Finite Group Databasebeta

← #29698495

Subgroups — #29698495

Order 15616.

846 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
1C2×#16839878C211yesmaximal, characteristic
2#21454696C211yesmaximal, characteristic
3#21454693C211yesmaximal, characteristic
4#21454413C212yesmaximal, complemented
5#21446605C211yesmaximal, characteristic, complemented
6#21446055C212yesmaximal, complemented
7#21446049C212yesmaximal, complemented
8#21445982C211yesmaximal, characteristic, complemented
9#21445877C212yesmaximal, complemented
10#21445699C211yesmaximal, characteristic, complemented
11C61×#1952C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C2×#14519785C2212yes—
14#16840243C2212yes—
15#16840242C2212yes—
16#16839878C418yescomplemented
17#16839864—22no—
18#16839861—22no—
19C4×Dic244—21no—
20#16839856—21no—
21C4×D488—21no—
22#16839844—21no—
23C2×#14519712C2211yescharacteristic
24#16839804C2212yes—
25#16839803—22no—
26#16839801—22no—
27#16839799—22no—
28#16839798C2211yescharacteristic
29C2×#14519711C2211yescharacteristic
30C2×#14519708C2212yes—
31#106×D61—22no—
32C2×#14519703C2212yes—
33#16839764C2212yes—
34#16839761C2212yes—
35#16839717C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839627C2212yes—
38#16839530C2212yes—
39#16839523C2211yescharacteristic
40#16839521C2211yescharacteristic
41C2×#108×C61C2211yescharacteristic
42C61×#428C2212yes—
43C2×#107×C61C2211yescharacteristic
44C61×#405C2211yescharacteristic
45C61×#343C2212yes—
46C2×#11758222C2312yes—
47#14519799C2×C414yes—
48#14519799Q814yes—
49C2×Dic244D411yescharacteristic
50C2×#11758190D412yes—
51C2×D488D411yescharacteristic
52#14519785—24no—
53#14519785C2×C418yescomplemented
54C2×#11758194C2311yescharacteristic
55C2×#11758189—22no—
56C22×#92418C2311yescharacteristic
57C2×C8×D61—22no—
58C4×Dic122—22no—
59#14519742—22no—
60C4×D244—22no—
61#14519739—22no—
62C4×C22⋊D61—42no—
63#14519737—42no—
64#14519736C2311yescharacteristic
65#14519735—22no—
66#14519735—22no—
67C2×C4⋊Dic61C2312yes—
68C4⋊C4×D61—22no—
69C4⋊C4×D61—22no—
70C2×C4×Dic61C2311yescharacteristic
71#14519712—22no—
72#14519711—21no—
73#14519711—21no—
74#14519711—22no—
75#14519710D411yescharacteristic
76#14519710D411yescharacteristic
77#14519709—22no—
78#14519708—22no—
79#14519708—22no—
80#14519708D411yescharacteristic
81#14519708D411yescharacteristic
82#14519703C2×C418yescomplemented
83#14519702—22no—
84#14519700—22no—
85#14519699—22no—
86#14519697—22no—
87#14519687—21no—
88C8×Dic61—21no—
89C8×Dic61C2×C414yescomplemented
90#14519684—42no—
91C2×M16×C61C2311yescharacteristic
92C2×M16×C61C2312yes—
93C22×C8×C61C2311yescharacteristic
94#117×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2312yes—
96#108×C61C2×C414yescomplemented
97#107×C61—21no—
98#107×C61—21no—
99#107×C61—22no—
100#106×C61—22no—
101#97×C61—21no—
102C4×C8×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61C2411yescharacteristic
105C2×C22⋊D61—22no—
106C22×Dic61—21no—
107C22×Dic61—22no—
108#11758222—22no—
109#11758222—22no—
110#11758222C22×C414yes—
111#11758222C2×Q814yes—
112C2×D244C2×D412yes—
113C2×C4×D61—22no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×Dic122C2×D412yes—
117M16×C61—22no—
118M16×C61—21no—
119M16×C61—21no—
120M16×C61C22×C414yes—
121C2×C8×C61—22no—
122C2×C8×C61—21no—
123C2×C8×C61C22×C412yes—
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×Q812yes—
127C4⋊C4×C61—22no—
128C4⋊C4×C61—22no—
129C4⋊C4×C61C2×D411yescharacteristic
130C4⋊C4×C61C2×D411yescharacteristic
131C22⋊C4×C61—21no—
132C42×C61—21no—
133C22⋊Dic61—21no—
