Finite Group Databasebeta

← C4×#16840192 #29833293

Subgroups — C4×#16840192 #29833293

Order 15616.

690 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840192C211yesmaximal, characteristic
2C4×#14519799C211yesmaximal, characteristic, complemented
3C4×#14519723C212yesmaximal, complemented
4C4×#14519720C212yesmaximal, complemented
5C4×#14519721C212yesmaximal, complemented
6C4×#14519718C212yesmaximal, complemented
7#21447601C211yesmaximal, characteristic, complemented
8#21447526C211yesmaximal, characteristic, complemented
9#21447524C211yesmaximal, characteristic, complemented
10C2×C4×#11758185C211yesmaximal, characteristic, complemented
11C4×#135×C61C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C4×#11758222—21no—
14#16840192C418yesdirect product factor
15C2×#14519723C2211yescharacteristic
16C2×#14519721C2211yescharacteristic
17C2×#14519720C2211yescharacteristic
18C2×#14519718C2211yescharacteristic
19C22×#11758185C2211yescharacteristic
20C22×#11758185C2211yescharacteristic
21C4×Dic244C2212yes—
22C4×#11758190—22no—
23C4×D488C2212yes—
24#16839800C2211yescharacteristic
25#16839759—21no—
26#16839589C2212yes—
27#16839587C2212yes—
28#16839566C2212yes—
29#16839565C2212yes—
30#16839563C2212yes—
31#16839562C2212yes—
32C4×#11758185C2212yes—
33C4×#11758185C2212yes—
34C2×#135×C61C2211yescharacteristic
35C4×#41×C61—21no—
36C4×Q16×C61C2212yes—
37C4×SD16×C61—22no—
38C4×D8×C61C2212yes—
39C61×#427C2211yescharacteristic
40C61×#416—21no—
41C2×C4×C8×C61C2211yescharacteristic
42C2×#11758222—21no—
43#14519799—22no—
44#14519799C2×C414yescomplemented
45C2×Dic244C2311yescharacteristic
46C2×#11758190—21no—
47C2×D488C2311yescharacteristic
48C4×Dic122—22no—
49C4×D244—22no—
50C4×C22⋊D61—42no—
51#14519736—21no—
52#14519734—41no—
53C42×D61—41no—
54#14519723C2×C414yescomplemented
55#14519721C2×C414yescomplemented
56#14519720C2×C414yescomplemented
57#14519718C2×C414yescomplemented
58C2×#11758185—22no—
59C2×#11758185C2×C414yescomplemented
60C2×#11758185C2312yes—
61C2×#11758185C2311yescharacteristic
62C2×#11758185C2311yescharacteristic
63#14519711C2312yes—
64#14519709—21no—
65#14519702—22no—
66#14519699—22no—
67C2×#41×C61—21no—
68#135×C61—22no—
69#135×C61C2×C414yescomplemented
70C2×Q16×C61C2311yescharacteristic
71C2×SD16×C61—21no—
72C2×D8×C61C2311yescharacteristic
73C22×C8×C61D411yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C4×Q8×C61—22no—
76C4×D4×C61—22no—
77C4×D4×C61—42no—
78#117×C61—21no—
79#117×C61—41no—
80C2×C42×C61—41no—
81C2×C42×C61D411yescharacteristic
82#107×C61C2312yes—
83#106×C61—21no—
84#103×C61—22no—
85#102×C61—22no—
86C4×C8×C61D412yes—
87C4×C8×C61C2312yes—
88#41×C61—24no—
89#41×C61—42no—
90C2×Q8×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—42no—
95C22×C4×C61D812yes—
96C22×C4×C61C2×D411yescharacteristic
97C2×C22⋊D61—41no—
98#11758222—24no—
99#11758222—42no—
100C2×D244—21no—
101C2×C4×D61—41no—
102C2×C4×D61—42no—
103C2×Dic122—21no—
104Q16×C61—21no—
105Q16×C61C22×C412yes—
106SD16×C61—24no—
107D8×C61—21no—
108D8×C61C22×C412yes—
109C2×C8×C61—22no—
110C2×C8×C61C22×C412yes—
111C2×C8×C61C2×D412yes—
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61#4112yes—
114C2×C8×C61C2411yescharacteristic
115C4⋊C4×C61—22no—
