Finite Group Databasebeta

← #19139937

Subgroups — #19139937

Order 5504.

584 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#14582832C211yesmaximal, characteristic, complemented
4#14582829C211yesmaximal, characteristic, complemented
5#14582822C211yesmaximal, characteristic, complemented
6#14582785C211yesmaximal, characteristic, complemented
7#14582781C211yesmaximal, characteristic, complemented
8#14582775C211yesmaximal, characteristic
9#14582775C211yesmaximal, characteristic
10#14582774C211yesmaximal, characteristic, complemented
11#14582773C211yesmaximal, characteristic, complemented
12#14582771C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582756C211yesmaximal, characteristic, complemented
15C43×#396C211yesmaximal, characteristic, complemented
16C22×C22⋊D43C2211yescharacteristic
17C23×Dic43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic
21(C22⋊D43)⋊C4—24no—
22C2×C4⋊Dic43C2211yescharacteristic
23C2×C4⋊Dic43C2211yescharacteristic
24C2×C4⋊Dic43C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×Dic43⋊C4C2211yescharacteristic
30C4⋊C4×D43—24no—
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
33C2×(C2×D43)⋊C4C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×C4×Dic43C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C4⋊C4×C43C2211yescharacteristic
48C2×C4⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53C24×C43C2311yescharacteristic
54C23×D43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—22no—
62C2×C22⋊D43—22no—
63C2×C22⋊D43Q814yes—
64C22×Dic43—22no—
65C22×Dic43—41no—
66C22×Dic43—41no—
67C22×Dic43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C2×C4×D43—22no—
75C2×C4×D43—22no—
76C2×C4×D43—22no—
77C2×C4×D43—22no—
78C2×C4×D43—41no—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81C2×C4×D43—41no—
82C2×C4×D43D414yes—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—41no—
86C22⋊C4×C43—22no—
87C22⋊C4×C43—22no—
88C22⋊C4×C43—41no—
89C22⋊Dic43—22no—
90C22⋊Dic43—41no—
91(C2×D43)⋊C4—22no—
92(C2×D43)⋊C4—22no—
93(C2×D43)⋊C4—22no—
94C4⋊Dic43—22no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97Dic43⋊C4—22no—
98Dic43⋊C4—22no—
99Dic43⋊C4—22no—
100Dic43⋊C4—22no—
101Dic43⋊C4—41no—
102C4×Dic43—22no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43C2×Q812yes—
110C23×C43C2411yescharacteristic
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—21no—
115C22×D43C2×D412yes—
116C22×D43C2×Q812yes—
117C22×D43#4112yes—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43C2×D412yes—
135C2×C4×C43#4112yes—
136C22⋊D43—28no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—44no—
156C2×Dic43C2×D412yes—
157C2×Dic43C2×Q812yes—
158C2×Dic43#4112yes—
159C4×D43—28no—
160C4×D43—44no—
161C4×D43—44no—
162C22×C43—22no—
163C22×C43—22no—
164C22×C43—22no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43C22×D411yescharacteristic
170C22×C43C22×Q811yescharacteristic
171C22×C43C2×#4111yescharacteristic
172C22×C43C2×#4111yescharacteristic
173C22×C43C2×#4111yescharacteristic
174C22×C43H(5,𝔽2)11yescharacteristic
175C22×C43H(5,𝔽2)11yescharacteristic
176C2×D43—22no—
177C2×D43—22no—
178C2×D43—22no—
179C2×D43—22no—
180C2×D43—22no—
181C2×D43—22no—
182C2×D43C22⋊Q814yes—
183C4×C43—22no—
184C4×C43—22no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43—41no—
189Dic43—22no—
190Dic43—22no—
191Dic43—22no—
192Dic43—41no—
193Dic43—41no—
194Dic43—41no—
195Dic43—41no—
196#2579—431nomaximal, Sylow
197C2×C43—42no—
198C2×C43C2×C22⋊Q811yescharacteristic
199C2×C43#52511yescharacteristic
200C2×C43#53411yescharacteristic
201C2×C43#55311yescharacteristic
202C2×C43#55311yescharacteristic
203C2×C43#55411yescharacteristic
204C2×C43#55411yescharacteristic
205D43—24no—
206C2×C4×D4—431no—
207C22×C4⋊C4—431no—
208#398—431no—
209#398—431no—
210#396—431no—
