Finite Group Databasebeta

← C23×#9652 #19157278

Subgroups — C23×#9652 #19157278

Order 5888.

704 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#388C211yesmaximal, characteristic
2C23×#1797C211yesmaximal, characteristic, complemented
3C23×#1749C211yesmaximal, characteristic, complemented
4C2×C23×#324C212yesmaximal, complemented
5C2×C23×#323C212yesmaximal
6C22×C4⋊C4×C23C2211yescharacteristic
7C22×C22⋊C4×C23C411yescharacteristic
8C22×C22⋊C4×C23C411yescharacteristic
9C22×C22⋊C4×C23C2211yescharacteristic
10C22×C42×C23C2211yescharacteristic
11C2×C23×C4⋊C8—21no—
12C2×C23×C22⋊C8C2212yes—
13C2×C23×C22⋊C8C2212yes—
14C2×C23×#97—21no—
15C23×#388—21no—
16C23×#388—21no—
17C23×#388—21no—
18C23×#388—21no—
19C2×C23×#95C411yescharacteristic
20C2×C23×#95C411yescharacteristic
21C23×#336—21no—
22C23×#336—21no—
23C23×#324—24no—
24C23×#323—24no—
25C25×C23C2×C411yescharacteristic
26C23×C4×C23C2×C411yescharacteristic
27C23×C4×C23C2×C411yescharacteristic
28C23×C4×C23C2×C411yescharacteristic
29C23×C4×C23C2×C411yescharacteristic
30C23×C4×C23C2×C411yescharacteristic
31C23×C4×C23C2311yescharacteristic
32C22×C8×C23—22no—
33C22×C8×C23—22no—
34C2×C4⋊C4×C23—22no—
35C2×C4⋊C4×C23—21no—
36C2×C4⋊C4×C23—21no—
37C2×C4⋊C4×C23—22no—
38C2×C22⋊C4×C23—22no—
39C2×C22⋊C4×C23—21no—
40C2×C22⋊C4×C23—21no—
41C2×C22⋊C4×C23—22no—
42C2×C22⋊C4×C23—21no—
43C2×C22⋊C4×C23—21no—
44C2×C22⋊C4×C23—22no—
45C2×C22⋊C4×C23—21no—
46C2×C22⋊C4×C23—21no—
47C2×C22⋊C4×C23—22no—
48C2×C22⋊C4×C23—42no—
49C2×C42×C23—42no—
50C2×C42×C23D411yescharacteristic
51C2×C42×C23D411yescharacteristic
52C2×C42×C23D411yescharacteristic
53C2×C42×C23D411yescharacteristic
54C23×C4⋊C8—42no—
55C23×C22⋊C8—22no—
56C23×C22⋊C8—22no—
57C23×C22⋊C8—22no—
58C23×C22⋊C8D414yes—
59C23×#97—42no—
60C23×#95—21no—
61C23×#95—21no—
62C23×#95—21no—
63C23×#95—21no—
64C24×C23—21no—
65C24×C23—21no—
66C24×C23—22no—
67C24×C23—22no—
68C24×C23—41no—
69C24×C23—41no—
70C24×C23—41no—
71C24×C23—41no—
72C24×C23M1612yes—
73C24×C23C22×C411yescharacteristic
74C22×C4×C23—21no—
75C22×C4×C23—22no—
76C22×C4×C23—21no—
77C22×C4×C23—21no—
78C22×C4×C23—21no—
79C22×C4×C23—22no—
80C22×C4×C23—22no—
81C22×C4×C23—22no—
82C22×C4×C23—21no—
83C22×C4×C23—21no—
84C22×C4×C23—22no—
85C22×C4×C23—22no—
86C22×C4×C23—41no—
87C22×C4×C23—41no—
88C22×C4×C23—41no—
89C22×C4×C23—41no—
90C22×C4×C23—41no—
91C22×C4×C23—41no—
92C22×C4×C23—41no—
93C22×C4×C23—41no—
94C22×C4×C23—41no—
95C22×C4×C23C22⋊C411yescharacteristic
96C22×C4×C23C22⋊C411yescharacteristic
97C22×C4×C23C22⋊C411yescharacteristic
98C22×C4×C23C22⋊C411yescharacteristic
99C22×C4×C23M1612yes—
100C22×C4×C23C2×D411yescharacteristic
101C22×C4×C23C2×D411yescharacteristic
102C22×C4×C23C2×D412yes—
103C22×C4×C23#4112yes—
104C2×C8×C23—24no—
105C2×C8×C23—42no—
106C2×C8×C23—42no—
107C2×C8×C23—42no—
108C2×C8×C23—42no—
109C2×C8×C23—42no—
110C4⋊C4×C23—42no—
111C4⋊C4×C23—41no—
112C4⋊C4×C23—41no—
113C22⋊C4×C23—24no—
114C22⋊C4×C23—24no—
115C22⋊C4×C23—42no—
116C22⋊C4×C23—42no—
117C22⋊C4×C23—42no—
118C22⋊C4×C23—41no—
119C22⋊C4×C23—41no—
120C42×C23—22no—
121C42×C23—22no—
122C42×C23—41no—
123C42×C23—41no—
124#9652C2311yesmaximal, characteristic, direct product factor, Sylow
125C23×C23—21no—