116C4⋊C4×C61—42no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—42no—
119C42×C61—41no—
120C42×C61—42no—
121C42×C61D811yescharacteristic
122C42×C61D811yescharacteristic
123C42×C61C2×D412yes—
124C22⋊Dic61—41no—
125#11758198—42no—
126C4⋊Dic61—22no—
127#11758196—42no—
128C4×Dic61—41no—
129C4×Dic61—42no—
130Dic244—21no—
131Dic244C22×C412yes—
132D488—21no—
133D488C22×C412yes—
134#11758190—24no—
135#11758185—22no—
136#11758185C22×C412yes—
137#11758185C22×C412yes—
138C23×C61—41no—
139C23×C61C2×D811yescharacteristic
140C22×D61—41no—
141Q8×C61—22no—
142Q8×C61—41no—
143D4×C61—22no—
144D4×C61—44no—
145D4×C61—41no—
146C2×C4×C61—24no—
147C2×C4×C61—41no—
148C2×C4×C61—44no—
149C2×C4×C61—42no—
150C2×C4×C61—84no—
151C2×C4×C61C4×D412yes—
152C2×C4×C61C2×D812yes—
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61C2×D812yes—
155C2×C4×C61#13512yes—
156C2×C4×C61C22×D411yescharacteristic
157C22⋊D61—44no—
158C2×Dic61—41no—
159C2×Dic61—42no—
160D244—22no—
161D244—41no—
162C4×D61—44no—
163C4×D61—84no—
164Dic122—22no—
165Dic122—41no—
166C8×C61—22no—
167C8×C61C4×D412yes—
168C8×C61C23×C411yescharacteristic
169C8×C61C2×#4111yescharacteristic
170C4×#508—611nomaximal, Sylow
171C22×C61—22no—
172C22×C61—42no—
173C22×C61—82no—
174C22×C61C4×D812yes—
175C22×C61C22×D811yescharacteristic
176C2×D61—42no—
177C2×D61—82no—
178C4×C61—22no—
179C4×C61—42no—
180C4×C61—82no—
181C4×C61C4×D812yes—
182C4×C61#50814yescomplemented
183C4×C61C2×C4×D411yescharacteristic
184C4×C61C2×#13511yescharacteristic
185Dic61—42no—
186Dic61—82no—
187C2×#508—611no—
188C4×#135—611no—
189C4×#135D6111yescharacteristic, complemented
190C4×Q32—612no—
191C4×SD32—612no—
192C4×SD32—612no—
193C4×D16—612no—
194#2158—611no—
195#2138—611no—
196#2138—611no—
197C2×C4×C16—611no—
198C2×C61—22no—
199C2×C61—82no—
200C2×C61C2×C4×D811yescharacteristic
201C2×C61C2×#50812yes—
202D61—82no—
203C2×#135—611no—
204C2×#135C2×D6111yescharacteristic
205C4×#41—21no—
206C4×#41—1221no—
207#508—618no—
208C2×Q32—611no—
209C2×SD32—611no—
210C2×SD32—611no—
211C2×D16—611no—
212C22×C16—611no—
213C22×C16—611no—
214C4×Q16—612no—
215C4×Q16C2×D6112yes—
216C4×SD16—22no—
217C4×SD16—1222no—
218C4×D8—612no—
219C4×D8C2×D6112yes—
220#427—611no—
221#427C2×D6111yescharacteristic
222#416—21no—
223#416—1221no—
224C2×C4×C8C2×D6111yescharacteristic
225#367—612no—
226#366—612no—
227#358—612no—
228#358—612no—
229#357—612no—
230#357—612no—
231C4×C16—612no—
232C4×C16—612no—
233C61C4×#50811yescharacteristic, complemented, Sylow
234C2×#41—21no—
235C2×#41—1221no—
236#135—22no—
237#135—614no—
238#135—1222no—
239#135C4×D6114yescomplemented
240C2×Q16—611no—
241C2×Q16C22×D6111yescharacteristic
242C2×SD16—21no—
243C2×SD16—1221no—
244C2×D8—611no—
245C2×D8C22×D6111yescharacteristic
246C22×C8C22⋊D6111yescharacteristic
247C22×C8C22×D6111yescharacteristic
248C4×Q8—22no—
249C4×Q8—1222no—
250C4×D4—22no—
251C4×D4—42no—
252C4×D4—1222no—
253C4×D4—2442no—
254#117—21no—
255#117—41no—
256#117—1221no—
257#117—2441no—
258C2×C42—41no—
259C2×C42—2441no—
260C2×C42C22⋊D6111yescharacteristic
261Q32—614no—
262SD32—614no—
263SD32—614no—
264D16—614no—
265C2×C16—614no—
266C2×C16—611no—
267C2×C16—611no—
268C2×C16—612no—
269C2×C16—1222no—
270#107—612no—
271#107C22×D6112yes—
272#106—21no—
273#106—1221no—
274#103—22no—
275#103—1222no—
