Finite Group Databasebeta

← #19212142

Subgroups — #19212142

Order 5888.

538 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675859C211yesmaximal, characteristic
2#15673245C211yesmaximal, characteristic, complemented
3#15673141C211yesmaximal, characteristic, complemented
4#15671221C211yesmaximal, characteristic, complemented
5#15671219C211yesmaximal, characteristic, complemented
6#15671218C211yesmaximal, characteristic
7C23×#1270C211yesmaximal, characteristic
8C2×D4×Dic23C411yescharacteristic
9C2×#10625048—21no—
10C2×Dic23⋊C8—21no—
11C2×C8×Dic23—21no—
12C2×C8×Dic23—21no—
13#13092320C411yescharacteristic
14#13092315C2211yescharacteristic
15#13092313C411yescharacteristic
16#13092311—21no—
17#13092305—21no—
18C4⋊C4×Dic23C411yescharacteristic
19C22⋊C4×Dic23—21no—
20C42×Dic23C2211yescharacteristic
21#13092172C2211yescharacteristic
22#13092172C2211yescharacteristic
23#13092171—21no—
24C23×#390C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×D4×C23C2×C411yescharacteristic
28C23×Dic23—21no—
29C22×C8×C23—21no—
30C22×C8×C23—21no—
31C2×C4⋊C4×C23C2×C411yescharacteristic
32C2×C22⋊C4×C23—21no—
33C2×C22⋊C4×C23—21no—
34C2×C42×C23C2311yescharacteristic
35C2×C22⋊Dic23—21no—
36C2×C22⋊Dic23—21no—
37C2×C22⋊Dic23—21no—
38D4×Dic23—22no—
39D4×Dic23C814yescomplemented
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×C4⋊Dic23C2×C411yescharacteristic
42C2×Dic23⋊C4—21no—
43C2×Dic23⋊C4—21no—
44C2×C4×Dic23—21no—
45C2×C4×Dic23C2×C411yescharacteristic
46C2×C4×Dic23C2×C411yescharacteristic
47C2×C4×Dic23D411yescharacteristic
48C2×C4×Dic23D411yescharacteristic
49C2×C4×Dic23D411yescharacteristic
50C2×C4×Dic23D411yescharacteristic
51C22×C23⋊C8—21no—
52C22×C23⋊C8—21no—
53#10625048—42no—
54#10625048—42no—
55C23⋊#95—21no—
56C23⋊#95—21no—
57C23⋊#95—21no—
58Dic23⋊C8—24no—
59C8×Dic23—24no—
60C8×Dic23—42no—
61C24×C23—21no—
62C2×D4×C23—21no—
63C2×D4×C23—41no—
64C2×D4×C23—41no—
65C2×D4×C23C2×C812yes—
66C22×C4×C23—21no—
67C22×C4×C23C22×C411yescharacteristic
68C22×C4×C23C2×D411yescharacteristic
69C22×C4×C23C2×D411yescharacteristic
70C22×Dic23—21no—
71C22×Dic23—24no—
72C22×Dic23—21no—
73C22×Dic23—42no—
74C22×Dic23—42no—
75C22×Dic23C22⋊C411yescharacteristic
76C22×Dic23C22⋊C411yescharacteristic
77C22×Dic23C22⋊C411yescharacteristic
78C22×Dic23C22⋊C411yescharacteristic
79C2×C8×C23—22no—
80C2×C8×C23—22no—
81C2×C8×C23—41no—
82C2×C8×C23—41no—
83C2×C8×C23—41no—
84C2×C8×C23—41no—
85C4⋊C4×C23—41no—
86C22⋊C4×C23—41no—
87C22⋊C4×C23—41no—
88C22⋊C4×C23—41no—
89C22⋊C4×C23—41no—
90C42×C23—41no—
91C22⋊Dic23—24no—
92C22⋊Dic23—42no—
93C22⋊Dic23—42no—
94C4⋊Dic23—21no—
95C4⋊Dic23—41no—
96C4⋊Dic23C2×C812yes—
97Dic23⋊C4—41no—
98Dic23⋊C4—41no—
99Dic23⋊C4—42no—
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23—22no—
103C4×Dic23—22no—
104C4×Dic23—41no—
105C4×Dic23—42no—
106C4×Dic23C2×C812yes—
107C4×Dic23M1612yes—
