Finite Group Databasebeta

← #19212156

Subgroups — #19212156

Order 5888.

690 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675887C211yesmaximal, characteristic
2C4×C22⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
3#15671222C212yesmaximal, complemented
4#15671217C212yesmaximal, complemented
5C4×C23×C22⋊C8C211yesmaximal, characteristic, complemented
6C22×#67288C411yescharacteristic
7C2×#10625097C411yescharacteristic
8C2×C22⋊(C23⋊C8)—21no—
9C2×C4×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×C22⋊C8—21no—
21C2×C4×C8×C23—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×C22⋊C8—24no—
51C4×C8×C23—42no—
52C23⋊#95—21no—
53C23⋊#95—21no—
54C23⋊#95—21no—
55C23⋊#95—21no—
56C22⋊(C23⋊C8)—24no—
57C4×C23⋊C8—42no—
58C24×C23C22⋊C411yescharacteristic
59C23×D23—21no—
60C22×C4×C23—22no—
61C22×C4×C23—22no—
62C22×C4×C23—22no—
63C22×C4×C23—22no—
64C22×C4×C23—22no—
65C22×C4×C23—22no—
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×C23C22×C411yescharacteristic
74C22×C4×C23C2×D411yescharacteristic
75C22×C4×C23C2×D411yescharacteristic
76C2×C22⋊D23—24no—
77C2×C22⋊D23—42no—
78C2×C22⋊D23—42no—
79C22×Dic23—21no—
80C22×Dic23—21no—
81C22×Dic23—21no—
82#67288—48no—
83#67288—48no—
84C2×D92—21no—
85C2×D92—41no—
86C2×D92—41no—
87C2×D92C2×C812yes—
88C2×C4×D23—24no—
89C2×C4×D23—42no—
90C2×C4×D23—42no—
91C2×Dic46—21no—
92C2×Dic46—41no—
93C2×Dic46—41no—
94C2×Dic46C2×C812yes—
95C2×C8×C23—24no—
96C2×C8×C23—42no—
97C2×C8×C23—42no—
98C42×C23—22no—
99C42×C23—22no—
100C42×C23—41no—
101C42×C23—41no—
102C22⋊Dic23—42no—
103(C2×D23)⋊C4—42no—
104(C2×D23)⋊C4—42no—
105(C2×D23)⋊C4—42no—
106(C2×D23)⋊C4—42no—
107C4⋊Dic23—41no—
108C4⋊Dic23—41no—
109C4×Dic23—42no—
110C2×C23⋊C8—24no—
111C2×C23⋊C8—42no—
112C2×C23⋊C8—42no—
113#7563—231nomaximal, Sylow
114C23×C23—21no—
115C23×C23—21no—
116C23×C23—21no—
117C23×C23—21no—
118C23×C23—21no—
119C23×C23—21no—
120C23×C23C22⋊C812yes—
121C23×C23C2×C22⋊C411yescharacteristic
122C22×D23—22no—
123C22×D23—41no—
124C22×D23—41no—
125C22×D23—41no—
126C22×D23—41no—
127C22×D23—41no—
128C22×D23—41no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
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—44no—
142C2×C4×C23—44no—
143C2×C4×C23C22⋊C812yes—
144C2×C4×C23#9912yes—
145C2×C4×C23#10012yes—
146C2×C4×C23#10412yes—
147C2×C4×C23#10412yes—
148C2×C4×C23C22×C811yescharacteristic
149C2×C4×C23C2×M1611yescharacteristic
150C2×C4×C23#13512yes—
151C2×C4×C23#13512yes—
152C22⋊D23—48no—
153C2×Dic23—22no—
154C2×Dic23—41no—
155C2×Dic23—41no—
156C2×Dic23—41no—
157C2×Dic23—41no—
158C2×Dic23—41no—
159C2×Dic23—41no—
160C2×Dic23—41no—
161C2×Dic23—41no—
162D92—42no—
163D92—42no—
164C4×D23—48no—
165Dic46—42no—
166Dic46—42no—
167C8×C23—44no—
168C23⋊C8—44no—
169#2297—231no—
170C4×C22⋊C8—231no—
171C4×C22⋊C8D2311yescharacteristic, complemented
172#1272—232no—
173#1270—232no—
174C22×C23—22no—
175C22×C23—22no—
176C22×C23—22no—
177C22×C23—41no—
178C22×C23—41no—
179C22×C23—41no—
180C22×C23—41no—
181C22×C23C2×C22⋊C811yescharacteristic
182C22×C23C2×#9911yescharacteristic
183C22×C23C2×#10011yescharacteristic
184C22×C23#41611yescharacteristic
185C22×C23#41611yescharacteristic
186C22×C23C2×#10411yescharacteristic
187C22×C23C2×#10411yescharacteristic
188C2×D23—42no—
189C2×D23—42no—
190C2×D23—42no—
191C2×D23—81no—
192C2×D23—81no—
193C2×D23—81no—
194C2×D23—81no—
195C4×C23—21no—
196C4×C23—21no—
197C4×C23—22no—
198C4×C23—22no—
199C4×C23—22no—
200C4×C23—22no—
201C4×C23#32314yes—
202Dic23—42no—
203Dic23—81no—
204Dic23—81no—
205C22×#41—231no—
206C2×#117—231no—
207C22×C42C2×D2311yescharacteristic
208C2×C22⋊C8—21no—
209C2×C22⋊C8—461no—
210C2×C4×C8—21no—
211C2×C4×C8—461no—
212#391—231no—
213#391—231no—
214#390—231no—
215#390—231no—
216#386—461no—
217#386—461no—
218C4×C22⋊C4—461no—
219C4×C22⋊C4—461no—
220#336—232no—
221#336C2×D2312yes—
222C2×C23—42no—
223C2×C23C2×#32311yescharacteristic
