Finite Group Databasebeta

← #21448331

Subgroups — #21448331

Order 7808.

824 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519750C211yesmaximal, characteristic
2C2×#14519739C211yesmaximal, characteristic, complemented
3C2×#14519737C211yesmaximal, characteristic, complemented
4C2×#14519737C211yesmaximal, characteristic, complemented
5C2×C42×D61C211yesmaximal, characteristic, complemented
6#16839662C211yesmaximal, characteristic, complemented
7#16839657C211yesmaximal, characteristic, complemented
8#16839653C211yesmaximal, characteristic, complemented
9#16839640C211yesmaximal, characteristic, complemented
10#16839638C211yesmaximal, characteristic, complemented
11#16839621C211yesmaximal, characteristic, complemented
12#16839613C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14#16839609C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23C22×C4×D61C2211yescharacteristic
24#14519750C418yescomplemented
25#14519739—24no—
26#14519737—24no—
27#14519737—24no—
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×C4×Dic61C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
41C2×C4×Dic61C2211yescharacteristic
42C2×C4×Dic61C2211yescharacteristic
43C2×C4×Dic61C2211yescharacteristic
44C42×D61—24no—
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48#14519684C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C42×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55#95×C61C2211yescharacteristic
56C24×C61C2311yescharacteristic
57C23×D61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—22no—
66C2×C22⋊D61—22no—
67C2×C22⋊D61—22no—
68C2×C22⋊D61—22no—
69C2×C22⋊D61C2×C414yescomplemented
70C2×C22⋊D61C2×C414yescomplemented
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C2×D244—22no—
81C2×D244—22no—
82C2×D244C2×C414yescomplemented
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—22no—
93C2×C4×D61C2×C414yescomplemented
94C2×C4×D61D414yescomplemented
95C4⋊C4×C61—22no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61—22no—
98C22⋊C4×C61C2×C414yescomplemented
99C42×C61—22no—
100C22⋊Dic61—22no—
101#11758198—22no—
102#11758198—22no—
103#11758198—22no—
104#11758198—22no—
105#11758198—22no—
106#11758198C2×C414yescomplemented
107#11758196—22no—
108#11758196—22no—
109#11758196—22no—
110#11758196C2×C414yescomplemented
111C4×Dic61—22no—
112C4×Dic61—22no—
113C4×Dic61—22no—
114C4×Dic61—22no—
115C4×Dic61D414yescomplemented
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61C22×C412yes—
123C23×C61C2411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61C22×C412yes—
135C22×D61C22×C412yes—
136C22×D61C2×D412yes—
137C22×D61#4112yes—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61C22×C412yes—
153C2×C4×C61C22×C412yes—
154C2×C4×C61C2×D412yes—
155C2×C4×C61C2×D412yes—
156C22⋊D61—28no—
157C22⋊D61—28no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—44no—
169C2×Dic61C22×C412yes—
170C2×Dic61C22×C412yes—
171C2×Dic61C2×D412yes—
172C2×Dic61C2×D412yes—
173C2×Dic61C2×D412yes—
174C2×Dic61#4112yes—
175C2×Dic61#4112yes—
176C2×Dic61#4112yes—
177D244—28no—
178C4×D61—28no—
179C4×D61—28no—
180C4×D61—28no—
181C4×D61—44no—
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61C23×C411yescharacteristic
190C22×C61C22×D411yescharacteristic
191C22×C61C22×D411yescharacteristic
192C22×C61C2×#4111yescharacteristic
193C22×C61C2×#4111yescharacteristic
194C22×C61C2×#4111yescharacteristic
195C22×C61C2×#4111yescharacteristic
196C2×D61—22no—
197C2×D61—22no—
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61C4×D414yescomplemented
210C4×C61—22no—
211C4×C61—22no—
212C4×C61—22no—
213C4×C61—22no—
214C4×C61—41no—
215C4×C61—41no—
216Dic61—22no—
217Dic61—22no—
218Dic61—41no—
219Dic61—41no—
220Dic61C4×D414yescomplemented
221Dic61#12114yescomplemented
222C4×#121—611nomaximal, Sylow
223C2×C61—42no—
224C2×C61C2×C4×D411yescharacteristic
225C2×C61C2×C4×D411yescharacteristic
226C2×C61C4×#4111yescharacteristic
227C2×C61C2×#12111yescharacteristic
228C2×C61#52511yescharacteristic
229C2×C61#52911yescharacteristic
230C2×C61#53211yescharacteristic
231D61—24no—
232D61—42no—
233C2×#121—611no—
234C2×C4×D4—611no—
235C2×C4×D4—611no—
236C2×C4×D4—611no—
237C22×C42—611no—
238#390—611no—
239#389—611no—
240#388—611no—
241#388D6111yescharacteristic, complemented
242#386—611no—
243#386—611no—
244#380—611no—
245C4×C4⋊C4—611no—
246C4×C22⋊C4—611no—
247C4×C22⋊C4—611no—
248C61C4×#12111yescharacteristic, complemented, Sylow
