Finite Group Databasebeta

← #19212166

Subgroups — #19212166

Order 5888.

680 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625101C211yesmaximal, characteristic
2C2×#13092172C211yesmaximal, characteristic, complemented
3#15671219C212yesmaximal, complemented
4#15671217C212yesmaximal, complemented
5C4×C23×C22⋊C8C211yesmaximal, characteristic, complemented
6C23×C23⋊C8—21no—
7C2×#10625101C411yescharacteristic
8C2×C4×D92C411yescharacteristic
9C2×C4×C22⋊D23—21no—
10#13092319C2211yescharacteristic
11#13092315C2211yescharacteristic
12#13092308—21no—
13#13092296—21no—
14#13092277C411yescharacteristic
15C4×C4⋊Dic23C411yescharacteristic
16C4×(C2×D23)⋊C4—21no—
17#13092172—21no—
18#13092172C2212yes—
19C22×C42×C23C2211yescharacteristic
20C2×C23×C22⋊C8—21no—
21C2×C4×C8×C23—21no—
22C23×#336C2212yes—
23C23×C4×C23C2×C411yescharacteristic
24C23×C4×C23D411yescharacteristic
25C23×C4×C23D411yescharacteristic
26C22×C22⋊D23—21no—
27C22×D92C2×C411yescharacteristic
28C22×C4×D23—21no—
29C22×C8×C23—22no—
30C2×C42×C23—42no—
31C2×C42×C23C2×C411yescharacteristic
32C2×C42×C23D411yescharacteristic
33C2×C42×C23D411yescharacteristic
34C2×C42×C23C2311yescharacteristic
35C2×C22⋊Dic23—21no—
36#10625101—22no—
37#10625101C814yescomplemented
38C4×C22⋊D23—42no—
39C4×C22⋊D23—42no—
40C2×(C2×D23)⋊C4—21no—
41C2×(C2×D23)⋊C4—21no—
42C2×(C2×D23)⋊C4—21no—
43C2×(C2×D23)⋊C4—21no—
44C2×C4⋊Dic23C2×C411yescharacteristic
45C2×C4⋊Dic23C2×C411yescharacteristic
46C2×C4⋊Dic23C2×C411yescharacteristic
47C2×Dic23⋊C4—21no—
48C2×C4×Dic23—21no—
49C22×C23⋊C8—24no—
50C22×C23⋊C8—22no—
51C22×C23⋊C8—42no—
52C22×C23⋊C8—42no—
53C4×D92—42no—
54C23×C22⋊C8—24no—
55C4×C8×C23—42no—
56C23⋊#95—21no—
57C23⋊#95—21no—
58C23⋊#95—21no—
59C24×C23C22⋊C411yescharacteristic
60C23×D23—21no—
61C22×C4×C23—22no—
62C22×C4×C23—22no—
63C22×C4×C23—22no—
64C22×C4×C23—22no—
65C22×C4×C23—41no—
66C22×C4×C23—41no—
67C22×C4×C23—41no—
68C22×C4×C23C22⋊C411yescharacteristic
69C22×C4×C23C22⋊C411yescharacteristic
70C22×C4×C23C22⋊C411yescharacteristic
71C22×C4×C23C2×C812yes—
72C22×C4×C23M1612yes—
73C22×C4×C23D812yes—
74C22×C4×C23SD1612yes—
75C22×C4×C23C22×C411yescharacteristic
76C22×C4×C23C2×D411yescharacteristic
77C22×C4×C23C2×D411yescharacteristic
78C2×C22⋊D23—24no—
79C2×C22⋊D23—42no—
80C2×C22⋊D23—42no—
81C22×Dic23—21no—
82C22×Dic23—21no—
83C22×Dic23—21no—
84C2×D92—21no—
85C2×D92—41no—
86C2×D92—41no—
87C2×D92C2×C812yescomplemented
88C2×C4×D23—42no—
89C2×C4×D23—42no—
90C2×C4×D23—42no—
91C2×C8×C23—24no—
92C2×C8×C23—42no—
93C2×C8×C23—42no—
94C42×C23—22no—
95C42×C23—22no—
96C42×C23—41no—
97C42×C23—41no—
98C22⋊Dic23—42no—
99(C2×D23)⋊C4—24no—
100(C2×D23)⋊C4—42no—
101(C2×D23)⋊C4—41no—
102(C2×D23)⋊C4—41no—
103(C2×D23)⋊C4—42no—
104C4⋊Dic23—21no—
105C4⋊Dic23—41no—
106C4⋊Dic23—41no—
107C4⋊Dic23C2×C812yescomplemented
108Dic23⋊C4—41no—
109Dic23⋊C4—41no—
110C4×Dic23—42no—
111C2×C23⋊C8—24no—
112C2×C23⋊C8—42no—
113C2×C23⋊C8—48no—
114C2×C23⋊C8—42no—
115#7565—231nomaximal, Sylow
116C23×C23—21no—
117C23×C23—21no—
118C23×C23—21no—
