Finite Group Databasebeta

← #19212255

Subgroups — #19212255

Order 5888.

662 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675913C211yesmaximal, characteristic
2#15673376C211yesmaximal, characteristic, complemented
3D23×#336C211yesmaximal, characteristic, complemented
4#15671221C211yesmaximal, characteristic, complemented
5#15671219C211yesmaximal, characteristic, complemented
6#15671218C211yesmaximal, characteristic, complemented
7C23×#1270C211yesmaximal, characteristic, complemented
8C22×C8×D23—21no—
9C2×#10625109C411yescharacteristic
10C2×D4×Dic23C411yescharacteristic
11C2×(C22⋊D23)⋊C4—21no—
12C2×C42×D23C2211yescharacteristic
13C2×Dic23⋊C8—21no—
14C2×(C2×D23)⋊C8—21no—
15#13092315C2211yescharacteristic
16#13092311—21no—
17#13092293—21no—
18#13092274C411yescharacteristic
19C4⋊C4×Dic23C411yescharacteristic
20C22⋊C4×Dic23—21no—
21#13092172C2211yescharacteristic
22#13092172C2211yescharacteristic
23#13092171—21no—
24C23×#390C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×D4×C23C2×C411yescharacteristic
28C22×C22⋊D23—21no—
29C23×Dic23—21no—
30C22×C4×D23C2×C411yescharacteristic
31C22×C4×D23D411yescharacteristic
32C22×C4×D23D411yescharacteristic
33C22×C8×C23—21no—
34C22×C8×C23—21no—
35C2×C4⋊C4×C23C2×C411yescharacteristic
36C2×C22⋊C4×C23—21no—
37C2×C22⋊C4×C23—21no—
38C2×C42×C23C2311yescharacteristic
39C2×C22⋊Dic23—21no—
40C2×C22⋊Dic23—21no—
41#10625109—22no—
42#10625109C814yescomplemented
43D4×Dic23—42no—
44C2×(C2×D23)⋊C4—21no—
45C2×C4⋊Dic23C2×C411yescharacteristic
46C2×C4⋊Dic23C2×C411yescharacteristic
47C2×Dic23⋊C4—21no—
48C2×C4×Dic23—21no—
49C2×C4×Dic23C2×C411yescharacteristic
50C2×C4×Dic23D411yescharacteristic
51C2×C4×Dic23D411yescharacteristic
52C22×C23⋊C8—21no—
53C22×C23⋊C8—21no—
54C2×C8×D23—24no—
55C2×C8×D23—42no—
56C2×C8×D23—42no—
57(C22⋊D23)⋊C4—42no—
58(C22⋊D23)⋊C4—42no—
59C42×D23—42no—
60C23⋊#95—21no—
61C23⋊#95—21no—
62C23⋊#95—21no—
63(C2×D23)⋊C8—42no—
64Dic23⋊C8—42no—
65C24×C23—21no—
66C23×D23C22⋊C411yescharacteristic
67C2×D4×C23—21no—
68C2×D4×C23—41no—
69C2×D4×C23—41no—
70C2×D4×C23C2×C812yescomplemented
71C22×C4×C23—21no—
72C22×C4×C23C22×C411yescharacteristic
73C22×C4×C23C2×D411yescharacteristic
74C22×C4×C23C2×D411yescharacteristic
75C2×C22⋊D23—24no—
76C2×C22⋊D23—42no—
77C2×C22⋊D23—42no—
78C22×Dic23—21no—
79C22×Dic23—21no—
80C22×Dic23—42no—
81C22×Dic23—42no—
82C22×Dic23—42no—
83C22×Dic23C22⋊C411yescharacteristic
84C22×Dic23C22⋊C411yescharacteristic
85C22×Dic23C22⋊C411yescharacteristic
86C2×C4×D23—22no—
87C2×C4×D23—21no—
88C2×C4×D23—21no—
89C2×C4×D23—22no—
90C2×C4×D23—41no—
91C2×C4×D23—41no—
92C2×C4×D23—41no—
93C2×C4×D23—41no—
94C2×C4×D23C2×C812yes—
95C2×C4×D23M1612yes—
96C2×C4×D23D812yes—
97C2×C4×D23SD1612yes—
98C2×C8×C23—22no—
99C2×C8×C23—41no—
100C2×C8×C23—41no—
101C2×C8×C23—41no—
102C2×C8×C23—41no—
103C2×C8×C23—41no—
104C4⋊C4×C23—41no—
105C22⋊C4×C23—41no—
106C22⋊C4×C23—41no—
107C22⋊C4×C23—41no—
108C22⋊C4×C23—41no—
109C42×C23—41no—
110C22⋊Dic23—24no—
111C22⋊Dic23—42no—
112(C2×D23)⋊C4—42no—
113C4⋊Dic23—21no—
114C4⋊Dic23—41no—
115C4⋊Dic23C2×C812yescomplemented
116Dic23⋊C4—41no—
117Dic23⋊C4—41no—
118C4×Dic23—22no—
119C4×Dic23—22no—
120C4×Dic23—41no—
121C4×Dic23—42no—
122C2×C23⋊C8—22no—
123C2×C23⋊C8—41no—
124C2×C23⋊C8—41no—
125C2×C23⋊C8—41no—
126C2×C23⋊C8—41no—
127C2×C23⋊C8—41no—
128C8×D23—48no—
129#7586—231nomaximal, Sylow
