Finite Group Databasebeta

← #21449157

Subgroups — #21449157

Order 7808.

908 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11758224C211yesmaximal, characteristic, complemented
2C2×#14519754C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic, complemented
4C2×D4×Dic61C211yesmaximal, characteristic, complemented
5#16839678C211yesmaximal, characteristic, complemented
6#16839676C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839666C211yesmaximal, characteristic, complemented
9#16839662C211yesmaximal, characteristic, complemented
10#16839642C211yesmaximal, characteristic, complemented
11#16839638C211yesmaximal, characteristic, complemented
12#16839637C211yesmaximal, characteristic, complemented
13#16839636C211yesmaximal, characteristic, complemented
14#16839620C211yesmaximal, characteristic, complemented
15C61×#392C211yesmaximal, characteristic, complemented
16C2×#11758224—24no—
17C2×#11758224—24no—
18C2×#11758224—24no—
19C22×Dic122C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C23×Dic61C2211yescharacteristic
24C23×Dic61C2211yescharacteristic
25C23×Dic61C2211yescharacteristic
26C22×C4×D61C2211yescharacteristic
27#14519754—24no—
28#14519749—24no—
29D4×Dic61—24no—
30C2×C4⋊Dic61C2211yescharacteristic
31C2×C4⋊Dic61C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758196C2211yescharacteristic
34C2×#11758196C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic
38C2×C22⋊Dic61C2211yescharacteristic
39C2×C22⋊Dic61C2211yescharacteristic
40C2×C22⋊Dic61C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic
44C2×C4×Dic61C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48#14519684C2211yescharacteristic
49#14519684C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52C22×D4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic
55C2×C22⋊C4×C61C2211yescharacteristic
56#95×C61C2211yescharacteristic
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C24×C61C2311yescharacteristic
60C23×D61C2311yescharacteristic
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—22no—
64C2×D4×C61—22no—
65C2×D4×C61—22no—
66C2×D4×C61—22no—
67C2×D4×C61—22no—
68C2×D4×C61—22no—
69C2×D4×C61—41no—
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C2×C22⋊D61—22no—
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61D414yescomplemented
83C22×Dic61—22no—
84C22×Dic61—22no—
85C22×Dic61—22no—
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61—22no—
89C22×Dic61—22no—
90C22×Dic61—22no—
91C22×Dic61D414yescomplemented
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C22×Dic61C2311yescharacteristic
95C22×Dic61C2311yescharacteristic
96C22×Dic61C2311yescharacteristic
97C22×Dic61C2311yescharacteristic
98C22×Dic61C2311yescharacteristic
99#11758224—232no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×Dic122—22no—
104C2×Dic122—22no—
105C2×Dic122D414yescomplemented
106C22⋊C4×C61—22no—
107C22⋊C4×C61—22no—
108C22⋊C4×C61—41no—
109C22⋊Dic61—22no—
110C22⋊Dic61—22no—
111C22⋊Dic61—22no—
112C22⋊Dic61—22no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115#11758198—22no—
116#11758198—22no—
117#11758198—41no—
118C4⋊Dic61—22no—
119C4⋊Dic61—22no—
120#11758196—22no—
121#11758196—22no—
122#11758196—22no—
123C4×Dic61—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—21no—
142C23×C61C2×D412yes—
143C23×C61C2×D412yes—
144C23×C61#4112yescomplemented
145C23×C61C2411yescharacteristic
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61C2×D412yes—
153D4×C61—28no—
154D4×C61—28no—
155D4×C61—44no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61C2×D412yes—
167C2×C4×C61#4112yescomplemented
168C22⋊D61—28no—
169C22⋊D61—28no—
170C22⋊D61—44no—
171C2×Dic61—28no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—28no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—44no—
190C2×Dic61C2×D412yes—
191C2×Dic61C2×D412yes—
192C2×Dic61C2×D412yes—
193C2×Dic61C2×D412yes—
194C2×Dic61C2×D412yes—
195C4×D61—28no—
196Dic122—28no—
197C22×C61—22no—
198C22×C61—22no—
199C22×C61—22no—
200C22×C61—22no—
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61C22×D411yescharacteristic
219C22×C61C22×D411yescharacteristic
220C22×C61C22×D411yescharacteristic
221C22×C61C2×#4111yescharacteristic
222C22×C61C2×#4111yescharacteristic
223C22×C61H(5,𝔽2)11yescharacteristic
224C22×C612−1+411yescharacteristic
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—41no—
229C2×D61—41no—
230C2×D61—41no—
231C2×D61—41no—
232C4×C61—22no—
233C4×C61—22no—
234C4×C61—41no—
235C4×C61—41no—
236Dic61—22no—
237Dic61—22no—
238Dic61—41no—
239Dic61—41no—
240Dic61—41no—
241Dic61—41no—
242Dic61#12014yes—
243#2407—611nomaximal, Sylow
244C2×C61—42no—
