Finite Group Databasebeta

← #19212256

Subgroups — #19212256

Order 5888.

662 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625101C211yesmaximal, characteristic
2#15673377C211yesmaximal, characteristic, complemented
3#15671219C212yesmaximal, complemented
4#15671217C212yesmaximal, complemented
5C2×C23×#336C211yesmaximal, characteristic, complemented
6C2×#10625101C411yescharacteristic
7C2×C4×D92C411yescharacteristic
8C2×C4×C22⋊D23—21no—
9C2×C4⋊(C23⋊C8)—21no—
10C2×C22⋊(C23⋊C8)—21no—
11#13092319C2211yescharacteristic
12#13092315C2211yescharacteristic
13#13092308—21no—
14#13092296—21no—
15#13092277C411yescharacteristic
16C4×C4⋊Dic23C411yescharacteristic
17C4×(C2×D23)⋊C4—21no—
18#13092172C2212yes—
19C23×C8×C23—21no—
20C22×C42×C23C2211yescharacteristic
21C23×#336—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—24no—
30C22×C8×C23—22no—
31C22×C8×C23—42no—
32C22×C8×C23—42no—
33C2×C42×C23—42no—
34C2×C42×C23C2×C411yescharacteristic
35C2×C42×C23D411yescharacteristic
36C2×C42×C23D411yescharacteristic
37C2×C42×C23C2311yescharacteristic
38C2×C22⋊Dic23—21no—
39#10625101—22no—
40#10625101C814yescomplemented
41C4×C22⋊D23—42no—
42C4×C22⋊D23—42no—
43C2×(C2×D23)⋊C4—21no—
44C2×(C2×D23)⋊C4—21no—
45C2×(C2×D23)⋊C4—21no—
46C2×(C2×D23)⋊C4—21no—
47C2×C4⋊Dic23C2×C411yescharacteristic
48C2×C4⋊Dic23C2×C411yescharacteristic
49C2×C4⋊Dic23C2×C411yescharacteristic
50C2×Dic23⋊C4—21no—
51C2×C4×Dic23—21no—
52C22×C23⋊C8—22no—
53C4×D92—42no—
54C23⋊#95—21no—
55C23⋊#95—21no—
56C23⋊#95—21no—
57C22⋊(C23⋊C8)—42no—
58C4⋊(C23⋊C8)—42no—
59C24×C23C22⋊C411yescharacteristic
60C23×D23—21no—
61C22×C4×C23—22no—
62C22×C4×C23—22no—
63C22×C4×C23—21no—
64C22×C4×C23—21no—
65C22×C4×C23—41no—
66C22×C4×C23—41no—
67C22×C4×C23—41no—
68C22×C4×C23—41no—
69C22×C4×C23C22⋊C411yescharacteristic
70C22×C4×C23C22⋊C411yescharacteristic
71C22×C4×C23C22⋊C411yescharacteristic
72C22×C4×C23C2×C812yes—
73C22×C4×C23M1612yes—
74C22×C4×C23D812yes—
75C22×C4×C23SD1612yes—
76C22×C4×C23C22×C411yescharacteristic
77C22×C4×C23C2×D411yescharacteristic
78C22×C4×C23C2×D411yescharacteristic
79C2×C22⋊D23—24no—
80C2×C22⋊D23—42no—
81C2×C22⋊D23—42no—
82C22×Dic23—21no—
83C22×Dic23—21no—
84C22×Dic23—21no—
85C2×D92—21no—
86C2×D92—41no—
87C2×D92—41no—
88C2×D92C2×C812yescomplemented
89C2×C4×D23—42no—
90C2×C4×D23—42no—
91C2×C4×D23—42no—
92C2×C8×C23—24no—
93C2×C8×C23—48no—
94C2×C8×C23—42no—
95C2×C8×C23—42no—
96C42×C23—22no—
97C42×C23—22no—
98C42×C23—41no—
99C42×C23—41no—
100C22⋊Dic23—42no—
101(C2×D23)⋊C4—24no—
102(C2×D23)⋊C4—42no—
103(C2×D23)⋊C4—41no—
104(C2×D23)⋊C4—41no—
105(C2×D23)⋊C4—41no—
106(C2×D23)⋊C4—41no—
107C4⋊Dic23—21no—
108C4⋊Dic23—41no—
109C4⋊Dic23—41no—
110C4⋊Dic23C2×C812yescomplemented
111Dic23⋊C4—41no—
112Dic23⋊C4—41no—
113C4×Dic23—42no—
114C2×C23⋊C8—42no—
115C2×C23⋊C8—42no—
116C2×C23⋊C8—42no—
117#7586—231nomaximal, Sylow
118C23×C23—21no—
119C23×C23—21no—
120C23×C23—21no—
121C23×C23—21no—
122C23×C23C22⋊C812yes—
123C23×C23#10212yes—
124C23×C23#10412yes—
125C23×C23C2×C22⋊C411yescharacteristic
126C22×D23—22no—
127C22×D23—41no—
128C22×D23—41no—
129C22×D23—41no—
130C22×D23—41no—
