Finite Group Databasebeta

← C23×#9432 #19157058

Subgroups — C23×#9432 #19157058

Order 5888.

436 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3180C211yesmaximal, characteristic
2C23×#2968C211yesmaximal, characteristic, complemented
3C23×#1530C211yesmaximal, characteristic, complemented
4C23×#1517C211yesmaximal, characteristic, complemented
5C23×#1512C211yesmaximal, characteristic, complemented
6C23×#1302C211yesmaximal, characteristic, complemented
7C23×#1295C211yesmaximal, characteristic, complemented
8C23×#532C2211yescharacteristic
9C23×#529C2211yescharacteristic
10C23×#501C411yescharacteristic, complemented
11C23×#496C411yescharacteristic, complemented
12C23×#490C411yescharacteristic, complemented
13C23×#489C411yescharacteristic, complemented
14C23×#466—21no—
15C23×#465—21no—
16C23×#446—21no—
17C23×#442—21no—
18C23×#440—21no—
19C23×#435—21no—
20C23×#435—21no—
21C8×D4×C23—21no—
22C23×#433—21no—
23C23×#432C2211yescharacteristic
24C23×#431C2211yescharacteristic
25C23×#405—21no—
26C2×C23×#97C2211yescharacteristic
27C2×C23×#97C2211yescharacteristic
28C23×#382C2211yescharacteristic
29C23×#329—21no—
30C23×#329—21no—
31C23×#328—21no—
32C23×#327—21no—
33C23×#327—21no—
34C23×#327—21no—
35C2×#41×C23—21no—
36C2×SD16×C23—21no—
37C2×D8×C23—21no—
38C2×M16×C23—21no—
39C22×C8×C23—21no—
40C22×C8×C23—21no—
41C22×C8×C23—21no—
42C23×C4⋊Q8C2×C411yescharacteristic
43C23×#127C2×C411yescharacteristic
44C23×#126—21no—
45C23×#125C2×C411yescharacteristic
46C23×#124—21no—
47C23×#124C2×C411yescharacteristic
48C23×#123—21no—
49C23×C22⋊Q8D411yescharacteristic
50C23×#121—21no—
51C23×#121—21no—
52C23×#121D411yescharacteristic
53C4×Q8×C23D411yescharacteristic
54C4×D4×C23—21no—
55C4×D4×C23—21no—
56C4×D4×C23—21no—
57C4×D4×C23D411yescharacteristic
58C23×#117—21no—
59C2×C4⋊C4×C23—21no—
60C2×C42×C23C2311yescharacteristic
61C23×#107—21no—
62C23×#106—21no—
63C23×C4⋊C8—21no—
64C23×C4⋊C8—21no—
65C23×C4⋊C8—21no—
66C23×C4⋊C8—21no—
67C23×#103—21no—
68C23×#102—21no—
69C23×#102—21no—
70C23×#102—21no—
71C23×C22⋊C8—21no—
72C23×C22⋊C8—21no—
73C23×C22⋊C8—21no—
74C23×C22⋊C8D411yescharacteristic
75C23×C22⋊C8D411yescharacteristic
76C23×#97—21no—
77C23×#97—21no—
78C23×#97—21no—
79C23×#97—21no—
80C23×#97C2×C411yescharacteristic
81C23×#97C2×C411yescharacteristic
82C23×#97D411yescharacteristic
83C23×#97D411yescharacteristic
84C4×C8×C23—21no—
85C4×C8×C23—21no—
86C23×#95—21no—
87C23×#95—21no—
88#41×C23—81no—
89#41×C23—81no—
90C2×Q8×C23—21no—
91C2×Q8×C23C22⋊C411yescharacteristic
92C2×D4×C23—21no—
93C2×D4×C23—21no—
94C2×D4×C23—21no—
95C2×D4×C23—21no—
96C2×D4×C23—41no—
97C2×D4×C23C22⋊C411yescharacteristic
98C22×C4×C23—21no—
99C22×C4×C23—41no—
100C22×C4×C23—41no—
101C22×C4×C23C2×D411yescharacteristic
102C22×C4×C23C2×D411yescharacteristic
103C22×C4×C23#4111yescharacteristic
104SD16×C23—42no—
105D8×C23—42no—
106M16×C23—42no—
107C2×C8×C23—21no—
108C2×C8×C23—21no—
109C2×C8×C23—21no—
110C2×C8×C23—21no—
111C2×C8×C23—21no—
112C2×C8×C23—21no—
113C2×C8×C23—42no—
114C2×C8×C23—42no—
115C2×C8×C23—42no—
116C2×C8×C23—41no—
117C4⋊C4×C23—21no—
118C4⋊C4×C23—21no—
119C4⋊C4×C23—21no—
120C4⋊C4×C23—21no—
121C4⋊C4×C23—21no—
122C4⋊C4×C23—21no—
123C4⋊C4×C23—81no—
124C4⋊C4×C23C22⋊C411yescharacteristic
