Finite Group Databasebeta

← #19132855

Subgroups — #19132855

Order 5504.

476 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43⋊#95C211yesmaximal, characteristic
2C2×C43⋊#95C211yesmaximal, characteristic
3C2×C43⋊#95C211yesmaximal, characteristic
4C2×C43⋊#95C211yesmaximal, characteristic
5C2×C43⋊#95C211yesmaximal, characteristic
6C2×C43⋊#95C211yesmaximal, characteristic
7C2×#95×C43C211yesmaximal, characteristic
8C23×Dic43C2211yescharacteristic
9C23×Dic43C2211yescharacteristic
10C23×Dic43C2211yescharacteristic
11C23×Dic43C2211yescharacteristic
12C43⋊#95—22no—
13C43⋊#95—22no—
14C43⋊#95—22no—
15C43⋊#95—22no—
16C43⋊#95—22no—
17C43⋊#95C414yescomplemented
18C23×C4×C43C2211yescharacteristic
19C23×C4×C43C2211yescharacteristic
20C23×C4×C43C2211yescharacteristic
21#95×C43—22no—
22C24×C43C2311yescharacteristic
23C22×C4×C43—21no—
24C22×C4×C43—21no—
25C22×C4×C43—21no—
26C22×C4×C43—21no—
27C22×C4×C43—21no—
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43—21no—
31C22×C4×C43—21no—
32C22×C4×C43—21no—
33C22×C4×C43—21no—
34C22×C4×C43—21no—
35C22×C4×C43—21no—
36C22×C4×C43—21no—
37C22×C4×C43—21no—
38C22×C4×C43—21no—
39C22×C4×C43—21no—
40C22×C4×C43—21no—
41C22×C4×C43C2×C412yes—
42C22×C4×C43D412yes—
43C22×C4×C43D412yes—
44C22×Dic43—21no—
45C22×Dic43—21no—
46C22×Dic43—21no—
47C22×Dic43—21no—
48C22×Dic43—21no—
49C22×Dic43—21no—
50C22×Dic43—21no—
51C22×Dic43—21no—
52C22×Dic43—21no—
53C22×Dic43—21no—
54C22×Dic43—21no—
55C22×Dic43—21no—
56C22×Dic43—21no—
57C22×Dic43—21no—
58C22×Dic43—21no—
59C22×Dic43—21no—
60C22×Dic43—21no—
61C22×Dic43—21no—
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—21no—
65C22×Dic43—21no—
66C22×Dic43—21no—
67C22×Dic43—21no—
68C22×Dic43C2×C412yes—
69C22×Dic43C2×C412yes—
70C22×Dic43D412yes—
71C22×Dic43Q812yes—
72C23×C43C22×C411yescharacteristic
73C23×C43C2×D411yescharacteristic
74C23×C43C2×D411yescharacteristic
75C23×C43C2×D411yescharacteristic
76C23×C43C2×Q811yescharacteristic
77C23×C43#4111yescharacteristic
78C23×C43#4111yescharacteristic
79C23×C43#4111yescharacteristic
80C23×C43#4111yescharacteristic
81C23×C43#4111yescharacteristic
82C23×C43#4111yescharacteristic
83C23×C43#4111yescharacteristic
84C23×C43#4111yescharacteristic
85C23×C43#4111yescharacteristic
86C23×C43#4111yescharacteristic
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—22no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C22×C43#11711yescharacteristic
137C22×C43#11711yescharacteristic
138C22×C43#11711yescharacteristic
139C22×C43C4×D411yescharacteristic
140C22×C43C4×D411yescharacteristic
141C22×C43C4×D411yescharacteristic
142C22×C43C4×Q811yescharacteristic
143C22×C43#12111yescharacteristic
144C22×C43#12111yescharacteristic
145C22×C43#12111yescharacteristic
146C22×C43C22⋊Q811yescharacteristic
147C22×C43C22⋊Q811yescharacteristic
148C22×C43C22⋊Q811yescharacteristic
149C22×C43#12311yescharacteristic
150C22×C43#12311yescharacteristic
151C22×C43#12311yescharacteristic
152C22×C43#12311yescharacteristic
153C22×C43#12311yescharacteristic
154C22×C43#12311yescharacteristic
155C22×C43#12411yescharacteristic
156C22×C43#12411yescharacteristic
157C22×C43#12411yescharacteristic
158C22×C43#12511yescharacteristic
159C22×C43#12511yescharacteristic
160C22×C43#12511yescharacteristic
161C22×C43#12611yescharacteristic
162C22×C43#12611yescharacteristic
163C22×C43#12611yescharacteristic
164C22×C43#12611yescharacteristic
165C22×C43#12611yescharacteristic
166C22×C43#12611yescharacteristic
167C22×C43#12611yescharacteristic
168C22×C43#12611yescharacteristic
169C22×C43#12611yescharacteristic
170C22×C43#12611yescharacteristic
171C4×C43—42no—
172C4×C43—42no—
173C4×C43—42no—
174Dic43—42no—
175Dic43—42no—
176Dic43—42no—
177Dic43—42no—
178#1443—431nomaximal, Sylow
179C2×C43#38311yescharacteristic
180C2×C43#38711yescharacteristic
181C2×C43#38711yescharacteristic
182C2×C43#38711yescharacteristic
183C2×C43#38811yescharacteristic
184C2×C43#38811yescharacteristic
