Finite Group Databasebeta

← C4×C23×#562 #19181978

Subgroups — C4×C23×#562 #19181978

Order 5888.

2248 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#562C211yesmaximal, characteristic
2C23×#2382C211yesmaximal, characteristic, complemented
3C23×#2379C212yesmaximal, complemented
4C23×#2378C214yesmaximal, complemented
5C23×#2377C214yesmaximal, complemented
6C23×#2376C214yesmaximal, complemented
7C4×C23×#125C211yesmaximal, characteristic, complemented
8C4×C23×#124C212yesmaximal, complemented
9C4×C23×C22⋊Q8C214yesmaximal, complemented
10C4×C23×#123C214yesmaximal, complemented
11C4×C23×#121C214yesmaximal, complemented
12C23×#562C4116yesdirect product factor
13C2×C23×#125C2211yescharacteristic
14C2×C23×#124C2212yes—
15C2×C23×#123C2214yes—
16C2×C23×C22⋊Q8C2214yes—
17C2×C23×#121C2214yes—
18C2×C4×Q8×C23C2212yes—
19C2×C4×D4×C23C2214yes—
20C2×C4×D4×C23C2212yes—
21C22×C42×C23C2214yes—
22C23×#391C2214yes—
23C23×#391C2212yes—
24C23×#390C2214yes—
25C23×#390C2212yes—
26C23×#389C2214yes—
27C23×#389C2214yes—
28C23×#389C2212yes—
29C23×#388C2214yes—
30C23×#388C2214yes—
31C23×#388C2214yes—
32C23×#388C2214yes—
33C23×#388C2214yes—
34C23×#388C2214yes—
35C23×#387C2214yes—
36C23×#387C2214yes—
37C23×#387C2214yes—
38C23×#387C2214yes—
39C23×#387C2214yes—
40C23×#386C2214yes—
41C23×#386C2214yes—
42C23×#386C2214yes—
43C23×#385C2214yes—
44C23×#385C2214yes—
45C23×#385C2214yes—
46C23×#382C2212yes—
47C23×#382C2211yescharacteristic
48C23×#381C2214yes—
49C23×#380C2214yes—
50C23×#380C2214yes—
51C4×C4⋊C4×C23C2214yes—
52C4×C4⋊C4×C23C2212yes—
53C4×C4⋊C4×C23C2214yes—
54C4×C22⋊C4×C23C2214yes—
55C4×C22⋊C4×C23C2214yes—
56C4×C22⋊C4×C23C2214yes—
57C43×C23C2211yescharacteristic
58C22×Q8×C23C2312yes—
59C22×D4×C23C2314yes—
60C22×D4×C23C2312yes—
61C23×C4×C23C2314yes—
62C23×C4×C23C2314yes—
63C23×C4×C23C2314yes—
64C23×#125C2×C418yescomplemented
65C23×#124C2×C4116yescomplemented
66C23×#123C2×C4132yescomplemented
67C23×C22⋊Q8C2×C4132yescomplemented
68C23×#121C2×C4132yescomplemented
69C4×Q8×C23—44no—
70C4×D4×C23—48no—
71C4×D4×C23—44no—
72C2×C4⋊C4×C23C2314yes—
73C2×C4⋊C4×C23C2314yes—
74C2×C4⋊C4×C23C2312yes—
75C2×C4⋊C4×C23C2314yes—
76C2×C4⋊C4×C23C2314yes—
77C2×C4⋊C4×C23C2312yes—
78C2×C4⋊C4×C23C2312yes—
79C2×C4⋊C4×C23C2314yes—
80C2×C4⋊C4×C23C2314yes—
81C2×C4⋊C4×C23C2312yes—
82C2×C22⋊C4×C23C2314yes—
83C2×C22⋊C4×C23C2314yes—
84C2×C22⋊C4×C23C2314yes—
85C2×C22⋊C4×C23C2314yes—
86C2×C22⋊C4×C23C2314yes—
87C2×C22⋊C4×C23C2314yes—