134#11758198—42no—
135#11758198—42no—
136C4⋊Dic61—22no—
137C4⋊Dic61—22no—
138C4⋊Dic61C2×D411yescharacteristic
139C4⋊Dic61C2×D411yescharacteristic
140#11758196—42no—
141#11758196—42no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144C4×Dic61—42no—
145C4×Dic61—42no—
146C4×Dic61C22×C412yes—
147#11758194—21no—
148#11758194—21no—
149C2×#92418—21no—
150C2×#92418C22×C412yes—
151C2×#92418C2×D411yescharacteristic
152C2×#92418C2×D411yescharacteristic
153C2×#92418#4112yes—
154Dic244C4⋊C414yes—
155D488C4⋊C414yes—
156#11758190C4⋊C418yes—
157#11758189—28no—
158C8×D61—28no—
159C23×C61H(5,𝔽2)11yescharacteristic
160C22×D61—22no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—42no—
164C2×C4×C61—82no—
165C2×C4×C61C23×C411yescharacteristic
166C2×C4×C61C22×D411yescharacteristic
167C2×C4×C61C22×D411yescharacteristic
168C2×C4×C61C22×Q811yescharacteristic
169C2×C4×C61C2×#4111yescharacteristic
170C2×C4×C612−1+411yescharacteristic
171C22⋊D61—24no—
172C22⋊D61—24no—
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—42no—
180C2×Dic61—82no—
181D244—22no—
182D244C2×C4⋊C414yes—
183C4×D61—24no—
184C4×D61—24no—
185C4×D61—162no—
186C4×D61—162no—
187Dic122—22no—
188Dic122C2×C4⋊C414yes—
189C8×C61—24no—
190C8×C61—41no—
191C8×C61C2×C4⋊C412yes—
192C8×C61C2×C4⋊C412yes—
193#92418—41no—
194#92418C4×D412yes—
195#92418C4×D412yes—
196#22690—611nomaximal, Sylow
197C22×C61—21no—
198C22×C61—21no—
199C22×C61#52011yescharacteristic
200C22×C61D4211yescharacteristic
201C22×C61#55411yescharacteristic
202C2×D61—24no—
203C2×D61—42no—
204C2×D61—42no—
205C4×C61—41no—
206C4×C61—41no—
207C4×C61—82no—
208C4×C61C22×C4⋊C411yescharacteristic
209C4×C61C2×C4×D411yescharacteristic
210C4×C61#54711yescharacteristic
211C4×C61D4×Q811yescharacteristic
212Dic61—24no—
213Dic61—42no—
214Dic61—41no—
215Dic61—41no—
216Dic61—82no—
217C2×#443—611no—
218#2951—611no—
219#2951—611no—
220#2912—612no—
221#1952—611no—
222#1952D6111yescharacteristic, complemented
223#1860—612no—
224#1860—612no—
225#1846—611no—
226#1815—612no—
227#1772—611no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61D4×C4⋊C411yescharacteristic
231C2×C61#329011yescharacteristic
232C2×C61#329011yescharacteristic
233D61—44no—
234C2×#135—611no—
235C2×#131—612no—
236#520—612no—
237#520—612no—
238#443—618no—
239#440—1222no—
240#440—1222no—
241C4×Q16—1221no—
242C4×Q16—1221no—
243C4×D8—1221no—
244C4×D8—1221no—
245C2×#108—611no—
246C2×#108C2×D6111yescharacteristic
247#428—612no—
248#428—1222no—
249#428—1222no—
250#428C2×D6112yes—
251#427—611no—
252#427—1222no—
253C2×#107—611no—
254C2×#107C2×D6111yescharacteristic
255C2×#106—612no—
256C2×#106—1222no—
257C2×#104—612no—
258#417—612no—
259#417—612no—
260#405—611no—
261#405C2×D6111yescharacteristic
262C2×C4×C8—611no—
263#382—612no—
264#343—612no—
265#343C2×D6112yes—
266#339—611no—
267#339—611no—
268C61#2269011yescharacteristic, complemented, Sylow
269C2×#41—612no—
270#135—614no—
271#135—614no—
272C2×Q16—611no—
273C2×SD16—612no—
274C2×D8—611no—
275#131—618no—
276#131—1224no—
277C2×M16—611no—
278C2×M16—1222no—
279C2×M16C22×D6111yescharacteristic
280C2×M16C22×D6112yes—
281C22×C8—611no—
282C22×C8—1222no—
283C22×C8C22×D6111yescharacteristic
284C4×Q8—1222no—
285C4×Q8—1222no—
286C4×D4—1222no—
287C4×D4—1222no—
288C4×D4—2442no—
289C4×D4—2442no—
290#117—611no—
291#117—1222no—
292#117—1222no—
293#117C22×D6111yescharacteristic
294C2×C4⋊C4—612no—
295C2×C4⋊C4—1222no—
296C2×C4⋊C4—1222no—
297C2×C4⋊C4C22×D6112yes—
298C2×C42—611no—
299#108—1222no—
300#108C4×D6114yescomplemented
301#107—21no—
