Finite Group Databasebeta

← #19212201

Subgroups — #19212201

Order 5888.

520 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675861C211yesmaximal, characteristic
2C4×C4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
3#15671221C212yesmaximal, complemented
4#15671217C212yesmaximal
5C23×#1831C211yesmaximal, characteristic, complemented
6C2×C4×D92C411yescharacteristic
7C2×#10625043—21no—
8C2×C4⋊(C23⋊C8)—21no—
9C2×C4×C23⋊C8—21no—
10#13092319C411yescharacteristic
11#13092319C2211yescharacteristic
12#13092315C411yescharacteristic
13#13092315C2211yescharacteristic
14#13092308—21no—
15#13092308—21no—
16C4×C4⋊Dic23C411yescharacteristic
17C4×(C2×D23)⋊C4—21no—
18#13092172C2212yes—
19C2×C23×C4⋊C8—21no—
20C43×C23C2211yescharacteristic
21C23×#336—21no—
22C23×#336C2212yes—
23C22×D92C2×C411yescharacteristic
24C22×C4×D23—21no—
25C22×C8×C23—22no—
26C2×C42×C23C2×C411yescharacteristic
27C2×C42×C23C2×C411yescharacteristic
28C2×C42×C23D411yescharacteristic
29C2×C42×C23D411yescharacteristic
30C2×C42×C23D411yescharacteristic
31C2×C42×C23D411yescharacteristic
32C2×C42×C23C2311yescharacteristic
33C2×(C2×D23)⋊C4—21no—
34C2×(C2×D23)⋊C4—21no—
35C2×(C2×D23)⋊C4—21no—
36C2×(C2×D23)⋊C4—21no—
37C2×(C2×D23)⋊C4—21no—
38C2×C4⋊Dic23C2×C411yescharacteristic
39C2×C4⋊Dic23C2×C411yescharacteristic
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×Dic23⋊C4—21no—
42C2×Dic23⋊C4—21no—
43C2×C4×Dic23—21no—
44C22×C23⋊C8—22no—
45C4×D92—22no—
46C4×D92C814yescomplemented
47#10625043—42no—
48#10625043—42no—
49C23×C4⋊C8—42no—
50C23⋊#95—21no—
51C23⋊#95—21no—
52C23⋊#95—21no—
53C4⋊(C23⋊C8)—24no—
54C4×C23⋊C8—42no—
55C23×D23—21no—
56C22×C4×C23C22⋊C411yescharacteristic
57C22×C4×C23C22⋊C411yescharacteristic
58C22×C4×C23C22⋊C411yescharacteristic
59C22×C4×C23C22⋊C411yescharacteristic
60C22×C4×C23C22×C411yescharacteristic
61C22×C4×C23C2×D411yescharacteristic
62C22×C4×C23C2×D411yescharacteristic
63C22×Dic23—21no—
64C22×Dic23—21no—
65C22×Dic23—21no—
66C2×D92—21no—
67C2×D92—41no—
68C2×D92—41no—
69C2×D92C2×C812yes—
70C2×C4×D23—24no—
71C2×C4×D23—42no—
72C2×C4×D23—42no—
73C2×C8×C23—42no—
74C2×C8×C23—42no—
75C2×C8×C23—42no—
76C42×C23—22no—
77C42×C23—21no—
78C42×C23—21no—
79C42×C23—41no—
80C42×C23—41no—
81C42×C23—41no—
82C42×C23C2×C812yes—
83C42×C23M1612yes—
84C42×C23D812yes—
85C42×C23SD1612yes—
86(C2×D23)⋊C4—24no—
87(C2×D23)⋊C4—42no—
88(C2×D23)⋊C4—42no—
89(C2×D23)⋊C4—41no—
90(C2×D23)⋊C4—41no—
91(C2×D23)⋊C4—41no—
92(C2×D23)⋊C4—41no—
93C4⋊Dic23—21no—
94C4⋊Dic23—41no—
95C4⋊Dic23—41no—
96C4⋊Dic23C2×C812yes—
97Dic23⋊C4—42no—
98Dic23⋊C4—41no—
99Dic23⋊C4—41no—
100C4×Dic23—42no—
101C2×C23⋊C8—24no—
102C2×C23⋊C8—42no—
103C2×C23⋊C8—42no—
104#7574—231nomaximal, Sylow
105C23×C23C2×C22⋊C411yescharacteristic
106C22×D23—22no—
