Finite Group Databasebeta

← C23×#10035 #19157661

Subgroups — C23×#10035 #19157661

Order 5888.

498 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3135C211yesmaximal, characteristic
2C23×#3104C211yesmaximal, characteristic, complemented
3C23×#3103C211yesmaximal, characteristic
4C23×#1985C211yesmaximal, characteristic, complemented
5C23×#1481C211yesmaximal, characteristic, complemented
6C23×#1480C211yesmaximal, characteristic
7C23×#1275C211yesmaximal, characteristic, complemented
8C23×#533C2211yescharacteristic
9C23×#532C2211yescharacteristic
10C2×C4×Q8×C23C2211yescharacteristic
11C23×#491—21no—
12C23×#490—21no—
13C23×#489—21no—
14C23×#489—21no—
15C23×#484—21no—
16C23×#481—21no—
17C23×#477—21no—
18C23×#475—21no—
19C23×#462—21no—
20C23×#460—21no—
21C23×#451—21no—
22C23×#448—21no—
23C4×Q16×C23—22no—
24C4×SD16×C23—22no—
25C23×#431C2211yescharacteristic
26C23×#431C2211yescharacteristic
27C2×C23×C4⋊C8C2211yescharacteristic
28C23×#416—22no—
29C2×C23×#97C2211yescharacteristic
30C23×#336—22no—
31C23×Q8⋊C8—22no—
32C23×D4⋊C8—22no—
33C2×#41×C23—21no—
34C22×Q8×C23D411yescharacteristic
35C2×Q16×C23—22no—
36C2×SD16×C23—22no—
37C22×C8×C23—21no—
38C22×C8×C23D412yes—
39C23×C4⋊Q8D411yescharacteristic
40C23×C4⋊Q8D411yescharacteristic
41C23×C4⋊Q8D411yescharacteristic
42C23×#127D411yescharacteristic
43C23×#125—21no—
44C23×#124—21no—
45C23×C22⋊Q8—21no—
46C23×C22⋊Q8—21no—
47C23×#121—21no—
48C23×#121—21no—
49C4×Q8×C23—21no—
50C4×Q8×C23—21no—
51C4×Q8×C23—21no—
52C4×Q8×C23—21no—
53C4×Q8×C23—21no—
54C4×Q8×C23—21no—
55C4×D4×C23—21no—
56C4×D4×C23—21no—
57C23×#117—21no—
58C2×C4⋊C4×C23—21no—
59C2×C4⋊C4×C23D411yescharacteristic
60C2×C42×C23—21no—
61C2×C42×C23C2311yescharacteristic
62C23×#107—22no—
63C23×#106—22no—
64C23×C4⋊C8—21no—
65C23×C4⋊C8—21no—
66C23×C4⋊C8—21no—
67C23×C4⋊C8—21no—
68C23×#103—22no—
69C23×#103—22no—
70C23×#103—22no—
71C23×#103—22no—
72C23×#103—22no—
73C23×#102—22no—
74C23×#102—22no—
75C23×#102—22no—
76C23×C22⋊C8—21no—
77C23×C22⋊C8—21no—
78C23×#97—21no—
79C23×#97—21no—
80C4×C8×C23D412yes—
81C4×C8×C23D412yes—
82#41×C23—42no—
83#41×C23—42no—
84C2×Q8×C23—21no—
85C2×Q8×C23—21no—
86C2×Q8×C23—21no—
87C2×Q8×C23—21no—
88C2×Q8×C23—21no—
89C2×Q8×C23—42no—
90C2×D4×C23—21no—
91C2×D4×C23—21no—
92C2×D4×C23—21no—
93C2×D4×C23—41no—
94C22×C4×C23—21no—
95C22×C4×C23—21no—
96C22×C4×C23—41no—
97C22×C4×C23C2×D411yescharacteristic
98C22×C4×C23C2×D411yescharacteristic
99C22×C4×C23#4111yescharacteristic
100Q16×C23—44no—
101SD16×C23—44no—
102C2×C8×C23—22no—
103C2×C8×C23—22no—
104C2×C8×C23—22no—
105C2×C8×C23—22no—
106C2×C8×C23—22no—
107C2×C8×C23—41no—
108C2×C8×C23—42no—
109C4⋊C4×C23—21no—
110C4⋊C4×C23—21no—
111C4⋊C4×C23—21no—
112C4⋊C4×C23—21no—
113C4⋊C4×C23—21no—
114C4⋊C4×C23—21no—
115C4⋊C4×C23—21no—
116C4⋊C4×C23—21no—
117C4⋊C4×C23—41no—
118C4⋊C4×C23—41no—
119C4⋊C4×C23—41no—
120C4⋊C4×C23—41no—
121C22⋊C4×C23—41no—
122C22⋊C4×C23—41no—
123C22⋊C4×C23—41no—
124C42×C23—41no—
125C42×C23—41no—
126C42×C23—41no—
127C42×C23C2×D411yescharacteristic
128C42×C23C2×D411yescharacteristic
129C42×C23C2×D411yescharacteristic
130C42×C23C2×D411yescharacteristic
131#10035C2311yesmaximal, characteristic, direct product factor, Sylow
132C23×C23—41no—
133C23×C23#12111yescharacteristic
134Q8×C23—22no—
135Q8×C23—22no—
136Q8×C23—41no—
137Q8×C23—41no—
138Q8×C23—42no—
139Q8×C23—42no—
140Q8×C23—42no—
141D4×C23—42no—
142D4×C23—42no—
143D4×C23—42no—
144D4×C23—82no—
145C2×C4×C23—22no—
146C2×C4×C23—41no—
147C2×C4×C23—41no—
148C2×C4×C23—41no—
149C2×C4×C23—41no—
150C2×C4×C23—42no—
151C2×C4×C23—41no—
152C2×C4×C23—41no—
153C2×C4×C23—41no—
154C2×C4×C23—41no—
155C2×C4×C23—81no—
156C2×C4×C23—81no—
157C2×C4×C23#12011yescharacteristic
158C2×C4×C23#12011yescharacteristic
159C2×C4×C23#12011yescharacteristic
160C2×C4×C23#12111yescharacteristic
161C2×C4×C23#12111yescharacteristic
162C2×C4×C23#12711yescharacteristic
163C2×C4×C23#13512yes—
164C2×C4×C23#13712yes—
165C8×C23—42no—
166C8×C23—42no—
167C8×C23—42no—
168C8×C23—81no—
169#3135C2×C2311yescharacteristic
170#3104C2×C2311yescharacteristic, complemented
171#3103C2×C2311yescharacteristic
172#1985C2×C2311yescharacteristic, complemented
