Finite Group Databasebeta

← #29571447

Subgroups — #29571447

Order 15616.

812 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 123 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×#16840367C211yesmaximal, characteristic
2#21444211C212yesmaximal, complemented
3#21444209C212yesmaximal, complemented
4#21444133C211yesmaximal, characteristic, complemented
5C61×#1458C211yesmaximal, characteristic, complemented
6#16840367—24no—
7#16840367—24no—
8C2×#14519774C411yescharacteristic
9C2×#14519769C411yescharacteristic
10C2×#14519762—21no—
11C2×#14519762—21no—
12C2×#14519751C411yescharacteristic
13C2×#14519751C411yescharacteristic
14C2×#14519750—21no—
15C2×#14519750—21no—
16C2×C4×D244C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16839815C2212yes—
19#16839491—24no—
20#16839489—24no—
21#16839488—21no—
22#16839486—21no—
23C2×#117×C61C2211yescharacteristic
24C61×#431C2212yes—
25C61×#324—21no—
26C61×#323—21no—
27C22×D244—21no—
28C22×D244—21no—
29C22×D244C2×C411yescharacteristic
30C22×D244C2×C411yescharacteristic
31C22×C22⋊D61—21no—
32C22×C22⋊D61—21no—
33C22×C4×D61—21no—
34C22×C4×D61—21no—
35#14519774—22no—
36#14519774—22no—
37#14519769—22no—
38#14519769—22no—
39#14519762—28no—
40#14519762—28no—
41#14519751—22no—
42#14519751—22no—
43#14519751—22no—
44#14519751—22no—
45#14519750—28no—
46#14519750—28no—
47C4×D244—22no—
48C4×D244—22no—
49C4×D244D414yes—
50C4×D244D414yes—
51C2×C4⋊Dic61C2×C411yescharacteristic
52C2×C4⋊Dic61C2×C411yescharacteristic
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×#11758198—21no—
56C2×#11758198—21no—
57C2×#11758198—21no—
58C2×#11758198—21no—
59C4⋊#92418—22no—
60C22⋊#92418—22no—
61C4×#92418—22no—
62C23×C4×C61C2×C411yescharacteristic
63#117×C61—22no—
64#117×C61—22no—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C22⋊C4×C61D411yescharacteristic
68C2×C22⋊C4×C61D411yescharacteristic
69C2×C42×C61C2×C411yescharacteristic
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—22no—
72C22⋊C8×C61—22no—
73C4×C8×C61—22no—
74C24×C61C22⋊C411yescharacteristic
75C23×D61—21no—
76C23×D61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C2×C22⋊D61—24no—
88C2×C22⋊D61—24no—
89C2×C22⋊D61—82no—
90C2×C22⋊D61—82no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C2×D244—22no—
94C2×D244—22no—
95C2×D244—22no—
96C2×D244—22no—
97C2×D244—21no—
98C2×D244—21no—
99C2×D244—24no—
100C2×D244—24no—
101C2×D244—82no—
102C2×D244—82no—
103C2×D244C22⋊C412yes—
104C2×D244C22⋊C412yes—
105C2×C4×D61—24no—
106C2×C4×D61—24no—
107C2×C4×D61—82no—
108C2×C4×D61—82no—
109C2×C8×C61—42no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—22no—
112C22⋊C4×C61—22no—
113C22⋊C4×C61—22no—
114C42×C61—21no—
115C42×C61—21no—
116C42×C61C2×D412yes—
117C42×C61C2×D412yes—
118#11758198—24no—
119#11758198—24no—
120#11758198—24no—
121#11758198—24no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61C22⋊C412yes—
125C4⋊Dic61C22⋊C412yes—
126#11758196—24no—
127#11758196—24no—
128C2×#92418—42no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61C2×C22⋊C411yescharacteristic
135C22×D61—22no—
136C22×D61—22no—
137C22×D61—42no—
138C22×D61—42no—
139C22×D61—42no—
140C22×D61—42no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61C2×C22⋊C411yescharacteristic
157C2×C4×C61C2×C22⋊C411yescharacteristic
158C2×C4×C61#12012yes—
159C2×C4×C61#12012yes—
160C2×C4×C61#13112yes—
161C2×C4×C61#13112yes—
162C22⋊D61—84no—
163C22⋊D61—84no—
164C2×Dic61—22no—
165C2×Dic61—22no—
166C2×Dic61—42no—
167C2×Dic61—42no—
168D244—24no—
169D244—24no—
170D244—42no—
171D244—42no—
172D244—84no—
173D244—84no—
174C4×D61—84no—
175C4×D61—84no—
176C8×C61—82no—
177#92418—82no—
178#8326—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61#37911yescharacteristic
187C22×C61#40811yescharacteristic
188C22×C61#40811yescharacteristic
189C2×D61—42no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—42no—
193C2×D61—42no—
194C2×D61—42no—
195C2×D61—82no—
196C2×D61—82no—
197C2×D61—82no—
198C2×D61—82no—
199C4×C61—22no—
200C4×C61—22no—
201C4×C61—41no—
202C4×C61—41no—
203C4×C61—41no—
204C4×C61#40812yes—
205C4×C61#40812yes—
206Dic61—42no—
207Dic61—42no—
208C2×#540—611no—
209#1478—612no—
210#1478—612no—
211#1458—611no—
212#1458D6111yescharacteristic, complemented
213C2×C61—21no—
214C2×C61—21no—
215C2×C61—81no—
