Finite Group Databasebeta

← #29596943

Subgroups — #29596943

Order 15616.

518 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455396C211yesmaximal, characteristic
2C2×#108×D61C211yesmaximal, characteristic, complemented
3C2×#16839569C211yesmaximal, characteristic, complemented
4C2×#16839541C211yesmaximal, characteristic, complemented
5#21443916C211yesmaximal, characteristic, complemented
6#21443915C211yesmaximal, characteristic, complemented
7C2×C61×#359C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C22×C8×D61C2211yescharacteristic
10#16840269—21no—
11C22×#11758185C2211yescharacteristic
12#16840000C411yescharacteristic
13#16840000C411yescharacteristic
14#16839995C411yescharacteristic
15#16839995C411yescharacteristic
16#16839988—21no—
17#16839988—21no—
18C2×#14519713C2211yescharacteristic
19C2×#14519712—21no—
20#108×D61—22no—
21#108×D61—22no—
22#16839800C2211yescharacteristic
23#16839758—21no—
24#16839569—22no—
25#16839541—21no—
26#16839541—21no—
27C2×#135×C61C2211yescharacteristic
28C22×C16×C61C2211yescharacteristic
29C2×#108×C61C2211yescharacteristic
30C61×#359—22no—
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758189—41no—
34M16×D61—24no—
35M16×D61—42no—
36C22×#92418D411yescharacteristic
37C2×C8×D61—21no—
38C2×C8×D61—21no—
39C2×C8×D61—21no—
40C2×C8×D61—21no—
41C2×C8×D61—41no—
42C2×C8×D61C2×C411yescharacteristic
43C2×C8×D61C2×C411yescharacteristic
44C2×C8×D61D411yescharacteristic
45C2×C8×D61D411yescharacteristic
46#14519758—41no—
47#14519753—21no—
48#14519753—21no—
49#14519748—21no—
50#14519748—21no—
51#14519745—41no—
52C4×C22⋊D61—41no—
53C4×C22⋊D61—41no—
54#14519736—21no—
55C2×#11758185—21no—
56C2×#11758185—21no—
57C2×#11758185—21no—
58#14519713—21no—
59#14519713D412yescomplemented
60#14519712—24no—
61#14519711C2×C411yescharacteristic
62#14519711C2×C411yescharacteristic
63#14519709—21no—
64#14519701—21no—
65#14519701—21no—
66#14519698—21no—
67#14519698—21no—
68C2×#41×C61—21no—
69#135×C61—21no—
70#135×C61—21no—
71#135×C61—21no—
72#135×C61—21no—
73C2×Q16×C61C2×C411yescharacteristic
74C2×SD16×C61—21no—
75C2×D8×C61C2×C411yescharacteristic
76C2×M16×C61—21no—
77C22×C8×C61C2311yescharacteristic
78C2×C16×C61—21no—
79C2×C16×C61—21no—
80C2×C16×C61—21no—
81#108×C61—21no—
82#108×C61D412yescomplemented
83C23×D61SD1611yescharacteristic
84#41×C61—41no—
85#41×C61—41no—
86#41×C61—41no—
87#41×C61—41no—
88C2×Q8×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C2×D411yescharacteristic
93C2×C22⋊D61—41no—
94C2×C22⋊D61—41no—
95C22×Dic61SD1611yescharacteristic
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61C22⋊C411yescharacteristic
101C2×C4×D61C22⋊C411yescharacteristic
102C2×C4×D61D811yescharacteristic
103C2×C4×D61D811yescharacteristic
104Q16×C61—21no—
105Q16×C61—21no—
106SD16×C61—41no—
107SD16×C61—41no—
108D8×C61—21no—
109D8×C61—21no—
110M16×C61—22no—
111M16×C61—41no—
112C2×C8×C61—41no—
113C2×C8×C61C22×C411yescharacteristic
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61#4111yescharacteristic
118C2×C8×C61#4111yescharacteristic
119C22⋊Dic61—41no—
120C22⋊Dic61—41no—
121C22⋊Dic61—41no—
122#11758198—41no—
123#11758198—41no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126#11758196—41no—
127#11758196—41no—
128C4×Dic61—41no—
129#11758194—22no—
130#11758194—41no—
131C2×#92418—21no—
132C2×#92418—21no—
133C2×#92418—41no—
134C2×#92418C22⋊C411yescharacteristic
