Finite Group Databasebeta

← #29568170

Subgroups — #29568170

Order 15616.

656 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 103 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#21448308C211yesmaximal, characteristic
2#21445798C211yesmaximal, characteristic, complemented
3#21445580C211yesmaximal, characteristic, complemented
4#21443645C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#1272C211yesmaximal, characteristic, complemented
8C22×#11758226C411yescharacteristic
9C2×#14519735C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11C2×#14519706—21no—
12C2×#14519689—21no—
13C2×#14519689—21no—
14C2×#14519687—21no—
15#16839669C411yescharacteristic
16#16839664C2211yescharacteristic
17#16839663C411yescharacteristic
18#16839640—21no—
19#16839640—21no—
20#16839609—21no—
21#16839609—21no—
22#16839517C2211yescharacteristic
23#16839517C2211yescharacteristic
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C2×#11758226—22no—
28C2×#11758226—22no—
29C2×#11758226—42no—
30C2×#11758226—42no—
31C22×D244—21no—
32C22×D244C2×C411yescharacteristic
33C22×C4×D61—21no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×#92418—21no—
38C22×#92418—21no—
39#14519735—42no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C42×D61—42no—
51#14519706—42no—
52#14519689—24no—
53#14519689—42no—
54#14519687—42no—
55#14519684—21no—
56#14519684—21no—
57C22×Q8×C61C2×C411yescharacteristic
58C22×C8×C61—21no—
59C22×C8×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#95×C61—21no—
63#95×C61—21no—
64C23×D61—21no—
65C23×D61C22⋊C411yescharacteristic
66C2×Q8×C61—21no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61M1612yes—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79#11758226—48no—
80#11758226—48no—
81C2×D244—24no—
82C2×D244—21no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—42no—
86C2×D244—42no—
87C2×D244M1612yes—
88C2×C4×D61—22no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—22no—
92C2×C4×D61—24no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—22no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—42no—
102C2×C4×D61—42no—
103C2×C8×C61—22no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C4⋊C4×C61—41no—
110C42×C61—41no—
111#11758198—42no—
112#11758198—42no—
113#11758198—41no—
114#11758198—41no—
115#11758198—41no—
116#11758198—41no—
117#11758198—42no—
118C4⋊Dic61—41no—
119C4×Dic61—22no—
120C4×Dic61—22no—
121C4×Dic61—41no—
122C4×Dic61—42no—
123C2×#92418—22no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C2×#92418—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—22no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61#10012yes—
144Q8×C61—42no—
145Q8×C61—42no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—22no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61C2×M1611yescharacteristic
159C2×C4×C61C2×M1611yescharacteristic
160C2×C4×C61#13511yescharacteristic
161C2×C4×C61#13511yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61#13711yescharacteristic
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61#9912yes—
175C2×Dic61#10412yes—
176D244—42no—
177D244—42no—
178D244—48no—
179C4×D61—24no—
180C4×D61—24no—
181C4×D61—42no—
182C4×D61—42no—
183C4×D61—48no—
184C4×D61—42no—
185C4×D61—42no—
186C8×C61—42no—
187C8×C61—81no—
188#92418—42no—
189#92418—81no—
190#7612—611nomaximal, Sylow
191C22×C61#40711yescharacteristic
192C22×C61C2×#9911yescharacteristic
193C22×C61C2×#10011yescharacteristic
194C22×C61#41611yescharacteristic
195C22×C61#41711yescharacteristic
196C22×C61C2×#10411yescharacteristic
197C22×C61#42111yescharacteristic
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—42no—
206C2×D61—42no—
207C2×D61—42no—
208C2×D61—81no—
209C2×D61—81no—
210C2×D61—81no—
211C2×D61—81no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—42no—
219C4×C61—81no—
220Dic61—22no—
221Dic61—22no—
222Dic61—41no—
223Dic61—81no—
224#2297—611no—
225#1797—611no—
226#1749—611no—
227#1272—611no—
228#1272D6111yescharacteristic, complemented
229#1270—611no—
230#1270—611no—
231C2×C61#146211yescharacteristic
232C2×C61#148811yescharacteristic
233C2×C61#148911yescharacteristic
234C2×C61#150111yescharacteristic
235C2×C61#151311yescharacteristic
236C2×C61#153011yescharacteristic
237C2×C61#155111yescharacteristic
238D61—42no—
239D61—82no—