125C4⋊C4×C23C22⋊C411yescharacteristic
126C22⋊C4×C23—21no—
127C22⋊C4×C23—21no—
128C22⋊C4×C23—21no—
129C22⋊C4×C23—21no—
130C22⋊C4×C23—21no—
131C22⋊C4×C23—41no—
132C22⋊C4×C23—41no—
133C42×C23—21no—
134C42×C23C22×C411yescharacteristic
135C42×C23C2×D411yescharacteristic
136C42×C23C2×D411yescharacteristic
137C42×C23#4111yescharacteristic
138#9432C2311yesmaximal, characteristic, direct product factor, Sylow
139C23×C23—21no—
140C23×C23—41no—
141C23×C23#12111yescharacteristic
142Q8×C23—41no—
143Q8×C23—81no—
144D4×C23—41no—
145D4×C23—41no—
146D4×C23—41no—
147D4×C23—41no—
148D4×C23—41no—
149D4×C23—81no—
150D4×C23—81no—
151D4×C23—81no—
152D4×C23—81no—
153C2×C4×C23—21no—
154C2×C4×C23—21no—
155C2×C4×C23—21no—
156C2×C4×C23—21no—
157C2×C4×C23—21no—
158C2×C4×C23—41no—
159C2×C4×C23—41no—
160C2×C4×C23—41no—
161C2×C4×C23—41no—
162C2×C4×C23—41no—
163C2×C4×C23—82no—
164C2×C4×C23—81no—
165C2×C4×C23—81no—
166C2×C4×C23—81no—
167C2×C4×C23C2×C22⋊C411yescharacteristic
168C2×C4×C23C4×D411yescharacteristic
169C2×C4×C23C4×D411yescharacteristic
170C2×C4×C23#12011yescharacteristic
171C2×C4×C23#12111yescharacteristic
172C2×C4×C23#12311yescharacteristic
173C8×C23—22no—
174C8×C23—22no—
175C8×C23—41no—
176C8×C23—41no—
177C8×C23—41no—
178C8×C23—41no—
179C8×C23—81no—
180#3180C2×C2311yescharacteristic
181#2968C2×C2311yescharacteristic, complemented
182#1530C2×C2311yescharacteristic, complemented
183#1517C2×C2311yescharacteristic, complemented
184#1512C2×C2311yescharacteristic, complemented
185#1302C2×C2311yescharacteristic, complemented
186#1295C2×C2311yescharacteristic, complemented
187C22×C23—21no—
188C22×C23—21no—
189C22×C23—41no—
190C22×C23—41no—
191C22×C23—41no—
192C22×C23—81no—
193C22×C23—81no—
194C22×C23—81no—
195C22×C23#38611yescharacteristic
196C22×C23#47111yescharacteristic
197C22×C23#47211yescharacteristic
198C4×C23—21no—
199C4×C23—21no—
200C4×C23—21no—
201C4×C23—21no—
202C4×C23—21no—
203C4×C23—21no—
204C4×C23—41no—
205C4×C23—41no—
206C4×C23—41no—
207C4×C23—81no—
208C4×C23—161no—
209#532C22×C2311yescharacteristic
210#529C22×C2311yescharacteristic
211#501C4×C2311yescharacteristic, complemented
212#496C4×C2311yescharacteristic, complemented
213#490C4×C2311yescharacteristic, complemented
214#489C4×C2311yescharacteristic, complemented
215#466—21no—
216#465—21no—
217#446—21no—
218#442—21no—
219#440—21no—
220#435—21no—
221#435—21no—
222C8×D4—21no—
223#433—21no—
224#432C22×C2311yescharacteristic
225#431C22×C2311yescharacteristic
226#405—21no—
227C2×#97C22×C2311yescharacteristic
228C2×#97C22×C2311yescharacteristic
229#382C22×C2311yescharacteristic
230#329—21no—
231#329—21no—
232#328—21no—
233#327—21no—
234#327—21no—
235#327—21no—
236C2×C23—21no—
237C2×C23—21no—
238C2×C23—81no—
239C2×C23—161no—
240C2×C23#188411yescharacteristic
241C2×C23#190611yescharacteristic
242C2×C23#190711yescharacteristic
243C2×#41—21no—
244C2×SD16—21no—
245C2×D8—21no—
246C2×M16—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C4⋊Q8C2×C4×C2311yescharacteristic
251#127C2×C4×C2311yescharacteristic
252#126—21no—
253#125C2×C4×C2311yescharacteristic
254#124—21no—
255#124C2×C4×C2311yescharacteristic
256#123—21no—
257C22⋊Q8D4×C2311yescharacteristic
258#121—21no—
259#121—21no—