131C22×D23—41no—
132C22×D23—41no—
133C2×C4×C23—24no—
134C2×C4×C23—24no—
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—21no—
147C2×C4×C23—42no—
148C2×C4×C23—42no—
149C2×C4×C23—42no—
150C2×C4×C23—42no—
151C2×C4×C23C22⋊C812yes—
152C2×C4×C23#9912yes—
153C2×C4×C23#10212yes—
154C2×C4×C23C22×C811yescharacteristic
155C2×C4×C23C2×M1611yescharacteristic
156C2×C4×C23C2×D811yescharacteristic
157C2×C4×C23C2×SD1611yescharacteristic
158C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C23#13711yescharacteristic
160C22⋊D23—48no—
161C2×Dic23—22no—
162C2×Dic23—41no—
163C2×Dic23—41no—
164C2×Dic23—41no—
165C2×Dic23—41no—
166C2×Dic23—41no—
167C2×Dic23—41no—
168C2×Dic23—41no—
169C2×Dic23—41no—
170D92—42no—
171D92—42no—
172C4×D23—84no—
173C8×C23—44no—
174C23⋊C8—82no—
175C4×#121—231no—
176#1797—231no—
177C2×#336D2311yescharacteristic, complemented
178#1271—232no—
179#1270—232no—
180C22×C23—22no—
181C22×C23—22no—
182C22×C23—22no—
183C22×C23—22no—
184C22×C23—22no—
185C22×C23—22no—
186C22×C23D4⋊C814yes—
187C22×C23C2×C22⋊C811yescharacteristic
188C22×C23C2×#9911yescharacteristic
189C22×C23#41311yescharacteristic
190C22×C23C2×#10211yescharacteristic
191C22×C23#41711yescharacteristic
192C22×C23C2×#10411yescharacteristic
193C22×C23#42111yescharacteristic
194C2×D23—42no—
195C2×D23—42no—
196C2×D23—42no—
197C2×D23—81no—
198C2×D23—81no—
199C2×D23—81no—
200C2×D23—81no—
201C4×C23—21no—
202C4×C23—21no—
203C4×C23—22no—
204C4×C23—21no—
205C4×C23—22no—
206C4×C23—21no—
207C4×C23—21no—
208C4×C23—22no—
209C4×C23—21no—
210Dic23—42no—
211Dic23—81no—
212Dic23—81no—
213C23×C8—21no—
214C2×#121—231no—
215C2×C4×D4—231no—
216C2×C4×D4—461no—
217C22×C42C2×D2311yescharacteristic
218C2×C4⋊C8—461no—
219C2×C22⋊C8—461no—
220#390—231no—
221#389—231no—
222#388—461no—
223#386—461no—
224#380—231no—
225C4×C4⋊C4—231no—
226C4×C22⋊C4—461no—
227#336—21no—
228#336—232no—
229#336C2×D2312yes—
230C2×C23—24no—
231C2×C23#145911yescharacteristic
232C2×C23C2×D4⋊C811yescharacteristic
233C2×C23#147711yescharacteristic
234C2×C23#150411yescharacteristic
235C2×C23#151911yescharacteristic
236C2×C23#153211yescharacteristic
237C2×C23#154711yescharacteristic
238D23—82no—
239C22×D4—231no—
240C22×D4—461no—
241C23×C4—461no—
242C23×C4C4×D2311yescharacteristic
243C23×C4D9211yescharacteristic
244C23×C4C22⋊D2311yescharacteristic
245C22×C8—24no—
246C22×C8—22no—
247C22×C8—42no—
248C22×C8—42no—
249C22×C8—462no—
250#121—234no—
251#121—462no—
252C4×D4—922no—
253C4×D4—922no—
254C4×D4—922no—
255C2×C4⋊C4—231no—
256C2×C4⋊C4—231no—
257C2×C4⋊C4—231no—
258C2×C4⋊C4—461no—
259C2×C22⋊C4—461no—
260C2×C22⋊C4—461no—
261C2×C22⋊C4—461no—
262C2×C22⋊C4—461no—
263C2×C22⋊C4—461no—
264C2×C42—42no—
265C2×C42—461no—
266C2×C42C4×D2311yescharacteristic
267C2×C42D9211yescharacteristic
268C2×C42C22⋊D2311yescharacteristic
269C2×C42C22×D2311yescharacteristic
270C4⋊C8—922no—
271C22⋊C8—922no—
272#95—461no—
273#95—461no—
274#95—461no—
275C23#758611yescharacteristic, complemented, Sylow
276C24—461no—
277C24(C2×D23)⋊C411yescharacteristic
278C2×D4—232no—
279C2×D4—464no—
280C2×D4—461no—
281C2×D4—921no—
282C2×D4—921no—