88C2×C22⋊C4×C23C2314yes—
89C2×C22⋊C4×C23C2314yes—
90C2×C22⋊C4×C23C2314yes—
91C2×C42×C23—48no—
92C2×C42×C23C2311yescharacteristic
93C2×C42×C23C2312yes—
94C2×C42×C23C2314yes—
95C2×C42×C23C2314yes—
96C2×C42×C23C2312yes—
97C2×C42×C23C2311yescharacteristic
98C2×C42×C23C2314yes—
99C2×C42×C23C2314yes—
100C2×C42×C23C2311yescharacteristic
101C23×#95C2314yes—
102C23×#95C2314yes—
103C23×#95C2314yes—
104C23×#95C2314yes—
105C23×#95C2314yes—
106C23×#95C2314yes—
107C23×#95C2314yes—
108C23×#95C2314yes—
109C23×#95C2314yes—
110C23×#95C2314yes—
111C23×#95C2314yes—
112C24×C23C2414yes—
113C2×Q8×C23—42no—
114C2×Q8×C23—42no—
115C2×Q8×C23C22×C418yes—
116C2×D4×C23—44no—
117C2×D4×C23—42no—
118C2×D4×C23—42no—
119C2×D4×C23—44no—
120C2×D4×C23C22×C4116yes—
121C2×D4×C23C22×C418yes—
122C22×C4×C23—28no—
123C22×C4×C23—28no—
124C22×C4×C23—28no—
125C22×C4×C23—44no—
126C22×C4×C23—44no—
127C22×C4×C23—44no—
128C22×C4×C23—44no—
129C22×C4×C23—44no—
130C22×C4×C23C22×C4116yes—
131C22×C4×C23C2412yes—
132C22×C4×C23C2411yescharacteristic
133C22×C4×C23C2414yes—
134C22×C4×C23C2414yes—
135C22×C4×C23C2414yes—
136C22×C4×C23C2411yescharacteristic
137C22×C4×C23C2412yes—
138C22×C4×C23C2414yes—
139C22×C4×C23C2414yes—
140C22×C4×C23C2411yescharacteristic
141C4⋊C4×C23—42no—
142C4⋊C4×C23—44no—
143C4⋊C4×C23—44no—
144C4⋊C4×C23—44no—
145C4⋊C4×C23—42no—
146C4⋊C4×C23—44no—
147C4⋊C4×C23—42no—
148C4⋊C4×C23C22×C4116yes—
149C4⋊C4×C23C22×C4116yes—
150C4⋊C4×C23C22×C418yes—
151C22⋊C4×C23—44no—
152C22⋊C4×C23—44no—
153C22⋊C4×C23—44no—
154C22⋊C4×C23—44no—
155C22⋊C4×C23—44no—
156C22⋊C4×C23—44no—
157C22⋊C4×C23C22×C4116yes—
158C22⋊C4×C23C22×C4116yes—
159C22⋊C4×C23C22×C4116yes—
160C42×C23—28no—
161C42×C23—28no—
162C42×C23—24no—
163C42×C23—22no—
164C42×C23—44no—
165C42×C23—44no—
166C42×C23—41no—
167C42×C23—42no—
168C42×C23C22×C414yes—
169C4×#562C2311yesmaximal, characteristic, direct product factor, Sylow
170C23×C23—24no—
171C23×C23—24no—
172C23×C23—24no—
173C23×C23—24no—
174C23×C23—24no—
175C23×C23—24no—
176C23×C23C23×C418yes—
177C23×C23C2511yescharacteristic
178Q8×C23—48no—
179D4×C23—416no—
180D4×C23—48no—
181C2×C4×C23—24no—
182C2×C4×C23—24no—
183C2×C4×C23—22no—
184C2×C4×C23—21no—
185C2×C4×C23—21no—
186C2×C4×C23—22no—
187C2×C4×C23—24no—
188C2×C4×C23—24no—
189C2×C4×C23—24no—
190C2×C4×C23—24no—
191C2×C4×C23—22no—
192C2×C4×C23—24no—
193C2×C4×C23—24no—
194C2×C4×C23—21no—
195C2×C4×C23—24no—
196C2×C4×C23—22no—
197C2×C4×C23—22no—
198C2×C4×C23—22no—
199C2×C4×C23—24no—