126C23×C23—21no—
127C23×C23—21no—
128C23×C23—21no—
129C23×C23—22no—
130C23×C23—24no—
131C23×C23—42no—
132C23×C23—42no—
133C23×C23—42no—
134C23×C23—42no—
135C23×C23—41no—
136C23×C23—41no—
137C23×C23—41no—
138C23×C23—41no—
139C23×C23—41no—
140C23×C23—41no—
141C23×C23—42no—
142C23×C23—82no—
143C23×C23—82no—
144C23×C23—82no—
145C23×C23—82no—
146C23×C23C2×C22⋊C411yescharacteristic
147C23×C23C4×D412yes—
148C23×C23C2×M1611yescharacteristic
149C23×C23C2×M1611yescharacteristic
150C23×C23#13112yes—
151C2×C4×C23—21no—
152C2×C4×C23—21no—
153C2×C4×C23—21no—
154C2×C4×C23—21no—
155C2×C4×C23—21no—
156C2×C4×C23—21no—
157C2×C4×C23—21no—
158C2×C4×C23—21no—
159C2×C4×C23—22no—
160C2×C4×C23—21no—
161C2×C4×C23—21no—
162C2×C4×C23—21no—
163C2×C4×C23—21no—
164C2×C4×C23—21no—
165C2×C4×C23—21no—
166C2×C4×C23—21no—
167C2×C4×C23—24no—
168C2×C4×C23—42no—
169C2×C4×C23—42no—
170C2×C4×C23—44no—
171C2×C4×C23—42no—
172C2×C4×C23—42no—
173C2×C4×C23—41no—
174C2×C4×C23—41no—
175C2×C4×C23—42no—
176C2×C4×C23—41no—
177C2×C4×C23—41no—
178C2×C4×C23—41no—
179C2×C4×C23—41no—
180C2×C4×C23—41no—
181C2×C4×C23—41no—
182C2×C4×C23—82no—
183C2×C4×C23—82no—
184C2×C4×C23#9912yes—
185C2×C4×C23#12112yes—
186C2×C4×C23#12411yescharacteristic
187C2×C4×C23#12711yescharacteristic
188C8×C23—44no—
189C8×C23—82no—
190C2×#388C2×C2311yescharacteristic
191#1797C2×C2311yescharacteristic, complemented
192#1749C2×C2311yescharacteristic, complemented
193C2×#324C2×C2312yescomplemented
194C2×#323C2×C2312yes—
195C22×C23—22no—
196C22×C23—22no—
197C22×C23—21no—
198C22×C23—21no—
199C22×C23—21no—
200C22×C23—21no—
201C22×C23—22no—
202C22×C23—22no—
203C22×C23—42no—
204C22×C23—42no—
205C22×C23—42no—
206C22×C23—84no—
207C22×C23—84no—
208C22×C23—81no—
209C22×C23—81no—
210C22×C23—81no—
211C22×C23—81no—
212C22×C23#39011yescharacteristic
213C22×C23#40711yescharacteristic
214C22×C23#40811yescharacteristic
215C22×C23C2×#9911yescharacteristic
216C22×C23#41011yescharacteristic
217C22×C23#41311yescharacteristic
218C22×C23#41311yescharacteristic
219C22×C23#43512yes—
220C22×C23#43512yes—
221C4×C23—22no—
222C4×C23—21no—
223C4×C23—21no—
224C4×C23—22no—
225C4×C23—42no—
226C4×C23—41no—
227C4×C23—41no—
228C4×C23—41no—
229C4×C23—81no—
230C4×C23—81no—
231C22×C4⋊C4C22×C2311yescharacteristic
232C22×C22⋊C4C4×C2311yescharacteristic
233C22×C22⋊C4C4×C2311yescharacteristic
234C22×C22⋊C4C22×C2311yescharacteristic
235C22×C42C22×C2311yescharacteristic
236C2×C4⋊C8—21no—
237C2×C22⋊C8C22×C2312yes—
238C2×C22⋊C8C22×C2312yes—
239C2×#97—21no—
240#388—21no—
241#388—21no—
242#388—21no—
243#388—21no—
244C2×#95C4×C2311yescharacteristic
245C2×#95C4×C2311yescharacteristic
246#336—21no—
247#336—21no—
248#324—24no—
249#323—24no—
250C2×C23—22no—
251C2×C23—22no—
252C2×C23—82no—
253C2×C23#146411yescharacteristic
254C2×C23#146511yescharacteristic
255C2×C23#146811yescharacteristic
256C2×C23#147311yescharacteristic
257C2×C23#195511yescharacteristic
258C2×C23#196411yescharacteristic
259C2×C23#196711yescharacteristic
260C25C2×C4×C2311yescharacteristic
261C23×C4C2×C4×C2311yescharacteristic
262C23×C4C2×C4×C2311yescharacteristic
263C23×C4C2×C4×C2311yescharacteristic
264C23×C4C2×C4×C2311yescharacteristic
