Finite Group Databasebeta

← #21452040

Subgroups — #21452040

Order 7808.

796 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519766C211yesmaximal, characteristic, complemented
2C2×#14519747C211yesmaximal, characteristic, complemented
3C2×#14519745C211yesmaximal, characteristic, complemented
4#16839678C211yesmaximal, characteristic, complemented
5#16839677C211yesmaximal, characteristic, complemented
6#16839673C211yesmaximal, characteristic, complemented
7#16839671C211yesmaximal, characteristic, complemented
8#16839671C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839664C211yesmaximal, characteristic, complemented
11#16839662C211yesmaximal, characteristic, complemented
12#16839655C211yesmaximal, characteristic, complemented
13#16839653C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic, complemented
15C2×#124×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic, complemented
23#14519766—24no—
24#14519747—24no—
25#14519745—24no—
26C2×C4⋊Dic61C2211yescharacteristic, complemented
27C2×#11758196C2211yescharacteristic, complemented
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic, complemented
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic, complemented
40C2×#11758198C2211yescharacteristic, complemented
41C2×#11758198C2211yescharacteristic, complemented
42C2×C4×Dic61C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47C22×Q8×C61C2211yescharacteristic, complemented
48C22×D4×C61C2211yescharacteristic
49#124×C61—24no—
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic, complemented
53C2×C22⋊C4×C61C2211yescharacteristic, complemented
54C2×C42×C61C2211yescharacteristic, complemented
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—41no—
61C23×D61—41no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61C2311yescharacteristic
65C23×D61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C2×Q8×C61—22no—
68C2×Q8×C61—22no—
69C2×Q8×C61—41no—
70C2×D4×C61—22no—
71C2×D4×C61—22no—
72C2×D4×C61—41no—
73C22×C4×C61C2311yescharacteristic
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—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C22×Dic61C2311yescharacteristic
91C22×Dic61C2311yescharacteristic
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C22×Dic61C2311yescharacteristic
95C2×D244—22no—
96C2×D244—22no—
97C2×D244—22no—
98C2×D244—22no—
99C2×D244—41no—
100C2×D244—41no—
101C22⋊C4×C61—22no—
102C22⋊C4×C61—22no—
103C22⋊C4×C61—22no—
104C22⋊C4×C61D414yescomplemented
105C42×C61—22no—
106C22⋊Dic61—22no—
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109#11758198—22no—
110#11758198—22no—
111#11758198—22no—
112#11758198—22no—
113#11758198—22no—
114#11758198—22no—
115#11758198—41no—
116#11758198—41no—
117#11758198—41no—
118#11758198—41no—
119#11758198D414yescomplemented
120C4⋊Dic61—41no—
121#11758196—41no—
122C4×Dic61—22no—
123C23×C61—21no—
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×C61C2×D412yes—
137C23×C61C2411yescharacteristic
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—44no—
158C22×D61—44no—
159C22×D61—44no—
160C22×D61—44no—
161C22×D61—44no—
162C22×D61—44no—
163C22×D61—44no—
164C22×D61C2×D412yes—
165C22×D61#4112yes—
166Q8×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—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61C2×D412yes—
181C2×C4×C61C2×D412yes—
182C2×C4×C61C2×D412yes—
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×Dic61C2×D412yes—
202D244—44no—
203D244—44no—
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
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×C61C2×#4111yescharacteristic
221C22×C61H(5,𝔽2)11yescharacteristic
222C22×C61H(5,𝔽2)11yescharacteristic
223C22×C61H(5,𝔽2)11yescharacteristic
224C22×C61H(5,𝔽2)11yescharacteristic
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—22no—
230C2×D61—22no—
231C2×D61—416no—
232C2×D61—41no—
233C2×D61—41no—
234C2×D61—41no—
235C2×D61—41no—
236C2×D61—41no—
237C2×D61—41no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C4×C61—22no—
248C4×C61—22no—
249C4×C61—22no—
250C4×C61—41no—
251C4×C61—41no—
252Dic61—22no—
253Dic61—41no—
254Dic61—41no—
255Dic61—41no—
256Dic61—41no—
257#2670—611nomaximal, Sylow
258C2×C61—42no—
259C2×C61—81no—
260C2×C61#53511yescharacteristic
261C2×C61#53511yescharacteristic
262C2×C61#53811yescharacteristic
263C2×C61D4211yescharacteristic
264C2×C61#54611yescharacteristic
265C2×C61#54611yescharacteristic
266C2×C61H(3,𝔽4)11yescharacteristic
267D61—42no—
268D61—42no—
269D61—81no—
270C2×#124—611no—
271C2×#124D6111yescharacteristic, complemented
272C2×#120—611no—
273C2×#120—611no—
274#394—611no—
275#394—611no—
276#393—611no—
277#392—611no—
278#392—611no—
279#392—611no—
280#390—611no—
281#390—611no—
282#388—611no—
283#388—611no—
284#379—611no—
285C61#267011yescharacteristic, complemented, Sylow
286C25—611no—
287C22×Q8C2×D6111yescharacteristic, complemented
288C22×D4—611no—
289C22×D4—611no—
290C22×D4—611no—
291C22×D4—611no—
292C22×D4—611no—
293C22×D4—611no—
