Finite Group Databasebeta

← #19212302

Subgroups — #19212302

Order 5888.

654 conjugacy classes of subgroups.

The subgroup lattice has 438 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×#1797C211yesmaximal, 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×C4⋊C8—21no—
21C2×C23×C22⋊C8—21no—
22C23×#336C2212yes—
23C23×C4×C23C2×C411yescharacteristic
24C23×C4×C23D411yescharacteristic
25C23×C4×C23D411yescharacteristic
26C22×C22⋊D23—21no—
27C2×#67288—22no—
28C2×#67288—42no—
29C2×#67288—42no—
30C2×#67288C814yescomplemented
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×C4⋊C8—42no—
51C23×C22⋊C8—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—21no—
65C22×C4×C23—21no—
66C22×C4×C23—41no—
67C22×C4×C23—41no—
68C22×C4×C23—41no—
69C22×C4×C23—41no—
70C22×C4×C23C22⋊C411yescharacteristic
71C22×C4×C23C22⋊C411yescharacteristic
72C22×C4×C23C22⋊C411yescharacteristic
73C22×C4×C23C2×C812yes—
74C22×C4×C23M1612yes—
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—
84#67288—48no—
85#67288—48no—
86C2×D92—21no—
87C2×D92—41no—
88C2×D92—41no—
89C2×D92C2×C812yes—
90C2×C4×D23—24no—
91C2×C4×D23—42no—
92C2×C4×D23—42no—
93C2×Dic46—21no—
94C2×Dic46—41no—
95C2×Dic46—41no—
96C2×Dic46C2×C812yes—
97C2×C8×C23—42no—
98C2×C8×C23—42no—
99C2×C8×C23—42no—
100C42×C23—22no—
101C42×C23—22no—
102C42×C23—41no—
103C42×C23—41no—
104C22⋊Dic23—42no—
105(C2×D23)⋊C4—42no—
106(C2×D23)⋊C4—42no—
107(C2×D23)⋊C4—41no—
108(C2×D23)⋊C4—41no—
109(C2×D23)⋊C4—41no—
110(C2×D23)⋊C4—41no—
111C4⋊Dic23—41no—
112C4⋊Dic23—41no—
113C4×Dic23—42no—
114C2×C23⋊C8—42no—
115C2×C23⋊C8—42no—
116C2×C23⋊C8—42no—
117#7597—231nomaximal, Sylow
118C23×C23—21no—
119C23×C23—21no—
120C23×C23—21no—
121C23×C23—21no—
122C23×C23—21no—
123C23×C23—21no—
124C23×C23C22⋊C812yes—
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—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—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#10012yes—
154C2×C4×C23C22×C811yescharacteristic
155C2×C4×C23C2×M1611yescharacteristic
156C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C23#13711yescharacteristic
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—48no—
173Dic46—42no—
174Dic46—42no—
175C8×C23—82no—
176C23⋊C8—82no—
177#2297—231no—
178#1797—231no—
179#1797D2311yescharacteristic, complemented
180#1272—232no—
181#1270—232no—
182C22×C23—22no—
183C22×C23—22no—
184C22×C23—22no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—41no—
189C22×C23C2×C22⋊C811yescharacteristic
190C22×C23C2×#9911yescharacteristic
191C22×C23C2×#10011yescharacteristic
192C22×C23#41711yescharacteristic
193C22×C23#41711yescharacteristic
194C22×C23#42111yescharacteristic
195C22×C23#42111yescharacteristic
196C2×D23—42no—
197C2×D23—42no—
198C2×D23—42no—
199C2×D23—81no—
200C2×D23—81no—
201C2×D23—81no—
202C2×D23—81no—
203C4×C23—21no—
204C4×C23—21no—
205C4×C23—21no—
206C4×C23—21no—
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—41no—
210C4×C23—41no—
211C4×C23#32314yes—
212Dic23—42no—
213Dic23—81no—
214Dic23—81no—
215C22×#41—231no—
216C2×#117—231no—
217C22×C42C2×D2311yescharacteristic
218C2×C4⋊C8—21no—
219C2×C4⋊C8—461no—
220C2×C22⋊C8—21no—
221C2×C22⋊C8—461no—
222#391—231no—
223#391—231no—
224#390—231no—
225#390—231no—
226#386—461no—
227#386—461no—
228C4×C22⋊C4—461no—
229C4×C22⋊C4—461no—
230#336—232no—
231#336C2×D2312yes—
232C2×C23—42no—
233C2×C23C2×#32311yescharacteristic
234C2×C23#147711yescharacteristic
235C2×C23#147711yescharacteristic
236C2×C23#151311yescharacteristic
237C2×C23#151311yescharacteristic
238C2×C23#153611yescharacteristic
239C2×C23#156011yescharacteristic
240D23—82no—
241C2×#41—234no—
242C2×#41—462no—
243C2×#41—922no—
