Finite Group Databasebeta

← C23×#3119 #15670738

Subgroups — C23×#3119 #15670738

Order 2944.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#540C211yesmaximal, characteristic, complemented
2C23×#520C211yesmaximal, characteristic, complemented
3C23×#481C211yesmaximal, characteristic, complemented
4C23×#480C211yesmaximal, characteristic, complemented
5C23×#479C211yesmaximal, characteristic, complemented
6C23×#478C211yesmaximal, characteristic, complemented
7C23×#460C211yesmaximal, characteristic, complemented
8C23×#459C211yesmaximal, characteristic, complemented
9C23×#449C211yesmaximal, characteristic, complemented
10C23×#449C211yesmaximal, characteristic, complemented
11C23×#442C211yesmaximal, characteristic, complemented
12C23×#440C211yesmaximal, characteristic, complemented
13C4×SD16×C23C211yesmaximal, characteristic, complemented
14C4×D8×C23C211yesmaximal, characteristic, complemented
15C23×#433C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C2×D8×C23C2211yescharacteristic
20C2×D8×C23C2211yescharacteristic
21C23×#127C2211yescharacteristic
22C23×#125C2211yescharacteristic
23C23×#123—21no—
24C23×#123—21no—
25C23×#121—21no—
26C23×#121—21no—
27C23×#121C2211yescharacteristic
28C23×#121C2211yescharacteristic
29C4×Q8×C23C2211yescharacteristic
30C4×Q8×C23C2211yescharacteristic
31C4×D4×C23—21no—
32C4×D4×C23—21no—
33C4×D4×C23C2211yescharacteristic
34C4×D4×C23C2211yescharacteristic
35C4×D4×C23C2211yescharacteristic
36C4×D4×C23C2211yescharacteristic
37C23×#117—21no—
38C23×#117C2211yescharacteristic
39C2×C4⋊C4×C23—21no—
40C2×C4⋊C4×C23C2211yescharacteristic
41C23×#107C2211yescharacteristic
42C23×#107C2211yescharacteristic
43C23×#106C2211yescharacteristic
44C23×#106C2211yescharacteristic
45C23×C4⋊C8C2211yescharacteristic
46C23×C4⋊C8C2211yescharacteristic
47C23×#103C2211yescharacteristic
48C23×#103C2211yescharacteristic
49C23×#102C2211yescharacteristic
50C23×#102C2211yescharacteristic
51C23×#102C2211yescharacteristic
52C23×#102C2211yescharacteristic
53C23×#102C2211yescharacteristic
54C23×#102C2211yescharacteristic
55C23×C22⋊C8C2211yescharacteristic
56C23×C22⋊C8C2211yescharacteristic
57C23×#97C2211yescharacteristic
58C4×C8×C23C2211yescharacteristic
59#41×C23—22no—
60#41×C23—22no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23—21no—
64C2×D4×C23—21no—
65C2×D4×C23—21no—
66C2×D4×C23—21no—
67C2×D4×C23C2311yescharacteristic
68C2×D4×C23C2311yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C22×C4×C23—21no—
71C22×C4×C23—21no—
72C22×C4×C23—21no—
73C22×C4×C23—21no—
74C22×C4×C23—21no—
75C22×C4×C23—21no—
76C22×C4×C23C2311yescharacteristic
77SD16×C23—22no—
78SD16×C23—22no—
79D8×C23—22no—
80D8×C23—22no—
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C2×C8×C23C2311yescharacteristic
84C2×C8×C23C2311yescharacteristic
85C4⋊C4×C23—21no—
86C4⋊C4×C23—21no—
87C4⋊C4×C23—21no—
88C4⋊C4×C23—21no—
89C4⋊C4×C23—21no—
90C4⋊C4×C23D411yescharacteristic
91C4⋊C4×C23D411yescharacteristic
92C4⋊C4×C23C2311yescharacteristic
93C4⋊C4×C23C2311yescharacteristic
94C4⋊C4×C23C2311yescharacteristic
95C4⋊C4×C23C2311yescharacteristic
96C22⋊C4×C23—21no—
97C22⋊C4×C23—21no—
98C22⋊C4×C23—21no—
99C22⋊C4×C23—21no—
100C22⋊C4×C23—21no—
101C22⋊C4×C23—21no—