216C2×C61#178011yescharacteristic
217C2×C61#179511yescharacteristic
218C2×C61#179511yescharacteristic
219D61—82no—
220D61—82no—
221#540—1224no—
222#540—1224no—
223C2×#127—611no—
224C2×#125—611no—
225C2×#123—1221no—
226C2×#123—1221no—
227C2×#121—611no—
228C2×#121—611no—
229C2×#121—1221no—
230C2×#121—1221no—
231C2×C4×D4—611no—
232C2×C4×D4—611no—
233C2×#117C2×D6111yescharacteristic
234#431—612no—
235#431C2×D6112yes—
236D4⋊C8—1224no—
237D4⋊C8—1224no—
238#324—21no—
239#324—1221no—
240#323—21no—
241#323—1221no—
242C61#832611yescharacteristic, complemented, Sylow
243C22×D4—611no—
244C22×D4—611no—
245C22×D4—1221no—
246C22×D4—1221no—
247C22×D4—1221no—
248C22×D4—1221no—
249C23×C4—1221no—
250C23×C4—1221no—
251C23×C4C4×D6111yescharacteristic
252#127—1222no—
253#127—1222no—
254#125—1222no—
255#125—1222no—
256#123—1228no—
257#123—1228no—
258#121—1228no—
259#121—1228no—
260#121—1222no—
261#121—1222no—
262#121—1222no—
263#121—1222no—
264C4×D4—614no—
265C4×D4—614no—
266C4×D4—1222no—
267C4×D4—1222no—
268#117—22no—
269#117—22no—
270C2×C4⋊C4—611no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4D24411yescharacteristic
275C2×C4⋊C4C22⋊D6111yescharacteristic
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4D24411yescharacteristic
281C2×C22⋊C4C22⋊D6111yescharacteristic
282C2×C42C4×D6111yescharacteristic
283C2×C42C22×D6111yescharacteristic
284C4⋊C8—22no—
285C4⋊C8—1222no—
286C22⋊C8—22no—
287C22⋊C8—1222no—
288C4×C8—22no—
289C4×C8—1222no—
290C24—1221no—
291C24—1221no—
292C24#1175819811yescharacteristic
293C2×D4—612no—
294C2×D4—612no—
295C2×D4—1224no—
296C2×D4—1224no—
297C2×D4—1224no—
298C2×D4—1224no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1222no—
302C2×D4—1222no—
303C2×D4—1222no—
304C2×D4—1222no—
305C2×D4—4882no—
306C2×D4—4882no—
307C2×D4—4882no—
308C2×D4—4882no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1224no—
316C22×C4—1224no—
317C22×C4—4882no—
318C22×C4—4882no—
319C22×C4#1175819811yescharacteristic
320C22×C4#1175819811yescharacteristic
321C22×C4#1175819811yescharacteristic
322C22×C4C2×C4×D6111yescharacteristic
323C22×C4C2×D24411yescharacteristic
324C22×C4C2×C22⋊D6111yescharacteristic
325C2×C8—42no—
326C2×C8—2442no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—612no—
330C4⋊C4—612no—
331C4⋊C4—1224no—
332C4⋊C4—1224no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—1224no—
338C22⋊C4—1224no—
339C22⋊C4—1224no—
340C22⋊C4—1224no—
341C42—21no—
342C42—21no—
343C42D4×D6112yes—
344C42D4×D6112yes—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—1222no—
351C23—1222no—
352C23—2442no—
353C23—2442no—
354C23—2442no—
355C23—2442no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23C2×#1175819811yescharacteristic
361D4—1224no—
362D4—1224no—
363D4—4884no—
364D4—4884no—
365D4—4884no—
366D4—4884no—
367D4—2442no—
368D4—2442no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—1222no—
381C2×C4—1222no—
382C2×C4—4884no—
383C2×C4—4884no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4C22⋊C4×D6111yescharacteristic
387C2×C4C22⋊C4×D6111yescharacteristic
388C2×C4#1451974512yes—
389C2×C4#1451974712yes—
390C2×C4#1451978312yes—
391C2×C4#1451978512yes—
392C8—82no—
393C8—4882no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—81no—
401C22—4882no—
402C22—4882no—
403C22—4882no—
404C22—4882no—
405C22—2442no—
406C22—2442no—
407C22—2442no—
408C22—2442no—
409C22—2442no—
410C22—2442no—
411C22#1683961711yescharacteristic
412C22#1683972811yescharacteristic
413C22#1683973011yescharacteristic
414C4—22no—
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—2442no—
420C4—2442no—
421C4#1683972712yes—
422C4#1683972712yes—
423C2—21no—
424C2—21no—
425C2—81no—
426C2—4882no—
427C2—4882no—
428C2#2144573011yescharacteristic
429C2#2144578711yescharacteristic
430C2#2144579011yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#379
prime radicalC2×#16840367C2
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#8326
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #21444211C2semidirect
3. #21444209C2semidirect
4. #21444133C2semidirect
5. C61×#1458C2semidirect
212. #1458D61semidirect
242. C61#8326semidirect

Maximal subgroups

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

subgroupindex
C2×#168403672
#214442112
#214442092
#214441332
C61×#14582
#832661