294C22×D4C2×D6111yescharacteristic
295#124—24no—
296#124—1224no—
297#120—1224no—
298#120—1224no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4—611no—
303C2×C22⋊C4—611no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—611no—
307C2×C22⋊C4—611no—
308C2×C22⋊C4—611no—
309C2×C22⋊C4—611no—
310C2×C22⋊C4—611no—
311C2×C22⋊C4—611no—
312C2×C22⋊C4—611no—
313C2×C22⋊C4—611no—
314C2×C22⋊C4—611no—
315C2×C22⋊C4C2×D6111yescharacteristic
316C2×C22⋊C4C2×D6111yescharacteristic
317C2×C22⋊C4C2×D6111yescharacteristic, complemented
318C2×C22⋊C4C2×D6111yescharacteristic, complemented
319C2×C42—611no—
320C2×C42C2×D6111yescharacteristic, complemented
321#95—611no—
322#95—611no—
323#95—611no—
324#95—611no—
325C24—611no—
326C24—611no—
327C24—611no—
328C24—1222no—
329C24—1222no—
330C24—1222no—
331C24—2441no—
332C24—2441no—
333C24—2441no—
334C24—2441no—
335C24C22×D6111yescharacteristic
336C24C22×D6111yescharacteristic
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—41no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—41no—
343C2×D4—1222no—
344C2×D4—1222no—
345C2×D4—1222no—
346C2×D4—1222no—
347C2×D4—1222no—
348C2×D4—1222no—
349C2×D4—1222no—
350C2×D4—1222no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4—2441no—
359C2×D4—2441no—
360C2×D4—2441no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4C22×D6111yescharacteristic
367C22×C4C22×D6111yescharacteristic
368C22×C4C22×D6111yescharacteristic
369C22×C4C22×D6111yescharacteristic
370C22×C4C22×D6111yescharacteristic
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—614no—
377C22⋊C4—1222no—
378C22⋊C4—1222no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C22⋊C4—1222no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4C22⋊D6114yescomplemented
391C42—22no—
392C42—1222no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—612no—
407C23—612no—
408C23—1221no—
409C23—1221no—
410C23—1221no—
411C23—1221no—
412C23—1221no—
413C23—1221no—
414C23—1221no—
415C23—1221no—
416C23—1221no—
417C23—1221no—
418C23—1221no—
419C23—1221no—
420C23—1221no—
421C23—1221no—
422C23—1221no—
423C23—1221no—
424C23—1221no—
425C23—1221no—
426C23—1221no—
427C23—2444no—
428C23—2444no—
429C23—2444no—
430C23—2444no—
431C23—2444no—
432C23—2444no—
433C23—2444no—
434C23C2×C22⋊D6112yes—
435C23C23×D6111yescharacteristic
436Q8—44no—
437D4—44no—
438D4—2444no—
439D4—2444no—
440D4—2444no—
441D4—2444no—
442D4—2444no—
443D4—2444no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
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—612no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—1221no—
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×C4D4×D6112yes—
472C2×C4C2×C22⋊D6112yes—
473C2×C4C2×C22⋊D6112yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—1222no—
489C22—1222no—
490C22—1222no—
491C22—1222no—
492C22—1222no—
493C22—1222no—
494C22—24416no—
495C22—2441no—
496C22—2441no—
497C22—2441no—
498C22—2441no—
499C22—2441no—
500C22—2441no—
501C22—2441no—
502C22—2441no—
503C22—2441no—
504C22—2441no—
505C22—2441no—
506C22—2441no—
507C22—2441no—
508C22—2441no—
509C22—2441no—
510C22C2×D4×D6111yescharacteristic
511C22C22×C22⋊D6111yescharacteristic
512C22#41×D6111yescharacteristic
513C22#1451982211yescharacteristic
514C22#1451982311yescharacteristic
515C22#1451982311yescharacteristic
516C22#1451982311yescharacteristic
517C4—22no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—41no—
522C4—1222no—
523C4—2441no—
524C4—2441no—
525C4—2441no—
526C4—2441no—
527C2—42no—
528C2—81no—
529C2—4881no—
530C2—2442no—
531C2—2442no—
532C2#1684032611yescharacteristic
533C2#1684033011yescharacteristic
534C2#1684034611yescharacteristic
535C2D4×C22⋊D6111yescharacteristic
536C2#1684040011yescharacteristic
537C2#1684040511yescharacteristic
538C2#1684050411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#124×C61C2
hypercenterC2×#124D61
hypocenterC61#2670
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519766C2semidirect
2. C2×#14519747C2semidirect
3. C2×#14519745C2semidirect
4. #16839678C2semidirect
5. #16839677C2semidirect
6. #16839673C2semidirect
7. #16839671C2semidirect
8. #16839671C2semidirect
9. #16839670C2semidirect
10. #16839664C2semidirect
11. #16839662C2semidirect
12. #16839655C2semidirect
13. #16839653C2semidirect
14. #16839617C2semidirect
15. C2×#124×C61C2semidirect
22. C22×C22⋊D61C22semidirect
26. C2×C4⋊Dic61C22semidirect
27. C2×#11758196C22semidirect
30. C2×C22⋊Dic61C22semidirect
39. C2×#11758198C22semidirect
40. C2×#11758198C22semidirect
41. C2×#11758198C22semidirect
42. C2×C4×Dic61C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. C22×Q8×C61C22semidirect
52. C2×C22⋊C4×C61C22semidirect
53. C2×C22⋊C4×C61C22semidirect
54. C2×C42×C61C22semidirect
104. C22⋊C4×C61D4semidirect
119. #11758198D4semidirect
271. C2×#124D61semidirect
285. C61#2670semidirect
287. C22×Q8C2×D61semidirect
317. C2×C22⋊C4C2×D61semidirect
318. C2×C22⋊C4C2×D61semidirect
320. C2×C42C2×D61semidirect
390. C22⋊C4C22⋊D61semidirect