119C23×C23—21no—
120C23×C23C22⋊C812yes—
121C23×C23#10212yes—
122C23×C23#10412yes—
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—21no—
132C2×C4×C23—21no—
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—24no—
140C2×C4×C23—24no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—42no—
145C2×C4×C23—42no—
146C2×C4×C23—44no—
147C2×C4×C23C22⋊C812yes—
148C2×C4×C23#9912yes—
149C2×C4×C23#10212yes—
150C2×C4×C23#10412yes—
151C2×C4×C23C22×C811yescharacteristic
152C2×C4×C23C2×M1611yescharacteristic
153C2×C4×C23C2×D811yescharacteristic
154C2×C4×C23C2×SD1611yescharacteristic
155C2×C4×C23#13512yes—
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—84no—
169C8×C23—44no—
170C23⋊C8—44no—
171C4×#121—231no—
172C4×C22⋊C8D2311yescharacteristic, complemented
173C2×#336—231no—
174#1271—232no—
175#1270—232no—
176C22×C23—22no—
177C22×C23—22no—
178C22×C23—22no—
179C22×C23—22no—
180C22×C23—22no—
181C22×C23—22no—
182C22×C23D4⋊C814yes—
183C22×C23C2×C22⋊C811yescharacteristic
184C22×C23C2×#9911yescharacteristic
185C22×C23#41311yescharacteristic
186C22×C23C2×#10211yescharacteristic
187C22×C23#41611yescharacteristic
188C22×C23C2×#10411yescharacteristic
189C22×C23C2×#10411yescharacteristic
190C2×D23—42no—
191C2×D23—42no—
192C2×D23—42no—
193C2×D23—81no—
194C2×D23—81no—
195C2×D23—81no—
196C2×D23—81no—
197C4×C23—21no—
198C4×C23—21no—
199C4×C23—22no—
200C4×C23—21no—
201C4×C23—21no—
202C4×C23—22no—
203C4×C23—41no—
204C4×C23#32714yes—
205Dic23—42no—
206Dic23—81no—
207Dic23—81no—
208C23×C8—461no—
209C2×#121—231no—
210C2×C4×D4—231no—
211C2×C4×D4—461no—
212C22×C42C2×D2311yescharacteristic
213C2×C22⋊C8—21no—
214C2×C4×C8—21no—
215#390—231no—
216#389—231no—
217#388—461no—
218#386—461no—
219#380—231no—
220C4×C4⋊C4—231no—
221C4×C22⋊C4—461no—
222#336—232no—
223#336—461no—
224#336C2×D2312yes—
225C2×C23—24no—
226C2×C23#145911yescharacteristic
227C2×C23C2×D4⋊C811yescharacteristic
228C2×C23#147611yescharacteristic
229C2×C23C2×#32711yescharacteristic
230C2×C23#150111yescharacteristic
231C2×C23#152411yescharacteristic
232C2×C23#154011yescharacteristic
233D23—82no—
234C22×D4—231no—
235C22×D4—461no—
236C23×C4—461no—
237C23×C4C4×D2311yescharacteristic
238C23×C4D9211yescharacteristic
239C23×C4C22⋊D2311yescharacteristic
240C22×C8—22no—
241C22×C8—464no—
242C22×C8—462no—
243C22×C8—922no—
244C22×C8—922no—
245#121—234no—
246#121—462no—
247C4×D4—922no—
248C4×D4—922no—
249C4×D4—922no—
250C2×C4⋊C4—231no—
251C2×C4⋊C4—231no—
252C2×C4⋊C4—231no—
253C2×C4⋊C4—461no—
254C2×C22⋊C4—461no—
255C2×C22⋊C4—461no—
256C2×C22⋊C4—461no—
257C2×C22⋊C4—461no—
258C2×C22⋊C4—461no—
259C2×C42—42no—
260C2×C42—461no—
261C2×C42C4×D2311yescharacteristic
262C2×C42D9211yescharacteristic
263C2×C42C22⋊D2311yescharacteristic
264C2×C42C22×D2311yescharacteristic
265C22⋊C8—24no—
266C4×C8—42no—
267#95—461no—
268#95—461no—
269#95—461no—
270C23#756511yescharacteristic, complemented, Sylow
271C24—461no—
272C24(C2×D23)⋊C411yescharacteristic
273C2×D4—232no—
274C2×D4—464no—
275C2×D4—461no—
276C2×D4—921no—
