Finite Group Databasebeta

← #29663395

Subgroups — #29663395

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457139C212yesmaximal, complemented
2#21454794C211yesmaximal, characteristic, complemented
3#21445356C212yesmaximal, complemented
4#21445349C212yesmaximal, complemented
5#21445220C211yesmaximal, characteristic, complemented
6#21445215C211yesmaximal, characteristic, complemented
7#21445176C211yesmaximal, characteristic, complemented
8#21445171C211yesmaximal, characteristic, complemented
9C2×#16839515C211yesmaximal, characteristic, complemented
10#21444514C212yesmaximal, complemented
11C61×#3169C211yesmaximal, characteristic, complemented
12#16840296C2211yescharacteristic
13#16840062—22no—
14#16840054C2212yes—
15#16840049C2212yes—
16#16839996—22no—
17#16839989—22no—
18#16839977—22no—
19#16839959C2212yes—
20#16839954C2212yes—
21#16839892C2211yescharacteristic
22C8×Dic122C2211yescharacteristic
23#16839841C2211yescharacteristic
24#16839833—21no—
25C8×D244C2211yescharacteristic
26C8×C22⋊D61—21no—
27#16839821—21no—
28#16839819C2211yescharacteristic
29C2×C4⋊#92418C2212yes—
30#16839716—21no—
31#16839515C2211yescharacteristic
32#16839515C2211yescharacteristic
33#16839515C2212yes—
34#16839511C2212yes—
35#16839511C2212yes—
36#16839506C2212yes—
37#16839506C2212yes—
38C61×#532C2212yes—
39C61×#500C2211yescharacteristic
40C61×#493C2211yescharacteristic
41C61×#486C2212yes—
42C61×#466—21no—
43C61×#466—21no—
44C4×D8×C61—21no—
45C4×D8×C61—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758200—22no—
48C2×#11758199—22no—
49C2×#11758189—21no—
50C22×#92418—22no—
51C2×C8×D61—21no—
52#14519771—21no—
53#14519769D411yescharacteristic
54#14519765D411yescharacteristic
55#14519760—21no—
56#14519756D411yescharacteristic
57#14519751D411yescharacteristic
58C4×Dic122C2311yescharacteristic
59C4×D244C2311yescharacteristic
60C4×C22⋊D61—21no—
61#14519734—21no—
62#14519710—22no—
63#14519708—22no—
64C4⋊#92418—22no—
65C4⋊#92418C2312yes—
66C4⋊#92418C2312yes—
67C4⋊#92418C2311yescharacteristic
68C4⋊#92418C2311yescharacteristic
69#14519706—21no—
70#14519706—21no—
71#14519700—22no—
72#14519698—22no—
73#14519698—22no—
74#14519697—22no—
75C22⋊#92418—21no—
76#14519689—21no—
77#14519689—21no—
78#14519688—21no—
79#14519687—21no—
80C8×Dic61—21no—
81C2×#41×C61—22no—
82C2×D8×C61—21no—
83C2×D8×C61—21no—
84C22×C8×C61D411yescharacteristic
85C22×C8×C61D411yescharacteristic
86C4⋊Q8×C61C2312yes—
87#127×C61C2312yes—
88#124×C61—22no—
89#121×C61—22no—
90#121×C61—22no—
91C4×D4×C61—22no—
92C4×D4×C61—22no—
93C2×C42×C61C2311yescharacteristic
94#107×C61—21no—
95#107×C61—21no—
96#102×C61—22no—
97#102×C61—22no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102#41×C61—84no—
103C2×Q8×C61—22no—
104C2×D4×C61—22no—
105C2×D4×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61—42no—
108C22×C4×C61—42no—
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C2×C22⋊D61—21no—
113C2×D244C2×D411yescharacteristic
114C2×C4×D61—21no—
115C2×Dic122C2×D411yescharacteristic
116D8×C61—42no—
117D8×C61—42no—
118C2×C8×C61—22no—
119C2×C8×C61—41no—
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C22⋊C4×C61—42no—
127C22⋊C4×C61—42no—
128C42×C61C2×D411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C42×C61#4111yescharacteristic
131C42×C61C2411yescharacteristic
132C22⋊Dic61—21no—