302#107—21no—
303#107—22no—
304#107—611no—
305#107—611no—
306#107—1222no—
307#107—1221no—
308#107—1221no—
309#106—22no—
310#106—611no—
311#106—611no—
312#106—1222no—
313#106—1222no—
314#106—1222no—
315#104—618no—
316#103—1222no—
317#103—1222no—
318#102—1222no—
319#102—1222no—
320#97—21no—
321#97—1221no—
322C4×C8—21no—
323C4×C8—614no—
324C4×C8—1221no—
325#95—2442no—
326#41—614no—
327#41—614no—
328#41—1222no—
329#41—1222no—
330C2×Q8—612no—
331C2×D4—612no—
332C2×D4—1222no—
333C22×C4—22no—
334C22×C4—1222no—
335C22×C4—1221no—
336C22×C4—1222no—
337C22×C4—2442no—
338C22×C4—2442no—
339C22×C4C23×D6111yescharacteristic
340Q16—614no—
341SD16—618no—
342D8—614no—
343M16—22no—
344M16—21no—
345M16—21no—
346M16—1228no—
347M16—1221no—
348M16—1221no—
349M16C2×C4×D6114yes—
350C2×C8—22no—
351C2×C8—21no—
352C2×C8—612no—
353C2×C8—611no—
354C2×C8—611no—
355C2×C8—612no—
356C2×C8—1228no—
357C2×C8—1221no—
358C2×C8C2×C4×D6112yes—
359C2×C8D4×D6111yescharacteristic
360C2×C8D4×D6111yescharacteristic
361C2×C8Q8×D6112yes—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—611no—
365C4⋊C4—611no—
366C4⋊C4—1222no—
367C4⋊C4—1222no—
368C4⋊C4—2442no—
369C4⋊C4—2442no—
370C4⋊C4D4×D6111yescharacteristic
371C4⋊C4D4×D6111yescharacteristic
372C22⋊C4—21no—
373C22⋊C4—1221no—
374C22⋊C4—2442no—
375C22⋊C4—2442no—
376C42—21no—
377C42—612no—
378C42—1221no—
379C42—1221no—
380C42—2442no—
381C42—2442no—
382C23—1222no—
383C23#1451982311yescharacteristic
384Q8—614no—
385Q8—1222no—
386D4—614no—
387D4—1224no—
388D4—1224no—
389D4—1222no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—1222no—
395C2×C4—1224no—
396C2×C4—1224no—
397C2×C4—1222no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—9762no—
401C2×C4—9762no—
402C2×C4—4882no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4C22×C4×D6111yescharacteristic
407C2×C4C2×D4×D6111yescharacteristic
408C2×C4C2×D4×D6111yescharacteristic
409C2×C4C2×Q8×D6111yescharacteristic
410C2×C4#41×D6111yescharacteristic
411C2×C4#1451982511yescharacteristic
412C8—24no—
413C8—41no—
414C8—612no—
415C8—612no—
416C8—2441no—
417C8C4⋊C4×D6112yes—
418C8C4⋊C4×D6112yes—
419C22—21no—
420C22—21no—
421C22—1224no—
422C22—2442no—
423C22—2442no—
424C22#1684024411yescharacteristic
425C22#1684039611yescharacteristic
426C22#1684046811yescharacteristic
427C4—41no—
428C4—41no—
429C4—82no—
430C4—1224no—
431C4—4882no—
432C4—2442no—
433C4—2441no—
434C4—2441no—
435C4C2×C4⋊C4×D6111yescharacteristic
436C4C4×D4×D6111yescharacteristic
437C4#1684041411yescharacteristic
438C4#1684042711yescharacteristic
439C2—21no—
440C2—21no—
441C2—2444no—
442C2#2144872011yescharacteristic
443C2#2145760011yescharacteristic
444C2#2145760811yescharacteristic
subgroupG/H
centerC22#16840396
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1952C2
socleC22×C61D42
prime radicalC2×#14519799C22
cosocleC22×C4×C61C24
hypercenter#1952D61
hypocenterC61#22690
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
4. #21454413C2semidirect
5. #21446605C2semidirect
6. #21446055C2semidirect
7. #21446049C2semidirect
8. #21445982C2semidirect
9. #21445877C2semidirect
10. #21445699C2semidirect
11. C61×#1952C2semidirect
16. #16839878C4semidirect
53. #14519785C2×C4semidirect
82. #14519703C2×C4semidirect
89. C8×Dic61C2×C4semidirect
96. #108×C61C2×C4semidirect
222. #1952D61semidirect
268. C61#22690semidirect
300. #108C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398782
#214546962
#214546932
#214544132
#214466052
#214460552
#214460492
#214459822
#214458772
#214456992
C61×#19522
#2269061