244C2×#41—922no—
245C22×Q8—231no—
246C22×D4—231no—
247C22×D4—461no—
248C23×C4—461no—
249C23×C4C4×D2311yescharacteristic
250C23×C4D9211yescharacteristic
251C23×C4C22⋊D2311yescharacteristic
252C22×C8—22no—
253C22×C8—462no—
254#117—922no—
255C2×C4⋊C4—231no—
256C2×C4⋊C4—231no—
257C2×C22⋊C4—461no—
258C2×C22⋊C4—461no—
259C2×C22⋊C4—461no—
260C2×C22⋊C4—461no—
261C2×C22⋊C4—461no—
262C2×C42—42no—
263C2×C42—461no—
264C2×C42C4×D2311yescharacteristic
265C2×C42D9211yescharacteristic
266C2×C42C22⋊D2311yescharacteristic
267C2×C42C22×D2311yescharacteristic
268C4⋊C8—42no—
269C4⋊C8—922no—
270C22⋊C8—42no—
271C22⋊C8—922no—
272#95—461no—
273#95—461no—
274#95—461no—
275#95—461no—
276C23#759711yescharacteristic, complemented, Sylow
277C24—461no—
278C24(C2×D23)⋊C411yescharacteristic
279#41—928no—
280#41—928no—
281C2×Q8—232no—
282C2×Q8—461no—
283C2×Q8—921no—
284C2×Q8—921no—
285C2×D4—232no—
286C2×D4—464no—
287C2×D4—461no—
288C2×D4—921no—
289C2×D4—921no—
290C2×D4—922no—
291C2×D4—922no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—461no—
303C22×C4—464no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4—922no—
307C22×C4—922no—
308C22×C4C8×D2312yes—
309C22×C4#6726212yes—
310C22×C4(C2×D23)⋊C411yescharacteristic
311C22×C4(C2×D23)⋊C411yescharacteristic
312C22×C4(C2×D23)⋊C411yescharacteristic
313C22×C4C2×C4×D2311yescharacteristic
314C22×C4C2×D9211yescharacteristic
315C22×C4C2×C22⋊D2311yescharacteristic
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—922no—
320C2×C8—922no—
321C2×C8—922no—
322C4⋊C4—921no—
323C4⋊C4—921no—
324C22⋊C4—922no—
325C22⋊C4—922no—
326C22⋊C4—922no—
327C22⋊C4—921no—
328C22⋊C4—921no—
329C22⋊C4—921no—
330C22⋊C4—921no—
331C42—22no—
332C42—22no—
333C42—41no—
334C42—41no—
335C42—922no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—462no—
343C23—921no—
344C23—921no—
345C23—921no—
346C23—921no—
347C23—921no—
348C23—921no—
349C23(C2×D23)⋊C812yes—
350C23C2×(C2×D23)⋊C411yescharacteristic
351Q8—922no—
352Q8—922no—
353D4—922no—
354D4—922no—
355D4—928no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—462no—
375C2×C4—921no—
376C2×C4—921no—
377C2×C4—928no—
378C2×C4—921no—
379C2×C4—921no—
380C2×C4—921no—
381C2×C4—921no—
382C2×C4—921no—
383C2×C4—921no—
384C2×C4#1062498812yes—
385C2×C4(C2×D23)⋊C812yes—
386C2×C4#1062500512yes—
387C2×C4C2×C8×D2311yescharacteristic
388C2×C4C2×#6726211yescharacteristic
389C2×C4#1062507911yescharacteristic
390C2×C4#1062508011yescharacteristic
391C2×C4#1062510311yescharacteristic
392C2×C4#1062511311yescharacteristic
393C8—82no—
394C8—1842no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—922no—
403C22—922no—
404C22—922no—
405C22—1841no—
406C22—1841no—
407C22—1841no—
408C22—1841no—
409C22C2×(C2×D23)⋊C811yescharacteristic
410C22C2×#1062498811yescharacteristic
411C22C2×#1062500511yescharacteristic
412C22#1309241611yescharacteristic
413C22#1309241911yescharacteristic
414C22#1309243311yescharacteristic
415C22#1309243511yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—41no—
424C4—922no—
425C4—1841no—
426C4—1841no—
427C4#1309214014yes—
428C2—42no—
429C2—1842no—
430C2C2×#1309214011yescharacteristic
431C2#1567178211yescharacteristic
432C2#1567178511yescharacteristic
433C2#1567193811yescharacteristic
434C2#1567194111yescharacteristic
435C2#1567203111yescharacteristic
436C2#1567213011yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1797C2
socleC23×C23C2×C22⋊C4
hypercenter#1797D23
hypocenterC23#7597
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. #15673377C2semidirect
3. #15671222C2semidirect
4. #15671217C2semidirect
5. C23×#1797C2semidirect
30. C2×#67288C8semidirect
179. #1797D23semidirect
276. C23#7597semidirect