185C2×C43#38811yescharacteristic
186C2×C43#39611yescharacteristic
187C2×C43#39711yescharacteristic
188C2×C43#39711yescharacteristic
189C2×C43#39711yescharacteristic
190C2×C43#40011yescharacteristic
191C2×C43#40011yescharacteristic
192C2×C43#40011yescharacteristic
193C2×C43#40111yescharacteristic
194C2×#95—431no—
195C2×#95—431no—
196C2×#95—431no—
197C2×#95—431no—
198C2×#95—431no—
199C2×#95—431no—
200C2×#95D4311yescharacteristic
201C43#144311yescharacteristic, complemented, Sylow
202C23×C4—431no—
203C23×C4—431no—
204C23×C4—431no—
205C23×C4—431no—
206C23×C4C2×D4311yescharacteristic
207C23×C4C2×D4311yescharacteristic
208C23×C4C2×D4311yescharacteristic
209#95—22no—
210#95—434no—
211#95—862no—
212#95—862no—
213#95—862no—
214#95—862no—
215#95—862no—
216C24C22×D4311yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—432no—
236C22×C4—432no—
237C22×C4—432no—
238C22×C4—432no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—861no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4C4×D4312yes—
264C22×C4D17212yes—
265C22×C4C22⋊D4312yes—
266C23C2×C4×D4311yescharacteristic
267C23C2×D17211yescharacteristic
268C23#1062189811yescharacteristic
269C23#1062189811yescharacteristic
270C23#1062189811yescharacteristic
271C23#1062189811yescharacteristic
272C23D4×D4311yescharacteristic
273C23#1062190011yescharacteristic
274C23#1062190011yescharacteristic
275C23#1062190011yescharacteristic
276C23#1062190011yescharacteristic
277C23#1062190011yescharacteristic
278C23Q8×D4311yescharacteristic
279C23#1062190211yescharacteristic
280C23C2×C22⋊D4311yescharacteristic
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—862no—
303C2×C4—862no—
304C2×C4—862no—
305C2×C4—862no—
306C2×C4—862no—
307C2×C4—862no—
308C2×C4—862no—
309C2×C4—862no—
310C2×C4—862no—
311C2×C4—862no—
312C2×C4—862no—
313C2×C4—862no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C22#1306328111yescharacteristic
331C22#1306328211yescharacteristic
332C22#1306328311yescharacteristic
333C22(C22⋊D43)⋊C411yescharacteristic
334C22C4×C22⋊D4311yescharacteristic
335C22C4×D17211yescharacteristic
336C22#1306329011yescharacteristic
337C22#1306329711yescharacteristic
338C22#1306329911yescharacteristic
339C22#1306330011yescharacteristic
340C22#1306330111yescharacteristic
341C22#1306330311yescharacteristic
342C22#1306330511yescharacteristic
343C22#1306330611yescharacteristic
344C22#1306330711yescharacteristic
345C22#1306330711yescharacteristic
346C22#1306330811yescharacteristic
347C22#1306330911yescharacteristic
348C22#1306330911yescharacteristic
349C22#1306331111yescharacteristic
350C22#1306331211yescharacteristic
351C22#1306331311yescharacteristic
352C22#1306331511yescharacteristic
353C22#1306331511yescharacteristic
354C22#1306331511yescharacteristic
355C22#1306331811yescharacteristic
356C22#1306331811yescharacteristic
357C22#1306331811yescharacteristic
358C22#1306331811yescharacteristic
359C22#1306331811yescharacteristic
360C22#1306331911yescharacteristic
361C22#1306332011yescharacteristic
362C22#1306332011yescharacteristic
363C22#1306332011yescharacteristic
364C22#1306332011yescharacteristic
365C4—42no—
366C4—42no—
367C4—42no—
368C4—1722no—
369C4—1722no—
370C4—1722no—
371C4—1722no—
372C2#1458276611yescharacteristic
373C2#1458278011yescharacteristic
374C2#1458278111yescharacteristic
375C2#1458278411yescharacteristic
376C2#1458279011yescharacteristic
377C2#1458279111yescharacteristic
378C2#1458279311yescharacteristic
379C2#1458282111yescharacteristic
380C2#1458282411yescharacteristic
381C2#1458282611yescharacteristic
382C2#1458282711yescharacteristic
383C2#1458283711yescharacteristic
384C2#1458283911yescharacteristic
385C2#1458284011yescharacteristic
386C2C43⋊#40111yescharacteristic
subgroupG/H
center, FrattiniC24C22×D43
commutatorC23×C43C22×C4
FittingC2×#95×C43C2
socleC24×C43C23
hypercenterC2×#95D43
hypocenterC43#1443
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
17. C43⋊#95C4semidirect
201. C43#1443semidirect