Finite Group Databasebeta

← #29590576

Subgroups — #29590576

Order 15616.

532 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 71 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#21450774C211yesmaximal, characteristic
2#21445606C211yesmaximal, characteristic, complemented
3#21444158C211yesmaximal, characteristic, complemented
4#21443820C211yesmaximal, characteristic, complemented
5#21443818C211yesmaximal, characteristic, complemented
6#21443816C211yesmaximal, characteristic, complemented
7C61×#1343C211yesmaximal, characteristic, complemented
8C2×#14519748—21no—
9C2×#14519748C411yescharacteristic, complemented
10C2×#14519737C2211yescharacteristic
11#16839816—21no—
12C2×#14519691—21no—
13#16839694C411yescharacteristic, complemented
14#16839687C2211yescharacteristic
15#16839676C411yescharacteristic, complemented
16#16839655—21no—
17#16839642—21no—
18#16839638—21no—
19C22⋊C4×Dic61—21no—
20#95×D61C411yescharacteristic, complemented
21#16839529C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#392C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C22⋊D61D411yescharacteristic
29C23×Dic61D411yescharacteristic
30C22×C4×D61—21no—
31C22×C4×D61C2×C411yescharacteristic
32#14519748—42no—
33#14519748—42no—
34#14519748—41no—
35#14519748—41no—
36#14519737—41no—
37#14519737—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196C2×C411yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×#11758198D411yescharacteristic
47C2×C4×Dic61—41no—
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50#14519691—24no—
51C22⋊#92418—21no—
52#14519687—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—41no—
57#14519684C2×C411yescharacteristic
58C22×D4×C61—21no—
59C22×D4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61C2311yescharacteristic
63C22⋊C8×C61—21no—
64#95×C61C2×C411yescharacteristic
65C24×C61—21no—
66C24×C61C2×D411yescharacteristic
67C23×D61C22⋊C411yescharacteristic
68C2×D4×C61—42no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—81no—
73C2×D4×C61—81no—
74C22×C4×C61—21no—
75C22×C4×C61—41no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—42no—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—42no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—41no—
90C22×Dic61—81no—
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C22⋊C411yescharacteristic
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—42no—
97C2×C4×D61—42no—
98C2×C4×D61—81no—
99C2×C4×D61—81no—
100C2×C8×C61—41no—
101C22⋊C4×C61—22no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—42no—
104C22⋊C4×C61—41no—
105C22⋊Dic61—22no—
106C22⋊Dic61—42no—
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111C22⋊Dic61—41no—
112C22⋊Dic61—81no—
113#11758198—41no—
114C4⋊Dic61—42no—
115C4⋊Dic61—41no—
116#11758196—41no—
117C4×Dic61—21no—
118C4×Dic61—21no—
119C4×Dic61—82no—
120C2×#92418—41no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61C2×C22⋊C411yescharacteristic
133C23×C61AGL(1,ℤ/8)11yescharacteristic
134C23×C61AGL(1,ℤ/8)11yescharacteristic
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61#10412yes—
140D4×C61—82no—
141D4×C61—82no—
142D4×C61—82no—
143C2×C4×C61—22no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—42no—
151C2×C4×C61—81no—
152C2×C4×C61—81no—
153C22⋊D61—42no—
154C22⋊D61—42no—
155C22⋊D61—84no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—41no—
161C2×Dic61—42no—
162C2×Dic61—41no—
163C2×Dic61—42no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61#9911yescharacteristic
174C2×Dic61#9911yescharacteristic
175C4×D61—81no—
176C4×D61—81no—
177C4×D61—84no—
178C8×C61—81no—
179#92418—81no—
180#11775—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61C2×#9911yescharacteristic
198C22×C61#41811yescharacteristic
199C22×C61C2×#10411yescharacteristic
200C2×D61—22no—
201C2×D61—42no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—42no—
205C4×C61—42no—
206C4×C61—41no—
207C4×C61—41no—
208C4×C61—82no—
209Dic61—21no—
210Dic61—21no—
211Dic61—41no—
212Dic61—41no—
213Dic61—81no—
214Dic61—82no—