211#396D4311yescharacteristic, complemented
212#387—431no—
213#387—431no—
214#386—431no—
215#386—431no—
216#385—431no—
217#385—431no—
218#385—431no—
219#385—431no—
220#380—431no—
221C43#257911yescharacteristic, complemented, Sylow
222C22×D4—431no—
223C23×C4—431no—
224C23×C4—431no—
225C23×C4—431no—
226C23×C4—431no—
227C4×D4—864no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—431no—
231C2×C4⋊C4—431no—
232C2×C4⋊C4—431no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—864no—
237C2×C4⋊C4C2×D4311yescharacteristic
238C2×C4⋊C4C2×D4311yescharacteristic
239C2×C4⋊C4C2×D4311yescharacteristic
240C2×C22⋊C4—431no—
241C2×C22⋊C4—431no—
242C2×C22⋊C4—431no—
243C2×C22⋊C4—431no—
244C2×C22⋊C4—431no—
245C2×C22⋊C4C2×D4311yescharacteristic
246C2×C22⋊C4C2×D4311yescharacteristic
247C2×C22⋊C4C2×D4311yescharacteristic
248C2×C42—431no—
249#95—431no—
250#95—431no—
251#95—431no—
252#95—431no—
253#95—431no—
254#95—431no—
255#95—431no—
256#95—431no—
257#95—431no—
258#95C2×D4311yescharacteristic
259C24—431no—
260C24C22×D4311yescharacteristic
261C2×D4—434no—
262C2×D4—862no—
263C2×D4—862no—
264C22×C4—431no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—434no—
268C22×C4—431no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—431no—
272C22×C4—862no—
273C22×C4—862no—
274C22×C4—862no—
275C22×C4—862no—
276C22×C4—862no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4—1721no—
280C22×C4—1721no—
281C22×C4—1721no—
282C22×C4—1721no—
283C22×C4C22×D4311yescharacteristic
284C22×C4C22×D4311yescharacteristic
285C22×C4C22×D4311yescharacteristic
286C22×C4C22×D4311yescharacteristic
287C22×C4C22×D4311yescharacteristic
288C22×C4C22×D4311yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—862no—
293C4⋊C4—862no—
294C4⋊C4—862no—
295C4⋊C4—862no—
296C4⋊C4—862no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1721no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—41no—
303C22⋊C4—862no—
304C22⋊C4—862no—
305C22⋊C4—862no—
306C22⋊C4—862no—
307C22⋊C4—1721no—
308C42—862no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—432no—
316C23—432no—
317C23—432no—
318C23—861no—
319C23—861no—
320C23—861no—
321C23—861no—
322C23Q8×D4312yes—
323C23C23×D4311yescharacteristic
324D4—868no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—432no—
342C2×C4—432no—
343C2×C4—432no—
344C2×C4—868no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—1724no—
364C2×C4—1724no—
365C2×C4—1724no—
366C2×C4D4×D4312yes—
367C2×C4#1062190012yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—434no—
376C22—862no—
377C22—862no—
378C22—862no—
379C22—862no—
380C22—862no—
381C22—862no—
382C22C2×D4×D4311yescharacteristic
383C22C2×Q8×D4311yescharacteristic
384C22#41×D4311yescharacteristic
385C22#41×D4311yescharacteristic
386C22C2×#1062190011yescharacteristic
387C22#1306337011yescharacteristic
388C22#1306337111yescharacteristic
389C4—22no—
390C4—22no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—862no—
396C4—862no—
397C4—862no—
398C4—1721no—
399C4—1721no—
400C4—1721no—
401C4—1721no—
402C2—42no—
403C2—864no—
404C2C22⋊Q8×D4311yescharacteristic
405C2#1458340911yescharacteristic
406C2#1458345711yescharacteristic
407C2#1458359611yescharacteristic
408C2#1458360011yescharacteristic
409C2#1458360311yescharacteristic
410C2#1458360711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#396C2
hypercenter#396D43
hypocenterC43#2579
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D43C2semidirect
3. #14582832C2semidirect
4. #14582829C2semidirect
5. #14582822C2semidirect
6. #14582785C2semidirect
7. #14582781C2semidirect
10. #14582774C2semidirect
11. #14582773C2semidirect
12. #14582771C2semidirect
13. #14582770C2semidirect
14. #14582756C2semidirect
15. C43×#396C2semidirect
211. #396D43semidirect
221. C43#2579semidirect