108C4×Dic23D812yes—
109C4×Dic23SD1612yes—
110C2×C23⋊C8—22no—
111C2×C23⋊C8—22no—
112C2×C23⋊C8—41no—
113C2×C23⋊C8—41no—
114C2×C23⋊C8—41no—
115C2×C23⋊C8—41no—
116#7560—231nomaximal, Sylow
117C23×C23—22no—
118C23×C23—41no—
119C23×C23—41no—
120C23×C23—41no—
121C23×C23—41no—
122C23×C23—41no—
123C23×C23—41no—
124C23×C23C2×C22⋊C411yescharacteristic
125D4×C23—42no—
126D4×C23—42no—
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—41no—
134C2×C4×C23—41no—
135C2×C4×C23—41no—
136C2×C4×C23C22×C811yescharacteristic
137C2×C4×C23C2×M1611yescharacteristic
138C2×C4×C23C2×D811yescharacteristic
139C2×C4×C23C2×SD1611yescharacteristic
140C2×C4×C23#13511yescharacteristic
141C2×C4×C23#13511yescharacteristic
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—22no—
149C2×Dic23—41no—
150C2×Dic23—41no—
151C2×Dic23—48no—
152C2×Dic23—41no—
153C2×Dic23—41no—
154C2×Dic23—41no—
155C2×Dic23C22⋊C812yes—
156C2×Dic23C22⋊C812yes—
157C2×Dic23#10212yes—
158C2×Dic23#10212yes—
159C2×Dic23#10412yes—
160C2×Dic23#10412yes—
161C8×C23—42no—
162C8×C23—42no—
163C23⋊C8—42no—
164C23⋊C8—42no—
165#2293—231no—
166C4×C4⋊C8—231no—
167#1744—231no—
168#1271—231no—
169#1271—231no—
170#1270—231no—
171#1270D2311yescharacteristic
172C22×C23—42no—
173C22×C23—42no—
174C22×C23—42no—
175C22×C23—81no—
176C22×C23—81no—
177C22×C23—81no—
178C22×C23—81no—
179C22×C23C2×C22⋊C811yescharacteristic
180C22×C23#41011yescharacteristic
181C22×C23#41311yescharacteristic
182C22×C23C2×#10211yescharacteristic
183C22×C23#41611yescharacteristic
184C22×C23C2×#10411yescharacteristic
185C22×C23C2×#10411yescharacteristic
186C4×C23—21no—
187C4×C23—21no—
188C4×C23—21no—
189C4×C23—21no—
190C4×C23—21no—
191C4×C23—21no—
192C4×C23—81no—
193Dic23—22no—
194Dic23—22no—
195Dic23—22no—
196Dic23—42no—
197Dic23—81no—
198Dic23D4⋊C814yes—
199C2×C4×D4—231no—
200C2×#117—461no—
201C2×C4⋊C8—461no—
202C2×C4×C8—461no—
203C2×C4×C8—461no—
204#390—231no—
205#390C2×D2311yescharacteristic
206#389—231no—
207#389—231no—
208#388—461no—
209#388—461no—
210C4×C4⋊C4—231no—
211C4×C22⋊C4—461no—
212C43—231no—
213#336—231no—
214#336—231no—
215#336—461no—
216#336C2×D2311yescharacteristic
217#336C2×D2311yescharacteristic
218C2×C23—82no—
219C2×C23#145811yescharacteristic
220C2×C23C2×D4⋊C811yescharacteristic
221C2×C23#147611yescharacteristic
222C2×C23#150011yescharacteristic
223C2×C23#150211yescharacteristic
224C2×C23#152411yescharacteristic
225C2×C23#154011yescharacteristic
226C22×D4C4×D2311yescharacteristic
227C23×C4—461no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—461no—
231C22×C8—461no—
232C4×D4—234no—
233C4×D4—462no—
234#117—922no—
235#117—922no—
236C2×C4⋊C4—231no—
237C2×C4⋊C4—231no—
238C2×C4⋊C4—461no—
239C2×C4⋊C4—461no—
240C2×C4⋊C4C4×D2311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—461no—
244C2×C22⋊C4—461no—
245C2×C22⋊C4—461no—
246C2×C42—231no—
