Finite Group Databasebeta

← #29568690

Subgroups — #29568690

Order 15616.

520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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#21454119C211yesmaximal, characteristic
2#21445886C211yesmaximal, characteristic, complemented
3#21445798C211yesmaximal, characteristic, complemented
4#21443644C211yesmaximal, characteristic, complemented
5#21443644C211yesmaximal, characteristic, complemented
6#21443640C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic, complemented
8C2×#14519764C411yescharacteristic
9C2×#14519757C411yescharacteristic
10C2×#14519748C411yescharacteristic
11C2×C42×D61C2211yescharacteristic
12C2×#14519706—21no—
13C2×#14519689—21no—
14C2×#14519689—21no—
15#16839668C2211yescharacteristic
16#16839655—21no—
17#16839655—21no—
18#16839638—21no—
19#16839638—21no—
20#16839627C411yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×#92418—21no—
33C22×#92418—21no—
34#14519764—42no—
35#14519757—42no—
36#14519748—42no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C42×D61—42no—
47#14519706—42no—
48#14519689—42no—
49#14519689—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C22×D4×C61C2×C411yescharacteristic
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C24×C61—21no—
62C23×D61C22⋊C411yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C2×C22⋊D61—42no—
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—22no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C4⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C42×C61—41no—
107C22⋊Dic61—42no—
108C22⋊Dic61—42no—
109C22⋊Dic61—42no—
110#11758198—42no—
111C4⋊Dic61—42no—
112C4⋊Dic61—41no—
113C4×Dic61—22no—
114C4×Dic61—22no—
115C4×Dic61—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C23×C61—41no—
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—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61#10012yes—
137D4×C61—81no—
138D4×C61—81no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61#13111yescharacteristic
149C2×C4×C61#13111yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C22⋊D61—84no—
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—
169C2×Dic61#9912yes—
170C4×D61—42no—
171C4×D61—42no—
172C4×D61—42no—
173C4×D61—42no—
174C4×D61—42no—
175C4×D61—42no—
176Dic122—81no—
177Dic122—81no—
178C8×C61—81no—
179C8×C61—81no—
180#92418—81no—
181#92418—81no—
182#7730—611nomaximal, Sylow
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61#40811yescharacteristic
191C22×C61C2×#9911yescharacteristic
192C22×C61C2×#10011yescharacteristic
193C22×C61#41611yescharacteristic
194C22×C61#41711yescharacteristic
195C22×C61#42111yescharacteristic
196C22×C61#42111yescharacteristic
197C2×D61—22no—
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—81no—
211Dic61—22no—
212Dic61—41no—
213Dic61—41no—
214Dic61—81no—
215Dic61—81no—
216#2850—611no—
217#1817—611no—
218#1797—611no—
219#1272—611no—
220#1272—611no—
221#1270—611no—
222#1270D6111yescharacteristic, complemented
223C2×C61—161no—
224C2×C61#147111yescharacteristic
225C2×C61#148211yescharacteristic
226C2×C61#149511yescharacteristic
227C2×C61#151311yescharacteristic
228C2×C61#151611yescharacteristic
229C2×C61#153311yescharacteristic
230C2×C61#155111yescharacteristic
231D61—42no—
232C2×#124—611no—
233C2×C22⋊Q8—611no—
234C2×#121—611no—
235C22×C42—611no—
236C2×C4⋊C8—1221no—
237C2×C22⋊C8—1221no—
238C2×C22⋊C8—1221no—
239#391—611no—
240#390C2×D6111yescharacteristic
241#388—1221no—
242#388—1221no—
243#386—1221no—
244#386—1221no—
245#382—611no—
246#336—611no—
247#336—611no—
248#336—1221no—
249#336C2×D6111yescharacteristic
250#336C2×D6111yescharacteristic
251C61#773011yescharacteristic, complemented, Sylow
252C22×Q8—611no—
253C22×D4—1221no—
254C22×D4C4×D6111yescharacteristic
255C23×C4—611no—
256C23×C4—611no—
257C23×C4—611no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—1221no—
261C22×C8—1221no—
262#124—2442no—
263C22⋊Q8—2442no—
264#121—2442no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4C4×D6111yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C42—611no—
275C2×C42—611no—
276C2×C42—611no—
277C2×C42—2442no—
278C2×C42C22×D6111yescharacteristic
279C4⋊C8—2442no—
280C22⋊C8—2442no—
281C22⋊C8—2442no—
282#95—1221no—
283#95—1221no—
284#95—1221no—
285#95—1221no—
286C24—21no—
287C24—611no—
288C2×Q8—1221no—
289C2×Q8—1221no—
290C2×Q8—2441no—
291C2×Q8—2441no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—2442no—
297C2×D4—2442no—
298C2×D4—2442no—
299C22×C4—21no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—1222no—
304C22×C4—1222no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4C2×C4×D6111yescharacteristic
318C22×C4D4×D6111yescharacteristic
319C22×C4D4×D6111yescharacteristic
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—2441no—
327C2×C8—2441no—
328C2×C8—2441no—
329C2×C8—2441no—
330C2×C8—2441no—
331C2×C8—2441no—
332C4⋊C4—41no—
333C4⋊C4—2441no—
334C4⋊C4—2442no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C22⋊C4—2442no—
342C22⋊C4—2442no—
343C42—41no—
344C42—1222no—
345C42—1222no—
346C42—2441no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—612no—
355C23—1221no—
356C23—1221no—
357C23—1221no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23C22⋊C4×D6111yescharacteristic
362Q8—4881no—
363Q8—4881no—
364D4—81no—
365D4—81no—
366D4—4884no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—612no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2442no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4#1451978311yescharacteristic
398C2×C4#1451978511yescharacteristic
399C2×C4#1451979611yescharacteristic
400C2×C4#1451979811yescharacteristic
401C2×C4#1451980111yescharacteristic
402C2×C4#1451980611yescharacteristic
403C8—81no—
404C8—81no—
405C8—4881no—
406C8—4881no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—1222no—
415C22—1222no—
416C22—1222no—
417C22—2441no—
418C22—2441no—
419C22—2441no—
420C22—2441no—
421C22#1683972711yescharacteristic
422C22#99×D6111yescharacteristic
423C22#100×D6111yescharacteristic
424C22#1683975511yescharacteristic
425C22#1683976011yescharacteristic
426C22#1683977711yescharacteristic
427C22#1683977711yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—81no—
435C4—1222no—
436C4—4881no—
437C4—4881no—
438C4—2441no—
439C4—2441no—
440C2—161no—
441C2—2442no—
442C2#2144417711yescharacteristic
443C2#2144422411yescharacteristic
444C2#2144428111yescharacteristic
445C2#2144435911yescharacteristic
446C2#2144437211yescharacteristic
447C2#2144444111yescharacteristic
448C2#2144451111yescharacteristic
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#7730
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. #21445798C2semidirect
4. #21443644C2semidirect
5. #21443644C2semidirect
6. #21443640C2semidirect
7. C61×#1270C2semidirect
222. #1270D61semidirect
251. C61#7730semidirect

Maximal subgroups

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

subgroupindex
#214541192
#214458862
#214457982
#214436442
#214436402
C61×#12702
#773061