102C22⋊C4×C23D411yescharacteristic
103C22⋊C4×C23D411yescharacteristic
104C42×C23—21no—
105C42×C23—21no—
106C42×C23C2311yescharacteristic
107C42×C23C2311yescharacteristic
108C23×C23—21no—
109C23×C23—21no—
110C23×C23—21no—
111C23×C23C2×D411yescharacteristic
112Q8×C23—21no—
113Q8×C23#4112yes—
114D4×C23—24no—
115D4×C23—21no—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—81no—
121D4×C23—81no—
122D4×C23—81no—
123D4×C23—81no—
124D4×C23#4112yes—
125C2×C4×C23—24no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—81no—
134C2×C4×C23—81no—
135C2×C4×C23—81no—
136C2×C4×C23—81no—
137C2×C4×C23—81no—
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2×D411yescharacteristic
142C2×C4×C23C2×D411yescharacteristic
143C2×C4×C23C2411yescharacteristic
144C8×C23—21no—
145C8×C23—21no—
146C8×C23—21no—
147C8×C23—21no—
148#3119C2311yesmaximal, characteristic, direct product factor, Sylow
149C22×C23—21no—
150C22×C23—22no—
151C22×C23—21no—
152C22×C23—21no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23C22×D411yescharacteristic
162C4×C23—21no—
163C4×C23—22no—
164C4×C23—21no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23—41no—
171C4×C23—41no—
172C4×C23C2×#4111yescharacteristic
173C4×C23C2×#4111yescharacteristic
174#540C2×C2311yescharacteristic, complemented
175#520C2×C2311yescharacteristic, complemented
176#481C2×C2311yescharacteristic, complemented
177#480C2×C2311yescharacteristic, complemented
178#479C2×C2311yescharacteristic, complemented
179#478C2×C2311yescharacteristic, complemented
180#460C2×C2311yescharacteristic, complemented
181#459C2×C2311yescharacteristic, complemented
182#449C2×C2311yescharacteristic, complemented
183#449C2×C2311yescharacteristic, complemented
184#442C2×C2311yescharacteristic, complemented
185#440C2×C2311yescharacteristic, complemented
186C4×SD16C2×C2311yescharacteristic, complemented
187C4×D8C2×C2311yescharacteristic, complemented
188#433C2×C2311yescharacteristic, complemented
189C2×C23—41no—
190C2×C23—42no—
191C2×C23—81no—
192C2×C23—81no—
193C2×C23#52511yescharacteristic
194C2×C23#57611yescharacteristic
195C2×C23#57711yescharacteristic
196C2×#41C22×C2311yescharacteristic
197C2×SD16C22×C2311yescharacteristic
198C2×SD16C22×C2311yescharacteristic
199C2×D8C22×C2311yescharacteristic
200C2×D8C22×C2311yescharacteristic
201#127C22×C2311yescharacteristic
202#125C22×C2311yescharacteristic
203#123—21no—
204#123—21no—
205#121—21no—
206#121—21no—
207#121C22×C2311yescharacteristic
208#121C22×C2311yescharacteristic
209C4×Q8C22×C2311yescharacteristic
210C4×Q8C22×C2311yescharacteristic
211C4×D4—21no—
212C4×D4—21no—
213C4×D4C22×C2311yescharacteristic
214C4×D4C22×C2311yescharacteristic
215C4×D4C22×C2311yescharacteristic
216C4×D4C22×C2311yescharacteristic
217#117—21no—
218#117C22×C2311yescharacteristic
219C2×C4⋊C4—21no—
220C2×C4⋊C4C22×C2311yescharacteristic
221#107C22×C2311yescharacteristic
222#107C22×C2311yescharacteristic
223#106C22×C2311yescharacteristic
224#106C22×C2311yescharacteristic
225C4⋊C8C22×C2311yescharacteristic
226C4⋊C8C22×C2311yescharacteristic
227#103C22×C2311yescharacteristic
228#103C22×C2311yescharacteristic
229#102C22×C2311yescharacteristic
230#102C22×C2311yescharacteristic