245C2×C61—42no—
246C2×C61—42no—
247C2×C61C2×#12011yescharacteristic
248C2×C61#52511yescharacteristic
249C2×C61#53711yescharacteristic
250C2×C61#54611yescharacteristic
251C2×C61#54711yescharacteristic
252C2×C61#54811yescharacteristic
253C2×C61#55011yescharacteristic
254D61—42no—
255C22×#41—611no—
256C2×C22⋊Q8—611no—
257C2×#121—611no—
258C2×C4×D4—611no—
259#394—611no—
260#394—611no—
261#392—611no—
262#392D6111yescharacteristic, complemented
263#391—611no—
264#390—611no—
265#386—611no—
266#386—611no—
267#385—611no—
268#385—611no—
269#380—611no—
270C61#240711yescharacteristic, complemented, Sylow
271C2×#41—1224no—
272C2×#41—1224no—
273C2×#41—1224no—
274C22×Q8—611no—
275C22×D4—611no—
276C22×D4—611no—
277C22×D4—611no—
278C22×D4C2×D6111yescharacteristic
279C22×D4C2×D6111yescharacteristic
280C22×D4C2×D6111yescharacteristic
281C23×C4—611no—
282C23×C4—611no—
283C23×C4—611no—
284C23×C4—611no—
285C22⋊Q8—1224no—
286#121—1224no—
287C4×D4—1224no—
288C2×C4⋊C4—611no—
289C2×C4⋊C4—611no—
290C2×C4⋊C4—611no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—611no—
293C2×C22⋊C4—611no—
294C2×C22⋊C4—611no—
295C2×C22⋊C4—611no—
296C2×C22⋊C4—611no—
297C2×C22⋊C4—611no—
298C2×C22⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4C2×D6111yescharacteristic
303C2×C22⋊C4C2×D6111yescharacteristic
304C2×C22⋊C4C2×D6111yescharacteristic
305C2×C42—611no—
306#95—611no—
307#95—611no—
308#95—611no—
309#95—611no—
310#95—611no—
311#95C2×D6111yescharacteristic
312C24—611no—
313C24C22×D6111yescharacteristic
314C24C22×D6111yescharacteristic
315C24C22×D6111yescharacteristic
316#41—12232no—
317C2×Q8—614no—
318C2×Q8—1222no—
319C2×Q8—1222no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—41no—
329C2×D4—614no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—1222no—
333C2×D4—1222no—
334C2×D4—1222no—
335C2×D4—1222no—
336C2×D4—1222no—
337C2×D4—2441no—
338C22×C4—611no—
339C22×C4—614no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4C22×D6111yescharacteristic
358C22×C4C22×D6111yescharacteristic
359C22×C4C22×D6111yescharacteristic
360C22×C4C22×D6111yescharacteristic
361C4⋊C4—1222no—
362C4⋊C4—1222no—
363C4⋊C4—1222no—
364C4⋊C4—1222no—
365C4⋊C4—1222no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—41no—
369C22⋊C4—1222no—
370C22⋊C4—1222no—
371C22⋊C4—1222no—
372C22⋊C4—1222no—
373C22⋊C4—1222no—
374C22⋊C4—1222no—
375C22⋊C4—2441no—
376C22⋊C4—2441no—
377C22⋊C4—2441no—
378C42—1222no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—612no—
398C23—1221no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23D4×D6112yes—
405C23D4×D6112yes—
406C23#1175822412yescomplemented
407C23C23×D6111yescharacteristic
408Q8—1228no—
409D4—28no—
410D4—28no—
411D4—44no—
412D4—1228no—
413D4—1228no—
414D4—2444no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—612no—
426C2×C4—612no—
427C2×C4—612no—
428C2×C4—612no—
429C2×C4—612no—
430C2×C4—1228no—
431C2×C4—1228no—
432C2×C4—1228no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—1221no—
449C2×C4—2444no—
450C2×C4D4×D6112yes—
451C2×C4#1175822412yescomplemented
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—1222no—
474C22—1222no—
475C22—1222no—
476C22—2441no—
477C22—2441no—
478C22—2441no—
479C22—2441no—
480C22C2×D4×D6111yescharacteristic
481C22C2×D4×D6111yescharacteristic
482C22C2×D4×D6111yescharacteristic
483C22C2×#1175822411yescharacteristic
484C22C2×#1175822411yescharacteristic
485C22#1451982211yescharacteristic
486C22#1451982411yescharacteristic
487C4—22no—
488C4—22no—
489C4—41no—
490C4—41no—
491C4—614no—
492C4—1222no—
493C4—1222no—
494C4—2441no—
495C4—2441no—
496C4—2441no—
497C4—2441no—
498C2—42no—
499C2—42no—
500C2—42no—
501C2—2442no—
502C2#120×D6111yescharacteristic
503C2#1684026811yescharacteristic
504C2#1684033911yescharacteristic
505C2#1684039911yescharacteristic
506C2#1684041211yescharacteristic
507C2#1684041811yescharacteristic
508C2#1684043211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2407
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#11758224C2semidirect
2. C2×#14519754C2semidirect
3. C2×#14519749C2semidirect
4. C2×D4×Dic61C2semidirect
5. #16839678C2semidirect
6. #16839676C2semidirect
7. #16839670C2semidirect
8. #16839666C2semidirect
9. #16839662C2semidirect
10. #16839642C2semidirect
11. #16839638C2semidirect
12. #16839637C2semidirect
13. #16839636C2semidirect
14. #16839620C2semidirect
15. C61×#392C2semidirect
82. C2×C22⋊D61D4semidirect
91. C22×Dic61D4semidirect
105. C2×Dic122D4semidirect
144. C23×C61#41semidirect
167. C2×C4×C61#41semidirect
262. #392D61semidirect
270. C61#2407semidirect
406. C23#11758224semidirect
451. C2×C4#11758224semidirect