Finite Group Databasebeta

← #19212362

Subgroups — #19212362

Order 5888.

656 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675887C211yesmaximal, characteristic
2#15673377C211yesmaximal, characteristic, complemented
3#15671222C212yesmaximal, complemented
4#15671217C212yesmaximal, complemented
5C23×#1749C211yesmaximal, characteristic, complemented
6C22×#67288C411yescharacteristic
7C2×#10625097C411yescharacteristic
8C2×C4⋊(C23⋊C8)—21no—
9C2×C22⋊(C23⋊C8)—21no—
10#13092323C411yescharacteristic
11#13092323C2211yescharacteristic
12#13092319C411yescharacteristic
13#13092319C2211yescharacteristic
14#13092296—21no—
15#13092296—21no—
16C4×(C2×D23)⋊C4—21no—
17C4×(C2×D23)⋊C4—21no—
18#13092172C2212yes—
19C22×C42×C23C2211yescharacteristic
20C2×C23×C22⋊C8—21no—
21C2×C23×#97—21no—
22C23×#336C2212yes—
23C23×C4×C23C2×C411yescharacteristic
24C23×C4×C23D411yescharacteristic
25C23×C4×C23D411yescharacteristic
26C22×C22⋊D23—21no—
27C2×#67288—22no—
28C2×#67288—22no—
29C2×#67288—42no—
30C2×#67288—42no—
31C22×D92C2×C411yescharacteristic
32C22×C4×D23—21no—
33C22×Dic46C2×C411yescharacteristic
34C22×C8×C23—22no—
35C2×C42×C23—42no—
36C2×C42×C23C2×C411yescharacteristic
37C2×C42×C23D411yescharacteristic
38C2×C42×C23D411yescharacteristic
39C2×C42×C23C2311yescharacteristic
40C2×C22⋊Dic23—21no—
41C2×(C2×D23)⋊C4—21no—
42C2×(C2×D23)⋊C4—21no—
43C2×(C2×D23)⋊C4—21no—
44C2×(C2×D23)⋊C4—21no—
45#10625097—42no—
46C2×C4⋊Dic23C2×C411yescharacteristic
47C2×C4⋊Dic23C2×C411yescharacteristic
48C2×C4×Dic23—21no—
49C22×C23⋊C8—22no—
50C23×C22⋊C8—24no—
51C23×#97—42no—
52C23⋊#95—21no—
53C23⋊#95—21no—
54C23⋊#95—21no—
55C23⋊#95—21no—
56C22⋊(C23⋊C8)—42no—
57C4⋊(C23⋊C8)—42no—
58C24×C23C22⋊C411yescharacteristic
59C23×D23—21no—
60C22×C4×C23—22no—
61C22×C4×C23—22no—
62C22×C4×C23—21no—
63C22×C4×C23—21no—
64C22×C4×C23—22no—
65C22×C4×C23—22no—
66C22×C4×C23—21no—
67C22×C4×C23—21no—
68C22×C4×C23—41no—
69C22×C4×C23—41no—
70C22×C4×C23—41no—
71C22×C4×C23C22⋊C411yescharacteristic
72C22×C4×C23C22⋊C411yescharacteristic
73C22×C4×C23C22⋊C411yescharacteristic
74C22×C4×C23C22×C411yescharacteristic
75C22×C4×C23C2×D411yescharacteristic
76C22×C4×C23C2×D411yescharacteristic
77C2×C22⋊D23—24no—
78C2×C22⋊D23—42no—
79C2×C22⋊D23—42no—
80C22×Dic23—21no—
81C22×Dic23—21no—
82C22×Dic23—21no—
83#67288—48no—
84#67288—48no—
85C2×D92—21no—
86C2×D92—41no—
87C2×D92—41no—
88C2×D92M1612yes—
89C2×C4×D23—24no—
90C2×C4×D23—42no—
91C2×C4×D23—42no—
92C2×Dic46—21no—
93C2×Dic46—41no—
94C2×Dic46—41no—
95C2×Dic46M1612yes—
96C2×C8×C23—24no—
97C2×C8×C23—42no—
98C2×C8×C23—42no—
99C42×C23—22no—
100C42×C23—22no—
101C42×C23—41no—
102C42×C23—41no—
103C22⋊Dic23—42no—
104(C2×D23)⋊C4—42no—
105(C2×D23)⋊C4—42no—
106(C2×D23)⋊C4—42no—
107(C2×D23)⋊C4—41no—
108(C2×D23)⋊C4—41no—
109C4⋊Dic23—41no—
110C4⋊Dic23—41no—
111C4×Dic23—42no—
112C2×C23⋊C8—42no—
113C2×C23⋊C8—42no—
114C2×C23⋊C8—42no—
115#7612—231nomaximal, Sylow
116C23×C23—21no—
117C23×C23—21no—
118C23×C23—21no—