215Dic61—81no—
216#2543—611no—
217C4×#99—611no—
218#1466—611no—
219#1344—611no—
220#1344—611no—
221#1343—611no—
222#1343D6111yescharacteristic, complemented
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—41no—
226C2×C61—41no—
227C2×C61—161no—
228C2×C61#150711yescharacteristic
229C2×C61#212111yescharacteristic
230C2×C61#212611yescharacteristic
231D61—42no—
232C2×#121—611no—
233C2×#121—1221no—
234C2×C4×D4—611no—
235#432—1221no—
236C2×#99—1221no—
237#398—611no—
238#397—611no—
239#394—611no—
240#392C2×D6111yescharacteristic
241#388—1221no—
242#386—1221no—
243#386—1221no—
244C4×C22⋊C4—1221no—
245C2×#95—611no—
246#342—611no—
247#342C2×D6111yescharacteristic
248#323—611no—
249#323—1221no—
250#323C2×D6111yescharacteristic
251C61#1177511yescharacteristic, complemented, Sylow
252C22×D4—21no—
253C22×D4—611no—
254C22×D4—1221no—
255C22×D4C4×D6111yescharacteristic
256C23×C4—611no—
257C23×C4—611no—
258C23×C4—1221no—
259#121—2442no—
260#121—2442no—
261#121—2441no—
262#121—2441no—
263C4×D4—2441no—
264C4×D4—2441no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4C22×D6111yescharacteristic
277C2×C42—611no—
278C2×C42—2441no—
279C4⋊C8—2441no—
280#99—1224no—
281C22⋊C8—21no—
282C22⋊C8—1221no—
283#97—2441no—
284#95—611no—
285#95—1221no—
286#95—1221no—
287#95—1221no—
288#95—2441no—
289#95C4×D6111yescharacteristic
290C24—21no—
291C24—611no—
292C24D4×D6111yescharacteristic
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—81no—
298C2×D4—81no—
299C2×D4—1222no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—2441no—
303C2×D4—2442no—
304C2×D4—2442no—
305C2×D4—2442no—
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—4881no—
318C22×C4—4881no—
319C22×C4—4881no—
320C22×C4—2442no—
321C22×C4—2442no—
322C22×C4—2441no—
323C22×C4C2×C4×D6111yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C2×C8—41no—
326C2×C8—2441no—
327C4⋊C4—2441no—
328C4⋊C4—2441no—
329C4⋊C4—2442no—
330C22⋊C4—22no—
331C22⋊C4—41no—
332C22⋊C4—42no—
333C22⋊C4—41no—
334C22⋊C4—1222no—
335C22⋊C4—4881no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C22⋊C4—2442no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C42—1221no—
344C42—1221no—
345C42—4882no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—612no—
358C23—1221no—
359C23—1221no—
360C23—2441no—
361C23—2441no—
362C23C22⋊C4×D6111yescharacteristic
363C23#1451980111yescharacteristic
364C23#1451980411yescharacteristic
365D4—82no—
366D4—82no—
367D4—82no—
368D4—4884no—
369D4—2442no—
370D4—2442no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—611no—
382C2×C4—611no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—4884no—
390C2×C4—4881no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—2441no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C8—81no—
404C8—4881no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—1222no—
422C22—2442no—
423C22—2442no—
424C22—2441no—
425C22—2441no—
426C22#99×D6111yescharacteristic
427C22#1683976511yescharacteristic
428C22#104×D6111yescharacteristic
429C4—42no—
430C4—41no—
431C4—41no—
432C4—82no—
433C4—1221no—
434C4—1221no—
435C4—4881no—
436C4—4882no—
437C4—4881no—
438C4—2441no—
439C4—2441no—
440C2—21no—
441C2—21no—
442C2—41no—
443C2—41no—
444C2—161no—
445C2—2442no—
446C2#2144433311yescharacteristic
447C2#2144746211yescharacteristic
448C2#2144748111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1343C2
socleC22×C61C2×#99
prime radical#21450774C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1343D61
hypocenterC61#11775
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #21445606C2semidirect
3. #21444158C2semidirect
4. #21443820C2semidirect
5. #21443818C2semidirect
6. #21443816C2semidirect
7. C61×#1343C2semidirect
9. C2×#14519748C4semidirect
13. #16839694C4semidirect
15. #16839676C4semidirect
20. #95×D61C4semidirect
222. #1343D61semidirect
251. C61#11775semidirect

Maximal subgroups

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

subgroupindex
#214507742
#214456062
#214441582
#214438202
#214438182
#214438162
C61×#13432
#1177561