107C22×D23—41no—
108C22×D23—41no—
109C22×D23—41no—
110C22×D23—41no—
111C22×D23—41no—
112C22×D23—41no—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23C22⋊C812yes—
127C2×C4×C23C22⋊C812yes—
128C2×C4×C23#10212yes—
129C2×C4×C23#10212yes—
130C2×C4×C23#10412yes—
131C2×C4×C23C22×C811yescharacteristic
132C2×C4×C23C2×M1611yescharacteristic
133C2×C4×C23C2×D811yescharacteristic
134C2×C4×C23C2×SD1611yescharacteristic
135C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C23#13711yescharacteristic
137C2×Dic23—22no—
138C2×Dic23—41no—
139C2×Dic23—41no—
140C2×Dic23—41no—
141C2×Dic23—41no—
142C2×Dic23—41no—
143C2×Dic23—41no—
144C2×Dic23—41no—
145C2×Dic23—41no—
146D92—42no—
147D92—42no—
148C4×D23—48no—
149C8×C23—82no—
150C23⋊C8—44no—
151#2293—231no—
152#1831D2311yescharacteristic, complemented
153C4×C4⋊C8—231no—
154#1271—232no—
155#1270—232no—
156C22×C23C2×C22⋊C811yescharacteristic
157C22×C23#41011yescharacteristic
158C22×C23#41311yescharacteristic
159C22×C23C2×#10211yescharacteristic
160C22×C23#41711yescharacteristic
161C22×C23C2×#10411yescharacteristic
162C22×C23#42111yescharacteristic
163C2×D23—42no—
164C2×D23—42no—
165C2×D23—42no—
166C2×D23—81no—
167C2×D23—81no—
168C2×D23—81no—
169C2×D23—81no—
170C4×C23—22no—
171C4×C23—21no—
172C4×C23—21no—
173C4×C23—22no—
174C4×C23—21no—
175C4×C23—21no—
176C4×C23—21no—
177C4×C23—21no—
178C4×C23—41no—
179C4×C23D4⋊C814yes—
180Dic23—42no—
181Dic23—81no—
182Dic23—81no—
183C2×C4×D4—231no—
184C2×#117—461no—
185C2×C4⋊C8—21no—
186C2×C4⋊C8—461no—
187C2×C4×C8—461no—
188#390—231no—
189#390—231no—
190#389—231no—
191#389—231no—
192#388—461no—
193#388—461no—
194C4×C4⋊C4—231no—
195C4×C22⋊C4—461no—
196C43C2×D2311yescharacteristic
197#336—21no—
198#336—232no—
199#336C2×D2312yes—
200C2×C23#145811yescharacteristic
201C2×C23C2×D4⋊C811yescharacteristic
202C2×C23#147711yescharacteristic
203C2×C23#150911yescharacteristic
204C2×C23#151711yescharacteristic
205C2×C23#152911yescharacteristic
206C2×C23#154711yescharacteristic
207D23—82no—
208C22×D4—231no—
209C23×C4—461no—
210C22×C8—22no—
211C22×C8—462no—
212C4×D4—234no—
213C4×D4—462no—
214#117—922no—
215#117—922no—
216C2×C4⋊C4—231no—
217C2×C4⋊C4—231no—
218C2×C4⋊C4—231no—
219C2×C4⋊C4—461no—
220C2×C4⋊C4—461no—
221C2×C22⋊C4—461no—
222C2×C22⋊C4—461no—
223C2×C22⋊C4—461no—
224C2×C22⋊C4—461no—
225C2×C22⋊C4—461no—
226C2×C42—461no—
227C2×C42C4×D2311yescharacteristic
228C2×C42C4×D2311yescharacteristic
229C2×C42D9211yescharacteristic
230C2×C42D9211yescharacteristic
231C2×C42C22⋊D2311yescharacteristic
232C2×C42C22⋊D2311yescharacteristic
233C2×C42C22×D2311yescharacteristic
234C4⋊C8—42no—
235C4⋊C8—464no—
236C4×C8—922no—
237#95—461no—
238#95—461no—
239#95—461no—
240C23#757411yescharacteristic, complemented, Sylow
