Finite Group Databasebeta

← C4×#16840203 #29833342

Subgroups — C4×#16840203 #29833342

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840203C211yesmaximal, characteristic
2C4×#14519799C211yesmaximal, characteristic
3#21447688C212yesmaximal, complemented
4#21447681C212yesmaximal, complemented
5C4×#14519723C212yesmaximal, complemented
6C4×#14519720C212yesmaximal, complemented
7#21447605C211yesmaximal, characteristic, complemented
8#21447539C211yesmaximal, characteristic, complemented
9#21447529C211yesmaximal, characteristic
10C4×#14519717C211yesmaximal, characteristic, complemented
11C2×C4×Q16×C61C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C4×#11758222—21no—
14#16840203C418yesdirect product factor
15C2×#14519723C2212yes—
16C2×#14519720C2212yes—
17C2×#14519717C2211yescharacteristic
18C2×#14519717C2211yescharacteristic
19C4×Dic244C2211yescharacteristic
20C4×Dic244C2211yescharacteristic
21C4×#11758190—21no—
22C4×#11758190—21no—
23C4×D488C2211yescharacteristic
24C4×D488C2211yescharacteristic
25#16839800C2211yescharacteristic
26#16839759—21no—
27#16839589C2212yes—
28#16839587C2212yes—
29#16839566C2212yes—
30#16839566C2212yes—
31#16839565C2212yes—
32#16839562C2212yes—
33#16839538C2212yes—
34C4×#11758185C2212yes—
35C22×Q16×C61C2211yescharacteristic
36C2×C4×Q8×C61—21no—
37C4×Q16×C61—21no—
38C4×Q16×C61—21no—
39C4×Q16×C61C2212yes—
40C4×Q16×C61C2212yes—
41C2×#107×C61C2211yescharacteristic
42C2×#103×C61—21no—
43C2×C4×C8×C61C2211yescharacteristic
44C2×#11758222—21no—
45#14519799—22no—
46#14519799C2×C414yes—
47C2×Dic244C2311yescharacteristic
48C2×#11758190—21no—
49C2×D488C2311yescharacteristic
50C4×Dic122—21no—
51C4×Dic122—21no—
52C4×D244—21no—
53C4×D244—21no—
54C4×C22⋊D61—41no—
55C4×C22⋊D61—41no—
56#14519736—21no—
57#14519734—41no—
58C42×D61—41no—
59#14519723C2×C418yescomplemented
60#14519720C2×C418yescomplemented
61#14519717—22no—
62#14519717C2×C414yescomplemented
63C2×#11758185C2312yes—
64C2×#11758185C2312yes—
65#14519711C2311yescharacteristic
66#14519711C2311yescharacteristic
67#14519709—21no—
68#14519702—21no—
69#14519702—21no—
70#14519699—21no—
71#14519699—21no—
72C22×Q8×C61—21no—
73C2×Q16×C61—21no—
74C2×Q16×C61—22no—
75C2×Q16×C61C2×C414yescomplemented
76C2×Q16×C61C2312yes—
77C22×C8×C61D411yescharacteristic
78C22×C8×C61C2311yescharacteristic
79C4×Q8×C61—22no—
80C4×Q8×C61—22no—
81C4×Q8×C61—41no—
82C4×Q8×C61—41no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—41no—
85C2×C42×C61—41no—
86C2×C42×C61D411yescharacteristic
87#107×C61—21no—
88#107×C61C2312yes—
89#103×C61—22no—
90#103×C61—22no—
91C4×C8×C61D411yescharacteristic
92C4×C8×C61D411yescharacteristic
93C4×C8×C61C2311yescharacteristic
94C4×C8×C61C2311yescharacteristic
95C2×Q8×C61—24no—
96C2×Q8×C61—22no—
97C2×Q8×C61—41no—
98C2×Q8×C61—42no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61D811yescharacteristic
102C22×C4×C61D811yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C2×C22⋊D61—41no—
105#11758222—24no—
106#11758222—42no—
107C2×D244—21no—
108C2×C4×D61—41no—
109C2×C4×D61—41no—
110C2×C4×D61—41no—
111C2×Dic122—21no—
112Q16×C61—24no—
113Q16×C61—22no—
114Q16×C61C22×C414yes—
115C2×C8×C61—22no—
116C2×C8×C61C22×C412yes—
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61#4112yes—
121C2×C8×C61C2411yescharacteristic
122C4⋊C4×C61—22no—
123C4⋊C4×C61—41no—
124C4⋊C4×C61—42no—
125C4⋊C4×C61—42no—
126C42×C61—42no—
127C42×C61—42no—
128C42×C61D811yescharacteristic
