Finite Group Databasebeta

← #29590571

Subgroups — #29590571

Order 15616.

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

normal subgroups only

This group has 544 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#21450715C211yesmaximal, characteristic
2#21445606C211yesmaximal, characteristic, complemented
3#21444154C211yesmaximal, characteristic, complemented
4#21443820C211yesmaximal, characteristic, complemented
5#21443818C211yesmaximal, characteristic, complemented
6#21443816C211yesmaximal, characteristic, complemented
7C61×#1343C211yesmaximal, characteristic, complemented
8C2×#14519749—21no—
9C2×D4×Dic61C411yescharacteristic, complemented
10C2×#14519737C2211yescharacteristic
11C2×#14519691—21no—
12#16839724—21no—
13#16839689C411yescharacteristic, complemented
14#16839687C2211yescharacteristic
15#16839670C411yescharacteristic, complemented
16#16839642—21no—
17#16839638—21no—
18#16839626C411yescharacteristic, complemented
19#16839620—21no—
20C22⋊C4×Dic61—21no—
21#16839529C2211yescharacteristic
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#392C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C22⋊D61D411yescharacteristic
29C23×Dic61—21no—
30C23×Dic61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758189—41no—
33#14519749—42no—
34#14519749—42no—
35D4×Dic61—41no—
36D4×Dic61—41no—
37#14519737—41no—
38#14519737—41no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×#11758198—21no—
47C2×#11758198C2×C411yescharacteristic
48C2×C4×Dic61—41no—
49C2×C4×Dic61C2×C411yescharacteristic
50#14519691—24no—
51C22⋊#92418—21no—
52#14519689—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—41no—
57#14519684C2×C411yescharacteristic
58C22×D4×C61—21no—
59C22×D4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61C2311yescharacteristic
63C22⋊C8×C61—21no—
64#95×C61C2×C411yescharacteristic
65C24×C61—21no—
66C24×C61C2×D411yescharacteristic
67C23×D61C22⋊C411yescharacteristic
68C2×D4×C61—41no—
69C2×D4×C61—42no—
70C2×D4×C61—42no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—81no—
74C22×C4×C61—21no—
75C22×C4×C61—41no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—42no—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—81no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—42no—
90C22×Dic61—42no—
91C22×Dic61—41no—
92C22×Dic61—42no—
93C22×Dic61—81no—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—81no—
100C2×C8×C61—41no—
101C22⋊C4×C61—22no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—81no—
105C22⋊Dic61—22no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111C22⋊Dic61—81no—
112#11758198—41no—
113#11758198—42no—
114C4⋊Dic61—41no—
115#11758196—41no—
116#11758196—42no—
117C4×Dic61—21no—
118C4×Dic61—21no—
119C4×Dic61—82no—
120C2×#92418—41no—
121#11758189—82no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—22no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61C2×C22⋊C411yescharacteristic
134C23×C61AGL(1,ℤ/8)11yescharacteristic
135C23×C61AGL(1,ℤ/8)11yescharacteristic
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—41no—
140C22×D61—41no—
141D4×C61—42no—
142D4×C61—42no—
143D4×C61—82no—
144D4×C61—82no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—81no—
154C2×C4×C61—81no—
155C22⋊D61—42no—
156C22⋊D61—42no—
157C22⋊D61—84no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—41no—
164C2×Dic61—42no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—81no—
172C2×Dic61—84no—
173C2×Dic61—81no—
174C2×Dic61—81no—
175C2×Dic61#9911yescharacteristic
176C2×Dic61#9911yescharacteristic
177C2×Dic61#10412yes—
178C4×D61—42no—
179C4×D61—81no—
180C8×C61—81no—
181#92418—81no—
182#11774—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—42no—
190C22×C61—42no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—42no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61C2×#9911yescharacteristic
200C22×C61#41811yescharacteristic
201C22×C61C2×#10411yescharacteristic
202C2×D61—42no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—81no—
207C4×C61—41no—
208C4×C61—41no—
209C4×C61—81no—
210C4×C61—82no—
211Dic61—21no—
212Dic61—21no—
213Dic61—22no—
214Dic61—41no—
215Dic61—81no—
216Dic61—82no—
217Dic61—81no—
218#2535—611no—
219C4×#99—611no—
220#1465—611no—
221#1344—611no—