249C22×D4—611no—
250C22×D4—611no—
251C22×D4—611no—
252C23×C4—611no—
253C23×C4—611no—
254C23×C4—611no—
255C23×C4—611no—
256C23×C4—611no—
257#121—618no—
258C4×D4—1224no—
259C4×D4—1224no—
260C4×D4—1224no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4C2×D6111yescharacteristic
266C2×C22⋊C4—611no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4C2×D6111yescharacteristic
274C2×C22⋊C4C2×D6111yescharacteristic
275C2×C22⋊C4C2×D6111yescharacteristic
276C2×C42—611no—
277C2×C42—611no—
278C2×C42—611no—
279C2×C42—611no—
280C2×C42—611no—
281C2×C42—1224no—
282C2×C42C2×D6111yescharacteristic
283#95—611no—
284#95—611no—
285#95—611no—
286#95—611no—
287#95C2×D6111yescharacteristic
288#95C2×D6111yescharacteristic
289C24—611no—
290C24—611no—
291C24C22×D6111yescharacteristic
292C2×D4—614no—
293C2×D4—614no—
294C2×D4—614no—
295C2×D4—1222no—
296C2×D4—1222no—
297C2×D4—1222no—
298C2×D4—1222no—
299C2×D4—1222no—
300C2×D4—1222no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—614no—
306C22×C4—614no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—1222no—
310C22×C4—1222no—
311C22×C4—1222no—
312C22×C4—1222no—
313C22×C4—1222no—
314C22×C4—1222no—
315C22×C4—1222no—
316C22×C4—1222no—
317C22×C4—1222no—
318C22×C4—1222no—
319C22×C4—1222no—
320C22×C4—1222no—
321C22×C4—1222no—
322C22×C4C22×D6111yescharacteristic
323C22×C4C22×D6111yescharacteristic
324C22×C4C22×D6111yescharacteristic
325C22×C4C22×D6111yescharacteristic
326C22×C4C22×D6111yescharacteristic
327C22×C4C22×D6111yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—614no—
330C4⋊C4—1222no—
331C4⋊C4—1222no—
332C4⋊C4—1222no—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—614no—
336C22⋊C4—1222no—
337C22⋊C4—1222no—
338C22⋊C4—1222no—
339C22⋊C4—1222no—
340C22⋊C4—1222no—
341C22⋊C4—1222no—
342C22⋊C4C4×D6114yescomplemented
343C42—22no—
344C42—614no—
345C42—1222no—
346C42—1222no—
347C42—1222no—
348C42—1222no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—612no—
356C23—612no—
357C23—612no—
358C23—612no—
359C23—1221no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23C2×C4×D6112yes—
370C23C23×D6111yescharacteristic
371D4—1228no—
372D4—1228no—
373D4—1228no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—612no—
389C2×C4—612no—
390C2×C4—612no—
391C2×C4—612no—
392C2×C4—612no—
393C2×C4—612no—
394C2×C4—612no—
395C2×C4—612no—
396C2×C4—1228no—
397C2×C4—1228no—
398C2×C4—1228no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—2444no—
410C2×C4—2444no—
411C2×C4C2×C4×D6112yes—
412C2×C4C2×C4×D6112yes—
413C2×C4D4×D6112yes—
414C2×C4D4×D6112yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—614no—
423C22—1222no—
424C22—1222no—
425C22—1222no—
426C22—1222no—
427C22—1222no—
428C22—1222no—
429C22—1222no—
430C22—1222no—
431C22—1222no—
432C22—2441no—
433C22—2441no—
434C22—2441no—
435C22—2441no—
436C22C22×C4×D6111yescharacteristic
437C22C2×D4×D6111yescharacteristic
438C22C2×D4×D6111yescharacteristic
439C22#41×D6111yescharacteristic
440C22#41×D6111yescharacteristic
441C22#41×D6111yescharacteristic
442C22#41×D6111yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—41no—
449C4—614no—
450C4—614no—
451C4—1222no—
452C4—1222no—
453C4—2441no—
454C4—2441no—
455C2—42no—
456C2—1224no—
457C2—2442no—
458C2C4×D4×D6111yescharacteristic
459C2C4×D4×D6111yescharacteristic
460C2#1684023011yescharacteristic
461C2#121×D6111yescharacteristic
462C2#1684027011yescharacteristic
463C2#1684029511yescharacteristic
464C2#1684031111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#388C2
socleC23×C61C24
hypercenter#388D61
hypocenterC61C4×#121
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#14519739C2semidirect
3. C2×#14519737C2semidirect
4. C2×#14519737C2semidirect
5. C2×C42×D61C2semidirect
6. #16839662C2semidirect
7. #16839657C2semidirect
8. #16839653C2semidirect
9. #16839640C2semidirect
10. #16839638C2semidirect
11. #16839621C2semidirect
12. #16839613C2semidirect
13. C22⋊C4×Dic61C2semidirect
14. #16839609C2semidirect
15. C61×#388C2semidirect
24. #14519750C4semidirect
69. C2×C22⋊D61C2×C4semidirect
70. C2×C22⋊D61C2×C4semidirect
82. C2×D244C2×C4semidirect
93. C2×C4×D61C2×C4semidirect
94. C2×C4×D61D4semidirect
98. C22⋊C4×C61C2×C4semidirect
106. #11758198C2×C4semidirect
110. #11758196C2×C4semidirect
115. C4×Dic61D4semidirect
209. C2×D61C4×D4semidirect
220. Dic61C4×D4semidirect
221. Dic61#121semidirect
241. #388D61semidirect
248. C61C4×#121semidirect
342. C22⋊C4C4×D61semidirect