Finite Group Databasebeta

← #21452109

Subgroups — #21452109

Order 7808.

804 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519751C211yesmaximal, characteristic, complemented
2C2×#14519750C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic, complemented
4C2×#14519749C211yesmaximal, characteristic, complemented
5C2×#14519748C211yesmaximal, characteristic, complemented
6#16839685C211yesmaximal, characteristic, complemented
7#16839684C211yesmaximal, characteristic, complemented
8#16839671C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839670C211yesmaximal, characteristic, complemented
11#16839670C211yesmaximal, characteristic, complemented
12#16839637C211yesmaximal, characteristic, complemented
13#16839635C211yesmaximal, characteristic, complemented
14#16839633C211yesmaximal, characteristic, complemented
15C2×#121×C61C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C23×Dic61C2211yescharacteristic
24C22×C4×D61C2211yescharacteristic
25#14519751—24no—
26#14519750—24no—
27#14519749—24no—
28#14519749—24no—
29#14519748—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×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic
44C2×#11758198C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48#14519684C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52C23×C4×C61C2211yescharacteristic
53#121×C61—24no—
54C2×C4⋊C4×C61C2211yescharacteristic
55C2×C22⋊C4×C61C2211yescharacteristic
56C2×C22⋊C4×C61C2211yescharacteristic
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C24×C61C2311yescharacteristic
60C23×D61C2311yescharacteristic
61C23×D61C2311yescharacteristic
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—41no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—41no—
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C22×C4×C61C2311yescharacteristic
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—22no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—22no—
84C2×C22⋊D61—22no—
85C2×C22⋊D61—22no—
86C2×C22⋊D61—22no—
87C2×C22⋊D61—22no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61—41no—
95C2×C22⋊D61—41no—
96C22×Dic61—22no—
97C22×Dic61—22no—
98C22×Dic61—41no—
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102C22×Dic61C2311yescharacteristic
103C22×Dic61C2311yescharacteristic
104C22×Dic61C2311yescharacteristic
105C2×D244—22no—
106C2×D244—22no—
107C2×D244—41no—
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—41no—
111C4⋊C4×C61—22no—
112C22⋊C4×C61—22no—
113C22⋊C4×C61D414yescomplemented
114C22⋊Dic61—22no—
115C22⋊Dic61—22no—
116C22⋊Dic61—41no—
117C22⋊Dic61—41no—
118C22⋊Dic61D414yescomplemented
119#11758198—22no—
120#11758198—22no—
121#11758198—22no—
122#11758198—41no—
123#11758198D414yescomplemented
124C4⋊Dic61—22no—
125C4⋊Dic61—22no—
126#11758196—22no—
127#11758196—22no—
128#11758196—22no—
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×C61—21no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61C2×D412yes—
149C23×C61C2×D412yes—
150C23×C61C2411yescharacteristic
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61C2×D412yes—
165D4×C61—44no—
166D4×C61—44no—
167D4×C61—44no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—44no—
178C2×C4×C61C2×D412yes—
179C2×C4×C61C2×D412yes—
180C2×C4×C61C2×D412yes—
181C22⋊D61—44no—
182C22⋊D61—44no—
183C22⋊D61—44no—
184C22⋊D61—44no—
185C22⋊D61—44no—
186C22⋊D61—44no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61—21no—
202C2×Dic61—44no—
203C2×Dic61C2×D412yes—
204C2×Dic61C2×D412yes—
205C2×Dic61C2×D412yes—
206D244—44no—
207C4×D61—44no—
208C22×C61—22no—
209C22×C61—22no—
210C22×C61—22no—
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—22no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—41no—
222C22×C61—41no—
223C22×C61—41no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61—41no—
227C22×C61—41no—
228C22×C61—41no—
229C22×C61C22×D411yescharacteristic
230C22×C61C22×D411yescharacteristic
231C22×C61C22×D411yescharacteristic
232C22×C61H(5,𝔽2)11yescharacteristic
233C22×C61H(5,𝔽2)11yescharacteristic
234C22×C61H(5,𝔽2)11yescharacteristic
235C22×C612−1+411yescharacteristic
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—22no—
239C2×D61—41no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—41no—
248C2×D61—41no—
249C2×D61—41no—
250C4×C61—22no—
251C4×C61—22no—
252C4×C61—22no—
253C4×C61—41no—
254Dic61—22no—
255Dic61—22no—
256Dic61—22no—
257Dic61—41no—
258Dic61—41no—
259Dic61—41no—
260#2675—611nomaximal, Sylow
261C2×C61—42no—
262C2×C61—42no—
263C2×C61—81no—
264C2×C61#53711yescharacteristic
265C2×C61#53711yescharacteristic
266C2×C61#53711yescharacteristic
267C2×C61D4211yescharacteristic
268C2×C61D4211yescharacteristic
269C2×C61D4211yescharacteristic
270C2×C61#56011yescharacteristic
271D61—42no—
272D61—81no—
273C2×#121—611no—
