Finite Group Databasebeta

← #29568416

Subgroups — #29568416

Order 15616.

538 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 97 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#21454123C211yesmaximal, characteristic
2#21445886C211yesmaximal, characteristic, complemented
3#21445576C211yesmaximal, characteristic, complemented
4#21443645C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#1272C211yesmaximal, characteristic, complemented
8C2×#14519766C411yescharacteristic
9C2×#14519753C411yescharacteristic
10C2×#14519752C411yescharacteristic
11C2×C42×D61C2211yescharacteristic
12C2×#14519689—21no—
13C2×#14519689—21no—
14C2×C8×Dic61—21no—
15#16839664C2211yescharacteristic
16#16839651—21no—
17#16839651—21no—
18#16839640—21no—
19#16839640—21no—
20#16839627C411yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×#92418—21no—
33C22×#92418—21no—
34#14519766—42no—
35#14519753—42no—
36#14519752—42no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C42×D61—42no—
49#14519689—24no—
50#14519689—42no—
51C8×Dic61—42no—
52#14519684—21no—
53#14519684—21no—
54C22×Q8×C61C2×C411yescharacteristic
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2311yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61C23×D61—21no—
62C23×D61C22⋊C411yescharacteristic
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—42no—
81C2×D244—42no—
82C2×D244—42no—
83C2×C4×D61—22no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C4⋊C4×C61—41no—
102C42×C61—41no—
103#11758198—42no—
104#11758198—42no—
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108#11758198—41no—
109#11758198—42no—
110#11758198—42no—
111C4⋊Dic61—41no—
112#11758196—42no—
113C4×Dic61—22no—
114C4×Dic61—22no—
115C4×Dic61—41no—
116C2×#92418—22no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61#10412yes—
137Q8×C61—81no—
138Q8×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—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61#13111yescharacteristic
152C2×C4×C61#13111yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61#13511yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61#9912yes—
168C2×Dic61#10012yes—
169D244—81no—
170D244—81no—
171D244—84no—
172C4×D61—42no—
173C4×D61—42no—
174C4×D61—42no—
175C4×D61—42no—
176C4×D61—42no—
177C4×D61—42no—
178C8×C61—42no—
179C8×C61—81no—
180#92418—42no—
181#92418—81no—
182#7670—611nomaximal, Sylow
183C22×C61#40811yescharacteristic
184C22×C61C2×#9911yescharacteristic
185C22×C61C2×#10011yescharacteristic
186C22×C61#41611yescharacteristic
187C22×C61#41611yescharacteristic
188C22×C61C2×#10411yescharacteristic
189C22×C61#42111yescharacteristic
190C2×D61—22no—
191C2×D61—22no—
192C2×D61—22no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—81no—
211C4×C61—81no—
212Dic61—22no—
213Dic61—22no—
214Dic61—41no—
215Dic61—81no—
216#2850—611no—
217#1817—611no—
218C4×C22⋊C8—611no—
219#1272—611no—
220#1272D6111yescharacteristic, complemented
221#1270—611no—
222#1270—611no—
223C2×C61#147111yescharacteristic
224C2×C61#148211yescharacteristic
225C2×C61#149411yescharacteristic
226C2×C61#150111yescharacteristic
227C2×C61#151611yescharacteristic
228C2×C61#152711yescharacteristic
229C2×C61#154311yescharacteristic
230D61—42no—
231D61—161no—
232C2×#124—611no—
233C2×C22⋊Q8—611no—
234C2×#121—611no—
235C22×C42—611no—
236C2×C22⋊C8—1221no—
237C2×C22⋊C8—1221no—
238C2×C4×C8—1221no—
239#391C2×D6111yescharacteristic
240#390—611no—
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#767011yescharacteristic, complemented, Sylow
252C22×Q8C4×D6111yescharacteristic
253C22×D4—611no—
254C22×D4—1221no—
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—1221no—
269C2×C22⋊C4—1221no—
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
279C22⋊C8—1224no—
280C22⋊C8—2442no—
281C4×C8—2442no—
282#95—21no—
283#95—21no—
284#95—1221no—
285#95—1221no—
286C24—611no—
287C24—1221no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2442no—
297C2×D4—2442no—
298C2×D4—2442no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—1222no—
305C22×C4—1222no—
306C22×C4—1222no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4C2×C4×D6111yescharacteristic
318C22×C4D4×D6111yescharacteristic
319C22×C4D4×D6111yescharacteristic
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—1222no—
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—2442no—
336C22⋊C4—2442no—
337C22⋊C4—2442no—
338C22⋊C4—2442no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C42—41no—
344C42—1222no—
345C42—1222no—
346C42—2441no—
347C23—612no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—2441no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23C22⋊C4×D6111yescharacteristic
362Q8—81no—
363Q8—81no—
364D4—4881no—
365D4—4881no—
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—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—612no—
380C2×C4—612no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2442no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4#1451978311yescharacteristic
398C2×C4#1451978511yescharacteristic
399C2×C4#1451979811yescharacteristic
400C2×C4#1451979811yescharacteristic
401C2×C4#1451980011yescharacteristic
402C2×C4#1451980011yescharacteristic
403C8—42no—
404C8—81no—
405C8—4881no—
406C8—2442no—
407C22—1222no—
408C22—1222no—
409C22—1222no—
410C22—4881no—
411C22—4881no—
412C22—4881no—
413C22—4881no—
414C22—4881no—
415C22—4881no—
416C22—4881no—
417C22—2441no—
418C22—2441no—
419C22—2441no—
420C22—2441no—
421C22#1683972711yescharacteristic
422C22#99×D6111yescharacteristic
423C22#100×D6111yescharacteristic
424C22#1683975711yescharacteristic
425C22#1683975711yescharacteristic
426C22#104×D6111yescharacteristic
427C22#1683977711yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—81no—
435C4—81no—
436C4—1222no—
437C4—1222no—
438C4—4881no—
439C4—2441no—
440C2—9761no—
441C2—2442no—
442C2#2144417711yescharacteristic
443C2#2144422611yescharacteristic
444C2#2144427811yescharacteristic
445C2#2144430911yescharacteristic
446C2#2144437411yescharacteristic
447C2#2144441511yescharacteristic
448C2#2144448011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7670
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. #21445886C2semidirect
3. #21445576C2semidirect
4. #21443645C2semidirect
5. #21443639C2semidirect
6. #21443639C2semidirect
7. C61×#1272C2semidirect
220. #1272D61semidirect
251. C61#7670semidirect

Maximal subgroups

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

subgroupindex
#214541232
#214458862
#214455762
#214436452
#214436392
C61×#12722
#767061