277C2×D4—921no—
278C2×D4—922no—
279C2×D4—922no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—461no—
288C22×C4—461no—
289C22×C4—461no—
290C22×C4—922no—
291C22×C4—922no—
292C22×C4—922no—
293C22×C4C8×D2312yes—
294C22×C4#6726212yes—
295C22×C4#6726312yes—
296C22×C4D18412yes—
297C22×C4(C2×D23)⋊C411yescharacteristic
298C22×C4(C2×D23)⋊C411yescharacteristic
299C22×C4(C2×D23)⋊C411yescharacteristic
300C22×C4C2×C4×D2311yescharacteristic
301C22×C4C2×D9211yescharacteristic
302C22×C4C2×C22⋊D2311yescharacteristic
303C2×C8—24no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—464no—
307C2×C8—922no—
308C2×C8—928no—
309C2×C8—922no—
310C4⋊C4—232no—
311C4⋊C4—461no—
312C4⋊C4—921no—
313C4⋊C4—921no—
314C4⋊C4—921no—
315C4⋊C4—921no—
316C22⋊C4—464no—
317C22⋊C4—922no—
318C22⋊C4—922no—
319C22⋊C4—921no—
320C22⋊C4—921no—
321C22⋊C4—922no—
322C42—22no—
323C42—22no—
324C42—41no—
325C42—41no—
326C42—922no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—462no—
332C23—921no—
333C23—921no—
334C23—921no—
335C23—921no—
336C23—921no—
337C23—921no—
338C23#1062498712yes—
339C23(C2×D23)⋊C812yes—
340C23#1062500312yes—
341C23C2×(C2×D23)⋊C411yescharacteristic
342D4—922no—
343D4—922no—
344D4—928no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—462no—
362C2×C4—921no—
363C2×C4—921no—
364C2×C4—921no—
365C2×C4—921no—
366C2×C4—921no—
367C2×C4—921no—
368C2×C4—921no—
369C2×C4—921no—
370C2×C4—1844no—
371C2×C4#1062498812yes—
372C2×C4(C2×D23)⋊C812yes—
373C2×C4#1062500312yes—
374C2×C4#1062500712yes—
375C2×C4C2×C8×D2311yescharacteristic
376C2×C4C2×#6726211yescharacteristic
377C2×C4C2×#6726311yescharacteristic
378C2×C4C2×D18411yescharacteristic
379C2×C4#1062512112yes—
380C8—44no—
381C8—924no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—922no—
389C22—922no—
390C22—922no—
391C22—1841no—
392C22—1841no—
393C22—1841no—
394C22—1841no—
395C22#1309214614yes—
396C22C2×(C2×D23)⋊C811yescharacteristic
397C22C2×#1062498811yescharacteristic
398C22#1309239911yescharacteristic
399C22C2×#1062500311yescharacteristic
400C22#1309241111yescharacteristic
401C22C2×#1062500711yescharacteristic
402C22C2×#1062498711yescharacteristic
403C4—21no—
404C4—21no—
405C4—22no—
406C4—21no—
407C4—21no—
408C4—22no—
409C4—41no—
410C4—922no—
411C4—1841no—
412C4—1841no—
413C4#1309215214yes—
414C2—24no—
415C2—1842no—
416C2#1567171311yescharacteristic
417C2C2×#1309214611yescharacteristic
418C2#1567177711yescharacteristic
419C2C2×#1309215211yescharacteristic
420C2#1567188611yescharacteristic
421C2#1567198611yescharacteristic
422C2#1567204411yescharacteristic
subgroupG/H
centerC22×C4(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC4×C23×C22⋊C8C2
socleC23×C23C2×C22⋊C4
hypercenterC4×C22⋊C8D23
hypocenterC23#7565
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#13092172C2semidirect
3. #15671219C2semidirect
4. #15671217C2semidirect
5. C4×C23×C22⋊C8C2semidirect
37. #10625101C8semidirect
87. C2×D92C2×C8semidirect
107. C4⋊Dic23C2×C8semidirect
172. C4×C22⋊C8D23semidirect
270. C23#7565semidirect