224C2×C23#147611yescharacteristic
225C2×C23#147611yescharacteristic
226C2×C23#150111yescharacteristic
227C2×C23#150111yescharacteristic
228C2×C23#152511yescharacteristic
229C2×C23#154311yescharacteristic
230D23—82no—
231C2×#41—234no—
232C2×#41—462no—
233C2×#41—922no—
234C2×#41—922no—
235C22×Q8—231no—
236C22×D4—231no—
237C22×D4—461no—
238C23×C4—461no—
239C23×C4C4×D2311yescharacteristic
240C23×C4D9211yescharacteristic
241C23×C4C22⋊D2311yescharacteristic
242C22×C8—22no—
243C22×C8—462no—
244#117—922no—
245C2×C4⋊C4—231no—
246C2×C4⋊C4—231no—
247C2×C22⋊C4—461no—
248C2×C22⋊C4—461no—
249C2×C22⋊C4—461no—
250C2×C22⋊C4—461no—
251C2×C22⋊C4—461no—
252C2×C42—42no—
253C2×C42—461no—
254C2×C42C4×D2311yescharacteristic
255C2×C42D9211yescharacteristic
256C2×C42C22⋊D2311yescharacteristic
257C2×C42C22×D2311yescharacteristic
258C22⋊C8—24no—
259C22⋊C8—464no—
260C4×C8—42no—
261C4×C8—922no—
262#95—461no—
263#95—461no—
264#95—461no—
265#95—461no—
266C23#756311yescharacteristic, complemented, Sylow
267C24—461no—
268C24(C2×D23)⋊C411yescharacteristic
269#41—928no—
270#41—928no—
271C2×Q8—232no—
272C2×Q8—461no—
273C2×Q8—921no—
274C2×Q8—921no—
275C2×D4—232no—
276C2×D4—464no—
277C2×D4—461no—
278C2×D4—921no—
279C2×D4—921no—
280C2×D4—922no—
281C2×D4—922no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—461no—
291C22×C4—464no—
292C22×C4—461no—
293C22×C4—461no—
294C22×C4—922no—
295C22×C4—922no—
296C22×C4C8×D2312yes—
297C22×C4#6726212yes—
298C22×C4(C2×D23)⋊C411yescharacteristic
299C22×C4(C2×D23)⋊C411yescharacteristic
300C22×C4(C2×D23)⋊C411yescharacteristic
301C22×C4C2×C4×D2311yescharacteristic
302C22×C4C2×D9211yescharacteristic
303C22×C4C2×C22⋊D2311yescharacteristic
304C2×C8—24no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—464no—
308C2×C8—922no—
309C2×C8—922no—
310C4⋊C4—921no—
311C4⋊C4—921no—
312C22⋊C4—922no—
313C22⋊C4—922no—
314C22⋊C4—922no—
315C22⋊C4—922no—
316C22⋊C4—922no—
317C42—22no—
318C42—22no—
319C42—41no—
320C42—41no—
321C42—922no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—462no—
329C23—921no—
330C23—921no—
331C23—921no—
332C23—921no—
333C23—921no—
334C23—921no—
335C23(C2×D23)⋊C812yes—
336C23C2×(C2×D23)⋊C411yescharacteristic
337Q8—922no—
338Q8—922no—
339D4—922no—
340D4—922no—
341D4—928no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—462no—
357C2×C4—921no—
358C2×C4—921no—
359C2×C4—928no—
360C2×C4—921no—
361C2×C4—921no—
362C2×C4—921no—
363C2×C4—921no—
364C2×C4—921no—
365C2×C4—921no—
366C2×C4#1062498712yes—
367C2×C4#1062498812yes—
368C2×C4(C2×D23)⋊C812yes—
369C2×C4#1062500512yes—
370C2×C4#1062500712yes—
371C2×C4C2×C8×D2311yescharacteristic
372C2×C4C2×#6726211yescharacteristic
373C2×C4#1062507512yes—
374C2×C4#1062512112yes—
375C8—44no—
376C8—924no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—922no—
385C22—922no—
386C22—922no—
387C22—1841no—
388C22—1841no—
389C22—1841no—
390C22—1841no—
391C22C2×(C2×D23)⋊C811yescharacteristic
392C22C2×#1062498811yescharacteristic
393C22C2×#1062500511yescharacteristic
394C22#1309241111yescharacteristic
395C22#1309241411yescharacteristic
396C22C2×#1062500711yescharacteristic
397C22C2×#1062498711yescharacteristic
398C4—22no—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—21no—
403C4—21no—
404C4—922no—
405C4—1841no—
406C4—1841no—
407C4#1309214014yes—
408C2—42no—
409C2—1842no—
410C2C2×#1309214011yescharacteristic
411C2#1567177711yescharacteristic
412C2#1567178011yescharacteristic
413C2#1567188611yescharacteristic
414C2#1567188911yescharacteristic
415C2#1567198811yescharacteristic
416C2#1567205711yescharacteristic
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#7563
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. C4×C22⋊(C23⋊C8)C2semidirect
3. #15671222C2semidirect
4. #15671217C2semidirect
5. C4×C23×C22⋊C8C2semidirect
30. C2×#67288C8semidirect
171. C4×C22⋊C8D23semidirect
266. C23#7563semidirect