247C2×C42—231no—
248C2×C42—231no—
249C2×C42—231no—
250C2×C42—231no—
251C2×C42—231no—
252C2×C42—461no—
253C2×C42C22×D2311yescharacteristic
254C4⋊C8—464no—
255C4×C8—464no—
256C4×C8—922no—
257#95—461no—
258#95—461no—
259#95—461no—
260C23#756011yescharacteristic, complemented, Sylow
261C24—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4C8×D2312yes—
266C22×C4—21no—
267C22×C4—231no—
268C22×C4—231no—
269C22×C4—231no—
270C22×C4—231no—
271C22×C4—464no—
272C22×C4—461no—
273C22×C4—461no—
274C22×C4—922no—
275C22×C4—922no—
276C22×C4C2×C4×D2311yescharacteristic
277C22×C4D4×D2311yescharacteristic
278C22×C4D4×D2311yescharacteristic
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—462no—
286C2×C8—462no—
287C2×C8—921no—
288C2×C8—921no—
289C2×C8—921no—
290C2×C8—921no—
291C4⋊C4—41no—
292C4⋊C4—232no—
293C4⋊C4—461no—
294C4⋊C4—921no—
295C4⋊C4—922no—
296C4⋊C4—921no—
297C4⋊C4—921no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—464no—
303C22⋊C4—922no—
304C22⋊C4—922no—
305C42—41no—
306C42—232no—
307C42—232no—
308C42—232no—
309C42—232no—
310C42—462no—
311C42—462no—
312C42—461no—
313C42—461no—
314C42—921no—
315C42—922no—
316C23—22no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23C22⋊C4×D2311yescharacteristic
324D4—42no—
325D4—42no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—232no—
336C2×C4—232no—
337C2×C4—232no—
338C2×C4—232no—
339C2×C4—232no—
340C2×C4—232no—
341C2×C4—461no—
342C2×C4—461no—
343C2×C4—461no—
344C2×C4—461no—
345C2×C4—461no—
346C2×C4—461no—
347C2×C4—462no—
348C2×C4—928no—
349C2×C4—921no—
350C2×C4—921no—
351C2×C4—921no—
352C2×C4—921no—
353C2×C4—921no—
354C2×C4C2×C8×D2311yescharacteristic
355C2×C4M16×D2311yescharacteristic
356C2×C4D8×D2311yescharacteristic
357C2×C4#1062508311yescharacteristic
358C2×C4SD16×D2311yescharacteristic
359C2×C4#1062508711yescharacteristic
360C8—42no—
361C8—42no—
362C8—922no—
363C8—922no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C22⋊C8×D2311yescharacteristic
372C22#1309238911yescharacteristic
373C22#1309239811yescharacteristic
374C22#102×D2311yescharacteristic
375C22#1309241011yescharacteristic
376C22#104×D2311yescharacteristic
377C22#104×D2311yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—234no—
386C4—462no—
387C4—462no—
388C4—462no—
389C4—922no—
390C4—1841no—
391C2—82no—
392C2#1567170811yescharacteristic
393C2D23×D4⋊C811yescharacteristic
394C2#1567177611yescharacteristic
395C2#1567188011yescharacteristic
396C2#1567189011yescharacteristic
397C2#1567198211yescharacteristic
398C2#1567204311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1270C2
socleC23×C23C2×C22⋊C4
hypercenter#1270D23
hypocenterC23#7560
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. #15673245C2semidirect
3. #15673141C2semidirect
4. #15671221C2semidirect
5. #15671219C2semidirect
39. D4×Dic23C8semidirect
260. C23#7560semidirect