Finite Group Databasebeta

← #29580776

Subgroups — #29580776

Order 15616.

568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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#21455823C211yesmaximal, characteristic
2#21450724C211yesmaximal, characteristic
3#21444383C211yesmaximal, characteristic, complemented
4#21444243C211yesmaximal, characteristic
5#21444214C211yesmaximal, characteristic, complemented
6#21443679C211yesmaximal, characteristic, complemented
7C61×#3078C211yesmaximal, characteristic, complemented
8C2×#14519753—21no—
9C2×C4×D244C2211yescharacteristic
10#16840090—21no—
11#16840049—21no—
12#16839964—21no—
13#16839912—21no—
14C4×#11758201—22no—
15#16839815C2211yescharacteristic
16#16839815C2211yescharacteristic
17#16839692—21no—
18#16839679—21no—
19#16839653—22no—
20#16839628C2211yescharacteristic
21#16839619—21no—
22#16839499—22no—
23Q8⋊#92418—22no—
24#16839489—22no—
25C61×#533C2211yescharacteristic
26C2×C4×Q8×C61C2211yescharacteristic
27C61×#479—22no—
28C61×#477—21no—
29C61×#475—21no—
30C61×#428—21no—
31C61×#423C2211yescharacteristic
32C61×#419—21no—
33C22×D244D411yescharacteristic
34C22×C4×D61—21no—
35C2×#11758201—22no—
36#14519753—42no—
37#14519753—42no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196—22no—
45C2×#11758198—22no—
46C2×#11758198—22no—
47C2×#11758198—21no—
48#14519708—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51#14519701—22no—
52#14519697—22no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C4×#92418—21no—
56C4×#92418D412yes—
57#14519684—22no—
58#14519684—21no—
59#14519684D412yes—
60C22×Q8×C61D411yescharacteristic
61C2×M16×C61—21no—
62C4⋊Q8×C61D411yescharacteristic
63C4⋊Q8×C61D411yescharacteristic
64#125×C61—21no—
65C22⋊Q8×C61—21no—
66C22⋊Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71C4×Q8×C61—21no—
72C4×Q8×C61—21no—
73#117×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C42×C61—21no—
77C2×C42×C61C2311yescharacteristic
78#107×C61—22no—
79#106×C61—22no—
80C4⋊C8×C61—21no—
81C4⋊C8×C61D412yes—
82#103×C61—22no—
83#103×C61—22no—
84C23×D61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61—21no—
89C2×Q8×C61—21no—
90C2×Q8×C61—21no—
91C2×Q8×C61—21no—
92C2×Q8×C61SD1612yescomplemented
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×Dic61—21no—
99C22×Dic61—22no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—42no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61—41no—
109M16×C61—41no—
110M16×C61—41no—
111C2×C8×C61—22no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C42×C61—41no—
124C42×C61—41no—
125C42×C61—41no—
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128C42×C61C2×D411yescharacteristic
129C42×C61#4111yescharacteristic
130#11758201—44no—
131#11758198—44no—
132#11758198—44no—
133#11758198—41no—
134#11758198—41no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61—41no—
138C4⋊Dic61—41no—
139#11758196—44no—
140C2×#92418—22no—
141C2×#92418—41no—
142C23×C61#12011yescharacteristic
143C22×D61—22no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150Q8×C61—22no—
151Q8×C61—22no—
152Q8×C61—42no—
153Q8×C61—41no—
154Q8×C61—41no—
155Q8×C61—81no—
156C2×C4×C61—22no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61#12011yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12711yescharacteristic
171C2×C4×C61C2×SD1611yescharacteristic
172C2×C4×C61#13511yescharacteristic
173C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C61#13711yescharacteristic
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—42no—
180C2×Dic61—41no—
181D244—22no—
182D244—22no—
183D244—41no—
184D244—41no—
185C4×D61—81no—
186C4×D61—81no—
187C4×D61—81no—
188C4×D61—81no—
189C8×C61—42no—
190#92418—42no—
191#92418—81no—
192#10001—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61#39211yescharacteristic
196C22×C61#45011yescharacteristic
197C22×C61#45211yescharacteristic
198C2×D61—42no—
199C2×D61—42no—
200C2×D61—42no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—42no—
210C4×C61—81no—
211C4×C61—81no—
212C4×C61—81no—
213C4×C61#44811yescharacteristic
214C4×C61#44911yescharacteristic
215C4×C61#46511yescharacteristic
216C4×C61#46811yescharacteristic
217Dic61—82no—
218Dic61—81no—
219#3101—611no—
220#3078D6111yescharacteristic, complemented
221#2536—611no—
222#1518—611no—
223#1486—611no—
224#1479—611no—
225#1286—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61#200011yescharacteristic
229C2×C61#200911yescharacteristic