129C42×C61D811yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C22⋊Dic61—41no—
133#11758198—41no—
134#11758198—41no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137#11758196—41no—
138#11758196—41no—
139C4×Dic61—41no—
140C4×Dic61—41no—
141C4×Dic61—41no—
142Dic244—21no—
143Dic244C22×C412yes—
144D488—21no—
145D488C22×C412yes—
146#11758190—24no—
147#11758185—22no—
148#11758185C22×C414yes—
149C23×C61C2×D811yescharacteristic
150C22×D61—41no—
151Q8×C61—24no—
152Q8×C61—42no—
153Q8×C61—44no—
154C2×C4×C61—22no—
155C2×C4×C61—41no—
156C2×C4×C61—42no—
157C2×C4×C61—44no—
158C2×C4×C61—42no—
159C2×C4×C61—82no—
160C2×C4×C61C4×D412yes—
161C2×C4×C61C2×D811yescharacteristic
162C2×C4×C61C2×D811yescharacteristic
163C2×C4×C61C2×D811yescharacteristic
164C2×C4×C61C2×D811yescharacteristic
165C2×C4×C61C2×D811yescharacteristic
166C2×C4×C61#13512yes—
167C2×C4×C61C22×D411yescharacteristic
168C22⋊D61—44no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172D244—22no—
173D244—41no—
174C4×D61—44no—
175C4×D61—82no—
176C4×D61—82no—
177Dic122—22no—
178Dic122—41no—
179C8×C61—21no—
180C8×C61—21no—
181C8×C61C4×D412yes—
182C8×C61C23×C411yescharacteristic
183C8×C61C2×#4111yescharacteristic
184C4×#510—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61C4×D812yes—
188C22×C61C22×D811yescharacteristic
189C2×D61—42no—
190C2×D61—81no—
191C2×D61—81no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—44no—
196C4×C61—82no—
197C4×C61C4×D812yes—
198C4×C61#51012yescomplemented
199C4×C61C2×C4×D411yescharacteristic
200C4×C61C2×#13511yescharacteristic
201Dic61—42no—
202Dic61—81no—
203Dic61—81no—
204C2×#510—611no—
205C4×#135—611no—
206C2×C4×Q16D6111yescharacteristic, complemented
207#2176—612no—
208#2175—612no—
209C4×Q32—612no—
210C4×SD32—612no—
211#2159—611no—
212#2141—611no—
213#2139—611no—
214C4×M32—611no—
215C2×C61—22no—
216C2×C61C2×C4×D811yescharacteristic
217C2×C61C2×#51011yescharacteristic
218C2×C61#341411yescharacteristic
219D61—82no—
220C2×#135—611no—
221C22×Q16C2×D6111yescharacteristic
222C4×#41—1221no—
223C2×C4×Q8—21no—
224#510—618no—
225C2×Q32—612no—
226C2×SD32—612no—
227C2×M32—611no—
228C2×M32—611no—
229C4×Q16—21no—
230C4×Q16—21no—
231C4×Q16—611no—
232C4×Q16—611no—
233C4×Q16C2×D6112yes—
234C4×Q16C2×D6112yes—
235C4×SD16—1221no—
236C4×SD16—1221no—
237C4×D8—611no—
238C4×D8—611no—
239#427—611no—
240C2×#107C2×D6111yescharacteristic
241#416—1221no—
242C2×#103—21no—
243C2×C4×C8C2×D6111yescharacteristic
244#367—612no—
245#366—612no—
246#358—612no—
247#358—612no—
248#358—612no—
249#357—612no—
250#346—612no—
251C4×C16—612no—
252C61C4×#51011yescharacteristic, complemented, Sylow
253C2×#41—1221no—
254C22×Q8—21no—
255#135—614no—
256#135—1222no—
257C2×Q16—22no—
258C2×Q16—21no—
259C2×Q16—611no—
260C2×Q16C4×D6114yescomplemented
261C2×Q16C22×D6112yes—
262C2×SD16—1221no—
263C2×D8—611no—
264C22×C8C22⋊D6111yescharacteristic
265C22×C8C22×D6111yescharacteristic
266C4×Q8—22no—
267C4×Q8—22no—
268C4×Q8—41no—
269C4×Q8—41no—
270C4×Q8—1221no—
271C4×Q8—1221no—
272C4×D4—1221no—
273C4×D4—1221no—
274C4×D4—2441no—
275C4×D4—2441no—
276#117—1221no—
277#117—2441no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—41no—
280C2×C42—41no—
281C2×C42—2441no—
282C2×C42C22⋊D6111yescharacteristic
283Q32—618no—
284SD32—618no—
285M32—614no—
286M32—1222no—
287C2×C16—612no—
288C2×C16—612no—
289#107—21no—
290#107—611no—
291#107—611no—
292#107C22×D6112yes—
293#106—1221no—
294#103—22no—
