Finite Group Databasebeta

← #19132829

Subgroups — #19132829

Order 5504.

612 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Dic43C211yesmaximal, characteristic
2C22×C4×Dic43C211yesmaximal, 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
12C2×C4⋊Dic43—22no—
13C2×C4⋊Dic43—22no—
14C2×C4⋊Dic43C414yescomplemented
15C2×C4×Dic43—22no—
16C2×C4×Dic43—22no—
17C2×C4×Dic43—22no—
18C43⋊#95—22no—
19C43⋊#95—22no—
20C43⋊#95—22no—
21C43⋊#95C414yescomplemented
22C23×C4×C43C2211yescharacteristic
23C23×C4×C43C2211yescharacteristic
24C23×C4×C43C2211yescharacteristic
25#95×C43C414yescomplemented
26C24×C43C2311yescharacteristic
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×C43C2×C412yes—
43C22×C4×C43C2×C412yes—
44C22×C4×C43C2×C412yes—
45C22×C4×C43C2×C412yes—
46C22×C4×C43D412yes—
47C22×C4×C43Q812yes—
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×Dic43C2×C412yes—
71C22×Dic43C2×C412yes—
72C22×Dic43D412yes—
73C22×Dic43D412yes—
74C22×Dic43D412yes—
75C22×Dic43Q812yes—
76C4⋊Dic43—28no—
77C4×Dic43—28no—
78C23×C43C22×C411yescharacteristic
79C23×C43C22×C411yescharacteristic
80C23×C43C22×C411yescharacteristic
81C23×C43C2×D411yescharacteristic
82C23×C43C2×D411yescharacteristic
83C23×C43C2×D411yescharacteristic
84C23×C43C2×D411yescharacteristic
85C23×C43C2×Q811yescharacteristic
86C23×C43C2×Q811yescharacteristic
87C23×C43#4111yescharacteristic
88C23×C43#4111yescharacteristic
89C23×C43#4111yescharacteristic
90C23×C43#4111yescharacteristic
91C23×C43#4111yescharacteristic
92C23×C43#4111yescharacteristic
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43C4214yescomplemented
113C2×C4×C43C4⋊C414yescomplemented
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—22no—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—22no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43—22no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131C2×Dic43—22no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43C22⋊C414yes—
141C2×Dic43C4⋊C414yescomplemented
142C22×C43C2×C4211yescharacteristic
143C22×C43C2×C22⋊C411yescharacteristic
144C22×C43C2×C4⋊C411yescharacteristic
145C22×C43C2×C4⋊C411yescharacteristic
146C22×C43#11711yescharacteristic
147C22×C43#11711yescharacteristic
148C22×C43#11711yescharacteristic
149C22×C43C4×D411yescharacteristic
150C22×C43C4×D411yescharacteristic
151C22×C43C4×D411yescharacteristic
152C22×C43C4×D411yescharacteristic
153C22×C43C4×D411yescharacteristic
154C22×C43C4×D411yescharacteristic
155C22×C43C4×D411yescharacteristic
156C22×C43C4×D411yescharacteristic
157C22×C43C4×Q811yescharacteristic
158C22×C43C4×Q811yescharacteristic
159C22×C43C4×Q811yescharacteristic
160C22×C43C4×Q811yescharacteristic
161C22×C43#12011yescharacteristic
162C22×C43#12111yescharacteristic
163C22×C43#12111yescharacteristic
164C22×C43C22⋊Q811yescharacteristic
165C22×C43C22⋊Q811yescharacteristic
166C22×C43C22⋊Q811yescharacteristic
167C22×C43C22⋊Q811yescharacteristic
168C22×C43#12311yescharacteristic
169C22×C43#12311yescharacteristic
170C22×C43#12311yescharacteristic
171C22×C43#12411yescharacteristic
172C22×C43#12511yescharacteristic
173C22×C43#12511yescharacteristic
174C22×C43#12611yescharacteristic
175C22×C43#12611yescharacteristic
176C22×C43C4⋊Q811yescharacteristic
177C4×C43—24no—
178C4×C43—24no—
179C4×C43—42no—
180Dic43—24no—
181Dic43—24no—
182Dic43—42no—
183Dic43—42no—
184#1436—431nomaximal, Sylow
185C2×C43C4×C22⋊C411yescharacteristic
186C2×C43C4×C4⋊C411yescharacteristic
187C2×C43C4×C4⋊C411yescharacteristic
188C2×C43#38511yescharacteristic
189C2×C43#38511yescharacteristic
190C2×C43#38611yescharacteristic
191C2×C43#38711yescharacteristic
192C2×C43#38711yescharacteristic
193C2×C43#38711yescharacteristic
194C2×C43#38711yescharacteristic
195C2×C43#38811yescharacteristic
196C2×C43#38811yescharacteristic
197C2×C43#38911yescharacteristic
198C2×C43#38911yescharacteristic
199C2×C43#39111yescharacteristic
200C22×C4⋊C4—431no—
201C22×C42—431no—
202C2×#95—431no—
203C2×#95—431no—
204C2×#95—431no—
205C2×#95—431no—
206C2×#95D4311yescharacteristic
207C43#143611yescharacteristic, complemented, Sylow
208C23×C4—431no—
209C23×C4—431no—
210C23×C4—431no—
211C23×C4—431no—