260#121D4×C2311yescharacteristic
261C4×Q8D4×C2311yescharacteristic
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4D4×C2311yescharacteristic
266#117—21no—
267C2×C4⋊C4—21no—
268C2×C42C23×C2311yescharacteristic
269#107—21no—
270#106—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275#103—21no—
276#102—21no—
277#102—21no—
278#102—21no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8D4×C2311yescharacteristic
283C22⋊C8D4×C2311yescharacteristic
284#97—21no—
285#97—21no—
286#97—21no—
287#97—21no—
288#97C2×C4×C2311yescharacteristic
289#97C2×C4×C2311yescharacteristic
290#97D4×C2311yescharacteristic
291#97D4×C2311yescharacteristic
292C4×C8—21no—
293C4×C8—21no—
294#95—21no—
295#95—21no—
296C23#943211yescharacteristic, direct product factor, Sylow
297#41—81no—
298#41—81no—
299C2×Q8—21no—
300C2×Q8C22⋊C4×C2311yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4C22⋊C4×C2311yescharacteristic
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4C2×D4×C2311yescharacteristic
311C22×C4C2×D4×C2311yescharacteristic
312C22×C4#41×C2311yescharacteristic
313SD16—42no—
314D8—42no—
315M16—42no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—41no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—81no—
333C4⋊C4C22⋊C4×C2311yescharacteristic
334C4⋊C4C22⋊C4×C2311yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—21no—
343C42C22×C4×C2311yescharacteristic
344C42C2×D4×C2311yescharacteristic
345C42C2×D4×C2311yescharacteristic
346C42#41×C2311yescharacteristic
347C23—21no—
348C23—41no—
349C23C23×#12111yescharacteristic
350Q8—41no—
351Q8—81no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—82no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4C2×C22⋊C4×C2311yescharacteristic
376C2×C4C4×D4×C2311yescharacteristic
377C2×C4C4×D4×C2311yescharacteristic
378C2×C4C23×#12011yescharacteristic
379C2×C4C23×#12111yescharacteristic
380C2×C4C23×#12311yescharacteristic
381C8—22no—
382C8—22no—
383C8—41no—
384C8—41no—
385C8—41no—
386C8—41no—
387C8—81no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22C23×#38611yescharacteristic
397C22C23×#47111yescharacteristic
398C22C23×#47211yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—81no—
409C4—161no—
410C2—21no—
411C2—21no—
412C2—81no—
413C2—161no—
414C2C23×#188411yescharacteristic
415C2C23×#190611yescharacteristic
416C2C23×#190711yescharacteristic
subgroupG/H
center, socleC22×C23#386
commutatorC42C22×C4×C23
Frattini, cosocleC2×C42C23×C23
prime radicalC23×#3180C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#2968C2semidirect
3. C23×#1530C2semidirect
4. C23×#1517C2semidirect
5. C23×#1512C2semidirect
6. C23×#1302C2semidirect
7. C23×#1295C2semidirect
10. C23×#501C4semidirect
11. C23×#496C4semidirect
12. C23×#490C4semidirect
13. C23×#489C4semidirect
138. #9432C23direct (N × H)
181. #2968C2×C23semidirect
182. #1530C2×C23semidirect
183. #1517C2×C23semidirect
184. #1512C2×C23semidirect
185. #1302C2×C23semidirect
186. #1295C2×C23semidirect
211. #501C4×C23semidirect
212. #496C4×C23semidirect
213. #490C4×C23semidirect
214. #489C4×C23semidirect
296. C23#9432direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#31802
C23×#29682
C23×#15302
C23×#15172
C23×#15122
C23×#13022
C23×#12952
#943223