231#102C22×C2311yescharacteristic
232#102C22×C2311yescharacteristic
233#102C22×C2311yescharacteristic
234#102C22×C2311yescharacteristic
235C22⋊C8C22×C2311yescharacteristic
236C22⋊C8C22×C2311yescharacteristic
237#97C22×C2311yescharacteristic
238C4×C8C22×C2311yescharacteristic
239C23#311911yescharacteristic, direct product factor, Sylow
240#41—22no—
241#41—22no—
242C2×Q8C23×C2311yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C23×C2311yescharacteristic
249C2×D4C23×C2311yescharacteristic
250C2×D4C23×C2311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4C23×C2311yescharacteristic
258SD16—22no—
259SD16—22no—
260D8—22no—
261D8—22no—
262C2×C8C23×C2311yescharacteristic
263C2×C8C23×C2311yescharacteristic
264C2×C8C23×C2311yescharacteristic
265C2×C8C23×C2311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4D4×C2311yescharacteristic
272C4⋊C4D4×C2311yescharacteristic
273C4⋊C4C23×C2311yescharacteristic
274C4⋊C4C23×C2311yescharacteristic
275C4⋊C4C23×C2311yescharacteristic
276C4⋊C4C23×C2311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4D4×C2311yescharacteristic
284C22⋊C4D4×C2311yescharacteristic
285C42—21no—
286C42—21no—
287C42C23×C2311yescharacteristic
288C42C23×C2311yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23C2×D4×C2311yescharacteristic
293Q8—21no—
294Q8#41×C2312yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—81no—
302D4—81no—
303D4—81no—
304D4—81no—
305D4#41×C2312yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4C2×D4×C2311yescharacteristic
320C2×C4C2×D4×C2311yescharacteristic
321C2×C4C2×D4×C2311yescharacteristic
322C2×C4C2×D4×C2311yescharacteristic
323C2×C4C2×D4×C2311yescharacteristic
324C2×C4C24×C2311yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22C22×D4×C2311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—22no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4C2×#41×C2311yescharacteristic
353C4C2×#41×C2311yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—81no—
358C2C23×#52511yescharacteristic
359C2C23×#57611yescharacteristic
360C2C23×#57711yescharacteristic
subgroupG/H
center, socleC22×C23C22×D4
commutator, Frattini, cosocleC2×C4C24×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#540C2semidirect
2. C23×#520C2semidirect
3. C23×#481C2semidirect
4. C23×#480C2semidirect
5. C23×#479C2semidirect
6. C23×#478C2semidirect
7. C23×#460C2semidirect
8. C23×#459C2semidirect
9. C23×#449C2semidirect
10. C23×#449C2semidirect
11. C23×#442C2semidirect
12. C23×#440C2semidirect
13. C4×SD16×C23C2semidirect
14. C4×D8×C23C2semidirect
15. C23×#433C2semidirect
148. #3119C23direct (N × H)
174. #540C2×C23semidirect
175. #520C2×C23semidirect
176. #481C2×C23semidirect
177. #480C2×C23semidirect
178. #479C2×C23semidirect
179. #478C2×C23semidirect
180. #460C2×C23semidirect
181. #459C2×C23semidirect
182. #449C2×C23semidirect
183. #449C2×C23semidirect
184. #442C2×C23semidirect
185. #440C2×C23semidirect
186. C4×SD16C2×C23semidirect
187. C4×D8C2×C23semidirect
188. #433C2×C23semidirect
239. C23#3119direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5402
C23×#5202
C23×#4812
C23×#4802
C23×#4792
C23×#4782
C23×#4602
C23×#4592
C23×#4492
C23×#4422
C23×#4402
C4×SD16×C232
C4×D8×C232
C23×#4332
#311923