Finite Group Databasebeta

← #29568638

Subgroups — #29568638

Order 15616.

506 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454149C211yesmaximal, characteristic
2#21445886C211yesmaximal, characteristic, complemented
3#21445886C211yesmaximal, characteristic, complemented
4#21443643C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443640C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic, complemented
8C2×#14519759—21no—
9C2×#14519748C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11C2×#14519689—21no—
12C2×#14519689—21no—
13#16839665C411yescharacteristic
14#16839661C411yescharacteristic
15#16839660C2211yescharacteristic
16#16839656—21no—
17#16839655—21no—
18#16839638—21no—
19#16839619C411yescharacteristic
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×#92418—21no—
32C22×#92418—21no—
33#14519759—42no—
34#14519759—42no—
35#14519748—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C42×D61—42no—
48#14519689—42no—
49#14519689—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×D4×C61C2×C411yescharacteristic
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C42×C61C2311yescharacteristic
60C24×C61—21no—
61C23×D61C22⋊C411yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C2×C22⋊D61—42no—
71C2×C22⋊D61—42no—
72C2×C22⋊D61—42no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—22no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C42×C61—41no—
102C22⋊Dic61—42no—
103C22⋊Dic61—42no—
104C22⋊Dic61—42no—
105#11758198—42no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—42no—
109C4⋊Dic61—41no—
110#11758196—41no—
111#11758196—41no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61C2×C22⋊C411yescharacteristic
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61#9912yes—
136D4×C61—81no—
137D4×C61—81no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61#13111yescharacteristic
148C2×C4×C61#13111yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C22⋊D61—84no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C4×D61—42no—
170C4×D61—42no—
171C4×D61—42no—
172C4×D61—42no—
173C4×D61—42no—
174C4×D61—42no—
175C8×C61—81no—
176C8×C61—81no—
177#92418—81no—
178#92418—81no—
179#7718—611nomaximal, Sylow
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61#40811yescharacteristic
188C22×C61C2×#9911yescharacteristic
189C22×C61#41311yescharacteristic
190C22×C61#41611yescharacteristic
191C22×C61#41811yescharacteristic
192C22×C61#42111yescharacteristic
193C22×C61#42111yescharacteristic
194C2×D61—22no—
195C2×D61—22no—
196C2×D61—22no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—81no—
208Dic61—41no—
209Dic61—41no—
210Dic61—41no—
211Dic61—81no—
212Dic61—81no—
213#2854—611no—
214#1817—611no—
215#1817—611no—
216#1271—611no—
217#1271—611no—
218#1270—611no—
219#1270D6111yescharacteristic, complemented
220C2×C61—161no—
221C2×C61#146811yescharacteristic
222C2×C61#148211yescharacteristic
223C2×C61#149611yescharacteristic
224C2×C61#151011yescharacteristic
225C2×C61#151611yescharacteristic
226C2×C61#153511yescharacteristic
227C2×C61#155311yescharacteristic
228D61—42no—
229C2×#123—1221no—
230C2×#121—611no—
231C22×C42—611no—
232C2×C22⋊C8—1221no—
233C2×C22⋊C8—1221no—
234#390—611no—
235#390C2×D6111yescharacteristic
236#389—611no—
237#389—611no—
238#388—1221no—
239#388—1221no—
240#386—1221no—
241#380—611no—
242#336—611no—
243#336—611no—
244#336—1221no—
245#336—1221no—
246#336C2×D6111yescharacteristic
247#336C2×D6111yescharacteristic
248C61#771811yescharacteristic, complemented, Sylow
249C22×D4—1221no—
250C22×D4C4×D6111yescharacteristic
251C23×C4—611no—
252C23×C4—611no—
253C23×C4—611no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—1221no—
257C22×C8—1221no—
258#123—2442no—
259#123—2442no—
260#121—2442no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4C4×D6111yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C42—611no—
273C2×C42—611no—
274C2×C42—611no—
275C2×C42—2442no—
276C2×C42C22×D6111yescharacteristic
277C22⋊C8—2442no—
278C22⋊C8—2442no—
279#95—1221no—
280#95—1221no—
281#95—1221no—
282C24—21no—
283C24—611no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—2442no—
289C2×D4—2442no—
290C2×D4—2442no—
291C22×C4—21no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—1222no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4C2×C4×D6111yescharacteristic
310C22×C4D4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C4⋊C4—41no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—2441no—
328C4⋊C4—2442no—
329C4⋊C4—2441no—
330C4⋊C4—2441no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—2442no—
336C22⋊C4—2442no—
337C22⋊C4—2442no—
338C22⋊C4—2442no—
339C42—41no—
340C42—2441no—
341C42—2441no—
342C42—2441no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—612no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—1221no—
357C23C22⋊C4×D6111yescharacteristic
358D4—81no—
359D4—81no—
360D4—4884no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4#1451978311yescharacteristic
392C2×C4#1451978511yescharacteristic
393C2×C4#1451979611yescharacteristic
394C2×C4#1451979811yescharacteristic
395C2×C4#1451980111yescharacteristic
396C2×C4#1451980411yescharacteristic
397C8—81no—
398C8—81no—
399C8—4881no—
400C8—4881no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—1222no—
409C22—1222no—
410C22—1222no—
411C22—2441no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22#1683972711yescharacteristic
416C22#99×D6111yescharacteristic
417C22#1683974311yescharacteristic
418C22#1683975511yescharacteristic
419C22#1683976511yescharacteristic
420C22#1683977711yescharacteristic
421C22#1683977711yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—81no—
429C4—4881no—
430C4—4881no—
431C4—2441no—
432C4—2441no—
433C4—2441no—
434C2—161no—
435C2—2442no—
436C2#2144416411yescharacteristic
437C2#2144422411yescharacteristic
438C2#2144428611yescharacteristic
439C2#2144434611yescharacteristic
440C2#2144437211yescharacteristic
441C2#2144444711yescharacteristic
442C2#2144452111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C42×C61C23
hypercenter#1270D61
hypocenterC61#7718
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21445886C2semidirect
3. #21445886C2semidirect
4. #21443643C2semidirect
5. #21443641C2semidirect
6. #21443640C2semidirect
7. C61×#1270C2semidirect
219. #1270D61semidirect
248. C61#7718semidirect

Maximal subgroups

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

subgroupindex
#214541492
#214458862
#214436432
#214436412
#214436402
C61×#12702
#771861