Finite Group Databasebeta

← #29568261

Subgroups — #29568261

Order 15616.

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

normal subgroups only

This group has 640 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#21448335C211yesmaximal, characteristic
2#21445580C211yesmaximal, characteristic, complemented
3#21445511C211yesmaximal, characteristic, complemented
4#21443643C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443640C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×#14519748C411yescharacteristic
10C2×D4×Dic61C411yescharacteristic
11C2×#14519737—21no—
12C2×C42×D61C2211yescharacteristic
13C2×#14519689—21no—
14C2×#14519687—21no—
15#16839660C2211yescharacteristic
16#16839656—21no—
17#16839638—21no—
18#16839619C411yescharacteristic
19C4⋊C4×Dic61C411yescharacteristic
20C22⋊C4×Dic61—21no—
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×C22⋊D61—21no—
28C23×Dic61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758189—24no—
33C2×#11758189—42no—
34C2×#11758189—42no—
35C22×#92418—21no—
36C22×#92418—21no—
37#14519748—22no—
38#14519748—22no—
39D4×Dic61—42no—
40#14519737—42no—
41#14519737—42no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×#11758198—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C42×D61—42no—
53#14519689—24no—
54#14519687—42no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C22×D4×C61C2×C411yescharacteristic
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C24×C61—21no—
66C23×D61C22⋊C411yescharacteristic
67C2×D4×C61—21no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61M1612yescomplemented
71C22×C4×C61—21no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—24no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—42no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C2×C4×D61—22no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—22no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—22no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C4⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C42×C61—41no—
110C22⋊Dic61—24no—
111C22⋊Dic61—42no—
112#11758198—42no—
113C4⋊Dic61—21no—
114C4⋊Dic61—41no—
115C4⋊Dic61M1612yescomplemented
116#11758196—41no—
117#11758196—41no—
118C4×Dic61—22no—
119C4×Dic61—22no—
120C4×Dic61—41no—
121C4×Dic61—42no—
122C2×#92418—22no—
123C2×#92418—22no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128#11758189—48no—
129C23×C61—22no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61C2×C22⋊C411yescharacteristic
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61#10412yes—
144D4×C61—42no—
145D4×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—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61C2×M1611yescharacteristic
156C2×C4×C61C2×M1611yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61#13711yescharacteristic
161C22⋊D61—48no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—22no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—84no—
176C2×Dic61#9912yes—
177C2×Dic61#10412yes—
178C4×D61—24no—
179C4×D61—24no—
180C4×D61—42no—
181C4×D61—42no—
182C4×D61—42no—
183C4×D61—42no—
184C8×C61—42no—
185C8×C61—42no—
186#92418—42no—
187#92418—42no—
188#7633—611nomaximal, Sylow
189C22×C61—42no—
190C22×C61—42no—
191C22×C61—42no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61#40711yescharacteristic
197C22×C61C2×#9911yescharacteristic
198C22×C61#41311yescharacteristic
199C22×C61#41711yescharacteristic
200C22×C61#41811yescharacteristic
201C22×C61C2×#10411yescharacteristic
202C22×C61C2×#10411yescharacteristic
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—41no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—81no—
217Dic61—22no—
218Dic61—22no—
219Dic61—41no—
220Dic61—42no—
221Dic61—81no—
222C4×#121—611no—
223#1749—611no—
224#1728—611no—
225#1271—611no—
226#1271—611no—
227#1270—611no—
228#1270D6111yescharacteristic, complemented
229C2×C61—82no—
230C2×C61#146511yescharacteristic
231C2×C61#148911yescharacteristic
232C2×C61#149011yescharacteristic
233C2×C61#150411yescharacteristic
234C2×C61#150711yescharacteristic
235C2×C61#152411yescharacteristic
236C2×C61#155711yescharacteristic
237D61—42no—
238C22×M16—1221no—
239C2×#121—611no—