133#11758200—82no—
134#11758199—82no—
135#11758198—21no—
136#11758198—21no—
137#11758198—21no—
138#11758198—21no—
139C4⋊Dic61C2×D411yescharacteristic
140C4⋊Dic61C2×D411yescharacteristic
141#11758196—21no—
142#11758196—21no—
143#11758196—21no—
144#11758196—21no—
145C4×Dic61—21no—
146C2×#92418—21no—
147C2×#92418—21no—
148C2×#92418—22no—
149C2×#92418—22no—
150C2×#92418—82no—
151#11758189—42no—
152C8×D61—42no—
153C23×C61—42no—
154C23×C61#12111yescharacteristic
155C22×D61—21no—
156Q8×C61—82no—
157D4×C61—42no—
158D4×C61—42no—
159D4×C61—42no—
160D4×C61—42no—
161D4×C61—82no—
162D4×C61—84no—
163C2×C4×C61—22no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—42no—
169C2×C4×C61—84no—
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61C22×D411yescharacteristic
174C2×C4×C61C22×D411yescharacteristic
175C2×C4×C61C2×#4111yescharacteristic
176C22⋊D61—42no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180D244—21no—
181D244—21no—
182C4×D61—41no—
183C4×D61—41no—
184Dic122—21no—
185Dic122—21no—
186C8×C61—21no—
187C8×C61—21no—
188C8×C61—21no—
189C8×C61#13512yes—
190#92418—41no—
191#92418—41no—
192#92418—42no—
193#92418—42no—
194#19222—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—82no—
198C22×C61—82no—
199C22×C61—82no—
200C22×C61#47212yes—
201C22×C61C2×#12111yescharacteristic
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—82no—
210C4×C61C2×#13511yescharacteristic
211C4×C61#57511yescharacteristic
212C4×C61#57611yescharacteristic
213C4×C61#57811yescharacteristic
214Dic61—41no—
215Dic61—41no—
216Dic61—41no—
217#3247—612no—
218#3169D6111yescharacteristic, complemented
219#2966—611no—
220#1698—612no—
221#1697—612no—
222#1676—611no—
223#1675—611no—
224#1668—611no—
225#1667—611no—
226C2×#335—611no—
227#1551—612no—
228C2×C61—22no—
229C2×C61—162no—
230C2×C61#303511yescharacteristic
231C2×C61#306111yescharacteristic
232C2×C61C2×#47211yescharacteristic
233D61—81no—
234#532C2×D6112yes—
235#529—611no—
236#500C2×D6111yescharacteristic
237#493C2×D6111yescharacteristic
238#486C2×D6112yes—
239#478—1222no—
240#477—612no—
241#476—612no—
242#466—21no—
243#466—21no—
244#466—1222no—
245#465—1222no—
246#463—1222no—
247#460—612no—
248#459—612no—
249#446—611no—
250C8×Q8—611no—
251C4×D8—21no—
252C4×D8—21no—
253#436—611no—
254#435—1221no—
255C8×D4—611no—
256C8×D4—1221no—
257#433—1221no—
258#432—611no—
259C2×C4⋊C8—612no—
260#405—1221no—
261C2×C4×C8C2×D6111yescharacteristic
262#335—611no—
263#335—611no—
264#335—612no—
265#333—612no—
266#333—612no—
267#331—612no—
268#331—612no—
269C61#1922211yescharacteristic, complemented, Sylow
270C2×#41—22no—
271C2×SD16—1222no—
272C2×D8—21no—
273C2×D8—21no—
274C2×D8—1222no—
275C2×M16—1221no—
276C22×C8—1222no—
277C22×C8—1221no—
278C22×C8C22⋊D6111yescharacteristic
279C22×C8C22⋊D6111yescharacteristic
280C4⋊Q8C22×D6112yes—
281#127C22×D6112yes—
282#126—1221no—
283#125—611no—
284#124—22no—
285#124—611no—
286#123—1221no—
287C22⋊Q8—611no—
288#121—22no—
289#121—22no—
290#121—611no—
291C4×Q8—611no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—611no—
295C4×D4—1221no—
296#117—1221no—
297C2×C42C22×D6111yescharacteristic
298#107—21no—
299#107—21no—
300#107—1222no—
301#106—1222no—
302C4⋊C8—611no—
303C4⋊C8—611no—
304C4⋊C8—612no—
305C4⋊C8—612no—
306C4⋊C8—1221no—
307C4⋊C8—1221no—
308C4⋊C8—1222no—
309#103—1222no—
310#102—22no—