200C2×C4×C23—24no—
201C2×C4×C23—24no—
202C2×C4×C23—24no—
203C2×C4×C23—416no—
204C2×C4×C23—416no—
205C2×C4×C23—416no—
206C2×C4×C23C23×C412yes—
207C2×C4×C23C23×C414yes—
208C2×C4×C23C23×C418yes—
209C2×C4×C23C23×C418yes—
210C2×C4×C23H(5,𝔽2)14yes—
211C2×C4×C232−1+412yes—
212C2×#562C2×C2311yescharacteristic
213#2382C2×C2311yescharacteristic, complemented
214#2379C2×C2312yescomplemented
215#2378C2×C2314yescomplemented
216#2377C2×C2314yescomplemented
217#2376C2×C2314yescomplemented
218C4×#125C2×C2311yescharacteristic, complemented
219C4×#124C2×C2312yescomplemented
220C4×C22⋊Q8C2×C2314yescomplemented
221C4×#123C2×C2314yescomplemented
222C4×#121C2×C2314yescomplemented
223C22×C23—28no—
224C22×C23—28no—
225C22×C23—28no—
226C22×C23—44no—
227C22×C23—44no—
228C22×C23—44no—
229C22×C23—44no—
230C22×C23C24×C411yescharacteristic
231C22×C23C2×H(5,𝔽2)12yes—
232C22×C23C2×2−1+411yescharacteristic
233C22×C23#58512yes—
234C22×C23#58511yescharacteristic
235C4×C23—28no—
236C4×C23—28no—
237C4×C23—24no—
238C4×C23—22no—
239C4×C23—44no—
240C4×C23—42no—
241C4×C23—44no—
242C4×C23—44no—
243C4×C23—41no—
244C4×C23#56214yesdirect product factor
245#562C4×C23116yesdirect product factor
246C2×#125C22×C2311yescharacteristic
247C2×#124C22×C2312yes—
248C2×#123C22×C2314yes—
249C2×C22⋊Q8C22×C2314yes—
250C2×#121C22×C2314yes—
251C2×C4×Q8C22×C2312yes—
252C2×C4×D4C22×C2314yes—
253C2×C4×D4C22×C2312yes—
254C22×C42C22×C2314yes—
255#391C22×C2312yes—
256#391C22×C2314yes—
257#390C22×C2314yes—
258#390C22×C2312yes—
259#389C22×C2312yes—
260#389C22×C2314yes—
261#389C22×C2314yes—
262#388C22×C2314yes—
263#388C22×C2314yes—
264#388C22×C2314yes—
265#388C22×C2314yes—
266#388C22×C2314yes—
267#388C22×C2314yes—
268#387C22×C2314yes—
269#387C22×C2314yes—
270#387C22×C2314yes—
271#387C22×C2314yes—
272#387C22×C2314yes—
273#386C22×C2314yes—
274#386C22×C2314yes—
275#386C22×C2314yes—
276#385C22×C2314yes—
277#385C22×C2314yes—
278#385C22×C2314yes—
279#382C22×C2311yescharacteristic
280#382C22×C2312yes—
281#381C22×C2314yes—
282#380C22×C2314yes—
283#380C22×C2314yes—
284C4×C4⋊C4C22×C2314yes—
285C4×C4⋊C4C22×C2312yes—
286C4×C4⋊C4C22×C2314yes—
287C4×C22⋊C4C22×C2314yes—
288C4×C22⋊C4C22×C2314yes—
289C4×C22⋊C4C22×C2314yes—
290C43C22×C2311yescharacteristic
291C2×C23—48no—
292C2×C23C4×H(5,𝔽2)12yes—
293C2×C23C4×2−1+411yescharacteristic
294C2×C23C2×#56211yescharacteristic
295C2×C23#352912yes—
296C2×C23#353111yescharacteristic
297C22×Q8C23×C2312yes—
298C22×D4C23×C2314yes—