240C2×C4×D4—611no—
241C2×C4×D4—1221no—
242C22×C42—611no—
243C2×C22⋊C8—1221no—
244C2×#97—1221no—
245#390C2×D6111yescharacteristic
246#389—611no—
247#388—1221no—
248#386—1221no—
249#380—611no—
250C4×C4⋊C4—611no—
251C4×C22⋊C4—1221no—
252#336—611no—
253#336—611no—
254#336—1221no—
255#336C2×D6111yescharacteristic
256#336C2×D6111yescharacteristic
257C61#763311yescharacteristic, complemented, Sylow
258C22×D4—1221no—
259C22×D4C4×D6111yescharacteristic
260C23×C4—611no—
261C23×C4—611no—
262C23×C4—611no—
263C23×C4—1221no—
264C2×M16—1224no—
265C2×M16—2442no—
266C2×M16—2442no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—1221no—
270C22×C8—1221no—
271#121—1222no—
272#121—1222no—
273C4×D4—2442no—
274C4×D4—2442no—
275C4×D4—2442no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4C4×D6111yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C42—611no—
286C2×C42—611no—
287C2×C42—611no—
288C2×C42—1221no—
289C2×C42—2442no—
290C2×C42C22×D6111yescharacteristic
291C22⋊C8—1224no—
292#97—2442no—
293#95—1221no—
294#95—1221no—
295#95—1221no—
296C24—21no—
297C24—611no—
298C2×D4—21no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—1224no—
302C2×D4—2442no—
303C2×D4—2442no—
304C2×D4#1175818912yescomplemented
305C22×C4—21no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—1222no—
310C22×C4—1222no—
311C22×C4—1222no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4—2442no—
324C22×C4—2442no—
325C22×C4—2442no—
326C22×C4C2×C4×D6111yescharacteristic
327C22×C4D4×D6111yescharacteristic
328C22×C4D4×D6111yescharacteristic
329M16—2448no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—1222no—
337C2×C8—1222no—
338C2×C8—2441no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8—2441no—
342C4⋊C4—41no—
343C4⋊C4—612no—
344C4⋊C4—1221no—
345C4⋊C4—2441no—
346C4⋊C4—2441no—
347C4⋊C4—2441no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—1224no—
353C22⋊C4—2442no—
354C22⋊C4—2442no—
355C42—41no—
356C42—1222no—
357C42—1222no—
358C42—2441no—
359C42—2442no—
360C23—22no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—612no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23—1221no—
372C23—1221no—
373C23—1221no—
374C23C22⋊C4×D6111yescharacteristic
375D4—42no—
376D4—42no—
377D4—2448no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—612no—
388C2×C4—612no—
389C2×C4—1224no—
390C2×C4—1224no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1222no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—4884no—
400C2×C4—2442no—
401C2×C4—2442no—
402C2×C4—2442no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4M16×D6111yescharacteristic
410C2×C4C2×#1175818911yescharacteristic
411C2×C4#1451980111yescharacteristic
412C2×C4#1451980111yescharacteristic
413C2×C4#1451980411yescharacteristic
414C2×C4#1451980611yescharacteristic
415C8—42no—
416C8—42no—
417C8—2442no—
418C8—2442no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—1222no—
427C22—1222no—
428C22—1222no—
429C22—2441no—
430C22—2441no—
431C22—2441no—
432C22—2441no—
433C22#1683972411yescharacteristic
434C22#99×D6111yescharacteristic
435C22#1683974311yescharacteristic
436C22#1683976011yescharacteristic
437C22#1683976511yescharacteristic
438C22#104×D6111yescharacteristic
439C22#104×D6111yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—1222no—
448C4—1222no—
449C4—4881no—
450C4—2441no—
451C4—2442no—
452C2—82no—
453C2—2442no—
454C2#2144415411yescharacteristic
455C2#2144425511yescharacteristic
456C2#2144426011yescharacteristic
457C2#2144432011yescharacteristic
458C2#2144433311yescharacteristic
459C2#2144440411yescharacteristic
460C2#2144453811yescharacteristic
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#7633
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. #21445580C2semidirect
3. #21445511C2semidirect
4. #21443643C2semidirect
5. #21443641C2semidirect
6. #21443640C2semidirect
7. C61×#1270C2semidirect
70. C2×D4×C61M16semidirect
115. C4⋊Dic61M16semidirect
228. #1270D61semidirect
257. C61#7633semidirect
304. C2×D4#11758189semidirect

Maximal subgroups

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

subgroupindex
#214483352
#214455802
#214455112
#214436432
#214436412
#214436402
C61×#12702
#763361