311#102—22no—
312#102—1222no—
313#102—1222no—
314#102—1222no—
315C22⋊C8—1221no—
316C22⋊C8—1221no—
317C22⋊C8—1221no—
318#97—1221no—
319#97—1221no—
320C4×C8—1221no—
321C4×C8C22⋊D6111yescharacteristic
322C4×C8C22⋊D6111yescharacteristic
323C4×C8C22×D6111yescharacteristic
324C4×C8C22×D6111yescharacteristic
325#41—84no—
326C2×Q8—22no—
327C2×Q8—611no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—42no—
332C2×D4—611no—
333C2×D4—1221no—
334C22×C4—42no—
335C22×C4—1221no—
336C22×C4D4×D6111yescharacteristic
337C22×C4#1175822411yescharacteristic
338C22×C4C2×C22⋊D6111yescharacteristic
339SD16—4882no—
340D8—42no—
341D8—42no—
342D8—4882no—
343M16—2442no—
344C2×C8—22no—
345C2×C8—41no—
346C2×C8—1222no—
347C2×C8—1222no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—4882no—
351C2×C8—2442no—
352C2×C8C2×C22⋊D6111yescharacteristic
353C2×C8C2×C22⋊D6111yescharacteristic
354C2×C8C2×C22⋊D6111yescharacteristic
355C2×C8C2×C22⋊D6111yescharacteristic
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—611no—
359C4⋊C4—611no—
360C4⋊C4—1221no—
361C4⋊C4—1221no—
362C4⋊C4—1221no—
363C4⋊C4—1221no—
364C22⋊C4—42no—
365C22⋊C4—42no—
366C22⋊C4—1221no—
367C22⋊C4—1221no—
368C22⋊C4—1221no—
369C22⋊C4—1221no—
370C22⋊C4—1221no—
371C42—1221no—
372C42D4×D6111yescharacteristic
373C42#1175822411yescharacteristic
374C42C2×C22⋊D6111yescharacteristic
375C42C23×D6111yescharacteristic
376C23—42no—
377C23—1221no—
378C23#1451974811yescharacteristic
379Q8—82no—
380Q8—1221no—
381Q8—1221no—
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—84no—
388D4—1221no—
389D4—1221no—
390D4—2442no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—42no—
397C2×C4—84no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4#1451974811yescharacteristic
404C2×C4#1451974811yescharacteristic
405C2×C4#1451974811yescharacteristic
406C2×C4C2×D4×D6111yescharacteristic
407C2×C4C22×C22⋊D6111yescharacteristic
408C2×C4C2×#1175822411yescharacteristic
409C8—21no—
410C8—21no—
411C8—21no—
412C8—2441no—
413C8—2441no—
414C8—2442no—
415C8—2442no—
416C8#1451979712yes—
417C22—21no—
418C22—21no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—2441no—
423C22—2441no—
424C22—2441no—
425C22#1684002912yes—
426C22C2×#1451974811yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—82no—
432C4—2441no—
433C4—2441no—
434C4—2441no—
435C4C2×#1451979711yescharacteristic
436C4#1684056011yescharacteristic
437C4#1684056411yescharacteristic
438C4#1684057611yescharacteristic
439C2—22no—
440C2—162no—
441C2—4881no—
442C2#2145526811yescharacteristic
443C2#2145548511yescharacteristic
444C2C2×#1684002911yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3169C2
socleC22×C61C2×#121
hypercenter#3169D61
hypocenterC61#19222
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #21457139C2semidirect
2. #21454794C2semidirect
3. #21445356C2semidirect
4. #21445349C2semidirect
5. #21445220C2semidirect
6. #21445215C2semidirect
7. #21445176C2semidirect
8. #21445171C2semidirect
9. C2×#16839515C2semidirect
10. #21444514C2semidirect
11. C61×#3169C2semidirect
218. #3169D61semidirect
269. C61#19222semidirect

Maximal subgroups

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

subgroupindex
#214571392
#214547942
#214453562
#214453492
#214452202
#214452152
#214451762
#214451712
C2×#168395152
#214445142
C61×#31692
#1922261