276#102—22no—
277#102—1222no—
278C4×C8C22⋊D6112yes—
279C4×C8C22×D6112yes—
280#41—24no—
281#41—42no—
282#41—1224no—
283#41—2442no—
284C2×Q8—21no—
285C2×Q8—1221no—
286C2×D4—21no—
287C2×D4—41no—
288C2×D4—1221no—
289C2×D4—2441no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—2442no—
293C22×C4—2441no—
294C22×C4#1175819912yes—
295C22×C4C2×C22⋊D6111yescharacteristic
296Q16—21no—
297Q16—612no—
298Q16—1221no—
299Q16C2×C4×D6112yes—
300SD16—24no—
301SD16—1224no—
302D8—21no—
303D8—612no—
304D8—1221no—
305D8C2×C4×D6112yes—
306C2×C8—22no—
307C2×C8C2×C4×D6112yes—
308C2×C8#1175822212yes—
309C2×C8C2×C22⋊D6112yes—
310C2×C8C2×C22⋊D6111yescharacteristic
311C2×C8C23×D6111yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—42no—
314C4⋊C4—1222no—
315C4⋊C4—2442no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—2441no—
319C22⋊C4—2442no—
320C42—41no—
321C42—42no—
322C42—2441no—
323C42—2442no—
324C42#1175819911yescharacteristic
325C42#1175819911yescharacteristic
326C42C2×C22⋊D6112yes—
327C16—612no—
328C16—612no—
329C16—1222no—
330C23—41no—
331C23—2441no—
332C23C2×#1175819911yescharacteristic
333Q8—22no—
334Q8—41no—
335Q8—1222no—
336Q8—2441no—
337D4—22no—
338D4—44no—
339D4—41no—
340D4—1222no—
341D4—2444no—
342D4—2441no—
343C2×C4—24no—
344C2×C4—41no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—84no—
348C2×C4—4884no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2444no—
352C2×C4C4×C22⋊D6112yes—
353C2×C4C2×#1175819912yes—
354C2×C4C2×#1175819912yes—
355C2×C4C2×#1175819911yescharacteristic
356C2×C4#1451979712yes—
357C2×C4C22×C22⋊D6111yescharacteristic
358C8—22no—
359C8C4×C22⋊D6112yes—
360C8C22×C4×D6111yescharacteristic
361C8C2×#1175822211yescharacteristic
362C22—22no—
363C22—42no—
364C22—82no—
365C22—4882no—
366C22—2442no—
367C22C4×#1175819912yes—
368C22C22×#1175819911yescharacteristic
369C4—22no—
370C4—42no—
371C4—82no—
372C4—4882no—
373C4—2442no—
374C4C4×#1175819912yes—
375C4#1684019214yesdirect product factor
376C4C2×C4×C22⋊D6111yescharacteristic
377C4C2×#1451979711yescharacteristic
378C2—22no—
379C2—82no—
380C2—4882no—
381C2C2×C4×#1175819911yescharacteristic
382C2C2×#1684019212yes—
subgroupG/H
centerC42#11758199
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC4×#135×C61C2
socleC22×C61C22×D8
prime radicalC2×#16840192C2
cosocleC2×C8×C61C24
hypercenterC4×#135D61
hypocenterC61C4×#508
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
2. C4×#14519799C2semidirect
3. C4×#14519723C2semidirect
4. C4×#14519720C2semidirect
5. C4×#14519721C2semidirect
6. C4×#14519718C2semidirect
7. #21447601C2semidirect
8. #21447526C2semidirect
9. #21447524C2semidirect
10. C2×C4×#11758185C2semidirect
11. C4×#135×C61C2semidirect
14. #16840192C4direct (N × H)
44. #14519799C2×C4semidirect
54. #14519723C2×C4semidirect
55. #14519721C2×C4semidirect
56. #14519720C2×C4semidirect
57. #14519718C2×C4semidirect
59. C2×#11758185C2×C4semidirect
69. #135×C61C2×C4semidirect
182. C4×C61#508semidirect
189. C4×#135D61semidirect
233. C61C4×#508semidirect
239. #135C4×D61semidirect
375. C4#16840192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401922
C4×#145197992
C4×#145197232
C4×#145197202
C4×#145197212
C4×#145197182
#214476012
#214475262
#214475242
C2×C4×#117581852
C4×#135×C612
C4×#50861