295#103—22no—
296#103—1221no—
297#103—1221no—
298#102—1221no—
299#102—1221no—
300C4×C8C22⋊D6111yescharacteristic
301C4×C8C22⋊D6111yescharacteristic
302C4×C8C22×D6111yescharacteristic
303C4×C8C22×D6111yescharacteristic
304#41—1224no—
305#41—2442no—
306C2×Q8—22no—
307C2×Q8—24no—
308C2×Q8—41no—
309C2×Q8—42no—
310C2×Q8—1221no—
311C2×D4—1221no—
312C2×D4—2441no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4#1175819911yescharacteristic
319C22×C4#1175819911yescharacteristic
320C22×C4C2×C22⋊D6111yescharacteristic
321Q16—22no—
322Q16—24no—
323Q16—612no—
324Q16—1221no—
325Q16C2×C4×D6114yes—
326SD16—1224no—
327D8—612no—
328D8—1221no—
329C2×C8—22no—
330C2×C8C2×C4×D6112yes—
331C2×C8#1175822212yes—
332C2×C8C2×C22⋊D6111yescharacteristic
333C2×C8C2×C22⋊D6111yescharacteristic
334C2×C8C2×C22⋊D6111yescharacteristic
335C2×C8C23×D6111yescharacteristic
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C22⋊C4—2441no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C42—42no—
348C42—42no—
349C42—2441no—
350C42—2441no—
351C42—2441no—
352C42#1175819911yescharacteristic
353C42#1175819911yescharacteristic
354C42C2×C22⋊D6111yescharacteristic
355C42C2×C22⋊D6111yescharacteristic
356C16—614no—
357C16—1222no—
358C23—2441no—
359C23C2×#1175819911yescharacteristic
360Q8—24no—
361Q8—42no—
362Q8—44no—
363Q8—1222no—
364Q8—2441no—
365D4—1222no—
366D4—2444no—
367D4—2441no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—82no—
374C2×C4—4882no—
375C2×C4—4882no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2444no—
380C2×C4C4×C22⋊D6112yes—
381C2×C4C2×#1175819911yescharacteristic
382C2×C4C2×#1175819911yescharacteristic
383C2×C4C2×#1175819911yescharacteristic
384C2×C4C2×#1175819911yescharacteristic
385C2×C4C2×#1175819911yescharacteristic
386C2×C4#1451979712yes—
387C2×C4C22×C22⋊D6111yescharacteristic
388C8—21no—
389C8—21no—
390C8C4×C22⋊D6112yes—
391C8C22×C4×D6111yescharacteristic
392C8C2×#1175822211yescharacteristic
393C22—21no—
394C22—21no—
395C22—4881no—
396C22—4881no—
397C22—2442no—
398C22C4×#1175819912yes—
399C22C22×#1175819911yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—82no—
405C4—4881no—
406C4—4881no—
407C4—2442no—
408C4C4×#1175819912yes—
409C4#1684020312yesdirect product factor
410C4C2×C4×C22⋊D6111yescharacteristic
411C4C2×#1451979711yescharacteristic
412C2—22no—
413C2—4882no—
414C2C2×C4×#1175819911yescharacteristic
415C2C2×#1684020311yescharacteristic
416C2#2145895311yescharacteristic
subgroupG/H
centerC2×C4C2×#11758199
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC2×C4×Q16×C61C2
socleC22×C61C22×D8
prime radicalC2×#14519799C22
cosocleC2×C8×C61C24
hypercenterC2×C4×Q16D61
hypocenterC61C4×#510
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #21447688C2semidirect
4. #21447681C2semidirect
5. C4×#14519723C2semidirect
6. C4×#14519720C2semidirect
7. #21447605C2semidirect
8. #21447539C2semidirect
10. C4×#14519717C2semidirect
11. C2×C4×Q16×C61C2semidirect
14. #16840203C4direct (N × H)
59. #14519723C2×C4semidirect
60. #14519720C2×C4semidirect
62. #14519717C2×C4semidirect
75. C2×Q16×C61C2×C4semidirect
198. C4×C61#510semidirect
206. C2×C4×Q16D61semidirect
252. C61C4×#510semidirect
260. C2×Q16C4×D61semidirect
409. C4#16840203direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402032
C4×#145197992
#214476882
#214476812
C4×#145197232
C4×#145197202
#214476052
#214475392
#214475292
C4×#145197172
C2×C4×Q16×C612
C4×#51061