130C23×C23—22no—
131C23×C23—41no—
132C23×C23—41no—
133C23×C23—41no—
134C23×C23—41no—
135C23×C23—41no—
136C23×C23—41no—
137C23×C23C2×C22⋊C411yescharacteristic
138C22×D23—21no—
139C22×D23—21no—
140C22×D23—21no—
141C22×D23—21no—
142C22×D23C22⋊C812yes—
143C22×D23#10212yes—
144C22×D23#10412yes—
145D4×C23—42no—
146D4×C23—42no—
147C2×C4×C23—21no—
148C2×C4×C23—21no—
149C2×C4×C23—21no—
150C2×C4×C23—21no—
151C2×C4×C23—21no—
152C2×C4×C23—21no—
153C2×C4×C23—41no—
154C2×C4×C23—41no—
155C2×C4×C23—41no—
156C2×C4×C23C22×C811yescharacteristic
157C2×C4×C23C2×M1611yescharacteristic
158C2×C4×C23C2×D811yescharacteristic
159C2×C4×C23C2×SD1611yescharacteristic
160C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C23#13711yescharacteristic
162C22⋊D23—48no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—21no—
166C2×Dic23—21no—
167C2×Dic23—21no—
168C2×Dic23—21no—
169C2×Dic23—22no—
170C2×Dic23—41no—
171C2×Dic23—41no—
172C2×Dic23—41no—
173C2×Dic23—41no—
174C2×Dic23—41no—
175C2×Dic23—84no—
176C2×Dic23C22⋊C812yes—
177C2×Dic23#9912yes—
178C2×Dic23#10212yes—
179C4×D23—24no—
180C4×D23—24no—
181C4×D23—42no—
182C4×D23—42no—
183C4×D23—42no—
184C4×D23—42no—
185C8×C23—42no—
186C8×C23—81no—
187C23⋊C8—42no—
188C23⋊C8—81no—
189C4×#121—231no—
190#1797—231no—
191C2×#336—231no—
192#1271—231no—
193#1271—231no—
194#1270—231no—
195#1270D2311yescharacteristic, complemented
196C22×C23—42no—
197C22×C23—42no—
198C22×C23—42no—
199C22×C23—81no—
200C22×C23—81no—
201C22×C23—81no—
202C22×C23—81no—
203C22×C23C2×C22⋊C811yescharacteristic
204C22×C23C2×#9911yescharacteristic
205C22×C23#41311yescharacteristic
206C22×C23C2×#10211yescharacteristic
207C22×C23#41711yescharacteristic
208C22×C23C2×#10411yescharacteristic
209C22×C23#42111yescharacteristic
210C2×D23—22no—
211C2×D23—22no—
212C2×D23—22no—
213C2×D23—22no—
214C2×D23—22no—
215C2×D23—22no—
216C2×D23D4⋊C814yes—
217C4×C23—21no—
218C4×C23—21no—
219C4×C23—21no—
220C4×C23—21no—
221C4×C23—21no—
222C4×C23—21no—
223C4×C23—81no—
224Dic23—22no—
225Dic23—22no—
226Dic23—22no—
227Dic23—42no—
228Dic23—81no—
229C23×C8—461no—
230C2×#121—231no—
231C2×C4×D4—231no—
232C2×C4×D4—461no—
233C22×C42—231no—
234C2×C4⋊C8—461no—
235C2×C22⋊C8—461no—
236#390C2×D2311yescharacteristic
237#389—231no—
238#388—461no—
239#386—461no—
240#380—231no—
241C4×C4⋊C4—231no—
242C4×C22⋊C4—461no—
243#336—231no—
244#336—231no—
245#336—461no—
246#336C2×D2311yescharacteristic
247#336C2×D2311yescharacteristic
248C2×C23—82no—
249C2×C23#145911yescharacteristic
250C2×C23C2×D4⋊C811yescharacteristic
251C2×C23#147711yescharacteristic
252C2×C23#150411yescharacteristic
253C2×C23#151911yescharacteristic
254C2×C23#153211yescharacteristic
255C2×C23#154711yescharacteristic
256D23—24no—
257C22×D4—461no—
258C22×D4C4×D2311yescharacteristic
259C23×C4—231no—
260C23×C4—231no—
261C23×C4—231no—
262C23×C4—461no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—464no—
266C22×C8—461no—
267C22×C8—461no—
268C22×C8—922no—
269C22×C8—922no—
270#121—234no—
271#121—462no—
272C4×D4—922no—
273C4×D4—922no—
274C4×D4—922no—
275C2×C4⋊C4—231no—
276C2×C4⋊C4—231no—
277C2×C4⋊C4—461no—
278C2×C4⋊C4C4×D2311yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—461no—
282C2×C22⋊C4—461no—
283C2×C22⋊C4—461no—
284C2×C42—231no—
285C2×C42—231no—
286C2×C42—231no—
287C2×C42—461no—
288C2×C42—922no—
289C2×C42C22×D2311yescharacteristic