230C2×C61#201011yescharacteristic
231D61—82no—
232#533C2×D6111yescharacteristic
233C2×C22⋊Q8—1221no—
234C2×C4×Q8C2×D6111yescharacteristic
235C2×C4×D4—611no—
236#483—1221no—
237#479—22no—
238#477—21no—
239#476—1221no—
240#475—21no—
241#461—1221no—
242#450—1221no—
243C4×SD16—1222no—
244#431—611no—
245#431—611no—
246#428—21no—
247#423C2×D6111yescharacteristic
248#419—21no—
249#398—1221no—
250#394—1221no—
251#388—1222no—
252#382—611no—
253#380—1221no—
254#328—1222no—
255Q8⋊C8—1222no—
256D4⋊C8—1222no—
257C61#1000111yescharacteristic, complemented, Sylow
258C22×Q8C22⋊D6111yescharacteristic
259C22×D4—611no—
260C23×C4—1221no—
261C2×SD16—1222no—
262C2×M16—21no—
263C4⋊Q8C22⋊D6111yescharacteristic
264C4⋊Q8C22⋊D6111yescharacteristic
265#125—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—2442no—
269C22⋊Q8—2442no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×D4—1221no—
277C4×D4—1221no—
278C4×D4—1221no—
279C4×D4—1221no—
280#117—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—611no—
283C2×C4⋊C4—1222no—
284C2×C4⋊C4—1221no—
285C2×C4⋊C4C22⋊D6111yescharacteristic
286C2×C22⋊C4—1222no—
287C2×C22⋊C4—1222no—
288C2×C22⋊C4—1221no—
289C2×C42—21no—
290C2×C42C22×D6111yescharacteristic
291#107—22no—
292#106—22no—
293#106—1222no—
294C4⋊C8—21no—
295C4⋊C8—1221no—
296C4⋊C8—1221no—
297C4⋊C8C22⋊D6112yes—
298#103—22no—
299#103—22no—
300#103—1222no—
301#102—1222no—
302C22⋊C8—1221no—
303C22⋊C8—1221no—
304C4×C8—612no—
305C4×C8—1221no—
306#95—612no—
307#95—1222no—
308#95—1221no—
309C24—1221no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8#1175820112yescomplemented
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—2442no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—1222no—
324C22×C4—1221no—
325C22×C4—2441no—
326C22×C4—2441no—
327C22×C4—2441no—
328C22×C4—2441no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4D4×D6111yescharacteristic
332C22×C4D4×D6111yescharacteristic
333C22×C4C2×C22⋊D6111yescharacteristic
334SD16—2444no—
335M16—41no—
336M16—41no—
337C2×C8—22no—
338C2×C8—1222no—
339C2×C8—2441no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—2444no—
353C4⋊C4—2441no—
354C4⋊C4—2441no—
355C22⋊C4—41no—
356C22⋊C4—2444no—
357C22⋊C4—2444no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—41no—
361C42—41no—
362C42—41no—
363C42D4×D6111yescharacteristic
364C42#1175822411yescharacteristic
365C42C2×C22⋊D6111yescharacteristic
366C42C2×C22⋊D6111yescharacteristic
367C23—1222no—
368C23—2441no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23—2441no—
373C23—2441no—
374C23#1451974511yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—42no—
378Q8—41no—
379Q8—41no—
380Q8—81no—
381D4—1222no—
382D4—1222no—
383D4—2441no—
384D4—2441no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—4881no—
395C2×C4—4881no—
396C2×C4—4881no—
397C2×C4—4881no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4#1451974511yescharacteristic
405C2×C4#1451974611yescharacteristic
406C2×C4#1451974811yescharacteristic
407C2×C4#1451974911yescharacteristic
408C2×C4#1451974911yescharacteristic
409C2×C4#1451977311yescharacteristic
410C2×C4C2×#1175820111yescharacteristic
411C2×C4#1451979711yescharacteristic
412C2×C4#1451980211yescharacteristic
413C2×C4#1451980811yescharacteristic
414C8—42no—
415C8—4881no—
416C8—2442no—
417C22—21no—
418C22—21no—
419C22—4881no—
420C22—4881no—
421C22—4881no—
422C22—4881no—
423C22—2442no—
424C22—2442no—
425C22—2442no—
426C22#1683967011yescharacteristic
427C22#1683991211yescharacteristic
428C22#1683992211yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—4882no—
438C4—4881no—
439C4#1683990111yescharacteristic
440C4#1683990711yescharacteristic
441C4#1683999311yescharacteristic
442C4#1684001011yescharacteristic
443C2—21no—
444C2—21no—
445C2—4882no—
446C2#2144682011yescharacteristic
447C2#2144687711yescharacteristic
448C2#2144688311yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3078C2
socleC22×C61#392
prime radicalC22×D244D4
hypercenter#3078D61
hypocenterC61#10001
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #21444383C2semidirect
5. #21444214C2semidirect
6. #21443679C2semidirect
7. C61×#3078C2semidirect
92. C2×Q8×C61SD16semidirect
220. #3078D61semidirect
257. C61#10001semidirect
317. C2×Q8#11758201semidirect

Maximal subgroups

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

subgroupindex
#214558232
#214507242
#214443832
#214442432
#214442142
#214436792
C61×#30782
#1000161