Finite Group Databasebeta

← C4×#16813594 #28393083

Subgroups — C4×#16813594 #28393083

Order 14464.

824 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813594C211yesmaximal, characteristic
2C2×C4×C22⋊D113C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D113C211yesmaximal, characteristic, complemented
4C22×C4×Dic113C211yesmaximal, characteristic, complemented
5#20298498C211yesmaximal, characteristic, complemented
6#20298493C211yesmaximal, characteristic, complemented
7#20298492C211yesmaximal, characteristic, complemented
8#20298488C211yesmaximal, characteristic, complemented
9#20298478C211yesmaximal, characteristic, complemented
10#20298475C211yesmaximal, characteristic, complemented
11#20298456C211yesmaximal, characteristic, complemented
12C4×#14268626C211yesmaximal, characteristic, complemented
13C4×#14268624C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic113C211yesmaximal, characteristic, complemented
15C2×C4×D4×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113C2211yescharacteristic
17C22×C22⋊D113C2211yescharacteristic
18C23×Dic113C2211yescharacteristic
19C23×Dic113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21#16813594C418yesdirect product factor
22C4×C22⋊D113—24no—
23C4×C22⋊D113—24no—
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268626C2211yescharacteristic
27C2×#14268626C2211yescharacteristic
28C2×C22⋊Dic113C2211yescharacteristic
29C2×C22⋊Dic113C2211yescharacteristic
30C2×C22⋊Dic113C2211yescharacteristic
31C2×C22⋊Dic113C2211yescharacteristic
32C2×#14268624C2211yescharacteristic
33C2×#14268624C2211yescharacteristic
34C2×#14268624C2211yescharacteristic
35C2×#14268624C2211yescharacteristic
36C2×C4×Dic113—24no—
37C2×C4×Dic113C2211yescharacteristic
38C2×C4×Dic113C2211yescharacteristic
39C2×C4×Dic113C2211yescharacteristic
40C2×C4×Dic113C2211yescharacteristic
41C2×C4×Dic113C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46#16813529C2211yescharacteristic
47#16813529C2211yescharacteristic
48C22×D4×C113C2211yescharacteristic
49C23×C4×C113C2211yescharacteristic
50C23×C4×C113C2211yescharacteristic
51C4×D4×C113—24no—
52C2×C4⋊C4×C113C2211yescharacteristic
53C2×C22⋊C4×C113C2211yescharacteristic
54C2×C22⋊C4×C113C2211yescharacteristic
55C2×C42×C113C2211yescharacteristic
56C23×D113C2311yescharacteristic
57C2×C22⋊D113—22no—
58C2×C22⋊D113—22no—
59C2×C22⋊D113—22no—
60C2×C22⋊D113—22no—
61C2×C22⋊D113C2×C414yescomplemented
62C2×C22⋊D113C2×C414yescomplemented
63C22×Dic113—22no—
64C22×Dic113—22no—
65C22×Dic113—22no—
66C22×Dic113—22no—
67C22×Dic113—22no—
68C22×Dic113C2×C414yescomplemented
69C22×Dic113C2311yescharacteristic
70C22×Dic113C2311yescharacteristic
71C22×Dic113C2311yescharacteristic
72C22×Dic113C2311yescharacteristic
73C22×Dic113C2311yescharacteristic
74C22×Dic113C2311yescharacteristic
75C22×Dic113C2311yescharacteristic
76C2×C4×D113—22no—
77C2×C4×D113—22no—
78C2×C4×D113—22no—
79#14268626—22no—
80#14268626—22no—
81#14268626—22no—
82#14268626C2×C414yescomplemented
83C22⋊Dic113—22no—