119C23×C23—21no—
120C23×C23—21no—
121C23×C23—21no—
122C23×C23#10012yes—
123C23×C23C2×C22⋊C411yescharacteristic
124C22×D23—22no—
125C22×D23—41no—
126C22×D23—41no—
127C22×D23—41no—
128C22×D23—41no—
129C22×D23—41no—
130C22×D23—41no—
131C2×C4×C23—24no—
132C2×C4×C23—24no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—44no—
147C2×C4×C23—42no—
148C2×C4×C23—42no—
149C2×C4×C23#9912yes—
150C2×C4×C23#10412yes—
151C2×C4×C23C2×M1611yescharacteristic
152C2×C4×C23C2×M1611yescharacteristic
153C2×C4×C23#13512yes—
154C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C23#13711yescharacteristic
156C22⋊D23—48no—
157C2×Dic23—22no—
158C2×Dic23—41no—
159C2×Dic23—41no—
160C2×Dic23—41no—
161C2×Dic23—41no—
162C2×Dic23—41no—
163C2×Dic23—41no—
164C2×Dic23—41no—
165C2×Dic23—41no—
166D92—42no—
167D92—42no—
168C4×D23—48no—
169Dic46—42no—
170Dic46—42no—
171C8×C23—44no—
172C23⋊C8—82no—
173#2297—231no—
174#1797—231no—
175#1749D2311yescharacteristic, complemented
176#1272—232no—
177#1270—232no—
178C22×C23—22no—
179C22×C23—22no—
180C22×C23—22no—
181C22×C23—41no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23#40711yescharacteristic
186C22×C23C2×#9911yescharacteristic
187C22×C23C2×#10011yescharacteristic
188C22×C23#41611yescharacteristic
189C22×C23#41711yescharacteristic
190C22×C23C2×#10411yescharacteristic
191C22×C23#42111yescharacteristic
192C2×D23—42no—
193C2×D23—42no—
194C2×D23—42no—
195C2×D23—81no—
196C2×D23—81no—
197C2×D23—81no—
198C2×D23—81no—
199C4×C23—21no—
200C4×C23—21no—
201C4×C23—22no—
202C4×C23—22no—
203C4×C23—22no—
204C4×C23—21no—
205C4×C23—21no—
206C4×C23—41no—
207Dic23—42no—
208Dic23—81no—
209Dic23—81no—
210C22×#41—231no—
211C2×#117—231no—
212C22×C42C2×D2311yescharacteristic
213C2×C4⋊C8—461no—
214C2×C22⋊C8—21no—
215C2×C22⋊C8—461no—
216C2×#97—21no—
217#391—231no—
218#391—231no—
219#390—231no—
220#390—231no—
221#386—461no—
222#386—461no—
223C4×C22⋊C4—461no—
224C4×C22⋊C4—461no—
225#336—232no—
226#336C2×D2312yes—
227C2×C23—42no—
228C2×C23#146211yescharacteristic
229C2×C23#148811yescharacteristic
230C2×C23#148911yescharacteristic
231C2×C23#150111yescharacteristic
232C2×C23#151311yescharacteristic
233C2×C23#153011yescharacteristic
234C2×C23#155111yescharacteristic
235D23—82no—
236C2×#41—462no—
237C2×#41—462no—
238C2×#41—922no—
239C2×#41—922no—
240C22×Q8—231no—
241C22×D4—231no—
242C22×D4—461no—
243C23×C4—461no—
244C23×C4C4×D2311yescharacteristic
245C23×C4D9211yescharacteristic
246C23×C4C22⋊D2311yescharacteristic
247C22×C8—22no—
248C22×C8—462no—
249#117—922no—
250C2×C4⋊C4—231no—
251C2×C4⋊C4—231no—
252C2×C22⋊C4—461no—
253C2×C22⋊C4—461no—
254C2×C22⋊C4—461no—
255C2×C22⋊C4—461no—
256C2×C22⋊C4—461no—
257C2×C42—42no—
258C2×C42—461no—
259C2×C42C4×D2311yescharacteristic
260C2×C42D9211yescharacteristic
261C2×C42C22⋊D2311yescharacteristic
262C2×C42C22×D2311yescharacteristic
263C4⋊C8—922no—
264C22⋊C8—24no—
265C22⋊C8—922no—
266#97—42no—
267#95—461no—
268#95—461no—