265C23×C4C2×C4×C2311yescharacteristic
266C23×C4C23×C2311yescharacteristic
267C22×C8—22no—
268C22×C8—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—42no—
284C2×C42—42no—
285C2×C42D4×C2311yescharacteristic
286C2×C42D4×C2311yescharacteristic
287C2×C42D4×C2311yescharacteristic
288C2×C42D4×C2311yescharacteristic
289C4⋊C8—42no—
290C22⋊C8—22no—
291C22⋊C8—22no—
292C22⋊C8—22no—
293C22⋊C8D4×C2314yes—
294#97—42no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95—21no—
299C23#965211yescharacteristic, direct product factor, Sylow
300C24—21no—
301C24—21no—
302C24—22no—
303C24—22no—
304C24—41no—
305C24—41no—
306C24—41no—
307C24—41no—
308C24M16×C2312yes—
309C24C22×C4×C2311yescharacteristic
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C22⋊C4×C2311yescharacteristic
332C22×C4C22⋊C4×C2311yescharacteristic
333C22×C4C22⋊C4×C2311yescharacteristic
334C22×C4C22⋊C4×C2311yescharacteristic
335C22×C4M16×C2312yes—
336C22×C4C2×D4×C2311yescharacteristic
337C22×C4C2×D4×C2311yescharacteristic
338C22×C4C2×D4×C2312yes—
339C22×C4#41×C2312yes—
340C2×C8—24no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C42—22no—
357C42—22no—
358C42—41no—
359C42—41no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—22no—
365C23—24no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—82no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23C2×C22⋊C4×C2311yescharacteristic
382C23C4×D4×C2312yes—
383C23C2×M16×C2311yescharacteristic
384C23C2×M16×C2311yescharacteristic
385C23C23×#13112yes—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—24no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4C23×#9912yes—
420C2×C4C23×#12112yes—
421C2×C4C23×#12411yescharacteristic
422C2×C4C23×#12711yescharacteristic
423C8—44no—
424C8—82no—
425C22—22no—
426C22—22no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—22no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—84no—
437C22—84no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22C23×#39011yescharacteristic
443C22C23×#40711yescharacteristic
444C22C23×#40811yescharacteristic
445C22C2×C23×#9911yescharacteristic
446C22C23×#41011yescharacteristic
447C22C23×#41311yescharacteristic
448C22C23×#41311yescharacteristic
449C22C23×#43512yes—
450C22C23×#43512yes—
451C4—22no—
452C4—21no—
453C4—21no—
454C4—22no—
455C4—42no—
456C4—41no—
457C4—41no—
458C4—41no—
459C4—81no—
460C4—81no—
461C2—22no—
462C2—22no—
463C2—82no—
464C2C23×#146411yescharacteristic
465C2C23×#146511yescharacteristic
466C2C23×#146811yescharacteristic
467C2C23×#147311yescharacteristic
468C2C23×#195511yescharacteristic
469C2C23×#196411yescharacteristic
470C2C23×#196711yescharacteristic
subgroupG/H
center, socleC23×C23C2×C22⋊C4
commutatorC24C22×C4×C23
Frattini, cosocleC23×C4C23×C23
prime radicalC25×C23C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C22×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#1797C2semidirect
3. C23×#1749C2semidirect
4. C2×C23×#324C2semidirect
124. #9652C23direct (N × H)
191. #1797C2×C23semidirect
192. #1749C2×C23semidirect
193. C2×#324C2×C23semidirect
299. C23#9652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3882
C23×#17972
C23×#17492
C2×C23×#3242
C2×C23×#3232
#965223