84C22⋊Dic113—22no—
85C22⋊Dic113—22no—
86C22⋊Dic113C2×C414yescomplemented
87#14268624—22no—
88#14268624—22no—
89#14268624—22no—
90#14268624C2×C414yescomplemented
91C4×Dic113—22no—
92C4×Dic113—22no—
93C4×Dic113—22no—
94C4×Dic113—22no—
95C4×Dic113D414yescomplemented
96C24×C113C2311yescharacteristic
97C24×C113C2311yescharacteristic
98C2×D4×C113—22no—
99C2×D4×C113—22no—
100C2×D4×C113C2×C414yescomplemented
101C22×C4×C113—22no—
102C22×C4×C113—22no—
103C22×C4×C113—22no—
104C22×C4×C113—22no—
105C22×C4×C113—22no—
106C22×C4×C113D414yescomplemented
107C22×C4×C113C2311yescharacteristic
108C22×C4×C113C2311yescharacteristic
109C22×C4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
111C22×C4×C113C2311yescharacteristic
112C4⋊C4×C113—22no—
113C22⋊C4×C113—22no—
114C22⋊C4×C113—22no—
115C42×C113—22no—
116C23×C113—21no—
117C23×C113—21no—
118C23×C113—21no—
119C23×C113—21no—
120C23×C113—21no—
121C23×C113—21no—
122C23×C113—21no—
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
126C23×C113C22×C412yes—
127C23×C113C22×C412yes—
128C23×C113C2×D412yes—
129C23×C113#4112yes—
130C23×C113C2411yescharacteristic
131C22×D113—21no—
132C22×D113—21no—
133C22×D113—21no—
134C22×D113—21no—
135C22×D113—21no—
136C22×D113—21no—
137C22×D113C22×C412yes—
138D4×C113—28no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—28no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—21no—
149C2×C4×C113—21no—
150C2×C4×C113—44no—
151C2×C4×C113C22×C412yes—
152C2×C4×C113C2×D412yes—
153C2×C4×C113C2×D412yes—
154C2×C4×C113C2×D412yes—
155C2×C4×C113#4112yes—
156C22⋊D113—28no—
157C22⋊D113—28no—
158C2×Dic113—28no—
159C2×Dic113—21no—
160C2×Dic113—21no—
161C2×Dic113—21no—
162C2×Dic113—21no—
163C2×Dic113—21no—
164C2×Dic113—21no—
165C2×Dic113—21no—
166C2×Dic113—21no—
167C2×Dic113—28no—
168C2×Dic113—21no—
169C2×Dic113—21no—
170C2×Dic113—21no—
171C2×Dic113—21no—
172C2×Dic113—21no—
173C2×Dic113—21no—
174C2×Dic113C22×C412yes—
175C2×Dic113C22×C412yes—
176C2×Dic113C22×C412yes—
177C2×Dic113C2×D412yes—
178C2×Dic113C2×D412yes—
179C2×Dic113#4112yes—
180C2×Dic113#4112yes—
181C4×D113—44no—
182C22×C113—22no—
183C22×C113—22no—
184C22×C113—22no—
185C22×C113—22no—
186C22×C113—22no—
187C22×C113—22no—
188C22×C113—22no—
189C22×C113—22no—
190C22×C113—22no—
191C22×C113—41no—
192C22×C113—41no—
193C22×C113—41no—
194C22×C113—41no—
195C22×C113C4×D414yescomplemented
196C22×C113C23×C411yescharacteristic
197C22×C113C22×D411yescharacteristic
198C22×C113C22×D411yescharacteristic
199C22×C113C2×#4111yescharacteristic
200C22×C113C2×#4111yescharacteristic
201C22×C113C2×#4111yescharacteristic
202C22×C113C2×#4111yescharacteristic
203C2×D113—22no—
204C2×D113—22no—
205C2×D113—22no—
206C2×D113—41no—
207C2×D113—41no—
208C2×D113—41no—
209C2×D113—41no—
210C4×C113—22no—
211C4×C113—22no—
212C4×C113—41no—
213C4×C113—41no—
214C4×C113#12114yescomplemented
215Dic113—22no—
216Dic113—22no—
217Dic113—22no—
218Dic113—22no—
219Dic113—41no—
220Dic113—41no—
221Dic113C4×D414yescomplemented
222C2×C113—24no—
223C2×C113—42no—