135C2×#92418C22⋊C411yescharacteristic
136#11758189—44no—
137C8×D61—21no—
138C8×D61—21no—
139C8×D61—21no—
140C8×D61—21no—
141C8×D61—21no—
142C8×D61—21no—
143C8×D61—21no—
144C8×D61—21no—
145C8×D61—44no—
146C16×C61—41no—
147#11758185—41no—
148C23×C61—41no—
149C23×C61C2×SD1611yescharacteristic
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—22no—
153C22×D61—41no—
154C22×D61#10211yescharacteristic
155C22×D61#10211yescharacteristic
156Q8×C61—41no—
157Q8×C61—41no—
158D4×C61—41no—
159D4×C61—41no—
160D4×C61—81no—
161D4×C61—81no—
162C2×C4×C61—41no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61C2×C22⋊C411yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12311yescharacteristic
168C2×C4×C61C2×D811yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C61#13711yescharacteristic
171C22⋊D61—82no—
172C22⋊D61—82no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61#10211yescharacteristic
178C2×Dic61#10211yescharacteristic
179C4×D61—21no—
180C4×D61—21no—
181C4×D61—21no—
182C4×D61—21no—
183C4×D61—21no—
184C4×D61—21no—
185C4×D61—21no—
186C4×D61—21no—
187C8×C61—42no—
188C8×C61C4×D411yescharacteristic
189C8×C61C4×D411yescharacteristic
190C8×C61#12111yescharacteristic
191C8×C61#12111yescharacteristic
192#92418—21no—
193#92418—21no—
194#92418—42no—
195#12990—611nomaximal, Sylow
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61C2×#10211yescharacteristic
202C22×C61#44811yescharacteristic
203C22×C61#48111yescharacteristic
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—21no—
209C2×D61—42no—
210C2×D61—42no—
211C2×D61#35912yescomplemented
212C4×C61—81no—
213C4×C61#38611yescharacteristic
214C4×C61#41711yescharacteristic
215C4×C61#44711yescharacteristic
216C4×C61#48011yescharacteristic
217Dic61—21no—
218Dic61—21no—
219Dic61—81no—
220Dic61—81no—
221#3050—611no—
222C22×#108—611no—
223C2×#359—611no—
224C2×#359D6111yescharacteristic, complemented
225C2×C22⋊C16—611no—
226#1382—611no—
227#1382—611no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—161no—
231C2×C61#187411yescharacteristic
232C2×C61C2×#35911yescharacteristic
233C2×C61#214311yescharacteristic
234D61—22no—
235D61—41no—
236C2×#135C2×D6111yescharacteristic
237C22×M16—1221no—
238C23×C8—611no—
239#525—1221no—
240C22×C16—611no—
241C22×C16C2×D6111yescharacteristic
242#467—611no—
243#467—611no—
244#466—611no—
245#466—611no—
246#465—1221no—
247#465—1221no—
248C2×#108—611no—
249C2×#108—1222no—
250C2×#108—1221no—
251C2×#108—1222no—
252C2×#108C2×D6111yescharacteristic
253#427—611no—
254#416—1221no—
255#359—22no—
256#359—1222no—
257C22⋊C16—1221no—
258C22⋊C16—1221no—
259C61#1299011yescharacteristic, complemented, Sylow
260C2×#41—21no—
261C23×C4—611no—
262#135—21no—
263#135—21no—
264#135—21no—
265#135—21no—
266C2×Q16C4×D6111yescharacteristic
267C2×SD16—21no—
268C2×D8C4×D6111yescharacteristic
269C2×M16—21no—
270C2×M16—1224no—
271C2×M16—1221no—
272C2×M16—2441no—
273C2×M16—2442no—
274C22×C8—611no—
275C22×C8—611no—
276C22×C8—611no—
277C22×C8—611no—
278C22×C8—611no—
279C22×C8—1221no—
280C22×C8—1221no—
281C22×C8—1221no—
282C22×C8—1221no—
283C22×C8—2441no—
284C22×C8C22×D6111yescharacteristic
285#123—2441no—
286C22⋊Q8—1221no—
287C22⋊Q8—1221no—
288#121—1221no—
289#121—1221no—
290#120—2441no—
291C4×D4—2441no—
292C4×D4—2441no—
293#117—1221no—
294C2×C16—21no—
295C2×C16—21no—
296C2×C16—21no—
297C2×C16—1221no—
298C2×C16—1221no—
