Finite Group Databasebeta

← #29590671

Subgroups — #29590671

Order 15616.

572 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 73 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#397×D61C211yesmaximal, characteristic
2#21445892C211yesmaximal, characteristic
3#21444144C211yesmaximal, characteristic
4#21443820C211yesmaximal, characteristic, complemented
5#21443819C211yesmaximal, characteristic, complemented
6#21443818C211yesmaximal, characteristic, complemented
7C61×#1344C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D61C411yescharacteristic, complemented
9C2×C22⋊C4×D61—21no—
10C2×C22⋊C4×D61C2211yescharacteristic
11#16839724—21no—
12#16839691—21no—
13#16839690—21no—
14#16839689C411yescharacteristic, complemented
15#16839688C411yescharacteristic, complemented
16#16839687C2211yescharacteristic
17#16839617—21no—
18#95×D61—21no—
19#95×D61C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×C4×D61—21no—
29C22×C4×D61—21no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758189—41no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C4⋊C4×D61—41no—
36C4⋊C4×D61—41no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61D411yescharacteristic
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—41no—
43C2×#11758198—41no—
44C2×#11758198C2×C411yescharacteristic
45C2×#11758198D411yescharacteristic
46C22⋊C4×D61—41no—
47C22⋊C4×D61—41no—
48C22⋊C4×D61—42no—
49C22⋊C4×D61—42no—
50C22⋊#92418—21no—
51#14519689—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C23×D61—21no—
66C23×D61—21no—
67C23×D61—21no—
68C23×D61—21no—
69C23×D61—41no—
70C23×D61—42no—
71C23×D61—42no—
72C23×D61C22⋊C411yescharacteristic
73C23×D61C22⋊C411yescharacteristic
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—42no—
89C2×C4×D61—42no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊Dic61—41no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109#11758198—41no—
110#11758198—41no—
111#11758198—42no—
112#11758198—42no—
113#11758198—82no—
114#11758198—82no—
115C4⋊Dic61—41no—
116#11758196—42no—
117C2×#92418—41no—
118#11758189—82no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C23×C61AGL(1,ℤ/8)11yescharacteristic
125C23×C61AGL(1,ℤ/8)11yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—22no—
129C22×D61—22no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—44no—
138C22×D61—44no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—42no—
142C22×D61—42no—
143C22×D61—81no—
144C22×D61—81no—
145C22×D61—84no—
146C22×D61#9911yescharacteristic
147C22×D61#9911yescharacteristic
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
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—41no—
170C2×Dic61—41no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61—81no—
174C4×D61—42no—
175C4×D61—42no—
176C4×D61—42no—
177C4×D61—81no—
178C4×D61—84no—
179C4×D61—82no—
180C4×D61—82no—
181C8×C61—81no—
182#92418—81no—
183#11797—611nomaximal, Sylow
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—81no—
193C22×C61C2×#9911yescharacteristic
194C22×C61#41811yescharacteristic
195C22×C61#42111yescharacteristic
196C2×D61—24no—
197C2×D61—24no—
198C2×D61—21no—
199C2×D61—21no—
200C2×D61—21no—
201C2×D61—21no—
202C2×D61—42no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—82no—
207C2×D61—82no—
208C2×D61—82no—
209C2×D61—82no—
210C2×D61—81no—
211C2×D61#35212yes—
212C2×D61#35412yes—
213C4×C61—41no—
214C4×C61—41no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61—161no—
218Dic61—41no—
219Dic61—41no—
220Dic61—81no—
221Dic61—81no—
222Dic61—161no—
223C2×#397—611no—
224#1819—611no—
225#1462—611no—
226#1344—611no—
227#1344—611no—
228#1344—611no—
229#1344D6111yescharacteristic, complemented
230C2×C61—21no—
231C2×C61—21no—
232C2×C61—41no—
233C2×C61—41no—
234C2×C61#151011yescharacteristic
235C2×C61C2×#35211yescharacteristic
236C2×C61C2×#35411yescharacteristic
237D61—22no—
238D61—22no—