290C4⋊C8—922no—
291C22⋊C8—922no—
292#95—461no—
293#95—461no—
294#95—461no—
295C23#758611yescharacteristic, complemented, Sylow
296C24—21no—
297C24—231no—
298C2×D4—21no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—464no—
302C2×D4—922no—
303C2×D4—922no—
304C2×D4C8×D2312yescomplemented
305C22×C4—21no—
306C22×C4—231no—
307C22×C4—231no—
308C22×C4—231no—
309C22×C4—232no—
310C22×C4—232no—
311C22×C4—232no—
312C22×C4—232no—
313C22×C4—462no—
314C22×C4—462no—
315C22×C4—461no—
316C22×C4—461no—
317C22×C4—461no—
318C22×C4—461no—
319C22×C4—921no—
320C22×C4—921no—
321C22×C4—921no—
322C22×C4—921no—
323C22×C4—922no—
324C22×C4—922no—
325C22×C4—922no—
326C22×C4C2×C4×D2311yescharacteristic
327C22×C4D4×D2311yescharacteristic
328C22×C4D4×D2311yescharacteristic
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—462no—
336C2×C8—928no—
337C2×C8—921no—
338C2×C8—921no—
339C2×C8—921no—
340C2×C8—921no—
341C2×C8—921no—
342C4⋊C4—41no—
343C4⋊C4—232no—
344C4⋊C4—461no—
345C4⋊C4—921no—
346C4⋊C4—921no—
347C4⋊C4—921no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—464no—
353C22⋊C4—922no—
354C22⋊C4—922no—
355C42—41no—
356C42—462no—
357C42—462no—
358C42—921no—
359C42—922no—
360C23—22no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—232no—
368C23—232no—
369C23—232no—
370C23—461no—
371C23—461no—
372C23—461no—
373C23—461no—
374C23C22⋊C4×D2311yescharacteristic
375D4—42no—
376D4—42no—
377D4—928no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—232no—
388C2×C4—232no—
389C2×C4—232no—
390C2×C4—464no—
391C2×C4—464no—
392C2×C4—461no—
393C2×C4—461no—
394C2×C4—461no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—461no—
398C2×C4—462no—
399C2×C4—922no—
400C2×C4—922no—
401C2×C4—922no—
402C2×C4—922no—
403C2×C4—921no—
404C2×C4—921no—
405C2×C4—921no—
406C2×C4—921no—
407C2×C4—921no—
408C2×C4—1844no—
409C2×C4C2×C8×D2311yescharacteristic
410C2×C4M16×D2311yescharacteristic
411C2×C4D8×D2311yescharacteristic
412C2×C4#1062508211yescharacteristic
413C2×C4SD16×D2311yescharacteristic
414C2×C4#1062508611yescharacteristic
415C8—42no—
416C8—81no—
417C8—922no—
418C8—1841no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—234no—
427C22—462no—
428C22—462no—
429C22—462no—
430C22—462no—
431C22—462no—
432C22—462no—
433C22C22⋊C8×D2311yescharacteristic
434C22#99×D2311yescharacteristic
435C22#1309239811yescharacteristic
436C22#102×D2311yescharacteristic
437C22#1309241511yescharacteristic
438C22#104×D2311yescharacteristic
439C22#1309243211yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—462no—
448C4—462no—
449C4—462no—
450C4—922no—
451C4—1841no—
452C2—82no—
453C2—464no—
454C2#1567171211yescharacteristic
455C2D23×D4⋊C811yescharacteristic
456C2#1567178111yescharacteristic
457C2#1567189811yescharacteristic
458C2#1567196311yescharacteristic
459C2#1567201411yescharacteristic
460C2#1567207111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1270C2
socleC23×C23C2×C22⋊C4
hypercenter#1270D23
hypocenterC23#7586
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #15673376C2semidirect
3. D23×#336C2semidirect
4. #15671221C2semidirect
5. #15671219C2semidirect
6. #15671218C2semidirect
7. C23×#1270C2semidirect
42. #10625109C8semidirect
70. C2×D4×C23C2×C8semidirect
115. C4⋊Dic23C2×C8semidirect
195. #1270D23semidirect
295. C23#7586semidirect
304. C2×D4C8×D23semidirect