283C2×D4—922no—
284C2×D4—922no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—461no—
294C22×C4—461no—
295C22×C4—461no—
296C22×C4—922no—
297C22×C4—922no—
298C22×C4—922no—
299C22×C4C8×D2312yes—
300C22×C4#6726212yes—
301C22×C4#6726312yes—
302C22×C4D18412yes—
303C22×C4(C2×D23)⋊C411yescharacteristic
304C22×C4(C2×D23)⋊C411yescharacteristic
305C22×C4(C2×D23)⋊C411yescharacteristic
306C22×C4C2×C4×D2311yescharacteristic
307C22×C4C2×D9211yescharacteristic
308C22×C4C2×C22⋊D2311yescharacteristic
309C2×C8—24no—
310C2×C8—48no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—922no—
314C2×C8—922no—
315C2×C8—922no—
316C4⋊C4—232no—
317C4⋊C4—461no—
318C4⋊C4—921no—
319C4⋊C4—921no—
320C4⋊C4—921no—
321C4⋊C4—921no—
322C22⋊C4—464no—
323C22⋊C4—922no—
324C22⋊C4—921no—
325C22⋊C4—921no—
326C22⋊C4—921no—
327C22⋊C4—921no—
328C22⋊C4—922no—
329C42—22no—
330C42—22no—
331C42—41no—
332C42—41no—
333C42—922no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—462no—
339C23—921no—
340C23—921no—
341C23—921no—
342C23—921no—
343C23—921no—
344C23—921no—
345C23#1062498712yes—
346C23(C2×D23)⋊C812yes—
347C23#1062500312yes—
348C23C2×(C2×D23)⋊C411yescharacteristic
349D4—922no—
350D4—922no—
351D4—928no—
352C2×C4—24no—
353C2×C4—24no—
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—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—462no—
371C2×C4—921no—
372C2×C4—921no—
373C2×C4—921no—
374C2×C4—921no—
375C2×C4—921no—
376C2×C4—921no—
377C2×C4—921no—
378C2×C4—921no—
379C2×C4—1844no—
380C2×C4#1062498812yes—
381C2×C4(C2×D23)⋊C812yes—
382C2×C4#1062500312yes—
383C2×C4C2×C8×D2311yescharacteristic
384C2×C4C2×#6726211yescharacteristic
385C2×C4C2×#6726311yescharacteristic
386C2×C4C2×D18411yescharacteristic
387C2×C4#1062510311yescharacteristic
388C2×C4#1062511311yescharacteristic
389C8—44no—
390C8—1842no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—922no—
398C22—922no—
399C22—922no—
400C22—1841no—
401C22—1841no—
402C22—1841no—
403C22—1841no—
404C22#1309214614yes—
405C22C2×(C2×D23)⋊C811yescharacteristic
406C22C2×#1062498811yescharacteristic
407C22#1309239911yescharacteristic
408C22C2×#1062500311yescharacteristic
409C22#1309241611yescharacteristic
410C22C2×#1062498711yescharacteristic
411C22#1309243311yescharacteristic
412C4—21no—
413C4—21no—
414C4—22no—
415C4—21no—
416C4—22no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—22no—
421C4—922no—
422C4—1841no—
423C4—1841no—
424C2—24no—
425C2—1842no—
426C2#1567171311yescharacteristic
427C2C2×#1309214611yescharacteristic
428C2#1567178211yescharacteristic
429C2#1567189911yescharacteristic
430C2#1567196611yescharacteristic
431C2#1567201511yescharacteristic
432C2#1567207211yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC2×C23×#336C2
socleC23×C23C2×C22⋊C4
hypercenterC2×#336D23
hypocenterC23#7586
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
2. #15673377C2semidirect
3. #15671219C2semidirect
4. #15671217C2semidirect
5. C2×C23×#336C2semidirect
40. #10625101C8semidirect
88. C2×D92C2×C8semidirect
110. C4⋊Dic23C2×C8semidirect
177. C2×#336D23semidirect
275. C23#7586semidirect