239D61—81no—
240C22×C4⋊C4—611no—
241C22×C22⋊C4—611no—
242C22×C22⋊C4—1221no—
243#407—1221no—
244#397—611no—
245#397—611no—
246#397—611no—
247#397—1221no—
248#397—1221no—
249#397C2×D6111yescharacteristic
250#379—1221no—
251C2×#95—611no—
252C2×#95—1221no—
253#342—611no—
254#342—1221no—
255#342C2×D6111yescharacteristic
256#323—611no—
257#323—1221no—
258#323C2×D6111yescharacteristic
259C61#1179711yescharacteristic, complemented, Sylow
260C25—611no—
261C23×C4—611no—
262C23×C4—611no—
263C23×C4—1221no—
264C23×C4—1221no—
265C2×M16—2441no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—2441no—
269C2×C4⋊C4—2441no—
270C2×C4⋊C4C4×D6111yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—611no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—2441no—
281C2×C22⋊C4—2441no—
282C2×C22⋊C4—2442no—
283C2×C22⋊C4—2442no—
284C2×C22⋊C4—2441no—
285C2×C22⋊C4—2441no—
286C2×C22⋊C4C22×D6111yescharacteristic
287C22⋊C8—21no—
288C22⋊C8—1221no—
289C22⋊C8—2441no—
290#95—21no—
291#95—611no—
292#95—1221no—
293#95—1221no—
294#95—1221no—
295#95—1221no—
296#95C4×D6111yescharacteristic
297C24—611no—
298C24—611no—
299C24—1221no—
300C24—1221no—
301C24—1221no—
302C24—1221no—
303C24—2441no—
304C24—2442no—
305C24—2442no—
306C24D4×D6111yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4—2442no—
321C22×C4—2442no—
322C22×C4—2442no—
323C22×C4—2442no—
324C22×C4—2442no—
325C22×C4—2442no—
326C22×C4—2442no—
327C22×C4—2441no—
328C22×C4C2×C4×D6111yescharacteristic
329C22×C4D4×D6111yescharacteristic
330M16—4882no—
331C2×C8—41no—
332C2×C8—2441no—
333C4⋊C4—41no—
334C4⋊C4—2441no—
335C4⋊C4—2442no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—4882no—
342C22⋊C4—4882no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C22⋊C4—2442no—
346C22⋊C4—2442no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—611no—
357C23—611no—
358C23—1222no—
359C23—1222no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23—1221no—
365C23—4881no—
366C23—4881no—
367C23—4884no—
368C23—2441no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23—2441no—
373C23—2441no—
374C23—2442no—
375C23—2442no—
376C23—2444no—
377C23—2444no—
378C23C22⋊C4×D6111yescharacteristic
379C23#1451980111yescharacteristic
380C23#1451980411yescharacteristic
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—4881no—
397C2×C4—4884no—
398C2×C4—4882no—
399C2×C4—4882no—
400C2×C4—4881no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—2442no—
404C2×C4—2442no—
405C2×C4—2442no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C8—81no—
415C8—4881no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—81no—
425C22—612no—
426C22—612no—
427C22—1224no—
428C22—1224no—
429C22—1221no—
430C22—1221no—
431C22—1221no—
432C22—1221no—
433C22—4881no—
434C22—4882no—
435C22—4882no—
436C22—4882no—
437C22—4882no—
438C22—2442no—
439C22—2441no—
440C22—2441no—
441C22—2441no—
442C22#99×D6111yescharacteristic
443C22#1683976511yescharacteristic
444C22#1683977711yescharacteristic
445C4—41no—
446C4—41no—
447C4—81no—
448C4—81no—
449C4—161no—
450C4—9761no—
451C4—4881no—
452C4—4881no—
453C4—2441no—
454C4—2441no—
455C2—21no—
456C2—21no—
457C2—41no—
458C2—41no—
459C2—1222no—
460C2—1222no—
461C2—4881no—
462C2#2144434611yescharacteristic
463C2#352×D6111yescharacteristic
464C2#354×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC24×D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11797
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #21443820C2semidirect
5. #21443819C2semidirect
6. #21443818C2semidirect
7. C61×#1344C2semidirect
8. C2×C4⋊C4×D61C4semidirect
14. #16839689C4semidirect
15. #16839688C4semidirect
19. #95×D61C4semidirect
229. #1344D61semidirect
259. C61#11797semidirect

Maximal subgroups

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

subgroupindex
#397×D612
#214458922
#214441442
#214438202
#214438192
#214438182
C61×#13442
#1179761