212C23×C4C2×D4311yescharacteristic
213C23×C4C2×D4311yescharacteristic
214C23×C4C2×D4311yescharacteristic
215C2×C4⋊C4—434no—
216C2×C4⋊C4—862no—
217C2×C4⋊C4—862no—
218C2×C42—862no—
219C2×C42—862no—
220C2×C42—862no—
221#95—434no—
222#95—862no—
223#95—862no—
224#95—862no—
225#95Dic4314yescomplemented
226C24C22×D4311yescharacteristic
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—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—432no—
242C22×C4—432no—
243C22×C4—432no—
244C22×C4—432no—
245C22×C4—432no—
246C22×C4—432no—
247C22×C4—432no—
248C22×C4—432no—
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×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4Dic8612yes—
270C22×C4C4×D4312yes—
271C22×C4C4×D4312yes—
272C22×C4D17212yes—
273C22×C4C2×Dic4312yes—
274C22×C4C2×Dic4312yes—
275C22×C4C2×Dic4312yes—
276C4⋊C4—868no—
277C42—868no—
278C23C2×Dic8611yescharacteristic
279C23C2×C4×D4311yescharacteristic
280C23C2×C4×D4311yescharacteristic
281C23C2×D17211yescharacteristic
282C23#1062189811yescharacteristic
283C23#1062189811yescharacteristic
284C23D4×D4311yescharacteristic
285C23D4×D4311yescharacteristic
286C23D4×D4311yescharacteristic
287C23#1062190011yescharacteristic
288C23#1062190011yescharacteristic
289C23#1062190011yescharacteristic
290C23Q8×D4311yescharacteristic
291C23#1062190211yescharacteristic
292C23C22×Dic4311yescharacteristic
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—434no—
313C2×C4—434no—
314C2×C4—862no—
315C2×C4—862no—
316C2×C4—862no—
317C2×C4—862no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—862no—
321C2×C4—862no—
322C2×C4—862no—
323C2×C4—862no—
324C2×C4—862no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4—862no—
329C2×C4—862no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4C4×Dic4314yescomplemented
341C2×C4C4⋊Dic4314yescomplemented
342C22C2×C4×Dic4311yescharacteristic
343C22C22⋊C4×D4311yescharacteristic
344C22C4⋊C4×D4311yescharacteristic
345C22C2×C4⋊Dic4311yescharacteristic
346C22#1306328111yescharacteristic
347C22#1306328311yescharacteristic
348C22#1306328411yescharacteristic
349C22(C22⋊D43)⋊C411yescharacteristic
350C22(C22⋊D43)⋊C411yescharacteristic
351C22#1306328711yescharacteristic
352C22D4×Dic4311yescharacteristic
353C22D4×Dic4311yescharacteristic
354C22D4×Dic4311yescharacteristic
355C22C4×D17211yescharacteristic
356C22C4×D17211yescharacteristic
357C22#1306329011yescharacteristic
358C22C4×Dic8611yescharacteristic
359C22C4×Dic8611yescharacteristic
360C22Q8×Dic4311yescharacteristic
361C22#1306329511yescharacteristic
362C22#1306329811yescharacteristic
363C22#1306330011yescharacteristic
364C22#1306330211yescharacteristic
365C22#1306330211yescharacteristic
366C22#1306330311yescharacteristic
367C22#1306330511yescharacteristic
368C22#1306330711yescharacteristic
369C22#1306330911yescharacteristic
370C22#1306331011yescharacteristic
371C22#1306331111yescharacteristic
372C22#1306331511yescharacteristic
373C22#1306331611yescharacteristic
374C22#1306331811yescharacteristic
375C22#1306332011yescharacteristic
376C22#1306332411yescharacteristic
377C4—24no—
378C4—24no—
379C4—42no—
380C4—864no—
381C4—864no—
382C4—1722no—
383C4—1722no—
384C2C22⋊C4×Dic4311yescharacteristic
385C2C4×C4⋊Dic4311yescharacteristic
386C2C4⋊C4×Dic4311yescharacteristic
387C2#1458277311yescharacteristic
388C2#1458277411yescharacteristic
389C2#1458277711yescharacteristic
390C2#1458278211yescharacteristic
391C2#1458278411yescharacteristic
392C2#1458278511yescharacteristic
393C2#1458278611yescharacteristic
394C2#1458279111yescharacteristic
395C2#1458279211yescharacteristic
396C2#1458279611yescharacteristic
397C2#1458279811yescharacteristic
398C2#1458280311yescharacteristic
subgroupG/H
center, FrattiniC24C22×D43
commutatorC22×C43C2×C42
FittingC2×#95×C43C2
socleC24×C43C23
hypercenterC2×#95D43
hypocenterC43#1436
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
14. C2×C4⋊Dic43C4semidirect
21. C43⋊#95C4semidirect
25. #95×C43C4semidirect
112. C2×C4×C43C42semidirect
113. C2×C4×C43C4⋊C4semidirect
141. C2×Dic43C4⋊C4semidirect
207. C43#1436semidirect
225. #95Dic43semidirect
340. C2×C4C4×Dic43semidirect
341. C2×C4C4⋊Dic43semidirect