Finite Group Databasebeta

← #29580573

Subgroups — #29580573

Order 15616.

804 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#16839920C211yesmaximal, characteristic
2C2×#16839917C211yesmaximal, characteristic
3#21451935C211yesmaximal, characteristic
4C2×#16839498C211yesmaximal, characteristic
5#21444089C211yesmaximal, characteristic
6#21443661C211yesmaximal, characteristic
7C2×C61×#328C211yesmaximal, characteristic
8C23×Dic122C2211yescharacteristic
9C22×Dic244—21no—
10C22×#11758202—21no—
11C2×#14519756C2211yescharacteristic
12#16839920—22no—
13#16839920—22no—
14#16839917—22no—
15#16839917—22no—
16C2×#14519702—21no—
17C2×#14519700—21no—
18C2×C22⋊#92418C2211yescharacteristic
19#16839693—21no—
20#16839692—21no—
21#16839682—21no—
22#16839681—21no—
23#16839620—22no—
24C2×#14519684—22no—
25C2×#14519684C2211yescharacteristic
26#16839498—22no—
27C2×C22⋊Q8×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×#95×C61C2211yescharacteristic
30C61×#328—22no—
31C22×Dic122—21no—
32C22×Dic122—21no—
33C22×Dic122—21no—
34C22×Dic122—21no—
35C22×Dic122—21no—
36C22×Dic122—44no—
37C22×Dic122D411yescharacteristic
38C22×Dic122D412yes—
39C23×Dic61—21no—
40C23×Dic61D412yes—
41C2×Dic244—24no—
42C2×Dic244—44no—
43C2×#11758202—24no—
44C2×#11758202—44no—
45C22×#92418—21no—
46#14519756—21no—
47#14519756—21no—
48#14519756—21no—
49#14519756—21no—
50C2×C4⋊Dic61D411yescharacteristic
51C2×#11758196—21no—
52C2×#11758196—22no—
53C2×#11758196—22no—
54C2×C22⋊Dic61—21no—
55#14519702—24no—
56#14519700—24no—
57C22⋊#92418—21no—
58C22⋊#92418D412yes—
59#14519684—22no—
60#14519684—22no—
61#14519684—21no—
62#14519684—21no—
63#14519684—44no—
64C22×Q8×C61D411yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61—21no—
70C22⋊Q8×C61—21no—
71C22⋊Q8×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61D412yes—
77#95×C61—21no—
78#95×C61—21no—
79C24×C61C2×D411yescharacteristic
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—42no—
83C22×C4×C61—22no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—42no—
87C22×C4×C61—41no—
88C22×C4×C61—42no—
89C22×C4×C61—41no—
90C22×C4×C61—42no—
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×Dic61—24no—
98C22×Dic61—22no—
99C22×Dic61—22no—
100C22×Dic61—22no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—42no—
104C22×Dic61—41no—
105C22×Dic61—41no—
106C22×Dic61—42no—
107C22×Dic61—42no—
108C22×Dic61Q1614yescomplemented
109C2×Dic122—24no—
110C2×Dic122—24no—
111C2×Dic122—22no—
112C2×Dic122—22no—
113C2×Dic122—21no—
114C2×Dic122—21no—
115C2×Dic122—44no—
116C2×Dic122—44no—
117C2×Dic122—44no—
118C2×Dic122—44no—
119C2×Dic122—42no—
120C2×Dic122—42no—
121C2×Dic122—41no—
122C2×Dic122—41no—
123C2×Dic122—42no—
124C2×C8×C61—22no—
125C2×C8×C61—42no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊Dic61—41no—
133C22⋊Dic61—41no—
134#11758202—48no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137#11758196—41no—
138#11758196—41no—
139#11758196—82no—
140#11758196—82no—
141C2×#92418—22no—
142C2×#92418—42no—
143Dic244—48no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—22no—
147C23×C61#12011yescharacteristic
148C23×C61#12111yescharacteristic
149C23×C61#12711yescharacteristic
150C23×C61C2×Q1612yes—
151C23×C61#13712yes—
152Q8×C61—42no—
153Q8×C61—81no—
154C2×C4×C61—22no—
155C2×C4×C61—22no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—44no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61—82no—
168C2×C4×C61—81no—
169C2×C4×C61—81no—
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×Dic61—24no—
175C2×Dic61—24no—
176C2×Dic61—42no—
177C2×Dic61—44no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181C2×Dic61—44no—
182C2×Dic61—44no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—42no—
188C2×Dic61—82no—
189Dic122—24no—
190Dic122—24no—
191Dic122—42no—
192Dic122—42no—
193Dic122—44no—
194Dic122—44no—
195Dic122—42no—
196Dic122—81no—
197C8×C61—42no—
198#92418—42no—
199#9967—611nomaximal, Sylow
200C22×C61—22no—
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61#39211yescharacteristic
209C22×C61#45112yes—
210C22×C61#45511yescharacteristic
211C22×C61#45611yescharacteristic
212C22×C61B(4,𝔽2)12yes—
213C22×C61#46212yes—
214C22×C61#49411yescharacteristic
215C22×C61#49711yescharacteristic
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—82no—
221C4×C61—81no—
222C4×C61—81no—
223Dic61—44no—
224Dic61—44no—
225Dic61—81no—
226Dic61—81no—
227C2×#451—611no—
228C2×#451—611no—
229#2659—611no—
230C2×#328—611no—
231C2×#328D6111yescharacteristic
232#1446—611no—
233#1280—611no—
234C2×C61—21no—
235C2×C61—22no—
236C2×C61—21no—
237C2×C61#160212yes—
238C2×C61#160512yes—