299C22×D4C23×C2312yes—
300C23×C4C23×C2314yes—
301C23×C4C23×C2314yes—
302C23×C4C23×C2314yes—
303#125C2×C4×C2318yescomplemented
304#124C2×C4×C23116yescomplemented
305#123C2×C4×C23132yescomplemented
306C22⋊Q8C2×C4×C23132yescomplemented
307#121C2×C4×C23132yescomplemented
308C4×Q8—44no—
309C4×D4—48no—
310C4×D4—44no—
311C2×C4⋊C4C23×C2314yes—
312C2×C4⋊C4C23×C2312yes—
313C2×C4⋊C4C23×C2314yes—
314C2×C4⋊C4C23×C2312yes—
315C2×C4⋊C4C23×C2314yes—
316C2×C4⋊C4C23×C2314yes—
317C2×C4⋊C4C23×C2312yes—
318C2×C4⋊C4C23×C2314yes—
319C2×C4⋊C4C23×C2314yes—
320C2×C4⋊C4C23×C2312yes—
321C2×C22⋊C4C23×C2314yes—
322C2×C22⋊C4C23×C2314yes—
323C2×C22⋊C4C23×C2314yes—
324C2×C22⋊C4C23×C2314yes—
325C2×C22⋊C4C23×C2314yes—
326C2×C22⋊C4C23×C2314yes—
327C2×C22⋊C4C23×C2314yes—
328C2×C22⋊C4C23×C2314yes—
329C2×C22⋊C4C23×C2314yes—
330C2×C42—48no—
331C2×C42C23×C2312yes—
332C2×C42C23×C2314yes—
333C2×C42C23×C2314yes—
334C2×C42C23×C2311yescharacteristic
335C2×C42C23×C2312yes—
336C2×C42C23×C2311yescharacteristic
337C2×C42C23×C2314yes—
338C2×C42C23×C2314yes—
339C2×C42C23×C2311yescharacteristic
340#95C23×C2314yes—
341#95C23×C2314yes—
342#95C23×C2314yes—
343#95C23×C2314yes—
344#95C23×C2314yes—
345#95C23×C2314yes—
346#95C23×C2314yes—
347#95C23×C2314yes—
348#95C23×C2314yes—
349#95C23×C2314yes—
350#95C23×C2314yes—
351C23C4×#56211yescharacteristic, direct product factor, Sylow
352C24C24×C2314yes—
353C2×Q8—42no—
354C2×Q8—42no—
355C2×Q8C22×C4×C2318yes—
356C2×D4—44no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—44no—
360C2×D4C22×C4×C23116yes—
361C2×D4C22×C4×C2318yes—
362C22×C4—28no—
363C22×C4—28no—
364C22×C4—28no—
365C22×C4—44no—
366C22×C4—44no—
367C22×C4—44no—
368C22×C4—44no—
369C22×C4—44no—
370C22×C4C22×C4×C23116yes—
371C22×C4C24×C2311yescharacteristic
372C22×C4C24×C2314yes—
373C22×C4C24×C2314yes—
374C22×C4C24×C2314yes—
375C22×C4C24×C2312yes—
376C22×C4C24×C2311yescharacteristic
377C22×C4C24×C2312yes—
378C22×C4C24×C2314yes—
379C22×C4C24×C2314yes—
380C22×C4C24×C2311yescharacteristic
381C4⋊C4—44no—
382C4⋊C4—42no—
383C4⋊C4—44no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—44no—
387C4⋊C4—44no—
388C4⋊C4C22×C4×C23116yes—
389C4⋊C4C22×C4×C23116yes—
390C4⋊C4C22×C4×C2318yes—
391C22⋊C4—44no—
392C22⋊C4—44no—
393C22⋊C4—44no—
394C22⋊C4—44no—
395C22⋊C4—44no—
396C22⋊C4—44no—
397C22⋊C4C22×C4×C23116yes—
398C22⋊C4C22×C4×C23116yes—
399C22⋊C4C22×C4×C23116yes—
400C42—28no—
401C42—28no—
402C42—24no—
403C42—22no—
404C42—44no—
405C42—44no—
406C42—41no—