222#1344—611no—
223#1343—611no—
224#1343D6111yescharacteristic, complemented
225C2×C61—21no—
226C2×C61—21no—
227C2×C61—41no—
228C2×C61—41no—
229C2×C61—82no—
230C2×C61#150711yescharacteristic
231C2×C61#212011yescharacteristic
232C2×C61#212711yescharacteristic
233D61—81no—
234C2×#121—1221no—
235C2×C4×D4—611no—
236C2×C4×D4—611no—
237C2×#99—1221no—
238#407—1221no—
239#397—611no—
240#397—611no—
241#392—611no—
242#392C2×D6111yescharacteristic
243#386—1221no—
244#386—1221no—
245#382—611no—
246#380—1221no—
247C4×C22⋊C4—1221no—
248#342—611no—
249#342C2×D6111yescharacteristic
250#324—1221no—
251#323—611no—
252#323C2×D6111yescharacteristic
253C61#1177411yescharacteristic, complemented, Sylow
254C22×D4—21no—
255C22×D4—611no—
256C22×D4—1221no—
257C22×D4C4×D6111yescharacteristic
258C23×C4—611no—
259C23×C4—611no—
260C23×C4—1221no—
261C2×M16—2441no—
262#121—2442no—
263#121—2442no—
264C4×D4—2441no—
265C4×D4—2441no—
266C4×D4—2441no—
267C4×D4—2441no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—1221no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4C22×D6111yescharacteristic
280C2×C42—611no—
281C2×C42—2441no—
282#99—1224no—
283C22⋊C8—21no—
284C22⋊C8—1221no—
285C22⋊C8—2441no—
286#95—611no—
287#95—1221no—
288#95—1221no—
289#95—1221no—
290#95—2441no—
291#95C4×D6111yescharacteristic
292C24—21no—
293C24—611no—
294C24D4×D6111yescharacteristic
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—81no—
301C2×D4—1222no—
302C2×D4—1221no—
303C2×D4—1221no—
304C2×D4—4881no—
305C2×D4—2441no—
306C2×D4—2442no—
307C2×D4—2442no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—611no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—4881no—
320C22×C4—4881no—
321C22×C4—2442no—
322C22×C4—2442no—
323C22×C4—2442no—
324C22×C4—2441no—
325C22×C4C2×C4×D6111yescharacteristic
326C22×C4D4×D6111yescharacteristic
327M16—4882no—
328C2×C8—41no—
329C2×C8—2441no—
330C4⋊C4—2441no—
331C4⋊C4—2441no—
332C4⋊C4—2442no—
333C22⋊C4—22no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—81no—
337C22⋊C4—1222no—
338C22⋊C4—4881no—
339C22⋊C4—2441no—
340C22⋊C4—2442no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C22⋊C4—2441no—
346C42—1221no—
347C42—1221no—
348C42—4882no—
349C23—21no—
350C23—21no—
351C23—22no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—2441no—
364C23—2441no—
365C23C22⋊C4×D6111yescharacteristic
366C23#1451980111yescharacteristic
367C23#1451980411yescharacteristic
368D4—42no—
369D4—42no—
370D4—82no—
371D4—82no—
372D4—4884no—
373D4—2442no—
374D4—2442no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—611no—
386C2×C4—611no—
387C2×C4—612no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—4881no—
392C2×C4—4884no—
393C2×C4—4881no—
394C2×C4—4881no—
395C2×C4—4881no—
396C2×C4—2442no—
397C2×C4—2441no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C8—81no—
408C8—4881no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—41no—
414C22—41no—
415C22—42no—
416C22—42no—
417C22—41no—
418C22—41no—
419C22—42no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—4881no—
426C22—2442no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22#99×D6111yescharacteristic
431C22#1683976511yescharacteristic
432C22#104×D6111yescharacteristic
433C4—41no—
434C4—41no—
435C4—81no—
436C4—82no—
437C4—1221no—
438C4—1221no—
439C4—1222no—
440C4—4881no—
441C4—4882no—
442C4—4881no—
443C4—2441no—
444C2—21no—
445C2—21no—
446C2—41no—
447C2—41no—
448C2—82no—
449C2—4881no—
450C2#2144433311yescharacteristic
451C2#2144745711yescharacteristic
452C2#2144748511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1343C2
socleC22×C61C2×#99
prime radical#21450715C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1343D61
hypocenterC61#11774
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #21445606C2semidirect
3. #21444154C2semidirect
4. #21443820C2semidirect
5. #21443818C2semidirect
6. #21443816C2semidirect
7. C61×#1343C2semidirect
9. C2×D4×Dic61C4semidirect
13. #16839689C4semidirect
15. #16839670C4semidirect
18. #16839626C4semidirect
224. #1343D61semidirect
253. C61#11774semidirect

Maximal subgroups

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

subgroupindex
#214507152
#214456062
#214441542
#214438202
#214438182
#214438162
C61×#13432
#1177461