224C2×C113C2×C4×D411yescharacteristic
225C2×C113C2×C4×D411yescharacteristic
226C2×C113C4×#4111yescharacteristic
227C2×C113C2×#12111yescharacteristic
228C2×C113#52511yescharacteristic
229C2×C113#52911yescharacteristic
230C2×C113#53211yescharacteristic
231D113—42no—
232C4×#121—1131nomaximal, Sylow
233C113C4×#12111yescharacteristic, complemented, Sylow
234C2×#121—1131no—
235C2×C4×D4—1131no—
236C2×C4×D4—1131no—
237C2×C4×D4D11311yescharacteristic, complemented
238C22×C42—1131no—
239#390—1131no—
240#389—1131no—
241#388—1131no—
242#388—1131no—
243#386—1131no—
244#386—1131no—
245#380—1131no—
246C4×C4⋊C4—1131no—
247C4×C22⋊C4—1131no—
248C4×C22⋊C4—1131no—
249C22×D4—1131no—
250C22×D4—1131no—
251C22×D4C2×D11311yescharacteristic
252C23×C4—1131no—
253C23×C4—1131no—
254C23×C4—1131no—
255C23×C4C2×D11311yescharacteristic
256C23×C4C2×D11311yescharacteristic
257#121—1138no—
258C4×D4—24no—
259C4×D4—2264no—
260C4×D4—2264no—
261C2×C4⋊C4—1131no—
262C2×C4⋊C4—1131no—
263C2×C4⋊C4—1131no—
264C2×C4⋊C4—1131no—
265C2×C4⋊C4C2×D11311yescharacteristic
266C2×C22⋊C4—1131no—
267C2×C22⋊C4—1131no—
268C2×C22⋊C4—1131no—
269C2×C22⋊C4—1131no—
270C2×C22⋊C4—1131no—
271C2×C22⋊C4—1131no—
272C2×C22⋊C4—1131no—
273C2×C22⋊C4—1131no—
274C2×C22⋊C4C2×D11311yescharacteristic
275C2×C22⋊C4C2×D11311yescharacteristic
276C2×C42—1131no—
277C2×C42—1131no—
278C2×C42—1131no—
279C2×C42—1131no—
280C2×C42—1131no—
281C2×C42—2264no—
282C2×C42C2×D11311yescharacteristic
283#95—1131no—
284#95—1131no—
285#95—1131no—
286#95—1131no—
287#95—1131no—
288#95—1131no—
289C24—1131no—
290C24C22×D11311yescharacteristic
291C24C22×D11311yescharacteristic
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—1134no—
295C2×D4—1134no—
296C2×D4—2262no—
297C2×D4—2262no—
298C2×D4—2262no—
299C2×D4—2262no—
300C2×D4C4×D11314yescomplemented
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—1131no—
307C22×C4—1134no—
308C22×C4—1131no—
309C22×C4—1131no—
310C22×C4—1131no—
311C22×C4—1131no—
312C22×C4—1131no—
313C22×C4—1131no—
314C22×C4—2262no—
315C22×C4—2262no—
316C22×C4—2262no—
317C22×C4—2262no—
318C22×C4—2262no—
319C22×C4—2262no—
320C22×C4—2262no—
321C22×C4—2262no—
322C22×C4C22⋊D11314yescomplemented
323C22×C4C22×D11311yescharacteristic
324C22×C4C22×D11311yescharacteristic
325C22×C4C22×D11311yescharacteristic
326C22×C4C22×D11311yescharacteristic
327C22×C4C22×D11311yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—1134no—
330C4⋊C4—2262no—
331C4⋊C4—2262no—
332C4⋊C4—2262no—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—1134no—
336C22⋊C4—1134no—
337C22⋊C4—2262no—
338C22⋊C4—2262no—
339C22⋊C4—2262no—
340C22⋊C4—2262no—
341C22⋊C4—2262no—
342C22⋊C4—2262no—
343C42—22no—
344C42—1134no—
345C42—2262no—
346C42—2262no—
347C42—2262no—
348C42—2262no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—1132no—
360C23—2261no—
361C23—2261no—
362C23—2261no—
363C23—2261no—
364C23—2261no—
365C23—2261no—
366C23C2×C4×D11312yes—
367C23C2×C4×D11312yes—
368C23C2×C22⋊D11312yes—
369C23#1426864712yes—
370C23C23×D11311yescharacteristic
371D4—28no—