239C2×C61#200711yescharacteristic
240C2×C61#201611yescharacteristic
241C2×C61#202111yescharacteristic
242C23×Q8—611no—
243C22×Q16—1221no—
244C22×Q16—1221no—
245C2×C22⋊Q8—611no—
246C2×C22⋊Q8C2×D6111yescharacteristic
247#451—1222no—
248#451—1222no—
249#451—1222no—
250#451—1222no—
251C2×#103—1221no—
252C2×#103—1221no—
253C2×C22⋊C8—611no—
254C2×C22⋊C8C2×D6111yescharacteristic
255#398—1221no—
256#398—1221no—
257#395—1221no—
258#395—1221no—
259#380—1222no—
260C2×#95—611no—
261C2×#95—1222no—
262C2×#95C2×D6111yescharacteristic
263#328—22no—
264#328—1222no—
265C61#996711yescharacteristic, complemented, Sylow
266C22×Q8—611no—
267C22×Q8—612no—
268C22×Q8—1221no—
269C22×Q8—1221no—
270C22×Q8—1221no—
271C22×Q8—1221no—
272C22×Q8—1221no—
273C22×Q8—2444no—
274C22×Q8D24411yescharacteristic
275C23×C4—21no—
276C23×C4—612no—
277C23×C4—1221no—
278C23×C4C22×D6111yescharacteristic
279C2×Q16—1224no—
280C2×Q16—1224no—
281C2×Q16—2444no—
282C2×Q16—2444no—
283C22×C8—21no—
284C22×C8—1221no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—1221no—
290C22⋊Q8—1221no—
291C22⋊Q8—1221no—
292C22⋊Q8—1221no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—611no—
295C2×C4⋊C4—1222no—
296C2×C4⋊C4—1222no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4D24411yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—1221no—
301#103—1224no—
302#103—1224no—
303C22⋊C8—21no—
304C22⋊C8—612no—
305C22⋊C8—1221no—
306C22⋊C8C22⋊D6112yes—
307#95—21no—
308#95—21no—
309#95—1222no—
310#95—1222no—
311#95—1221no—
312#95—1221no—
313#95—2444no—
314C24D4×D6111yescharacteristic
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—42no—
318C2×Q8—1224no—
319C2×Q8—1224no—
320C2×Q8—1222no—
321C2×Q8—1221no—
322C2×Q8—1222no—
323C2×Q8—1221no—
324C2×Q8—2442no—
325C2×Q8—2442no—
326C2×Q8—2442no—
327C2×Q8—2444no—
328C2×Q8—2444no—
329C2×Q8—2444no—
330C2×Q8—2444no—
331C2×Q8—2441no—
332C2×Q8—2441no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—42no—
341C22×C4—614no—
342C22×C4—1222no—
343C22×C4—1224no—
344C22×C4—1222no—
345C22×C4—1222no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—2442no—
349C22×C4—2442no—
350C22×C4—2442no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4C2×D24411yescharacteristic
354C22×C4#1175822211yescharacteristic
355C22×C4D4×D6111yescharacteristic
356C22×C4D4×D6111yescharacteristic
357C22×C4D4×D6111yescharacteristic
358C22×C4C2×C22⋊D6111yescharacteristic
359Q16—2448no—
360Q16—2448no—
361C2×C8—22no—
362C2×C8—42no—
363C2×C8—1222no—
364C2×C8—2442no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—1221no—
370C4⋊C4—1221no—
371C4⋊C4—4882no—
372C4⋊C4—4882no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—2441no—
378C22⋊C4—2441no—
379C23—21no—
380C23—21no—
381C23—22no—
382C23#1451974711yescharacteristic
383C23#1451975011yescharacteristic
384C23#1451977311yescharacteristic
385C23Q16×D6112yes—
386C23#1451980612yes—
387Q8—42no—
388Q8—81no—
389Q8—1224no—
390Q8—1224no—
391Q8—4881no—
392Q8—2442no—
393Q8—2442no—
394Q8—2442no—
395Q8—2444no—
396Q8—2444no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—82no—
412C2×C4—81no—
413C2×C4—1224no—
414C2×C4—1224no—
415C2×C4—4882no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2442no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2444no—
422C2×C4—2442no—
423C2×C4—2442no—
424C2×C4—2442no—
425C2×C4—2444no—
426C2×C4—2442no—
427C2×C4—2444no—
428C2×C4#1451974511yescharacteristic
429C2×C4#1451974711yescharacteristic
430C2×C4#1451975011yescharacteristic
431C2×C4#1451975111yescharacteristic
432C8—42no—
433C8—2442no—
434C22—21no—
435C22—21no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—21no—
441C22—21no—
442C22#1683967111yescharacteristic
443C22#1683991912yes—
444C22#1683994111yescharacteristic
445C22#1683994611yescharacteristic
446C22#1683995012yes—
447C22#1683997112yes—
448C22#1684014011yescharacteristic
449C22#1684015311yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—82no—
455C4—81no—
456C4—81no—
457C4—4881no—
458C4—4881no—
459C4—2444no—
460C4—2444no—
461C2—21no—
462C2—22no—
463C2—21no—
464C2#2144477712yes—
465C2#2144479412yes—
466C2#2144686711yescharacteristic
467C2#2144692011yescharacteristic
468C2#2144694411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#328C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#328D61
hypocenterC61#9967
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
108. C22×Dic61Q16semidirect
265. C61#9967semidirect

Maximal subgroups

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

subgroupindex
C2×#168399202
C2×#168399172
#214519352
C2×#168394982
#214440892
#214436612
C2×C61×#3282
#996761