274C2×#121—611no—
275C2×#121—611no—
276C2×#121—611no—
277C2×#121—611no—
278C2×#121D6111yescharacteristic, complemented
279#396—611no—
280#396—611no—
281#392—611no—
282#392—611no—
283#392—611no—
284#392—611no—
285#385—611no—
286#385—611no—
287#385—611no—
288C61#267511yescharacteristic, complemented, Sylow
289C22×D4—611no—
290C22×D4—611no—
291C22×D4—611no—
292C22×D4—611no—
293C22×D4—611no—
294C22×D4—611no—
295C22×D4—611no—
296C22×D4C2×D6111yescharacteristic
297C22×D4C2×D6111yescharacteristic
298C22×D4C2×D6111yescharacteristic
299C23×C4—611no—
300C23×C4—611no—
301C23×C4C2×D6111yescharacteristic
302#121—24no—
303#121—1224no—
304#121—1224no—
305#121—1224no—
306#121—1224no—
307#121—1224no—
308C2×C4⋊C4—611no—
309C2×C4⋊C4—611no—
310C2×C4⋊C4—611no—
311C2×C4⋊C4—611no—
312C2×C4⋊C4—611no—
313C2×C4⋊C4C2×D6111yescharacteristic
314C2×C22⋊C4—611no—
315C2×C22⋊C4—611no—
316C2×C22⋊C4—611no—
317C2×C22⋊C4—611no—
318C2×C22⋊C4—611no—
319C2×C22⋊C4—611no—
320C2×C22⋊C4—611no—
321C2×C22⋊C4—611no—
322C2×C22⋊C4—611no—
323C2×C22⋊C4—611no—
324C2×C22⋊C4C2×D6111yescharacteristic
325C2×C22⋊C4C2×D6111yescharacteristic
326#95—611no—
327#95—611no—
328#95—611no—
329#95—611no—
330C24—611no—
331C24—611no—
332C24C22×D6111yescharacteristic
333C24C22×D6111yescharacteristic
334C24C22×D6111yescharacteristic
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—1222no—
345C2×D4—1222no—
346C2×D4—1222no—
347C2×D4—1222no—
348C2×D4—1222no—
349C2×D4—1222no—
350C2×D4—1222no—
351C2×D4—1222no—
352C2×D4—1222no—
353C2×D4—1222no—
354C2×D4—1222no—
355C2×D4—1222no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4—2441no—
359C2×D4—2441no—
360C2×D4—2441no—
361C2×D4—2441no—
362C2×D4—2441no—
363C2×D4—2441no—
364C2×D4—2441no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—1222no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—2441no—
379C22×C4—2441no—
380C22×C4C22×D6111yescharacteristic
381C22×C4C22×D6111yescharacteristic
382C22×C4C22×D6111yescharacteristic
383C22×C4C22×D6111yescharacteristic
384C4⋊C4—22no—
385C4⋊C4—1222no—
386C4⋊C4—1222no—
387C4⋊C4—1222no—
388C4⋊C4—1222no—
389C4⋊C4—1222no—
390C22⋊C4—22no—
391C22⋊C4—614no—
392C22⋊C4—614no—
393C22⋊C4—1222no—
394C22⋊C4—1222no—
395C22⋊C4—1222no—
396C22⋊C4—1222no—
397C22⋊C4—1222no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C22⋊C4C22⋊D6114yescomplemented
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—612no—
422C23—1221no—
423C23—1221no—
424C23—1221no—
425C23—1221no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23—1221no—
430C23—1221no—
431C23—1221no—
432C23—1221no—
433C23—1221no—
434C23—1221no—
435C23D4×D6112yes—
436C23C2×C22⋊D6112yes—
437C23C23×D6111yescharacteristic
438D4—44no—
439D4—44no—
440D4—44no—
441D4—2444no—
442D4—2444no—
443D4—2444no—
444D4—2444no—
445D4—2444no—
446D4—2444no—
447D4—2444no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—44no—
458C2×C4—612no—
459C2×C4—612no—
460C2×C4—612no—
461C2×C4—1221no—
462C2×C4—1221no—
463C2×C4—1221no—
464C2×C4—1221no—
465C2×C4—1221no—
466C2×C4—1221no—
467C2×C4—1221no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—2444no—
477C2×C4—2444no—
478C2×C4D4×D6112yes—
479C2×C4C2×C22⋊D6112yes—
480C2×C4C2×C22⋊D6112yes—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—1222no—
503C22—1222no—
504C22—1222no—
505C22—2441no—
506C22—2441no—
507C22—2441no—
508C22—2441no—
509C22—2441no—
510C22—2441no—
511C22—2441no—
512C22—2441no—
513C22—2441no—
514C22—2441no—
515C22—2441no—
516C22C2×D4×D6111yescharacteristic
517C22C2×D4×D6111yescharacteristic
518C22C22×C22⋊D6111yescharacteristic
519C22#1451982211yescharacteristic
520C22#1451982211yescharacteristic
521C22#1451982311yescharacteristic
522C22#1451982411yescharacteristic
523C4—22no—
524C4—22no—
525C4—22no—
526C4—41no—
527C4—1222no—
528C4—1222no—
529C4—1222no—
530C4—2441no—
531C4—2441no—
532C4—2441no—
533C2—42no—
534C2—42no—
535C2—81no—
536C2—4881no—
537C2—2442no—
538C2#1684033911yescharacteristic
539C2#1684034011yescharacteristic
540C2#1684034111yescharacteristic
541C2D4×C22⋊D6111yescharacteristic
542C2D4×C22⋊D6111yescharacteristic
543C2#1684039611yescharacteristic
544C2#1684050011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2675
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519751C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519749C2semidirect
4. C2×#14519749C2semidirect
5. C2×#14519748C2semidirect
6. #16839685C2semidirect
7. #16839684C2semidirect
8. #16839671C2semidirect
9. #16839670C2semidirect
10. #16839670C2semidirect
11. #16839670C2semidirect
12. #16839637C2semidirect
13. #16839635C2semidirect
14. #16839633C2semidirect
15. C2×#121×C61C2semidirect
113. C22⋊C4×C61D4semidirect
118. C22⋊Dic61D4semidirect
123. #11758198D4semidirect
278. C2×#121D61semidirect
288. C61#2675semidirect
401. C22⋊C4C22⋊D61semidirect