299C2×C16—1221no—
300#108—21no—
301#108—612no—
302#108—1224no—
303#108—1221no—
304#108C22⋊D6112yescomplemented
305#107—611no—
306#107—611no—
307#106—1221no—
308#103—1221no—
309#103—1221no—
310#102—1221no—
311#102—1221no—
312C24—611no—
313#41—41no—
314#41—41no—
315#41—41no—
316#41—41no—
317C2×Q8—21no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—2441no—
321C2×D4—2441no—
322C22×C4—41no—
323C22×C4—611no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4D4×D6111yescharacteristic
333Q16—21no—
334Q16—21no—
335SD16—41no—
336SD16—41no—
337D8—21no—
338D8—21no—
339M16—22no—
340M16—41no—
341M16—1222no—
342M16—2444no—
343M16—2441no—
344C2×C8—41no—
345C2×C8—611no—
346C2×C8—611no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1221no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8—1221no—
357C2×C8—2444no—
358C2×C8—2441no—
359C2×C8C2×C4×D6111yescharacteristic
360C2×C8#1175822211yescharacteristic
361C2×C8D4×D6111yescharacteristic
362C2×C8D4×D6111yescharacteristic
363C2×C8#1175822411yescharacteristic
364C2×C8C2×C22⋊D6111yescharacteristic
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C22⋊C4—2441no—
370C22⋊C4—2441no—
371C22⋊C4—2441no—
372C22⋊C4—2441no—
373C22⋊C4—2441no—
374C42—2441no—
375C16—41no—
376C16—2441no—
377C23—41no—
378C23—611no—
379C23—611no—
380C23—1222no—
381C23—1221no—
382C23—1221no—
383C23—2441no—
384C23SD16×D6111yescharacteristic
385Q8—41no—
386Q8—41no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—81no—
391D4—4882no—
392D4—4882no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—611no—
397C2×C4—611no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4C22⋊C4×D6111yescharacteristic
411C2×C4#1451974511yescharacteristic
412C2×C4#1451975911yescharacteristic
413C2×C4D8×D6111yescharacteristic
414C2×C4#1451980111yescharacteristic
415C2×C4#1451980611yescharacteristic
416C8—42no—
417C8—1221no—
418C8—1221no—
419C8—2442no—
420C8#1451973711yescharacteristic
421C8C4×C22⋊D6111yescharacteristic
422C8#1451974811yescharacteristic
423C8#1451975011yescharacteristic
424C22—21no—
425C22—21no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—612no—
430C22—1221no—
431C22—1221no—
432C22—1221no—
433C22—1221no—
434C22—1221no—
435C22—2442no—
436C22—2442no—
437C22#102×D6111yescharacteristic
438C22#1683989911yescharacteristic
439C22#1684007911yescharacteristic
440C4—81no—
441C4—1221no—
442C4—1221no—
443C4—4881no—
444C4—4881no—
445C4#1683963811yescharacteristic
446C4#1683976011yescharacteristic
447C4#1683989411yescharacteristic
448C4#1684007411yescharacteristic
449C2—21no—
450C2—21no—
451C2—161no—
452C2—1222no—
453C2—2441no—
454C2#2144613311yescharacteristic
455C2#359×D6111yescharacteristic
456C2#2144754511yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#359C2
socleC22×C61C2×#102
prime radical#21455396C2
cosocleC22×C8×C61C23
hypercenterC2×#359D61
hypocenterC61#12990
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#108×D61C2semidirect
3. C2×#16839569C2semidirect
4. C2×#16839541C2semidirect
5. #21443916C2semidirect
6. #21443915C2semidirect
7. C2×C61×#359C2semidirect
59. #14519713D4semidirect
82. #108×C61D4semidirect
211. C2×D61#359semidirect
224. C2×#359D61semidirect
259. C61#12990semidirect
304. #108C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214553962
C2×#108×D612
C2×#168395692
C2×#168395412
#214439162
#214439152
C2×C61×#3592
#1299061