407C42—42no—
408C42C22×C4×C2314yes—
409C23—24no—
410C23—24no—
411C23—24no—
412C23—24no—
413C23—24no—
414C23—24no—
415C23C23×C4×C2318yes—
416C23C25×C2311yescharacteristic
417Q8—48no—
418D4—416no—
419D4—48no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—21no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—416no—
443C2×C4—416no—
444C2×C4—416no—
445C2×C4C23×C4×C2312yes—
446C2×C4C23×C4×C2314yes—
447C2×C4C23×C4×C2318yes—
448C2×C4C23×C4×C2318yes—
449C2×C4C23×H(5,𝔽2)14yes—
450C2×C4C23×2−1+412yes—
451C22—28no—
452C22—28no—
453C22—28no—
454C22—44no—
455C22—44no—
456C22—44no—
457C22—44no—
458C22C24×C4×C2311yescharacteristic
459C22C2×C23×H(5,𝔽2)12yes—
460C22C2×C23×2−1+411yescharacteristic
461C22C23×#58512yes—
462C22C23×#58511yescharacteristic
463C4—28no—
464C4—28no—
465C4—24no—
466C4—22no—
467C4—44no—
468C4—44no—
469C4—44no—
470C4—42no—
471C4—41no—
472C4C23×#56214yesdirect product factor
473C2—48no—
474C2C4×C23×H(5,𝔽2)12yes—
475C2C4×C23×2−1+411yescharacteristic
476C2C2×C23×#56211yescharacteristic
477C2C23×#352912yes—
478C2C23×#353111yescharacteristic
subgroupG/H
centerC22×C4×C23C24
commutatorC22C24×C4×C23
Frattini, cosocleC23C25×C23
socleC23×C23C25
prime radicalC2×C23×#562C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#2382C2semidirect
3. C23×#2379C2semidirect
4. C23×#2378C2semidirect
5. C23×#2377C2semidirect
6. C23×#2376C2semidirect
7. C4×C23×#125C2semidirect
8. C4×C23×#124C2semidirect
9. C4×C23×C22⋊Q8C2semidirect
10. C4×C23×#123C2semidirect
11. C4×C23×#121C2semidirect
12. C23×#562C4direct (N × H)
64. C23×#125C2×C4semidirect
65. C23×#124C2×C4semidirect
66. C23×#123C2×C4semidirect
67. C23×C22⋊Q8C2×C4semidirect
68. C23×#121C2×C4semidirect
169. C4×#562C23direct (N × H)
213. #2382C2×C23semidirect
214. #2379C2×C23semidirect
215. #2378C2×C23semidirect
216. #2377C2×C23semidirect
217. #2376C2×C23semidirect
218. C4×#125C2×C23semidirect
219. C4×#124C2×C23semidirect
220. C4×C22⋊Q8C2×C23semidirect
221. C4×#123C2×C23semidirect
222. C4×#121C2×C23semidirect
244. C4×C23#562direct (N × H)
245. #562C4×C23direct (N × H)
303. #125C2×C4×C23semidirect
304. #124C2×C4×C23semidirect
305. #123C2×C4×C23semidirect
306. C22⋊Q8C2×C4×C23semidirect
307. #121C2×C4×C23semidirect
351. C23C4×#562direct (N × H)
472. C4C23×#562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#5622
C23×#23822
C23×#23792
C23×#23782
C23×#23772
C23×#23762
C4×C23×#1252
C4×C23×#1242
C4×C23×C22⋊Q82
C4×C23×#1232
C4×C23×#1212
C4×#56223