269#95—461no—
270#95—461no—
271C23#761211yescharacteristic, complemented, Sylow
272C24—461no—
273C24(C2×D23)⋊C411yescharacteristic
274#41—928no—
275#41—928no—
276C2×Q8—232no—
277C2×Q8—461no—
278C2×Q8—921no—
279C2×Q8—921no—
280C2×D4—232no—
281C2×D4—464no—
282C2×D4—461no—
283C2×D4—921no—
284C2×D4—921no—
285C2×D4—922no—
286C2×D4—922no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—464no—
299C22×C4—461no—
300C22×C4—461no—
301C22×C4—461no—
302C22×C4—922no—
303C22×C4—922no—
304C22×C4(C2×D23)⋊C411yescharacteristic
305C22×C4(C2×D23)⋊C411yescharacteristic
306C22×C4(C2×D23)⋊C411yescharacteristic
307C22×C4C2×C4×D2311yescharacteristic
308C22×C4C2×D9211yescharacteristic
309C22×C4C2×C22⋊D2311yescharacteristic
310C2×C8—24no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—922no—
314C2×C8—922no—
315C2×C8—922no—
316C4⋊C4—921no—
317C4⋊C4—921no—
318C22⋊C4—922no—
319C22⋊C4—922no—
320C22⋊C4—921no—
321C22⋊C4—921no—
322C22⋊C4—922no—
323C22⋊C4—922no—
324C42—22no—
325C42—22no—
326C42—41no—
327C42—41no—
328C42—922no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—462no—
336C23—921no—
337C23—921no—
338C23—921no—
339C23—921no—
340C23—921no—
341C23—921no—
342C23#1062500512yes—
343C23C2×(C2×D23)⋊C411yescharacteristic
344Q8—922no—
345Q8—922no—
346D4—922no—
347D4—922no—
348D4—928no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—462no—
368C2×C4—928no—
369C2×C4—921no—
370C2×C4—921no—
371C2×C4—921no—
372C2×C4—921no—
373C2×C4—921no—
374C2×C4—921no—
375C2×C4—921no—
376C2×C4—921no—
377C2×C4#1062498712yes—
378C2×C4#1062498812yes—
379C2×C4M16×D2311yescharacteristic
380C2×C4M16×D2311yescharacteristic
381C2×C4#1062507911yescharacteristic
382C2×C4#1062508011yescharacteristic
383C2×C4#1062512112yes—
384C8—44no—
385C8—1842no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—922no—
394C22—922no—
395C22—922no—
396C22—1841no—
397C22—1841no—
398C22—1841no—
399C22—1841no—
400C22#1309238011yescharacteristic
401C22C2×#1062498811yescharacteristic
402C22C2×#1062500511yescharacteristic
403C22#1309241111yescharacteristic
404C22#1309241911yescharacteristic
405C22C2×#1062498711yescharacteristic
406C22#1309243311yescharacteristic
407C4—22no—
408C4—22no—
409C4—21no—
410C4—21no—
411C4—22no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—922no—
416C4—1841no—
417C4—1841no—
418C2—42no—
419C2—1842no—
420C2#1567172311yescharacteristic
421C2#1567182911yescharacteristic
422C2#1567183711yescharacteristic
423C2#1567188611yescharacteristic
424C2#1567194111yescharacteristic
425C2#1567200711yescharacteristic
426C2#1567209311yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC22×C4×C23C22×C4
FrattiniC2×C42C22×D23
FittingC23×#1749C2
socleC23×C23C2×C22⋊C4
hypercenter#1749D23
hypocenterC23#7612
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. #15673377C2semidirect
3. #15671222C2semidirect
4. #15671217C2semidirect
5. C23×#1749C2semidirect
175. #1749D23semidirect
271. C23#7612semidirect