372D4—2268no—
373D4—2268no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—28no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—1132no—
387C2×C4—1132no—
388C2×C4—1132no—
389C2×C4—1132no—
390C2×C4—1132no—
391C2×C4—1132no—
392C2×C4—1132no—
393C2×C4—4524no—
394C2×C4—2268no—
395C2×C4—2261no—
396C2×C4—2261no—
397C2×C4—2261no—
398C2×C4—2261no—
399C2×C4—2261no—
400C2×C4—2261no—
401C2×C4—2268no—
402C2×C4—2261no—
403C2×C4—2261no—
404C2×C4—2261no—
405C2×C4—2261no—
406C2×C4—2261no—
407C2×C4—2261no—
408C2×C4—2261no—
409C2×C4—2261no—
410C2×C4C2×C4×D11312yes—
411C2×C4D4×D11312yes—
412C2×C4C2×C22⋊D11312yes—
413C2×C4C2×C22⋊D11312yes—
414C2×C4#1426864612yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—4521no—
429C22—4521no—
430C22—4521no—
431C22—4521no—
432C22—2262no—
433C22—2262no—
434C22—2262no—
435C22C4×C22⋊D11314yescomplemented
436C22C22×C4×D11311yescharacteristic
437C22C2×D4×D11311yescharacteristic
438C22C22×C22⋊D11311yescharacteristic
439C22#41×D11311yescharacteristic
440C22#41×D11311yescharacteristic
441C22C2×#1426864611yescharacteristic
442C22C2×#1426864711yescharacteristic
443C4—22no—
444C4—22no—
445C4—41no—
446C4—41no—
447C4—1134no—
448C4—4521no—
449C4—4521no—
450C4—2262no—
451C4—2262no—
452C4—2262no—
453C4—2262no—
454C4#1681359414yesdirect product factor
455C2—24no—
456C2—42no—
457C2—4522no—
458C2C4×D4×D11311yescharacteristic
459C2C2×C4×C22⋊D11311yescharacteristic
460C2C4×#1426864611yescharacteristic
461C2C2×#1681359411yescharacteristic
462C2#2029910711yescharacteristic
463C2#2029912811yescharacteristic
464C2#2029914411yescharacteristic
subgroupG/H
centerC22×C4C22×D113
commutatorC22×C113C23×C4
FrattiniC23C23×D113
FittingC2×C4×D4×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813594C2
hypercenterC2×C4×D4D113
hypocenterC113C4×#121
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D113C2semidirect
3. C2×C4×C22⋊D113C2semidirect
4. C22×C4×Dic113C2semidirect
5. #20298498C2semidirect
6. #20298493C2semidirect
7. #20298492C2semidirect
8. #20298488C2semidirect
9. #20298478C2semidirect
10. #20298475C2semidirect
11. #20298456C2semidirect
12. C4×#14268626C2semidirect
13. C4×#14268624C2semidirect
14. C4×C22⋊Dic113C2semidirect
15. C2×C4×D4×C113C2semidirect
21. #16813594C4direct (N × H)
61. C2×C22⋊D113C2×C4semidirect
62. C2×C22⋊D113C2×C4semidirect
68. C22×Dic113C2×C4semidirect
82. #14268626C2×C4semidirect
86. C22⋊Dic113C2×C4semidirect
90. #14268624C2×C4semidirect
95. C4×Dic113D4semidirect
100. C2×D4×C113C2×C4semidirect
106. C22×C4×C113D4semidirect
195. C22×C113C4×D4semidirect
214. C4×C113#121semidirect
221. Dic113C4×D4semidirect
233. C113C4×#121semidirect
237. C2×C4×D4D113semidirect
300. C2×D4C4×D113semidirect
322. C22×C4C22⋊D113semidirect
435. C22C4×C22⋊D113semidirect
454. C4#16813594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168135942
C2×C4×C22⋊D1132
C22×C4×Dic1132
#202984982
#202984932
#202984922
#202984882
#202984782
#202984752
#202984562
C4×#142686262
C4×#142686242
C4×C22⋊Dic1132
C2×C4×D4×C1132
C4×#121113