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—1222no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—4881no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2448no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4#1451979611yescharacteristic
392C2×C4#1451979811yescharacteristic
393C8—81no—
394C8—81no—
395C8—4881no—
396C8—4881no—
397C22—21no—
398C22—21no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—612no—
407C22—1221no—
408C22—1221no—
409C22—1221no—
410C22—1221no—
411C22—1221no—
412C22—2442no—
413C22—2442no—
414C22#99×D6111yescharacteristic
415C22#1683975511yescharacteristic
416C22#1683977711yescharacteristic
417C4—21no—
418C4—21no—
419C4—41no—
420C4—41no—
421C4—81no—
422C4—4881no—
423C4—2441no—
424C4—2441no—
425C4—2441no—
426C4—2442no—
427C2—21no—
428C2—21no—
429C2—82no—
430C2—1222no—
431C2—2441no—
432C2#2144437211yescharacteristic
433C2AΣL(1,𝔽16)×D6111yescharacteristic
434C2#2144750511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radicalC22×#11758224C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61#11848
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #21445898C2semidirect
3. #324×D61C2semidirect
4. #21443850C2semidirect
5. #21443848C2semidirect
6. #21443822C2semidirect
7. C61×#1345C2semidirect
216. #1345D61semidirect
244. C61#11848semidirect

Maximal subgroups

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

subgroupindex
#214491492
#214458982
#324×D612
#214438502
#214438482
#214438222
C61×#13452
#1184861