241C24—461no—
242C2×D4—232no—
243C2×D4—461no—
244C2×D4—921no—
245C2×D4—921no—
246C22×C4—461no—
247C22×C4—464no—
248C22×C4—461no—
249C22×C4—461no—
250C22×C4—922no—
251C22×C4—922no—
252C22×C4(C2×D23)⋊C411yescharacteristic
253C22×C4(C2×D23)⋊C411yescharacteristic
254C22×C4(C2×D23)⋊C411yescharacteristic
255C22×C4(C2×D23)⋊C411yescharacteristic
256C22×C4C2×C4×D2311yescharacteristic
257C22×C4C2×D9211yescharacteristic
258C22×C4C2×C22⋊D2311yescharacteristic
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—464no—
263C2×C8—922no—
264C2×C8—922no—
265C4⋊C4—232no—
266C4⋊C4—461no—
267C4⋊C4—921no—
268C4⋊C4—921no—
269C4⋊C4—921no—
270C4⋊C4—921no—
271C4⋊C4—922no—
272C22⋊C4—464no—
273C22⋊C4—922no—
274C22⋊C4—921no—
275C22⋊C4—921no—
276C22⋊C4—921no—
277C22⋊C4—921no—
278C22⋊C4—922no—
279C42—21no—
280C42—21no—
281C42—22no—
282C42—41no—
283C42—41no—
284C42—41no—
285C42—922no—
286C42C8×D2312yes—
287C42#6726212yes—
288C42#6727212yes—
289C42#6727412yes—
290C23—462no—
291C23—921no—
292C23—921no—
293C23—921no—
294C23—921no—
295C23—921no—
296C23—921no—
297C23C2×(C2×D23)⋊C411yescharacteristic
298D4—922no—
299D4—922no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—462no—
314C2×C4—921no—
315C2×C4—921no—
316C2×C4—928no—
317C2×C4—921no—
318C2×C4—921no—
319C2×C4—921no—
320C2×C4—921no—
321C2×C4—921no—
322C2×C4—921no—
323C2×C4#1062499112yes—
324C2×C4#1062499112yes—
325C2×C4(C2×D23)⋊C812yes—
326C2×C4(C2×D23)⋊C812yes—
327C2×C4#1062500712yes—
328C2×C4C2×C8×D2311yescharacteristic
329C2×C4C2×#6726211yescharacteristic
330C2×C4#1062507911yescharacteristic
331C2×C4#1062508011yescharacteristic
332C2×C4C2×#6727211yescharacteristic
333C2×C4C2×#6727411yescharacteristic
334C8—82no—
335C8—924no—
336C22—922no—
337C22—922no—
338C22—922no—
339C22—1841no—
340C22—1841no—
341C22—1841no—
342C22—1841no—
343C22C2×(C2×D23)⋊C811yescharacteristic
344C22#1309239011yescharacteristic
345C22#1309239911yescharacteristic
346C22C2×#1062499111yescharacteristic
347C22#1309241911yescharacteristic
348C22C2×#1062500711yescharacteristic
349C22#1309243511yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—41no—
359C4—922no—
360C4—1841no—
361C4—1841no—
362C4#1309214414yes—
363C2—1842no—
364C2#1567170911yescharacteristic
365C2C2×#1309214411yescharacteristic
366C2#1567178511yescharacteristic
367C2#1567192311yescharacteristic
368C2#1567195611yescharacteristic
369C2#1567200511yescharacteristic
370C2#1567207511yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1831C2
socleC23×C23C2×C22⋊C4
hypercenter#1831D23
hypocenterC23#7574
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊(C23⋊C8)C2semidirect
3. #15671221C2semidirect
5. C23×#1831C2semidirect
46. C4×D92C8semidirect
152. #1831D23semidirect
240. C23#7574semidirect