173#1481C2×C2311yescharacteristic, complemented
174#1480C2×C2311yescharacteristic
175#1275C2×C2311yescharacteristic, complemented
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—81no—
179C22×C23—81no—
180C22×C23—81no—
181C22×C23#39211yescharacteristic
182C22×C23#46412yes—
183C4×C23—21no—
184C4×C23—21no—
185C4×C23—21no—
186C4×C23—21no—
187C4×C23—42no—
188C4×C23—81no—
189C4×C23—81no—
190C4×C23—81no—
191C4×C23—81no—
192C4×C23#45212yes—
193C4×C23#49511yescharacteristic
194C4×C23#49711yescharacteristic
195#533C22×C2311yescharacteristic
196#532C22×C2311yescharacteristic
197C2×C4×Q8C22×C2311yescharacteristic
198#491—21no—
199#490—21no—
200#489—21no—
201#489—21no—
202#484—21no—
203#481—21no—
204#477—21no—
205#475—21no—
206#462—21no—
207#460—21no—
208#451—21no—
209#448—21no—
210C4×Q16—22no—
211C4×SD16—22no—
212#431C22×C2311yescharacteristic
213#431C22×C2311yescharacteristic
214C2×C4⋊C8C22×C2311yescharacteristic
215#416—22no—
216C2×#97C22×C2311yescharacteristic
217#336—22no—
218Q8⋊C8—22no—
219D4⋊C8—22no—
220C2×C23—22no—
221C2×C23—161no—
222C2×C23#201011yescharacteristic
223C2×C23#201511yescharacteristic
224C2×C23#201711yescharacteristic
225C2×#41—21no—
226C22×Q8D4×C2311yescharacteristic
227C2×Q16—22no—
228C2×SD16—22no—
229C22×C8—21no—
230C22×C8D4×C2312yes—
231C4⋊Q8D4×C2311yescharacteristic
232C4⋊Q8D4×C2311yescharacteristic
233C4⋊Q8D4×C2311yescharacteristic
234#127D4×C2311yescharacteristic
235#125—21no—
236#124—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239#121—21no—
240#121—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×D4—21no—
248C4×D4—21no—
249#117—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D4×C2311yescharacteristic
252C2×C42—21no—
253C2×C42C23×C2311yescharacteristic
254#107—22no—
255#106—22no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260#103—22no—
261#103—22no—
262#103—22no—
263#103—22no—
264#103—22no—
265#102—22no—
266#102—22no—
267#102—22no—
268C22⋊C8—21no—
269C22⋊C8—21no—
270#97—21no—
271#97—21no—
272C4×C8D4×C2312yes—
273C4×C8D4×C2312yes—
274C23#1003511yescharacteristic, direct product factor, Sylow
275#41—42no—
276#41—42no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—42no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4C2×D4×C2311yescharacteristic
291C22×C4C2×D4×C2311yescharacteristic
292C22×C4#41×C2311yescharacteristic
293Q16—44no—
294SD16—44no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—42no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—41no—
318C42—41no—
319C42—41no—
320C42C2×D4×C2311yescharacteristic
321C42C2×D4×C2311yescharacteristic
322C42C2×D4×C2311yescharacteristic
323C42C2×D4×C2311yescharacteristic
324C23—41no—
325C23C23×#12111yescharacteristic
326Q8—22no—
327Q8—22no—
328Q8—41no—
329Q8—41no—
330Q8—42no—
331Q8—42no—
332Q8—42no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—82no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4C23×#12011yescharacteristic
350C2×C4C23×#12011yescharacteristic
351C2×C4C23×#12011yescharacteristic
352C2×C4C23×#12111yescharacteristic
353C2×C4C23×#12111yescharacteristic
354C2×C4C23×#12711yescharacteristic
355C2×C4C23×#13512yes—
356C2×C4C23×#13712yes—
357C8—42no—
358C8—42no—
359C8—42no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22C23×#39211yescharacteristic
367C22C23×#46412yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4C23×#45212yes—
378C4C23×#49511yescharacteristic
379C4C23×#49711yescharacteristic
380C2—22no—
381C2—161no—
382C2C23×#201011yescharacteristic
383C2C23×#201511yescharacteristic
384C2C23×#201711yescharacteristic
subgroupG/H
centerC2×C4×C23#127
commutator, Frattini, cosocleC2×C42C23×C23
socleC22×C23#392
prime radicalC23×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#3104C2semidirect
4. C23×#1985C2semidirect
5. C23×#1481C2semidirect
7. C23×#1275C2semidirect
131. #10035C23direct (N × H)
170. #3104C2×C23semidirect
172. #1985C2×C23semidirect
173. #1481C2×C23semidirect
175. #1275C2×C23semidirect
274. C23#10035direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#31352
C23×#31042
C23×#31032
C23×#19852
C23×#14812
C23×#14802
C23×#12752
#1003523