240C22×#41—611no—
241C2×#117—611no—
242C22×C42—611no—
243C2×C4⋊C8—1221no—
244C2×C22⋊C8—1221no—
245C2×C22⋊C8—1221no—
246C2×#97—1221no—
247#391—611no—
248#391C2×D6111yescharacteristic
249#390—611no—
250#390—611no—
251#386—1221no—
252#386—1221no—
253C4×C22⋊C4—1221no—
254C4×C22⋊C4—1221no—
255#336—611no—
256#336—611no—
257#336C2×D6111yescharacteristic
258#336C2×D6111yescharacteristic
259C61#761211yescharacteristic, complemented, Sylow
260C2×#41—1222no—
261C2×#41—1222no—
262C2×#41—2442no—
263C2×#41—2442no—
264C22×Q8C4×D6111yescharacteristic
265C22×D4—611no—
266C22×D4—1221no—
267C23×C4—611no—
268C23×C4—611no—
269C23×C4—611no—
270C23×C4—1221no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—1221no—
274C22×C8—1221no—
275#117—2442no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4C4×D6111yescharacteristic
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C42—611no—
284C2×C42—611no—
285C2×C42—611no—
286C2×C42—1221no—
287C2×C42—2442no—
288C2×C42C22×D6111yescharacteristic
289C4⋊C8—2442no—
290C22⋊C8—1224no—
291C22⋊C8—2442no—
292#97—2442no—
293#95—21no—
294#95—21no—
295#95—1221no—
296#95—1221no—
297C24—611no—
298C24—1221no—
299#41—2448no—
300#41—2448no—
301C2×Q8—21no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8#1175818912yes—
305C2×D4—612no—
306C2×D4—1224no—
307C2×D4—1221no—
308C2×D4—2441no—
309C2×D4—2441no—
310C2×D4—2442no—
311C2×D4—2442no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—1222no—
318C22×C4—1222no—
319C22×C4—1222no—
320C22×C4—1224no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—2441no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2442no—
332C22×C4—2442no—
333C22×C4C2×C4×D6111yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C2×C8—22no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—1222no—
343C2×C8—2441no—
344C2×C8—2441no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C4⋊C4—41no—
349C4⋊C4—2441no—
350C22⋊C4—2442no—
351C22⋊C4—2442no—
352C22⋊C4—2442no—
353C22⋊C4—2441no—
354C22⋊C4—2441no—
355C22⋊C4—2441no—
356C22⋊C4—2441no—
357C42—41no—
358C42—1222no—
359C42—1222no—
360C42—2441no—
361C42—2442no—
362C23—612no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23—1222no—
370C23—2441no—
371C23—2441no—
372C23—2441no—
373C23—2441no—
374C23—2441no—
375C23—2441no—
376C23C22⋊C4×D6111yescharacteristic
377Q8—42no—
378Q8—42no—
379D4—2442no—
380D4—2442no—
381D4—2448no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—612no—
395C2×C4—612no—
396C2×C4—1224no—
397C2×C4—1224no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—2442no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2448no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4M16×D6111yescharacteristic
414C2×C4C2×#1175818911yescharacteristic
415C2×C4#1451979811yescharacteristic
416C2×C4#1451980011yescharacteristic
417C2×C4#1451980411yescharacteristic
418C2×C4#1451980911yescharacteristic
419C8—42no—
420C8—81no—
421C8—4881no—
422C8—2442no—
423C22—1222no—
424C22—1222no—
425C22—1222no—
426C22—4881no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22—2442no—
431C22—2442no—
432C22—2442no—
433C22—2441no—
434C22—2441no—
435C22—2441no—
436C22—2441no—
437C22#1683972411yescharacteristic
438C22#99×D6111yescharacteristic
439C22#100×D6111yescharacteristic
440C22#1683975711yescharacteristic
441C22#1683976211yescharacteristic
442C22#104×D6111yescharacteristic
443C22#1683977711yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—42no—
451C4—81no—
452C4—1222no—
453C4—1222no—
454C4—4881no—
455C4—2441no—
456C2—4882no—
457C2—2442no—
458C2#2144414411yescharacteristic
459C2#2144425211yescharacteristic
460C2#2144425711yescharacteristic
461C2#2144430911yescharacteristic
462C2#2144436111yescharacteristic
463C2#2144442811yescharacteristic
464C2#2144451311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758226C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7612
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #21445798C2semidirect
3. #21445580C2semidirect
4. #21443645C2semidirect
5. #21443639C2semidirect
6. #21443639C2semidirect
7. C61×#1272C2semidirect
228. #1272D61semidirect
259. C61#7612semidirect

Maximal subgroups

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

subgroupindex
#214483082
#214457982
#214455802
#214436452
#214436392
C61×#12722
#761261